The art and science of hyperbolic tessellations.

PubMed

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.

Focal surfaces of hyperbolic cylinders

NASA Astrophysics Data System (ADS)

Georgiev, Georgi Hristov; Pavlov, Milen Dimov

2017-12-01

Cylindrical surfaces have many applications in geometric modeling, architecture and other branches of engineering. In this paper, we describe two cylindrical surfaces associated to a given hyperbolic cylinder. The first one is a focal surface which is determined by reciprocal principle curvature of the hyperbolic cylinder. The second one is a generalized focal surface obtained by reciprocal mean curvature of the same hyperbolic cylinder. In particular, we show that each of these surfaces admits three different parametric representations. As consequence, it is proved that the focal and generalized focal surfaces of the hyperbolic cylinder are rational surfaces. An illustrative example is included.

Linear guided waves in a hyperbolic planar waveguide. Dispersion relations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lyashko, E I; Maimistov, A I

2015-11-30

We have theoretically investigated waveguide modes propagating in a planar waveguide formed by a layer of an isotropic dielectric surrounded by hyperbolic media. The case, when the optical axis of hyperbolic media is perpendicular to the interface, is considered. Dispersion relations are derived for the cases of TE and TM waves. The differences in the characteristics of a hyperbolic and a conventional dielectric waveguide are found. In particular, it is shown that in hyperbolic waveguides for each TM mode there are two cut-off frequencies and the number of propagating modes is always limited. (metamaterials)

Hyperbolic Rendezvous at Mars: Risk Assessments and Mitigation Strategies

NASA Technical Reports Server (NTRS)

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.

Hyperbolic-symmetry vector fields.

PubMed

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

2015-12-14

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

Probability Weighting Functions Derived from Hyperbolic Time Discounting: Psychophysical Models and Their Individual Level Testing.

PubMed

Takemura, Kazuhisa; Murakami, Hajime

2016-01-01

A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 - k log p)(-1). Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a geometric distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

On the local well-posedness of Lovelock and Horndeski theories

NASA Astrophysics Data System (ADS)

Papallo, Giuseppe; Reall, Harvey S.

2017-08-01

We investigate local well-posedness of the initial value problem for Lovelock and Horndeski theories of gravity. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can fail for strong fields so we restrict to weak fields. The Einstein equation is known to be strongly hyperbolic in harmonic gauge so we study Lovelock theories in harmonic gauge. We show that the equation of motion is always weakly hyperbolic for weak fields but, in a generic weak-field background, it is not strongly hyperbolic. For Horndeski theories, we prove that, for weak fields, the equation of motion is always weakly hyperbolic in any generalized harmonic gauge. For some Horndeski theories there exists a generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a weak-field background. This includes "k-essence" like theories. However, for more general Horndeski theories, there is no generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a generic weak-field background. Our results show that the standard method used to establish local well-posedness of the Einstein equation does not extend to Lovelock or general Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields.

Hyperbolic metamaterials: Novel physics and applications

NASA Astrophysics Data System (ADS)

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.

13-Moment System with Global Hyperbolicity for Quantum Gas

NASA Astrophysics Data System (ADS)

Di, Yana; Fan, Yuwei; Li, Ruo

2017-06-01

We point out that the quantum Grad's 13-moment system (Yano in Physica A 416:231-241, 2014) is lack of global hyperbolicity, and even worse, the thermodynamic equilibrium is not an interior point of the hyperbolicity region of the system. To remedy this problem, by fully considering Grad's expansion, we split the expansion into the equilibrium part and the non-equilibrium part, and propose a regularization for the system with the help of the new hyperbolic regularization theory developed in Cai et al. (SIAM J Appl Math 75(5):2001-2023, 2015) and Fan et al. (J Stat Phys 162(2):457-486, 2016). This provides us a new model which is hyperbolic for all admissible thermodynamic states, and meanwhile preserves the approximate accuracy of the original system. It should be noted that this procedure is not a trivial application of the hyperbolic regularization theory.

Magnetic hyperbolic optical metamaterials

DOE PAGES

Kruk, Sergey S.; Wong, Zi Jing; Pshenay-Severin, Ekaterina; ...

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 then 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 hyperbolicmore » dispersion in three-dimensional metamaterials. We also 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. These findings show the possibilities for realizing efficient impedance-matched hyperbolic media for unpolarized light.« less

The Hype over Hyperbolic Browsers.

ERIC Educational Resources Information Center

Allen, Maryellen Mott

2002-01-01

Considers complaints about the usability in the human-computer interaction aspect of information retrieval and discusses information visualization, the Online Library of Information Visualization Environments, hyperbolic information structure, subject searching, real-world applications, relational databases and hyperbolic trees, and the future of…

Point coordinates extraction from localized hyperbolic reflections in GPR data

NASA Astrophysics Data System (ADS)

Ristić, Aleksandar; Bugarinović, Željko; Vrtunski, Milan; Govedarica, Miro

2017-09-01

In this paper, we propose an automated detection algorithm for the localization of apexes and points on the prongs of hyperbolic reflection incurred as a result of GPR scanning technology. The objects of interest encompass cylindrical underground utilities that have a distinctive form of hyperbolic reflection in radargram. Algorithm involves application of trained neural network to analyze radargram in the form of raster image, resulting with extracted segments of interest that contain hyperbolic reflections. This significantly reduces the amount of data for further analysis. Extracted segments represent the zone for localization of apices. This is followed by extraction of points on prongs of hyperbolic reflections which is carried out until stopping criterion is satisfied, regardless the borders of segment of interest. In final step a classification of false hyperbolic reflections caused by the constructive interference and their removal is done. The algorithm is implemented in MATLAB environment. There are several advantages of the proposed algorithm. It can successfully recognize true hyperbolic reflections in radargram images and extracts coordinates, with very low rate of false detections and without prior knowledge about the number of hyperbolic reflections or buried utilities. It can be applied to radargrams containing single and multiple hyperbolic reflections, intersected, distorted, as well as incomplete (asymmetric) hyperbolic reflections, all in the presence of higher level of noise. Special feature of algorithm is developed procedure for analysis and removal of false hyperbolic reflections generated by the constructive interference from reflectors associated with the utilities. Algorithm was tested on a number of synthetic and radargram acquired in the field survey. To illustrate the performances of the proposed algorithm, we present the characteristics of the algorithm through five representative radargrams obtained in real conditions. In these examples we present different acquisition scenarios by varying the number of buried objects, their disposition, size, and level of noise. Example with highest complexity was tested also as a synthetic radargram generated by gprMax. Processing time in examples with one or two hyperbolic reflections is from 0.1 to 0.3 s, while for the most complex examples it is from 2.2 to 4.9 s. In general, the obtained experimental results show that the proposed algorithm exhibits promising performances both in terms of utility detection and processing speed of the algorithm.

Wavelets and Affine Distributions: A Time-Frequency Perspective

DTIC Science & Technology

2005-01-07

Ville Distribution ( WVD ) • Prominent member of the AC: the WVD • Properties of the WVD : – Covariant to TF scaling and time shift (of course) – Covariant...QTFRs • Wigner - Ville distribution and affine smoothing • Doppler tolerance and hyperbolic impulses • Hyperbolic TF localization and Bertrand P0...satisfy hyperbolic TF localization property: • Not satisfied by WVD ! 25 – 49 –WAMA-04 Cargèse, France The Bertrand P0 distribution • The hyperbolic

Thermal emitter comprising near-zero permittivity materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luk, Ting S.; Campione, Salvatore; Sinclair, Michael B.

A novel thermal source comprising a semiconductor hyperbolic metamaterial provides control of the emission spectrum and the angular emission pattern. These properties arise because of epsilon-near-zero conditions in the semiconductor hyperbolic metamaterial. In particular, the thermal emission is dominated by the epsilon-near-zero effect in the doped quantum wells composing the semiconductor hyperbolic metamaterial. Furthermore, different properties are observed for s and p polarizations, following the characteristics of the strong anisotropy of hyperbolic metamaterials.

Traveling wave to a reaction-hyperbolic system for axonal transport

NASA Astrophysics Data System (ADS)

Huang, Feimin; Li, Xing; Zhang, Yinglong

2017-07-01

In this paper, we study a class of nonlinear reaction-hyperbolic systems modeling the neuronal signal transfer in neuroscience. This reaction-hyperbolic system can be regarded as n × n (n ≥ 2) hyperbolic system with relaxation. We first prove the existence of traveling wave by Gershgorin circle theorem and mathematically describe the neuronal signal transport. Then for a special case n = 2, we show the traveling wave is nonlinearly stable, and obtain the convergence rate simultaneously by a weighted estimate.

Infrared hyperbolic metasurface based on nanostructured van der Waals materials

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

On the Behavior of Eisenstein Series Through Elliptic Degeneration

NASA Astrophysics Data System (ADS)

Garbin, D.; Pippich, A.-M. V.

2009-12-01

Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane {mathbb{H}}, and let {M = Γbackslash mathbb{H}} be the associated finite volume hyperbolic Riemann surface. If γ is a primitive parabolic, hyperbolic, resp. elliptic element of Γ, there is an associated parabolic, hyperbolic, resp. elliptic Eisenstein series. In this article, we study the limiting behavior of these Eisenstein series on an elliptically degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. The elliptic Eisenstein series associated to a degenerating elliptic element converges up to a factor to the parabolic Eisenstein series associated to the parabolic element which fixes the newly developed cusp on the limit surface.

Hyperbolic metamaterials: new physics behind a classical problem.

PubMed

Drachev, Vladimir P; Podolskiy, Viktor A; Kildishev, Alexander V

2013-06-17

Hyperbolic materials enable numerous surprising applications that include far-field subwavelength imaging, nanolithography, and emission engineering. The wavevector of a plane wave in these media follows the surface of a hyperboloid in contrast to an ellipsoid for conventional anisotropic dielectric. The consequences of hyperbolic dispersion were first studied in the 50's pertaining to the problems of electromagnetic wave propagation in the Earth's ionosphere and in the stratified artificial materials of transmission lines. Recent years have brought explosive growth in optics and photonics of hyperbolic media based on metamaterials across the optical spectrum. Here we summarize earlier theories in the Clemmow's prescription for transformation of the electromagnetic field in hyperbolic media and provide a review of recent developments in this active research area.

Polyhedra and packings from hyperbolic honeycombs.

PubMed

Pedersen, Martin Cramer; Hyde, Stephen T

2018-06-20

We derive more than 80 embeddings of 2D hyperbolic honeycombs in Euclidean 3 space, forming 3-periodic infinite polyhedra with cubic symmetry. All embeddings are "minimally frustrated," formed by removing just enough isometries of the (regular, but unphysical) 2D hyperbolic honeycombs [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] to allow embeddings in Euclidean 3 space. Nearly all of these triangulated "simplicial polyhedra" have symmetrically identical vertices, and most are chiral. The most symmetric examples include 10 infinite "deltahedra," with equilateral triangular faces, 6 of which were previously unknown and some of which can be described as packings of Platonic deltahedra. We describe also related cubic crystalline packings of equal hyperbolic discs in 3 space that are frustrated analogues of optimally dense hyperbolic disc packings. The 10-coordinated packings are the least "loosened" Euclidean embeddings, although frustration swells all of the hyperbolic disc packings to give less dense arrays than the flat penny-packing even though their unfrustrated analogues in [Formula: see text] are denser.

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

NASA Astrophysics Data System (ADS)

Andrade, Tomás; Cáceres, Elena; Keeler, Cynthia

2017-07-01

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

Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas

PubMed Central

Alfaro-Mozaz, F. J.; Alonso-González, P.; Vélez, S.; Dolado, I.; Autore, M.; Mastel, S.; Casanova, F.; Hueso, L. E.; Li, P.; Nikitin, A. Y.; Hillenbrand, R.

2017-01-01

Polaritons in layered materials—including van der Waals materials—exhibit hyperbolic dispersion and strong field confinement, which makes them highly attractive for applications including optical nanofocusing, sensing and control of spontaneous emission. Here we report a near-field study of polaritonic Fabry–Perot resonances in linear antennas made of a hyperbolic material. Specifically, we study hyperbolic phonon–polaritons in rectangular waveguide antennas made of hexagonal boron nitride (h-BN, a prototypical van der Waals crystal). Infrared nanospectroscopy and nanoimaging experiments reveal sharp resonances with large quality factors around 100, exhibiting atypical modal near-field patterns that have no analogue in conventional linear antennas. By performing a detailed mode analysis, we can assign the antenna resonances to a single waveguide mode originating from the hybridization of hyperbolic surface phonon–polaritons (Dyakonov polaritons) that propagate along the edges of the h-BN waveguide. Our work establishes the basis for the understanding and design of linear waveguides, resonators, sensors and metasurface elements based on hyperbolic materials and metamaterials. PMID:28589941

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

NASA Astrophysics Data System (ADS)

Cammarota, V.; Orsingher, E.

2008-12-01

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincaré half-plane and Poincaré disk) is examined. Each particle can split into two particles only once at Poisson spaced times and deviates orthogonally when splitted. At time t, after N( t) Poisson events, there are N( t)+1 particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as t increases and for different values of the parameters c (hyperbolic velocity of motion) and λ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented.

Super-Coulombic atom–atom interactions in hyperbolic media

PubMed Central

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

Super-Coulombic atom-atom interactions in hyperbolic media

NASA Astrophysics Data System (ADS)

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.

Galileo disposal strategy: stability, chaos and predictability

NASA Astrophysics Data System (ADS)

Rosengren, Aaron J.; Daquin, Jérôme; Tsiganis, Kleomenis; Alessi, Elisa Maria; Deleflie, Florent; Rossi, Alessandro; Valsecchi, Giovanni B.

2017-02-01

Recent studies have shown that the medium-Earth orbit (MEO) region of the global navigation satellite systems is permeated by a devious network of lunisolar secular resonances, which can interact to produce chaotic and diffusive motions. The precarious state of the four navigation constellations, perched on the threshold of instability, makes it understandable why all past efforts to define stable graveyard orbits, especially in the case of Galileo, were bound to fail; the region is far too complex to allow for an adoption of the simple geosynchronous disposal strategy. We retrace one such recent attempt, funded by ESA's General Studies Programme in the frame of the GreenOPS initiative, that uses a systematic parametric approach and the straightforward maximum-eccentricity method to identify long-term-stable regions, suitable for graveyards, as well as large-scale excursions in eccentricity, which can be used for post-mission deorbiting of constellation satellites. We then apply our new results on the stunningly rich dynamical structure of the MEO region towards the analysis of these disposal strategies for Galileo, and discuss the practical implications of resonances and chaos in this regime. We outline how the identification of the hyperbolic and elliptic fixed points of the resonances near Galileo can lead to explicit criteria for defining optimal disposal strategies.

Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2007-08-01

We demonstrate that partner symmetries provide a lift of noninvariant solutions of the three-dimensional Boyer-Finley equation to noninvariant solutions of the four-dimensional hyperbolic complex Monge-Ampère equation. The lift is applied to noninvariant solutions of the Boyer-Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Monge-Ampère equation. Using these solutions we construct new Ricci-flat ultra-hyperbolic metrics with non-zero curvature tensor that have no Killing vectors.

On the lagrangian 1-form structure of the hyperbolic calogero-moser system

NASA Astrophysics Data System (ADS)

Jairuk, Umpon; Tanasittikosol, Monsit; Yoo-Kong, Sikarin

2017-06-01

In this work, we present the Lagrangian 1-form structure of the hyperbolic Calogero-Moser system in both discrete-time level and continuous-time level. The discrete-time hyperbolic Calogero-Moser system is obtained by considering pole reduction of the semi-discrete Kadomtsev-Petviashvili (KP) equation. Furthermore, it is shown that the hyperbolic Calogero-Moser system possesses the key relation, known as the discrete-time closure relation. This relation is a consequence of the compatibility property of the temporal Lax matrices. The continuous-time hierarchy of the hyperbolic Calogero-Moser system is obtained by taking two successive continuum limits, namely, the skewed limit and full limit. With these successive limits, the continuous-time closure relation is also obtained and is shown to hold at the continuous level.

Hyperbolic phonon polaritons in hexagonal boron nitride (Conference Presentation)

NASA Astrophysics Data System (ADS)

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).

"That's Really Clever!" Ironic Hyperbole Understanding in Children

ERIC Educational Resources Information Center

Aguert, Marc; Le Vallois, Coralie; Martel, Karine; Laval, Virginie

2018-01-01

Hyperbole supports irony comprehension in adults by heightening the contrast between what is said and the actual situation. Because young children do not perceive the communication situation as a whole, but rather give precedence to either the utterance or the context, we predicted that hyperbole would reduce irony comprehension in six-year-olds…

Hyperbolicity measures democracy in real-world networks

NASA Astrophysics Data System (ADS)

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).

Classification of Tidal Disruption Events Based on Stellar Orbital Properties

NASA Astrophysics Data System (ADS)

Hayasaki, Kimitake; Zhong, Shiyan; Li, Shuo; Berczik, Peter; Spurzem, Rainer

2018-03-01

We study the rates of tidal disruption of stars on bound to unbound orbits by intermediate-mass to supermassive black holes using high-accuracy direct N-body experiments. Stars from the star cluster approaching the black hole can have three types of orbit: eccentric, parabolic, and hyperbolic. Since the mass fallback rate shows different variabilities depending on the orbital type, we can classify tidal disruption events (TDEs) into three main categories: eccentric, parabolic, and hyperbolic. The respective TDEs are characterized by two critical values of the orbital eccentricity: the lower critical eccentricity is the one below which stars on eccentric orbits cause finite, intense accretion, and the upper critical eccentricity is the one above which stars on hyperbolic orbits cause no accretion. Moreover, we find that parabolic TDEs can be divided into three subclasses: precisely parabolic, marginally eccentric, and marginally hyperbolic. We analytically derive that the mass fallback rate of marginally eccentric TDEs can be flatter and slightly higher than the standard fallback rate proportional to t ‑5/3, whereas it can be flatter and lower for marginally hyperbolic TDEs. We confirm using N-body experiments that only a few eccentric, precisely parabolic, and hyperbolic TDEs can occur in a spherical stellar system with a single intermediate-mass to supermassive black hole. A substantial fraction of the stars approaching the black hole would cause marginally eccentric or marginally hyperbolic TDEs.

Delay, Probability, and Social Discounting in a Public Goods Game

ERIC Educational Resources Information Center

Jones, Bryan A.; Rachlin, Howard

2009-01-01

A human social discount function measures the value to a person of a reward to another person at a given social distance. Just as delay discounting is a hyperbolic function of delay, and probability discounting is a hyperbolic function of odds-against, social discounting is a hyperbolic function of social distance. Experiment 1 obtained individual…

Hyperbolic spoof plasmonic metasurfaces

DOE PAGES

Yang, Yihao; Jing, Liqiao; Shen, Lian; ...

2017-08-25

Hyperbolic metasurfaces have recently emerged as a new research frontier because of the unprecedented capabilities to manipulate surface plasmon polaritons (SPPs) and many potential applications. But, thus far, the existence of hyperbolic metasurfaces has neither been observed nor predicted at low frequencies because noble metals cannot support SPPs at longer wavelengths. Here, we propose and experimentally demonstrate spoof plasmonic metasurfaces with a hyperbolic dispersion, where the spoof SPPs propagate on complementary H-shaped, perfectly conducting surfaces at low frequencies. Therefore, non-divergent diffractions, negative refraction and dispersion-dependent spin-momentum locking are observed as the spoof SPPs travel over the hyperbolic spoof plasmonic metasurfacesmore » (HSPMs). The HSPMs provide fundamental new platforms to explore the propagation and spin of spoof SPPs. They show great capabilities for designing advanced surface wave devices such as spatial multiplexers, focusing and imaging devices, planar hyperlenses, and dispersion-dependent directional couplers, at both microwave and terahertz frequencies.« less

Lamb Shift in the Near Field of Hyperbolic Metamaterial Half Space

NASA Astrophysics Data System (ADS)

Deng, Nai Jing; Yu, Kin Wah

2013-03-01

Hyperbolic metamaterials give a large magnification of the density of states in a specific frequency ranges, and has motivated various applications in emission lifetime reduction, strong absorption, and extraordinary black body radiation, etc. The boost of vacuum energy, which is proportional to the density of states, is expected in hyperbolic metamaterial. We have studied the Lamb shift in vacuum-hyperbolic-metamterial half spaces and shown the non-trivial role of vacuum energy. In our calculation, the easy-fabricated multilayer structure is employed to generate a hyperbolic dispersion relation. The spectrum of hydrogen atoms is calculated with a perturbation method after quantizing the half spaces with a complete mode expansion. It appears that the shift of spectrum is mainly contributed by the terahertz response of materials, which has been well described and predicted in both theories and experiments. Work supported by the General Research Fund of the Hong Kong SAR Government

High-Order Residual-Distribution Schemes for Discontinuous Problems on Irregular Triangular Grids

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2016-01-01

In this paper, we develop second- and third-order non-oscillatory shock-capturing hyperbolic residual distribution schemes for irregular triangular grids, extending our second- and third-order schemes to discontinuous problems. We present extended first-order N- and Rusanov-scheme formulations for hyperbolic advection-diffusion system, and demonstrate that the hyperbolic diffusion term does not affect the solution of inviscid problems for vanishingly small viscous coefficient. We then propose second- and third-order blended hyperbolic residual-distribution schemes with the extended first-order Rusanov-scheme. We show that these proposed schemes are extremely accurate in predicting non-oscillatory solutions for discontinuous problems. We also propose a characteristics-based nonlinear wave sensor for accurately detecting shocks, compression, and expansion regions. Using this proposed sensor, we demonstrate that the developed hyperbolic blended schemes do not produce entropy-violating solutions (unphysical stocks). We then verify the design order of accuracy of these blended schemes on irregular triangular grids.

Second- and third-order upwind difference schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Yang, J. Y.

1984-01-01

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

Curvature and temperature of complex networks.

PubMed

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

2009-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

A new method of imposing boundary conditions for hyperbolic equations

NASA Technical Reports Server (NTRS)

Funaro, D.; ative.

1987-01-01

A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.

Euler and Navier-Stokes equations on the hyperbolic plane.

PubMed

Khesin, Boris; Misiolek, Gerard

2012-11-06

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

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

ERIC Educational Resources Information Center

El-Zawawy, Amr M.

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

Bouloc, Damien

2017-11-01

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

Hyperbolic polaritons in nanoparticles

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Rubio, Angel; Guinea, Francisco; Basov, Dimitri; Fogler, Michael

2015-03-01

Hyperbolic optical materials (HM) are characterized by permittivity tensor that has both positive and negative principal values. Collective electromagnetic modes (polaritons) of HM have novel properties promising for various applications including subdiffractional imaging and on-chip optical communication. Hyperbolic response is actively investigated in the context of metamaterials, anisotropic polar insulators, and layered superconductors. We study polaritons in spheroidal HM nanoparticles using Hamiltonian optics. The field equations are mapped to classical dynamics of fictitious particles (wave packets) of an indefinite Hamiltonian. This dynamics is quantized using the Einstein-Brillouin-Keller quantization rule. The eigenmodes are classified as either bulk or surface according to whether their transverse momenta are real or imaginary. To model how such hyperbolic polaritons can be probed by near-field experiments, we compute the field distribution induced inside and outside the spheroid by an external point dipole. At certain magic frequencies the field shows striking geometric patterns whose origin is traced to the classical periodic orbits. The theory is applied to natural hyperbolic materials hexagonal boron nitride and superconducting LaSrCuO.

Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

NASA Astrophysics Data System (ADS)

de Lima, Levi Lopes; Girão, Frederico

2015-03-01

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 an optimal Penrose inequality for certain graphs in hyperbolic space whose boundary has constant mean curvature . This settles, for this class of manifolds, an inequality first conjectured by Wang (J Differ Geom 57(2):273-299, 2001).

Euler and Navier–Stokes equations on the hyperbolic plane

PubMed Central

Khesin, Boris; Misiołek, Gerard

2012-01-01

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

Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement

PubMed Central

Gustman, Alan L.; Steinmeier, Thomas L.

2012-01-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest. Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used. PMID:22711946

Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement.

PubMed

Gustman, Alan L; Steinmeier, Thomas L

2012-06-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest.Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used.

A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 receivingmore » 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.« less

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gadella, M.; Kuru, Ş.; Negro, J., E-mail: jnegro@fta.uva.es

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

Links between quantum physics and thought.

PubMed

Robson, Barry

2009-01-01

Quantum mechanics (QM) provides a variety of ideas that can assist in developing Artificial Intelligence for healthcare, and opens the possibility of developing a unified system of Best Practice for inference that will embrace both QM and classical inference. Of particular interest is inference in the hyperbolic-complex plane, the counterpart of the normal i-complex plane of basic QM. There are two reasons. First, QM appears to rotate from i-complex Hilbert space to hyperbolic-complex descriptions when observations are made on wave functions as particles, yielding classical results, and classical laws of probability manipulation (e.g. the law of composition of probabilities) then hold, whereas in the i-complex plane they do not. Second, i-complex Hilbert space is not the whole story in physics. Hyperbolic complex planes arise in extension from the Dirac-Clifford calculus to particle physics, in relativistic correction thereby, and in regard to spinors and twisters. Generalization of these forms resemble grammatical constructions and promote the idea that probability-weighted algebraic elements can be used to hold dimensions of syntactic and semantic meaning. It is also starting to look as though when a solution is reached by an inference system in the hyperbolic-complex, the hyperbolic-imaginary values disappear, while conversely hyperbolic-imaginary values are associated with the un-queried state of a system and goal seeking behavior.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Collisions with meteoroid streams as one possible mechanism for the formation of hyperbolic cometary orbits

NASA Astrophysics Data System (ADS)

Guliyev, Ayyub; Nabiyev, Shaig

2017-07-01

This paper presents the results of a statistical analysis of the dynamic parameters of 300 comets that have osculating hyperbolic orbits. It is shown that such comets differ from other comets by their large perihelion distances and by a predominance of retrograde motion. It is shown that the values of i, the inclination of the hyperbolic comets, are in comparative excess over the interval 90-120°. The dominance by q, the perihelion distance, renders it difficult to suggest that the excess hyperbolic velocity of these comets can be the result of physical processes that take place in their nuclei. Aspects of the following working hypothesis, that the hyperbolic excess of parameter e might be formed after comets pass through meteoroid streams, are also studied. To evaluate this hypothesis, the distribution of the orbits of hyperbolic comets relative to the plane of motion of 112 established meteoroid streams are analyzed. The number (N) of orbit nodes for hyperbolic comets with respect to the plane of each stream at various distances is calculated. To determine the degree of redundancy of N, a special computing algorithm was applied that provided the expected value nav as well as the standard deviation σ for the number of cometary nodes at the plane of each stream. A comparative analysis of the N and nav values that take σ into account suggests an excess in 40 stream cases. This implies that the passage of comets through meteoroid streams can lead to an acceleration of the comets' heliocentric velocity.

Tunable VO2/Au Hyperbolic Metamaterial

DTIC Science & Technology

2016-02-12

phenomenon having a potential of advancing the control of light-matter interaction . Metamaterials are engineered composite materials containing sub...ellipsoids15 – the phenomenon known as hyperbolic dispersion. Hyperbolic metamaterials can propagate light waves with very large wave vectors and have a...incidence angles equal to 15°, 45° and 65°. The spectra measured at 45o are depicted in Fig. 6(a). The wavy pattern in the spectra is due to the parasitic

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

DTIC Science & Technology

2014-03-01

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

Concave utility, transaction costs, and risk in measuring discounting of delayed rewards.

PubMed

Kirby, Kris N; Santiesteban, Mariana

2003-01-01

Research has consistently found that the decline in the present values of delayed rewards as delay increases is better fit by hyperbolic than by exponential delay-discounting functions. However, concave utility, transaction costs, and risk each could produce hyperbolic-looking data, even when the underlying discounting function is exponential. In Experiments 1 (N = 45) and 2 (N = 103), participants placed bids indicating their present values of real future monetary rewards in computer-based 2nd-price auctions. Both experiments suggest that utility is not sufficiently concave to account for the superior fit of hyperbolic functions. Experiment 2 provided no evidence that the effects of transaction costs and risk are large enough to account for the superior fit of hyperbolic functions.

Guidance of Nonlinear Nonminimum-Phase Dynamic Systems

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1996-01-01

The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated 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 was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

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.

The curious case of large-N expansions on a (pseudo)sphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Polyakov, Alexander M.; Saleem, Zain H.; Stokes, James

We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand-Dikiy equations.

The curious case of large-N expansions on a (pseudo)sphere

DOE PAGES

Polyakov, Alexander M.; Saleem, Zain H.; Stokes, James

2015-02-03

We elucidate the large-N dynamics of one-dimensional sigma models with spherical and hyperbolic target spaces and find a duality between the Lagrange multiplier and the angular momentum. In the hyperbolic model we propose a new class of operators based on the irreducible representations of hyperbolic space. We also uncover unexpected zero modes which lead to the double scaling of the 1/N expansion and explore these modes using Gelfand-Dikiy equations.

New Techniques in Time-Frequency Analysis: Adaptive Band, Ultra-Wide Band and Multi-Rate Signal Processing

DTIC Science & Technology

2016-03-02

Nyquist tiles and sampling groups in Euclidean geometry, and discussed the extension of these concepts to hyperbolic and spherical geometry and...hyperbolic or spherical spaces. We look to develop a structure for the tiling of frequency spaces in both Euclidean and non-Euclidean domains. In particular...we establish Nyquist tiles and sampling groups in Euclidean geometry, and discuss the extension of these concepts to hyperbolic and spherical geometry

Fluid displacement between two parallel plates: a non-empirical model displaying change of type from hyperbolic to elliptic equations

NASA Astrophysics Data System (ADS)

Shariati, M.; Talon, L.; Martin, J.; Rakotomalala, N.; Salin, D.; Yortsos, Y. C.

2004-11-01

We consider miscible displacement between parallel plates in the absence of diffusion, with a concentration-dependent viscosity. By selecting a piecewise viscosity function, this can also be considered as ‘three-fluid’ flow in the same geometry. Assuming symmetry across the gap and based on the lubrication (‘equilibrium’) approximation, a description in terms of two quasi-linear hyperbolic equations is obtained. We find that the system is hyperbolic and can be solved analytically, when the mobility profile is monotonic, or when the mobility of the middle phase is smaller than its neighbours. When the mobility of the middle phase is larger, a change of type is displayed, an elliptic region developing in the composition space. Numerical solutions of Riemann problems of the hyperbolic system spanning the elliptic region, with small diffusion added, show good agreement with the analytical outside, but an unstable behaviour inside the elliptic region. In these problems, the elliptic region arises precisely at the displacement front. Crossing the elliptic region requires the solution of essentially an eigenvalue problem of the full higher-dimensional model, obtained here using lattice BGK simulations. The hyperbolic-to-elliptic change-of-type reflects the failing of the lubrication approximation, underlying the quasi-linear hyperbolic formalism, to describe the problem uniformly. The obtained solution is analogous to non-classical shocks recently suggested in problems with change of type.

A Theoretical Framework for Lagrangian Descriptors

NASA Astrophysics Data System (ADS)

Lopesino, C.; Balibrea-Iniesta, F.; García-Garrido, V. J.; Wiggins, S.; Mancho, A. M.

This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigorous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for LDs. The definition is stated for n-dimensional systems with general time dependence, however we rigorously prove that this method reveals the stable and unstable manifolds of hyperbolic points in four particular 2D cases: a hyperbolic saddle point for linear autonomous systems, a hyperbolic saddle point for nonlinear autonomous systems, a hyperbolic saddle point for linear nonautonomous systems and a hyperbolic saddle point for nonlinear nonautonomous systems. We also discuss further rigorous results which show the ability of LDs to highlight additional invariants sets, such as n-tori. These results are just a simple extension of the ergodic partition theory which we illustrate by applying this methodology to well-known examples, such as the planar field of the harmonic oscillator and the 3D ABC flow. Finally, we provide a thorough discussion on the requirement of the objectivity (frame-invariance) property for tools designed to reveal phase space structures and their implications for Lagrangian descriptors.

Discounting of reward sequences: a test of competing formal models of hyperbolic discounting

PubMed Central

Zarr, Noah; Alexander, William H.; Brown, Joshua W.

2014-01-01

Humans are known to discount future rewards hyperbolically in time. Nevertheless, a formal recursive model of hyperbolic discounting has been elusive until recently, with the introduction of the hyperbolically discounted temporal difference (HDTD) model. Prior to that, models of learning (especially reinforcement learning) have relied on exponential discounting, which generally provides poorer fits to behavioral data. Recently, it has been shown that hyperbolic discounting can also be approximated by a summed distribution of exponentially discounted values, instantiated in the μAgents model. The HDTD model and the μAgents model differ in one key respect, namely how they treat sequences of rewards. The μAgents model is a particular implementation of a Parallel discounting model, which values sequences based on the summed value of the individual rewards whereas the HDTD model contains a non-linear interaction. To discriminate among these models, we observed how subjects discounted a sequence of three rewards, and then we tested how well each candidate model fit the subject data. The results show that the Parallel model generally provides a better fit to the human data. PMID:24639662

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

NASA Technical Reports Server (NTRS)

Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)

1994-01-01

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

Transformations of asymptotically AdS hyperbolic initial data and associated geometric inequalities

NASA Astrophysics Data System (ADS)

Cha, Ye Sle; Khuri, Marcus

2018-01-01

We construct transformations which take asymptotically AdS hyperbolic initial data into asymptotically flat initial data, and which preserve relevant physical quantities. This is used to derive geometric inequalities in the asymptotically AdS hyperbolic setting from counterparts in the asymptotically flat realm, whenever a geometrically motivated system of elliptic equations admits a solution. The inequalities treated here relate mass, angular momentum, charge, and horizon area. Furthermore, new mass-angular momentum inequalities in this setting are conjectured and discussed.

Convergence results for pseudospectral approximations of hyperbolic systems by a penalty type boundary treatment

NASA Technical Reports Server (NTRS)

Funaro, Daniele; Gottlieb, David

1989-01-01

A new method of imposing boundary conditions in the pseudospectral approximation of hyperbolic systems of equations is proposed. It is suggested to collocate the equations, not only at the inner grid points, but also at the boundary points and use the boundary conditions as penalty terms. In the pseudo-spectral Legrendre method with the new boundary treatment, a stability analysis for the case of a constant coefficient hyperbolic system is presented and error estimates are derived.

Hyperbolic heat conduction problems involving non-Fourier effects - Numerical simulations via explicit Lax-Wendroff/Taylor-Galerkin finite element formulations

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; Namburu, Raju R.

1989-01-01

Numerical simulations are presented for hyperbolic heat-conduction problems that involve non-Fourier effects, using explicit, Lax-Wendroff/Taylor-Galerkin FEM formulations as the principal computational tool. Also employed are smoothing techniques which stabilize the numerical noise and accurately predict the propagating thermal disturbances. The accurate capture of propagating thermal disturbances at characteristic time-step values is achieved; numerical test cases are presented which validate the proposed hyperbolic heat-conduction problem concepts.

Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material

PubMed Central

Dai, S.; Ma, Q.; Andersen, T.; Mcleod, A. S.; Fei, Z.; Liu, M. K.; Wagner, M.; Watanabe, K.; Taniguchi, T.; Thiemens, M.; Keilmann, F.; Jarillo-Herrero, P.; Fogler, M. M.; Basov, D. N.

2015-01-01

Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. In such materials, light propagation is unusual leading to novel and often non-intuitive optical phenomena. Here we report infrared nano-imaging experiments demonstrating that crystals of hexagonal boron nitride, a natural mid-infrared hyperbolic material, can act as a ‘hyper-focusing lens' and as a multi-mode waveguide. The lensing is manifested by subdiffractional focusing of phonon–polaritons launched by metallic disks underneath the hexagonal boron nitride crystal. The waveguiding is revealed through the modal analysis of the periodic patterns observed around such launchers and near the sample edges. Our work opens new opportunities for anisotropic layered insulators in infrared nanophotonics complementing and potentially surpassing concurrent artificial hyperbolic materials with lower losses and higher optical localization. PMID:25902364

"That's really clever!" Ironic hyperbole understanding in children.

PubMed

Aguert, Marc; LE Vallois, Coralie; Martel, Karine; Laval, Virginie

2018-01-01

Hyperbole supports irony comprehension in adults by heightening the contrast between what is said and the actual situation. Because young children do not perceive the communication situation as a whole, but rather give precedence to either the utterance or the context, we predicted that hyperbole would reduce irony comprehension in six-year-olds (n = 40) by overemphasizing what was said. By contrast, ten-year-olds (n = 40) would benefit from hyperbole in the way that adults do, as they would perceive the utterance and context as a whole, highlighted by the speaker's ironic intent. Short animated cartoons featuring ironic criticisms were shown to participants. We assessed comprehension of the speaker's belief and speaker's intent. Results supported our predictions. The development of mentalization during school years and its impact on the development of irony comprehension is discussed.

