Multibunch solutions of the differential-difference equation for traffic flow

PubMed

Nakanishi

2000-09-01

The Newell-Whitham type of car-following model, with a hyperbolic tangent as the optimal velocity function, has a finite number of exact steady traveling wave solutions that can be expressed in terms of elliptic theta functions. Each such solution describes a density wave with a definite number of car bunches on a circuit. In our numerical simulations, we observe a transition process from uniform flow to congested flow described by a one-bunch analytic solution, which appears to be an attractor of the system. In this process, the system exhibits a series of transitions through which it comes to assume configurations closely approximating multibunch solutions with successively fewer bunches.

On One-Dimensional Stretching Functions for Finite-Difference Calculations

NASA Technical Reports Server (NTRS)

Vinokur, M.

1980-01-01

The class of one dimensional stretching function used in finite difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two sided stretching function, for which the arbitrary slopes at the two ends of the one dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. The general two sided function has many applications in the construction of finite difference grids.

On one-dimensional stretching functions for finite-difference calculations. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Vinokur, M.

1983-01-01

The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. Previously announced in STAR as N80-25055

Mixed convection and heat generation/absorption aspects in MHD flow of tangent-hyperbolic nanoliquid with Newtonian heat/mass transfer

NASA Astrophysics Data System (ADS)

Qayyum, Sajid; Hayat, Tasawar; Shehzad, Sabir Ali; Alsaedi, Ahmed

2018-03-01

This article concentrates on the magnetohydrodynamic (MHD) stagnation point flow of tangent hyperbolic nanofluid in the presence of buoyancy forces. Flow analysis caused due to stretching surface. Characteristics of heat transfer are examined under the influence of thermal radiation and heat generation/absorption. Newtonian conditions for heat and mass transfer are employed. Nanofluid model includes Brownian motion and thermophoresis. The governing nonlinear partial differential systems of the problem are transformed into a systems of nonlinear ordinary differential equations through appropriate variables. Impact of embedded parameters on the velocity, temperature and nanoparticle concentration fields are presented graphically. Numerical computations are made to obtain the values of skin friction coefficient, local Nusselt and Sherwood numbers. It is concluded that velocity field enhances in the frame of mixed convection parameter while reverse situation is observed due to power law index. Effect of Brownian motion parameter on the temperature and heat transfer rate is quite reverse. Moreover impact of solutal conjugate parameter on the concentration and local Sherwood number is quite similar.

Particle orbits in two-dimensional equilibrium models for the magnetotail

NASA Technical Reports Server (NTRS)

Karimabadi, H.; Pritchett, P. L.; Coroniti, F. V.

1990-01-01

Assuming that there exist an equilibrium state for the magnetotail, particle orbits are investigated in two-dimensional kinetic equilibrium models for the magnetotail. Particle orbits in the equilibrium field are compared with those calculated earlier with one-dimensional models, where the main component of the magnetic field (Bx) was approximated as either a hyperbolic tangent or a linear function of z with the normal field (Bz) assumed to be a constant. It was found that the particle orbits calculated with the two types of models are significantly different, mainly due to the neglect of the variation of Bx with x in the one-dimensional fields.

Optimization of motion control laws for tether crawler or elevator systems

NASA Technical Reports Server (NTRS)

Swenson, Frank R.; Von Tiesenhausen, Georg

1988-01-01

Based on the proposal of a motion control law by Lorenzini (1987), a method is developed for optimizing motion control laws for tether crawler or elevator systems in terms of the performance measures of travel time, the smoothness of acceleration and deceleration, and the maximum values of velocity and acceleration. The Lorenzini motion control law, based on powers of the hyperbolic tangent function, is modified by the addition of a constant-velocity section, and this modified function is then optimized by parameter selections to minimize the peak acceleration value for a selected travel time or to minimize travel time for the selected peak values of velocity and acceleration. It is shown that the addition of a constant-velocity segment permits further optimization of the motion control law performance.

Neural network processing of microbial fuel cell signals for the identification of chemicals present in water.

PubMed

Feng, Yinghua; Barr, William; Harper, W F

2013-05-15

Biosensing is emerging as an important element of water quality monitoring. This research demonstrated that microbial fuel cell (MFC)-based biosensing can be integrated with artificial neural networks (ANNs) to identify specific chemicals present in water samples. The non-fermentable substrates, acetate and butyrate, induced peak areas (PA) and peak heights (PH) that were generally larger than those caused by the injection of fermentable substrates, glucose and corn starch. The ANN successfully identified peaks associated with these four chemicals under a variety of experimental conditions and for two MFCs that had different levels of sensitivity. ANNs that employ the hyperbolic tangent sigmoid transfer function performed better than those using non-continuous transfer functions. ANNs should be integrated into water quality monitoring efforts for smart biosensing. Published by Elsevier Ltd.

Effect of heat release on the spatial stability of a supersonic reacting mixing layer

NASA Technical Reports Server (NTRS)

Jackson, T. L.; Grosch, C. E.

1988-01-01

A numerical study of the stability of compressible mixing layers in which a diffusion flame is embedded is described. The mean velocity profile has been approximated by a hyperbolic tangent profile and the limit of infinite activation energy taken, which reduces the diffusion flame to a flame sheet. The addition of combustion in the form of a flame sheet was found to have important, and complex, effects on the flow stability.

Mixing in Shear Coaxial Jets (Briefing Charts)

DTIC Science & Technology

2013-08-01

relevant boundary layers 9. Thermodynamic states (2 phase, 1 phase) 10. Transverse Acoustic mode from chamber/siren, f=f(c, geometry St=fDij/Uij 11...stability theory for inviscid instability of a hyperbolic tangent velocity profile for free boundary layers • U(y)=0.5[1 + tanh(y)] • Chigier and Beer , 1964...acoustics Natural OJ excited IJ excited From Chigier NA. and Beer JM, The Flow Region Near the Nozzle in Double Concentric Jets, J of

A Unified Overset Grid Generation Graphical Interface and New Concepts on Automatic Gridding Around Surface Discontinuities

NASA Technical Reports Server (NTRS)

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

2002-01-01

For many years, generation of overset grids for complex configurations has required the use of a number of different independently developed software utilities. Results created by each step were then visualized using a separate visualization tool before moving on to the next. A new software tool called OVERGRID was developed which allows the user to perform all the grid generation steps and visualization under one environment. OVERGRID provides grid diagnostic functions such as surface tangent and normal checks as well as grid manipulation functions such as extraction, extrapolation, concatenation, redistribution, smoothing, and projection. Moreover, it also contains hyperbolic surface and volume grid generation modules that are specifically suited for overset grid generation. It is the first time that such a unified interface existed for the creation of overset grids for complex geometries. New concepts on automatic overset surface grid generation around surface discontinuities will also be briefly presented. Special control curves on the surface such as intersection curves, sharp edges, open boundaries, are called seam curves. The seam curves are first automatically extracted from a multiple panel network description of the surface. Points where three or more seam curves meet are automatically identified and are called seam corners. Seam corner surface grids are automatically generated using a singular axis topology. Hyperbolic surface grids are then grown from the seam curves that are automatically trimmed away from the seam corners.

On the Optimization of the Doses of Chemical Fertilizers for Crops

NASA Astrophysics Data System (ADS)

Sala, Florin; Boldea, Marius

2011-09-01

The mono-factorial model, which gives the relation between the yield and the dose of chemical fertilizers, is based on the Mitscherlich function f1(x) = f1(0)+a1(1-e-11x). In addition to this function, we can consider f2(x) = f2(0)+a2 tanh(b2x), to be the basis for a new mathematical model, where tanh(b2x) represents the hyperbolic tangent. In the case of a bi-factorial model: f(x,y) = f(0,0)+a1 tanh(b1x)+a2 tanh(b2y)+a3 tanh(b1x)tanh(b2y) represents a generalization of the last relation. The constants that are involved in these functions are determined with the least squares method, by comparison with the experimental data. Taking into account both the market value of the products and the cost of fertilizers, we can find the optimal doses for maximizing certain economic indicators, such as revenue or profitability.

Density-transition scale at quasiperpendicular collisionless shocks.

PubMed

Bale, S D; Mozer, F S; Horbury, T S

2003-12-31

Measurements of a spacecraft floating potential, on the four Cluster spacecraft, are used as a proxy for electron plasma density to study, for the first time, the macroscopic density transition scale at 98 crossings of the quasiperpendicular terrestrial bow shock. A timing analysis gives shock speeds and normals; the shock speed is used to convert the temporal measurement to a spatial one. A hyperbolic tangent function is fitted to each density transition, which captures the main shock transition, but not overshoot or undershoot nor foot features. We find that, at a low Mach number M, the density transition is consistent with both ion inertial scales c/omega(pi) and convected gyroradii v(sh,n)/Omega(ci,2), while at M>/=4-5 only the convected gyroradius is the preferred scale for the shock density transition and takes the value L approximately 0.4v(sh,n)/Omega(ci,2).

Singularity-free backstepping controller for model helicopters.

PubMed

Zou, Yao; Huo, Wei

2016-11-01

This paper develops a backstepping controller for model helicopters to achieve trajectory tracking without singularity, which occurs in the attitude representation when the roll or pitch reaches ±π2. Based on a simplified model with unmodeled dynamics, backstepping technique is introduced to exploit the controller and hyperbolic tangent functions are utilized to compensate the unmodeled dynamics. Firstly, a position loop controller is designed for the position tracking, where an auxiliary dynamic system with suitable parameters is introduced to warrant the singularity-free requirement for the extracted command attitude. Then, a novel attitude loop controller is proposed to obviate singularity. It is demonstrated that, based on the established criteria for selecting controller parameters and desired trajectories, the proposed controller realizes the singularity-free trajectory tracking of the model helicopter. Simulations confirm the theoretical results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Relative position coordinated control for spacecraft formation flying with communication delays

NASA Astrophysics Data System (ADS)

Ran, Dechao; Chen, Xiaoqian; Misra, Arun K.; Xiao, Bing

2017-08-01

This study addresses a relative position coordinated control problem for spacecraft formation flying subject to directed communication topology. Two different kinds of communication delay cases, including time-varying delays and arbitrarily bounded delays are investigated. Using the backstepping control technique, two virtual velocity control inputs are firstly designed to achieve coordinated position tracking for the kinematic subsystem. Furthermore, a hyperbolic tangent function is introduced to guarantee the boundedness of the virtual controller. Then, a finite-time control algorithm is designed for the dynamic subsystem. It can guarantee that the virtual velocity can be followed by the real velocity after finite time. It is theoretically proved that the proposed control scheme can asymptotically stabilize the closed-loop system. Numerical simulations are further presented that not only highlight closed-loop performance benefiting from the proposed control scheme, but also illustrate its superiority in comparison with conventional formation control schemes.

Improvement of forecast skill for severe weather by merging radar-based extrapolation and storm-scale NWP corrected forecast

NASA Astrophysics Data System (ADS)

Wang, Gaili; Wong, Wai-Kin; Hong, Yang; Liu, Liping; Dong, Jili; Xue, Ming

2015-03-01

The primary objective of this study is to improve the performance of deterministic high resolution rainfall forecasts caused by severe storms by merging an extrapolation radar-based scheme with a storm-scale Numerical Weather Prediction (NWP) model. Effectiveness of Multi-scale Tracking and Forecasting Radar Echoes (MTaRE) model was compared with that of a storm-scale NWP model named Advanced Regional Prediction System (ARPS) for forecasting a violent tornado event that developed over parts of western and much of central Oklahoma on May 24, 2011. Then the bias corrections were performed to improve the forecast accuracy of ARPS forecasts. Finally, the corrected ARPS forecast and radar-based extrapolation were optimally merged by using a hyperbolic tangent weight scheme. The comparison of forecast skill between MTaRE and ARPS in high spatial resolution of 0.01° × 0.01° and high temporal resolution of 5 min showed that MTaRE outperformed ARPS in terms of index of agreement and mean absolute error (MAE). MTaRE had a better Critical Success Index (CSI) for less than 20-min lead times and was comparable to ARPS for 20- to 50-min lead times, while ARPS had a better CSI for more than 50-min lead times. Bias correction significantly improved ARPS forecasts in terms of MAE and index of agreement, although the CSI of corrected ARPS forecasts was similar to that of the uncorrected ARPS forecasts. Moreover, optimally merging results using hyperbolic tangent weight scheme further improved the forecast accuracy and became more stable.

Outer boundary as arrested history in general relativity

NASA Astrophysics Data System (ADS)

Lau, Stephen R.

2002-06-01

We present explicit outer boundary conditions for the canonical variables of general relativity. The conditions are associated with the causal evolution of a finite Cauchy domain, a so-called quasilocal boost, and they suggest a consistent scheme for modelling such an evolution numerically. The scheme involves a continuous boost in the spacetime orthogonal complement ⊥Tp(B) of the tangent space Tp(B) belonging to each point p on the system boundary B. We show how the boost rate may be computed numerically via equations similar to those appearing in canonical investigations of black-hole thermodynamics (although here holding at an outer two-surface rather than the bifurcate two-surface of a Killing horizon). We demonstrate the numerical scheme on a model example, the quasilocal boost of a spherical three-ball in Minkowski spacetime. Developing our general formalism with recent hyperbolic formulations of the Einstein equations in mind, we use Anderson and York's 'Einstein-Christoffel' hyperbolic system as the evolution equations for our numerical simulation of the model.

Numerical simulations of compressible mixing layers

NASA Technical Reports Server (NTRS)

Normand, Xavier

1990-01-01

Direct numerical simulations of two-dimensional temporally growing compressible mixing layers are presented. The Kelvin-Helmholtz instability is initially excited by a white-noise perturbation superimposed onto a hyperbolic tangent meanflow profile. The linear regime is studied at low resolution in the case of two flows of equal temperatures, for convective Mach numbers from 0.1 to 1 and for different values of the Reynolds number. At higher resolution, the complete evolution of a two-eddy mixing layer between two flows of different temperatures is simulated at moderate Reynolds number. Similarities and differences between flows of equal convective Mach numbers are discussed.