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

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2014-01-01

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Modified hyperbolic sine model for titanium dioxide-based memristive thin films

NASA Astrophysics Data System (ADS)

Abu Bakar, Raudah; Syahirah Kamarozaman, Nur; Fazlida Hanim Abdullah, Wan; Herman, Sukreen Hana

2018-03-01

Since the emergence of memristor as the newest fundamental circuit elements, studies on memristor modeling have been evolved. To date, the developed models were based on the linear model, linear ionic drift model using different window functions, tunnelling barrier model and hyperbolic-sine function based model. Although using hyperbolic-sine function model could predict the memristor electrical properties, the model was not well fitted to the experimental data. In order to improve the performance of the hyperbolic-sine function model, the state variable equation was modified. On the one hand, the addition of window function cannot provide an improved fitting. By multiplying the Yakopcic’s state variable model to Chang’s model on the other hand resulted in the closer agreement with the TiO2 thin film experimental data. The percentage error was approximately 2.15%.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Theory of hyperbolic stratified nanostructures for surface-enhanced Raman scattering

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

PubMed

Kim, Kyunghan; Guo, Zhixiong

2007-05-01

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

A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting

NASA Technical Reports Server (NTRS)

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.

Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Hyperbolic chaos in the klystron-type microwave vacuum tube oscillator

NASA Astrophysics Data System (ADS)

Emel'yanov, V. V.; Kuznetsov, S. P.; Ryskin, N. M.

2010-12-01

The ring-loop oscillator consisting of two coupled klystrons which is capable of generating hyperbolic chaotic signal in the microwave band is considered. The system of delayed-differential equations describing the dynamics of the oscillator is derived. This system is further reduced to the two-dimensional return map under the assumption of the instantaneous build-up of oscillations in the cavities. The results of detailed numerical simulation for both models are presented showing that there exists large enough range of control parameters where the sustained regime corresponds to the structurally stable hyperbolic chaos.

Motion Among Random Obstacles on a Hyperbolic Space

NASA Astrophysics Data System (ADS)

Orsingher, Enzo; Ricciuti, Costantino; Sisti, Francesco

2016-02-01

We consider the motion of a particle along the geodesic lines of the Poincaré half-plane. The particle is specularly reflected when it hits randomly-distributed obstacles that are assumed to be motionless. This is the hyperbolic version of the well-known Lorentz Process studied in the Euclidean context. We analyse the limit in which the density of the obstacles increases to infinity and the size of each obstacle vanishes: under a suitable scaling, we prove that our process converges to a Markovian process, namely a random flight on the hyperbolic manifold.

Exotica and the status of the strong cosmic censor conjecture in four dimensions

NASA Astrophysics Data System (ADS)

Etesi, Gábor

2017-12-01

An immense class of physical counterexamples to the four dimensional strong cosmic censor conjecture—in its usual broad formulation—is exhibited. More precisely, out of any closed and simply connected 4-manifold an open Ricci-flat Lorentzian 4-manifold is constructed which is not globally hyperbolic, and no perturbation of which, in any sense, can be globally hyperbolic. This very stable non-global-hyperbolicity is the consequence of our open spaces having a ‘creased end’—i.e. an end diffeomorphic to an exotic \

SAHARA: A package of PC computer programs for estimating both log-hyperbolic grain-size parameters and standard moments

NASA Astrophysics Data System (ADS)

Christiansen, Christian; Hartmann, Daniel

This paper documents a package of menu-driven POLYPASCAL87 computer programs for handling grouped observations data from both sieving (increment data) and settling tube procedures (cumulative data). The package is designed deliberately for use on IBM-compatible personal computers. Two of the programs solve the numerical problem of determining the estimates of the four (main) parameters of the log-hyperbolic distribution and their derivatives. The package also contains a program for determining the mean, sorting, skewness. and kurtosis according to the standard moments. Moreover, the package contains procedures for smoothing and grouping of settling tube data. A graphic part of the package plots the data in a log-log plot together with the estimated log-hyperbolic curve. Along with the plot follows all estimated parameters. Another graphic option is a plot of the log-hyperbolic shape triangle with the (χ,ζ) position of the sample.

Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes.

PubMed

Kapitanova, Polina V; Ginzburg, Pavel; Rodríguez-Fortuño, Francisco J; Filonov, Dmitry S; Voroshilov, Pavel M; Belov, Pavel A; Poddubny, Alexander N; Kivshar, Yuri S; Wurtz, Gregory A; Zayats, Anatoly V

2014-01-01

The routing of light in a deep subwavelength regime enables a variety of important applications in photonics, quantum information technologies, imaging and biosensing. Here we describe and experimentally demonstrate the selective excitation of spatially confined, subwavelength electromagnetic modes in anisotropic metamaterials with hyperbolic dispersion. A localized, circularly polarized emitter placed at the boundary of a hyperbolic metamaterial is shown to excite extraordinary waves propagating in a prescribed direction controlled by the polarization handedness. Thus, a metamaterial slab acts as an extremely broadband, nearly ideal polarization beam splitter for circularly polarized light. We perform a proof of concept experiment with a uniaxial hyperbolic metamaterial at radio-frequencies revealing the directional routing effect and strong subwavelength λ/300 confinement. The proposed concept of metamaterial-based subwavelength interconnection and polarization-controlled signal routing is based on the photonic spin Hall effect and may serve as an ultimate platform for either conventional or quantum electromagnetic signal processing.

Luminescent hyperbolic metasurfaces

NASA Astrophysics Data System (ADS)

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.

Realizing high-quality ultralarge momentum states and ultrafast topological transitions using semiconductor hyperbolic metamaterials

DOE PAGES

Campione, Salvatore; Liu, Sheng; Luk, Ting S.; ...

2015-08-05

We employ both the effective medium approximation (EMA) and Bloch theory to compare the dispersion properties of semiconductor hyperbolic metamaterials (SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs) at visible frequencies. This analysis reveals the conditions under which the EMA can be safely applied for both MHMs and SHMs. We find that the combination of precise nanoscale layering and the longer infrared operating wavelengths puts the SHMs well within the effective medium limit and, in contrast to MHMs, allows for the attainment of very high photon momentum states. Additionally, SHMs allow for new phenomena such as ultrafast creation ofmore » the hyperbolic manifold through optical pumping. Furthermore, we examine the possibility of achieving ultrafast topological transitions through optical pumping which can photo-dope appropriately designed quantum wells on the femtosecond time scale.« less

Chimeras and clusters in networks of hyperbolic chaotic oscillators

NASA Astrophysics Data System (ADS)

Cano, A. V.; Cosenza, M. G.

2017-03-01

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.

Path integration on the hyperbolic plane with a magnetic field

NASA Astrophysics Data System (ADS)

Grosche, Christian

1990-08-01

In this paper I discuss the path integrals on three formulations of hyperbolic geometry, where a constant magnetic field B is included. These are: the pseudosphere Λ2, the Poincaré disc D, and the hyperbolic strip S. The corresponding path integrals can be reformulated in terms of the path integral for the modified Pöschl-Teller potential. The wave-functions and the energy spectrum for the discrete and continuous part of the spectrum are explicitly calculated in each case. First the results are compared for the limit B → 0 with previous calculations and second with the path integration on the Poincaré upper half-plane U. This work is a continuation of the path integral calculations for the free motion on the various formulations on the hyperbolic plane and for the case of constant magnetic field on the Poincaré upper half-plane U.

Hyperbolic metamaterial lens with hydrodynamic nonlocal response.

PubMed

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.

Near-field heat transfer between graphene/hBN multilayers

NASA Astrophysics Data System (ADS)

Zhao, Bo; Guizal, Brahim; Zhang, Zhuomin M.; Fan, Shanhui; Antezza, Mauro

2017-06-01

We study the radiative heat transfer between multilayer structures made by a periodic repetition of a graphene sheet and a hexagonal boron nitride (hBN) slab. Surface plasmons in a monolayer graphene can couple with hyperbolic phonon polaritons in a single hBN film to form hybrid polaritons that can assist photon tunneling. For periodic multilayer graphene/hBN structures, the stacked metallic/dielectric array can give rise to a further effective hyperbolic behavior, in addition to the intrinsic natural hyperbolic behavior of hBN. The effective hyperbolicity can enable more hyperbolic polaritons that enhance the photon tunneling and hence the near-field heat transfer. However, the hybrid polaritons on the surface, i.e., surface plasmon-phonon polaritons, dominate the near-field heat transfer between multilayer structures when the topmost layer is graphene. The effective hyperbolic regions can be well predicted by the effective medium theory (EMT), thought EMT fails to capture the hybrid surface polaritons and results in a heat transfer rate much lower compared to the exact calculation. The chemical potential of the graphene sheets can be tuned through electrical gating and results in an additional modulation of the heat transfer. We found that the near-field heat transfer between multilayer structures does not increase monotonously with the number of layers in the stack, which provides a way to control the heat transfer rate by the number of graphene layers in the multilayer structure. The results may benefit the applications of near-field energy harvesting and radiative cooling based on hybrid polaritons in two-dimensional materials.

Inverse-Square Orbits: A Geometric Approach.

ERIC Educational Resources Information Center

Rainwater, James C.; Weinstock, Robert

1979-01-01

Presents a derivation of Kepler's first law of planetary motion from Newtonian principles. Analogus derivations of the hyperbolic and parabolic orbits of nonreturning comets and the hyperbolic orbit for a particle in a repulsive inverse-square field are also presented. (HM)

Use of hyperbolic partial differential equations to generate body fitted coordinates

NASA Technical Reports Server (NTRS)

Steger, J. L.; Sorenson, R. L.

1980-01-01

The hyperbolic scheme is used to efficiently generate smoothly varying grids with good step size control near the body. Although only two dimensional applications are presented, the basic concepts are shown to extend to three dimensions.

Accuracy limitations of hyperbolic multilateration systems

DOT National Transportation Integrated Search

1973-03-22

The report is an analysis of the accuracy limitations of hyperbolic multilateration systems. A central result is a demonstration that the inverse of the covariance matrix for positional errors corresponds to the moment of inertia matrix of a simple m...

Novel Plasmonic and Hyberbolic Optical Materials for Control of Quantum Nanoemitters

DTIC Science & Technology

2016-12-08

properties, metal ion implantation techniques, and multi- physics modeling to produce hyperbolic quantum nanoemitters. 15. SUBJECT TERMS nanotechnology 16...techniques, and multi- physics modeling to produce hyperbolic quantum nanoemitters. During the course of this project we studied plasmonic

Explicit formulae for Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation C(2n, 3)

NASA Astrophysics Data System (ADS)

Ham, Ji-Young; Lee, Joongul

2017-03-01

We calculate the Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation C(2n, 3) using the Schläfli formula for the generalized Chern-Simons function on the family of C(2n, 3) cone-manifold structures. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham and Lee's methods. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic C(2n, 3) orbifolds.

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

NASA Technical Reports Server (NTRS)

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

1998-01-01

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

Origin of hyperbolicity in brain-to-brain coordination networks

NASA Astrophysics Data System (ADS)

Tadić, Bosiljka; Andjelković, Miroslav; Šuvakov, Milovan

2018-02-01

Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are delta-hyperbolic with delta_max=1 and the graph diameter D=3 in each brain. While the emergent hyperbolicity in the two-brain networks satisfies delta_max/D/2 < 1 and can be attributed to the topology of the subgraph formed around the cross-brains linking channels. We identify these subgraphs in each studied two-brain network and decompose their structure into simple geometric descriptors (triangles, tetrahedra and cliques of higher orders) that contribute to hyperbolicity. Considering topologies that exceed two separate brain networks as a measure of coordination synergy between the brains, we identify different neuronal correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listener’s self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior.

Time discounting and smoking behavior: evidence from a panel survey(*).

PubMed

Kang, Myong-Il; Ikeda, Shinsuke

2014-12-01

By using a panel survey of Japanese adults, we show that smoking behavior is associated with personal time discounting and its biases, such as hyperbolic discounting and the sign effect, in the way that theory predicts: smoking depends positively on the discount rate and the degree of hyperbolic discounting and negatively on the presence of the sign effect. Positive effects of hyperbolic discounting on smoking are salient for naïve people, who are not aware of their self-control problem. By estimating smoking participation and smokers' cigarette consumption in Cragg's two-part model, we find that the two smoking decisions depend on different sets of time-discounting variables. Particularly, smoking participation is affected by being a naïve hyperbolic discounter, whereas the discount rate, the presence of the sign effect, and a hyperbolic discounting proxy constructed from procrastination behavior vis-à-vis doing homework assignments affect both types of decision making. The panel data enable us to analyze the over-time instability of elicited discount rates. The instability is shown to come from measurement errors, rather than preference shocks on time preference. Several evidences indicate that the detected associations between time preferences and smoking behavior are interpersonal one, rather than within-personal one. Copyright © 2013 John Wiley & Sons, Ltd.

Modeling of ultrashort pulsed laser irradiation in the cornea based on parabolic and hyperbolic heat equations using electrical analogy

NASA Astrophysics Data System (ADS)

Gheitaghy, A. M.; Takabi, B.; Alizadeh, M.

2014-03-01

Hyperbolic and parabolic heat equations are formulated to study a nonperfused homogeneous transparent cornea irradiated by high power and ultrashort pulsed laser in the Laser Thermo Keratoplasty (LTK) surgery. Energy absorption inside the cornea is modeled using the Beer-Lambert law that is incorporated as an exponentially decaying heat source. The hyperbolic and parabolic bioheat models of the tissue were solved by exploiting the mathematical analogy between thermal and electrical systems, by using robust circuit simulation program called Hspice to get the solutions of simultaneous RLC and RC transmission line networks. This method can be used to rapidly calculate the temperature in laser-irradiated tissue at time and space domain. It is found that internal energy gained from the irradiated field results in a rapid rise of temperature in the cornea surface during the early heating period, while the hyperbolic wave model predicts a higher temperature rise than the classical heat diffusion model. In addition, this paper investigates and examines the effect of some critical parameters such as relaxation time, convection coefficient, radiation, tear evaporation and variable thermal conductivity of cornea. Accordingly, it is found that a better accordance between hyperbolic and parabolic models will be achieved by time.

Correlation Functions of σ Fields with Values in a Hyperbolic Space

NASA Astrophysics Data System (ADS)

Haba, Z.

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

Distributions of Orbital Elements for Meteoroids on Near-Parabolic Orbits According to Radar Observational Data

NASA Technical Reports Server (NTRS)

Kolomiyets, S. V.

2011-01-01

Some results of the International Heliophysical Year (IHY) Coordinated Investigation Program (CIP) number 65 Meteors in the Earth Atmosphere and Meteoroids in the Solar System are presented. The problem of hyperbolic and near-parabolic orbits is discussed. Some possibilities for the solution of this problem can be obtained from the radar observation of faint meteors. The limiting magnitude of the Kharkov, Ukraine, radar observation program in the 1970 s was +12, resulting in a very large number of meteors being detected. 250,000 orbits down to even fainter limiting magnitude were determined in the 1972-78 period in Kharkov (out of them 7,000 are hyperbolic). The hypothesis of hyperbolic meteors was confirmed. In some radar meteor observations 1 10% of meteors are hyperbolic meteors. Though the Advanced Meteor Orbit Radar (AMOR, New Zealand) and Canadian Meteor Orbit Radar (CMOR, Canada) have accumulated millions of meteor orbits, there are difficulties in comparing the radar observational data obtained from these three sites (New Zealand, Canada, Kharkov). A new global program International Space Weather Initiative (ISWI) has begun in 2010 (http://www.iswi-secretariat.org). Today it is necessary to create the unified radar catalogue of nearparabolic and hyperbolic meteor orbits in the framework of the ISWI, or any other different way, in collaboration of Ukraine, Canada, New Zealand, the USA and, possibly, Japan. Involvement of the Virtual Meteor Observatory (Netherlands) and Meteor Data Centre (Slovakia) is desirable too. International unified radar catalogue of near-parabolic and hyperbolic meteor orbits will aid to a major advance in our understanding of the ecology of meteoroids within the Solar System and beyond.

Bianchi transformation between the real hyperbolic Monge-Ampère equation and the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Mokhov, O. I.; Nutku, Y.

1994-10-01

By casting the Born-Infeld equation and the real hyperbolic Monge-Ampère equation into the form of equations of hydrodynamic type, we find that there exists an explicit transformation between them. This is Bianchi transformation.

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Terahertz radiation in graphene hyperbolic medium excited by an electric dipole.

PubMed

Feng, Xiaodong; Gong, Sen; Zhong, Renbin; Zhao, Tao; Hu, Min; Zhang, Chao; Liu, Shenggang

2018-03-01

In this Letter, the enhanced and directional radiation in a wide terahertz (THz) frequency range in a graphene hyperbolic medium excited by an electric dipole is presented. The numerical simulations and theoretical analyses indicate that the enhanced radiation comes from the strong surface plasmon couplings in the graphene hyperbolic medium, consisting of alternative graphene and dielectric substrate layers. The simulation results also show that the peak power flow of the enhanced THz radiation in the graphene hyperbolic medium is dramatically enhanced by more than 1 order of magnitude over that in a general medium within a certain distance from the dipole, and the electromagnetic fields are strongly concentrated in a narrow angle. Also, the radiation fields can be manipulated, and the fields' angular distributions can be tuned by adjusting the dielectric permittivity and thickness of the substrates, and the chemical potential of graphene. Accordingly, it provides a good opportunity for developing miniature, integratable, high-power-density, and tunable radiation sources in the THz band at room temperature.

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

NASA Astrophysics Data System (ADS)

Canadell, Marta; Haro, Àlex

2017-12-01

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

Infrared metamaterial by RF magnetron sputtered ZnO/Al:ZnO multilayers

NASA Astrophysics Data System (ADS)

Santiago, Kevin C.; Mundle, Rajeh; White, Curtis; Bahoura, Messaoud; Pradhan, Aswini K.

2018-03-01

Hyperbolic metamaterials create artificial anisotropy using metallic wires suspended in dielectric media or alternating layers of a metal and dielectric (Type I or Type II). In this study we fabricated ZnO/Al:ZnO (AZO) multilayers by the RF magnetron sputtering deposition technique. Our fabricated multilayers satisfy the requirements for a type II hyperbolic metamaterial. The optical response of individual AZO and ZnO films, as well as the multilayered film were investigated via UV-vis-IR transmittance and spectroscopic ellipsometry. The optical response of the multilayered system is calculated using the nonlocal-corrected Effective Medium Approximation (EMA). The spectroscopic ellipsometry data of the multilayered system was modeled using a uniaxial material model and EMA model. Both theoretical and experimental studies validate the fabricated multilayers undergo a hyperbolic transition at a wavelength of 2.2 μm. To our knowledge this is the first AZO/ZnO type II hyperbolic metamaterial system fabricated by magnetron sputtering deposition method.

Can rodents conceive hyperbolic spaces?

PubMed Central

Urdapilleta, Eugenio; Troiani, Francesca; Stella, Federico; Treves, Alessandro

2015-01-01

The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet, one class of models describing the formation of grid unit selectivity is entirely based on developmental self-organization, and as such it predicts that the metric it expresses should reflect the environment to which the animal has adapted. We show that, according to self-organizing models, if raised in a non-Euclidean hyperbolic cage rats should be able to form hyperbolic grids. For a given range of grid spacing relative to the radius of negative curvature of the hyperbolic surface, such grids are predicted to appear as multi-peaked firing maps, in which each peak has seven neighbours instead of the Euclidean six, a prediction that can be tested in experiments. We thus demonstrate that a useful universal neuronal metric, in the sense of a multi-scale ruler and compass that remain unaltered when changing environments, can be extended to other than the standard Euclidean plane. PMID:25948611

A method for the investigation of hyperbolic motions in the gravitational field of a spheroidal planet

NASA Astrophysics Data System (ADS)

Konks, V. Ia.

1981-05-01

Barrar's (1961) method for the analysis of the motion of a satellite of an oblate planet is extended to the case of hyperbolic motion. An analysis is presented of the motion of a material point in the gravitational field of a fixed center, combined with a gravitational dipole located at the point of inertia of a dynamically symmetric planet. Formulas are obtained for the hyperbolic motion of a spacecraft in the gravitational field of a spheroidal planet with an accuracy up to the second zonal harmonic of the expansion of its potential into a Legendre polynomial series in spherical coordinates.

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

NASA Astrophysics Data System (ADS)

Sabari, S.; Murali, R.

2018-05-01

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

On the hyperbolicity of a two-fluid model for debris flows

NASA Astrophysics Data System (ADS)

Mineo, C.; Torrisi, M.

2010-05-01

We consider the system of partial differential equations associated with the mathematical model for debris flows proposed by E.B. Pitman and L. Le (Phil. Trans. R. Soc. A, 363, 1573-1601, 2005) and analyze the problem of the hyperbolicity of the model.

Euclidean, Spherical, and Hyperbolic Shadows

ERIC Educational Resources Information Center

Hoban, Ryan

2013-01-01

Many classical problems in elementary calculus use Euclidean geometry. This article takes such a problem and solves it in hyperbolic and in spherical geometry instead. The solution requires only the ability to compute distances and intersections of points in these geometries. The dramatically different results we obtain illustrate the effect…

On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach

NASA Technical Reports Server (NTRS)

Gastaldi, Fabio; Quarteroni, Alfio

1988-01-01

The coupling of hyperbolic and parabolic systems is discussed in a domain Omega divided into two distinct subdomains omega(+) and omega(-). The main concern is to find the proper interface conditions to be fulfilled at the surface separating the two domains. Next, they are used in the numerical approximation of the problem. The justification of the interface conditions is based on a singular perturbation analysis, i.e., the hyperbolic system is rendered parabolic by adding a small artifical viscosity. As this goes to zero, the coupled parabolic-parabolic problem degenerates into the original one, yielding some conditions at the interface. These are taken as interface conditions for the hyperbolic-parabolic problem. Actually, two alternative sets of interface conditions are discussed according to whether the regularization procedure is variational or nonvariational. It is shown how these conditions can be used in the frame of a numerical approximation to the given problem. Furthermore, a method of resolution is discussed which alternates the resolution of the hyperbolic problem within omega(-) and of the parabolic one within omega(+). The spectral collocation method is proposed, as an example of space discretization (different methods could be used as well); both explicit and implicit time-advancing schemes are considered. The present study is a preliminary step toward the analysis of the coupling between Euler and Navier-Stokes equations for compressible flows.

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

NASA Astrophysics Data System (ADS)

Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

2018-02-01

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

Comparing the Performance of Hyperbolic and Circular Rod Quadrupole Mass Spectrometers with Applied Higher Order Auxiliary Excitation

NASA Technical Reports Server (NTRS)

Gershman, D.J.; Block, B.P.; Rubin, M.; Benna, M.; Mahaffy, P. R.; Zurbuchen, T. H.

2012-01-01

This work applies higher order auxiliary excitation techniques to two types of quadrupole mass spectrometers (QMSs): commercial systems and spaceborne instruments. The operational settings of a circular rod geometry commercial system and an engineering test-bed for a hyperbolic rod geometry spaceborne instrument were matched, with the relative performance of each sensor characterized with and without applied excitation using isotopic measurements of Kr+. Each instrument was operated at the limit of the test electronics to determine the effect of auxiliary excitation on extending instrument capabilities. For the circular rod sensor, with applied excitation, a doubling of the mass resolution at 1% of peak transmission resulted from the elimination of the low-mass side peak tail typical of such rod geometries. The mass peak stability and ion rejection efficiency were also increased by factors of 2 and 10, respectively, with voltage scan lines passing through the center of stability islands formed from auxiliary excitation. Auxiliary excitation also resulted in factors of 6 and 2 in peak stability and ion rejection efficiency, respectively, for the hyperbolic rod sensor. These results not only have significant implications for the use of circular rod quadrupoles with applied excitation as a suitable replacement for traditional hyperbolic rod sensors, but also for extending the capabilities of existing hyperbolic rod QMSs for the next generation of spaceborne instruments and low-mass commercial systems.

Dynamics and control of high area-to-mass ratio spacecraft and its application to geomagnetic exploration

NASA Astrophysics Data System (ADS)

Luo, Tong; Xu, Ming; Colombo, Camilla

2018-04-01

This paper studies the dynamics and control of a spacecraft, whose area-to-mass ratio is increased by deploying a reflective orientable surface such as a solar sail or a solar panel. The dynamical system describing the motion of a non-zero attitude angle high area-to-mass ratio spacecraft under the effects of the Earth's oblateness and solar radiation pressure admits the existence of equilibrium points, whose number and the eccentricity values depend on the semi-major axis, the area-to-mass ratio and the attitude angle of the spacecraft together. When two out of three parameters are fixed, five different dynamical topologies successively occur through varying the third parameter. Two of these five topologies are critical cases characterized by the appearance of the bifurcation phenomena. A conventional Hamiltonian structure-preserving (HSP) controller and an improved HSP controller are both constructed to stabilize the hyperbolic equilibrium point. Through the use of a conventional HSP controller, a bounded trajectory around the hyperbolic equilibrium point is obtained, while an improved HSP controller allows the spacecraft to easily transfer to the hyperbolic equilibrium point and to follow varying equilibrium points. A bifurcation control using topologies and changes of behavior areas can also stabilize a spacecraft near a hyperbolic equilibrium point. Natural trajectories around stable equilibrium point and these stabilized trajectories around hyperbolic equilibrium point can all be applied to geomagnetic exploration.

Directional and monochromatic thermal emitter from epsilon-near-zero conditions in semiconductor hyperbolic metamaterials

DOE PAGES

Campione, Salvatore; Marquier, Francois; Hugonin, Jean -Paul; ...

2016-10-05

The development of novel thermal sources that control the emission spectrum and the angular emission pattern is of fundamental importance. In this paper, we investigate the thermal emission properties of semiconductor hyperbolic metamaterials (SHMs). Our structure does not require the use of any periodic corrugation to provide monochromatic and directional emission properties. We show that these properties arise because of epsilon-near-zero conditions in SHMs. The thermal emission is dominated by the epsilon-near-zero effect in the doped quantum wells composing the SHM. In conclusion, different properties are observed for s and p polarizations, following the characteristics of the strong anisotropy ofmore » hyperbolic metamaterials.« less

Directional and monochromatic thermal emitter from epsilon-near-zero conditions in semiconductor hyperbolic metamaterials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campione, Salvatore; Marquier, Francois; Hugonin, Jean -Paul

The development of novel thermal sources that control the emission spectrum and the angular emission pattern is of fundamental importance. In this paper, we investigate the thermal emission properties of semiconductor hyperbolic metamaterials (SHMs). Our structure does not require the use of any periodic corrugation to provide monochromatic and directional emission properties. We show that these properties arise because of epsilon-near-zero conditions in SHMs. The thermal emission is dominated by the epsilon-near-zero effect in the doped quantum wells composing the SHM. In conclusion, different properties are observed for s and p polarizations, following the characteristics of the strong anisotropy ofmore » hyperbolic metamaterials.« less

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

NASA Astrophysics Data System (ADS)

Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

2018-04-01

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

Single qubit operations using microwave hyperbolic secant pulses

NASA Astrophysics Data System (ADS)

Ku, H. S.; Long, J. L.; Wu, X.; Bal, M.; Lake, R. E.; Barnes, Edwin; Economou, Sophia E.; Pappas, D. P.

2017-10-01

It has been known since the early days of quantum mechanics that hyperbolic secant pulses possess the unique property that they can perform full-cycle Rabi oscillations on two-level quantum systems independently of the pulse detuning. More recently, it was realized that they induce detuning-controlled phases without changing state populations. Here, we experimentally demonstrate the properties of hyperbolic secant pulses on superconducting transmon qubits and contrast them with the more commonly used Gaussian and square waves. We further show that these properties can be exploited to implement phase gates, nominally without exiting the computational subspace. This enables us to demonstrate a microwave-driven Z rotation with a single control parameter, the detuning.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Automatic Control via Thermostats of a Hyperbolic Stefan Problem with Memory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Colli, P.; Grasselli, M.; Sprekels, J.

1999-03-15

A hyperbolic Stefan problem based on the linearized Gurtin-Pipkin heat conduction law is considered. The temperature and free boundary are controlled by a thermostat acting on the boundary. This feedback control is based on temperature measurements performed by real thermal sensors located within the domain containing the two-phase system and/or at its boundary. Three different types of thermostats are analyzed: simple switch, relay switch, and a Preisach hysteresis operator. The resulting models lead to integrodifferential hyperbolic Stefan problems with nonlinear and nonlocal boundary conditions. Existence results are proved in all the cases. Uniqueness is also shown, except in the situationmore » corresponding to the ideal switch.« less

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

EPA Science Inventory

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

The Hyperbolic Sine Cardinal and the Catenary

ERIC Educational Resources Information Center

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…

Computational methods for estimation of parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.; Murphy, K. A.

1983-01-01

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

Nonlinear sigma models with compact hyperbolic target spaces

NASA Astrophysics Data System (ADS)

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.

Gauss Modular-Arithmetic Congruence = Signal X Noise PRODUCT: Clock-model Archimedes HYPERBOLICITY Centrality INEVITABILITY: Definition: Complexity= UTTER-SIMPLICITY: Natural-Philosophy UNITY SIMPLICITY Redux!!!

NASA Astrophysics Data System (ADS)

Kummer, E. E.; Siegel, Edward Carl-Ludwig

2011-03-01

Clock-model Archimedes [http://linkage.rockeller.edu/ wli/moved.8.04/ 1fnoise/ index. ru.html] HYPERBOLICITY inevitability throughout physics/pure-maths: Newton-law F=ma, Heisenberg and classical uncertainty-principle=Parseval/Plancherel-theorems causes FUZZYICS definition: (so miscalled) "complexity" = UTTER-SIMPLICITY!!! Watkins[www.secamlocal.ex.ac.uk/people/staff/mrwatkin/]-Hubbard[World According to Wavelets (96)-p.14!]-Franklin[1795]-Fourier[1795;1822]-Brillouin[1922] dual/inverse-space(k,w) analysis key to Fourier-unification in Archimedes hyperbolicity inevitability progress up Siegel cognition hierarchy-of-thinking (HoT): data-info.-know.-understand.-meaning-...-unity-simplicity = FUZZYICS!!! Frohlich-Mossbauer-Goldanskii-del Guidice [Nucl.Phys.B:251,375(85);275,185 (86)]-Young [arXiv-0705.4678y2, (5/31/07] theory of health/life=aqueous-electret/ ferroelectric protoplasm BEC = Archimedes-Siegel [Schrodinger Cent.Symp.(87); Symp.Fractals, MRS Fall Mtg.(89)-5-pprs] 1/w-"noise" Zipf-law power-spectrum hyperbolicity INEVITABILITY= Chi; Dirac delta-function limit w=0 concentration= BEC = Chi-Quong.

On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitions

NASA Astrophysics Data System (ADS)

Morisse, Baptiste

2018-04-01

For first-order quasi-linear systems of partial differential equations, we formulate an assumption of a transition from initial hyperbolicity to ellipticity. This assumption bears on the principal symbol of the first-order operator. Under such an assumption, we prove a strong Hadamard instability for the associated Cauchy problem, namely an instantaneous defect of Hölder continuity of the flow from Gσ to L2, with 0 < σ <σ0, the limiting Gevrey index σ0 depending on the nature of the transition. We restrict here to scalar transitions, and non-scalar transitions in which the boundary of the hyperbolic zone satisfies a flatness condition. As in our previous work for initially elliptic Cauchy problems [B. Morisse, On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case, arxiv:arXiv:1611.07225], the instability follows from a long-time Cauchy-Kovalevskaya construction for highly oscillating solutions. This extends recent work of N. Lerner, T. Nguyen, and B. Texier [The onset of instability in first-order systems, to appear in J. Eur. Math. Soc.].

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

NASA Astrophysics Data System (ADS)

Engelbrecht, Jan; Chen, Bolun; Mirollo, Renato

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

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

NASA Astrophysics Data System (ADS)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

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

A teacher-developed inquiry model to teach the molecular basis of hyperbolic kinetics in biological membrane transport.

PubMed

Marcus, Leanne; Plumeri, Julia; Baker, Gary M; Miller, Jon S

2013-06-01

A previously published classroom teaching method for helping students visualize and understand Michaelis-Menten kinetics (19) was used as an anticipatory set with high school and middle school science teachers in an Illinois Math and Science Partnership Program. As part of the activity, the teachers were asked to collect data by replicating the method and to analyze and report the data. All concluded that the rate data they had collected were hyperbolic. As part of a guided inquiry plan, teachers were then prompted to reexamine the method and evaluate its efficacy as a teaching strategy for developing specific kinetic concepts. After further data collection and analysis, the teachers discovered that their data trends were not, in fact, hyperbolic, which led to several teacher-developed revisions aimed at obtaining a true hyperbolic outcome. This article outlines the inquiry process that led to these revisions and illustrates their alignment with several key concepts, such as rapid equilibrium kinetics. Instructional decisions were necessary at several key points, and these are discussed.

Nonlinear sigma models with compact hyperbolic target spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.

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 themore » 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. In conclusion, 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.« less

Nonlinear sigma models with compact hyperbolic target spaces

DOE PAGES

Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; ...

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 [1, 2]. Unlike in themore » 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. In conclusion, 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.« less

The Hartman-Grobman theorem for semilinear hyperbolic evolution equations

NASA Astrophysics Data System (ADS)

Hein, Marie-Luise; Prüss, Jan

2016-10-01

The famous Hartman-Grobman theorem for ordinary differential equations is extended to abstract semilinear hyperbolic evolution equations in Banach spaces by means of simple direct proof. It is also shown that the linearising map is Hölder continuous. Several applications to abstract and specific damped wave equations are given, to demonstrate the strength of our results.

Some remarks on the current status of the control theory of single space dimension hyperbolic systems

NASA Technical Reports Server (NTRS)

Russell, D. L.

1983-01-01

Various aspects of the control theory of hyperbolic systems, including controllability, stabilization, control canonical form theory, etc., are reviewed. To allow a unified and not excessively technical treatment, attention is restricted to the case of a single space variable. A newly developed procedure of canonical augmentation is discussed.

A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: The hyperbolic operator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Billet, G., E-mail: billet@onera.f; Ryan, J., E-mail: ryan@onera.f

2011-02-20

A Runge-Kutta discontinuous Galerkin method to solve the hyperbolic part of reactive Navier-Stokes equations written in conservation form is presented. Complex thermodynamics laws are taken into account. Particular care has been taken to solve the stiff gaseous interfaces correctly with no restrictive hypothesis. 1D and 2D test cases are presented.

COED Transactions, Vol. IX, No. 2, February 1977. Prism: An Educational Aide to Symbolic Differentiation and Simplification of Algebraic Expressions.

ERIC Educational Resources Information Center

Marcovitz, Alan B., Ed.

A computer program for numeric and symbolic manipulation and the methodology underlying its development are presented. Some features of the program are: an option for implied multiplication; computation of higher-order derivatives; differentiation of 26 different trigonometric, hyperbolic, inverse trigonometric, and inverse hyperbolic functions;…

Estimation of coefficients and boundary parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Murphy, K. A.

1984-01-01

Semi-discrete Galerkin approximation schemes are considered in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given.

Modelling the growth of porous alumina matrix for creating hyperbolic media

NASA Astrophysics Data System (ADS)

Aryslanova, E. M.; Alfimov, A. V.; Chivilikhin, S. A.

2016-08-01

Porous aluminum oxide is a regular self-assembled structure. During anodization it is possible to control nano-parameters of the structure using macroscopic parameters of anodization. Porous alumina films can be used as a template for the creation of hyperbolic media. In this work we consider the anodization process, our model takes into account the influence of layers of aluminum and electrolyte on the rate of growth of aluminum oxide, as well as the effect of surface diffusion. As a result of our model we obtain the minimum distance between centers of alumina pores in the beginning of anodizing process. We also present the results obtained by numerical modelling of hyperbolic media based on porous alumina film.

Clawpack: Building an open source ecosystem for solving hyperbolic PDEs

USGS Publications Warehouse

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

Winicour, Jeffrey

2017-08-01

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

A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms

PubMed Central

2014-01-01

Systems of hyperbolic partial differential equations with source terms (balance laws) arise in many applications where it is important to compute accurate time-dependent solutions modeling small perturbations of equilibrium solutions in which the source terms balance the hyperbolic part. The f-wave version of the wave-propagation algorithm is one approach, but requires the use of a particular averaged value of the source terms at each cell interface in order to be “well balanced” and exactly maintain steady states. A general approach to choosing this average is developed using the theory of path conservative methods. A scalar advection equation with a decay or growth term is introduced as a model problem for numerical experiments. PMID:24563581

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1994-01-01

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Algorithm Development and Application of High Order Numerical Methods for Shocked and Rapid Changing Solutions

DTIC Science & Technology

2007-12-06

high order well-balanced schemes to a class of hyperbolic systems with source terms, Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006...schemes to a class of hyperbolic systems with source terms, Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006), pp.69-80. 39. Y. Xu and C.-W

Well-posedness of characteristic symmetric hyperbolic systems

NASA Astrophysics Data System (ADS)

Secchi, Paolo

1996-06-01

We consider the initial-boundary-value problem for quasi-linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. We show the well-posedness in Hadamard's sense (i.e., existence, uniqueness and continuous dependence of solutions on the data) of regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cololla, P.

This review describes a structured approach to adaptivity. The Automated Mesh Refinement (ARM) algorithms developed by M Berger are described, touching on hyperbolic and parabolic applications. Adaptivity is achieved by overlaying finer grids only in areas flagged by a generalized error criterion. The author discusses some of the issues involved in abutting disparate-resolution grids, and demonstrates that suitable algorithms exist for dissipative as well as hyperbolic systems.

Addendum to "An update on the classical and quantum harmonic oscillators on the sphere and the hyperbolic plane in polar coordinates" [Phys. Lett. A 379 (26-27) (2015) 1589-1593

NASA Astrophysics Data System (ADS)

Quesne, C.

2016-02-01

The classical and quantum solutions of a nonlinear model describing harmonic oscillators on the sphere and the hyperbolic plane, derived in polar coordinates in a recent paper (Quesne, 2015) [1], are extended by the inclusion of an isotonic term.

Hyperbolic conservation laws and numerical methods

NASA Technical Reports Server (NTRS)

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.

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices

NASA Astrophysics Data System (ADS)

Lee, Yoju; Verstraete, Frank; Gendiar, Andrej

2016-08-01

The multistate Potts models on two-dimensional hyperbolic lattices are studied with respect to various boundary effects. The free energy is numerically calculated using the corner transfer matrix renormalization group method. We analyze phase transitions of the Potts models in the thermodynamic limit with respect to contracted boundary layers. A false phase transition is present even if a couple of the boundary layers are contracted. Its significance weakens, as the number of the contracted boundary layers increases, until the correct phase transition (deep inside the bulk) prevails over the false one. For this purpose, we derive a thermodynamic quantity, the so-called bulk excess free energy, which depends on the contracted boundary layers and memorizes additional boundary effects. In particular, the magnetic field is imposed on the outermost boundary layer. While the boundary magnetic field does not affect the second-order phase transition in the bulk if suppressing all the boundary effects on the hyperbolic lattices, the first-order (discontinuous) phase transition is significantly sensitive to the boundary magnetic field. Contrary to the phase transition on the Euclidean lattices, the discontinuous phase transition on the hyperbolic lattices can be continuously controlled (within a certain temperature coexistence region) by varying the boundary magnetic field.

The behavioral economics of will in recovery from addiction.

PubMed

Monterosso, John; Ainslie, George

2007-09-01

Behavioral economic studies demonstrate that rewards are discounted proportionally with their delay (hyperbolic discounting). Hyperbolic discounting implies temporary preference for smaller rewards when they are imminent, and this concept has been widely considered by researchers interested in the causes of addictive behavior. Far less consideration has been given to the fact that systematic preference reversal also predicts various self-control phenomena, which may also be analyzed from a behavioral economic perspective. Here we summarize self-control phenomena predicted by hyperbolic discounting, particularly with application to the field of addiction. Of greatest interest is the phenomenon of choice bundling, an increase in motivation to wait for delayed rewards that can be expected to result from making choices in whole categories. Specifically, when a person's expectations about her own future behavior are conditional upon her current behavior, the value of these expectations is added to the contingencies for the current behavior, resulting in reduced impulsivity. Hyperbolic discounting provides a bottom-up basis for the intuitive learning of choice bundling, the properties of which match common descriptions of willpower. We suggest that the bundling effect can also be discerned in the advice of 12-step programs.

3-D conditional hyperbolic method of moments for high-fidelity Euler-Euler simulations of particle-laden flows

NASA Astrophysics Data System (ADS)

Patel, Ravi; Kong, Bo; Capecelatro, Jesse; Fox, Rodney; Desjardins, Olivier

2017-11-01

Particle-laden turbulent flows are important features of many environmental and industrial processes. Euler-Euler (EE) simulations of these flows are more computationally efficient than Euler-Lagrange (EL) simulations. However, traditional EE methods, such as the two-fluid model, cannot faithfully capture dilute regions of flow with finite Stokes number particles. For this purpose, the multi-valued nature of the particle velocity field must be treated with a polykinetic description. Various quadrature-based moment methods (QBMM) can be used to approximate the full kinetic description by solving for a set of moments of the particle velocity distribution function (VDF) and providing closures for the higher-order moments. Early QBMM fail to maintain the strict hyperbolicity of the kinetic equations, producing unphysical delta shocks (i.e., mass accumulation at a point). In previous work, a 2-D conditional hyperbolic quadrature method of moments (CHyQMOM) was proposed as a fourth-order QBMM closure that maintains strict hyperbolicity. Here, we present the 3-D extension of CHyQMOM. We compare results from CHyQMOM to other QBMM and EL in the context of particle trajectory crossing, cluster-induced turbulence, and particle-laden channel flow. NSF CBET-1437903.

Doubly-focused echos from spheres unfold into a hyperbolic umbilic diffraction catastrophe

NASA Astrophysics Data System (ADS)

Dzikowicz, Ben; Marston, Philip L.

2003-04-01

An underwater spherical target resides in an Airy field formed by reflection off a curved surface representing the sea floor or sea surface. In prior work [B. Dzikowicz and P. L. Marston, J. Acoust. Soc Am. 110, 2778 (2001)] direct returns of a tone burst from the surface reflection focused toward the target were shown to have a dependence on the target position described by an Airy function. The return echo can also be focused again by the surface onto the source and receive transducer. This gives the square of an Airy function for the case of a point target. With a finite sized target (as in the experiment) this goes over to a hyperbolic umbilic catastrophe with symmetric arguments. The arguments of the hyperbolic umbilic function are derived from only the relative return times of a transient pulse. Experiment confirms the predicted merging of transient echoes in the time domain, as well as the hyperbolic umbilic diffraction integral amplitudes for a tone burst. This method would allow for the observation of a target at a greater distance in the presence of a focusing surface. [Research supported by ONR.

The behavioral economics of will in recovery from addiction

PubMed Central

Monterosso, John; Ainslie, George

2007-01-01

Behavioral economic studies demonstrate that rewards are discounted proportionally with their delay (hyperbolic discounting). Hyperbolic discounting implies temporary preference for smaller rewards when they are imminent, and this concept has been widely considered by researchers interested in the causes of addictive behavior. Far less consideration has been given to the fact that systematic preference reversal also predicts various self-control phenomena, which may also be analyzed from a behavioral economic perspective. Here we summarize self-control phenomena predicted by hyperbolic discounting, particularly with application to the field of addiction. Of greatest interest is the phenomenon of choice bundling, an increase in motivation to wait for delayed rewards that can be expected to result from making choices in whole categories. Specifically, when a person’s expectations about her own future behavior are conditional upon her current behavior, the value of these expectations is added to the contingencies for the current behavior, resulting in reduced impulsivity. Hyperbolic discounting provides a bottom-up basis for the intuitive learning of choice bundling, the properties of which match common descriptions of willpower. We suggest that the bundling effect can also be discerned in the advice of 12-step programs. PMID:17034958

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

PubMed

Markov, A V; Korotaev, A V

2008-01-01

Among diverse models that are used to describe and interpret the changes in global biodiversity through the Phanerozoic, the exponential and logistic models (traditionally used in population biology) are the most popular. As we have recently demonstrated (Markov, Korotayev, 2007), the growth of the Phanerozoic marine biodiversity at genus level correlates better with the hyperbolic model (widely used in demography and macrosociology). Here we show that the hyperbolic model is also applicable to the Phanerozoic continental biota at genus and family levels, and to the marine biota at species, genus, and family levels. There are many common features in the evolutionary dynamics of the marine and continental biotas that imply similarity and common nature of the factors and mechanisms underlying the hyperbolic growth. Both marine and continental biotas are characterized by continuous growth of the mean longevity of taxa, by decreasing extinction and origination rates, by similar pattern of replacement of dominant groups, by stepwise accumulation of evolutionary stable, adaptable and "physiologically buffered" taxa with effective mechanisms of parental care, protection of early developmental stages, etc. At the beginning of the development of continental biota, the observed taxonomic diversity was substantially lower than that predicted by the hyperbolic model. We suggest that this is due, firstly, to the fact that, during the earliest stages of the continental biota evolution, the groups that are not preserved in the fossil record (such as soil bacteria, unicellular algae, lichens, etc.) played a fundamental role, and secondly, to the fact that the continental biota initially formed as a marginal portion of the marine biota, rather than a separate system. The hyperbolic dynamics is most prominent when both marine and continental biotas are considered together. This fact can be interpreted as a proof of the integrated nature of the biosphere. In the macrosociological models, the hyperbolic pattern of the world population growth arises from a non-linear second-order positive feedback between the demographic growth and technological development (more people - more potential inventors - faster technological growth - the carrying capacity of the Earth grows faster - faster population growth - more people - more potential inventors, and so on). Based on the analogy with macrosociological models and diverse paleontological data, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by a non-linear second-order positive feedback between the diversity growth and community structure complexity. The feedback can work via two parallel mechanisms: 1) decreasing extinction rate (more taxa- higher alpha diversity, or mean number of taxa in a community - communities become more complex and stable - extinction rate decreases - more taxa, and so on) and 2) increasing origination rate (new taxa facilitate niche construction; newly formed niches can be occupied by the next "generation" of taxa). The latter possibility makes the mechanisms underlying the hyperbolic growth of biodiversity and human population even more similar, because the total ecospace of the biota is analogous to the "carrying capacity of the Earth" in demography. As far as new species can increase ecospace and facilitate opportunities for additional species entering the community, they are analogous to the "inventors" of the demographic models whose inventions increase the carrying capacity of the Earth. The hyperbolic growth of the Phanerozoic biodiverstiy suggests that "cooperative" interactions between taxa can play an important role in evolution, along with generally accepted competitive interactions. Due to this "cooperation", the evolution of biodiversity acquires some features of a self-accelerating process. Macroevolutionary "cooperation" reveals itself in: 1) increasing stability of communities that arises from alpha diversity growth; 2) ability of species to facilitate opportunities for additional species entering the community.

A shifted hyperbolic augmented Lagrangian-based artificial fish two-swarm algorithm with guaranteed convergence for constrained global optimization

NASA Astrophysics Data System (ADS)

Rocha, Ana Maria A. C.; Costa, M. Fernanda P.; Fernandes, Edite M. G. P.

2016-12-01

This article presents a shifted hyperbolic penalty function and proposes an augmented Lagrangian-based algorithm for non-convex constrained global optimization problems. Convergence to an ?-global minimizer is proved. At each iteration k, the algorithm requires the ?-global minimization of a bound constrained optimization subproblem, where ?. The subproblems are solved by a stochastic population-based metaheuristic that relies on the artificial fish swarm paradigm and a two-swarm strategy. To enhance the speed of convergence, the algorithm invokes the Nelder-Mead local search with a dynamically defined probability. Numerical experiments with benchmark functions and engineering design problems are presented. The results show that the proposed shifted hyperbolic augmented Lagrangian compares favorably with other deterministic and stochastic penalty-based methods.

Experimental demonstration of metamaterial "multiverse" in a ferrofluid.

PubMed

Smolyaninov, Igor I; Yost, Bradley; Bates, Evan; Smolyaninova, Vera N

2013-06-17

Extraordinary light rays propagating inside a hyperbolic metamaterial look similar to particle world lines in a 2 + 1 dimensional Minkowski spacetime. Magnetic nanoparticles in a ferrofluid are known to form nanocolumns aligned along the magnetic field, so that a hyperbolic metamaterial may be formed at large enough nanoparticle concentration nH. Here we investigate optical properties of such a metamaterial just below nH. While on average such a metamaterial is elliptical, thermal fluctuations of nanoparticle concentration lead to transient formation of hyperbolic regions (3D Minkowski spacetimes) inside this metamaterial. Thus, thermal fluctuations in a ferrofluid look similar to creation and disappearance of individual Minkowski spacetimes (universes) in the cosmological multiverse. This theoretical picture is supported by experimental measurements of polarization-dependent optical transmission of a cobalt based ferrofluid at 1500 nm.

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

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Ricchiuto, Mario; Nishikawa, Hiroaki

2016-01-01

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

On Another Edge of Defocusing: Hyperbolicity of Asymmetric Lemon Billiards

NASA Astrophysics Data System (ADS)

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.

Generalized heat-transport equations: parabolic and hyperbolic models

NASA Astrophysics Data System (ADS)

Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

2018-03-01

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

Self-assembled tunable photonic hyper-crystals

PubMed Central

Smolyaninova, Vera N.; Yost, Bradley; Lahneman, David; Narimanov, Evgenii E.; Smolyaninov, Igor I.

2014-01-01

We demonstrate a novel artificial optical material, the “photonic hyper-crystal”, which combines the most interesting features of hyperbolic metamaterials and photonic crystals. Similar to hyperbolic metamaterials, photonic hyper-crystals exhibit broadband divergence in their photonic density of states due to the lack of usual diffraction limit on the photon wave vector. On the other hand, similar to photonic crystals, hyperbolic dispersion law of extraordinary photons is modulated by forbidden gaps near the boundaries of photonic Brillouin zones. Three dimensional self-assembly of photonic hyper-crystals has been achieved by application of external magnetic field to a cobalt nanoparticle-based ferrofluid. Unique spectral properties of photonic hyper-crystals lead to extreme sensitivity of the material to monolayer coatings of cobalt nanoparticles, which should find numerous applications in biological and chemical sensing. PMID:25027947

Self-assembled tunable photonic hyper-crystals.

PubMed

Smolyaninova, Vera N; Yost, Bradley; Lahneman, David; Narimanov, Evgenii E; Smolyaninov, Igor I

2014-07-16

We demonstrate a novel artificial optical material, the "photonic hyper-crystal", which combines the most interesting features of hyperbolic metamaterials and photonic crystals. Similar to hyperbolic metamaterials, photonic hyper-crystals exhibit broadband divergence in their photonic density of states due to the lack of usual diffraction limit on the photon wave vector. On the other hand, similar to photonic crystals, hyperbolic dispersion law of extraordinary photons is modulated by forbidden gaps near the boundaries of photonic Brillouin zones. Three dimensional self-assembly of photonic hyper-crystals has been achieved by application of external magnetic field to a cobalt nanoparticle-based ferrofluid. Unique spectral properties of photonic hyper-crystals lead to extreme sensitivity of the material to monolayer coatings of cobalt nanoparticles, which should find numerous applications in biological and chemical sensing.

High order ADER schemes for a unified first order hyperbolic formulation of Newtonian continuum mechanics coupled with electro-dynamics

NASA Astrophysics Data System (ADS)

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

2017-11-01

In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to describe the behavior of moving elasto-plastic dielectric solids as well as viscous and inviscid fluids in the presence of electro-magnetic fields. It is actually a very peculiar feature of the proposed PDE system that viscous fluids are treated just as a special case of elasto-plastic solids. This is achieved by introducing a strain relaxation mechanism in the evolution equations of the distortion matrix A, which in the case of purely elastic solids maps the current configuration to the reference configuration. The model also contains a hyperbolic formulation of heat conduction as well as a dissipative source term in the evolution equations for the electric field given by Ohm's law. Via formal asymptotic analysis we show that in the stiff limit, the governing first order hyperbolic PDE system with relaxation source terms tends asymptotically to the well-known viscous and resistive magnetohydrodynamics (MHD) equations. Furthermore, a rigorous derivation of the model from variational principles is presented, together with the transformation of the Euler-Lagrange differential equations associated with the underlying variational problem from Lagrangian coordinates to Eulerian coordinates in a fixed laboratory frame. The present paper hence extends the unified first order hyperbolic model of Newtonian continuum mechanics recently proposed in [110,42] to the more general case where the continuum is coupled with electro-magnetic fields. The governing PDE system is symmetric hyperbolic and satisfies the first and second principle of thermodynamics, hence it belongs to the so-called class of symmetric hyperbolic thermodynamically compatible systems (SHTC), which have been studied for the first time by Godunov in 1961 [61] and later in a series of papers by Godunov and Romenski [67,69,119]. An important feature of the proposed model is that the propagation speeds of all physical processes, including dissipative processes, are finite. The model is discretized using high order accurate ADER discontinuous Galerkin (DG) finite element schemes with a posteriori subcell finite volume limiter and using high order ADER-WENO finite volume schemes. We show numerical test problems that explore a rather large parameter space of the model ranging from ideal MHD, viscous and resistive MHD over pure electro-dynamics to moving dielectric elastic solids in a magnetic field.

An iterative method for systems of nonlinear hyperbolic equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1989-01-01

An iterative algorithm for the efficient solution of systems of nonlinear hyperbolic equations is presented. Parallelism is evident at several levels. In the formation of the iteration, the equations are decoupled, thereby providing large grain parallelism. Parallelism may also be exploited within the solves for each equation. Convergence of the interation is established via a bounding function argument. Experimental results in two-dimensions are presented.

High-resolution schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.

1982-01-01

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurae scheme to an appropriately modified flux function. The so derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme.

Singularities and non-hyperbolic manifolds do not coincide

NASA Astrophysics Data System (ADS)

Simányi, Nándor

2013-06-01

We consider the billiard flow of elastically colliding hard balls on the flat ν-torus (ν ⩾ 2), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann-Sinai ergodic hypothesis.

A simple finite element method for linear hyperbolic problems

DOE PAGES

Mu, Lin; Ye, Xiu

2017-09-14

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

A simple finite element method for linear hyperbolic problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Ye, Xiu

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

Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations

NASA Astrophysics Data System (ADS)

Al-Islam, Najja Shakir

In this Dissertation, the existence of pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations is established. For that, (Al-Islam [4]) is first studied and then obtained under some suitable assumptions. That is, the existence of pseudo almost periodic solutions to a hyperbolic second-order partial differential equation with delay. The second-order partial differential equation (1) represents a mathematical model for the dynamics of gas absorption, given by uxt+a x,tux=Cx,t,u x,t , u0,t=4 t, 1 where a : [0, L] x RR , C : [0, L] x R x RR , and ϕ : RR are (jointly) continuous functions ( t being the greatest integer function) and L > 0. The results in this Dissertation generalize those of Poorkarimi and Wiener [22]. Secondly, a generalization of the above-mentioned system consisting of the non-linear hyperbolic second-order partial differential equation uxt+a x,tux+bx,t ut+cx,tu=f x,t,u, x∈ 0,L,t∈ R, 2 equipped with the boundary conditions ux,0 =40x, u0,t=u 0t, uxx,0=y 0x, x∈0,L, t∈R, 3 where a, b, c : [0, L ] x RR and f : [0, L] x R x RR are (jointly) continuous functions is studied. Under some suitable assumptions, the existence and uniqueness of pseudo almost periodic solutions to particular cases, as well as the general case of the second-order hyperbolic partial differential equation (2) are studied. The results of all studies contained within this text extend those obtained by Aziz and Meyers [6] in the periodic setting.

Cauchy problem as a two-surface based ‘geometrodynamics’

NASA Astrophysics Data System (ADS)

Rácz, István

2015-01-01

Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1 + (1 + 2) decomposition, the canonical form of the spacetime metric and a suitable specification of the conformal structure of the foliating two-surfaces, a gauge fixing is introduced. It is shown that, in terms of the chosen geometrically distinguished variables, the 1 + 3 Hamiltonian and momentum constraints can be recast into the form of a parabolic equation and a first order symmetric hyperbolic system, respectively. Initial data to this system can be given on one of the two-surfaces foliating the three-dimensional initial data surface. The 1 + 3 reduced Einstein's equations are also determined. By combining the 1 + 3 momentum constraint with the reduced system of the secondary 1 + 2 decomposition, a mixed hyperbolic-hyperbolic system is formed. It is shown that solutions to this mixed hyperbolic-hyperbolic system are also solutions to the full set of Einstein's equations provided that the 1 + 3 Hamiltonian constraint is solved on the initial data surface {{Σ }0} and the 1 + 2 Hamiltonian and momentum type expressions vanish on a world-tube yielded by the Lie transport of one of the two-surfaces foliating {{Σ }0} along the time evolution vector field. Whenever the foliating two-surfaces are compact without boundary in the spacetime and a regular origin exists on the time-slices—this is the location where the foliating two-surfaces smoothly reduce to a point—it suffices to guarantee that the 1 + 3 Hamiltonian constraint holds on the initial data surface. A short discussion on the use of the geometrically distinguished variables in identifying the degrees of freedom of gravity are also included. Dedicated to Zoltán Cseke on the occasion of his 70th birthday.

Incorporating inductances in tissue-scale models of cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Rossi, Simone; Griffith, Boyce E.

2017-09-01

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and we examine the effect of intracellular and extracellular inductances on the virtual electrode phenomenon.

Strong coupling of collection of emitters on hyperbolic meta-material

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Anomalous resonances of an optical microcavity with a hyperbolic metamaterial core

NASA Astrophysics Data System (ADS)

Travkin, Evgenij; Kiel, Thomas; Sadofev, Sergey; Busch, Kurt; Benson, Oliver; Kalusniak, Sascha

2018-05-01

We embed a hyperbolic metamaterial based on stacked layer pairs of epitaxially grown ZnO/ZnO:Ga in a monolithic optical microcavity, and we investigate the arising unique resonant effects experimentally and theoretically. Unlike traditional metals, the semiconductor-based approach allows us to utilize all three permittivity regions of the hyperbolic metamaterial in the near-infrared spectral range. This configuration gives rise to modes of identical orders appearing at different frequencies, a zeroth-order resonance in an all-positive permittivity region, and a continuum of high-order modes. In addition, an unusual lower cutoff frequency is introduced to the resonator mode spectrum. The observed effects expand the possibilities for customization of optical resonators; in particular, the zeroth-order and high-order modes hold strong potential for the realization of deeply subwavelength cavity sizes.

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

NASA Astrophysics Data System (ADS)

Sahoo, Sarmila

2016-08-01

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

Subwavelength focusing of terahertz waves in silicon hyperbolic metamaterials.

PubMed

Kannegulla, Akash; Cheng, Li-Jing

2016-08-01

We theoretically demonstrate the subwavelength focusing of terahertz (THz) waves in a hyperbolic metamaterial (HMM) based on a two-dimensional subwavelength silicon pillar array microstructure. The silicon microstructure with a doping concentration of at least 10¹⁷  cm^-3 offers a hyperbolic dispersion at terahertz frequency range and promises the focusing of terahertz Gaussian beams. The results agree with the simulation based on effective medium theory. The focusing effect can be controlled by the doping concentration, which determines the real part of the out-of-plane permittivity and, therefore, the refraction angles in HMM. The focusing property in the HMM structure allows the propagation of terahertz wave through a subwavelength aperture. The silicon-based HMM structure can be realized using microfabrication technologies and has the potential to advance terahertz imaging with subwavelength resolution.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

Designing optical metamaterial with hyperbolic dispersion based on Al:ZnO/ZnO nano-layered structure using Atomic Layer Deposition technique

DOE PAGES

Kelly, Priscilla; Liu, Mingzhao; Kuznetsova, Lyuba

2016-04-07

In this study, nano-layered Al:ZnO/ZnO hyperbolic dispersion metamaterial with a large number of layers was fabricated using the atomic layer deposition (ALD) technique. Experimental dielectric functions for Al:ZnO/ZnO structures are obtained by an ellipsometry technique in the visible and near-infrared spectral ranges. The theoretical modeling of the Al:ZnO/ZnO dielectric permittivity is done using effective medium approximation. A method for analysis of spectroscopic ellipsometry data is demonstrated to extract the optical permittivity for this highly anisotropic nano-layered metamaterial. The results of the ellipsometry analysis show that Al:ZnO/ZnO structures with a 1:9 ALD cycle ratio exhibit hyperbolic dispersion transition change near 1.8more » μm wavelength.« less

Universal properties of the near-horizon optical geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gibbons, G. W.; Warnick, C. M.

2009-03-15

Making use of the fact that the optical geometry near a static nondegenerate Killing horizon is asymptotically hyperbolic, we investigate some universal features of black-hole horizons. Applying the Gauss-Bonnet theorem allows us to establish some general properties of gravitational lensing, valid for all black holes. Hyperbolic geometry allows us to find rates for the loss of scalar, vector, and fermionic ''hair'' as objects fall quasistatically towards the horizon, extending previous results for Schwarzschild to all static Killing horizons. In the process we find the Lienard-Wiechert potential for hyperbolic space and calculate the force between electrons mediated by neutrinos, extending themore » flat space result of Feinberg and Sucher. We further demonstrate how these techniques allow us to derive the exact Copson-Linet potential due to a point charge in a Schwarzschild background in a simple fashion.« less

Tunable angle absorption of hyperbolic metamaterials based on plasma photonic crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiao, Zheng; Ning, Renxia, E-mail: nrxxiner@hsu.edu.cn; Xu, Yuan

2016-06-15

We present the design of a multilayer structure of hyperbolic metamaterials based on plasma photonic crystals which composed of two kinds of traditional dielectric and plasma. The relative permittivity of hyperbolic metamaterials has been studied at certain frequency range. The absorption and reflection of the multilayer period structure at normal and oblique incident have been investigated by the transfer matrix method. We discussed that the absorption is affected by the thickness of material and the electron collision frequency γ of the plasma. The results show that an absorption band at the low frequency can be obtained at normal incident anglemore » and another absorption band at the high frequency can be found at a large incident angle. The results may be applied by logical gate, stealth, tunable angle absorber, and large angle filter.« less

Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Montecinos, Gino I.; Müller, Lucas O.; Toro, Eleuterio F.

2014-06-01

The applicability of ADER finite volume methods to solve hyperbolic balance laws with stiff source terms in the context of well-balanced and non-conservative schemes is extended to solve a one-dimensional blood flow model for viscoelastic vessels, reformulated as a hyperbolic system, via a relaxation time. A criterion for selecting relaxation times is found and an empirical convergence rate assessment is carried out to support this result. The proposed methodology is validated by applying it to a network of viscoelastic vessels for which experimental and numerical results are available. The agreement between the results obtained in the present paper and thosemore » available in the literature is satisfactory. Key features of the present formulation and numerical methodologies, such as accuracy, efficiency and robustness, are fully discussed in the paper.« less

Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chhaiba, Hassan, E-mail: chhaiba.hassan@gmail.com; Demni, Nizar, E-mail: nizar.demni@univ-rennes1.fr; Mouayn, Zouhair, E-mail: mouayn@fstbm.ac.ma

2016-07-15

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

Optimal disturbance rejecting control of hyperbolic systems

NASA Technical Reports Server (NTRS)

Biswas, Saroj K.; Ahmed, N. U.

1994-01-01

Optimal regulation of hyperbolic systems in the presence of unknown disturbances is considered. Necessary conditions for determining the optimal control that tracks a desired trajectory in the presence of the worst possible perturbations are developed. The results also characterize the worst possible disturbance that the system will be able to tolerate before any degradation of the system performance. Numerical results on the control of a vibrating beam are presented.

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

NASA Astrophysics Data System (ADS)

Babicheva, Viktoriia E.

2017-12-01

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

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

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2015-01-01

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

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mauguière, Frédéric A. L., E-mail: frederic.mauguiere@bristol.ac.uk; Collins, Peter, E-mail: peter.collins@bristol.ac.uk; Wiggins, Stephen, E-mail: stephen.wiggins@mac.com

We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariantmore » manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories.« less

Deep-Ultraviolet Hyperbolic Metacavity Laser.

PubMed

Shen, Kun-Ching; Ku, Chen-Ta; Hsieh, Chiieh; Kuo, Hao-Chung; Cheng, Yuh-Jen; Tsai, Din Ping

2018-05-01

Given the high demand for miniaturized optoelectronic circuits, plasmonic devices with the capability of generating coherent radiation at deep subwavelength scales have attracted great interest for diverse applications such as nanoantennas, single photon sources, and nanosensors. However, the design of such lasing devices remains a challenging issue because of the long structure requirements for producing strong radiation feedback. Here, a plasmonic laser made by using a nanoscale hyperbolic metamaterial cube, called hyperbolic metacavity, on a multiple quantum-well (MQW), deep-ultraviolet emitter is presented. The specifically designed metacavity merges plasmon resonant modes within the cube and provides a unique resonant radiation feedback to the MQW. This unique plasmon field allows the dipoles of the MQW with various orientations into radiative emission, achieving enhancement of spontaneous emission rate by a factor of 33 and of quantum efficiency by a factor of 2.5, which is beneficial for coherent laser action. The hyperbolic metacavity laser shows a clear clamping of spontaneous emission above the threshold, which demonstrates a near complete radiation coupling of the MQW with the metacavity. This approach shown here can greatly simplify the requirements of plasmonic nanolaser with a long plasmonic structure, and the metacavity effect can be extended to many other material systems. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications. Volume 24. Note on Numerical Fluid Mechanics

DTIC Science & Technology

1989-01-01

Calculations and Experiments (B.van den Berg/ D.A. Humphreysl E. Krause /J.P. F. Lindhout) Volume 20 Proceedings of the Seventh GAMM-Conference on...GRID METHODS FOR HYPERBOLIC PROBLEMS Wolfgang Hackbusch Sigrid Hagemann Institut fUr Informatik und Praktische Mathematik Christian-Albrechts...Euler Equations. Proceedings of the 8th Inter- national Conference on Numerical Methods in Fluid Dynamics (E. Krause , ed.), Aachen, 1988. Springer

A New Time-Space Accurate Scheme for Hyperbolic Problems. 1; Quasi-Explicit Case

NASA Technical Reports Server (NTRS)

Sidilkover, David

1998-01-01

This paper presents a new discretization scheme for hyperbolic systems of conservations laws. It satisfies the TVD property and relies on the new high-resolution mechanism which is compatible with the genuinely multidimensional approach proposed recently. This work can be regarded as a first step towards extending the genuinely multidimensional approach to unsteady problems. Discontinuity capturing capabilities and accuracy of the scheme are verified by a set of numerical tests.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Note on the displacement of a trajectory of hyperbolic motion in curved space-time

NASA Astrophysics Data System (ADS)

Krikorian, R. A.

2012-04-01

The object of this note is to present a physical application of the theory of the infinitesimal deformations or displacements of curves developed by Yano using the concept of Lie derivative. It is shown that an infinitesimal point transformation which carries a given trajectory of hyperbolic motion into a trajectory of the same type, and preserves the affine parametrization of the trajectory, defines a homothetic motion.

The Hyperbolic Higgs

NASA Astrophysics Data System (ADS)

Cohen, Timothy; Craig, Nathaniel; Giudice, Gian F.; McCullough, Matthew

2018-05-01

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

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

PubMed Central

Zhang, Zhihua

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

On the construction and application of implicit factored schemes for conservation laws. [in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Warming, R. F.; Beam, R. M.

1978-01-01

Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

Design and fabrication of a basic mass analyzer and vacuum system

NASA Technical Reports Server (NTRS)

Judson, C. M.; Josias, C.; Lawrence, J. L., Jr.

1977-01-01

A two-inch hyperbolic rod quadrupole mass analyzer with a mass range of 400 to 200 amu and a sensitivity exceeding 100 packs per billion has been developed and tested. This analyzer is the basic hardware portion of a microprocessor-controlled quadrupole mass spectrometer for a Gas Analysis and Detection System (GADS). The development and testing of the hyperbolic-rod quadrupole mass spectrometer and associated hardware are described in detail.

Hyperbolic and semi-parametric models in finance

NASA Astrophysics Data System (ADS)

Bingham, N. H.; Kiesel, Rüdiger

2001-02-01

The benchmark Black-Scholes-Merton model of mathematical finance is parametric, based on the normal/Gaussian distribution. Its principal parametric competitor, the hyperbolic model of Barndorff-Nielsen, Eberlein and others, is briefly discussed. Our main theme is the use of semi-parametric models, incorporating the mean vector and covariance matrix as in the Markowitz approach, plus a non-parametric part, a scalar function incorporating features such as tail-decay. Implementation is also briefly discussed.

A graphene Zener-Klein transistor cooled by a hyperbolic substrate

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Lagrangian Coherent Structures, Hyperbolicity, and Lyapunov Exponents

NASA Astrophysics Data System (ADS)

Haller, George

2010-05-01

We review the fundamental physical motivation behind the definition of Lagrangian Coherent Structures (LCS) and show how it leads to the concept of finite-time hyperbolicity in non-autonomous dynamical systems. Using this concept of hyperbolicity, we obtain a self-consistent criterion for the existence of attracting and repelling material surfaces in unsteady fluid flows, such as those in the atmosphere and the ocean. The existence of LCS is often postulated in terms of features of the Finite-Time Lyapunov Exponent (FTLE) field associated with the system. As simple examples show, however, the FTLE field does not necessarily highlight LCS, or may ighlight structures that are not LCS. Under appropriate nondegeneracy conditions, we show that ridges of the FTLE field indeed coincide with LCS in volume-preserving flows. For general flows, we obtain a more general scalar field whose ridges correspond to LCS. We finally review recent applications of LCS techniques to flight safety analysis at Hong Kong International Airport.

Tunable VO{sub 2}/Au hyperbolic metamaterial

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prayakarao, S.; Noginov, M. A., E-mail: mnoginov@nsu.edu; Mendoza, B.

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}more » 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.« less

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Central Configurations of the Curved N-Body Problem

NASA Astrophysics Data System (ADS)

Diacu, Florin; Stoica, Cristina; Zhu, Shuqiang

2018-06-01

We consider the N-body problem of celestial mechanics in spaces of nonzero constant curvature. Using the concept of effective potential, we define the moment of inertia for systems moving on spheres and hyperbolic spheres and show that we can recover the classical definition in the Euclidean case. After proving some criteria for the existence of relative equilibria, we find a natural way to define the concept of central configuration in curved spaces using the moment of inertia and show that our definition is formally similar to the one that governs the classical problem. We prove that, for any given point masses on spheres and hyperbolic spheres, central configurations always exist. We end with results concerning the number of central configurations that lie on the same geodesic, thus extending the celebrated theorem of Moulton to hyperbolic spheres and pointing out that it has no straightforward generalization to spheres, where the count gets complicated even for two bodies.

Exact moduli space metrics for hyperbolic vortex polygons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krusch, S.; Speight, J. M.

2010-02-15

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

The limit space of a Cauchy sequence of globally hyperbolic spacetimes

NASA Astrophysics Data System (ADS)

Noldus, Johan

2004-02-01

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

A new method for recognizing quadric surfaces from range data and its application to telerobotics and automation

NASA Technical Reports Server (NTRS)

Alvertos, Nicolas; Dcunha, Ivan

1993-01-01

The problem of recognizing and positioning of objects in three-dimensional space is important for robotics and navigation applications. In recent years, digital range data, also referred to as range images or depth maps, have been available for the analysis of three-dimensional objects owing to the development of several active range finding techniques. The distinct advantage of range images is the explicitness of the surface information available. Many industrial and navigational robotics tasks will be more easily accomplished if such explicit information can be efficiently interpreted. In this research, a new technique based on analytic geometry for the recognition and description of three-dimensional quadric surfaces from range images is presented. Beginning with the explicit representation of quadrics, a set of ten coefficients are determined for various three-dimensional surfaces. For each quadric surface, a unique set of two-dimensional curves which serve as a feature set is obtained from the various angles at which the object is intersected with a plane. Based on a discriminant method, each of the curves is classified as a parabola, circle, ellipse, hyperbola, or a line. Each quadric surface is shown to be uniquely characterized by a set of these two-dimensional curves, thus allowing discrimination from the others. Before the recognition process can be implemented, the range data have to undergo a set of pre-processing operations, thereby making it more presentable to classification algorithms. One such pre-processing step is to study the effect of median filtering on raw range images. Utilizing a variety of surface curvature techniques, reliable sets of image data that approximate the shape of a quadric surface are determined. Since the initial orientation of the surfaces is unknown, a new technique is developed wherein all the rotation parameters are determined and subsequently eliminated. This approach enables us to position the quadric surfaces in a desired coordinate system. Experiments were conducted on raw range images of spheres, cylinders, and cones. Experiments were also performed on simulated data for surfaces such as hyperboloids of one and two sheets, elliptical and hyperbolic paraboloids, elliptical and hyperbolic cylinders, ellipsoids and the quadric cones. Both the real and simulated data yielded excellent results. Our approach is found to be more accurate and computationally inexpensive as compared to traditional approaches, such as the three-dimensional discriminant approach which involves evaluation of the rank of a matrix. Finally, we have proposed one other new approach, which involves the formulation of a mapping between the explicit and implicit forms of representing quadric surfaces. This approach, when fully realized, will yield a three-dimensional discriminant, which will recognize quadric surfaces based upon their component surfaces patches. This approach is faster than prior approaches and at the same time is invariant to pose and orientation of the surfaces in three-dimensional space.

A new method for recognizing quadric surfaces from range data and its application to telerobotics and automation

NASA Astrophysics Data System (ADS)

Alvertos, Nicolas; Dcunha, Ivan

1993-03-01

The problem of recognizing and positioning of objects in three-dimensional space is important for robotics and navigation applications. In recent years, digital range data, also referred to as range images or depth maps, have been available for the analysis of three-dimensional objects owing to the development of several active range finding techniques. The distinct advantage of range images is the explicitness of the surface information available. Many industrial and navigational robotics tasks will be more easily accomplished if such explicit information can be efficiently interpreted. In this research, a new technique based on analytic geometry for the recognition and description of three-dimensional quadric surfaces from range images is presented. Beginning with the explicit representation of quadrics, a set of ten coefficients are determined for various three-dimensional surfaces. For each quadric surface, a unique set of two-dimensional curves which serve as a feature set is obtained from the various angles at which the object is intersected with a plane. Based on a discriminant method, each of the curves is classified as a parabola, circle, ellipse, hyperbola, or a line. Each quadric surface is shown to be uniquely characterized by a set of these two-dimensional curves, thus allowing discrimination from the others. Before the recognition process can be implemented, the range data have to undergo a set of pre-processing operations, thereby making it more presentable to classification algorithms. One such pre-processing step is to study the effect of median filtering on raw range images. Utilizing a variety of surface curvature techniques, reliable sets of image data that approximate the shape of a quadric surface are determined. Since the initial orientation of the surfaces is unknown, a new technique is developed wherein all the rotation parameters are determined and subsequently eliminated. This approach enables us to position the quadric surfaces in a desired coordinate system. Experiments were conducted on raw range images of spheres, cylinders, and cones. Experiments were also performed on simulated data for surfaces such as hyperboloids of one and two sheets, elliptical and hyperbolic paraboloids, elliptical and hyperbolic cylinders, ellipsoids and the quadric cones. Both the real and simulated data yielded excellent results. Our approach is found to be more accurate and computationally inexpensive as compared to traditional approaches, such as the three-dimensional discriminant approach which involves evaluation of the rank of a matrix.