A modified sparse reconstruction method for three-dimensional synthetic aperture radar image

NASA Astrophysics Data System (ADS)

Zhang, Ziqiang; Ji, Kefeng; Song, Haibo; Zou, Huanxin

2018-03-01

There is an increasing interest in three-dimensional Synthetic Aperture Radar (3-D SAR) imaging from observed sparse scattering data. However, the existing 3-D sparse imaging method requires large computing times and storage capacity. In this paper, we propose a modified method for the sparse 3-D SAR imaging. The method processes the collection of noisy SAR measurements, usually collected over nonlinear flight paths, and outputs 3-D SAR imagery. Firstly, the 3-D sparse reconstruction problem is transformed into a series of 2-D slices reconstruction problem by range compression. Then the slices are reconstructed by the modified SL0 (smoothed l0 norm) reconstruction algorithm. The improved algorithm uses hyperbolic tangent function instead of the Gaussian function to approximate the l0 norm and uses the Newton direction instead of the steepest descent direction, which can speed up the convergence rate of the SL0 algorithm. Finally, numerical simulation results are given to demonstrate the effectiveness of the proposed algorithm. It is shown that our method, compared with existing 3-D sparse imaging method, performs better in reconstruction quality and the reconstruction time.

Fractional Snow Cover Mapping by Artificial Neural Networks and Support Vector Machines

NASA Astrophysics Data System (ADS)

Çiftçi, B. B.; Kuter, S.; Akyürek, Z.; Weber, G.-W.

2017-11-01

Snow is an important land cover whose distribution over space and time plays a significant role in various environmental processes. Hence, snow cover mapping with high accuracy is necessary to have a real understanding for present and future climate, water cycle, and ecological changes. This study aims to investigate and compare the design and use of artificial neural networks (ANNs) and support vector machines (SVMs) algorithms for fractional snow cover (FSC) mapping from satellite data. ANN and SVM models with different model building settings are trained by using Moderate Resolution Imaging Spectroradiometer surface reflectance values of bands 1-7, normalized difference snow index and normalized difference vegetation index as predictor variables. Reference FSC maps are generated from higher spatial resolution Landsat ETM+ binary snow cover maps. Results on the independent test data set indicate that the developed ANN model with hyperbolic tangent transfer function in the output layer and the SVM model with radial basis function kernel produce high FSC mapping accuracies with the corresponding values of R = 0.93 and R = 0.92, respectively.

Artificial neural network and classical least-squares methods for neurotransmitter mixture analysis.

PubMed

Schulze, H G; Greek, L S; Gorzalka, B B; Bree, A V; Blades, M W; Turner, R F

1995-02-01

Identification of individual components in biological mixtures can be a difficult problem regardless of the analytical method employed. In this work, Raman spectroscopy was chosen as a prototype analytical method due to its inherent versatility and applicability to aqueous media, making it useful for the study of biological samples. Artificial neural networks (ANNs) and the classical least-squares (CLS) method were used to identify and quantify the Raman spectra of the small-molecule neurotransmitters and mixtures of such molecules. The transfer functions used by a network, as well as the architecture of a network, played an important role in the ability of the network to identify the Raman spectra of individual neurotransmitters and the Raman spectra of neurotransmitter mixtures. Specifically, networks using sigmoid and hyperbolic tangent transfer functions generalized better from the mixtures in the training data set to those in the testing data sets than networks using sine functions. Networks with connections that permit the local processing of inputs generally performed better than other networks on all the testing data sets. and better than the CLS method of curve fitting, on novel spectra of some neurotransmitters. The CLS method was found to perform well on noisy, shifted, and difference spectra.

Impact angle constrained three-dimensional integrated guidance and control for STT missile in the presence of input saturation.

PubMed

Wang, Sen; Wang, Weihong; Xiong, Shaofeng

2016-09-01

Considering a class of skid-to-turn (STT) missile with fixed target and constrained terminal impact angles, a novel three-dimensional (3D) integrated guidance and control (IGC) scheme is proposed in this paper. Based on coriolis theorem, the fully nonlinear IGC model without the assumption that the missile flies heading to the target at initial time is established in the three-dimensional space. For this strict-feedback form of multi-variable system, dynamic surface control algorithm is implemented combining with extended observer (ESO) to complete the preliminary design. Then, in order to deal with the problems of the input constraints, a hyperbolic tangent function is introduced to approximate the saturation function and auxiliary system including a Nussbaum function established to compensate for the approximation error. The stability of the closed-loop system is proven based on Lyapunov theory. Numerical simulations results show that the proposed integrated guidance and control algorithm can ensure the accuracy of target interception with initial alignment angle deviation and the input saturation is suppressed with smooth deflection curves. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Particle swarm optimization-based local entropy weighted histogram equalization for infrared image enhancement

NASA Astrophysics Data System (ADS)

Wan, Minjie; Gu, Guohua; Qian, Weixian; Ren, Kan; Chen, Qian; Maldague, Xavier

2018-06-01

Infrared image enhancement plays a significant role in intelligent urban surveillance systems for smart city applications. Unlike existing methods only exaggerating the global contrast, we propose a particle swam optimization-based local entropy weighted histogram equalization which involves the enhancement of both local details and fore-and background contrast. First of all, a novel local entropy weighted histogram depicting the distribution of detail information is calculated based on a modified hyperbolic tangent function. Then, the histogram is divided into two parts via a threshold maximizing the inter-class variance in order to improve the contrasts of foreground and background, respectively. To avoid over-enhancement and noise amplification, double plateau thresholds of the presented histogram are formulated by means of particle swarm optimization algorithm. Lastly, each sub-image is equalized independently according to the constrained sub-local entropy weighted histogram. Comparative experiments implemented on real infrared images prove that our algorithm outperforms other state-of-the-art methods in terms of both visual and quantized evaluations.

Alternative Proofs for Inequalities of Some Trigonometric Functions

ERIC Educational Resources Information Center

Guo, Bai-Ni; Qi, Feng

2008-01-01

By using an identity relating to Bernoulli's numbers and power series expansions of cotangent function and logarithms of functions involving sine function, cosine function and tangent function, four inequalities involving cotangent function, sine function, secant function and tangent function are established.

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.

Consolidation of fatigue and fatigue-crack-propagation data for design use

NASA Technical Reports Server (NTRS)

Rice, R. C.; Davies, K. B.; Jaske, C. E.; Feddersen, C. E.

1975-01-01

Analytical methods developed for consolidation of fatigue and fatigue-crack-propagation data for use in design of metallic aerospace structural components are evaluated. A comprehensive file of data on 2024 and 7075 aluminums, Ti-6Al-4V alloy, and 300M steel was established by obtaining information from both published literature and reports furnished by aerospace companies. Analyses are restricted to information obtained from constant-amplitude load or strain cycling of specimens in air at room temperature. Both fatigue and fatigue-crack-propagation data are analyzed on a statistical basis using a least-squares regression approach. For fatigue, an equivalent strain parameter is used to account for mean stress or stress ratio effects and is treated as the independent variable; cyclic fatigue life is considered to be the dependent variable. An effective stress-intensity factor is used to account for the effect of load ratio on fatigue-crack-propagation and treated as the independent variable. In this latter case, crack-growth rate is considered to be the dependent variable. A two term power function is used to relate equivalent strain to fatigue life, and an arc-hyperbolic-tangent function is used to relate effective stress intensity to crack-growth rate.

Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.

PubMed

Si, Wenjie; Dong, Xunde; Yang, Feifei

2018-03-01

This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.

Effect of heteroscedasticity treatment in residual error models on model calibration and prediction uncertainty estimation

NASA Astrophysics Data System (ADS)

Sun, Ruochen; Yuan, Huiling; Liu, Xiaoli

2017-11-01

The heteroscedasticity treatment in residual error models directly impacts the model calibration and prediction uncertainty estimation. This study compares three methods to deal with the heteroscedasticity, including the explicit linear modeling (LM) method and nonlinear modeling (NL) method using hyperbolic tangent function, as well as the implicit Box-Cox transformation (BC). Then a combined approach (CA) combining the advantages of both LM and BC methods has been proposed. In conjunction with the first order autoregressive model and the skew exponential power (SEP) distribution, four residual error models are generated, namely LM-SEP, NL-SEP, BC-SEP and CA-SEP, and their corresponding likelihood functions are applied to the Variable Infiltration Capacity (VIC) hydrologic model over the Huaihe River basin, China. Results show that the LM-SEP yields the poorest streamflow predictions with the widest uncertainty band and unrealistic negative flows. The NL and BC methods can better deal with the heteroscedasticity and hence their corresponding predictive performances are improved, yet the negative flows cannot be avoided. The CA-SEP produces the most accurate predictions with the highest reliability and effectively avoids the negative flows, because the CA approach is capable of addressing the complicated heteroscedasticity over the study basin.

Fluid simulations of nonlocal dissipative drift-wave turbulence

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Cohen, R. H.; Crotinger, J. A.; Shestakov, A. I.

1995-03-01

A two-dimensional [2d(x,y)] fluid code has been developed to explore nonlocal dissipative drift-wave turbulence and anomalous transport. In order to obtain steady-state turbulence, the y-averaged fluctuating density has been forced to be zero in simulations, thus the difficulty of choosing proper sources and sinks in turbulence simulation codes has been avoided. If Ln≫Lc or Lαlc≫Lc, where Ln is the density gradient scale length, Lc the turbulence correlation length Lc, and Lαlc the adiabaticity-layer width, it has been shown that ``local'' turbulence simulations give reasonable results. However, for Ln˜Lc, or Lαlc˜Lc ``local'' turbulence codes are found to overestimate the flux. For a family of hyperbolic tangent background density profiles, n0(x)=nm-n1 tanh[(2x-Lx)/2Δn] with n1<0.5nm, it has been demonstrated that the nonlocality of the turbulence leads to a transition from local gyro-Bohm (Dlocal≂7.6(Te/eB)[ρs/Ln(x)] [αlc(x)/0.01]-1/3), where αlc(x)=α(x)/κ(x)<1, to nonlocal gyro-Bohm transport scaling [Dnonlocal≂7.6(Te/eB)(n1ρs/nmΔn) (αnlc/0.01)-1/3(Δn/40ρs)2/5 for αnlc(x)=α/κmax<1, κ(x)=ρs/Ln(x) and α=k2∥χe]. For the case Φ0(x)=-n0(x) with the model hyperbolic tangent density profiles n0(x), velocity shear increases the turbulence flux by 230% and the root-mean-square (RMS) fluctuating density by 36%. Otherwise, for Φ0(x)=n0(x), the turbulence flux is reduced by 71% and the RMS value of fluctuating density is decreased by 31% by velocity shear effects.

Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network.

PubMed

An-Min Zou; Kumar, K D; Zeng-Guang Hou; Xi Liu

2011-08-01

A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.

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…

GENIE(++): A Multi-Block Structured Grid System

NASA Technical Reports Server (NTRS)

Williams, Tonya; Nadenthiran, Naren; Thornburg, Hugh; Soni, Bharat K.

1996-01-01

The computer code GENIE++ is a continuously evolving grid system containing a multitude of proven geometry/grid techniques. The generation process in GENIE++ is based on an earlier version. The process uses several techniques either separately or in combination to quickly and economically generate sculptured geometry descriptions and grids for arbitrary geometries. The computational mesh is formed by using an appropriate algebraic method. Grid clustering is accomplished with either exponential or hyperbolic tangent routines which allow the user to specify a desired point distribution. Grid smoothing can be accomplished by using an elliptic solver with proper forcing functions. B-spline and Non-Uniform Rational B-splines (NURBS) algorithms are used for surface definition and redistribution. The built in sculptured geometry definition with desired distribution of points, automatic Bezier curve/surface generation for interior boundaries/surfaces, and surface redistribution is based on NURBS. Weighted Lagrance/Hermite transfinite interpolation methods, interactive geometry/grid manipulation modules, and on-line graphical visualization of the generation process are salient features of this system which result in a significant time savings for a given geometry/grid application.

TIGGERC: Turbomachinery Interactive Grid Generator for 2-D Grid Applications and Users Guide

NASA Technical Reports Server (NTRS)

Miller, David P.

1994-01-01

A two-dimensional multi-block grid generator has been developed for a new design and analysis system for studying multiple blade-row turbomachinery problems. TIGGERC is a mouse driven, interactive grid generation program which can be used to modify boundary coordinates and grid packing and generates surface grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries. The interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC can generate a blocked axisymmetric H-grid, C-grid, I-grid or O-grid for studying turbomachinery flow problems. TIGGERC was developed for operation on Silicon Graphics workstations. Detailed discussion of the grid generation methodology, menu options, operational features and sample grid geometries are presented.

A new Method for Determining the Interplanetary Current-Sheet Local Orientation

NASA Astrophysics Data System (ADS)

Blanco, J. J.; Rodríguez-pacheco, J.; Sequeiros, J.

2003-03-01

In this work we have developed a new method for determining the interplanetary current sheet local parameters. The method, called `HYTARO' (from Hyperbolic Tangent Rotation), is based on a modified Harris magnetic field. This method has been applied to a pool of 57 events, all of them recorded during solar minimum conditions. The model performance has been tested by comparing both, its outputs and noise response, with these of the `classic MVM' (from Minimum Variance Method). The results suggest that, despite the fact that in many cases they behave in a similar way, there are specific crossing conditions that produce an erroneous MVM response. Moreover, our method shows a lower noise level sensitivity than that of MVM.

A new method to approximate load-displacement relationships of spinal motion segments for patient-specific multi-body models of scoliotic spine.