Fabrication of ф 160 mm convex hyperbolic mirror for remote sensing instrument

NASA Astrophysics Data System (ADS)

Kuo, Ching-Hsiang; Yu, Zong-Ru; Ho, Cheng-Fang; Hsu, Wei-Yao; Chen, Fong-Zhi

2012-10-01

In this study, efficient polishing processes with inspection procedures for a large convex hyperbolic mirror of Cassegrain optical system are presented. The polishing process combines the techniques of conventional lapping and CNC polishing. We apply the conventional spherical lapping process to quickly remove the sub-surface damage (SSD) layer caused by grinding process and to get the accurate radius of best-fit sphere (BFS) of aspheric surface with fine surface texture simultaneously. Thus the removed material for aspherization process can be minimized and the polishing time for SSD removal can also be reduced substantially. The inspection procedure was carried out by using phase shift interferometer with CGH and stitching technique. To acquire the real surface form error of each sub aperture, the wavefront errors of the reference flat and CGH flat due to gravity effect of the vertical setup are calibrated in advance. Subsequently, we stitch 10 calibrated sub-aperture surface form errors to establish the whole irregularity of the mirror in 160 mm diameter for correction polishing. The final result of the In this study, efficient polishing processes with inspection procedures for a large convex hyperbolic mirror of Cassegrain optical system are presented. The polishing process combines the techniques of conventional lapping and CNC polishing. We apply the conventional spherical lapping process to quickly remove the sub-surface damage (SSD) layer caused by grinding process and to get the accurate radius of best-fit sphere (BFS) of aspheric surface with fine surface texture simultaneously. Thus the removed material for aspherization process can be minimized and the polishing time for SSD removal can also be reduced substantially. The inspection procedure was carried out by using phase shift interferometer with CGH and stitching technique. To acquire the real surface form error of each sub aperture, the wavefront errors of the reference flat and CGH flat due to gravity effect of the vertical setup are calibrated in advance. Subsequently, we stitch 10 calibrated sub-aperture surface form errors to establish the whole irregularity of the mirror in 160 mm diameter for correction polishing. The final result of the Fabrication of ф160 mm Convex Hyperbolic Mirror for Remote Sensing Instrument160 mm convex hyperbolic mirror is 0.15 μm PV and 17.9 nm RMS.160 mm convex hyperbolic mirror is 0.15 μm PV and 17.9 nm RMS.

International Conference on Hyperbolic Problems (2nd). Theory, Numerical Methods and Applications, 14-18 March 1988

DTIC Science & Technology

1988-01-01

of this abstract got a spontaneous development of a transverse wave-strucure in a shock-oriented coordinate system without per- turbing the global ...We develop a formal asymptotic theory for hyperbolic conservation laws with large amplitude, rapidly varying initial data [1]. For small times, the...HUnefelderstr. 1-S, D-2800 Bremen 1 Today the most accurate and cost effective industrial codes used for aircraft design are based on full potential equations

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

PubMed

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

2012-12-11

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

Fast wavelet based algorithms for linear evolution equations

NASA Technical Reports Server (NTRS)

Engquist, Bjorn; Osher, Stanley; Zhong, Sifen

1992-01-01

A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1985-01-01

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditins, thus generalizing many special cases studied in recent literature.

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1983-01-01

New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditions, thus generalizing many special cases studied in recent literature.

Four-mirror extreme ultraviolet (EUV) lithography projection system

DOEpatents

Cohen, Simon J; Jeong, Hwan J; Shafer, David R

2000-01-01

The invention is directed to a four-mirror catoptric projection system for extreme ultraviolet (EUV) lithography to transfer a pattern from a reflective reticle to a wafer substrate. In order along the light path followed by light from the reticle to the wafer substrate, the system includes a dominantly hyperbolic convex mirror, a dominantly elliptical concave mirror, spherical convex mirror, and spherical concave mirror. The reticle and wafer substrate are positioned along the system's optical axis on opposite sides of the mirrors. The hyperbolic and elliptical mirrors are positioned on the same side of the system's optical axis as the reticle, and are relatively large in diameter as they are positioned on the high magnification side of the system. The hyperbolic and elliptical mirrors are relatively far off the optical axis and hence they have significant aspherical components in their curvatures. The convex spherical mirror is positioned on the optical axis, and has a substantially or perfectly spherical shape. The spherical concave mirror is positioned substantially on the opposite side of the optical axis from the hyperbolic and elliptical mirrors. Because it is positioned off-axis to a degree, the spherical concave mirror has some asphericity to counter aberrations. The spherical concave mirror forms a relatively large, uniform field on the wafer substrate. The mirrors can be tilted or decentered slightly to achieve further increase in the field size.

Structural and optical characterization of highly anisotropic low loss Al:ZnO/ZnO multilayered metamaterial with hyperbolic dispersion grown by pulsed layer deposition

NASA Astrophysics Data System (ADS)

Kelly, Priscilla; Zhang, Wenrui; Liu, Mingzhao; Kuznetsova, Lyuba

2017-08-01

Transparent conductive oxide materials have shown unique optical properties, such as negative refraction, hyperbolic dispersion, and epsilon-near-zero dispersion. In particular, aluminum-doped zinc oxide (Al:ZnO) has shown the most promising results over traditionally used noble metals. Pulsed layer deposition is a popular technique due to its fast and controlled growth rate, as well as the stoichiometric target-to-substrate material transfer. But, since it uses large and inhomogeneous kinetic energy, samples could be prone to macro- and microscopic defects. In this work, we investigate multilayered samples of Al:ZnO/ZnO grown by pulsed laser deposition with the goal of developing a low-loss metamaterial with hyperbolic dispersion. Different fabrication conditions, such as Al:ZnO/ZnO ratio, the thickness of an individual layer, different substrates, and deposition temperatures, were investigated. Results of the ellipsometry analysis, based on fitting spectroscopy data using the Berreman formalism, show that the hyperbolic dispersion transition (Re ɛ∥>0, Re ɛ⊥< 0) is achieved at λc=1868 nm wavelength (Im (ɛ⊥) 0.03) for samples with 1:4 Al:ZnO/ZnO deposition ratio. The fitted dielectric functions for samples with various parameters show that a lower deposition temperature leads to a shorter transition wavelength.

Magnetostatic modes in ferromagnetic samples with inhomogeneous internal fields

NASA Astrophysics Data System (ADS)

Arias, Rodrigo

2015-03-01

Magnetostatic modes in ferromagnetic samples are very well characterized and understood in samples with uniform internal magnetic fields. More recently interest has shifted to the study of magnetization modes in ferromagnetic samples with inhomogeneous internal fields. The present work shows that under the magnetostatic approximation and for samples of arbitrary shape and/or arbitrary inhomogeneous internal magnetic fields the modes can be classified as elliptic or hyperbolic, and their associated frequency spectrum can be delimited. This results from the analysis of the character of the second order partial differential equation for the magnetostatic potential under these general conditions. In general, a sample with an inhomogeneous internal field and at a given frequency, may have regions of elliptic and hyperbolic character separated by a boundary. In the elliptic regions the magnetostatic modes have a smooth monotonic character (generally decaying form the surfaces (a ``tunneling'' behavior)) and in hyperbolic regions an oscillatory wave-like character. A simple local criterion distinguishes hyperbolic from elliptic regions: the sign of a susceptibility parameter. This study shows that one may control to some extent magnetostatic modes via external fields or geometry. R.E.A. acknowledges Financiamiento Basal para Centros Cientificos y Tecnologicos de Excelencia under Project No. FB 0807 (Chile), Grant No. ICM P10-061-F by Fondo de Innovacion para la Competitividad-MINECON, and Proyecto Fondecyt 1130192.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Time-dependent boundary conditions for hyperbolic systems. II

NASA Technical Reports Server (NTRS)

Thompson, Kevin W.

1990-01-01

A general boundary condition formalism is developed for all types of boundary conditions to which hyperbolic systems are subject; the formalism makes possible a 'cookbook' approach to boundary conditions, by means of which novel boundary 'recipes' may be derived and previously devised ones may be consulted as required. Numerous useful conditions are derived for such CFD problems as subsonic and supersonic inflows and outflows, nonreflecting boundaries, force-free boundaries, constant pressure boundaries, and constant mass flux. Attention is given to the computation and integration of time derivatives.

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the hyperbolicity of the Euler equation system and the first principle of plane (simple) wave propagation. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in ID, 2D and 3D space are illustrated to demonstrate its robustness in practical computations.

Asymptotic of the Solutions of Hyperbolic Equations with a Skew-Symmetric Perturbation

NASA Astrophysics Data System (ADS)

Gallagher, Isabelle

1998-12-01

Using methods introduced by S. Schochet inJ. Differential Equations114(1994), 476-512, we compute the first term of an asymptotic expansion of the solutions of hyperbolic equations perturbated by a skew-symmetric linear operator. That result is first applied to two systems describing the motion of geophysic fluids: the rotating Euler equations and the primitive system of the quasigeostrophic equations. Finally in the last part, we study the slightly compressible Euler equations by application of that same result.

A priori error estimates for an hp-version of the discontinuous Galerkin method for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. Tinsley

1993-01-01

A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.

A New Discretization Method of Order Four for the Numerical Solution of One-Space Dimensional Second-Order Quasi-Linear Hyperbolic Equation

ERIC Educational Resources Information Center

Mohanty, R. K.; Arora, Urvashi

2002-01-01

Three level-implicit finite difference methods of order four are discussed for the numerical solution of the mildly quasi-linear second-order hyperbolic equation A(x, t, u)u[subscript xx] + 2B(x, t, u)u[subscript xt] + C(x, t, u)u[subscript tt] = f(x, t, u, u[subscript x], u[subscript t]), 0 less than x less than 1, t greater than 0 subject to…

Time-dependent boundary conditions for hyperbolic systems. II

NASA Astrophysics Data System (ADS)

Thompson, Kevin W.

1990-08-01

A general boundary condition formalism is developed for all types of boundary conditions to which hyperbolic systems are subject; the formalism makes possible a 'cookbook' approach to boundary conditions, by means of which novel boundary 'recipes' may be derived and previously devised ones may be consulted as required. Numerous useful conditions are derived for such CFD problems as subsonic and supersonic inflows and outflows, nonreflecting boundaries, force-free boundaries, constant pressure boundaries, and constant mass flux. Attention is given to the computation and integration of time derivatives.

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the first principle of non-reflecting, plane wave propagation and the hyperbolicity of the Euler equation system. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in 1D, 2D, and 3D space are illustrated to demonstrate its robustness in practical computations.

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

PubMed

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

2016-03-16

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

Ruijsenaars-Schneider three-body models with N = 2 supersymmetry

NASA Astrophysics Data System (ADS)

Galajinsky, Anton

2018-04-01

The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N = 2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism. It is also known that the rational model can be described by the geodesic equations associated with a metric connection. We demonstrate that the hyperbolic systems are linked to non-metric connections.

Derivation of the Effective Nonlinear Schrodinger Equations for Dark and Power Law Spatial Plasmon-Polariton Solitons Using Nano Self-Focusing

DTIC Science & Technology

2011-03-01

An e?ective Nonlinear Schr?dinger Equation for propagation is derived for optical dark and power law spatial solitons at the subwavelength with a... soliton amplitude profiles are displayed as a hyperbolic secant function and hold there profile at short distances on the order of centimeters. Dark ...spatial solitons are similar but have hyperbolic tangent type profiles. Dark spatial solitons were first observed by Jerominek in 1985 and Belanger and

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems

NASA Technical Reports Server (NTRS)

Goldberg, M.; Tadmor, E.

1986-01-01

The purpose of this paper is to achieve more versatile, convenient stability criteria for a wide class of finite-difference approximations to initial boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter-plane x greater than or equal to 0, t greater than or equal to 0. With these criteria, stability is easily established for a large number of examples, thus incorporating and generalizing many of the cases studied in recent literature.

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

NASA Technical Reports Server (NTRS)

Wiegert, P. A.

2011-01-01

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

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

NASA Technical Reports Server (NTRS)

Dey, C.; Dey, S. K.

1983-01-01

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

On the superconvergence of Galerkin methods for hyperbolic IBVP

NASA Technical Reports Server (NTRS)

Gottlieb, David; Gustafsson, Bertil; Olsson, Pelle; Strand, BO

1993-01-01

Finite element Galerkin methods for periodic first order hyperbolic equations exhibit superconvergence on uniform grids at the nodes, i.e., there is an error estimate 0(h(sup 2r)) instead of the expected approximation order 0(h(sup r)). It will be shown that no matter how the approximating subspace S(sup h) is chosen, the superconvergence property is lost if there are characteristics leaving the domain. The implications of this result when constructing compact implicit difference schemes is also discussed.

Efficient embedding of complex networks to hyperbolic space via their Laplacian

PubMed Central

Alanis-Lobato, Gregorio; Mier, Pablo; Andrade-Navarro, Miguel A.

2016-01-01

The different factors involved in the growth process of complex networks imprint valuable information in their observable topologies. How to exploit this information to accurately predict structural network changes is the subject of active research. A recent model of network growth sustains that the emergence of properties common to most complex systems is the result of certain trade-offs between node birth-time and similarity. This model has a geometric interpretation in hyperbolic space, where distances between nodes abstract this optimisation process. Current methods for network hyperbolic embedding search for node coordinates that maximise the likelihood that the network was produced by the afore-mentioned model. Here, a different strategy is followed in the form of the Laplacian-based Network Embedding, a simple yet accurate, efficient and data driven manifold learning approach, which allows for the quick geometric analysis of big networks. Comparisons against existing embedding and prediction techniques highlight its applicability to network evolution and link prediction. PMID:27445157

Tunable infrared hyperbolic metamaterials with periodic indium-tin-oxide nanorods

DOE PAGES

Guo, Peijun; Chang, Robert P. H.; Schaller, Richard D.

2017-07-10

Hyperbolic metamaterials (HMMs) are artificially engineered optical media that have been used for light confinement, excited state decay rate engineering, and subwavelength imaging, due to their highly anisotropic permittivity and with it the capability of supporting high- k modes. HMMs in the infrared range can be conceived for additional applications such as free space communication, thermal engineering, and molecular sensing. Here, we demonstrate infrared HMMs comprised of periodic indium-tin-oxide nanorod arrays (ITO-NRAs). We show that the ITO-NRA based HMMs exhibit a stationary epsilon-near-pole resonance in the near-infrared regime that is insensitive to the filling ratio, and a highly tunable epsilon-near-zeromore » resonance in the mid-infrared range depending on the array periodicity. Experimental results are supported by finite-element simulations, in which the ITO-NRAs are treated both explicitly and as an effective hyperbolic media. Lastly, our work presents a low-loss HMM platform with favorable spectral tunability in the infrared range.« less

Tuning subwavelength-structured focus in the hyperbolic metamaterials

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Psychophysics of time perception and intertemporal choice models

NASA Astrophysics Data System (ADS)

Takahashi, Taiki; Oono, Hidemi; Radford, Mark H. B.

2008-03-01

Intertemporal choice and psychophysics of time perception have been attracting attention in econophysics and neuroeconomics. Several models have been proposed for intertemporal choice: exponential discounting, general hyperbolic discounting (exponential discounting with logarithmic time perception of the Weber-Fechner law, a q-exponential discount model based on Tsallis's statistics), simple hyperbolic discounting, and Stevens' power law-exponential discounting (exponential discounting with Stevens' power time perception). In order to examine the fitness of the models for behavioral data, we estimated the parameters and AICc (Akaike Information Criterion with small sample correction) of the intertemporal choice models by assessing the points of subjective equality (indifference points) at seven delays. Our results have shown that the orders of the goodness-of-fit for both group and individual data were [Weber-Fechner discounting (general hyperbola) > Stevens' power law discounting > Simple hyperbolic discounting > Exponential discounting], indicating that human time perception in intertemporal choice may follow the Weber-Fechner law. Indications of the results for neuropsychopharmacological treatments of addiction and biophysical processing underlying temporal discounting and time perception are discussed.

Evolution of finite-amplitude localized vortices in planar homogeneous shear flows

NASA Astrophysics Data System (ADS)

Karp, Michael; Shukhman, Ilia G.; Cohen, Jacob

2017-02-01

An analytical-based method is utilized to follow the evolution of localized initially Gaussian disturbances in flows with homogeneous shear, in which the base velocity components are at most linear functions of the coordinates, including hyperbolic, elliptic, and simple shear. Coherent structures, including counterrotating vortex pairs (CVPs) and hairpin vortices, are formed for the cases where the streamlines of the base flow are open (hyperbolic and simple shear). For hyperbolic base flows, the dominance of shear over rotation leads to elongation of the localized disturbance along the outlet asymptote and formation of CVPs. For simple shear CVPs are formed from linear and nonlinear disturbances, whereas hairpins are observed only for highly nonlinear disturbances. For elliptic base flows CVPs, hairpins and vortex loops form initially, however they do not last and break into various vortical structures that spread in the spanwise direction. The effect of the disturbance's initial amplitude and orientation is examined and the optimal orientation achieving maximal growth is identified.

A single-phase elastic hyperbolic metamaterial with anisotropic mass density.

PubMed

Zhu, R; Chen, Y Y; Wang, Y S; Hu, G K; Huang, G L

2016-06-01

Wave propagation can be manipulated at a deep subwavelength scale through the locally resonant metamaterial that possesses unusual effective material properties. Hyperlens due to metamaterial's anomalous anisotropy can lead to superior-resolution imaging. In this paper, a single-phase elastic metamaterial with strongly anisotropic effective mass density has been designed. The proposed metamaterial utilizes the independently adjustable locally resonant motions of the subwavelength-scale microstructures along the two principal directions. High anisotropy in the effective mass densities obtained by the numerical-based effective medium theory can be found and even have opposite signs. For practical applications, shunted piezoelectric elements are introduced into the microstructure to tailor the effective mass density in a broad frequency range. Finally, to validate the design, an elastic hyperlens made of the single-phase hyperbolic metamaterial is proposed with subwavelength longitudinal wave imaging illustrated numerically. The proposed single-phase hyperbolic metamaterial has many promising applications for high resolution damage imaging in nondestructive evaluation and structural health monitoring.

A Model for Displacements Between Parallel Plates That Shows Change of Type from Hyperbolic to Elliptic

NASA Astrophysics Data System (ADS)

Shariati, Maryam; Yortsos, Yannis; Talon, Laurent; Martin, Jerome; Rakotomalala, Nicole; Salin, Dominique

2003-11-01

We consider miscible displacement between parallel plates, where the viscosity is a function of the concentration. By selecting a piece-wise representation, the problem can be considered as ``three-phase'' flow. Assuming a lubrication-type approximation, the mathematical description is in terms of two quasi-linear hyperbolic equations. When the mobility of the middle phase is smaller than its neighbors, the system is genuinely hyperbolic and can be solved analytically. However, when it is larger, an elliptic region develops. This change-of-type behavior is for the first time proved here based on sound physical principles. Numerical solutions with a small diffusion are presented. Good agreement is obtained outside the elliptic region, but not inside, where the numerical results show unstable behavior. We conjecture that for the solution of the real problem in the mixed-type case, the full higher-dimensionality problem must be considered inside the elliptic region, in which the lubrication (parallel-flow) approximation is no longer appropriate. This is discussed in a companion presentation.

Tunnelling with a negative cosmological constant

NASA Astrophysics Data System (ADS)

Gibbons, G. W.

1996-02-01

The point of this paper is to see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the universe. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the 4-manifold. We raise the question of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its 3-volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.

Efficient embedding of complex networks to hyperbolic space via their Laplacian

NASA Astrophysics Data System (ADS)

Alanis-Lobato, Gregorio; Mier, Pablo; Andrade-Navarro, Miguel A.

2016-07-01

The different factors involved in the growth process of complex networks imprint valuable information in their observable topologies. How to exploit this information to accurately predict structural network changes is the subject of active research. A recent model of network growth sustains that the emergence of properties common to most complex systems is the result of certain trade-offs between node birth-time and similarity. This model has a geometric interpretation in hyperbolic space, where distances between nodes abstract this optimisation process. Current methods for network hyperbolic embedding search for node coordinates that maximise the likelihood that the network was produced by the afore-mentioned model. Here, a different strategy is followed in the form of the Laplacian-based Network Embedding, a simple yet accurate, efficient and data driven manifold learning approach, which allows for the quick geometric analysis of big networks. Comparisons against existing embedding and prediction techniques highlight its applicability to network evolution and link prediction.

Determination of Extensional Rheological Properties by Hyperbolic Contraction Flow

NASA Astrophysics Data System (ADS)

Stading, Mats

2008-07-01

Extensional rheologyy is important for diverse applications such as processing of viscoelastic fluids, mouthfeel of semi-solid foods, cell mitosis and baking, and is also a useful tool for testing the applicability of constitutive equations. Despite the documented influence of extensional rheological properties, it is seldom measured due to experimental difficulties. There are only commercial equipments available for low-viscosity fluids by Capillary Breakup and for polymer melts by Meissner-type winding of ribbons around cylinders. Both methods have limited applicability for medium-viscosity fluids such as foods and other biological systems. Contraction flows are extensively studied and a new test method has been developed based on contraction flow through a hyperbolic nozzle. The method is suitable for medium-viscosity fluids and has been validated by comparison to results from Filament Stretching and Capillary Breakup. The hyperbolic contraction flow method has been used to characterize food and medical systems, distinguish between different products having equal shear behavior, quantify ropy mouth feel and to predict foaming behavior of biopolymers.

Deadline rush: a time management phenomenon and its mathematical description.

PubMed

König, Cornelius J; Kleinmann, Martin

2005-01-01

A typical time management phenomenon is the rush before a deadline. Behavioral decision making research can be used to predict how behavior changes before a deadline. People are likely not to work on a project with a deadline in the far future because they generally discount future outcomes. Only when the deadline is close are people likely to work. On the basis of recent intertemporal choice experiments, the authors argue that a hyperbolic function should provide a more accurate description of the deadline rush than an exponential function predicted by an economic model of discounted utility. To show this, the fit of the hyperbolic and the exponential function were compared with data sets that describe when students study for exams. As predicted, the hyperbolic function fit the data significantly better than the exponential function. The implication for time management decisions is that they are most likely to be inconsistent over time (i.e., people make a plan how to use their time but do not follow it).

Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries

NASA Astrophysics Data System (ADS)

Startsev, Sergey Ya.

2017-05-01

The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if this system admits a full set of formal integrals (i.e., differential operators which map symmetries into integrals of the system). As a consequence, such systems possess both direct and inverse Noether operators (in the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and perform transformations in the opposite direction). Systems admitting Noether operators are not exhausted by Euler-Lagrange systems and the systems with formal integrals. In particular, a hyperbolic system admits an inverse Noether operator if a differential substitution maps this system into a system possessing an inverse Noether operator.

Use of selection indices to model the functional response of predators

USGS Publications Warehouse

Joly, D.O.; Patterson, B.R.

2003-01-01

The functional response of a predator to changing prey density is an important determinant of stability of predatora??prey systems. We show how Manly's selection indices can be used to distinguish between hyperbolic and sigmoidal models of a predator functional response to primary prey density in the presence of alternative prey. Specifically, an inverse relationship between prey density and preference for that prey results in a hyperbolic functional response while a positive relationship can yield either a hyperbolic or sigmoidal functional response, depending on the form and relative magnitudes of the density-dependent preference model, attack rate, and handling time. As an example, we examine wolf (Canis lupus) functional response to moose (Alces alces) density in the presence of caribou (Rangifer tarandus). The use of selection indices to evaluate the form of the functional response has significant advantages over previous attempts to fit Holling's functional response curves to killing-rate data directly, including increased sensitivity, use of relatively easily collected data, and consideration of other explanatory factors (e.g., weather, seasons, productivity).

Characterizing omega-limit sets which are closed orbits

NASA Astrophysics Data System (ADS)

Bautista, S.; Morales, C.

Let X be a vector field in a compact n-manifold M, n⩾2. Given Σ⊂M we say that q∈M satisfies (P) Σ if the closure of the positive orbit of X through q does not intersect Σ, but, however, there is an open interval I with q as a boundary point such that every positive orbit through I intersects Σ. Among those q having saddle-type hyperbolic omega-limit set ω(q) the ones with ω(q) being a closed orbit satisfy (P) Σ for some closed subset Σ. The converse is true for n=2 but not for n⩾4. Here we prove the converse for n=3. Moreover, we prove for n=3 that if ω(q) is a singular-hyperbolic set [C. Morales, M. Pacifico, E. Pujals, On C robust singular transitive sets for three-dimensional flows, C. R. Acad. Sci. Paris Sér. I 26 (1998) 81-86], [C. Morales, M. Pacifico, E. Pujals, Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers, Ann. of Math. (2) 160 (2) (2004) 375-432], then ω(q) is a closed orbit if and only if q satisfies (P) Σ for some Σ closed. This result improves [S. Bautista, Sobre conjuntos hiperbólicos-singulares (On singular-hyperbolic sets), thesis Uiversidade Federal do Rio de Janeiro, 2005 (in Portuguese)] and [C. Morales, M. Pacifico, Mixing attractors for 3-flows, Nonlinearity 14 (2001) 359-378].

Analysis of 2D hyperbolic metamaterial dispersion by elementary excitation coupling

NASA Astrophysics Data System (ADS)

Vaianella, Fabio; Maes, Bjorn

2016-04-01

Hyperbolic metamaterials are examined for many applications thanks to the large density of states and extreme confinement of light they provide. For classical hyperbolic metal/dielectric multilayer structures, it was demon- strated that the properties originate from a specific coupling of the surface plasmon polaritons between the metal/dielectric interfaces. We show a similar analysis for 2D hyperbolic arrays of square (or rectangular) silver nanorods in a TiO2 host. In this case the properties derive from a specific coupling of the plasmons carried by the corners of the nanorods. The dispersion can be seen as the coupling of single rods for a through-metal connection of the corners, as the coupling of structures made of four semi-infinite metallic blocks separated by dielectric for a through-dielectric connection, or as the coupling of two semi-infinite rods for a through-metal and through-dielectric situation. For arrays of small square nanorods the elementary structure that explains the dispersion of the array is the single rod, and for arrays of large square nanorods it is four metallic corners. The medium size square nanorod case is more complicated, because the elementary structure can be one of the three basic designs, depending on the frequency and symmetry of the modes. Finally, we show that for arrays of rectangular nanorods the dispersion is explained by coupling of the two coupled rod structure. This work opens the way for a better understanding of a wide class of metamaterials via their elementary excitations.

Entanglement entropy and the colored Jones polynomial

NASA Astrophysics Data System (ADS)

Balasubramanian, Vijay; DeCross, Matthew; Fliss, Jackson; Kar, Arjun; Leigh, Robert G.; Parrikar, Onkar

2018-05-01

We study the multi-party entanglement structure of states in Chern-Simons theory created by performing the path integral on 3-manifolds with linked torus boundaries, called link complements. For gauge group SU(2), the wavefunctions of these states (in a particular basis) are the colored Jones polynomials of the corresponding links. We first review the case of U(1) Chern-Simons theory where these are stabilizer states, a fact we use to re-derive an explicit formula for the entanglement entropy across a general link bipartition. We then present the following results for SU(2) Chern-Simons theory: (i) The entanglement entropy for a bipartition of a link gives a lower bound on the genus of surfaces in the ambient S 3 separating the two sublinks. (ii) All torus links (namely, links which can be drawn on the surface of a torus) have a GHZ-like entanglement structure — i.e., partial traces leave a separable state. By contrast, through explicit computation, we test in many examples that hyperbolic links (namely, links whose complements admit hyperbolic structures) have W-like entanglement — i.e., partial traces leave a non-separable state. (iii) Finally, we consider hyperbolic links in the complexified SL(2,C) Chern-Simons theory, which is closely related to 3d Einstein gravity with a negative cosmological constant. In the limit of small Newton constant, we discuss how the entanglement structure is controlled by the Neumann-Zagier potential on the moduli space of hyperbolic structures on the link complement.

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell-Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic-parabolic Navier-Stokes-Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER-WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff relaxation limit, and compare the numerical results with exact or numerical reference solutions obtained for the Euler and Navier-Stokes equations. Numerical convergence results are also provided. To show the universality of the HPR model, the paper is rounded-off with an application to wave propagation in elastic solids, for which one only needs to switch off the strain relaxation source term in the governing PDE system. We provide various examples showing that for the purpose of flow visualization, the distortion tensor A seems to be particularly useful.

Powered Explicit Guidance Modifications and Enhancements for Space Launch System Block-1 and Block-1B Vehicles

NASA Technical Reports Server (NTRS)

Von der Porten, Paul; Ahmad, Naeem; Hawkins, Matt; Fill, Thomas

2018-01-01

NASA is currently building the Space Launch System (SLS) Block-1 launch vehicle for the Exploration Mission 1 (EM-1) test flight. NASA is also currently designing the next evolution of SLS, the Block-1B. The Block-1 and Block-1B vehicles will use the Powered Explicit Guidance (PEG) algorithm (of Space Shuttle heritage) for closed loop guidance. To accommodate vehicle capabilities and design for future evolutions of SLS, modifications were made to PEG for Block-1 to handle multi-phase burns, provide PEG updated propulsion information, and react to a core stage engine out. In addition, due to the relatively low thrust-to-weight ratio of the Exploration Upper Stage (EUS) and EUS carrying out Lunar Vicinity and Earth Escape missions, certain enhancements to the Block-1 PEG algorithm are needed to perform Block-1B missions to account for long burn arcs and target translunar and hyperbolic orbits. This paper describes the design and implementation of modifications to the Block-1 PEG algorithm as compared to Space Shuttle. Furthermore, this paper illustrates challenges posed by the Block-1B vehicle and the required PEG enhancements. These improvements make PEG capable for use on the SLS Block-1B vehicle as part of the Guidance, Navigation, and Control (GN&C) System.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davidovich, M. V., E-mail: davidovichmv@info.sgu.ru

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.

High order filtering methods for approximating hyperbolic systems of conservation laws

NASA Technical Reports Server (NTRS)

Lafon, F.; Osher, S.

1991-01-01

The essentially nonoscillatory (ENO) schemes, while potentially useful in the computation of discontinuous solutions of hyperbolic conservation-law systems, are computationally costly relative to simple central-difference methods. A filtering technique is presented which employs central differencing of arbitrarily high-order accuracy except where a local test detects the presence of spurious oscillations and calls upon the full ENO apparatus to remove them. A factor-of-three speedup is thus obtained over the full-ENO method for a wide range of problems, with high-order accuracy in regions of smooth flow.

On the arbitrary l-wave solutions of the deformed hyperbolic manning-rosen potential including an improved approximation to the orbital centrifugal term

NASA Astrophysics Data System (ADS)

Xu, Chun-Long; Zhang, Min-Cang

2017-01-01

The arbitrary l-wave solutions to the Schrödinger equation for the deformed hyperbolic Manning-Rosen potential is investigated analytically by using the Nikiforov-Uvarov method, the centrifugal term is treated with an improved Greene and Aldrich's approximation scheme. The wavefunctions depend on the deformation parameter q, which is expressed in terms of the Jocobi polynomial or the hypergeometric function. The bound state energy is obtained, and the discrete spectrum is shown to be independent of the deformation parameter q.

Interaction phenomenon to dimensionally reduced p-gBKP equation

NASA Astrophysics Data System (ADS)

Zhang, Runfa; Bilige, Sudao; Bai, Yuexing; Lü, Jianqing; Gao, Xiaoqing

2018-02-01

Based on searching the combining of quadratic function and exponential (or hyperbolic cosine) function from the Hirota bilinear form of the dimensionally reduced p-gBKP equation, eight class of interaction solutions are derived via symbolic computation with Mathematica. The submergence phenomenon, presented to illustrate the dynamical features concerning these obtained solutions, is observed by three-dimensional plots and density plots with particular choices of the involved parameters between the exponential (or hyperbolic cosine) function and the quadratic function. It is proved that the interference between the two solitary waves is inelastic.

Travelling Randomly on the Poincaré Half-Plane with a Pythagorean Compass

NASA Astrophysics Data System (ADS)

Cammarota, V.; Orsingher, E.

2008-02-01

A random motion on the Poincaré half-plane is studied. A particle runs on the geodesic lines changing direction at Poisson-paced times. The hyperbolic distance is analyzed, also in the case where returns to the starting point are admitted. The main results concern the mean hyperbolic distance (and also the conditional mean distance) in all versions of the motion envisaged. Also an analogous motion on orthogonal circles of the sphere is examined and the evolution of the mean distance from the starting point is investigated.

Trading spaces: building three-dimensional nets from two-dimensional tilings

PubMed Central

Castle, Toen; Evans, Myfanwy E.; Hyde, Stephen T.; Ramsden, Stuart; Robins, Vanessa

2012-01-01

We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic (S2), Euclidean (E2) and hyperbolic (H2) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions. PMID:24098839

The properties of Q-deformed hyperbolic and trigonometric functions in quantum deformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deta, U. A., E-mail: utamaalan@yahoo.co.id, E-mail: utamadeta@unesa.ac.id; Suparmi

2015-09-30

Quantum deformation has been studied due to its relation with applications in nuclear physics, conformal field theory, and statistical-quantum theory. The q-deformation of hyperbolic function was introduced by Arai. The application of q-deformed functions has been widely used in quantum mechanics. The properties of this two kinds of system explained in this paper including their derivative. The graph of q-deformed functions presented using Matlab. The special case is given for modified Poschl-Teller plus q-deformed Scarf II trigonometry potentials.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives

NASA Astrophysics Data System (ADS)

Araujo, Vitor; Galatolo, Stefano; Pacifico, Maria José

We comment on the mathematical results about the statistical behavior of Lorenz equations and its attractor, and more generally on the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer-assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statistical behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated with the existence of physical measures: in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors: (1) there exists an invariant foliation whose leaves are forward contracted by the flow (and further properties which are useful to understand the statistical properties of the dynamics); (2) there exists a positive Lyapunov exponent at every orbit; (3) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (4) this measure is exact dimensional; (5) the induced measure on a suitable family of cross-sections has exponential decay of correlations for Lipschitz observables with respect to a suitable Poincaré return time map; (6) the hitting time associated to Lorenz-like attractors satisfy a logarithm law; (7) the geometric Lorenz flow satisfies the Almost Sure Invariance Principle (ASIP) and the Central Limit Theorem (CLT); (8) the rate of decay of large deviations for the volume measure on the ergodic basin of a geometric Lorenz attractor is exponential; (9) a class of geometric Lorenz flows exhibits robust exponential decay of correlations; (10) all geometric Lorenz flows are rapidly mixing and their time-1 map satisfies both ASIP and CLT.

Arithmetic and Hyperbolic Structures in String Theory

NASA Astrophysics Data System (ADS)

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 arithmetic groups G(Z) which are conjectured to be preserved in the effective action. The exact couplings are given by automorphic forms on the double quotient G(Z)G/K. We discuss in detail various methods of constructing automorphic forms, with particular emphasis on non-holomorphic Eisenstein series. We provide detailed examples for the physically relevant cases of SL(2,Z) and SL(3,Z), for which we construct their respective Eisenstein series and compute their (non-abelian) Fourier expansions. We also show how these techniques can be applied to hypermultiplet moduli spaces in type II Calabi-Yau compactifications, and we provide a detailed analysis for the universal hypermultiplet.

The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells.

PubMed

Levine, M W

1991-01-01

Simulated neural impulse trains were generated by a digital realization of the integrate-and-fire model. The variability in these impulse trains had as its origin a random noise of specified distribution. Three different distributions were used: the normal (Gaussian) distribution (no skew, normokurtic), a first-order gamma distribution (positive skew, leptokurtic), and a uniform distribution (no skew, platykurtic). Despite these differences in the distribution of the variability, the distributions of the intervals between impulses were nearly indistinguishable. These inter-impulse distributions were better fit with a hyperbolic gamma distribution than a hyperbolic normal distribution, although one might expect a better approximation for normally distributed inverse intervals. Consideration of why the inter-impulse distribution is independent of the distribution of the causative noise suggests two putative interval distributions that do not depend on the assumed noise distribution: the log normal distribution, which is predicated on the assumption that long intervals occur with the joint probability of small input values, and the random walk equation, which is the diffusion equation applied to a random walk model of the impulse generating process. Either of these equations provides a more satisfactory fit to the simulated impulse trains than the hyperbolic normal or hyperbolic gamma distributions. These equations also provide better fits to impulse trains derived from the maintained discharges of ganglion cells in the retinae of cats or goldfish. It is noted that both equations are free from the constraint that the coefficient of variation (CV) have a maximum of unity.(ABSTRACT TRUNCATED AT 250 WORDS)

Global Resolution of the Physical Vacuum Singularity for Three-Dimensional Isentropic Inviscid Flows with Damping in Spherically Symmetric Motions

NASA Astrophysics Data System (ADS)

Zeng, Huihui

2017-10-01

For the gas-vacuum interface problem with physical singularity and the sound speed being {C^{{1}/{2}}}-Hölder continuous near vacuum boundaries of the isentropic compressible Euler equations with damping, the global existence of smooth solutions and the convergence to Barenblatt self-similar solutions of the corresponding porous media equation are proved in this paper for spherically symmetric motions in three dimensions; this is done by overcoming the analytical difficulties caused by the coordinate's singularity near the center of symmetry, and the physical vacuum singularity to which standard methods of symmetric hyperbolic systems do not apply. Various weights are identified to resolve the singularity near the vacuum boundary and the center of symmetry globally in time. The results obtained here contribute to the theory of global solutions to vacuum boundary problems of compressible inviscid fluids, for which the currently available results are mainly for the local-in-time well-posedness theory, and also to the theory of global smooth solutions of dissipative hyperbolic systems which fail to be strictly hyperbolic.

An instability of hyperbolic space under the Yang-Mills flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gegenberg, Jack; Day, Andrew C.; Liu, Haitao

2014-04-15

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of constant curvature. We analytically solve the linearized flow equations for a large class of perturbations to the fixed point corresponding to hyperbolic 3-space. These can be expressed as a linear superposition of distinct modes, some of which are exponentially growing along the flow. The growing modes imply the divergence ofmore » the (gauge invariant) perturbative torsion for a wide class of initial data, indicating an instability of the background geometry that we confirm with numeric simulations in the partially compactified case. There are stable modes with zero torsion, but all the unstable modes are torsion-full. This leads us to speculate that the instability is induced by the torsion degrees of freedom present in the Yang-Mills flow.« less

Well-posedness of the Cauchy problem for models of large amplitude internal waves

NASA Astrophysics Data System (ADS)

Guyenne, Philippe; Lannes, David; Saut, Jean-Claude

2010-02-01

We consider in this paper the 'shallow-water/shallow-water' asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 1-36), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587-641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 538-66) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensional interfaces, this system is of hyperbolic type and its local well-posedness does not raise serious difficulties, although other issues (blow-up, loss of hyperbolicity, etc) turn out to be delicate. For two-dimensional interfaces, the system is nonlocal. Nevertheless, we prove that it conserves some properties of 'hyperbolic type' and show that the associated Cauchy problem is locally well posed in suitable Sobolev classes provided some natural restrictions are imposed on the data. These results are illustrated by numerical simulations with emphasis on the formation of shock waves.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

PubMed

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

2011-01-01

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

Hyperbolic geometrical optics: Hyperbolic glass

NASA Astrophysics Data System (ADS)

De Micheli, Enrico; Scorza, Irene; Viano, Giovanni Alberto

2006-02-01

We study the geometrical optics generated by a refractive index of the form n (x,y)=1/y (y>0), where y is the coordinate of the vertical axis in an orthogonal reference frame in R2. We thus obtain what we call "hyperbolic geometrical optics" since the ray trajectories are geodesics in the Poincaré-Lobachevsky half-plane H2. Then we prove that the constant phase surface are horocycles and obtain the horocyclic waves, which are closely related to the classical Poisson kernel and are the analogs of the Euclidean plane waves. By studying the transport equation in the Beltrami pseudosphere, we prove (i) the conservation of the flow in the entire strip 0

Tsien's method for generating non-Keplerian trajectories. Part 2: The question of thrust to orbit a sphere and the restricted three-body problem

NASA Technical Reports Server (NTRS)

Murad, P. A.

1993-01-01

Tsien's method is extended to treat the orbital motion of a body undergoing accelerations and decelerations. A generalized solution is discussed for the generalized case where a body undergoes azimuthal and radial thrust and the problem is further simplified for azimuthal thrust alone. Judicious selection of thrust could generate either an elliptic or hyperbolic trajectory. This is unexpected especially when the body has only enough energy for a lower state trajectory. The methodology is extended treating the problem of vehicle thrust for orbiting a sphere and vehicle thrust within the classical restricted three-body problem. Results for the latter situation can produce hyperbolic trajectories through eigen value decomposition. Since eigen values for no-thrust can be imaginary, thrust can generate real eigen values to describe hyperbolic trajectories. Keplerian dynamics appears to represent but a small subset of a much larger non-Keplerian domain especially when thrust effects are considered. The need for high thrust long duration space-based propulsion systems for changing a trajectory's canonical form is clearly demonstrated.

Ion beam figuring of Φ520mm convex hyperbolic secondary mirror

NASA Astrophysics Data System (ADS)

Meng, Xiaohui; Wang, Yonggang; Li, Ang; Li, Wenqing

2016-10-01

The convex hyperbolic secondary mirror is a Φ520-mm Zerodur lightweight hyperbolic convex mirror. Typically conventional methods like CCOS, stressed-lap polishing are used to manufacture this secondary mirror. Nevertheless, the required surface accuracy cannot be achieved through the use of conventional polishing methods because of the unpredictable behavior of the polishing tools, which leads to an unstable removal rate. Ion beam figuring is an optical fabrication method that provides highly controlled error of previously polished surfaces using a directed, inert and neutralized ion beam to physically sputter material from the optic surface. Several iterations with different ion beam size are selected and optimized to fit different stages of surface figure error and spatial frequency components. Before ion beam figuring, surface figure error of the secondary mirror is 2.5λ p-v, 0.23λ rms, and is improved to 0.12λ p-v, 0.014λ rms in several process iterations. The demonstration clearly shows that ion beam figuring can not only be used to the final correction of aspheric, but also be suitable for polishing the coarse surface of large, complex mirror.

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Selective radiative heating of nanostructures using hyperbolic metamaterials

DOE PAGES

Ding, Ding; Minnich, Austin J

2015-01-01

Hyperbolic metamaterials (HMM) are of great interest due to their ability to break the diffraction limit for imaging and enhance near-field radiative heat transfer. Here we demonstrate that an annular, transparent HMM enables selective heating of a sub-wavelength plasmonic nanowire by controlling the angular mode number of a plasmonic resonance. A nanowire emitter, surrounded by an HMM, appears dark to incoming radiation from an adjacent nanowire emitter unless the second emitter is surrounded by an identical lens such that the wavelength and angular mode of the plasmonic resonance match. Our result can find applications in radiative thermal management.

A pseudospectral Legendre method for hyperbolic equations with an improved stability condition

NASA Technical Reports Server (NTRS)

Tal-Ezer, Hillel

1986-01-01

A new pseudospectral method is introduced for solving hyperbolic partial differential equations. This method uses different grid points than previously used pseudospectral methods: in fact the grid points are related to the zeroes of the Legendre polynomials. The main advantage of this method is that the allowable time step is proportional to the inverse of the number of grid points 1/N rather than to 1/n(2) (as in the case of other pseudospectral methods applied to mixed initial boundary value problems). A highly accurate time discretization suitable for these spectral methods is discussed.

A pseudospectral Legendre method for hyperbolic equations with an improved stability condition

NASA Technical Reports Server (NTRS)

Tal-Ezer, H.

1984-01-01

A new pseudospectral method is introduced for solving hyperbolic partial differential equations. This method uses different grid points than previously used pseudospectral methods: in fact the grid are related to the zeroes of the Legendre polynomials. The main advantage of this method is that the allowable time step is proportional to the inverse of the number of grid points 1/N rather than to 1/n(2) (as in the case of other pseudospectral methods applied to mixed initial boundary value problems). A highly accurate time discretization suitable for these spectral methods is discussed.

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Stability of hyperbolic-parabolic mixed type equations with partial boundary condition

NASA Astrophysics Data System (ADS)

Zhan, Huashui; Feng, Zhaosheng

2018-06-01

In this paper, we are concerned with the hyperbolic-parabolic mixed type equations with the non-homogeneous boundary condition. If it is degenerate on the boundary, the part of the boundary whose boundary value should be imposed, is determined by the entropy condition from the convection term. If there is no convection term in the equation, we show that the stability of solutions can be proved without any boundary condition. If the equation is completely degenerate, we show that the stability of solutions can be established just based on the partial boundary condition.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

On the hyperbolic nature of the equations of alluvial river hydraulics and the equivalence of stable and energy dissipating shocks

NASA Astrophysics Data System (ADS)

Zanraea, D. D. L.; Needham, D. J.

The depth-averaged hydraulic equations augmented with a suitable bed-load sediment transport function form a closed system which governs the one-dimensional flow in an alluvial river or channel. In this paper, it is shown that this system is hyperbolic and yields three families of shock-wave solutions. These are determined to be temporally stable in restricted regions of the (H, F0)-plane, via the Lax shock inequalities. Further, it is demonstrated that this criterion is equivalent to the energy dissipation criterion developed by Needham and Hey (1991).

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Divergent conservation laws in hyperbolic thermoelasticity

NASA Astrophysics Data System (ADS)

Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present study is devoted to the problem of formulation of conservation laws in divergent form for hyperbolic thermoelastic continua. The field formalism is applied to study the problem. A natural density of thermoelastic action and the corresponding variational least action principle are formulated. A special form of the first variation of the action is employed to obtain 4-covariant divergent conservation laws. Differential field equations and constitutive laws are derived from a special form of the first variation of the action integral. The objectivity of constitutive equations is provided by the rotationally invariant forms of the Lagrangian employed.

Summation by parts, projections, and stability

NASA Technical Reports Server (NTRS)

Olsson, Pelle

1993-01-01

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.

Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul

1993-01-01

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

Triangle based TVD schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn

1990-01-01

A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

Computation of steady nozzle flow by a time-dependent method

NASA Technical Reports Server (NTRS)

Cline, M. C.

1974-01-01

The equations of motion governing steady, inviscid flow are of a mixed type, that is, hyperbolic in the supersonic region and elliptic in the subsonic region. These mathematical difficulties may be removed by using the so-called time-dependent method, where the governing equations become hyperbolic everywhere. The steady-state solution may be obtained as the asymptotic solution for large time. The object of this research was to develop a production type computer program capable of solving converging, converging-diverging, and plug two-dimensional nozzle flows in computational times of 1 min or less on a CDC 6600 computer.

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

NASA Astrophysics Data System (ADS)

Kang, Yongqiang; Liu, Hongmei

2018-02-01

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

Assessing the relative bioavailability of DOC in regional groundwater systems

USGS Publications Warehouse

Chapelle, Francis H.; Bradley, Paul M.; Journey, Celeste A.; McMahon, Peter B.

2013-01-01

It has been hypothesized that the degree to which a hyperbolic relationship exists between concentrations of dissolved organic carbon (DOC) and dissolved oxygen (DO) in groundwater may indicate the relative bioavailability of DOC. This hypothesis was examined for 73 different regional aquifers of the United States using 7745 analyses of groundwater compiled by the National Water Assessment (NAWQA) program of the U.S. Geological Survey. The relative reaction quotient (RRQ), a measure of the curvature of DOC concentrations plotted versus DO concentrations and regressed to a decaying hyperbolic equation, was used to assess the relative bioavailability of DOC. For the basalt aquifer of Oahu, Hawaii, RRQ values were low (0.0013 mM−2), reflecting a nearly random relationship between DOC and DO concentrations. In contrast, on the island of Maui, treated sewage effluent injected into a portion of the basalt aquifer resulted in pronounced hyperbolic DOC-DO behavior and a higher RRQ (142 mM−2). RRQ values for the 73 aquifers correlated positively with mean concentrations of ammonia, dissolved iron, and manganese, and correlated negatively with mean pH. This indicates that greater RRQ values are associated with greater concentrations of the final products of microbial reduction reactions. RRQ values and DOC concentrations were negatively correlated with the thickness of the unsaturated zone (UNST) and depth to the top of the screened interval. Finally, RRQ values were positively correlated with mean annual precipitation (MAP), and the highest observed RRQ values were associated with aquifers receiving MAP rates ranging between 900 and 1300 mm/year. These results are uniformly consistent with the hypothesis that the hyperbolic behavior of DOC-DO plots, as quantified by the RRQ metric, can be an indicator of relative DOC bioavailability in groundwater systems.

A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities

NASA Astrophysics Data System (ADS)

Muscoloni, Alessandro; Vittorio Cannistraci, Carlo

2018-05-01

The investigation of the hidden metric space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The popularity-similarity-optimization (PSO) model simulates how random geometric graphs grow in the hyperbolic space, generating realistic networks with clustering, small-worldness, scale-freeness and rich-clubness. However, it misses to reproduce an important feature of real complex networks, which is the community organization. The geometrical-preferential-attachment (GPA) model was recently developed in order to confer to the PSO also a soft community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have a variable level of attractiveness. However, the number and size of the communities cannot be explicitly controlled in the GPA, which is a clear limitation for real applications. Here, we introduce the nonuniform PSO (nPSO) model. Differently from GPA, the nPSO generates synthetic networks in the hyperbolic space where heterogeneous angular node attractiveness is forced by sampling the angular coordinates from a tailored nonuniform probability distribution (for instance a mixture of Gaussians). The nPSO differs from GPA in other three aspects: it allows one to explicitly fix the number and size of communities; it allows one to tune their mixing property by means of the network temperature; it is efficient to generate networks with high clustering. Several tests on the detectability of the community structure in nPSO synthetic networks and wide investigations on their structural properties confirm that the nPSO is a valid and efficient model to generate realistic complex networks with communities.

Relationship Between β-cell Response and Insulin Sensitivity in Horses based on the Oral Sugar Test and the Euglycemic Hyperinsulinemic Clamp.

PubMed

Lindåse, S; Nostell, K; Söder, J; Bröjer, J

2017-09-01

A hyperbolic relationship between β-cell response and insulin sensitivity (IS) has been described in several species including rodents, dogs, and humans. This relationship has not been elucidated in the horse. To determine whether the hyperbolic relationship between β-cell response and IS exists in horses by using indices of β-cell response from the oral sugar test (OST) and IS measurements from the euglycemic hyperinsulinemic clamp (EHC). A second aim was to compare how well IS estimates from the OST and EHC correlate. Forty-nine horses with different degrees of insulin regulation (normal-to-severe insulin dysregulation). Cross-sectional study. Horses were examined with an OST and an EHC. Decreased IS was associated with increased β-cell response in the horses. Nine of 12 comparisons between indices of β-cell response and IS measures fulfilled the criteria for a hyperbolic relationship. Indices of IS calculated from the OST correlated highly with the insulin-dependent glucose disposal rate (M) and the insulin-dependent glucose disposal rate per unit of insulin (M/I) determined from the EHC (r = 0.81-0.87). A hyperbolic relationship between β-cell response and IS exists in horses, which suggest that horses with insulin dysregulation respond not only with postprandial hyperinsulinemia but are also insulin resistant. The OST is primarily a test for β-cell response rather than a test for IS, but calculated indices of IS from the OST may be useful to estimate IS in horses, especially when the horse is insulin resistant. Copyright © 2017 The Authors. Journal of Veterinary Internal Medicine published by Wiley Periodicals, Inc. on behalf of the American College of Veterinary Internal Medicine.

Using periodic orbits to compute chaotic transport rates between resonance zones.

PubMed

Sattari, Sulimon; Mitchell, Kevin A

2017-11-01

Transport properties of chaotic systems are computable from data extracted from periodic orbits. Given a sufficient number of periodic orbits, the escape rate can be computed using the spectral determinant, a function that incorporates the eigenvalues and periods of periodic orbits. The escape rate computed from periodic orbits converges to the true value as more and more periodic orbits are included. Escape from a given region of phase space can be computed by considering only periodic orbits that lie within the region. An accurate symbolic dynamics along with a corresponding partitioning of phase space is useful for systematically obtaining all periodic orbits up to a given period, to ensure that no important periodic orbits are missing in the computation. Homotopic lobe dynamics (HLD) is an automated technique for computing accurate partitions and symbolic dynamics for maps using the topological forcing of intersections of stable and unstable manifolds of a few periodic anchor orbits. In this study, we apply the HLD technique to compute symbolic dynamics and periodic orbits, which are then used to find escape rates from different regions of phase space for the Hénon map. We focus on computing escape rates in parameter ranges spanning hyperbolic plateaus, which are parameter intervals where the dynamics is hyperbolic and the symbolic dynamics does not change. After the periodic orbits are computed for a single parameter value within a hyperbolic plateau, periodic orbit continuation is used to compute periodic orbits over an interval that spans the hyperbolic plateau. The escape rates computed from a few thousand periodic orbits agree with escape rates computed from Monte Carlo simulations requiring hundreds of billions of orbits.

A simple hyperbolic model for communication in parallel processing environments

NASA Technical Reports Server (NTRS)

Stoica, Ion; Sultan, Florin; Keyes, David

1994-01-01

We introduce a model for communication costs in parallel processing environments called the 'hyperbolic model,' which generalizes two-parameter dedicated-link models in an analytically simple way. Dedicated interprocessor links parameterized by a latency and a transfer rate that are independent of load are assumed by many existing communication models; such models are unrealistic for workstation networks. The communication system is modeled as a directed communication graph in which terminal nodes represent the application processes that initiate the sending and receiving of the information and in which internal nodes, called communication blocks (CBs), reflect the layered structure of the underlying communication architecture. The direction of graph edges specifies the flow of the information carried through messages. Each CB is characterized by a two-parameter hyperbolic function of the message size that represents the service time needed for processing the message. The parameters are evaluated in the limits of very large and very small messages. Rules are given for reducing a communication graph consisting of many to an equivalent two-parameter form, while maintaining an approximation for the service time that is exact in both large and small limits. The model is validated on a dedicated Ethernet network of workstations by experiments with communication subprograms arising in scientific applications, for which a tight fit of the model predictions with actual measurements of the communication and synchronization time between end processes is demonstrated. The model is then used to evaluate the performance of two simple parallel scientific applications from partial differential equations: domain decomposition and time-parallel multigrid. In an appropriate limit, we also show the compatibility of the hyperbolic model with the recently proposed LogP model.

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

NASA Astrophysics Data System (ADS)

Kay, Bernard S.; Radzikowski, Marek J.; Wald, Robert M.

1997-02-01

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M,g_{ab}), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as 'past terminal accumulation points' of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's 'Chronology Protection Conjecture', according to which the laws of physics prevent one from manufacturing a 'time machine'. Specifically, we prove: Theorem 1. There is no extension to (M,g_{ab}) of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2. The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in M 2 M) of (x,x). In consequence of Theorem 2, quantities such as the renormalized expectation value of J2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proof of these theorems relies on the 'Propagation of Singularities' theorems of Duistermaat and Hörmander.

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

PubMed

Harrison, John A

2008-09-04

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

Neural coding of image structure and contrast polarity of Cartesian, hyperbolic, and polar gratings in the primary and secondary visual cortex of the tree shrew.

PubMed

Poirot, Jordan; De Luna, Paolo; Rainer, Gregor

2016-04-01

We comprehensively characterize spiking and visual evoked potential (VEP) activity in tree shrew V1 and V2 using Cartesian, hyperbolic, and polar gratings. Neural selectivity to structure of Cartesian gratings was higher than other grating classes in both visual areas. From V1 to V2, structure selectivity of spiking activity increased, whereas corresponding VEP values tended to decrease, suggesting that single-neuron coding of Cartesian grating attributes improved while the cortical columnar organization of these neurons became less precise from V1 to V2. We observed that neurons in V2 generally exhibited similar selectivity for polar and Cartesian gratings, suggesting that structure of polar-like stimuli might be encoded as early as in V2. This hypothesis is supported by the preference shift from V1 to V2 toward polar gratings of higher spatial frequency, consistent with the notion that V2 neurons encode visual scene borders and contours. Neural sensitivity to modulations of polarity of hyperbolic gratings was highest among all grating classes and closely related to the visual receptive field (RF) organization of ON- and OFF-dominated subregions. We show that spatial RF reconstructions depend strongly on grating class, suggesting that intracortical contributions to RF structure are strongest for Cartesian and polar gratings. Hyperbolic gratings tend to recruit least cortical elaboration such that the RF maps are similar to those generated by sparse noise, which most closely approximate feedforward inputs. Our findings complement previous literature in primates, rodents, and carnivores and highlight novel aspects of shape representation and coding occurring in mammalian early visual cortex. Copyright © 2016 the American Physiological Society.

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza R.; Nishikawa, Hiroaki

2014-01-01

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

MUSTA fluxes for systems of conservation laws

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2006-08-01

This paper is about numerical fluxes for hyperbolic systems and we first present a numerical flux, called GFORCE, that is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first-order upwind method. Then we incorporate GFORCE in the framework of the MUSTA approach [E.F. Toro, Multi-Stage Predictor-Corrector Fluxes for Hyperbolic Equations. Technical Report NI03037-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 17th June, 2003], resulting in a version that we call GMUSTA. For non-linear systems this gives results that are comparable to those of the Godunov method in conjunction with the exact Riemann solver or complete approximate Riemann solvers, noting however that in our approach, the solution of the Riemann problem in the conventional sense is avoided. Both the GFORCE and GMUSTA fluxes are extended to multi-dimensional non-linear systems in a straightforward unsplit manner, resulting in linearly stable schemes that have the same stability regions as the straightforward multi-dimensional extension of Godunov's method. The methods are applicable to general meshes. The schemes of this paper share with the family of centred methods the common properties of being simple and applicable to a large class of hyperbolic systems, but the schemes of this paper are distinctly more accurate. Finally, we proceed to the practical implementation of our numerical fluxes in the framework of high-order finite volume WENO methods for multi-dimensional non-linear hyperbolic systems. Numerical results are presented for the Euler equations and for the equations of magnetohydrodynamics.

Numerical methods for systems of conservation laws of mixed type using flux splitting

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1990-01-01

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

NASA Astrophysics Data System (ADS)

Zhura, N. A.; Soldatov, A. P.

2017-06-01

We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.

Some special solutions to the Hyperbolic NLS equation

NASA Astrophysics Data System (ADS)

Vuillon, Laurent; Dutykh, Denys; Fedele, Francesco

2018-04-01

The Hyperbolic Nonlinear SCHRöDINGER equation (HypNLS) arises as a model for the dynamics of three-dimensional narrow-band deep water gravity waves. In this study, the symmetries and conservation laws of this equation are computed. The PETVIASHVILI method is then exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly accurate FOURIER solver.

Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Kofane, T. C.; Fokou, M.; Mohamadou, A.; Yomba, E.

2017-11-01

In this work, the lump solution and the kink solitary wave solution from the (2 + 1) -dimensional third-order evolution equation, using the Hirota bilinear method are obtained through symbolic computation with Maple. We have assumed that the lump solution is centered at the origin, when t = 0 . By considering a mixing positive quadratic function with exponential function, as well as a mixing positive quadratic function with hyperbolic cosine function, interaction solutions like lump-exponential and lump-hyperbolic cosine are presented. A completely non-elastic interaction between a lump and kink soliton is observed, showing that a lump solution can be swallowed by a kink soliton.

Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guth, Larry, E-mail: lguth@math.mit.edu; Lubotzky, Alexander, E-mail: alex.lubotzky@mail.huji.ac.il

2014-08-15

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 n{sup ε}. Their rate is evaluated via Euler characteristic arguments and their distance using Z{sub 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.

Grammatical complexity for two-dimensional maps

NASA Astrophysics Data System (ADS)

Hagiwara, Ryouichi; Shudo, Akira

2004-11-01

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

Plasmonic slow light waveguide with hyperbolic metamaterials claddings

NASA Astrophysics Data System (ADS)

Liang, Shuhai; Jiang, Chuhao; Yang, Zhiqiang; Li, Dacheng; Zhang, Wending; Mei, Ting; Zhang, Dawei

2018-06-01

Plasmonic waveguides with an insulator core sandwiched between hyperbolic metamaterials (HMMs) claddings, i.e. HIH waveguide, are investigated for achieving wide slow-light band with adjustable working wavelength. The transfer matrix method and the finite-difference-time-domain simulation are employed to study waveguide dispersion characteristics and pulse propagation. By selecting proper silver filling ratios for HMMs, the hetero-HIH waveguide presents a slow-light band with a zero group velocity dispersion wavelength of 1.55 μm and is capable of buffering pulses with pulse width as short as ∼20 fs. This type of waveguides might be applicable for ultrafast slow-light application.

Circulating transportation orbits between earth and Mars

NASA Technical Reports Server (NTRS)

Friedlander, A. L.; Niehoff, J. C.; Byrnes, D. V.; Longuski, J. M.

1986-01-01

This paper describes the basic characteristics of circulating (cyclical) orbit design as applied to round-trip transportation of crew and materials between earth and Mars in support of a sustained manned Mars Surface Base. The two main types of nonstopover circulating trajectories are the socalled VISIT orbits and the Up/Down Escalator orbits. Access to the large transportation facilities placed in these orbits is by way of taxi vehicles using hyperbolic rendezvous techniques during the successive encounters with earth and Mars. Specific examples of real trajectory data are presented in explanation of flight times, encounter frequency, hyperbolic velocities, closest approach distances, and Delta V maneuver requirements in both interplanetary and planetocentric space.

Emotional Hypochondriasis, Hyperbole, and the Borderline Patient

PubMed Central

ZANARINI, MARY C.; FRANKENBURG, FRANCES R.

1994-01-01

The authors define a new defense mechanism, emotional hypochondriasis, that is hypothesized to be central to borderline psychopathology. The behavioral manifestation of this defense—the hyperbolic stance of the borderline patient—is also defined and related to the complex phenomenology of borderline personality disorder. Borderline patients are seen as making an active attempt to maintain a tolerable, if tenuous, adaptation in the face of tremendous subjective emotional pain that has been shaped in large measure by traumatic childhood events that have never been validated. Twelve treatment implications and three expectable, if overlapping, stages of treatment stemming from the use of this defense and its behavioral sequelae are detailed. PMID:22700171

Bessel Plasmon-Polaritons at the Boundaries of Metamaterials with Near-Zero Dielectric Constants

NASA Astrophysics Data System (ADS)

Kurilkina, S. N.; Belyi, V. N.; Kazak, N. S.; Binhussain, M. A.

2015-07-01

The conditions for and features of the excitation of Bessel plasmon-polaritons (BPP) are examined at the boundary of a hyperbolic metamaterial with a near-zero dielectric constant made of a dielectric matrix with metal nanorods embedded in it normal to its surface. This material is compared with BPP that have traditional surface plasmons. The effect of the absorption of the metamaterial on the excitation of BPP is studied. The possibility of changes in the direction of the radial energy fl ows in BPP excited at the surface of an isotropic medium, a hyperbolic metamaterial, is demonstrated and the conditions for these changes are determined.

Self-adjusting grid methods for one-dimensional hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.; Hyman, J. M.

1983-01-01

The automatic adjustment of a grid which follows the dynamics of the numerical solution of hyperbolic conservation laws is given. The grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals. The resulting algorithm is a simple extension of many currently popular Godunov-type methods. Computer codes using one of these methods can be easily modified to add the moving mesh as an option. Numerical examples are given that illustrate the improved accuracy of Godunov's and Roe's methods on a self-adjusting mesh. Previously announced in STAR as N83-15008

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

PubMed

Biala, T A; Jator, S N

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

O(2) Hopf bifurcation of viscous shock waves in a channel

NASA Astrophysics Data System (ADS)

Pogan, Alin; Yao, Jinghua; Zumbrun, Kevin

2015-07-01

Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O(2) transverse Hopf bifurcation, or "cellular instability", of viscous shock waves in a channel, for a class of quasilinear hyperbolic-parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fréchet differentiability of the time- T solution operator by appropriate hyperbolic-parabolic energy estimates, and (ii) handle O(2) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic-parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov-Schmidt reduction of the time- T map, yielding a four-dimensional problem with O(2) plus approximate S1 symmetry, which we treat "by hand" using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.

Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jan Hesthaven

2012-02-06

Final report for DOE Contract DE-FG02-98ER25346 entitled Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences. Principal Investigator Jan S. Hesthaven Division of Applied Mathematics Brown University, Box F Providence, RI 02912 Jan.Hesthaven@Brown.edu February 6, 2012 Note: This grant was originally awarded to Professor David Gottlieb and the majority of the work envisioned reflects his original ideas. However, when Prof Gottlieb passed away in December 2008, Professor Hesthaven took over as PI to ensure proper mentoring of students and postdoctoral researchers already involved in the project. This unusual circumstance has naturally impacted themore » project and its timeline. However, as the report reflects, the planned work has been accomplished and some activities beyond the original scope have been pursued with success. Project overview and main results The effort in this project focuses on the development of high order accurate computational methods for the solution of hyperbolic equations with application to problems with strong shocks. While the methods are general, emphasis is on applications to gas dynamics with strong shocks.« less

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

NASA Astrophysics Data System (ADS)

Finster, Felix; Strohmaier, Alexander

2015-08-01

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

Delay, probability, and social discounting in a public goods game.

PubMed

Jones, Bryan A; Rachlin, Howard

2009-01-01

A human social discount function measures the value to a person of a reward to another person at a given social distance. Just as delay discounting is a hyperbolic function of delay, and probability discounting is a hyperbolic function of odds-against, social discounting is a hyperbolic function of social distance. Experiment 1 obtained individual social, delay, and probability discount functions for a hypothetical $75 reward; participants also indicated how much of an initial $100 endowment they would contribute to a common investment in a public good. Steepness of discounting correlated, across participants, among all three discount dimensions. However, only social and probability discounting were correlated with the public-good contribution; high public-good contributors were more altruistic and also less risk averse than low contributors. Experiment 2 obtained social discount functions with hypothetical $75 rewards and delay discount functions with hypothetical $1,000 rewards, as well as public-good contributions. The results replicated those of Experiment 1; steepness of the two forms of discounting correlated with each other across participants but only social discounting correlated with the public-good contribution. Most participants in Experiment 2 predicted that the average contribution would be lower than their own contribution.

Gummel Symmetry Test on charge based drain current expression using modified first-order hyperbolic velocity-field expression

NASA Astrophysics Data System (ADS)

Singh, Kirmender; Bhattacharyya, A. B.

2017-03-01

Gummel Symmetry Test (GST) has been a benchmark industry standard for MOSFET models and is considered as one of important tests by the modeling community. BSIM4 MOSFET model fails to pass GST as the drain current equation is not symmetrical because drain and source potentials are not referenced to bulk. BSIM6 MOSFET model overcomes this limitation by taking all terminal biases with reference to bulk and using proper velocity saturation (v -E) model. The drain current equation in BSIM6 is charge based and continuous in all regions of operation. It, however, adopts a complicated method to compute source and drain charges. In this work we propose to use conventional charge based method formulated by Enz for obtaining simpler analytical drain current expression that passes GST. For this purpose we adopt two steps: (i) In the first step we use a modified first-order hyperbolic v -E model with adjustable coefficients which is integrable, simple and accurate, and (ii) In the second we use a multiplying factor in the modified first-order hyperbolic v -E expression to obtain correct monotonic asymptotic behavior around the origin of lateral electric field. This factor is of empirical form, which is a function of drain voltage (vd) and source voltage (vs) . After considering both the above steps we obtain drain current expression whose accuracy is similar to that obtained from second-order hyperbolic v -E model. In modified first-order hyperbolic v -E expression if vd and vs is replaced by smoothing functions for the effective drain voltage (vdeff) and effective source voltage (vseff), it will as well take care of discontinuity between linear to saturation regions of operation. The condition of symmetry is shown to be satisfied by drain current and its higher order derivatives, as both of them are odd functions and their even order derivatives smoothly pass through the origin. In strong inversion region and technology node of 22 nm the GST is shown to pass till sixth-order derivative and for weak inversion it is shown till fifth-order derivative. In the expression of drain current major short channel phenomena like vertical field mobility reduction, velocity saturation and velocity overshoot have been taken into consideration.

Waves in hyperbolic and double negative metamaterials including rogues and solitons

NASA Astrophysics Data System (ADS)

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

2017-11-01

The topics here deal with some current progress in electromagnetic wave propagation in a family of substances known as metamaterials. To begin with, it is discussed how a pulse can develop a leading edge that steepens and it is emphasised that such self-steepening is an important inclusion within a metamaterial environment together with Raman scattering and third-order dispersion whenever very short pulses are being investigated. It is emphasised that the self-steepening parameter is highly metamaterial-driven compared to Raman scattering, which is associated with a coefficient of the same form whether a normal positive phase, or a metamaterial waveguide is the vehicle for any soliton propagation. It is also shown that the influence of magnetooptics provides a beautiful and important control mechanism for metamaterial devices and that, in the future, this feature will have a significant impact upon the design of data control systems for optical computing. A major objective is fulfiled by the investigations of the fascinating properties of hyperbolic media that exhibit asymmetry of supported modes due to the tilt of optical axes. This is a topic that really merits elaboration because structural and optical asymmetry in optical components that end up manipulating electromagnetic waves is now the foundation of how to operate some of the most successful devices in photonics and electronics. It is pointed out, in this context, that graphene is one of the most famous plasmonic media with very low losses. It is a two-dimensional material that makes the implementation of an effective-medium approximation more feasible. Nonlinear non-stationary diffraction in active planar anisotropic hyperbolic metamaterials is discussed in detail and two approaches are compared. One of them is based on the averaging over a unit cell, while the other one does not include sort of averaging. The formation and propagation of optical spatial solitons in hyperbolic metamaterials is also considered with a model of the response of hyperbolic metamaterials in terms of the homogenisation (‘effective medium’) approach. The model has a macroscopic dielectric tensor encompassing at least one negative eigenvalue. It is shown that light propagating in the presence of hyperbolic dispersion undergoes negative (anomalous) diffraction. The theory is ten broadened out to include the influence of the orientation of the optical axis with respect to the propagation wave vector. Optical rogue waves are discussed in terms of how they are influenced, but not suppressed, by a metamaterial background. It is strongly discussed that metamaterials and optical rogue waves have both been making headlines in recent years and that they are, separately, large areas of research to study. A brief background of the inevitable linkage of them is considered and important new possibilities are discussed. After this background is revealed some new rogue wave configurations combining the two areas are presented alongside a discussion of the way forward for the future.

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nordström, Jan, E-mail: jan.nordstrom@liu.se; Wahlsten, Markus, E-mail: markus.wahlsten@liu.se

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for themore » Euler equations.« less

A model and numerical method for compressible flows with capillary effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidmayer, Kevin, E-mail: kevin.schmidmayer@univ-amu.fr; Petitpas, Fabien, E-mail: fabien.petitpas@univ-amu.fr; Daniel, Eric, E-mail: eric.daniel@univ-amu.fr

2017-04-01

A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results onmore » droplet breakup induced by a shock wave.« less

OVERGRID: A Unified Overset Grid Generation Graphical Interface

NASA Technical Reports Server (NTRS)

Chan, William M.; Akien, Edwin W. (Technical Monitor)

1999-01-01

This paper presents a unified graphical interface and gridding strategy for performing overset grid generation. The interface called OVERGRID has been specifically designed to follow an efficient overset gridding strategy, and contains general grid manipulation capabilities as well as modules that are specifically suited for overset grids. General grid utilities include functions for grid redistribution, smoothing, concatenation, extraction, extrapolation, projection, and many others. Modules specially tailored for overset grids include a seam curve extractor, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, and a Cartesian box grid generator, Grid visualization is achieved using OpenGL while widgets are constructed with Tcl/Tk. The software is portable between various platforms from UNIX workstations to personal computers.

Nonimaging radiant energy device

DOEpatents

Winston, Roland; Ning, Xiaohui

1993-01-01

A nonimaging radiant energy device may include a hyperbolically shaped reflective element with a radiant energy inlet and a radiant energy outlet. A convex lens is provided at the radiant energy inlet and a concave lens is provided at the radiant energy outlet. Due to the provision of the lenses and the shape of the walls of the reflective element, the radiant energy incident at the radiant energy inlet within a predetermined angle of acceptance is emitted from the radiant energy outlet exclusively within an acute exit angle. In another embodiment, the radiant energy device may include two interconnected hyperbolically shaped reflective elements with a respective convex lens being provided at each aperture of the device.

Nonimaging radiant energy device

DOEpatents

Winston, Roland; Ning, Xiaohui

1996-01-01

A nonimaging radiant energy device may include a hyperbolically shaped reflective element with a radiant energy inlet and a radiant energy outlet. A convex lens is provided at the radiant energy inlet and a concave lens is provided at the radiant energy outlet. Due to the provision of the lenses and the shape of the walls of the reflective element, the radiant energy incident at the radiant energy inlet within a predetermined angle of acceptance is emitted from the radiant energy outlet exclusively within an acute exit angle. In another embodiment, the radiant energy device may include two interconnected hyperbolically shaped reflective elements with a respective convex lens being provided at each aperture of the device.

Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Mahak, Nadia

2018-06-01

The nonlinear Schrödinger equation (NLSE) with the aid of three order dispersion terms is investigated to find the exact solutions via the extended (G'/G2)-expansion method and the first integral method. Many exact traveling wave solutions, such as trigonometric, hyperbolic, rational, soliton and complex function solutions, are characterized with some free parameters of the problem studied. It is corroborated that the proposed techniques are manageable, straightforward and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Some figures are plotted to describe the propagation of traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions.

A Note on Expansiveness and Hyperbolicity for Generic Geodesic Flows

NASA Astrophysics Data System (ADS)

Bessa, Mário

2018-06-01

In this short note we contribute to the generic dynamics of geodesic flows associated to metrics on compact Riemannian manifolds of dimension ≥ 2. We prove that there exists a C 2-residual subset R of metrics on a given compact Riemannian manifold such that if g\\in R, then its associated geodesic flow φ tg is expansive if and only if the closure of the set of periodic orbits of φtg is a uniformly hyperbolic set. For surfaces, we obtain a stronger statement: there exists a C 2-residual R such that if g\\in R, then its associated geodesic flow φtg is expansive if and only if φtg is an Anosov flow.