PubMed

Jalalian, Athena; Tay, Francis E H; Arastehfar, Soheil; Liu, Gabriel

2017-06-01

Load-displacement relationships of spinal motion segments are crucial factors in characterizing the stiffness of scoliotic spine models to mimic the spine responses to loads. Although nonlinear approach to approximation of the relationships can be superior to linear ones, little mention has been made to deriving personalized nonlinear load-displacement relationships in previous studies. A method is developed for nonlinear approximation of load-displacement relationships of spinal motion segments to assist characterizing in vivo the stiffness of spine models. We propose approximation by tangent functions and focus on rotational displacements in lateral direction. The tangent functions are characterized using lateral bending test. A multi-body model was characterized to 18 patients and utilized to simulate four spine positions; right bending, left bending, neutral, and traction. The same was done using linear functions to assess the performance of the proposed tangent function in comparison with the linear function. Root-mean-square error (RMSE) of the displacements estimated by the tangent functions was 44 % smaller than the linear functions. This shows the ability of our tangent function in approximation of the relationships for a range of infinitesimal to large displacements involved in the spine movement to the four positions. In addition, the models based on the tangent functions yielded 67, 55, and 39 % smaller RMSEs of Ferguson angles, locations of vertebrae, and orientations of vertebrae, respectively, implying better estimates of spine responses to loads. Overall, it can be concluded that our method for approximating load-displacement relationships of spinal motion segments can offer good estimates of scoliotic spine stiffness.

Modeling the Collisional-Plastic Stress Transition for Bin Discharge of Granular Material

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

Pannala, Sreekanth; Daw, C Stuart; FINNEY, Charles E A

2009-01-01

We propose a heuristic model for the transition between collisional and frictional/plastic stresses in the flow of granular material. Our approach is based on a physically motivated, nonlinear blending function that produces a weighted average of the limiting stresses, depending on the local void fraction in the flow field. Previously published stress models are utilized to describe the behavior in the collisional (Lun et al., 1984) and quasi-static limits (Schaeffer, 1987 and Syamlal et al., 1993). Sigmoidal and hyperbolic tangent functions are used to mimic the observed smooth yet rapid transition between the collisional and plastic stress zones. We implementmore » our stress transition model in an opensource multiphase flow solver, MFIX (Multiphase Flow with Interphase eXchanges, www.mfix.org) and demonstrate its application to a standard bin discharge problem. The model s effectiveness is illustrated by comparing computational predictions to the experimentally derived Beverloo correlation. With the correct choice of function parameters, the model predicts bin discharge rates within the error margins of the Beverloo correlation and is more accurate than one of the alternative granular stress models proposed in the literature. Although a second granular stress model in the literature is also reasonably consistent with the Beverloo correlation, we propose that our alternative blending function is likely to be more adaptable to situations with more complex solids properties (e.g., sticky solids).« less

An arc tangent function demodulation method of fiber-optic Fabry-Perot high-temperature pressure sensor

NASA Astrophysics Data System (ADS)

Ren, Qianyu; Li, Junhong; Hong, Yingping; Jia, Pinggang; Xiong, Jijun

2017-09-01

A new demodulation algorithm of the fiber-optic Fabry-Perot cavity length based on the phase generated carrier (PGC) is proposed in this paper, which can be applied in the high-temperature pressure sensor. This new algorithm based on arc tangent function outputs two orthogonal signals by utilizing an optical system, which is designed based on the field-programmable gate array (FPGA) to overcome the range limit of the original PGC arc tangent function demodulation algorithm. The simulation and analysis are also carried on. According to the analysis of demodulation speed and precision, the simulation of different numbers of sampling points, and measurement results of the pressure sensor, the arc tangent function demodulation method has good demodulation results: 1 MHz processing speed of single data and less than 1% error showing practical feasibility in the fiber-optic Fabry-Perot cavity length demodulation of the Fabry-Perot high-temperature pressure sensor.

Travelling-wave amplitudes as solutions of the phase-field crystal equation

NASA Astrophysics Data System (ADS)

Nizovtseva, I. G.; Galenko, P. K.

2018-01-01

The dynamics of the diffuse interface between liquid and solid states is analysed. The diffuse interface is considered as an envelope of atomic density amplitudes as predicted by the phase-field crystal model (Elder et al. 2004 Phys. Rev. E 70, 051605 (doi:10.1103/PhysRevE.70.051605); Elder et al. 2007 Phys. Rev. B 75, 064107 (doi:10.1103/PhysRevB.75.064107)). The propagation of crystalline amplitudes into metastable liquid is described by the hyperbolic equation of an extended Allen-Cahn type (Galenko & Jou 2005 Phys. Rev. E 71, 046125 (doi:10.1103/PhysRevE.71.046125)) for which the complete set of analytical travelling-wave solutions is obtained by the method (Malfliet & Hereman 1996 Phys. Scr. 15, 563-568 (doi:10.1088/0031-8949/54/6/003); Wazwaz 2004 Appl. Math. Comput. 154, 713-723 (doi:10.1016/S0096-3003(03)00745-8)). The general solution of travelling waves is based on the function of hyperbolic tangent. Together with its set of particular solutions, the general solution is analysed within an example of specific task about the crystal front invading metastable liquid (Galenko et al. 2015 Phys. D 308, 1-10 (doi:10.1016/j.physd.2015.06.002)). The influence of the driving force on the phase-field profile, amplitude velocity and correlation length is investigated for various relaxation times of the gradient flow. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

Symplectic Propagation of the Map, Tangent Map and Tangent Map Derivative through Quadrupole and Combined-Function Dipole Magnets without Truncation

NASA Astrophysics Data System (ADS)

Bruhwiler, D. L.; Cary, J. R.; Shasharina, S.

1998-04-01

The MAPA accelerator modeling code symplectically advances the full nonlinear map, tangent map and tangent map derivative through all accelerator elements. The tangent map and its derivative are nonlinear generalizations of Browns first- and second-order matrices(K. Brown, SLAC-75, Rev. 4 (1982), pp. 107-118.), and they are valid even near the edges of the dynamic aperture, which may be beyond the radius of convergence for a truncated Taylor series. In order to avoid truncation of the map and its derivatives, the Hamiltonian is split into pieces for which the map can be obtained analytically. Yoshidas method(H. Yoshida, Phys. Lett. A 150 (1990), pp. 262-268.) is then used to obtain a symplectic approximation to the map, while the tangent map and its derivative are appropriately composed at each step to obtain them with equal accuracy. We discuss our splitting of the quadrupole and combined-function dipole Hamiltonians and show that typically few steps are required for a high-energy accelerator.

Tangent Lines without Calculus

ERIC Educational Resources Information Center

Rabin, Jeffrey M.

2008-01-01

This article presents a problem that can help high school students develop the concept of instantaneous velocity and connect it with the slope of a tangent line to the graph of position versus time. It also gives a method for determining the tangent line to the graph of a polynomial function at any point without using calculus. (Contains 1 figure.)

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.

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%.

Evaluation of extra virgin olive oil stability by artificial neural network.

PubMed

Silva, Simone Faria; Anjos, Carlos Alberto Rodrigues; Cavalcanti, Rodrigo Nunes; Celeghini, Renata Maria dos Santos

2015-07-15

The stability of extra virgin olive oil in polyethylene terephthalate bottles and tinplate cans stored for 6 months under dark and light conditions was evaluated. The following analyses were carried out: free fatty acids, peroxide value, specific extinction at 232 and 270 nm, chlorophyll, L(∗)C(∗)h color, total phenolic compounds, tocopherols and squalene. The physicochemical changes were evaluated by artificial neural network (ANN) modeling with respect to light exposure conditions and packaging material. The optimized ANN structure consists of 11 input neurons, 18 hidden neurons and 5 output neurons using hyperbolic tangent and softmax activation functions in hidden and output layers, respectively. The five output neurons correspond to five possible classifications according to packaging material (PET amber, PET transparent and tinplate can) and light exposure (dark and light storage). The predicted physicochemical changes agreed very well with the experimental data showing high classification accuracy for test (>90%) and training set (>85). Sensitivity analysis showed that free fatty acid content, peroxide value, L(∗)Cab(∗)hab(∗) color parameters, tocopherol and chlorophyll contents were the physicochemical attributes with the most discriminative power. Copyright © 2015 Elsevier Ltd. All rights reserved.

Embedding recurrent neural networks into predator-prey models.

PubMed

Moreau, Yves; Louiès, Stephane; Vandewalle, Joos; Brenig, Leon

1999-03-01

We study changes of coordinates that allow the embedding of ordinary differential equations describing continuous-time recurrent neural networks into differential equations describing predator-prey models-also called Lotka-Volterra systems. We transform the equations for the neural network first into quasi-monomial form (Brenig, L. (1988). Complete factorization and analytic solutions of generalized Lotka-Volterra equations. Physics Letters A, 133(7-8), 378-382), where we express the vector field of the dynamical system as a linear combination of products of powers of the variables. In practice, this transformation is possible only if the activation function is the hyperbolic tangent or the logistic sigmoid. From this quasi-monomial form, we can directly transform the system further into Lotka-Volterra equations. The resulting Lotka-Volterra system is of higher dimension than the original system, but the behavior of its first variables is equivalent to the behavior of the original neural network. We expect that this transformation will permit the application of existing techniques for the analysis of Lotka-Volterra systems to recurrent neural networks. Furthermore, our results show that Lotka-Volterra systems are universal approximators of dynamical systems, just as are continuous-time neural networks.

High-velocity impact loading of thick GFRP blocks

NASA Astrophysics Data System (ADS)

Ernst, H.-J.; Merkel, Th.; Wolf, Th.; Hoog, K.

2003-09-01

In previous depth of penetration experiments with tungsten long rod projectiles was found that the ballistic resistance of a relatively thick-up to the penetrator length-glass fibre reinforced plastic block grows with increasing penetration depth. This penetration behaviour significantly differs from that of other inert armour materials. Until now, no significant difference between unconfined and totally confined GFRP configurations bas been found. Newest experiments with up to semi-infinite thick GFRP blocks show a change in the penetration process: For thicknesses significantly higher than the penetrator length the protective power may saturate. During the late penetration phase the shortening and deceleration of the projectile induce a change of penetration mechanism from erosion to rigid body penetration. Additionally, the projectile may break into several individually tumbling parts. Reflected tension waves and, probably, pyrolysis effects may cause increasing precursory damage. These effects together are likely to explain the reduction of the ballistic resistance increase during the late penetration phase. Based on these experimental results the published working hypothesis on the governing mechanism of the GFRP penetration behaviour had to be completed. A new approach based on a hyperbolic tangent function seems to satisfactorily describe the observed thickness dependent phenomena.

TDIGG - TWO-DIMENSIONAL, INTERACTIVE GRID GENERATION CODE

NASA Technical Reports Server (NTRS)

Vu, B. T.

1994-01-01

TDIGG is a fast and versatile program for generating two-dimensional computational grids for use with finite-difference flow-solvers. Both algebraic and elliptic grid generation systems are included. The method for grid generation by algebraic transformation is based on an interpolation algorithm and the elliptic grid generation is established by solving the partial differential equation (PDE). Non-uniform grid distributions are carried out using a hyperbolic tangent stretching function. For algebraic grid systems, interpolations in one direction (univariate) and two directions (bivariate) are considered. These interpolations are associated with linear or cubic Lagrangian/Hermite/Bezier polynomial functions. The algebraic grids can subsequently be smoothed using an elliptic solver. For elliptic grid systems, the PDE can be in the form of Laplace (zero forcing function) or Poisson. The forcing functions in the Poisson equation come from the boundary or the entire domain of the initial algebraic grids. A graphics interface procedure using the Silicon Graphics (GL) Library is included to allow users to visualize the grid variations at each iteration. This will allow users to interactively modify the grid to match their applications. TDIGG is written in FORTRAN 77 for Silicon Graphics IRIS series computers running IRIX. This package requires either MIT's X Window System, Version 11 Revision 4 or SGI (Motif) Window System. A sample executable is provided on the distribution medium. It requires 148K of RAM for execution. The standard distribution medium is a .25 inch streaming magnetic IRIX tape cartridge in UNIX tar format. This program was developed in 1992.

Obliquely propagating low frequency electromagnetic shock waves in two dimensional quantum magnetoplasmas

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

Masood, W.

2009-04-15

Linear and nonlinear propagation characteristics of low frequency magnetoacoustic waves in quantum magnetoplasmas are studied employing the quantum magnetohydrodynamic model. In this regard, a quantum Kadomtsev-Petviashvili-Burgers (KPB) equation is derived using the small amplitude expansion method. The dissipation is introduced by taking into account the kinematic viscosity among the plasma constituents. Furthermore, the solution of KPB equation is presented using the tangent hyperbolic (tanh) method. The variation in the fast and slow magnetoacoustic shock profiles with the quantum Bohm potential via increasing number density, obliqueness angle {theta}, magnetic field, and the resistivity are also investigated. It is observed that themore » aforementioned plasma parameters significantly modify the propagation characteristics of nonlinear magnetoacoustic shock waves in quantum magnetoplasmas. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.« less

The interaction of turbulence with parallel and perpendicular shocks

NASA Astrophysics Data System (ADS)

Adhikari, L.; Zank, G. P.; Hunana, P.; Hu, Q.

2016-11-01

Interplanetary shocks exist in most astrophysical flows, and modify the properties of the background flow. We apply the Zank et al 2012 six coupled turbulence transport model equations to study the interaction of turbulence with parallel and perpendicular shock waves in the solar wind. We model the 1D structure of a stationary perpendicular or parallel shock wave using a hyperbolic tangent function and the Rankine-Hugoniot conditions. A reduced turbulence transport model (the 4-equation model) is applied to parallel and perpendicular shock waves, and solved using a 4th- order Runge Kutta method. We compare the model results with ACE spacecraft observations. We identify one quasi-parallel and one quasi-perpendicular event in the ACE spacecraft data sets, and compute various turbulent observed values such as the fluctuating magnetic and kinetic energy, the energy in forward and backward propagating modes, the total turbulent energy in the upstream and downstream of the shock. We also calculate the error associated with each turbulent observed value, and fit the observed values by a least square method and use a Fourier series fitting function. We find that the theoretical results are in reasonable agreement with observations. The energy in turbulent fluctuations is enhanced and the correlation length is approximately constant at the shock. Similarly, the normalized cross helicity increases across a perpendicular shock, and decreases across a parallel shock.

Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks.