A Novel Higher Order Artificial Neural Networks

NASA Astrophysics Data System (ADS)

Xu, Shuxiang

2010-05-01

In this paper a new Higher Order Neural Network (HONN) model is introduced and applied in several data mining tasks. Data Mining extracts hidden patterns and valuable information from large databases. A hyperbolic tangent function is used as the neuron activation function for the new HONN model. Experiments are conducted to demonstrate the advantages and disadvantages of the new HONN model, when compared with several conventional Artificial Neural Network (ANN) models: Feedforward ANN with the sigmoid activation function; Feedforward ANN with the hyperbolic tangent activation function; and Radial Basis Function (RBF) ANN with the Gaussian activation function. The experimental results seem to suggest that the new HONN holds higher generalization capability as well as abilities in handling missing data.

Spectral approach to homogenization of hyperbolic equations with periodic coefficients

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Current from a nano-gap hyperbolic diode using shape-factors: Theory

NASA Astrophysics Data System (ADS)

Jensen, Kevin L.; Shiffler, Donald A.; Peckerar, Martin; Harris, John R.; Petillo, John J.

2017-08-01

Quantum tunneling by field emission from nanoscale features or sharp field emission structures for which the anode-cathode gap is nanometers in scale ("nano diodes") experience strong deviations from the planar image charge lowered tunneling barrier used in the Murphy and Good formulation of the Fowler-Nordheim equation. These deviations alter the prediction of total current from a curved surface. Modifications to the emission barrier are modeled using a hyperbolic (prolate spheroidal) geometry to determine the trajectories along which the Gamow factor in a WKB-like treatment is undertaken; a quadratic equivalent potential is determined, and a method of shape factors is used to evaluate the corrected total current from a protrusion or wedge geometry.

Demonstrator of atmospheric reentry system with hyperbolic velocity—DASH

NASA Astrophysics Data System (ADS)

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

2003-01-01

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

An improved numerical method for the kernel density functional estimation of disperse flow

NASA Astrophysics Data System (ADS)

Smith, Timothy; Ranjan, Reetesh; Pantano, Carlos

2014-11-01

We present an improved numerical method to solve the transport equation for the one-point particle density function (pdf), which can be used to model disperse flows. The transport equation, a hyperbolic partial differential equation (PDE) with a source term, is derived from the Lagrangian equations for a dilute particle system by treating position and velocity as state-space variables. The method approximates the pdf by a discrete mixture of kernel density functions (KDFs) with space and time varying parameters and performs a global Rayleigh-Ritz like least-square minimization on the state-space of velocity. Such an approximation leads to a hyperbolic system of PDEs for the KDF parameters that cannot be written completely in conservation form. This system is solved using a numerical method that is path-consistent, according to the theory of non-conservative hyperbolic equations. The resulting formulation is a Roe-like update that utilizes the local eigensystem information of the linearized system of PDEs. We will present the formulation of the base method, its higher-order extension and further regularization to demonstrate that the method can predict statistics of disperse flows in an accurate, consistent and efficient manner. This project was funded by NSF Project NSF-DMS 1318161.

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

NASA Technical Reports Server (NTRS)

Goodrich, John W.

1995-01-01

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1986-01-01

A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Macías-Díaz, Jorge E.; Kofané, Timoléon Crépin

2018-03-01

We investigate analytically and numerically the conditions for wave instabilities in a hyperbolic activator-inhibitor system with species undergoing anomalous superdiffusion. In the present work, anomalous superdiffusion is modeled using the two-dimensional Weyl fractional operator, with derivative orders α ∈ [1,2]. We perform a linear stability analysis and derive the conditions for diffusion-driven wave instabilities. Emphasis is placed on the effect of the superdiffusion exponent α , the diffusion ratio d , and the inertial time τ . As the superdiffusive exponent increases, so does the wave number of the Turing instability. Opposite to the requirement for Turing instability, the activator needs to diffuse sufficiently faster than the inhibitor in order for the wave instability to occur. The critical wave number for wave instability decreases with the superdiffusive exponent and increases with the inertial time. The maximum value of the inertial time for a wave instability to occur in the system is τmax=3.6 . As one of the main results of this work, we conclude that both anomalous diffusion and inertial time influence strongly the conditions for wave instabilities in hyperbolic fractional reaction-diffusion systems. Some numerical simulations are conducted as evidence of the analytical predictions derived in this work.

Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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

2017-07-21

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

Sustained fitness gains and variability in fitness trajectories in the long-term evolution experiment with Escherichia coli

PubMed Central

Lenski, Richard E.; Wiser, Michael J.; Ribeck, Noah; Blount, Zachary D.; Nahum, Joshua R.; Morris, J. Jeffrey; Zaman, Luis; Turner, Caroline B.; Wade, Brian D.; Maddamsetti, Rohan; Burmeister, Alita R.; Baird, Elizabeth J.; Bundy, Jay; Grant, Nkrumah A.; Card, Kyle J.; Rowles, Maia; Weatherspoon, Kiyana; Papoulis, Spiridon E.; Sullivan, Rachel; Clark, Colleen; Mulka, Joseph S.; Hajela, Neerja

2015-01-01

Many populations live in environments subject to frequent biotic and abiotic changes. Nonetheless, it is interesting to ask whether an evolving population's mean fitness can increase indefinitely, and potentially without any limit, even in a constant environment. A recent study showed that fitness trajectories of Escherichia coli populations over 50 000 generations were better described by a power-law model than by a hyperbolic model. According to the power-law model, the rate of fitness gain declines over time but fitness has no upper limit, whereas the hyperbolic model implies a hard limit. Here, we examine whether the previously estimated power-law model predicts the fitness trajectory for an additional 10 000 generations. To that end, we conducted more than 1100 new competitive fitness assays. Consistent with the previous study, the power-law model fits the new data better than the hyperbolic model. We also analysed the variability in fitness among populations, finding subtle, but significant, heterogeneity in mean fitness. Some, but not all, of this variation reflects differences in mutation rate that evolved over time. Taken together, our results imply that both adaptation and divergence can continue indefinitely—or at least for a long time—even in a constant environment. PMID:26674951

Micro-scale extensional rheometry using hyperbolic converging/diverging channels and jet breakup

PubMed Central

Keshavarz, Bavand

2016-01-01

Understanding the elongational rheology of dilute polymer solutions plays an important role in many biological and industrial applications ranging from microfluidic lab-on-a-chip diagnostics to phenomena such as fuel atomization and combustion. Making quantitative measurements of the extensional viscosity for dilute viscoelastic fluids is a long-standing challenge and it motivates developments in microfluidic fabrication techniques and high speed/strobe imaging of millifluidic capillary phenomena in order to develop new classes of instruments. In this paper, we study the elongational rheology of a family of dilute polymeric solutions in two devices: first, steady pressure-driven flow through a hyperbolic microfluidic contraction/expansion and, second, the capillary driven breakup of a thin filament formed from a small diameter jet (Dj∼O(100 μm)). The small length scale of the device allows very large deformation rates to be achieved. Our results show that in certain limits of low viscosity and elasticity, jet breakup studies offer significant advantages over the hyperbolic channel measurements despite the more complex implementation. Using our results, together with scaling estimates of the competing viscous, elastic, inertial and capillary timescales that control the dynamics, we construct a dimensionless map or nomogram summarizing the operating space for each instrument. PMID:27375824

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations

NASA Astrophysics Data System (ADS)

Müller, Ingo

2008-12-01

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

On the hyperbolicity and stability of 3+1 formulations of metric f( R) gravity

NASA Astrophysics Data System (ADS)

Mongwane, Bishop

2016-11-01

3+1 formulations of the Einstein field equations have become an invaluable tool in Numerical relativity, having been used successfully in modeling spacetimes of black hole collisions, stellar collapse and other complex systems. It is plausible that similar considerations could prove fruitful for modified gravity theories. In this article, we pursue from a numerical relativistic viewpoint the 3+1 formulation of metric f( R) gravity as it arises from the fourth order equations of motion, without invoking the dynamical equivalence with Brans-Dicke theories. We present the resulting system of evolution and constraint equations for a generic function f( R), subject to the usual viability conditions. We confirm that the time propagation of the f( R) Hamiltonian and Momentum constraints take the same Mathematical form as in general relativity, irrespective of the f( R) model. We further recast the 3+1 system in a form akin to the BSSNOK formulation of numerical relativity. Without assuming any specific model, we show that the ADM version of f( R) is weakly hyperbolic and is plagued by similar zero speed modes as in the general relativity case. On the other hand the BSSNOK version is strongly hyperbolic and hence a promising formulation for numerical simulations in metric f( R) theories.

Human red blood cell behavior under homogeneous extensional flow in a hyperbolic-shaped microchannel.

PubMed

Yaginuma, T; Oliveira, M S N; Lima, R; Ishikawa, T; Yamaguchi, T

2013-01-01

It is well known that certain pathological conditions result in a decrease of red blood cells (RBCs) deformability and subsequently can significantly alter the blood flow in microcirculation, which may block capillaries and cause ischemia in the tissues. Microfluidic systems able to obtain reliable quantitative measurements of RBC deformability hold the key to understand and diagnose RBC related diseases. In this work, a microfluidic system composed of a microchannel with a hyperbolic-shaped contraction followed by a sudden expansion is presented. We provide a detailed quantitative description of the degree of deformation of human RBCs under a controlled homogeneous extensional flow field. We measured the deformation index (DI) as well as the velocity of the RBCs travelling along the centerline of the channel for four different flow rates and analyze the impact of the particle Reynolds number. The results show that human RBC deformation tends to reach a plateau value in the region of constant extensional rate, the value of which depends on the extension rate. Additionally, we observe that the presence of a sudden expansion downstream of the hyperbolic contraction modifies the spatial distribution of cells and substantially increases the cell free layer (CFL) downstream of the expansion plane similarly to what is seen in other expansion flows. Beyond a certain value of flow rate, there is only a weak effect of inlet flow rates on the enhancement of the downstream CFL. These in vitro experiments show the potential of using microfluidic systems with hyperbolic-shaped microchannels both for the separation of the RBCs from plasma and to assess changes in RBC deformability in physiological and pathological situations for clinical purposes. However, the selection of the geometry and the identification of the most suitable region to evaluate the changes on the RBC deformability under extensional flows are crucial if microfluidics is to be used as an in vitro clinical methodology to detect circulatory diseases.

Human red blood cell behavior under homogeneous extensional flow in a hyperbolic-shaped microchannel

PubMed Central

Yaginuma, T.; Oliveira, M. S. N.; Lima, R.; Ishikawa, T.; Yamaguchi, T.

2013-01-01

It is well known that certain pathological conditions result in a decrease of red blood cells (RBCs) deformability and subsequently can significantly alter the blood flow in microcirculation, which may block capillaries and cause ischemia in the tissues. Microfluidic systems able to obtain reliable quantitative measurements of RBC deformability hold the key to understand and diagnose RBC related diseases. In this work, a microfluidic system composed of a microchannel with a hyperbolic-shaped contraction followed by a sudden expansion is presented. We provide a detailed quantitative description of the degree of deformation of human RBCs under a controlled homogeneous extensional flow field. We measured the deformation index (DI) as well as the velocity of the RBCs travelling along the centerline of the channel for four different flow rates and analyze the impact of the particle Reynolds number. The results show that human RBC deformation tends to reach a plateau value in the region of constant extensional rate, the value of which depends on the extension rate. Additionally, we observe that the presence of a sudden expansion downstream of the hyperbolic contraction modifies the spatial distribution of cells and substantially increases the cell free layer (CFL) downstream of the expansion plane similarly to what is seen in other expansion flows. Beyond a certain value of flow rate, there is only a weak effect of inlet flow rates on the enhancement of the downstream CFL. These in vitro experiments show the potential of using microfluidic systems with hyperbolic-shaped microchannels both for the separation of the RBCs from plasma and to assess changes in RBC deformability in physiological and pathological situations for clinical purposes. However, the selection of the geometry and the identification of the most suitable region to evaluate the changes on the RBC deformability under extensional flows are crucial if microfluidics is to be used as an in vitro clinical methodology to detect circulatory diseases. PMID:24404073

Cation activation of the pig kidney sodium pump: transmembrane allosteric effects of sodium.

PubMed Central

Karlish, S J; Stein, W D

1985-01-01

We have studied activation by Na or Rb ions of different transport modes of the Na-K pump, using phospholipid vesicles reconstituted with pig kidney Na-K-ATPase. The shape of the activation curves, sigmoid or quasi-hyperbolic, depends on the nature of the cation at the opposite surface and not on the specific mode of transport. ATP-dependent Na uptake into K-containing vesicles (Na-K exchange) is activated by cytoplasmic Na along a highly sigmoid curve in the absence of extracellular Na (Hill number, nH = 1.9). Activation displays progressively less-sigmoid curves as extracellular Na is raised to 150 mM (nH = 1.2). The maximal rate of the Na-K exchange is not affected. Na is not transported from the extracellular face by the pump in the presence of excess extracellular K, and the transmembrane effects of the extracellular Na are therefore 'allosteric' in nature. ATP-dependent Na-Na exchange (Lee & Blostein, 1980) and classical ATP-plus-ADP-dependent Na-Na exchange are activated by cytoplasmic Na along hyperbolic curves. ATP-dependent Na uptake into Tris-containing vesicles is activated by cytoplasmic Na along a somewhat sigmoidal curve. (ATP + Pi)-dependent Rb-Rb exchange is activated by cytoplasmic and extracellular Rb along strictly hyperbolic curves. The same applies for Rb-Rb exchange in the presence or absence of ATP or Pi alone. The presence of a high concentration of extracellular Na together with extracellular Rb induces a sigmoidal activation by cytoplasmic Rb of (ATP + Pi)-dependent Rb-Rb exchange (nH = 1.45) but does not affect the maximal rate of exchange. Slow passive Rb fluxes through the pump observed in the absence of other pump ligands (see Karlish & Stein, 1982 alpha) are activated by cytoplasmic Rb along a strictly hyperbolic curve with extracellular Rb, nH = 1.0 (Rb-Rb exchange), along a strongly sigmoid curve with extracellular Na, nH = 1.5 (Rb-Na exchange), and along less-sigmoid curves with extracellular Tris, nH = 1.24 (net Rb flux) or extracellular Li, nH = 1.2 (Rb-Li exchange). Activation of the passive Rb fluxes by extracellular Rb is hyperbolic in the presence of cytoplasmic Rb, Li or Tris but is sigmoid in the presence of cytoplasmic Na (nH = 1.36). Inhibition by cytoplasmic Na of passive Rb fluxes from the cytoplasmic to the extracellular face of the pump depends on the nature of the cation at the extracellular surface.(ABSTRACT TRUNCATED AT 400 WORDS) PMID:2582111

PEG Enhancement for EM1 and EM2+ Missions

NASA Technical Reports Server (NTRS)

Von der Porten, Paul; Ahmad, Naeem; Hawkins, Matt

2018-01-01

NASA is currently building the Space Launch System (SLS) Block-1 launch vehicle for the Exploration Mission 1 (EM-1) test flight. The next evolution of SLS, the Block-1B Exploration Mission 2 (EM-2), is currently being designed. The Block-1 and Block-1B vehicles will use the Powered Explicit Guidance (PEG) algorithm. Due to the relatively low thrust-to-weight ratio of the Exploration Upper Stage (EUS), certain enhancements to the Block-1 PEG algorithm are needed to perform Block-1B missions. In order to accommodate mission design for EM-2 and beyond, PEG has been significantly improved since its use on the Space Shuttle program. The current version of PEG has the ability to switch to different targets during Core Stage (CS) or EUS flight, and can automatically reconfigure for a single Engine Out (EO) scenario, loss of communication with the Launch Abort System (LAS), and Inertial Navigation System (INS) failure. The Thrust Factor (TF) algorithm uses measured state information in addition to a priori parameters, providing PEG with an improved estimate of propulsion information. This provides robustness against unknown or undetected engine failures. A loft parameter input allows LAS jettison while maximizing payload mass. The current PEG algorithm is now able to handle various classes of missions with burn arcs much longer than were seen in the shuttle program. These missions include targeting a circular LEO orbit with a low-thrust, long-burn-duration upper stage, targeting a highly eccentric Trans-Lunar Injection (TLI) orbit, targeting a disposal orbit using the low-thrust Reaction Control System (RCS), and targeting a hyperbolic orbit. This paper will describe the design and implementation of the TF algorithm, the strategy to handle EO in various flight regimes, algorithms to cover off-nominal conditions, and other enhancements to the Block-1 PEG algorithm. This paper illustrates challenges posed by the Block-1B vehicle, and results show that the improved PEG algorithm is capable for use on the SLS Block 1-B vehicle as part of the Guidance, Navigation, and Control System.

Existence and Regularity Results for the Inviscid Primitive Equations with Lateral Periodicity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamouda, Makram, E-mail: mahamoud@indiana.edu; Jung, Chang-Yeol, E-mail: changyeoljung@gmail.com; Temam, Roger, E-mail: temam@indiana.edu

2016-06-15

The article is devoted to prove the existence and regularity of the solutions of the 3D inviscid Linearized Primitive Equations (LPEs) in a channel with lateral periodicity. This was assumed in a previous work (Hamouda et al. in Discret Contin Dyn Syst Ser S 6(2):401–422, 2013) which is concerned with the boundary layers generated by the corresponding viscous problem. Although the equations under investigation here are of hyperbolic type, the standard methods do not apply because of the specificity of the hyperbolic system. A set of non-local boundary conditions for the inviscid LPEs has to be imposed at the lateralmore » boundary of the channel making thus the system well-posed.« less

Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws

NASA Astrophysics Data System (ADS)

Barré, J.; Bernardin, C.; Chetrite, R.

2018-02-01

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31-45, 2010). When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a more general weak solution, and leave the general large deviation function upper bound as a conjecture.

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Lustman, L.; Tadmor, E.

1986-01-01

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

NASA Astrophysics Data System (ADS)

Huang, Juntao; Shu, Chi-Wang

2018-05-01

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu [43]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.

LETTER TO THE EDITOR: Landau levels on the hyperbolic plane

NASA Astrophysics Data System (ADS)

Fakhri, H.; Shariati, M.

2004-11-01

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

Tunable graphene-based hyperbolic metamaterial operating in SCLU telecom bands.

PubMed

Janaszek, Bartosz; Tyszka-Zawadzka, Anna; Szczepański, Paweł

2016-10-17

The tunability of graphene-based hyperbolic metamaterial structure operating in SCLU telecom bands is investigated. For the first time it has been shown that for the proper design of a graphene/dielectric multilayer stack, the HMM Type I, Epsilon-Near-Zero and Type II regimes are possible by changing the biasing potential. Numerical results reveal the effect of structure parameters such as the thickness of the dielectric layer as well as a number of graphene sheets in a unit cell (i.e., dielectric/graphene bilayer) on the tunability range and shape of the dispersion characteristics (i.e., Type I/ENZ/Type II) in SCLU telecom bands. This kind of materials could offer a technological platform for novel devices having various applications in optical communications technology.

Hyperbolic Interfaces

NASA Astrophysics Data System (ADS)

Giomi, Luca

2012-09-01

Fluid interfaces, such as soap films, liquid droplets, or lipid membranes, are known to give rise to several special geometries, whose complexity and beauty continue to fascinate us, as observers of the natural world, and challenge us as scientists. Here I show that a special class of surfaces of constant negative Gaussian curvature can be obtained in fluid interfaces equipped with an orientational ordered phase. These arise in various soft and biological materials, such as nematic liquid crystals, cytoskeletal assemblies, or hexatic colloidal suspensions. The purely hyperbolic morphology originates from the competition between surface tension, that reduces the area of the interface at the expense of increasing its Gaussian curvature, and the orientational elasticity of the ordered phase, that in turn suffers for the distortion induced by the underlying curvature.

Encke-Beta Predictor for Orion Burn Targeting and Guidance

NASA Technical Reports Server (NTRS)

Robinson, Shane; Scarritt, Sara; Goodman, John L.

2016-01-01

The state vector prediction algorithm selected for Orion on-board targeting and guidance is known as the Encke-Beta method. Encke-Beta uses a universal anomaly (beta) as the independent variable, valid for circular, elliptical, parabolic, and hyperbolic orbits. The variable, related to the change in eccentric anomaly, results in integration steps that cover smaller arcs of the trajectory at or near perigee, when velocity is higher. Some burns in the EM-1 and EM-2 mission plans are much longer than burns executed with the Apollo and Space Shuttle vehicles. Burn length, as well as hyperbolic trajectories, has driven the use of the Encke-Beta numerical predictor by the predictor/corrector guidance algorithm in place of legacy analytic thrust and gravity integrals.

Hyperbolic geometry of cosmological attractors

NASA Astrophysics Data System (ADS)

Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei; Roest, Diederik

2015-08-01

Cosmological α attractors give a natural explanation for the spectral index ns of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r , consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial role of the hyperbolic geometry of the Poincaré disk or half plane in the supergravity construction. These geometries are isometric under Möbius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kähler potential frame that explicitly preserves this symmetry, enabling the inflaton to be light. Moreover, we include higher-order curvature deformations, which can stabilize a direction orthogonal to the inflationary trajectory. We illustrate this new framework by stabilizing the single superfield α attractors.

An intrinsic approach in the curved n-body problem: The negative curvature case

NASA Astrophysics Data System (ADS)

Diacu, Florin; Pérez-Chavela, Ernesto; Reyes Victoria, J. Guadalupe

We consider the motion of n point particles of positive masses that interact gravitationally on the 2-dimensional hyperbolic sphere, which has negative constant Gaussian curvature. Using the stereographic projection, we derive the equations of motion of this curved n-body problem in the Poincaré disk, where we study the elliptic relative equilibria. Then we obtain the equations of motion in the Poincaré upper half plane in order to analyze the hyperbolic and parabolic relative equilibria. Using techniques of Riemannian geometry, we characterize each of the above classes of periodic orbits. For n=2 and n=3 we recover some previously known results and find new qualitative results about relative equilibria that were not apparent in an extrinsic setting.

Multigrid methods for differential equations with highly oscillatory coefficients

NASA Technical Reports Server (NTRS)

Engquist, Bjorn; Luo, Erding

1993-01-01

New coarse grid multigrid operators for problems with highly oscillatory coefficients are developed. These types of operators are necessary when the characters of the differential equations on coarser grids or longer wavelengths are different from that on the fine grid. Elliptic problems for composite materials and different classes of hyperbolic problems are practical examples. The new coarse grid operators can be constructed directly based on the homogenized differential operators or hierarchically computed from the finest grid. Convergence analysis based on the homogenization theory is given for elliptic problems with periodic coefficients and some hyperbolic problems. These are classes of equations for which there exists a fairly complete theory for the interaction between shorter and longer wavelengths in the problems. Numerical examples are presented.

A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

NASA Technical Reports Server (NTRS)

Xu, Kun

1999-01-01

A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

A Hermite WENO reconstruction for fourth order temporal accurate schemes based on the GRP solver for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Du, Zhifang; Li, Jiequan

2018-02-01

This paper develops a new fifth order accurate Hermite WENO (HWENO) reconstruction method for hyperbolic conservation schemes in the framework of the two-stage fourth order accurate temporal discretization in Li and Du (2016) [13]. Instead of computing the first moment of the solution additionally in the conventional HWENO or DG approach, we can directly take the interface values, which are already available in the numerical flux construction using the generalized Riemann problem (GRP) solver, to approximate the first moment. The resulting scheme is fourth order temporal accurate by only invoking the HWENO reconstruction twice so that it becomes more compact. Numerical experiments show that such compactness makes significant impact on the resolution of nonlinear waves.

Generalized -deformed correlation functions as spectral functions of hyperbolic geometry

NASA Astrophysics Data System (ADS)

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.

Trivial dynamics in discrete-time systems: carrying simplex and translation arcs

NASA Astrophysics Data System (ADS)

Niu, Lei; Ruiz-Herrera, Alfonso

2018-06-01

In this paper we show that the dynamical behavior in (first octant) of the classical Kolmogorov systems of competitive type admitting a carrying simplex can be sometimes determined completely by the number of fixed points on the boundary and the local behavior around them. Roughly speaking, T has trivial dynamics (i.e. the omega limit set of any orbit is a connected set contained in the set of fixed points) provided T has exactly four hyperbolic nontrivial fixed points in with local attractors on the carrying simplex and local repellers on the carrying simplex; and there exists a unique hyperbolic fixed point in Int. Our results are applied to some classical models including the Leslie–Gower models, Atkinson-Allen systems and Ricker maps.

Multifunctional Hyperbolic Nanogroove Metasurface for Submolecular Detection.

PubMed

Jiang, Li; Zeng, Shuwen; Xu, Zhengji; Ouyang, Qingling; Zhang, Dao-Hua; Chong, Peter Han Joo; Coquet, Philippe; He, Sailing; Yong, Ken-Tye

2017-08-01

Metasurface serves as a promising plasmonic sensing platform for engineering the enhanced light-matter interactions. Here, a hyperbolic metasurface with the nanogroove structure in the subwavelength scale is designed. This metasurface is able to modify the wavefront and wavelength of surface plasmon wave with the variation of the nanogroove width or periodicity. At the specific optical frequency, surface plasmon polaritons are tightly confined and propagated with a diffraction-free feature due to the epsilon-near-zero effect. Most importantly, the groove hyperbolic metasurface can enhance the plasmonic sensing with an ultrahigh phase sensitivity of 30 373 deg RIU -1 and Goos-Hänchen shift sensitivity of 10.134 mm RIU -1 . The detection resolution for refractive index change of glycerol solution is achieved as 10 -8 RIU based on the phase measurement. The detection limit of bovine serum albumin (BSA) molecule is measured as low as 0.1 × 10 -18 m (1 × 10 -19 mol L -1 ), which corresponds to a submolecular detection level (0.13 BSA mm -2 ). As for low-weight biotin molecule, the detection limit is estimated below 1 × 10 -15 m (1 × 10 -15 mol L -1 , 1300 biotin mm -2 ). This enhanced plasmonic sensing performance is two orders of magnitude higher than those with current state-of-art plasmonic metamaterials and metasurfaces. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal

PubMed Central

Sayem, Ayed Al; Rahman, Md. Masudur; Mahdy, M. R. C.; Jahangir, Ifat; Rahman, Md. Saifur

2016-01-01

In this article, we have theoretically investigated the performance of graphene-hexagonal Boron Nitride (hBN) multilayer structure (hyper crystal) to demonstrate all angle negative refraction along with superior transmission. hBN, one of the latest natural hyperbolic materials, can be a very strong contender to form a hyper crystal with graphene due to its excellence as a graphene-compatible substrate. Although bare hBN can exhibit negative refraction, the transmission is generally low due to its high reflectivity. Whereas due to graphene’s 2D nature and metallic characteristics in the frequency range where hBN behaves as a type-I hyperbolic material, we have found graphene-hBN hyper-crystals to exhibit all angle negative refraction with superior transmission. Interestingly, superior transmission from the whole structure can be fully controlled by the tunability of graphene without hampering the negative refraction originated mainly from hBN. We have also presented an effective medium description of the hyper crystal in the low-k limit and validated the proposed theory analytically and with full wave simulations. Along with the current extensive research on hybridization of graphene plasmon polaritons with (hyperbolic) hBN phonon polaritons, this work might have some substantial impact on this field of research and can be very useful in applications such as hyper-lensing. PMID:27146561

Storage and retrieval of time-entangled soliton trains in a three-level atom system coupled to an optical cavity

NASA Astrophysics Data System (ADS)

Welakuh, Davis D. M.; Dikandé, Alain M.

2017-11-01

The storage and subsequent retrieval of coherent pulse trains in the quantum memory (i.e. cavity-dark state) of three-level Λ atoms, are considered for an optical medium in which adiabatic photon transfer occurs under the condition of quantum impedance matching. The underlying mechanism is based on intracavity Electromagnetically-Induced Transparency, by which properties of a cavity filled with three-level Λ-type atoms are manipulated by an external control field. Under the impedance matching condition, we derive analytic expressions that suggest a complete transfer of an input field into the cavity-dark state by varying the mixing angle in a specific way, and its subsequent retrieval at a desired time. We illustrate the scheme by demonstrating the complete transfer and retrieval of a Gaussian, a single hyperbolic-secant and a periodic train of time-entangled hyperbolic-secant input photon pulses in the atom-cavity system. For the time-entangled hyperbolic-secant input field, a total controllability of the periodic evolution of the dark state population is made possible by changing the Rabi frequency of the classical driving field, thus allowing to alternately store and retrieve high-intensity photons from the optically dense Electromagnetically-Induced transparent medium. Such multiplexed photon states, which are expected to allow sharing quantum information among many users, are currently of very high demand for applications in long-distance and multiplexed quantum communication.

Synchronization of relativistic particles in the hyperbolic Kuramoto model

NASA Astrophysics Data System (ADS)

Ritchie, Louis M.; Lohe, M. A.; Williams, Anthony G.

2018-05-01

We formulate a noncompact version of the Kuramoto model by replacing the invariance group SO(2) of the plane rotations by the noncompact group SO(1, 1). The N equations of the system are expressed in terms of hyperbolic angles αi and are similar to those of the Kuramoto model, except that the trigonometric functions are replaced by hyperbolic functions. Trajectories are generally unbounded, nevertheless synchronization occurs for any positive couplings κi, arbitrary positive multiplicative parameters λi and arbitrary exponents ωi. There are no critical values for the coupling constants. We measure the onset of synchronization by means of several order and disorder parameters. We show numerically and by means of exact solutions for N = 2 that solutions can develop singularities if the coupling constants are negative, or if the initial values are not suitably restricted. We describe a physical interpretation of the system as a cluster of interacting relativistic particles in 1 + 1 dimensions, subject to linear repulsive forces with space-time trajectories parametrized by the rapidity αi. The trajectories synchronize provided that the particle separations remain predominantly time-like, and the synchronized cluster can be viewed as a bound state of N relativistic particle constituents. We extend the defining equations of the system to higher dimensions by means of vector equations which are covariant with respect to SO(p, q).

Hyperbolic Discounting: Value and Time Processes of Substance Abusers and Non-Clinical Individuals in Intertemporal Choice

PubMed Central

2014-01-01

The single parameter hyperbolic model has been frequently used to describe value discounting as a function of time and to differentiate substance abusers and non-clinical participants with the model's parameter k. However, k says little about the mechanisms underlying the observed differences. The present study evaluates several alternative models with the purpose of identifying whether group differences stem from differences in subjective valuation, and/or time perceptions. Using three two-parameter models, plus secondary data analyses of 14 studies with 471 indifference point curves, results demonstrated that adding a valuation, or a time perception function led to better model fits. However, the gain in fit due to the flexibility granted by a second parameter did not always lead to a better understanding of the data patterns and corresponding psychological processes. The k parameter consistently indexed group and context (magnitude) differences; it is thus a mixed measure of person and task level effects. This was similar for a parameter meant to index payoff devaluation. A time perception parameter, on the other hand, fluctuated with contexts in a non-predicted fashion and the interpretation of its values was inconsistent with prior findings that supported enlarged perceived delays for substance abusers compared to controls. Overall, the results provide mixed support for hyperbolic models of intertemporal choice in terms of the psychological meaning afforded by their parameters. PMID:25390941

Positivity of the universal pairing in 3 dimensions

NASA Astrophysics Data System (ADS)

Calegari, Danny; Freedman, Michael H.; Walker, Kevin

2010-01-01

Associated to a closed, oriented surface S is the complex vector space with basis the set of all compact, oriented 3 -manifolds which it bounds. Gluing along S defines a Hermitian pairing on this space with values in the complex vector space with basis all closed, oriented 3 -manifolds. The main result in this paper is that this pairing is positive, i.e. that the result of pairing a nonzero vector with itself is nonzero. This has bearing on the question of what kinds of topological information can be extracted in principle from unitary (2+1) -dimensional TQFTs. The proof involves the construction of a suitable complexity function c on all closed 3 -manifolds, satisfying a gluing axiom which we call the topological Cauchy-Schwarz inequality, namely that c(AB) le max(c(AA),c(BB)) for all A,B which bound S , with equality if and only if A=B . The complexity function c involves input from many aspects of 3 -manifold topology, and in the process of establishing its key properties we obtain a number of results of independent interest. For example, we show that when two finite-volume hyperbolic 3 -manifolds are glued along an incompressible acylindrical surface, the resulting hyperbolic 3 -manifold has minimal volume only when the gluing can be done along a totally geodesic surface; this generalizes a similar theorem for closed hyperbolic 3 -manifolds due to Agol-Storm-Thurston.

Jacobian-free approximate solvers for hyperbolic systems: Application to relativistic magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Castro, Manuel J.; Gallardo, José M.; Marquina, Antonio

2017-10-01

We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method, sharing most of it interesting features and being applicable to general hyperbolic systems. To test the properties of our schemes a number of numerical experiments involving the RMHD equations are presented, both in one and two dimensions. The obtained results are in good agreement with those found in the literature and show that our schemes are robust and accurate, running stable under a satisfactory time step restriction. It is worth emphasizing that, although this work focuses on RMHD, the proposed schemes are suitable to be applied to general hyperbolic systems.

Flow Visualization and Pattern Formation in Vertically Falling Liquid Films

NASA Astrophysics Data System (ADS)

Balakotaiah, Vemuri; Malamataris, Nikolaos

2008-11-01

Analytical results of a low-dimensional two equation h-q model and results of a direct numerical simulation of the transient two-dimensional Navier Stokes equations are presented for vertically falling liquid films along a solid wall. The numerical study aims at the elucidation of the hydrodynamics of the falling film. The analytical study aims at the calculation of the parameter space where pattern formation occurs for this flow. It has been found that when the wave amplitude exceeds a certain magnitude, flow reversal occurs in the film underneath the minimum of the waves [1]. The instantaneous vortical structures possess two hyperbolic points on the vertical wall and an elliptic point in the film. As the wave amplitude increases further, the elliptic point reaches the free surface of the film and two more hyperbolic points are formed in the free surface that replace the elliptic point. Between the two hyperbolic points on the free surface, the streamwise component of velocity is negative and the film is divided into asymmetric patterns of up and down flows. Depending on the value of the Kapitza number, these patterns are either stationary or oscillatory. Physical reasons for the influence of the Kapitza number on pattern formation are given. Movies are shown where the pattern formation is demonstrated. [1] N.A.Malamataris and V.Balakotaiah (2008), AIChE J., 54(7), p. 1725-1740

Numerical solution of chemically reactive non-Newtonian fluid flow: Dual stratification

NASA Astrophysics Data System (ADS)

Rehman, Khalil Ur; Malik, M. Y.; Khan, Abid Ali; Zehra, Iffat; Zahri, Mostafa; Tahir, M.

2017-12-01

We have found that only a few attempts are available in the literature relatively to the tangent hyperbolic fluid flow induced by stretching cylindrical surfaces. In particular, temperature and concentration stratification effects have not been investigated until now with respect to the tangent hyperbolic fluid model. Therefore, we have considered the tangent hyperbolic fluid flow induced by an acutely inclined cylindrical surface in the presence of both temperature and concentration stratification effects. To be more specific, the fluid flow is attained with the no slip condition, which implies that the bulk motion of the fluid particles is the same as the stretching velocity of a cylindrical surface. Additionally, the flow field situation is manifested with heat generation, mixed convection and chemical reaction effects. The flow partial differential equations give a complete description of the present problem. Therefore, to trace out the solution, a set of suitable transformations is introduced to convert these equations into ordinary differential equations. In addition, a self-coded computational algorithm is executed to inspect the numerical solution of these reduced equations. The effect logs of the involved parameters are provided graphically. Furthermore, the variations of the physical quantities are examined and given with the aid of tables. It is observed that the fluid temperature is a decreasing function of the thermal stratification parameter and a similar trend is noticed for the concentration via the solutal stratification parameter.

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

PubMed

Simões, Gustavo Ferreira; Catapreta, Cícero Antônio Antunes

2013-02-01

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

New approach of a traditional analysis for predicting near-exit jet liquid instabilities

NASA Astrophysics Data System (ADS)

Jaramillo, Guillermo; Collicott, Steven

2015-11-01

Traditional linear instability theory for round liquid jets requires an exit-plane velocity profile be assumed so as to derive the characteristic growth rates and wavelengths of instabilities. This requires solving an eigenvalue problem for the Rayleigh Equation. In this new approach, a hyperbolic tangent velocity profile is assumed at the exit-plane of a round jet and a comparison is made with a hyperbolic secant profile. Temporal and Spatial Stability Analysis (TSA and SSA respectively) are the employed analytical tools to compare results of predicted most-unstable wavelengths from the given analytical velocity profiles and from previous experimental work. The local relevance of the velocity profile in the near-exit region of a liquid jet and the validity of an inviscid formulation through the Rayleigh equation are discussed as well. A comparison of numerical accuracy is made between two different mathematical approaches for the hyperbolic tangent profile with and without the Ricatti transformation. Reynolds number based on the momentum thickness of the boundary layer at the exit plane non-dimensionalizes the problem and, the Re range, based on measurements by Portillo in 2011, is 185 to 600. Wavelength measurements are taken from Portillo's experiment. School of Mechanical Engineering at Universidad del Valle, supported by a grant from Fulbright and Colciencias. Ph.D. student at the School of Aeronautics and Astronautics Purdue University.

Arnold diffusion for smooth convex systems of two and a half degrees of freedom

NASA Astrophysics Data System (ADS)

Kaloshin, V.; Zhang, K.