PubMed

Zou, An-Min; Dev Kumar, Krishna; Hou, Zeng-Guang

2010-09-01

This paper investigates the problem of output feedback attitude control of an uncertain spacecraft. Two robust adaptive output feedback controllers based on Chebyshev neural networks (CNN) termed adaptive neural networks (NN) controller-I and adaptive NN controller-II are proposed for the attitude tracking control of spacecraft. The four-parameter representations (quaternion) are employed to describe the spacecraft attitude for global representation without singularities. The nonlinear reduced-order observer is used to estimate the derivative of the spacecraft output, and the CNN is introduced to further improve the control performance through approximating the spacecraft attitude motion. The implementation of the basis functions of the CNN used in the proposed controllers depends only on the desired signals, and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the CNN approximation errors and external disturbances. The adaptive NN controller-II can efficiently avoid the over-estimation problem (i.e., the bound of the CNNs output is much larger than that of the approximated unknown function, and hence, the control input may be very large) existing in the adaptive NN controller-I. Both adaptive output feedback controllers using CNN can guarantee that all signals in the resulting closed-loop system are uniformly ultimately bounded. For performance comparisons, the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed. Simulation studies are presented to show the advantages of the proposed CNN-based output feedback approach over the standard adaptive output feedback approach.

Potential energy function for CH3+CH3 ⇆ C2H6: Attributes of the minimum energy path

NASA Astrophysics Data System (ADS)

Robertson, S. H.; Wardlaw, D. M.; Hirst, D. M.

1993-11-01

The region of the potential energy surface for the title reaction in the vicinity of its minimum energy path has been predicted from the analysis of ab initio electronic energy calculations. The ab initio procedure employs a 6-31G** basis set and a configuration interaction calculation which uses the orbitals obtained in a generalized valence bond calculation. Calculated equilibrium properties of ethane and of isolated methyl radical are compared to existing theoretical and experimental results. The reaction coordinate is represented by the carbon-carbon interatomic distance. The following attributes are reported as a function of this distance and fit to functional forms which smoothly interpolate between reactant and product values of each attribute: the minimum energy path potential, the minimum energy path geometry, normal mode frequencies for vibrational motion orthogonal to the reaction coordinate, a torsional potential, and a fundamental anharmonic frequency for local mode, out-of-plane CH3 bending (umbrella motion). The best representation is provided by a three-parameter modified Morse function for the minimum energy path potential and a two-parameter hyperbolic tangent switching function for all other attributes. A poorer but simpler representation, which may be satisfactory for selected applications, is provided by a standard Morse function and a one-parameter exponential switching function. Previous applications of the exponential switching function to estimate the reaction coordinate dependence of the frequencies and geometry of this system have assumed the same value of the range parameter α for each property and have taken α to be less than or equal to the ``standard'' value of 1.0 Å-1. Based on the present analysis this is incorrect: The α values depend on the property and range from ˜1.2 to ˜1.8 Å-1.

Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.

PubMed

Sun, Shiliang; Xie, Xijiong

2016-09-01

Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

How should spin-weighted spherical functions be defined?

NASA Astrophysics Data System (ADS)

Boyle, Michael

2016-09-01

Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the normal to the sphere. These component functions are usually presented as functions on the sphere itself, but this requires an implicit choice of distinguished tangent vectors with which to contract. Thus, we may more accurately say that spin-weighted spherical functions are functions of both a point on the sphere and a choice of frame in the tangent space at that point. The distinction becomes extremely important when transforming the coordinates in which these functions are expressed, because the implicit choice of frame will also transform. Here, it is proposed that spin-weighted spherical functions should be treated as functions on the spin or rotation groups, which simultaneously tracks the point on the sphere and the choice of tangent frame by rotating elements of an orthonormal basis. In practice, the functions simply take a quaternion argument and produce a complex value. This approach more cleanly reflects the geometry involved, and allows for a more elegant description of the behavior of spin-weighted functions. In this form, the spin-weighted spherical harmonics have simple expressions as elements of the Wigner 𝔇 representations, and transformations under rotation are simple. Two variants of the angular-momentum operator are defined directly in terms of the spin group; one is the standard angular-momentum operator L, while the other is shown to be related to the spin-raising operator ð.

Nonplanar electrostatic shock waves in dense plasmas

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

Masood, W.; Rizvi, H.

2010-02-15

Two-dimensional quantum ion acoustic shock waves (QIASWs) are studied in an unmagnetized plasma consisting of electrons and ions. In this regard, a nonplanar quantum Kadomtsev-Petviashvili-Burgers (QKPB) equation is derived using the small amplitude perturbation expansion method. Using the tangent hyperbolic method, an analytical solution of the planar QKPB equation is obtained and subsequently used as the initial profile to numerically solve the nonplanar QKPB equation. It is observed that the increasing number density (and correspondingly the quantum Bohm potential) and kinematic viscosity affect the propagation characteristics of the QIASW. The temporal evolution of the nonplanar QIASW is investigated both inmore » Cartesian and polar planes and the results are discussed from the numerical stand point. The results of the present study may be applicable in the study of propagation of small amplitude localized electrostatic shock structures in dense astrophysical environments.« less

A new equation in two dimensional fast magnetoacoustic shock waves in electron-positron-ion plasmas

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

Masood, W.; Jehan, Nusrat; Mirza, Arshad M.

2010-03-15

Nonlinear properties of the two dimensional fast magnetoacoustic waves are studied in a three-component plasma comprising of electrons, positrons, and ions. In this regard, Kadomtsev-Petviashvili-Burger (KPB) equation is derived using the small amplitude perturbation expansion method. Under the condition that the electron and positron inertia are ignored, Burger-Kadomtsev-Petviashvili (Burger-KP) for a fast magnetoacoustic wave is derived for the first time, to the best of author's knowledge. The solutions of both KPB and Burger-KP equations are obtained using the tangent hyperbolic method. The effects of positron concentration, kinematic viscosity, and plasma beta are explored both for the KPB and the Burger-KPmore » shock waves and the differences between the two are highlighted. The present investigation may have relevance in the study of nonlinear electromagnetic shock waves both in laboratory and astrophysical plasmas.« less

Ion acoustic shock waves in plasmas with warm ions and kappa distributed electrons and positrons

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

Hussain, S.; Mahmood, S.; Hafeez Ur-Rehman

2013-06-15

The monotonic and oscillatory ion acoustic shock waves are investigated in electron-positron-ion plasmas (e-p-i) with warm ions (adiabatically heated) and nonthermal kappa distributed electrons and positrons. The dissipation effects are included in the model due to kinematic viscosity of the ions. Using reductive perturbation technique, the Kadomtsev-Petviashvili-Burgers (KPB) equation is derived containing dispersion, dissipation, and diffraction effects (due to perturbation in the transverse direction) in e-p-i plasmas. The analytical solution of KPB equation is obtained by employing tangent hyperbolic (Tanh) method. The analytical condition for the propagation of oscillatory and monotonic shock structures are also discussed in detail. The numericalmore » results of two dimensional monotonic shock structures are obtained for graphical representation. The dependence of shock structures on positron equilibrium density, ion temperature, nonthermal spectral index kappa, and the kinematic viscosity of ions are also discussed.« less

Dynamic transport study of the plasmas with transport improvement in LHD and JT-60U

NASA Astrophysics Data System (ADS)

Ida, K.; Sakamoto, Y.; Inagaki, S.; Takenaga, H.; Isayama, A.; Matsunaga, G.; Sakamoto, R.; Tanaka, K.; Ide, S.; Fujita, T.; Funaba, H.; Kubo, S.; Yoshinuma, M.; Shimozuma, T.; Takeiri, Y.; Ikeda, K.; Michael, C.; Tokuzawa, T.; LHD experimental Group; JT-60 Team

2009-01-01

Transport analysis during the transient phase of heating (a dynamic transport study) applied to the plasma with internal transport barriers (ITBs) in the Large Helical Device (LHD) heliotron and the JT-60U tokamak is described. In the dynamic transport study the time of transition from the L-mode plasma to the ITB plasma is clearly determined by the onset of flattening of the temperature profile in the core region and a spontaneous phase transition from a zero curvature ITB (hyperbolic tangent shaped ITB) or a positive curvature ITB (concaved shaped ITB) to a negative curvature ITB (convex shaped ITB) and its back-transition are observed. The flattening of the core region of the ITB transition and the back-transition between a zero curvature ITB and a convex ITB suggest the strong interaction of turbulent transport in space.

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.

Comparison of irradiation-induced shifts of K{sub Jc} and Charpy impact toughness for reactor pressure vessel steels

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

Sokolov, M.A.; Nanstad, R.K.

1999-10-01

The current provisions for determination of the upward temperature shift of the lower-bound static fracture toughness curve due to irradiation of reactor pressure vessel steels are based on the assumption that they are the same as the Charpy 41-J shifts as a consequence of irradiation. The objective of this paper is to evaluate this assumption relative to data reported in open publications. Depending on the specific source, different sizes of fracture toughness specimens, procedures of the K{sub Jc} determination, and fitting functions were used. It was anticipated that the scatter might be reduced by using a consistent approach to analyzemore » the published data. A method employing Weibull statistics is applied to analyze original fracture toughness data of unirradiated and irradiated pressure vessel steels. Application of the master curve concept is used to determine shifts of fracture toughness transition curves. A hyperbolic tangent function is used to fit charpy absorbed energy data. The fracture toughness shifts are compared to Charpy impact shifts evaluated with various criteria. Linear regression analysis showed that for weld metals, on average, the fracture toughness shift is the same as the Charpy 41-J temperature shift, while for base metals, on average, the fracture toughness shift at 41 J is 16% greater than the shift of the Charpy 41-J transition temperature, with both correlations having relatively large 95% confidence intervals.« less

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

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).

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.

Dynamic Geometry Software and Tracing Tangents in the Context of the Mean Value Theorem: Technique and Theory Production

ERIC Educational Resources Information Center

Martínez-Hernández, Cesar; Ulloa-Azpeitia, Ricardo

2017-01-01

Based on the theoretical elements of the instrumental approach to tool use known as Task-Technique-Theory (Artigue, 2002), this paper analyses and discusses the performance of graduate students enrolled in a Teacher Training program. The latter performance relates to tracing tangent lines to the curve of a quadratic function in Dynamic Geometry…

Three-dimensional boundary layer calculation by a characteristic method

NASA Technical Reports Server (NTRS)

Houdeville, R.

1992-01-01

A numerical method for solving the three-dimensional boundary layer equations for bodies of arbitrary shape is presented. In laminar flows, the application domain extends from incompressible to hypersonic flows with the assumption of chemical equilibrium. For turbulent boundary layers, the application domain is limited by the validity of the mixing length model used. In order to respect the hyperbolic nature of the equations reduced to first order partial derivative terms, the momentum equations are discretized along the local streamlines using of the osculator tangent plane at each node of the body fitted coordinate system. With this original approach, it is possible to overcome the use of the generalized coordinates, and therefore, it is not necessary to impose an extra hypothesis about the regularity of the mesh in which the boundary conditions are given. By doing so, it is possible to limit, and sometimes to suppress, the pre-treatment of the data coming from an inviscid calculation. Although the proposed scheme is only semi-implicit, the method remains numerically very efficient.

Calculation of the flow field including boundary layer effects for supersonic mixed compression inlets at angles of attack

NASA Technical Reports Server (NTRS)

Vadyak, J.; Hoffman, J. D.

1982-01-01

The flow field in supersonic mixed compression aircraft inlets at angle of attack is calculated. A zonal modeling technique is employed to obtain the solution which divides the flow field into different computational regions. The computational regions consist of a supersonic core flow, boundary layer flows adjacent to both the forebody/centerbody and cowl contours, and flow in the shock wave boundary layer interaction regions. The zonal modeling analysis is described and some computational results are presented. The governing equations for the supersonic core flow form a hyperbolic system of partial differential equations. The equations for the characteristic surfaces and the compatibility equations applicable along these surfaces are derived. The characteristic surfaces are the stream surfaces, which are surfaces composed of streamlines, and the wave surfaces, which are surfaces tangent to a Mach conoid. The compatibility equations are expressed as directional derivatives along streamlines and bicharacteristics, which are the lines of tangency between a wave surface and a Mach conoid.

Evolution of inviscid Kelvin-Helmholtz instability from a piecewise linear shear layer

NASA Astrophysics Data System (ADS)

Guha, Anirban; Rahmani, Mona; Lawrence, Gregory

2012-11-01

Here we study the evolution of 2D, inviscid Kelvin-Helmholtz instability (KH) ensuing from a piecewise linear shear layer. Although KH pertaining to smooth shear layers (eg. Hyperbolic tangent profile) has been thorough investigated in the past, very little is known about KH resulting from sharp shear layers. Pozrikidis and Higdon (1985) have shown that piecewise shear layer evolves into elliptical vortex patches. This non-linear state is dramatically different from the well known spiral-billow structure of KH. In fact, there is a little acknowledgement that elliptical vortex patches can represent non-linear KH. In this work, we show how such patches evolve through the interaction of vorticity waves. Our work is based on two types of computational methods (i) Contour Dynamics: a boundary-element method which tracks the evolution of the contour of a vortex patch using Lagrangian marker points, and (ii) Direct Numerical Simulation (DNS): an Eulerian pseudo-spectral method heavily used in studying hydrodynamic instability and turbulence.

Bifurcation analysis for ion acoustic waves in a strongly coupled plasma including trapped electrons

NASA Astrophysics Data System (ADS)

El-Labany, S. K.; El-Taibany, W. F.; Atteya, A.

2018-02-01

The nonlinear ion acoustic wave propagation in a strongly coupled plasma composed of ions and trapped electrons has been investigated. The reductive perturbation method is employed to derive a modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation. To solve this equation in case of dissipative system, the tangent hyperbolic method is used, and a shock wave solution is obtained. Numerical investigations show that, the ion acoustic waves are significantly modified by the effect of polarization force, the trapped electrons and the viscosity coefficients. Applying the bifurcation theory to the dynamical system of the derived mKdV-Burgers equation, the phase portraits of the traveling wave solutions of both of dissipative and non-dissipative systems are analyzed. The present results could be helpful for a better understanding of the waves nonlinear propagation in a strongly coupled plasma, which can be produced by photoionizing laser-cooled and trapped electrons [1], and also in neutron stars or white dwarfs interior.