2015-08-01

In the present note we announce a proof of a strong form of Arnold diffusion for smooth convex Hamiltonian systems. Let { T}2 be a 2-dimensional torus and B2 be the unit ball around the origin in { R}2 . Fix ρ > 0. Our main result says that for a ‘generic’ time-periodic perturbation of an integrable system of two degrees of freedom H_0(p)+\\varepsilon H_1(θ,p,t),\\quad θ\\in { T}^2, p\\in B^2, t\\in { T}={ R}/{ Z} , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in { T}2 × B2 × { T} , namely, a ρ-neighborhood of the orbit contains { T}2 × B2 × { T} . Our proof is a combination of geometric and variational methods. The fundamental elements of the construction are the usage of crumpled normally hyperbolic invariant cylinders from [9], flower and simple normally hyperbolic invariant manifolds from [36] as well as their kissing property at a strong double resonance. This allows us to build a ‘connected’ net of three-dimensional normally hyperbolic invariant manifolds. To construct diffusing orbits along this net we employ a version of the Mather variational method [41] equipped with weak KAM theory [28], proposed by Bernard in [7].

Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

NASA Technical Reports Server (NTRS)

Larson, V. H.

1982-01-01

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1989-01-01

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.

Stability of an abstract system of coupled hyperbolic and parabolic equations

NASA Astrophysics Data System (ADS)

Hao, Jianghao; Liu, Zhuangyi

2013-08-01

In this paper, we provide a complete stability analysis for an abstract system of coupled hyperbolic and parabolic equations = -Au + γ A^{α} θ, quad θ_t = -γ A^{α}u_t - kA^{β}θ, u(0) = u_0, quad u_t(0) = v_0, quad θ(0) = θ_0 where A is a self-adjoint, positive definite operator on a Hilbert space H. For {(α,β) in [0,1] × [0,1]} , the region of exponential stability had been identified in Ammar-Khodja et al. (ESAIM Control Optim Calc Var 4:577-593,1999). Our contribution is to show that the rest of the region can be classified as region of polynomial stability and region of instability. Moreover, we obtain the optimality of the order of polynomial stability.

Non-oscillatory central differencing for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Nessyahu, Haim; Tadmor, Eitan

1988-01-01

Many of the recently developed high resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block for these schemes is the averaging of an appropriate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the direction of the wind. Instead, the use of the more robust Lax-Friedrichs (LxF) solver is proposed. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. This is compensated for by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of results obtained by such convenient central differencing is comparable with those of the upwind schemes.

Efficiency of Launching Highly Confined Polaritons by Infrared Light Incident on a Hyperbolic Material.

PubMed

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.

Enhanced superconductivity in aluminum-based hyperbolic metamaterials

NASA Astrophysics Data System (ADS)

Smolyaninova, Vera; Jensen, Christopher; Zimmerman, William; Prestigiacomo, Joseph; Osofsky, Michael; Kim, Heungsoo; Bassim, Nabil; Xing, Zhen; Qazilbash, Mumtaz; Smolyaninov, Igor

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. This work was supported in part by NSF Grant DMR-1104676 and the School of Emerging Technologies at Towson University.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

Scattering on hyperbolic microspheres: From photonic nanojets to Poisson-Arago bright spots

NASA Astrophysics Data System (ADS)

Hodges, Reed; Dean, Cleon; Durach, Maxim

We investigate optical properties of metal-dielectric metamaterial microspheres composed of subwavelength spherical shells of two different materials alternating in an onion-layer fashion. Recently such metamaterial spheres were considered as cavities and their whispering gallery modes were investigated. We focus on the scattering of external radiation by the meta-micropheres in this work. We show that different scenarios are produced by altering the metal fraction in the spheres: as the microsphere transitions from all-dielectric to hyperbolic to all-metal, the photonic nanojets transform into Poisson-Arago bright spots. A new phenomenon also emerges as the percentage of metal in the microsphere increases. ``Hot spots'' of optical fields intensity appear at the center of the sphere. Their intensity is much higher than that of the incident plane wave.

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, W.; Almgren, A.; Bell, J.

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunovmore » scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.« less

Black hole evolution by spectral methods

NASA Astrophysics Data System (ADS)

Kidder, Lawrence E.; Scheel, Mark A.; Teukolsky, Saul A.; Carlson, Eric D.; Cook, Gregory B.

2000-10-01

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast with finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.

On the Rotation Period and Shape of the Hyperbolic Asteroid 1I/‘Oumuamua (2017 U1) from Its Lightcurve

NASA Astrophysics Data System (ADS)

Knight, Matthew M.; Protopapa, Silvia; Kelley, Michael S. P.; Farnham, Tony L.; Bauer, James M.; Bodewits, Dennis; Feaga, Lori M.; Sunshine, Jessica M.

2017-12-01

We observed the newly discovered hyperbolic minor planet 1I/‘Oumuamua (2017 U1) on 2017 October 30 with Lowell Observatory’s 4.3 m Discovery Channel Telescope. From these observations, we derived a partial lightcurve with a peak-to-trough amplitude of at least 1.2 mag. This lightcurve segment rules out rotation periods less than 3 hr and suggests that the period is at least 5 hr. On the assumption that the variability is due to a changing cross-section, the axial ratio is at least 3:1. We saw no evidence for a coma or tail in either individual images or in a stacked image having an equivalent exposure time of 9000 s.

Adaptive aperture for Geiger mode avalanche photodiode flash ladar systems.

PubMed

Wang, Liang; Han, Shaokun; Xia, Wenze; Lei, Jieyu

2018-02-01

Although the Geiger-mode avalanche photodiode (GM-APD) flash ladar system offers the advantages of high sensitivity and simple construction, its detection performance is influenced not only by the incoming signal-to-noise ratio but also by the absolute number of noise photons. In this paper, we deduce a hyperbolic approximation to estimate the noise-photon number from the false-firing percentage in a GM-APD flash ladar system under dark conditions. By using this hyperbolic approximation function, we introduce a method to adapt the aperture to reduce the number of incoming background-noise photons. Finally, the simulation results show that the adaptive-aperture method decreases the false probability in all cases, increases the detection probability provided that the signal exceeds the noise, and decreases the average ranging error per frame.

Adaptive aperture for Geiger mode avalanche photodiode flash ladar systems

NASA Astrophysics Data System (ADS)

Wang, Liang; Han, Shaokun; Xia, Wenze; Lei, Jieyu

2018-02-01

Although the Geiger-mode avalanche photodiode (GM-APD) flash ladar system offers the advantages of high sensitivity and simple construction, its detection performance is influenced not only by the incoming signal-to-noise ratio but also by the absolute number of noise photons. In this paper, we deduce a hyperbolic approximation to estimate the noise-photon number from the false-firing percentage in a GM-APD flash ladar system under dark conditions. By using this hyperbolic approximation function, we introduce a method to adapt the aperture to reduce the number of incoming background-noise photons. Finally, the simulation results show that the adaptive-aperture method decreases the false probability in all cases, increases the detection probability provided that the signal exceeds the noise, and decreases the average ranging error per frame.

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Rainbow Trapping in Hyperbolic Metamaterial Waveguide

PubMed Central

Hu, Haifeng; Ji, Dengxin; Zeng, Xie; Liu, Kai; Gan, Qiaoqiang

2013-01-01

The recent reported trapped “rainbow” storage of light using metamaterials and plasmonic graded surface gratings has generated considerable interest for on-chip slow light. The potential for controlling the velocity of broadband light in guided photonic structures opens up tremendous opportunities to manipulate light for optical modulation, switching, communication and light-matter interactions. However, previously reported designs for rainbow trapping are generally constrained by inherent difficulties resulting in the limited experimental realization of this intriguing effect. Here we propose a hyperbolic metamaterial structure to realize a highly efficient rainbow trapping effect, which, importantly, is not limited by those severe theoretical constraints required in previously reported insulator-negative-index-insulator, insulator-metal-insulator and metal-insulator-metal waveguide tapers, and therefore representing a significant promise to realize the rainbow trapping structure practically. PMID:23409240

Broadband Enhancement of Spontaneous Emission in Two-Dimensional Semiconductors Using Photonic Hypercrystals.

PubMed

Galfsky, Tal; Sun, Zheng; Considine, Christopher R; Chou, Cheng-Tse; Ko, Wei-Chun; Lee, Yi-Hsien; Narimanov, Evgenii E; Menon, Vinod M

2016-08-10

The low quantum yield observed in two-dimensional semiconductors of transition metal dichalcogenides (TMDs) has motivated the quest for approaches that can enhance the light emission from these systems. Here, we demonstrate broadband enhancement of spontaneous emission and increase in Raman signature from archetype two-dimensional semiconductors: molybdenum disulfide (MoS2) and tungsten disulfide (WS2) by placing the monolayers in the near field of a photonic hypercrystal having hyperbolic dispersion. Hypercrystals are characterized by a large broadband photonic density of states due to hyperbolic dispersion while having enhanced light in/out coupling by a subwavelength photonic crystal lattice. This dual advantage is exploited here to enhance the light emission from the 2D TMDs and can be utilized for developing light emitters and solar cells using two-dimensional semiconductors.

On the proof of the C 0-inextendibility of the Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Sbierski, Jan

2018-02-01

This article presents a streamlined version of the author’s original proof of the C 0-inextendibility of the maximal analytic Schwarzschild spacetime. Firstly, we deviate from the original proof by using the result, recently established in collaboration with Galloway and Ling, that given a C 0-extension of a globally hyperbolic spacetime, one can find a timelike geodesic that leaves this spacetime. This result much simplifies the proof of the inextendibility through the exterior region of the Schwarzschild spacetime. Secondly, we give a more flexible and shorter argument for the inextendibility through the interior region. Furthermore, we present a small new structural result for the boundary of a globally hyperbolic spacetime within a C 0-extension which serves as a new and simpler starting point for the proof.

Investigation of statistical iterative reconstruction for dedicated breast CT

PubMed Central

Makeev, Andrey; Glick, Stephen J.

2013-01-01

Purpose: Dedicated breast CT has great potential for improving the detection and diagnosis of breast cancer. Statistical iterative reconstruction (SIR) in dedicated breast CT is a promising alternative to traditional filtered backprojection (FBP). One of the difficulties in using SIR is the presence of free parameters in the algorithm that control the appearance of the resulting image. These parameters require tuning in order to achieve high quality reconstructions. In this study, the authors investigated the penalized maximum likelihood (PML) method with two commonly used types of roughness penalty functions: hyperbolic potential and anisotropic total variation (TV) norm. Reconstructed images were compared with images obtained using standard FBP. Optimal parameters for PML with the hyperbolic prior are reported for the task of detecting microcalcifications embedded in breast tissue. Methods: Computer simulations were used to acquire projections in a half-cone beam geometry. The modeled setup describes a realistic breast CT benchtop system, with an x-ray spectra produced by a point source and an a-Si, CsI:Tl flat-panel detector. A voxelized anthropomorphic breast phantom with 280 μm microcalcification spheres embedded in it was used to model attenuation properties of the uncompressed woman's breast in a pendant position. The reconstruction of 3D images was performed using the separable paraboloidal surrogates algorithm with ordered subsets. Task performance was assessed with the ideal observer detectability index to determine optimal PML parameters. Results: The authors' findings suggest that there is a preferred range of values of the roughness penalty weight and the edge preservation threshold in the penalized objective function with the hyperbolic potential, which resulted in low noise images with high contrast microcalcifications preserved. In terms of numerical observer detectability index, the PML method with optimal parameters yielded substantially improved performance (by a factor of greater than 10) compared to FBP. The hyperbolic prior was also observed to be superior to the TV norm. A few of the best-performing parameter pairs for the PML method also demonstrated superior performance for various radiation doses. In fact, using PML with certain parameter values results in better images, acquired using 2 mGy dose, than FBP-reconstructed images acquired using 6 mGy dose. Conclusions: A range of optimal free parameters for the PML algorithm with hyperbolic and TV norm-based potentials is presented for the microcalcification detection task, in dedicated breast CT. The reported values can be used as starting values of the free parameters, when SIR techniques are used for image reconstruction. Significant improvement in image quality can be achieved by using PML with optimal combination of parameters, as compared to FBP. Importantly, these results suggest improved detection of microcalcifications can be obtained by using PML with lower radiation dose to the patient, than using FBP with higher dose. PMID:23927318

Quantitative imaging technique using the layer-stripping algorithm

NASA Astrophysics Data System (ADS)

Beilina, L.

2017-07-01

We present the layer-stripping algorithm for the solution of the hyperbolic coefficient inverse problem (CIP). Our numerical examples show quantitative reconstruction of small tumor-like inclusions in two-dimensions.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Area distortion under certain classes of quasiconformal mappings.

PubMed

Hernández-Montes, Alfonso; Reséndis O, Lino F

2017-01-01

In this paper we study the hyperbolic and Euclidean area distortion of measurable sets under some classes of K -quasiconformal mappings from the upper half-plane and the unit disk onto themselves, respectively.

Critiquing Neoliberalism in Australian Universities

ERIC Educational Resources Information Center

Rea, Jeannie

2016-01-01

While students chanting "No cuts, No fees, No corporate universities" may be dismissed as youthful hyperbole by some, it is not as superficial a characterisation of the state of our public university system as it seems.

Cotton-type and joint invariants for linear elliptic systems.

PubMed

Aslam, A; Mahomed, F M

2013-01-01

Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.

Experimental validation of systematically designed acoustic hyperbolic meta material slab exhibiting negative refraction

NASA Astrophysics Data System (ADS)

Christiansen, Rasmus E.; Sigmund, Ole

2016-09-01

This Letter reports on the experimental validation of a two-dimensional acoustic hyperbolic metamaterial slab optimized to exhibit negative refractive behavior. The slab was designed using a topology optimization based systematic design method allowing for tailoring the refractive behavior. The experimental results confirm the predicted refractive capability as well as the predicted transmission at an interface. The study simultaneously provides an estimate of the attenuation inside the slab stemming from the boundary layer effects—insight which can be utilized in the further design of the metamaterial slabs. The capability of tailoring the refractive behavior opens possibilities for different applications. For instance, a slab exhibiting zero refraction across a wide angular range is capable of funneling acoustic energy through it, while a material exhibiting the negative refractive behavior across a wide angular range provides lensing and collimating capabilities.

Initial value formulation of dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

Delsate, Térence; Hilditch, David; Witek, Helvi

2015-01-01

We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.

Optimal heliocentric trajectories for solar sail with minimum area

NASA Astrophysics Data System (ADS)

Petukhov, Vyacheslav G.

2018-05-01

The fixed-time heliocentric trajectory optimization problem is considered for planar solar sail with minimum area. Necessary optimality conditions are derived, a numerical method for solving the problem is developed, and numerical examples of optimal trajectories to Mars, Venus and Mercury are presented. The dependences of the minimum area of the solar sail from the date of departure from the Earth, the time of flight and the departing hyperbolic excess of velocity are analyzed. In particular, for the rendezvous problem (approaching a target planet with zero relative velocity) with zero departing hyperbolic excess of velocity for a flight duration of 1200 days it was found that the minimum area-to-mass ratio should be about 12 m2/kg for trajectory to Venus, 23.5 m2/kg for the trajectory to Mercury and 25 m2/kg for trajectory to Mars.

An iterative Riemann solver for systems of hyperbolic conservation law s, with application to hyperelastic solid mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miller, Gregory H.

2003-08-06

In this paper we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military ballistics, dramatic differences are seen between the exact and approximate Riemann solution. The greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver, resulting in nonphysical entropy and temperature estimates. Several pathological conditions arise in commonmore » practice, and modifications to the method to handle these are discussed. These include points where genuine nonlinearity is lost, degeneracies, and eigenvector deficiencies that occur upon melting.« less

Effects of mode profile on tunneling and traversal of ultracold atoms through vacuum-induced potentials

NASA Astrophysics Data System (ADS)

Badshah, Fazal; Irfan, Muhammad; Qamar, Sajid; Qamar, Shahid

2016-04-01

We consider the resonant interaction of an ultracold two-level atom with an electromagnetic field inside a high-Q micromaser cavity. In particular, we study the tunneling and traversal of ultracold atoms through vacuum-induced potentials for secant hyperbolic square and sinusoidal cavity mode functions. The phase time which may be considered as an appropriate measure of the time required for the atoms to cross the cavity, significantly modifies with the change of cavity mode profile. For example, switching between the sub and superclassical behaviors in phase time can occur due to the mode function. Similarly, negative phase time appears for the transmission of the two-level atoms in both excited and ground states for secant hyperbolic square mode function which is in contrast to the mesa mode case.

Computation of Quasiperiodic Normally Hyperbolic Invariant Tori: Rigorous Results

NASA Astrophysics Data System (ADS)

Canadell, Marta; Haro, Àlex

2017-12-01

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

Numerical Simulations of Free Surface Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Glimm, James; Oh, Wonho; Prykarpatskyy, Yarema

2003-11-01

We have developed a numerical algorithm and performed simulations of magnetohydrodynamic (MHD) free surface flows. The corresponding system of MHD equations is a system of strongly coupled hyperbolic and parabolic/elliptic equations in moving and geometrically complex domains. The hyperbolic system is solved using the front tracking technique for the free fluid interface. Parallel algorithms for solving elliptic and parabolic equations are based on a finite element discretization on moving grids dynamically conforming to fluid interfaces. The method has been implemented as an MHD extension of the FronTier code. The code has been applied for modeling the behavior of lithium and mercury jets in magnetic fields, laser ablation plumes, and the Richtmyer-Meshkov instability of a liquid mercury jet interacting with a high energy proton pulse in a strong magnetic field. Such an instability occurs in the target for the Muon Collider.

Chromatic aberration of light focusing in hyperbolic anisotropic metamaterial made of metallic slit array.

PubMed

Guo, Kai; Liu, Jianlong; Zhang, Yan; Liu, Shutian

2012-12-17

The dispersion of a hyperbolic anisotropic metamaterial (HAM) and the chromatic aberration of light focusing in this kind of HAM are studied. The HAM is formed by alternately stacking metal and dielectric layers. The rules of materials and filling factors affecting the optical property of HAM are given. The chromatic aberration of light focusing is demonstrated both theoretically and numerically. By comparing the theory with the simulation results, the factors influencing the focal length, including the heat loss of material and low spatial frequency modes, are discussed. The investigation emphasizes the anomalous properties, such as chromatic aberration and low spatial frequency modes influencing focus position, of HAM compared with that in conventional lens. Based on the analysis, the possibility of using HAM to focus light with two different wavelengths at the same point is studied.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

An autonomous dynamical system captures all LCSs in three-dimensional unsteady flows.

PubMed

Oettinger, David; Haller, George

2016-10-01

Lagrangian coherent structures (LCSs) are material surfaces that shape the finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from different variational principles, solving different equations. Here we observe that, in three dimensions, initial positions of all variational LCSs are invariant manifolds of the same autonomous dynamical system, generated by the intermediate eigenvector field, ξ 2 (x 0 ), of the Cauchy-Green strain tensor. This ξ 2 -system allows for the detection of LCSs in any unsteady flow by classical methods, such as Poincaré maps, developed for autonomous dynamical systems. As examples, we consider both steady and time-aperiodic flows, and use their dual ξ 2 -system to uncover both hyperbolic and elliptic LCSs from a single computation.

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

PubMed Central

Aoi, Shinya; Tsuchiya, Kazuo; Kokubu, Hiroshi

2016-01-01

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

A Harmonic Solution for the Hyperbolic Heat Conduction Equation and Its Relationship to the Guyer-Krumhansl Equation

NASA Astrophysics Data System (ADS)

Zhukovsky, K. V.

2018-01-01

A particular solution of the hyperbolic heat-conduction equation was constructed using the method of operators. The evolution of a harmonic solution is studied, which simulates the propagation of electric signals in long wire transmission lines. The structures of the solutions of the telegraph equation and of the Guyer-Krumhansl equation are compared. The influence of the phonon heat-transfer mechanism in the environment is considered from the point of view of heat conductivity. The fulfillment of the maximum principle for the obtained solutions is considered. The frequency dependences of heat conductivity in the telegraph equation and in an equation of the Guyer-Krumhansl type are studied and compared with each other. The influence of the Knudsen number on heat conductivity in the model of thin films is studied.

Cotton-Type and Joint Invariants for Linear Elliptic Systems

PubMed Central

Aslam, A.; Mahomed, F. M.

2013-01-01

Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results. PMID:24453871

Does temporal discounting explain unhealthy behavior? A systematic review and reinforcement learning perspective

PubMed Central

Story, Giles W.; Vlaev, Ivo; Seymour, Ben; Darzi, Ara; Dolan, Raymond J.

2014-01-01

The tendency to make unhealthy choices is hypothesized to be related to an individual's temporal discount rate, the theoretical rate at which they devalue delayed rewards. Furthermore, a particular form of temporal discounting, hyperbolic discounting, has been proposed to explain why unhealthy behavior can occur despite healthy intentions. We examine these two hypotheses in turn. We first systematically review studies which investigate whether discount rates can predict unhealthy behavior. These studies reveal that high discount rates for money (and in some instances food or drug rewards) are associated with several unhealthy behaviors and markers of health status, establishing discounting as a promising predictive measure. We secondly examine whether intention-incongruent unhealthy actions are consistent with hyperbolic discounting. We conclude that intention-incongruent actions are often triggered by environmental cues or changes in motivational state, whose effects are not parameterized by hyperbolic discounting. We propose a framework for understanding these state-based effects in terms of the interplay of two distinct reinforcement learning mechanisms: a “model-based” (or goal-directed) system and a “model-free” (or habitual) system. Under this framework, while discounting of delayed health may contribute to the initiation of unhealthy behavior, with repetition, many unhealthy behaviors become habitual; if health goals then change, habitual behavior can still arise in response to environmental cues. We propose that the burgeoning development of computational models of these processes will permit further identification of health decision-making phenotypes. PMID:24659960

Does temporal discounting explain unhealthy behavior? A systematic review and reinforcement learning perspective.

PubMed

Story, Giles W; Vlaev, Ivo; Seymour, Ben; Darzi, Ara; Dolan, Raymond J

2014-01-01

The tendency to make unhealthy choices is hypothesized to be related to an individual's temporal discount rate, the theoretical rate at which they devalue delayed rewards. Furthermore, a particular form of temporal discounting, hyperbolic discounting, has been proposed to explain why unhealthy behavior can occur despite healthy intentions. We examine these two hypotheses in turn. We first systematically review studies which investigate whether discount rates can predict unhealthy behavior. These studies reveal that high discount rates for money (and in some instances food or drug rewards) are associated with several unhealthy behaviors and markers of health status, establishing discounting as a promising predictive measure. We secondly examine whether intention-incongruent unhealthy actions are consistent with hyperbolic discounting. We conclude that intention-incongruent actions are often triggered by environmental cues or changes in motivational state, whose effects are not parameterized by hyperbolic discounting. We propose a framework for understanding these state-based effects in terms of the interplay of two distinct reinforcement learning mechanisms: a "model-based" (or goal-directed) system and a "model-free" (or habitual) system. Under this framework, while discounting of delayed health may contribute to the initiation of unhealthy behavior, with repetition, many unhealthy behaviors become habitual; if health goals then change, habitual behavior can still arise in response to environmental cues. We propose that the burgeoning development of computational models of these processes will permit further identification of health decision-making phenotypes.

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumbser, Michael, E-mail: michael.dumbser@unitn.it; Peshkov, Ilya, E-mail: peshkov@math.nsc.ru; Romenski, Evgeniy, E-mail: evrom@math.nsc.ru

Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. Inmore » that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier–Stokes–Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER–WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff relaxation limit, and compare the numerical results with exact or numerical reference solutions obtained for the Euler and Navier–Stokes equations. Numerical convergence results are also provided. To show the universality of the HPR model, the paper is rounded-off with an application to wave propagation in elastic solids, for which one only needs to switch off the strain relaxation source term in the governing PDE system. We provide various examples showing that for the purpose of flow visualization, the distortion tensor A seems to be particularly useful.« less

Investigation of statistical iterative reconstruction for dedicated breast CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makeev, Andrey; Glick, Stephen J.

2013-08-15

Purpose: Dedicated breast CT has great potential for improving the detection and diagnosis of breast cancer. Statistical iterative reconstruction (SIR) in dedicated breast CT is a promising alternative to traditional filtered backprojection (FBP). One of the difficulties in using SIR is the presence of free parameters in the algorithm that control the appearance of the resulting image. These parameters require tuning in order to achieve high quality reconstructions. In this study, the authors investigated the penalized maximum likelihood (PML) method with two commonly used types of roughness penalty functions: hyperbolic potential and anisotropic total variation (TV) norm. Reconstructed images weremore » compared with images obtained using standard FBP. Optimal parameters for PML with the hyperbolic prior are reported for the task of detecting microcalcifications embedded in breast tissue.Methods: Computer simulations were used to acquire projections in a half-cone beam geometry. The modeled setup describes a realistic breast CT benchtop system, with an x-ray spectra produced by a point source and an a-Si, CsI:Tl flat-panel detector. A voxelized anthropomorphic breast phantom with 280 μm microcalcification spheres embedded in it was used to model attenuation properties of the uncompressed woman's breast in a pendant position. The reconstruction of 3D images was performed using the separable paraboloidal surrogates algorithm with ordered subsets. Task performance was assessed with the ideal observer detectability index to determine optimal PML parameters.Results: The authors' findings suggest that there is a preferred range of values of the roughness penalty weight and the edge preservation threshold in the penalized objective function with the hyperbolic potential, which resulted in low noise images with high contrast microcalcifications preserved. In terms of numerical observer detectability index, the PML method with optimal parameters yielded substantially improved performance (by a factor of greater than 10) compared to FBP. The hyperbolic prior was also observed to be superior to the TV norm. A few of the best-performing parameter pairs for the PML method also demonstrated superior performance for various radiation doses. In fact, using PML with certain parameter values results in better images, acquired using 2 mGy dose, than FBP-reconstructed images acquired using 6 mGy dose.Conclusions: A range of optimal free parameters for the PML algorithm with hyperbolic and TV norm-based potentials is presented for the microcalcification detection task, in dedicated breast CT. The reported values can be used as starting values of the free parameters, when SIR techniques are used for image reconstruction. Significant improvement in image quality can be achieved by using PML with optimal combination of parameters, as compared to FBP. Importantly, these results suggest improved detection of microcalcifications can be obtained by using PML with lower radiation dose to the patient, than using FBP with higher dose.« less

Power and Roots by Recursion.

ERIC Educational Resources Information Center

Aieta, Joseph F.

1987-01-01

This article illustrates how questions from elementary finance can serve as motivation for studying high order powers, roots, and exponential functions using Logo procedures. A second discussion addresses a relatively unknown algorithm for the trigonometric exponential and hyperbolic functions. (PK)

Accuracy limitations of range-range (spherical) multilateration systems.

DOT National Transportation Integrated Search

1973-10-11

This report presents a novel procedure for determining the accuracy of range-range (or spherical) multilateration systems. The procedure is a generalization of one previously described for hyperbolic multilateration systems. A central result is a dem...

Impact of MAC Delay on AUV Localization: Underwater Localization Based on Hyperbolic Frequency Modulation Signal

PubMed Central

2018-01-01

Medium Access Control (MAC) delay which occurs between the anchor node’s transmissions is one of the error sources in underwater localization. In particular, in AUV localization, the MAC delay significantly degrades the ranging accuracy. The Cramer-Rao Low Bound (CRLB) definition theoretically proves that the MAC delay significantly degrades the localization performance. This paper proposes underwater localization combined with multiple access technology to decouple the localization performance from the MAC delay. Towards this goal, we adopt hyperbolic frequency modulation (HFM) signal that provides multiplexing based on its good property, high-temporal correlation. Owing to the multiplexing ability of the HFM signal, the anchor nodes can transmit packets without MAC delay, i.e., simultaneous transmission is possible. In addition, the simulation results show that the simultaneous transmission is not an optional communication scheme, but essential for the localization of mobile object in underwater. PMID:29373518

Impact of MAC Delay on AUV Localization: Underwater Localization Based on Hyperbolic Frequency Modulation Signal.

PubMed

Kim, Sungryul; Yoo, Younghwan

2018-01-26

Medium Access Control (MAC) delay which occurs between the anchor node's transmissions is one of the error sources in underwater localization. In particular, in AUV localization, the MAC delay significantly degrades the ranging accuracy. The Cramer-Rao Low Bound (CRLB) definition theoretically proves that the MAC delay significantly degrades the localization performance. This paper proposes underwater localization combined with multiple access technology to decouple the localization performance from the MAC delay. Towards this goal, we adopt hyperbolic frequency modulation (HFM) signal that provides multiplexing based on its good property, high-temporal correlation. Owing to the multiplexing ability of the HFM signal, the anchor nodes can transmit packets without MAC delay, i.e., simultaneous transmission is possible. In addition, the simulation results show that the simultaneous transmission is not an optional communication scheme, but essential for the localization of mobile object in underwater.

Hyperbolic cooling of graphene Zener-Klein transistors

NASA Astrophysics Data System (ADS)

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

Engineering of cooling mechanisms is a bottleneck in nanoelectroniscs. In graphene/hBN transistors, Wiedemann-Frantz cooling and supercollision-cooling prevails, and the latter is suppressed in high mobility graphene/hBN samples and substituted by the super-Planckian radiation of hyperbolic phonon-polaritons (HPPs) in the hBN substrate. Using electrical Joule heating and sensitive noise thermometry in several GHz range we report on prevailing HPP cooling in the upper Reststrahlen-band of hBN at high bias. We predict and observe its activation threshold, along with interband Zener-Klein tunneling. HPP cooling is able to evacuate at least several GW/m2 to the bottom gate, resulting in an unusual clipping of electronic temperature. As a scattering counterpart, HPPs of the lower Reststrahlen-band control current saturation at high doping. The combination of both mechanisms promotes graphene/hBN as a valuable nanotechnology for applications in the high power devices and radio frequency electronics.

Extreme current fluctuations in lattice gases: Beyond nonequilibrium steady states

NASA Astrophysics Data System (ADS)

Meerson, Baruch; Sasorov, Pavel V.

2014-01-01

We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in nonstationary diffusive lattice gases. We identify two universality classes of these fluctuations, which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of effective fluid, obtained by mapping the MFT into an inviscid hydrodynamics. An example of the elliptic class is the symmetric simple exclusion process, where, for some initial conditions, we can solve the effective hydrodynamics exactly. This leads to a super-Gaussian extreme current statistics conjectured by Derrida and Gerschenfeld [J. Stat. Phys. 137, 978 (2009), 10.1007/s10955-009-9830-1] and yields the optimal path of the system. For models of the hyperbolic class, the deterministic mass flux cannot be neglected, leading to a different extreme current statistics.

Third-harmonic generation in tunable nonlinear hyperbolic metamaterial

NASA Astrophysics Data System (ADS)

Wicharn, Surawut; Buranasiri, Prathan

2018-03-01

In this research, a third-harmonic generation (THG) in a tunable nonlinear hyperbolic metamaterial (TNHM) has been investigated numerically. The TNHM is consisted of periodically arranging of multilayered graphene layers system for controlled optical properties purpose, and ordinary nonlinear dielectric layer. The possibility of TNHM permittivity dispersion controlled by number of graphene layers and external bias voltage to graphene layers was satisfied, then the structure has created the nearly perfect phase-matching scheme based on epsilon-near-zero (ENZ) behavior of the nonlinear medium. Finally, the optimal designed TNHM structure with sufficient bias voltage have given the forwardand backward-direction TH pulses, which the backward-forward TH intensity ratio is closely unity. The THG conversion efficiencies have been maximized after increasing the pumping level to 800 MW/cm2 . From this study, the optimal designed TNHM can be applied as a bi-directional nonlinear frequency converters in nanophotonic systems.

Curvature bound from gravitational catalysis

NASA Astrophysics Data System (ADS)

Gies, Holger; Martini, Riccardo

2018-04-01

We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective potential for the chiral order parameter, as induced by fermionic fluctuations on a curved spacetime with local hyperbolic properties. The bound is expressed in terms of the local curvature scalar measured in units of a gauge-invariant coarse-graining scale. We argue that any effective field theory of quantum gravity obeying this curvature bound is safe from chiral symmetry breaking through gravitational catalysis and thus compatible with the simultaneous existence of chiral fermions in the low-energy spectrum. With increasing number of dimensions, the curvature bound in terms of the hyperbolic scale parameter becomes stronger. Applying the curvature bound to the asymptotic safety scenario for quantum gravity in four spacetime dimensions translates into bounds on the matter content of particle physics models.

Individual discount rates and smoking: evidence from a field experiment in Denmark.

PubMed

Harrison, Glenn W; Lau, Morten I; Rutström, E Elisabet

2010-09-01

We elicit measures of individual discount rates from a representative sample of the Danish population and test two substantive hypotheses. The first hypothesis is that smokers have higher individual discount rates than non-smokers. The second hypothesis is that smokers are more likely to have time inconsistent preferences than non-smokers, where time inconsistency is indicated by a hyperbolic discounting function. We control for the concavity of the utility function in our estimates of individual discount rates and find that male smokers have significantly higher discount rates than male non-smokers. However, smoking has no significant association with discount rates among women. This result is robust across exponential and hyperbolic discounting functions. We consider the sensitivity of our conclusions to a statistical specification that allows each observation to potentially be generated by more than one latent data-generating process. Copyright 2010 Elsevier B.V. All rights reserved.

Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student’s t-distribution*

PubMed Central

Leão, William L.; Chen, Ming-Hui

2017-01-01

A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor’s 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model. PMID:29333210

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Yan, E-mail: yan.z@chula.ac.th

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

Hyperbolic/parabolic development for the GIM-STAR code. [flow fields in supersonic inlets

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Stalnaker, J. F.; Ratliff, A. W.

1980-01-01

Flow fields in supersonic inlet configurations were computed using the eliptic GIM code on the STAR computer. Spillage flow under the lower cowl was calculated to be 33% of the incoming stream. The shock/boundary layer interaction on the upper propulsive surface was computed including separation. All shocks produced by the flow system were captured. Linearized block implicit (LBI) schemes were examined to determine their application to the GIM code. Pure explicit methods have stability limitations and fully implicit schemes are inherently inefficient; however, LBI schemes show promise as an effective compromise. A quasiparabolic version of the GIM code was developed using elastical parabolized Navier-Stokes methods combined with quasitime relaxation. This scheme is referred to as quasiparabolic although it applies equally well to hyperbolic supersonic inviscid flows. Second order windward differences are used in the marching coordinate and either explicit or linear block implicit time relaxation can be incorporated.

Conservation laws with coinciding smooth solutions but different conserved variables

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Guerra, Graziano

2018-04-01

Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

Surface waves on multilayer hyperbolic metamaterials: Operator approach to effective medium approximation

NASA Astrophysics Data System (ADS)

Popov, Vladislav; Lavrinenko, Andrei V.; Novitsky, Andrey

2018-03-01

In this paper, we elaborate on the operator effective medium approximation developed recently in Popov et al. [Phys. Rev. B 94, 085428 (2016), 10.1103/PhysRevB.94.085428] to get insight into the surface polariton excitation at the interface of a multilayer hyperbolic metamaterial (HMM). In particular, we find that HMMs with bilayer unit cells support the TE- and TM-polarized surface waves beyond the Maxwell Garnett approximation due to the spatial dispersion interpreted as effective magnetoelectric coupling. The latter is also responsible for the dependence of surface wave propagation on the order of layers in the unit cell. Elimination of the magnetoelectric coupling in three-layer unit cells complying with inversion symmetry restores the qualitative regularity of the Maxwell Garnett approximation, as well as strongly suppresses the influence of the order of layers in the unit cell.

Flows of Newtonian and Power-Law Fluids in Symmetrically Corrugated Cappilary Fissures and Tubes

NASA Astrophysics Data System (ADS)

Walicka, A.

2018-02-01

In this paper, an analytical method for deriving the relationships between the pressure drop and the volumetric flow rate in laminar flow regimes of Newtonian and power-law fluids through symmetrically corrugated capillary fissures and tubes is presented. This method, which is general with regard to fluid and capillary shape, can also be used as a foundation for different fluids, fissures and tubes. It can also be a good base for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. Five converging-diverging or diverging-converging geometrics, viz. wedge and cone, parabolic, hyperbolic, hyperbolic cosine and cosine curve, are used as examples to illustrate the application of this method. For the wedge and cone geometry the present results for the power-law fluid were compared with the results obtained by another method; this comparison indicates a good compatibility between both the results.

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

PubMed

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

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

NASA Astrophysics Data System (ADS)

Yudin, M. S.

2017-11-01

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

String Theory: exact solutions, marginal deformations and hyperbolic spaces

NASA Astrophysics Data System (ADS)

Orlando, Domenico

2006-10-01

This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze direct products of constant-curvature spaces and find solutions with hyperbolic spaces.

Post optimization paradigm in maximum 3-satisfiability logic programming

NASA Astrophysics Data System (ADS)

Mansor, Mohd. Asyraf; Sathasivam, Saratha; Kasihmuddin, Mohd Shareduwan Mohd

2017-08-01

Maximum 3-Satisfiability (MAX-3SAT) is a counterpart of the Boolean satisfiability problem that can be treated as a constraint optimization problem. It deals with a conundrum of searching the maximum number of satisfied clauses in a particular 3-SAT formula. This paper presents the implementation of enhanced Hopfield network in hastening the Maximum 3-Satisfiability (MAX-3SAT) logic programming. Four post optimization techniques are investigated, including the Elliot symmetric activation function, Gaussian activation function, Wavelet activation function and Hyperbolic tangent activation function. The performances of these post optimization techniques in accelerating MAX-3SAT logic programming will be discussed in terms of the ratio of maximum satisfied clauses, Hamming distance and the computation time. Dev-C++ was used as the platform for training, testing and validating our proposed techniques. The results depict the Hyperbolic tangent activation function and Elliot symmetric activation function can be used in doing MAX-3SAT logic programming.