Effects of using two- versus three-dimensional computational modeling of fluidized beds Part I, hydrodynamics

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

Xie, Nan; Battaglia, Francine; Pannala, Sreekanth

2008-01-01

Simulations of fluidized beds are performed to study and determine the effect on the use of coordinate systems and geometrical configurations to model fluidized bed reactors. Computational fluid dynamics is employed for an Eulerian-Eulerian model, which represents each phase as an interspersed continuum. The transport equation for granular temperature is solved and a hyperbolic tangent function is used to provide a smooth transition between the plastic and viscous regimes for the solid phase. The aim of the present work is to show the range of validity for employing simulations based on a 2D Cartesian coordinate system to approximate both cylindricalmore » and rectangular fluidized beds. Three different fluidization regimes, bubbling, slugging and turbulent regimes, are investigated and the results of 2D and 3D simulations are presented for both cylindrical and rectangular domains. The results demonstrate that a 2D Cartesian system can be used to successfully simulate and predict a bubbling regime. However, caution must be exercised when using 2D Cartesian coordinates for other fluidized regimes. A budget analysis that explains all the differences in detail is presented in Part II [N. Xie, F. Battaglia, S. Pannala, Effects of Using Two-Versus Three-Dimensional Computational Modeling of Fluidized Beds: Part II, budget analysis, 182 (1) (2007) 14] to complement the hydrodynamic theory of this paper.« less

The Interaction of Turbulence with Parallel and Perpendicular Shocks: Theory and Observations at 1 au

NASA Astrophysics Data System (ADS)

Adhikari, L.; Zank, G. P.; Hunana, P.; Hu, Q.

2016-12-01

Shocks are thought to be responsible for the amplification of turbulence as well as for generating turbulence throughout the heliosphere. We study the interaction of turbulence with parallel and perpendicular shock waves using the six-coupled-equation turbulence transport model of Zank et al. We model a 1D stationary shock wave using a hyperbolic tangent function and the Rankine-Hugoniot conditions for both a reduced model with four coupled equations and the full model. Eight quasi-parallel and five quasi-perpendicular events in the WIND spacecraft data sets are identified, and we compute the fluctuating magnetic and kinetic energy, the energy in forward and backward propagating modes, the total turbulent energy, the normalized residual energy, and the normalized cross helicity upstream and downstream of the observed shocks. We compare the observed fitted values upstream and downstream of the shock with numerical solutions to our model equations. The comparison shows that our theoretical results are in reasonable agreement with observations for both quasi-parallel and perpendicular shocks. We find that (1) the total turbulent energy, the energy in forward and backward propagating modes, and the normalized residual energy increase across the shock, (2) the normalized cross helicity increases or decreases across the shock, and (3) the correlation length increases upstream and downstream of the shock, and slightly flattens or decreases across the shock.

An Efficient Approach for Lipase-Catalyzed Synthesis of Retinyl Laurate Nutraceutical by Combining Ultrasound Assistance and Artificial Neural Network Optimization.

PubMed

Huang, Shang-Ming; Li, Hsin-Ju; Liu, Yung-Chuan; Kuo, Chia-Hung; Shieh, Chwen-Jen

2017-11-15

Although retinol is an important nutrient, retinol is highly sensitive to oxidation. At present, some ester forms of retinol are generally used in nutritional supplements because of its stability and bioavailability. However, such esters are commonly synthesized by chemical procedures which are harmful to the environment. Thus, this study utilized a green method using lipase as a catalyst with sonication assistance to produce a retinol derivative named retinyl laurate. Moreover, the process was optimized by an artificial neural network (ANN). First, a three-level-four-factor central composite design (CCD) was employed to design 27 experiments, which the highest relative conversion was 82.64%. Further, the optimal architecture of the CCD-employing ANN was developed, including the learning Levenberg-Marquardt algorithm, the transfer function (hyperbolic tangent), iterations (10,000), and the nodes of the hidden layer (6). The best performance of the ANN was evaluated by the root mean squared error (RMSE) and the coefficient of determination ( R ²) from predicting and observed data, which displayed a good data-fitting property. Finally, the process performed with optimal parameters actually obtained a relative conversion of 88.31% without long-term reactions, and the lipase showed great reusability for biosynthesis. Thus, this study utilizes green technology to efficiently produce retinyl laurate, and the bioprocess is well established by ANN-mediated modeling and optimization.

Linear Temporal Stability Analysis of a Low-Density Round Gas Jet Injected into a High-Density Gas

NASA Technical Reports Server (NTRS)

Lawson, Anthony L.; Parthasarathy, Ramkumar N.

2002-01-01

It has been observed in previous experimental studies that round helium jets injected into air display a repetitive structure for a long distance, somewhat similar to the buoyancy-induced flickering observed in diffusion flames. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis of a round helium jet injected into air was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. The temporal growth rates of the disturbances increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity.

THE INTERACTION OF TURBULENCE WITH PARALLEL AND PERPENDICULAR SHOCKS: THEORY AND OBSERVATIONS AT 1 au

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

Adhikari, L.; Zank, G. P.; Hunana, P.

Shocks are thought to be responsible for the amplification of turbulence as well as for generating turbulence throughout the heliosphere. We study the interaction of turbulence with parallel and perpendicular shock waves using the six-coupled-equation turbulence transport model of Zank et al. We model a 1D stationary shock wave using a hyperbolic tangent function and the Rankine–Hugoniot conditions for both a reduced model with four coupled equations and the full model. Eight quasi-parallel and five quasi-perpendicular events in the WIND spacecraft data sets are identified, and we compute the fluctuating magnetic and kinetic energy, the energy in forward and backwardmore » propagating modes, the total turbulent energy, the normalized residual energy, and the normalized cross helicity upstream and downstream of the observed shocks. We compare the observed fitted values upstream and downstream of the shock with numerical solutions to our model equations. The comparison shows that our theoretical results are in reasonable agreement with observations for both quasi-parallel and perpendicular shocks. We find that (1) the total turbulent energy, the energy in forward and backward propagating modes, and the normalized residual energy increase across the shock, (2) the normalized cross helicity increases or decreases across the shock, and (3) the correlation length increases upstream and downstream of the shock, and slightly flattens or decreases across the shock.« less

Supervised artificial neural network-based method for conversion of solar radiation data (case study: Algeria)

NASA Astrophysics Data System (ADS)

Laidi, Maamar; Hanini, Salah; Rezrazi, Ahmed; Yaiche, Mohamed Redha; El Hadj, Abdallah Abdallah; Chellali, Farouk

2017-04-01

In this study, a backpropagation artificial neural network (BP-ANN) model is used as an alternative approach to predict solar radiation on tilted surfaces (SRT) using a number of variables involved in physical process. These variables are namely the latitude of the site, mean temperature and relative humidity, Linke turbidity factor and Angstrom coefficient, extraterrestrial solar radiation, solar radiation data measured on horizontal surfaces (SRH), and solar zenith angle. Experimental solar radiation data from 13 stations spread all over Algeria around the year (2004) were used for training/validation and testing the artificial neural networks (ANNs), and one station was used to make the interpolation of the designed ANN. The ANN model was trained, validated, and tested using 60, 20, and 20 % of all data, respectively. The configuration 8-35-1 (8 inputs, 35 hidden, and 1 output neurons) presented an excellent agreement between the prediction and the experimental data during the test stage with determination coefficient of 0.99 and root meat squared error of 5.75 Wh/m2, considering a three-layer feedforward backpropagation neural network with Levenberg-Marquardt training algorithm, a hyperbolic tangent sigmoid and linear transfer function at the hidden and the output layer, respectively. This novel model could be used by researchers or scientists to design high-efficiency solar devices that are usually tilted at an optimum angle to increase the solar incident on the surface.

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.

Artificial neural networks can be effectively used to model changes of intracranial pressure (ICP) during spinal surgery using different non invasive ICP surrogate estimators.

PubMed

Watad, Abdulla; Bragazzi, Nicola L; Bacigaluppi, Susanna; Amital, Howard; Watad, Samaa; Sharif, Kassem; Bisharat, Bishara; Siri, Anna; Mahamid, Ala; Abu Ras, Hakim; Nasr, Ahmed; Bilotta, Federico; Robba, Chiara; Adawi, Mohammad

2018-02-23

Artificial Intelligence (AI) techniques play a major role in anesthesiology, even though their importance is often overlooked. In the extant literature, AI approaches, such as Artificial Neural Networks (ANNs), have been underutilized, mainly being used to model patient's consciousness state, to predict the precise amount of anesthetic gases, the level of analgesia, or the need of anesthesiological blocks, among others. In the field of neurosurgery, ANNs have been effectively applied to the diagnosis and prognosis of cerebral tumors, seizures, low back pain, and also to the monitoring of intracranial pressure (ICP). A MultiLayer Perceptron (MLP), which is a feedforward ANN, with hyperbolic tangent as activation function in the input/hidden layers, softmax as activation function in the output layer, and cross-entropy as error function, was used to model the impact of prone versus supine position and the use of positive end expiratory pressure (PEEP) on ICP in a sample of 30 patients undergoing spinal surgery. Different non invasive surrogate estimations of ICP have been used and compared: namely, mean optic nerve sheath diameter (ONSD), non invasive estimated cerebral perfusion pressure (NCPP), pulsatility index (PI), ICP derived from PI (ICP-PI), and flow velocity diastolic formula (FVDICP). ONSD proved to be a more robust surrogate estimation of ICP, with a predictive power of 75%, whilst the power of NCPP, ICP-PI, PI, and FVDICP were 60.5%, 54.8%, 53.1%, and 47.7%, respectively. Our MLP analysis confirmed our findings previously obtained with regression, correlation, multivariate Receiving Operator Curve (multi-ROC) analyses. ANNs can be successfully used to predict the effects of prone versus supine position and PEEP on ICP in patients undergoing spinal surgery using different non invasive surrogate estimators of ICP.

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

Mathematical analysis demonstrates that interferons-β and -γ Interact in a multiplicative manner to disrupt herpes simplex virus replication

USGS Publications Warehouse

Halford, William P.; Halford, Keith J.; Pierce, Amy T.

2005-01-01

Several studies suggest that the innate interferons (IFNs), IFN-α and IFN-β, can act in concert with IFN-γto synergistically inhibit the replication of cytomegalovirus and herpes simplex virus type 1 (HSV-1). The significance of this observation is not yet agreed upon in large part because the nature and magnitude of the interaction between IFN-α/β and IFN-γ is not well defined. In the current study, we resolve this issue by demonstrating three points. First, the hyperbolic tangent function, tanh (x  ), can be used to describe the individual effects of IFN-β or IFN-γ on HSV-1 replication over a 320,000-fold range of IFN concentration. Second, pharmacological methods prove that IFN-β and IFN-γ interact in a greater-than-additive manner to inhibit HSV-1 replication. Finally, the potency with which combinations of IFN-β and IFN-γ inhibit HSV-1 replication is accurately predicted by multiplying the individual inhibitory effects of each cytokine. Thus, IFN-β and IFN-γ interact in a multiplicative manner. We infer that a primary antiviral function of IFN-γ lies in its capacity to multiply the potency with which IFN-α/β restricts HSV-1 replication in vivo. This hypothesis has important ramifications for understanding how T lymphocyte-secreted cytokines such as IFN-γ can force herpesviruses into a latent state without destroying the neurons or leukocytes that continue to harbor these viral infections for the lifetime of the host.

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).

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.

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.

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.

Arctic curves in path models from the tangent method

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Lapa, Matthew F.

2018-04-01

Recently, Colomo and Sportiello introduced a powerful method, known as the tangent method, for computing the arctic curve in statistical models which have a (non- or weakly-) intersecting lattice path formulation. We apply the tangent method to compute arctic curves in various models: the domino tiling of the Aztec diamond for which we recover the celebrated arctic circle; a model of Dyck paths equivalent to the rhombus tiling of a half-hexagon for which we find an arctic half-ellipse; another rhombus tiling model with an arctic parabola; the vertically symmetric alternating sign matrices, where we find the same arctic curve as for unconstrained alternating sign matrices. The latter case involves lattice paths that are non-intersecting but that are allowed to have osculating contact points, for which the tangent method was argued to still apply. For each problem we estimate the large size asymptotics of a certain one-point function using LU decomposition of the corresponding Gessel–Viennot matrices, and a reformulation of the result amenable to asymptotic analysis.

Navier-Stokes dynamics on a differential one-form

NASA Astrophysics Data System (ADS)

Story, Troy L.

2006-11-01

After transforming the Navier-Stokes dynamic equation into a characteristic differential one-form on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position x^k and the conjugate to the position bk as functions of time. The solution bk is shown to be divergence-free by contracting the differential 3-form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution bk shows it is bounded since it remains finite as | x^k | ->,, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian is obtained.

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.

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.

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.

Finding Equations of Tangents to Conics

ERIC Educational Resources Information Center

Baloglou, George; Helfgott, Michel

2004-01-01

A calculus-free approach is offered for determining the equation of lines tangent to conics. Four types of problems are discussed: line tangent to a conic at a given point, line tangent to a conic passing through a given point outside the conic, line of a given slope tangent to a conic, and line tangent to two conics simultaneously; in each case,…

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.

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.

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.

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;…

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.

Linear and nonlinear stability of periodic orbits in annular billiards.

PubMed

Dettmann, Carl P; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Linear and nonlinear stability of periodic orbits in annular billiards

NASA Astrophysics Data System (ADS)

Dettmann, Carl P.; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Nonlinear dissipative and dispersive electrostatic structures in unmagnetized relativistic electron-ion plasma with warm ions and trapped electrons

NASA Astrophysics Data System (ADS)

Masood, W.; Hamid, Naira; Ilyas, Iffat; Siddiq, M.

2017-06-01

In this paper, we have investigated electrostatic solitary and shock waves in an unmagnetized relativistic electron-ion (ei) plasma in the presence of warm ions and trapped electrons. In this regard, we have derived the trapped Korteweg-de Vries Burgers (TKdVB) equation using the small amplitude approximation method, which to the best of our knowledge has not been investigated in plasmas. Since the TKdVB equation involves fractional nonlinearity on account of trapped electrons, we have employed a smartly crafted extension of the tangent hyperbolic method and presented the solution of the TKdVB equation in this paper. The limiting cases of the TKdVB equation yield trapped Burgers (TB) and trapped Korteweg-de Vries (TKdV) equations. We have also presented the solutions of TB and TKdV equations. We have also explored how the plasma parameters affect the propagation characteristics of the nonlinear structures obtained for these modified nonlinear partial differential equations. We hope that the present work will open new vistas of research in the nonlinear plasma theory both in classical and quantum plasmas.

Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons

NASA Astrophysics Data System (ADS)

El-Hanbaly, A. M.; El-Shewy, E. K.; Kassem, A. I.; Darweesh, H. F.

2016-01-01

The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained. The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.

Nonlinear Korteweg-de Vries-Burger equation for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma with thermal ions

NASA Astrophysics Data System (ADS)

Saeed, R.; Shah, Asif

2010-03-01

The nonlinear propagation of ion acoustic waves in electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries-Burger equation has been derived by reductive perturbation technique, and its shock like solution is determined analytically through tangent hyperbolic method. The effect of various plasma parameters on strength and structure of shock wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that strength and steepness of the shock wave enervate with an increase in the ion temperature, relativistic streaming factor, positron concentrations, electron temperature and they accrue with an increase in coefficient of kinematic viscosity. The convective, dispersive, and dissipative properties of the plasma are also discussed. It is determined that the electron temperature has remarkable influence on the propagation and structure of nonlinear wave in such relativistic plasmas. The numerical analysis has been done based on the typical numerical data from a pulsar magnetosphere.

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.

Status of the Topside Vary-Chap Ionospheric Model

NASA Astrophysics Data System (ADS)

Reinisch, Bodo; Nsumei, Patrick; Huang, Xueqin; Bilitza, Dieter

Status of the Topside Vary-Chap Ionospheric Model The general alpha-Chapman function for a multi-constituent gas which includes a continuously varying scale height and was therefore dubbed the Vary-Chap function, can present the topside electron density profiles in analytical form. The Vary-Chap profile is defined by the scale height function H(h) and the height and density of the F2 layer peak. By expressing 80,000 ISIS-2 measured topside density profiles as Vary-Chap functions we derived 80,000 scale height functions, which form the basis for the topside density profile modeling. The normalized scale height profiles Hn = H(h)/Hm were grouped according to season, MLAT, and MLT for each 50 km height bin from 200 km to 1400 km, and the median, lower, and upper quartiles for each bin were calculated. Hm is the scale height at the F2 layer peak. The resulting Hn functions are modeled in terms of hyperbolic tangent functions using 5 parameters that are determined by multivariate least squares, including the transition height hT where the scale height gradient has a maximum. These normalized scale height functions, representing the model of the topside electron density profiles from hmF2 to 1,400 km altitude, are independent of hmF2 and NmF2 and can therefore be directly used for the topside Ne profile in IRI. Similarly, this model can extend measured bottomside profiles to the topside, replacing the simple alpha-Chapman function with constant scale height that is currently used for construction of the topside profile in the Digisondes / ARTIST of the Global Ionospheric Radio Observatory (GIRO). It turns out that Hm(top) calculated from the topside profiles is generally several times larger than Hm(bot) derived from the bottomside profiles. This follows necessarily from the difference in the definition of the scale height functions for the topside and bottomside profiles. The diurnal variations of the ratio Hm(top) / Hm(bot) has been determined for different latitudes which makes it now possible to specify the topside profile for any given bottomside profile.

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.

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.

The derivative and tangent operators of a motion in Lorentzian space

NASA Astrophysics Data System (ADS)

Durmaz, Olgun; Aktaş, Buşra; Gündoğan, Hali˙t

In this paper, by using Lorentzian matrix multiplication, L-Tangent operator is obtained in Lorentzian space. The L-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. L-Tangent operators are related to vectors. Some illustrative examples for applications of L-Tangent operators are also presented.

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.

Calculation of symmetric and asymmetric vortex seperation on cones and tangent ogives based on discrete vortex models

NASA Technical Reports Server (NTRS)

Chin, S.; Lan, C. Edward

1988-01-01

An inviscid discrete vortex model, with newly derived expressions for the tangential velocity imposed at the separation points, is used to investigate the symmetric and asymmetric vortex separation on cones and tangent ogives. The circumferential locations of separation are taken from experimental data. Based on a slender body theory, the resulting simultaneous nonlinear algebraic equations in a cross-flow plane are solved with Broyden's modified Newton-Raphson method. Total force coefficients are obtained through momentum principle with new expressions for nonconical flow. It is shown through the method of function deflation that multiple solutions exist at large enough angles of attack, even with symmetric separation points. These additional solutions are asymmetric in vortex separation and produce side force coefficients which agree well with data for cones and tangent ogives.

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.

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.

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.

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.

Facilitating the Genesis of Functional Working Spaces in Guided Explorations

ERIC Educational Resources Information Center

Miranda, Vicente Carrión; Pluvinage, François; Adjiage, Robert

2016-01-01

Approximating given real-valued functions by affine functions is among the most basic activities with functions. In this study we examine two contexts in which two such approximations are performed. The first involves a microscopic representation of functions for the study of tangents; the second a macroscopic representation of functions for the…

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.

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.

TernaryNet: faster deep model inference without GPUs for medical 3D segmentation using sparse and binary convolutions.

PubMed

Heinrich, Mattias P; Blendowski, Max; Oktay, Ozan

2018-05-30

Deep convolutional neural networks (DCNN) are currently ubiquitous in medical imaging. While their versatility and high-quality results for common image analysis tasks including segmentation, localisation and prediction is astonishing, the large representational power comes at the cost of highly demanding computational effort. This limits their practical applications for image-guided interventions and diagnostic (point-of-care) support using mobile devices without graphics processing units (GPU). We propose a new scheme that approximates both trainable weights and neural activations in deep networks by ternary values and tackles the open question of backpropagation when dealing with non-differentiable functions. Our solution enables the removal of the expensive floating-point matrix multiplications throughout any convolutional neural network and replaces them by energy- and time-preserving binary operators and population counts. We evaluate our approach for the segmentation of the pancreas in CT. Here, our ternary approximation within a fully convolutional network leads to more than 90% memory reductions and high accuracy (without any post-processing) with a Dice overlap of 71.0% that comes close to the one obtained when using networks with high-precision weights and activations. We further provide a concept for sub-second inference without GPUs and demonstrate significant improvements in comparison with binary quantisation and without our proposed ternary hyperbolic tangent continuation. We present a key enabling technique for highly efficient DCNN inference without GPUs that will help to bring the advances of deep learning to practical clinical applications. It has also great promise for improving accuracies in large-scale medical data retrieval.

Reflection characterization of nano-sized dielectric structure in Morpho butterfly wings

NASA Astrophysics Data System (ADS)

Zhu, Dong

2017-10-01

Morpho butterflies living in Central and South America are well-known for their structural-colored blue wings. The blue coloring originates from the interaction of light with nano-sized dielectric structures that are equipped on the external surface of scales covering over their wings. The high-accuracy nonstandard finite-difference time domain (NS-FDTD) method is used to investigate the reflection characterization from the nanostructures. In the NS-FDTD calculation, a computational model is built to mimic the actual tree-like multilayered structures wherever possible using the hyperbolic tangent functions. It is generally known that both multilayer interference and diffraction grating phenomena can occur when light enters the nano-sized multilayered structure. To answer the question that which phenomenon is mainly responsible for the blue coloring, the NS-FDTD calculation is performed under various incidence angles at wavelengths from 360 to 500 nm. The calculated results at one incident wavelength under different incidence angles are visualized in a two-dimensional mapping image, where horizontal and vertical axes are incidence and reflection angles, respectively. The images demonstrate a remarkable transition from a ring-like pattern at shorter wavelengths to a retro-reflection pattern at longer wavelengths. To clarify the origin of the pattern transition, the model is separated into several simpler parts and compared their mapping images with the theoretical diffraction calculations. It can be concluded that the blue coloring at longer wavelengths is mainly caused by the cooperation of multilayer interference and retro-reflection while the effect of diffraction grating is predominant at shorter wavelengths.

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.

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

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.

Examining Students' Generalizations of the Tangent Concept: A Theoretical Perspective

ERIC Educational Resources Information Center

Çekmez, Erdem; Baki, Adnan

2016-01-01

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

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.

Melting of Domain Wall in Charge Ordered Dirac Electron of Organic Conductor α-(BEDT-TTF)2I3

NASA Astrophysics Data System (ADS)

Ohki, Daigo; Matsuno, Genki; Omori, Yukiko; Kobayashi, Akito

2018-05-01

The origin of charge order melting is identified by using the real space dependent mean-field theory in the extended Hubbard model describing an organic Dirac electron system α-(BEDT-TTF)2I3. In this model, the width of a domain wall which arises between different types of the charge ordered phase exhibits a divergent increase with decreasing the strength of electron-electron correlations. By analyzing the finite-size effect carefully, it is shown that the divergence coincides with a topological transition where a pair of Dirac cones merges in keeping with a finite gap. It is also clarified that the gap opening point and the topological transition point are different, which leads to the existence of an exotic massive Dirac electron phase with melted-type domain wall and gapless edge states. The present result also indicated that multiple metastable states are emerged in massive Dirac Electron phase. In the trivial charge ordered phase, the gapless domain-wall bound state takes place instead of the gapless edge states, accompanying with a form change of the domain wall from melted-type into hyperbolic-tangent-type.

Coupled nonlinear drift and ion acoustic waves in dense dissipative electron-positron-ion magnetoplasmas

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

Masood, W.; Siddiq, M.; Karim, S.

2009-11-15

Linear and nonlinear propagation characteristics of drift ion acoustic waves are investigated in an inhomogeneous electron-positron-ion (e-p-i) quantum magnetoplasma with neutrals in the background using the well known quantum hydrodynamic model. In this regard, Korteweg-de Vries-Burgers (KdVB) and Kadomtsev-Petviashvili-Burgers (KPB) equations are obtained. Furthermore, the solutions of KdVB and KPB equations are presented by using the tangent hyperbolic (tanh) method. The variation in the shock profile with the quantum Bohm potential, collision frequency, and the ratio of drift to shock velocity in the comoving frame, v{sub *}/u, is also investigated. It is found that increasing the positron concentration and collisionmore » frequency decreases the strength of the shock. It is also shown that when the localized structure propagates with velocity greater than the diamagnetic drift velocity (i.e., u>v{sub *}), the shock strength decreases. However, the shock strength is observed to increase when the localized structure propagates with velocity less than that of drift velocity (i.e., u

Physical effects of magnetic fields on the Kelvin-Helmholtz instability in a free shear layer

NASA Astrophysics Data System (ADS)

Liu, Y.; Chen, Z. H.; Zhang, H. H.; Lin, Z. Y.

2018-04-01

The Kelvin-Helmholtz instability of a parallel shear flow with a hyperbolic-tangent velocity profile has been simulated numerically at a high Reynolds number. The fluid is perfectly conducting with low viscosity, and the strength of the applied magnetic field varies from weak to strong. We found that the magnetic field parallel to the mainstream direction has a stabilizing effect on the shear flow. The magnetic field mainly stabilizes short-wave perturbations. Small viscosity and/or slight compressibility could introduce some instability even in the presence of a strong magnetic field in a certain circumstance. The suppressing effect of the magnetic field on the instability is accomplished by two parts: the separating effect of the transverse magnetic pressure and the anti-bending effect of magnetic tension pointing to the center of curvature. The former shows prevailingly stronger effect on the fluid interface than the latter does, which is different from the conventional opinion that magnetic tension dominates. Essentially it is mainly the Maxwell stress that weakens and balances the momentum transport conducted by the Reynolds stress, reducing the mixing degree of the upper fluid and the lower fluid.

Predicting electroporation of cells in an inhomogeneous electric field based on mathematical modeling and experimental CHO-cell permeabilization to propidium iodide determination.

PubMed

Dermol, Janja; Miklavčič, Damijan

2014-12-01

High voltage electric pulses cause electroporation of the cell membrane. Consequently, flow of the molecules across the membrane increases. In our study we investigated possibility to predict the percentage of the electroporated cells in an inhomogeneous electric field on the basis of the experimental results obtained when cells were exposed to a homogeneous electric field. We compared and evaluated different mathematical models previously suggested by other authors for interpolation of the results (symmetric sigmoid, asymmetric sigmoid, hyperbolic tangent and Gompertz curve). We investigated the density of the cells and observed that it has the most significant effect on the electroporation of the cells while all four of the mathematical models yielded similar results. We were able to predict electroporation of cells exposed to an inhomogeneous electric field based on mathematical modeling and using mathematical formulations of electroporation probability obtained experimentally using exposure to the homogeneous field of the same density of cells. Models describing cell electroporation probability can be useful for development and presentation of treatment planning for electrochemotherapy and non-thermal irreversible electroporation. Copyright © 2014 Elsevier B.V. All rights reserved.

Direct simulation of high-speed mixing layers

NASA Technical Reports Server (NTRS)

Mukunda, H. S.; Sekar, B.; Carpenter, M. H.; Drummond, J. Philip; Kumar, Ajay

1992-01-01

A computational study of a nonreacting high-speed mixing layer is performed. A higher order algorithm with sufficient grid points is used to resolve all relevant scales. In all cases, a temporal free-stream disturbance is introduced. The resulting flow is time-sampled to generate a statistical cross section of the flow properties. The studies are conducted at two convective Mach numbers, three free-stream turbulence intensities, three Reynolds numbers, and two types of initial profiles-hyperbolic tangent (tanh) and boundary layer. The boundary-layer profile leads to more realistic predictions of the transition processes. The predicted transition Reynolds number of 0.18 x 10(exp 6) compares well with experimental data. Normalized vortex spacings for the boundary-layer case are about 3.5 and compare favorably with the 1.5 to 2.5 found in experimental measurements. The tanh profile produces spacings of about 10. The growth rate of the layer is shown to be moderately affected by the initial disturbance field, but comparison with experimental data shows moderate agreement. For the boundary-layer case, it is shown that noise at the Strouhal number of 0.007 is selectively amplified and shows little Reynolds number dependence.