Parabolic discounting of monetary rewards by physical effort.

PubMed

Hartmann, Matthias N; Hager, Oliver M; Tobler, Philippe N; Kaiser, Stefan

2013-11-01

When humans and other animals make decisions in their natural environments prospective rewards have to be weighed against costs. It is well established that increasing costs lead to devaluation or discounting of reward. While our knowledge about discount functions for time and probability costs is quite advanced, little is known about how physical effort discounts reward. In the present study we compared three different models in a binary choice task in which human participants had to squeeze a handgrip to earn monetary rewards: a linear, a hyperbolic, and a parabolic model. On the group as well as the individual level, the concave parabolic model explained most variance of the choice data, thus contrasting with the typical hyperbolic discounting of reward value by delay. Research on effort discounting is not only important to basic science but also holds the potential to quantify aberrant motivational states in neuropsychiatric disorders. Copyright © 2013 Elsevier B.V. All rights reserved.

Absorbing boundary conditions for second-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Jiang, Hong; Wong, Yau Shu

1989-01-01

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

Discretizing singular point sources in hyperbolic wave propagation problems

DOE PAGES

Petersson, N. Anders; O'Reilly, Ossian; Sjogreen, Bjorn; ...

2016-06-01

Here, 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 themore » 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.« less

Internal friction between fluid particles of MHD tangent hyperbolic fluid with heat generation: Using coefficients improved by Cash and Karp

NASA Astrophysics Data System (ADS)

Salahuddin, T.; Khan, Imad; Malik, M. Y.; Khan, Mair; Hussain, Arif; Awais, Muhammad

2017-05-01

The present work examines the internal resistance between fluid particles of tangent hyperbolic fluid flow due to a non-linear stretching sheet with heat generation. Using similarity transformations, the governing system of partial differential equations is transformed into a coupled non-linear ordinary differential system with variable coefficients. Unlike the current analytical works on the flow problems in the literature, the main concern here is to numerically work out and find the solution by using Runge-Kutta-Fehlberg coefficients improved by Cash and Karp (Naseer et al., Alexandria Eng. J. 53, 747 (2014)). To determine the relevant physical features of numerous mechanisms acting on the deliberated problem, it is sufficient to have the velocity profile and temperature field and also the drag force and heat transfer rate all as given in the current paper.

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, E. F.

1974-01-01

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

Ultra-wideband microwave absorber by connecting multiple absorption bands of two different-sized hyperbolic metamaterial waveguide arrays.

PubMed

Yin, Xiang; Long, Chang; Li, Junhao; Zhu, Hua; Chen, Lin; Guan, Jianguo; Li, Xun

2015-10-19

Microwave absorbers have important applications in various areas including stealth, camouflage, and antenna. Here, we have designed an ultra-broadband light absorber by integrating two different-sized tapered hyperbolic metamaterial (HMM) waveguides, each of which has wide but different absorption bands due to broadband slow-light response, into a unit cell. Both the numerical and experimental results demonstrate that in such a design strategy, the low absorption bands between high absorption bands with a single-sized tapered HMM waveguide array can be effectively eliminated, resulting in a largely expanded absorption bandwidth ranging from 2.3 to 40 GHz. The presented ultra-broadband light absorber is also insensitive to polarization and robust against incident angle. Our results offer a further step in developing practical artificial electromagnetic absorbers, which will impact a broad range of applications at microwave frequencies.

No elliptic islands for the universal area-preserving map

NASA Astrophysics Data System (ADS)

Johnson, Tomas

2011-07-01

A renormalization approach has been used in Eckmann et al (1982) and Eckmann et al (1984) to prove the existence of a universal area-preserving map, a map with hyperbolic orbits of all binary periods. The existence of a horseshoe, with positive Hausdorff dimension, in its domain was demonstrated in Gaidashev and Johnson (2009a). In this paper the coexistence problem is studied, and a computer-aided proof is given that no elliptic islands with period less than 18 exist in the domain. It is also shown that less than 1.5% of the measure of the domain consists of elliptic islands. This is proven by showing that the measure of initial conditions that escape to infinity is at least 98.5% of the measure of the domain, and we conjecture that the escaping set has full measure. This is highly unexpected, since generically it is believed that for conservative systems hyperbolicity and ellipticity coexist.

A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Du, Jian; Glimm, James; Xu, Zhiliang

2007-10-01

We have developed a numerical algorithm and computational software for the study of magnetohydrodynamics (MHD) of free surface flows at low magnetic Reynolds numbers. The governing system of equations is a coupled hyperbolic-elliptic system in moving and geometrically complex domains. The numerical algorithm employs the method of front tracking and the Riemann problem for material interfaces, second order Godunov-type hyperbolic solvers, and the embedded boundary method for the elliptic problem in complex domains. The numerical algorithm has been implemented as an MHD extension of FronTier, a hydrodynamic code with free interface support. The code is applicable for numerical simulations of free surface flows of conductive liquids or weakly ionized plasmas. The code has been validated through the comparison of numerical simulations of a liquid metal jet in a non-uniform magnetic field with experiments and theory. Simulations of the Muon Collider/Neutrino Factory target have also been discussed.

Tunable slow light in graphene-based hyperbolic metamaterial waveguide operating in SCLU telecom bands.

PubMed

Tyszka-Zawadzka, Anna; Janaszek, Bartosz; Szczepański, Paweł

2017-04-03

The tunability of slow light in graphene-based hyperbolic metamaterial waveguide operating in SCLU telecom bands is investigated. For the first time it has been shown that proper design of a GHMM structure forming waveguide layer and the geometry of the waveguide itself allows stopped light to be obtained in an almost freely selected range of wavelengths within SCLU bands. In particular, the possibility of controlling light propagation in GHMM waveguides by external biasing has been presented. The change of external electric field enables the stop light of the selected wavelength as well as the control of a number of modes, which can be stopped, cut off or supported. Proposed GHMM waveguides could offer great opportunities in the field of integrated photonics that are compatible with CMOS technology, especially since such structures can be utilized as photonic memory cells, tunable optical buffers, delays, optical modulators etc.

"Coherence-incoherence" transition in ensembles of nonlocally coupled chaotic oscillators with nonhyperbolic and hyperbolic attractors

NASA Astrophysics Data System (ADS)

Semenova, Nadezhda I.; Rybalova, Elena V.; Strelkova, Galina I.; Anishchenko, Vadim S.

2017-03-01

We consider in detail similarities and differences of the "coherence-incoherence" transition in ensembles of nonlocally coupled chaotic discrete-time systems with nonhyperbolic and hyperbolic attractors. As basic models we employ the Hénon map and the Lozi map. We show that phase and amplitude chimera states appear in a ring of coupled Hénon maps, while no chimeras are observed in an ensemble of coupled Lozi maps. In the latter, the transition to spatio-temporal chaos occurs via solitary states. We present numerical results for the coupling function which describes the impact of neighboring oscillators on each partial element of an ensemble with nonlocal coupling. Varying the coupling strength we analyze the evolution of the coupling function and discuss in detail its role in the "coherence-incoherence" transition in the ensembles of Hénon and Lozi maps.

Nonlinear hyperbolic theory of thermal waves in metals

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.; Choi, S. H.

1975-01-01

A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.

On the identification of continuous vibrating systems modelled by hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Udwadia, F. E.; Garba, J. A.

1983-01-01

This paper deals with the identification of spatially varying parameters in systems of finite spatial extent which can be described by second order hyperbolic differential equations. Two questions have been addressed. The first deals with 'partial identification' and inquires into the possibility of retrieving all the eigenvalues of the system from response data obtained at one location x-asterisk epsilon (0, 1). The second deals with the identification of the distributed coefficients rho(x), a(x) and b(x). Sufficient conditions for unique identification of all the eigenvalues of the system are obtained, and conditions under which the coefficients can be uniquely identified using suitable response data obtained at one point in the spatial domain are determined. Application of the results and their usefulness is demonstrated in the identification of the properties of tall building structural systems subjected to dynamic load environments.

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

An hp-adaptivity and error estimation for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1995-01-01

This paper presents an hp-adaptive discontinuous Galerkin method for linear hyperbolic conservation laws. A priori and a posteriori error estimates are derived in mesh-dependent norms which reflect the dependence of the approximate solution on the element size (h) and the degree (p) of the local polynomial approximation. The a posteriori error estimate, based on the element residual method, provides bounds on the actual global error in the approximate solution. The adaptive strategy is designed to deliver an approximate solution with the specified level of error in three steps. The a posteriori estimate is used to assess the accuracy of a given approximate solution and the a priori estimate is used to predict the mesh refinements and polynomial enrichment needed to deliver the desired solution. Numerical examples demonstrate the reliability of the a posteriori error estimates and the effectiveness of the hp-adaptive strategy.

Boundary conformal anomalies on hyperbolic spaces and Euclidean balls

NASA Astrophysics Data System (ADS)

Rodriguez-Gomez, Diego; Russo, Jorge G.

2017-12-01

We compute conformal anomalies for conformal field theories with free conformal scalars and massless spin 1/2 fields in hyperbolic space ℍ d and in the ball B^d , for 2≤d≤7. These spaces are related by a conformal transformation. In even dimensional spaces, the conformal anomalies on ℍ2 n and B^{2n} are shown to be identical. In odd dimensional spaces, the conformal anomaly on B^{2n+1} comes from a boundary contribution, which exactly coincides with that of ℍ2 n + 1 provided one identifies the UV short-distance cutoff on B^{2n+1} with the inverse large distance IR cutoff on ℍ2 n + 1, just as prescribed by the conformal map. As an application, we determine, for the first time, the conformal anomaly coefficients multiplying the Euler characteristic of the boundary for scalars and half-spin fields with various boundary conditions in d = 5 and d = 7.

The solution of non-linear hyperbolic equation systems by the finite element method

NASA Technical Reports Server (NTRS)

Loehner, R.; Morgan, K.; Zienkiewicz, O. C.

1984-01-01

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1997-01-01

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton- Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the reader can understand the algorithms and code them up for applications.

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

The Overgrid Interface for Computational Simulations on Overset Grids

NASA Technical Reports Server (NTRS)

Chan, William M.; Kwak, Dochan (Technical Monitor)

2002-01-01

Computational simulations using overset grids typically involve multiple steps and a variety of software modules. A graphical interface called OVERGRID has been specially designed for such purposes. Data required and created by the different steps include geometry, grids, domain connectivity information and flow solver input parameters. The interface provides a unified environment for the visualization, processing, generation and diagnosis of such data. General modules are available for the manipulation of structured grids and unstructured surface triangulations. Modules more specific for the overset approach include surface curve generators, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, Cartesian box grid generators, and domain connectivity: pre-processing tools. An interface provides automatic selection and viewing of flow solver boundary conditions, and various other flow solver inputs. For problems involving multiple components in relative motion, a module is available to build the component/grid relationships and to prescribe and animate the dynamics of the different components.

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert

2018-07-01

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy.more » The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.« less

Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student's t-distribution.

PubMed

Leão, William L; Abanto-Valle, Carlos A; Chen, Ming-Hui

2017-01-01

A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor's 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model.

COMPASS Final Report: Enceladus Solar Electric Propulsion Stage

NASA Technical Reports Server (NTRS)

Oleson, Steven R.; McGuire, Melissa L.

2011-01-01

The results of the NASA Glenn Research Center (GRC) COllaborative Modeling and Parametric Assessment of Space Systems (COMPASS) internal Solar Electric Propulsion (SEP) stage design are documented in this report (Figure 1.1). The SEP Stage was designed to deliver a science probe to Saturn (the probe design was performed separately by the NASA Goddard Space Flight Center s (GSFC) Integrated Mission Design Center (IMDC)). The SEP Stage delivers the 2444 kg probe on a Saturn trajectory with a hyperbolic arrival velocity of 5.4 km/s. The design carried 30 percent mass, 10 percent power, and 6 percent propellant margins. The SEP Stage relies on the probe for substantial guidance, navigation and control (GN&C), command and data handling (C&DH), and Communications functions. The stage is configured to carry the probe and to minimize the packaging interference between the probe and the stage. The propulsion system consisted of a 1+1 (one active, one spare) configuration of gimbaled 7 kW NASA Evolutionary Xenon Thruster (NEXT) ion propulsion thrusters with a throughput of 309 kg Xe propellant. Two 9350 W GaAs triple junction (at 1 Astronomical Unit (AU), includes 10 percent margin) ultra-flex solar arrays provided power to the stage, with Li-ion batteries for launch and contingency operations power. The base structure was an Al-Li hexagonal skin-stringer frame built to withstand launch loads. A passive thermal control system consisted of heat pipes to north and south radiator panels, multilayer insulation (MLI) and heaters for the Xe tank. All systems except tanks and solar arrays were designed to be single fault tolerant.

Spectral Skyline Separation: Extended Landmark Databases and Panoramic Imaging

PubMed Central

Differt, Dario; Möller, Ralf

2016-01-01

Evidence from behavioral experiments suggests that insects use the skyline as a cue for visual navigation. However, changes of lighting conditions, over hours, days or possibly seasons, significantly affect the appearance of the sky and ground objects. One possible solution to this problem is to extract the “skyline” by an illumination-invariant classification of the environment into two classes, ground objects and sky. In a previous study (Insect models of illumination-invariant skyline extraction from UV (ultraviolet) and green channels), we examined the idea of using two different color channels available for many insects (UV and green) to perform this segmentation. We found out that for suburban scenes in temperate zones, where the skyline is dominated by trees and artificial objects like houses, a “local” UV segmentation with adaptive thresholds applied to individual images leads to the most reliable classification. Furthermore, a “global” segmentation with fixed thresholds (trained on an image dataset recorded over several days) using UV-only information is only slightly worse compared to using both the UV and green channel. In this study, we address three issues: First, to enhance the limited range of environments covered by the dataset collected in the previous study, we gathered additional data samples of skylines consisting of minerals (stones, sand, earth) as ground objects. We could show that also for mineral-rich environments, UV-only segmentation achieves a quality comparable to multi-spectral (UV and green) segmentation. Second, we collected a wide variety of ground objects to examine their spectral characteristics under different lighting conditions. On the one hand, we found that the special case of diffusely-illuminated minerals increases the difficulty to reliably separate ground objects from the sky. On the other hand, the spectral characteristics of this collection of ground objects covers well with the data collected in the skyline databases, increasing, due to the increased variety of ground objects, the validity of our findings for novel environments. Third, we collected omnidirectional images, as often used for visual navigation tasks, of skylines using an UV-reflective hyperbolic mirror. We could show that “local” separation techniques can be adapted to the use of panoramic images by splitting the image into segments and finding individual thresholds for each segment. Contrarily, this is not possible for ‘global’ separation techniques. PMID:27690053

Causal implications of viscous damping in compressible fluid flows

PubMed

Jordan; Meyer; Puri

2000-12-01

Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to investigate this apparent contradiction. To this end the exact solutions, as well as their special and limiting cases, are found and compared for the two models. The effects of the physical parameters on the solutions and associated quantities are also studied. It is shown that propagating wave fronts are only possible under the hyperbolic model and that the concept of phase speed has different meanings in the two formulations. In addition, discontinuities and shock waves are noted and a physical system is modeled under both formulations. Overall, it is shown that the hyperbolic form gives a more realistic description of the physical problem than does the classical theory. Lastly, a simple mechanical analog is given and connections to viscoelastic fluids are noted. In particular, the research presented here supports the notion that linear compressible, isothermal, viscous fluids can, at least in terms of causality, be better characterized as a type of viscoelastic fluid.

Operational models of pharmacological agonism.

PubMed

Black, J W; Leff, P

1983-12-22

The traditional receptor-stimulus model of agonism began with a description of drug action based on the law of mass action and has developed by a series of modifications, each accounting for new experimental evidence. By contrast, in this paper an approach to modelling agonism is taken that begins with the observation that experimental agonist-concentration effect, E/[A], curves are commonly hyperbolic and develops using the deduction that the relation between occupancy and effect must be hyperbolic if the law of mass action applies at the agonist-receptor level. The result is a general model that explicitly describes agonism by three parameters: an agonist-receptor dissociation constant, KA; the total receptor concentration, [R0]; and a parameter, KE, defining the transduction of agonist-receptor complex, AR, into pharmacological effect. The ratio, [R0]/KE, described here as the 'transducer ratio', tau, is a logical definition for the efficacy of an agonist in a system. The model may be extended to account for non-hyperbolic E/[A] curves with no loss of meaning. Analysis shows that an explicit formulation of the traditional receptor-stimulus model is one particular form of the general model but that it is not the simplest. An alternative model is proposed, representing the cognitive and transducer functions of a receptor, that describes agonist action with one fewer parameter than the traditional model. In addition, this model provides a chemical definition of intrinsic efficacy making this parameter experimentally accessible in principle. The alternative models are compared and contrasted with regard to their practical and conceptual utilities in experimental pharmacology.

Extending unified-theory-of-reinforcement neural networks to steady-state operant behavior.

PubMed

Calvin, Olivia L; McDowell, J J

2016-06-01

The unified theory of reinforcement has been used to develop models of behavior over the last 20 years (Donahoe et al., 1993). Previous research has focused on the theory's concordance with the respondent behavior of humans and animals. In this experiment, neural networks were developed from the theory to extend the unified theory of reinforcement to operant behavior on single-alternative variable-interval schedules. This area of operant research was selected because previously developed neural networks could be applied to it without significant alteration. Previous research with humans and animals indicates that the pattern of their steady-state behavior is hyperbolic when plotted against the obtained rate of reinforcement (Herrnstein, 1970). A genetic algorithm was used in the first part of the experiment to determine parameter values for the neural networks, because values that were used in previous research did not result in a hyperbolic pattern of behavior. After finding these parameters, hyperbolic and other similar functions were fitted to the behavior produced by the neural networks. The form of the neural network's behavior was best described by an exponentiated hyperbola (McDowell, 1986; McLean and White, 1983; Wearden, 1981), which was derived from the generalized matching law (Baum, 1974). In post-hoc analyses the addition of a baseline rate of behavior significantly improved the fit of the exponentiated hyperbola and removed systematic residuals. The form of this function was consistent with human and animal behavior, but the estimated parameter values were not. Copyright © 2016 Elsevier B.V. All rights reserved.

HAM2D: 2D Shearing Box Model

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; Guan, Xiaoyue

2012-10-01

HAM solves non-relativistic hyperbolic partial differential equations in conservative form using high-resolution shock-capturing techniques. This version of HAM has been configured to solve the magnetohydrodynamic equations of motion in axisymmetry to evolve a shearing box model.

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

NASA Astrophysics Data System (ADS)

De La Chevrotière, Michèle; Khouider, Boualem

2017-02-01

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

Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Zanotti, Olindo

2009-10-01

In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space dimensions. The nonlinear system under consideration is purely hyperbolic and contains a source term, the one for the evolution of the electric field, that becomes stiff for low values of the resistivity. For the spatial discretization we propose to use high order PNPM schemes as introduced in Dumbser et al. [M. Dumbser, D. Balsara, E.F. Toro, C.D. Munz, A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes, Journal of Computational Physics 227 (2008) 8209-8253] for hyperbolic conservation laws and a high order accurate unsplit time-discretization is achieved using the element-local space-time discontinuous Galerkin approach proposed in Dumbser et al. [M. Dumbser, C. Enaux, E.F. Toro, Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws, Journal of Computational Physics 227 (2008) 3971-4001] for one-dimensional balance laws with stiff source terms. The divergence-free character of the magnetic field is accounted for through the divergence cleaning procedure of Dedner et al. [A. Dedner, F. Kemm, D. Kröner, C.-D. Munz, T. Schnitzer, M. Wesenberg, Hyperbolic divergence cleaning for the MHD equations, Journal of Computational Physics 175 (2002) 645-673]. To validate our high order method we first solve some numerical test cases for which exact analytical reference solutions are known and we also show numerical convergence studies in the stiff limit of the RRMHD equations using PNPM schemes from third to fifth order of accuracy in space and time. We also present some applications with shock waves such as a classical shock tube problem with different values for the conductivity as well as a relativistic MHD rotor problem and the relativistic equivalent of the Orszag-Tang vortex problem. We have verified that the proposed method can handle equally well the resistive regime and the stiff limit of ideal relativistic MHD. For these reasons it provides a powerful tool for relativistic astrophysical simulations involving the appearance of magnetic reconnection.

Preliminary estimates of Gulf Stream characteristics from TOPEX data and a precise gravimetric geoid

NASA Technical Reports Server (NTRS)

Rapp, Richard H.; Smith, Dru A.

1994-01-01

TOPEX sea surface height data has been used, with a gravimetric geoid, to calculate sea surface topography across the Gulf Stream. This topography was initially computed for nine tracks on cycles 21 to 29. Due to inaccurate geoid undulations on one track, results for eight tracks are reported. The sea surface topography estimates were used to calculate parameters that describe Gulf Stream characteristics from two models of the Gulf Stream. One model was based on a Gaussian representation of the velocity while the other was a hyperbolic representation of velocity or the sea surface topography. The parameters of the Gaussian velocity model fit were a width parameter, a maximum velocity value, and the location of the maximum velocity. The parameters of the hyperbolic sea surface topography model were the width, the height jump, position, and sea surface topography at the center of the stream. Both models were used for the eight tracks and nine cycles studied. Comparisons were made between the width parameters, the maximum velocities, and the height jumps. Some of the parameter estimates were found to be highly (0.9) correlated when the hyperbolic sea surface topography fit was carried out, but such correlations were reduced for either the Gaussian velocity fits or the hyperbolic velocity model fit. A comparison of the parameters derived from 1-year TOPEX data showed good agreement with values derived by Kelly (1991) using 2.5 years of Geosat data near 38 deg N, 66 deg W longitude. Accuracy of the geoid undulations used in the calculations was of order of +/- 16 cm with the accuracy of a geoid undulation difference equal to +/- 15 cm over a 100-km line in areas with good terrestrial data coverage. This paper demonstrates that our knowledge or geoid undulations and undulation differences, in a portion of the Gulf Stream region, is sufficiently accurate to determine characteristics of the jet when used with TOPEX altimeter data. The method used here has not been shown to be more accurate than methods that average altimeter data to form a reference surface used in analysis to obtain the Gulf Stream characteristics. However, the results show the geoid approach may be used in areas where lack of current meandering reduces the accuracy of the average surface procedure.

z -classes of isometries of the hyperbolic space

NASA Astrophysics Data System (ADS)

Gongopadhyay, Krishnendu; Kulkarni, Ravi S.

Let G be a group. Two elements x, y are said to be z -equivalent if their centralizers are conjugate in G . The class equation of G is the partition of G into conjugacy classes. Further decomposition of conjugacy classes into z -classes provides important information about the internal structure of the group; cf. J. Ramanujan Math. Soc. 22 (2007), 35-56, for the elaboration of this theme. Let I(H^n) denote the group of isometries of the hyperbolic n -space, and let I_o(H^n) be the identity component of I(H^n) . We show that the number of z -classes in I(H^n) is finite. We actually compute their number; cf. theorem 1.3. We interpret the finiteness of z -classes as accounting for the finiteness of ``dynamical types'' in I(H^n) . Along the way we also parametrize conjugacy classes. We mainly use the linear model of the hyperbolic space for this purpose. This description of parametrizing conjugacy classes appears to be new; cf. Academic Press, New York, 1974, 49-87 and Conformal geometry (Bonn, 1985/1986), 41-64, Aspects Math., E12, Vieweg, Braunschweig, 1988, for previous attempts. Ahlfors (Differential Geometry and Complex Analysis (Springer, 1985), 65-73) suggested the use of Clifford algebras to deal with higher dimensional hyperbolic geometry; cf. Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 15-27, Quasiconformal Mappings and Analysis (Springer, 1998), 109-139, Complex Variables Theory Appl. 15 (1990), 125-133, and Adv. Math. 101 (1993), 87-113. These works may be compared to the approach suggested in this paper. In dimensions 2 and 3 , by remarkable Lie-theoretic isomorphisms, I_o(H2) and I_o(H3) can be lifted to GL_o(2, R) , and GL(2, C) respectively. For orientation-reversing isometries there are some modifications of these liftings. Using these liftings, in the appendix A, we have introduced a single numerical invariant c(A) , to classify the elements of I(H2) and I(H3) , and explained the classical terminology. Using the ``Iwasawa decomposition'' of I_o(H^n) , it is possible to equip H^n with a group structure. In the appendix B, we visualize the stratification of the group H^n into its conjugacy and z -classes.

Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

ERIC Educational Resources Information Center

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

The study of the physics of cometary nuclei

NASA Technical Reports Server (NTRS)

Whipple, F. L.; Marsden, B. G.; Sekanina, Z.

1975-01-01

Research in the area of split and hyperbolic comets, orbital calculations, and interstellar comets is discussed. Other topics discussed include the role of comets in galactic chemistry, gamma ray bursts, and predicted favorable visibility conditions for anomalous tails of comets.

Nonlinear load-deflection behavior of abutment backwalls with varying height and soil density.

DOT National Transportation Integrated Search

2011-12-01

We address the scaling of abutment wall lateral response with wall height and compaction condition through testing and analytical work. The : analytical work was undertaken to develop hyperbolic curves representing the load-deflection response of bac...

A Geometric Perspective on the Method of Descent

NASA Astrophysics Data System (ADS)

Wang, Qian

2018-06-01

We derive a first order representation formula for the tensorial wave equation \\Box_g φ^I=F^I in globally hyperbolic Lorentzian spacetimes {(M^{2+1}, g) by giving a geometric formulation of the method of descent which is applicable for any dimension.

Beyond the Hyperbole: Information Literacy Reconsidered

ERIC Educational Resources Information Center

Julien, Heidi

2016-01-01

Information literacy, as a concept, has suffered from terminological confusion and has been burdened with untenable expectations. In addition, insufficient attention has been given to the place of information with the context of information behavior or information practices generally. Significant challenges remain to developing information…

The Sweetness of Aspartame: A Biochemistry Lab for Health Science Chemistry Courses.

ERIC Educational Resources Information Center

Stein, Paul J.

1997-01-01

Explains the procedures used in an experiment that reinforces the universality of the concepts of saturation using the binding of the ligand aspartame to the protein receptor that determines taste. Illustrates the hyperbolic nature of protein binding. (DDR)

Ergodicity of two hard balls in integrable polygons

NASA Astrophysics Data System (ADS)

Bálint, Péter; Troubetzkoy, Serge

2004-11-01

We prove the hyperbolicity, ergodicity and thus the Bernoulli property of two hard balls in one of the following four polygons: the square, the equilateral triangle, the 45°-45°-90° triangle or the 30°-60°-90° triangle.

Conference Space

ERIC Educational Resources Information Center

Tillett, Wade

2016-01-01

The following is an exploration of the spatial configurations (and their implications) within a typical panel session at an academic conference. The presenter initially takes up different roles and hyperbolically describes some possible messages that the spatial arrangement sends. Eventually, the presenter engages the audience members in atypical…

Researched applied to transonic compressors in numerical fluid mechanics of inviscid flow and viscous flow

NASA Technical Reports Server (NTRS)

Thompkins, W. T., Jr.

1985-01-01

A streamline Euler solver which combines high accuracy and good convergence rates with capabilities for inverse or direct mode solution modes and an analysis technique for finite difference models of hyperbolic partial difference equations were developed.

Experimentally demonstrate the surface state and optical topological phase transition of one dimensional hyperbolic metamaterials in Otto and KR configuration (Conference Presentation)

NASA Astrophysics Data System (ADS)

Wei, Chih Chung; Un, Leng-Wai; Yen, Ta-Jen

2017-05-01

One-dimension hyperbolic metamaterials (1DHMMs) possess marvelous and considerable applications: hyperlens, spontaneous emission engineering and nonlinear optics. Conventionally, effective medium theory, which is only valid for long wavelength limit, was used to predict and analyze the optical properties and applications. In our previous works, we considered a binary 1DHMM which consists of alternative metallic and dielectric layers, and rigorously demonstrated the existence of surface states and bulk-interface correspondence with the plasmonic band theory from the coupled surface plasmon point of view. In the plasmonic band structure, we can classify 1DHMMs into two classes: metallic-like and dielectric-like, depending on the formation of the surface states with dielectric and metallic material, respectively. Band crossing exists only when the dielectric layers are thicker than the metallic ones, which is independent from the dielectric constants. Furthermore, the 1DHMMs are all metallic-like without band crossing. On the other hand, the 1DHMMs with band crossing are metal-like before the band crossing point, while they are dielectric-like after the band crossing point. In this work, we measure the surface states formed by dielectric material and 1DHMMs with band crossing in Otto configuration. With white light source and fixed incident angle, we measure the reflectance to investigate the existence of the surface states of 1DHMMs with various thickness ratio of metallic to dielectric layers. Conclusively, our results show that the surface states of 1DHMMs exist only when the thickness ratio is larger than 0.15. The disappearance of the surface states indicates the topological phase transition of 1DHMMs. Our experimental results will benefit new applications for manipulating light on the surface of hyperbolic metamaterials.

Studying ventricular abnormalities in mild cognitive impairment with hyperbolic Ricci flow and tensor-based morphometry.

PubMed

Shi, Jie; Stonnington, Cynthia M; Thompson, Paul M; Chen, Kewei; Gutman, Boris; Reschke, Cole; Baxter, Leslie C; Reiman, Eric M; Caselli, Richard J; Wang, Yalin

2015-01-01

Mild Cognitive Impairment (MCI) is a transitional stage between normal aging and dementia and people with MCI are at high risk of progression to dementia. MCI is attracting increasing attention, as it offers an opportunity to target the disease process during an early symptomatic stage. Structural magnetic resonance imaging (MRI) measures have been the mainstay of Alzheimer's disease (AD) imaging research, however, ventricular morphometry analysis remains challenging because of its complicated topological structure. Here we describe a novel ventricular morphometry system based on the hyperbolic Ricci flow method and tensor-based morphometry (TBM) statistics. Unlike prior ventricular surface parameterization methods, hyperbolic conformal parameterization is angle-preserving and does not have any singularities. Our system generates a one-to-one diffeomorphic mapping between ventricular surfaces with consistent boundary matching conditions. The TBM statistics encode a great deal of surface deformation information that could be inaccessible or overlooked by other methods. We applied our system to the baseline MRI scans of a set of MCI subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI: 71 MCI converters vs. 62 MCI stable). Although the combined ventricular area and volume features did not differ between the two groups, our fine-grained surface analysis revealed significant differences in the ventricular regions close to the temporal lobe and posterior cingulate, structures that are affected early in AD. Significant correlations were also detected between ventricular morphometry, neuropsychological measures, and a previously described imaging index based on fluorodeoxyglucose positron emission tomography (FDG-PET) scans. This novel ventricular morphometry method may offer a new and more sensitive approach to study preclinical and early symptomatic stage AD. Copyright © 2014 Elsevier Inc. All rights reserved.

Active optics and modified-Rumsey wide-field telescopes: MINITRUST demonstrators with vase- and tulip-form mirrors

NASA Astrophysics Data System (ADS)

Lemaître, Gérard R.; Montiel, Pierre; Joulié, Patrice; Dohlen, Kjetil; Lanzoni, Patrick

2005-12-01

Wide-field astronomy requires the development of larger aperture telescopes. The optical properties of a three-mirror modified-Rumsey design provide significant advantages when compared to other telescope designs: (i) at any wavelength, the design has a flat field and is anastigmatic; (ii) the system is extremely compact, i.e., it is almost four times shorter than a Schmidt. Compared to the equally compact flat-field Ritchey-Chrétien with a doublet-lens corrector, as developed for the Sloan digital sky survey - and which requires the polishing of six optical surfaces - the proposed modified-Rumsey design requires only a two-surface polishing and provides a better imaging quality. All the mirrors are spheroids of the hyperboloid type. Starting from the classical Rumsey design, it is shown that the use of all eight available free parameters allows the simultaneous aspherization of the primary and tertiary mirrors by active optics methods from a single deformable substrate. The continuity conditions between the primary and the tertiary hyperbolizations are achieved by an intermediate narrow ring of constant thickness that is not optically used. After the polishing of a double vase form in a spherical shape, the primary-tertiary hyperbolizations are achieved by in situ stressing. The tulip-form secondary is hyperbolized by stress polishing. Other active optics alternatives are possible for a space telescope. The modified-Rumsey design is of interest for developing large space- and ground-based survey telescopes in UV, visible, or IR ranges, such as currently demonstrated with the construction of identical telescopes MINITRUST-1 and -2, f/5 - 2° field of view. Double-pass optical tests show diffraction-limited images.

Discontinuous Galerkin finite element method for the nonlinear hyperbolic problems with entropy-based artificial viscosity stabilization

NASA Astrophysics Data System (ADS)

Zingan, Valentin Nikolaevich

This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.

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

PubMed

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

2018-04-15

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

A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion.

PubMed

Dipierro, Serena; Valdinoci, Enrico

2018-07-01

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.

Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, L. D., E-mail: lachlan.smith@monash.edu; CSIRO Mineral Resources, Clayton, Victoria 3800; Rudman, M.

2016-05-15

Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversalmore » in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.« less

Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution.

PubMed

Atlas, Glen; Li, John K-J; Amin, Shawn; Hahn, Robert G

2017-01-01

A closed-form integro-differential equation (IDE) model of plasma dilution (PD) has been derived which represents both the intravenous (IV) infusion of crystalloid and the postinfusion period. Specifically, PD is mathematically represented using a combination of constant ratio, differential, and integral components. Furthermore, this model has successfully been applied to preexisting data, from a prior human study, in which crystalloid was infused for a period of 30 minutes at the beginning of thyroid surgery. Using Euler's formula and a Laplace transform solution to the IDE, patients could be divided into two distinct groups based on their response to PD during the infusion period. Explicitly, Group 1 patients had an infusion-based PD response which was modeled using an exponentially decaying hyperbolic sine function, whereas Group 2 patients had an infusion-based PD response which was modeled using an exponentially decaying trigonometric sine function. Both Group 1 and Group 2 patients had postinfusion PD responses which were modeled using the same combination of hyperbolic sine and hyperbolic cosine functions. Statistically significant differences, between Groups 1 and 2, were noted with respect to the area under their PD curves during both the infusion and postinfusion periods. Specifically, Group 2 patients exhibited a response to PD which was most likely consistent with a preoperative hypovolemia. Overall, this IDE model of PD appears to be highly "adaptable" and successfully fits clinically-obtained human data on a patient-specific basis, during both the infusion and postinfusion periods. In addition, patient-specific IDE modeling of PD may be a useful adjunct in perioperative fluid management and in assessing clinical volume kinetics, of crystalloid solutions, in real time.

Reduction and relative equilibria for the two-body problem on spaces of constant curvature

NASA Astrophysics Data System (ADS)

Borisov, A. V.; García-Naranjo, L. C.; Mamaev, I. S.; Montaldi, J.

2018-06-01

We consider the two-body problem on surfaces of constant nonzero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each q>0 we show there are two relative equilibria where the masses are separated by a distance q. One of these is geometrically of elliptic type and the other of hyperbolic type. The hyperbolic ones are always unstable, while the elliptic ones are stable when sufficiently close, but unstable when far apart. On the sphere of positive curvature, if the masses are different, there is a unique relative equilibrium (RE) for every angular separation except π /2. When the angle is acute, the RE is elliptic, and when it is obtuse the RE can be either elliptic or linearly unstable. We show using a KAM argument that the acute ones are almost always nonlinearly stable. If the masses are equal, there are two families of relative equilibria: one where the masses are at equal angles with the axis of rotation (`isosceles RE') and the other when the two masses subtend a right angle at the centre of the sphere. The isosceles RE are elliptic if the angle subtended by the particles is acute and is unstable if it is obtuse. At π /2, the two families meet and a pitchfork bifurcation takes place. Right-angled RE are elliptic away from the bifurcation point. In each of the two geometric settings, we use a global reduction to eliminate the group of symmetries and analyse the resulting reduced equations which live on a five-dimensional phase space and possess one Casimir function.

Précis of Breakdown of Will.

PubMed

Ainslie, George

2005-10-01

Behavioral science has long been puzzled by the experience of temptation, the resulting impulsiveness, and the variably successful control of this impulsiveness. In conventional theories, a governing faculty like the ego evaluates future choices consistently over time, discounting their value for delay exponentially, that is, by a constant rate; impulses arise when this ego is confronted by a conditioned appetite. Breakdown of Will (Ainslie 2001) presents evidence that contradicts this model. Both people and nonhuman animals spontaneously discount the value of expected events in a curve where value is divided approximately by expected delay, a hyperbolic form that is more bowed than the rational, exponential curve. With hyperbolic discounting, options that pay off quickly will be temporarily preferred to richer but slower-paying alternatives, a phenomenon that, over periods from minutes to days, can account for impulsive behaviors, and over periods of fractional seconds can account for involuntary behaviors. Contradictory reward-getting processes can in effect bargain with each other, and stable preferences can be established by the perception of recurrent choices as test cases (precedents) in recurrent intertemporal prisoner's dilemmas. The resulting motivational pattern resembles traditional descriptions of the will, as well as of compulsive phenomena that can now be seen as side-effects of will: over-concern with precedent, intractable but circumscribed failures of self-control, a motivated ("dynamic") unconscious, and an inability to exploit emotional rewards. Hyperbolic curves also suggest a means of reducing classical conditioning to motivated choice, the last necessary step for modeling many involuntary processes like emotion and appetite as reward-seeking behaviors; such modeling, in turn, provides a rationale for empathic reward and the "construction" of reality.