Propagation of a radio-frequency pulsed signal over the Earth. The JOLLY programs

NASA Astrophysics Data System (ADS)

Carroll, D.; Detch, J. L.; Malik, J.

1983-07-01

The interpretation of observed radioflash/electromagnetic pulse (emp) observed signals from nuclear detonations in terms of theoretical models or extrapolation to signals expected at military systems involves correction for ground-wave propagation effects. For most applications, previously developed programs have been adequate. There have been problems when these techniques have been tried for situations in the near tangent regime where a considerable concern exists. It has been found that the problem of predicting propagation response functions in the near tangent regime has been the inconsistent derivation of the equations. Resolution of this problem has evolved into a program to better predict ground-wave propagation. The description of the method and detailed description of the programs are described for both propagation over realistic earth and sea-water paths. Results can be given in terms of amplitude and phase as a function of the frequency or as amplitude versus time, the usual Green's or resolution function.

Variations in plasma wave intensity with distance along the electron foreshock boundary at Venus

NASA Technical Reports Server (NTRS)

Crawford, G. K.; Strangeway, R. J.; Russell, C. T.

1991-01-01

Plasma waves are observed in the solar wind upstream of the Venus bow shock by the Pioneer Venus Orbiter. These wave signatures occur during periods when the interplanetary magnetic field through the spacecraft position intersects the bow shock, thereby placing the spacecraft in the foreshock region. Wave intensity is analyzed as a function of distance along the electron foreshock boundary. It is found that the peak wave intensity may increase along the foreshock boundary from the tangent point to a maximum value at several Venus radii, then decrease in intensity with subsequent increase in distance. These observations could be associated with the instability process: the instability of the distribution function increasing with distance from the tangent point to saturation at the peak. Thermalization of the beam for distances beyond this point could reduce the distribution function instability resulting in weaker wave signatures.

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.

Potential function of element measurement for form-finding of wide sense tensegrity

NASA Astrophysics Data System (ADS)

Soe, C. K.; Obiya, H.; Koga, D.; Nizam, Z. M.; Ijima, K.

2018-04-01

Tensegrity is a unique morphological structure in which disconnected compression members and connected tension members make the whole structure in self-equilibrium. Many researches have been done on tensegrity structure because of its mysteriousness in form-finding analysis. This study is proposed to investigate the trends and to group into some patterns of the shape that a tensegrity structure can have under the same connectivity and support condition. In this study, tangent stiffness method adopts two different functions, namely power function and logarithm function to element measurement. Numerical examples are based on a simplex initial shape with statically determinate support condition to examine the pure effectiveness of two proposed methods. The tangent stiffness method that can evaluate strict rigid body displacement of elements has a superiority to define various measure potentials and to allow the use of virtual element stiffness freely. From the results of numerical examples, the finding of the dominant trends and patterns of the equilibrium solutions is achieved although it has many related solutions under the same circumstances.

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.

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.

Internal mammary lymph node inclusion in standard tangent breast fields: effects of body habitus.

PubMed

Proulx, G M; Lee, R J; Stomper, P C

2001-01-01

The purpose of this study was to determine the variability of internal mammary node (IMN) coverage with standard breast tangent fields using surface anatomy as determined by computed tomography (CT) planning for patients treated with either breast-conserving treatment or postmastectomy, and to evaluate the influence of body habitus and shape on IMN coverage with standard tangent fields. This prospective study included consecutive women with breast cancer who underwent either local excision or mastectomy and had standard tangent fields intended to cover the breast plus a margin simulated using surface anatomy. CT planning determined the location of the IMN with respect to the tangent fields designed from surface anatomy. The internal mammary vessels were used as surrogates for the IMNs. CT measurements of the presternal fat thickness and anteroposterior (AP) and transverse skeletal diameters were made to determine their relationship to the inclusion of IMNs within the tangent fields. Only seven patients (14%) had their IMNs completely within the tangent fields. Twenty patients (40%) had partial coverage of their IMNs, and 23 (46%) had their IMNs completely outside the fields. IMN inclusion was inversely correlated with presternal fat thickness. Thoracic skeletal shape was not associated with IMN inclusion. Standard tangent fields generally do not cover the IMNs completely but may cover them at least partially in a majority of patients. The presternal fat thickness is inversely correlated with IMN inclusion in the tangent fields.

Antiholomorphic perturbations of Weierstrass Zeta functions and Green’s function on tori

NASA Astrophysics Data System (ADS)

Bogdanov, Konstantin; Mamayusupov, Khudoyor; Mukherjee, Sabyasachi; Schleicher, Dierk

2017-08-01

In Bergweiler and Eremenko (2016 Proc. Am. Math. Soc. 144 2911-22), Bergweiler and Eremenko computed the number of critical points of the Green’s function on a torus by investigating the dynamics of a certain family of antiholomorphic meromorphic functions on tori. They also observed that hyperbolic maps are dense in this family of meromorphic functions in a rather trivial way. In this paper, we study the parameter space of this family of meromorphic functions, which can be written as antiholomorphic perturbations of Weierstrass Zeta functions. On the one hand, we give a complete topological description of the hyperbolic components and their boundaries, and on the other hand, we show that these sets admit natural parametrizations by associated dynamical invariants. This settles a conjecture, made in Lin and Wang (2010 Ann. Math. 172 911-54), on the topology of the regions in the upper half plane {H} where the number of critical points of the Green’s function remains constant.

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

The Geometry of the Universe: Part 2

ERIC Educational Resources Information Center

Francis, Stephanie

2009-01-01

Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…

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.

Edge profile analysis of Joint European Torus (JET) Thomson scattering data: Quantifying the systematic error due to edge localised mode synchronisation.

PubMed

Leyland, M J; Beurskens, M N A; Flanagan, J C; Frassinetti, L; Gibson, K J; Kempenaars, M; Maslov, M; Scannell, R

2016-01-01

The Joint European Torus (JET) high resolution Thomson scattering (HRTS) system measures radial electron temperature and density profiles. One of the key capabilities of this diagnostic is measuring the steep pressure gradient, termed the pedestal, at the edge of JET plasmas. The pedestal is susceptible to limiting instabilities, such as Edge Localised Modes (ELMs), characterised by a periodic collapse of the steep gradient region. A common method to extract the pedestal width, gradient, and height, used on numerous machines, is by performing a modified hyperbolic tangent (mtanh) fit to overlaid profiles selected from the same region of the ELM cycle. This process of overlaying profiles, termed ELM synchronisation, maximises the number of data points defining the pedestal region for a given phase of the ELM cycle. When fitting to HRTS profiles, it is necessary to incorporate the diagnostic radial instrument function, particularly important when considering the pedestal width. A deconvolved fit is determined by a forward convolution method requiring knowledge of only the instrument function and profiles. The systematic error due to the deconvolution technique incorporated into the JET pedestal fitting tool has been documented by Frassinetti et al. [Rev. Sci. Instrum. 83, 013506 (2012)]. This paper seeks to understand and quantify the systematic error introduced to the pedestal width due to ELM synchronisation. Synthetic profiles, generated with error bars and point-to-point variation characteristic of real HRTS profiles, are used to evaluate the deviation from the underlying pedestal width. We find on JET that the ELM synchronisation systematic error is negligible in comparison to the statistical error when assuming ten overlaid profiles (typical for a pre-ELM fit to HRTS profiles). This confirms that fitting a mtanh to ELM synchronised profiles is a robust and practical technique for extracting the pedestal structure.

Daily variation in net primary production and net calcification in coral reef communities exposed to elevated pCO2

NASA Astrophysics Data System (ADS)

Comeau, Steeve; Edmunds, Peter J.; Lantz, Coulson A.; Carpenter, Robert C.

2017-07-01

The threat represented by ocean acidification (OA) for coral reefs has received considerable attention because of the sensitivity of calcifiers to changing seawater carbonate chemistry. However, most studies have focused on the organismic response of calcification to OA, and only a few have addressed community-level effects, or investigated parameters other than calcification, such as photosynthesis. Light (photosynthetically active radiation, PAR) is a driver of biological processes on coral reefs, and the possibility that these processes might be perturbed by OA has important implications for community function. Here we investigate how CO2 enrichment affects the relationships between PAR and community net O2 production (Pnet), and between PAR and community net calcification (Gnet), using experiments on three coral communities constructed to match (i) the back reef of Mo'orea, French Polynesia, (ii) the fore reef of Mo'orea, and (iii) the back reef of O'ahu, Hawaii. The results were used to test the hypothesis that OA affects the relationship between Pnet and Gnet. For the three communities tested, pCO2 did not affect the Pnet-PAR relationship, but it affected the intercept of the hyperbolic tangent curve fitting the Gnet-PAR relationship for both reef communities in Mo'orea (but not in O'ahu). For the three communities, the slopes of the linear relationships between Pnet and Gnet were not affected by OA, although the intercepts were depressed by the inhibitory effect of high pCO2 on Gnet. Our result indicates that OA can modify the balance between net calcification and net photosynthesis of reef communities by depressing community calcification, but without affecting community photosynthesis.

Linear Stability Analysis of Gravitational Effects on a Low-Density Gas Jet Injected into a High-Density Medium

NASA Technical Reports Server (NTRS)

Lawson, Anthony L.; Parthasarathy, Ramkumar N.

2005-01-01

The objective of this study was to determine the effects of buoyancy on the absolute instability of low-density gas jets injected into high-density gas mediums. Most of the existing analyses of low-density gas jets injected into a high-density ambient have been carried out neglecting effects of gravity. In order to investigate the influence of gravity on the near-injector development of the flow, a spatio-temporal stability analysis of a low-density round jet injected into a high-density ambient gas was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The Briggs-Bers criterion was combined with the spatio-temporal stability analysis to determine the nature of the absolute instability of the jet whether absolutely or convectively unstable. The roles of the density ratio, Froude number, Schmidt number, and the lateral shift between the density and velocity profiles on the absolute instability of the jet were determined. Comparisons of the results with previous experimental studies show good agreement when the effects of these variables are combined together. Thus, the combination of these variables determines how absolutely unstable the jet will be.

A fully dynamic magneto-rheological fluid damper model

NASA Astrophysics Data System (ADS)

Jiang, Z.; Christenson, R. E.

2012-06-01

Control devices can be used to dissipate the energy of a civil structure subjected to dynamic loading, thus reducing structural damage and preventing failure. Semiactive control devices have received significant attention in recent years. The magneto-rheological (MR) fluid damper is a promising type of semiactive device for civil structures due to its mechanical simplicity, inherent stability, high dynamic range, large temperature operating range, robust performance, and low power requirements. The MR damper is intrinsically nonlinear and rate-dependent, both as a function of the displacement across the MR damper and the command current being supplied to the MR damper. As such, to develop control algorithms that take maximum advantage of the unique features of the MR damper, accurate models must be developed to describe its behavior for both displacement and current. In this paper, a new MR damper model that includes a model of the pulse-width modulated (PWM) power amplifier providing current to the damper, a proposed model of the time varying inductance of the large-scale 200 kN MR dampers coils and surrounding MR fluid—a dynamic behavior that is not typically modeled—and a hyperbolic tangent model of the controllable force behavior of the MR damper is presented. Validation experimental tests are conducted with two 200 kN large-scale MR dampers located at the Smart Structures Technology Laboratory (SSTL) at the University of Illinois at Urbana-Champaign and the Lehigh University Network for Earthquake Engineering Simulation (NEES) facility. Comparison with experimental test results for both prescribed motion and current and real-time hybrid simulation of semiactive control of the MR damper shows that the proposed MR damper model can accurately predict the fully dynamic behavior of the large-scale 200 kN MR damper.

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)

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.

Calculus, Paper, Scissors

ERIC Educational Resources Information Center

Flores, Luis; Flores, Alfinio

2006-01-01

The idea of cutting out a curve while looking at the direction of cut of the scissors is used to explore concepts related to curves, tangents and derivatives, especially tangent line, concavity and points of inflection, curvature, and a curve as envelope of tangent lines. (Contains 6 figures.)

On equivalent characterizations of convexity of functions

NASA Astrophysics Data System (ADS)

Gkioulekas, Eleftherios

2013-04-01

A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.

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.

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.

Modelling duality between bound and resonant meson spectra by means of free quantum motions on the de Sitter space-time dS4

NASA Astrophysics Data System (ADS)

Kirchbach, M.; Compean, C. B.

2016-07-01

The real parts of the complex squared energies defined by the resonance poles of the transfer matrix of the Pöschl-Teller barrier, are shown to equal the squared energies of the levels bound within the trigonometric Scarf well potential. By transforming these potentials into parts of the Laplacians describing free quantum motions on the mutually orthogonal open-time-like hyperbolic-, and closed-space-like spherical geodesics on the conformally invariant de Sitter space-time, dS4, the conformal symmetries of these interactions are revealed. On dS4 the potentials under consideration naturally relate to interactions within colorless two-body systems and to cusped Wilson loops. In effect, with the aid of the dS4 space-time as unifying geometry, a conformal symmetry based bijective correspondence (duality) between bound and resonant meson spectra is established at the quantum mechanics level and related to confinement understood as color charge neutrality. The correspondence allows to link the interpretation of mesons as resonance poles of a scattering matrix with their complementary description as states bound by an instantaneous quark interaction and to introduce a conformal symmetry based classification scheme of mesons. As examples representative of such a duality we organize in good agreement with data 71 of the reported light flavor mesons with masses below ˜ 2350 MeV into four conformal families of particles placed on linear f0, π , η , and a0 resonance trajectories, plotted on the ℓ/ M plane. Upon extending the sec2 χ by a properly constructed conformal color dipole potential, shaped after a tangent function, we predict the masses of 12 "missing" mesons. We furthermore notice that the f0 and π trajectories can be viewed as chiral partners, same as the η and a0 trajectories, an indication that chiral symmetry for mesons is likely to be realized in terms of parity doubled conformal multiplets rather than, as usually assumed, only in terms of parity doubled single SO(3) states. We attribute the striking measured meson degeneracies to conformal symmetry dynamics within color neutral two-body systems, and conclude on the usefulness of the de Sitter space-time, dS4, as a tool for modelling strong interactions, on the one side, and on the relevance of hyperbolic and trigonometric potentials in constituent quark models of hadrons, on the other.

A Critical Evaluation of the Thermophysical Properties of Mercury

NASA Astrophysics Data System (ADS)

Holman, G. J. F.; ten Seldam, C. A.

1994-09-01

For the use of a mercury column for precise pressure measurements—such as the pressurized 30 meter mercury-in-steel column used at the Van der Waals-Zeeman Laboratory for the calibration of piston gauges up to nearly 300 MPa—it is highly important to have accurate knowledge of such properties of mercury as density, isobaric secant and tangent volume thermal expansion coefficients, and isothermal secant and tangent compressibilities as functions of temperature and pressure. In this paper we present a critical assessment of the available information on these properties. Recommended values are given for the properties mentioned and, in addition, for properties derived from theses such as entropy, enthalpy, internal energy, and the specific heat capacities.

Mathematical Features of the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2010-01-01

The fundamental theorems of the calculus describe the relationships between derivatives and integrals of functions. The value of any function at a particular location is the definite derivative of its integral and the definite integral of its derivative. Thus, any value is the magnitude of the slope of the tangent of its integral at that position,…

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.

Pursuit Eye-Movements in Curve Driving Differentiate between Future Path and Tangent Point Models

PubMed Central

Lappi, Otto; Pekkanen, Jami; Itkonen, Teemu H.

2013-01-01

For nearly 20 years, looking at the tangent point on the road edge has been prominent in models of visual orientation in curve driving. It is the most common interpretation of the commonly observed pattern of car drivers looking through a bend, or at the apex of the curve. Indeed, in the visual science literature, visual orientation towards the inside of a bend has become known as “tangent point orientation”. Yet, it remains to be empirically established whether it is the tangent point the drivers are looking at, or whether some other reference point on the road surface, or several reference points, are being targeted in addition to, or instead of, the tangent point. Recently discovered optokinetic pursuit eye-movements during curve driving can provide complementary evidence over and above traditional gaze-position measures. This paper presents the first detailed quantitative analysis of pursuit eye movements elicited by curvilinear optic flow in real driving. The data implicates the far zone beyond the tangent point as an important gaze target area during steady-state cornering. This is in line with the future path steering models, but difficult to reconcile with any pure tangent point steering model. We conclude that the tangent point steering models do not provide a general explanation of eye movement and steering during a curve driving sequence and cannot be considered uncritically as the default interpretation when the gaze position distribution is observed to be situated in the region of the curve apex. PMID:23894300

21 CFR 886.1810 - Tangent screen (campimeter).

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Tangent screen (campimeter). 886.1810 Section 886.1810 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED... a patient's visual field. This generic type of device includes projection tangent screens, target...

21 CFR 886.1810 - Tangent screen (campimeter).

Code of Federal Regulations, 2013 CFR

2013-04-01

...) Identification. A tangent screen (campimeter) is an AC-powered or battery-powered device that is a large square... a patient's visual field. This generic type of device includes projection tangent screens, target... (general controls). The AC-powered device and the battery-powered device are exempt from the premarket...

21 CFR 886.1810 - Tangent screen (campimeter).

Code of Federal Regulations, 2012 CFR

2012-04-01

...) Identification. A tangent screen (campimeter) is an AC-powered or battery-powered device that is a large square... a patient's visual field. This generic type of device includes projection tangent screens, target... (general controls). The AC-powered device and the battery-powered device are exempt from the premarket...

21 CFR 886.1810 - Tangent screen (campimeter).

Code of Federal Regulations, 2011 CFR

2011-04-01

...) Identification. A tangent screen (campimeter) is an AC-powered or battery-powered device that is a large square... a patient's visual field. This generic type of device includes projection tangent screens, target... (general controls). The AC-powered device and the battery-powered device are exempt from the premarket...

21 CFR 886.1810 - Tangent screen (campimeter).

Code of Federal Regulations, 2014 CFR

2014-04-01

...) Identification. A tangent screen (campimeter) is an AC-powered or battery-powered device that is a large square... a patient's visual field. This generic type of device includes projection tangent screens, target... (general controls). The AC-powered device and the battery-powered device are exempt from the premarket...

Cascaded K-means convolutional feature learner and its application to face recognition

NASA Astrophysics Data System (ADS)

Zhou, Daoxiang; Yang, Dan; Zhang, Xiaohong; Huang, Sheng; Feng, Shu

2017-09-01

Currently, considerable efforts have been devoted to devise image representation. However, handcrafted methods need strong domain knowledge and show low generalization ability, and conventional feature learning methods require enormous training data and rich parameters tuning experience. A lightened feature learner is presented to solve these problems with application to face recognition, which shares similar topology architecture as a convolutional neural network. Our model is divided into three components: cascaded convolution filters bank learning layer, nonlinear processing layer, and feature pooling layer. Specifically, in the filters learning layer, we use K-means to learn convolution filters. Features are extracted via convoluting images with the learned filters. Afterward, in the nonlinear processing layer, hyperbolic tangent is employed to capture the nonlinear feature. In the feature pooling layer, to remove the redundancy information and incorporate the spatial layout, we exploit multilevel spatial pyramid second-order pooling technique to pool the features in subregions and concatenate them together as the final representation. Extensive experiments on four representative datasets demonstrate the effectiveness and robustness of our model to various variations, yielding competitive recognition results on extended Yale B and FERET. In addition, our method achieves the best identification performance on AR and labeled faces in the wild datasets among the comparative methods.

SIMULATIONS OF THE KELVIN–HELMHOLTZ INSTABILITY DRIVEN BY CORONAL MASS EJECTIONS IN THE TURBULENT CORONA

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

Gómez, Daniel O.; DeLuca, Edward E.; Mininni, Pablo D.

Recent high-resolution Atmospheric Imaging Assembly/Solar Dynamics Observatory images show evidence of the development of the Kelvin–Helmholtz (KH) instability, as coronal mass ejections (CMEs) expand in the ambient corona. A large-scale magnetic field mostly tangential to the interface is inferred, both on the CME and on the background sides. However, the magnetic field component along the shear flow is not strong enough to quench the instability. There is also observational evidence that the ambient corona is in a turbulent regime, and therefore the criteria for the development of the instability are a priori expected to differ from the laminar case. To studymore » the evolution of the KH instability with a turbulent background, we perform three-dimensional simulations of the incompressible magnetohydrodynamic equations. The instability is driven by a velocity profile tangential to the CME–corona interface, which we simulate through a hyperbolic tangent profile. The turbulent background is generated by the application of a stationary stirring force. We compute the instability growth rate for different values of the turbulence intensity, and find that the role of turbulence is to attenuate the growth. The fact that KH instability is observed sets an upper limit on the correlation length of the coronal background turbulence.« less

Pressure Sounding of the Middle Atmosphere from ATMOS Solar Occultation Measurements of Atmospheric CO(sub 2) Absorption Lines

NASA Technical Reports Server (NTRS)

Abrams, M.; Gunson, M.; Lowes, L.; Rinsland, C.; Zander, R.

1994-01-01

A method for retrieving the atmospheric pressure corresponding to the tangent point of an infrared spectrum recorded in the solar occultation mode is described and applied to measurements made by the Atmospheric Trace Molecule Spectroscopy (ATMOS) Fourier transform spectrometer. Tangent pressure values are inferred from measurements of isolated CO(sub 2) lines with temperature-insensitive intensities. Tangent pressures are determined with a spectroscopic precision of 1-3%, corresponding to a tangent point height precision, depending on the scale height, of 70-210 meters.

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.

Perspective Space as a Model for Distance and Size Perception.

PubMed

Erkelens, Casper J

2017-01-01

In the literature, perspective space has been introduced as a model of visual space. Perspective space is grounded on the perspective nature of visual space during both binocular and monocular vision. A single parameter, that is, the distance of the vanishing point, transforms the geometry of physical space into that of perspective space. The perspective-space model predicts perceived angles, distances, and sizes. The model is compared with other models for distance and size perception. Perspective space predicts that perceived distance and size as a function of physical distance are described by hyperbolic functions. Alternatively, power functions have been widely used to describe perceived distance and size. Comparison of power and hyperbolic functions shows that both functions are equivalent within the range of distances that have been judged in experiments. Two models describing perceived distance on the ground plane appear to be equivalent with the perspective-space model too. The conclusion is that perspective space unifies a number of models of distance and size perception.

Perspective Space as a Model for Distance and Size Perception

PubMed Central

2017-01-01

In the literature, perspective space has been introduced as a model of visual space. Perspective space is grounded on the perspective nature of visual space during both binocular and monocular vision. A single parameter, that is, the distance of the vanishing point, transforms the geometry of physical space into that of perspective space. The perspective-space model predicts perceived angles, distances, and sizes. The model is compared with other models for distance and size perception. Perspective space predicts that perceived distance and size as a function of physical distance are described by hyperbolic functions. Alternatively, power functions have been widely used to describe perceived distance and size. Comparison of power and hyperbolic functions shows that both functions are equivalent within the range of distances that have been judged in experiments. Two models describing perceived distance on the ground plane appear to be equivalent with the perspective-space model too. The conclusion is that perspective space unifies a number of models of distance and size perception. PMID:29225765

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

NASA Technical Reports Server (NTRS)

Devasia, Santosh

1996-01-01

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

The incidence and effect of fatty atrophy, positive tangent sign, and rotator cuff tears on outcomes after total shoulder arthroplasty.

PubMed

Choate, W Stephen; Shanley, Ellen; Washburn, Richard; Tolan, Stefan J; Salim, Tariq I; Tadlock, Josh; Shealy, Elizabeth C; Long, Catherine D; Crawford, Ashley E; Kissenberth, Michael J; Lonergan, Keith T; Hawkins, Richard J; Tokish, John M

2017-12-01

Treatment choices for total shoulder arthroplasty (TSA) in the absence of full-thickness rotator cuff tears (RCTs) are not clearly defined in current literature. This study investigated the prevalence and effect of preoperative partial-thickness RCTs and muscular degenerative changes on postoperative outcomes after TSA. Medical records and magnetic resonance imaging studies were reviewed for patients who underwent TSA for primary glenohumeral osteoarthritis with minimum 2-year follow-up to determine preoperative tear classification, Goutallier grade, and supraspinatus tangent sign. Postoperative pain on the visual analog scale, range of motion, and patient outcomes scores were obtained to correlate preoperative RCT status, Goutallier grading, tangent sign, and postoperative outcomes. Patients with full-thickness RCT on preoperative magnetic resonance imaging were excluded. Forty-five patients met all inclusion criteria (average age, 65 ± 10 years; average follow-up, 43 months). Of the patients undergoing TSA, 40% had a significant (>50% thickness) partial RCT. Grade 3 to 4 Goutallier changes were noted in 22% of all patients, and 13% demonstrated grade 3 to 4 changes in the context of no tear. Positive tangent sign was present in 7% of all patients. The preoperative Goutallier grade of the infraspinatus was significantly negatively correlated with postoperative forward elevation (P = .02) and external rotation (P = .05), but rotator cuff pathology, including tear status, Goutallier grade, and the presence of a tangent sign, did not correlate with postoperative functional outcome scores. Even in the absence of a full-thickness RCT, rotator cuff atrophy, fatty infiltration, and partial thickness tearing are common findings. Although postoperative range of motion is correlated to Goutallier changes of the infraspinatus, rotator cuff pathology is not correlated to outcomes after TSA; therefore, one may proceed with TSA without concern of their effect on postoperative outcomes. Copyright © 2017 Journal of Shoulder and Elbow Surgery Board of Trustees. Published by Elsevier Inc. All rights reserved.

The First Derivative of an Exponential Function with the "White Box/Black Box" Didactical Principle and Observations with GeoGebra

ERIC Educational Resources Information Center

Budinski, Natalija; Subramaniam, Stephanie

2013-01-01

This paper shows how GeoGebra--a dynamic mathematics software--can be used to experiment, visualize and connect various concepts such as function, first derivative, slope, and tangent line. Students were given an assignment to determine the first derivative of the exponential function that they solved while experimenting with GeoGebra. GeoGebra…

Sign Lines, Asymptotes, and Tangent Carriers--An Introduction to Curve Sketching.

ERIC Educational Resources Information Center

Spikell, Mark A.; Deane, William R.

This paper discusses methods of sketching various types of algebraic functions from an analysis of the portions of the plane where the curve will be found and where it will not be found. The discussion is limited to rational functions. Methods and techniques presented are applicable to the secondary mathematics curriculum from algebra through…

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.

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).

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.

Hyperbolic and semi-hyperbolic surface codes for quantum storage

NASA Astrophysics Data System (ADS)

Breuckmann, Nikolas P.; Vuillot, Christophe; Campbell, Earl; Krishna, Anirudh; Terhal, Barbara M.

2017-09-01

We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3 % for the \\{4,5\\}-hyperbolic surface code in a phenomenological noise model (as compared with 2.9 % for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the \\{4,5\\}-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.

Representation of the contextual statistical model by hyperbolic amplitudes

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

Khrennikov, Andrei

We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. Wemore » also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy.« less

Representation of the contextual statistical model by hyperbolic amplitudes

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2005-06-01

We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. We also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy.

Investigation of the reproducibility and reliability of sagittal vertebral inclination measurements from MR images of the spine.

PubMed

Vrtovec, Tomaž; Pernuš, Franjo; Likar, Boštjan

2014-10-01

In this study, sagittal vertebral inclination (SVI) was systematically evaluated for 28 vertebrae (segments between T4 and L5) in magnetic resonance (MR) images of one normal and one scoliotic subject to compare the performance of manual and computerized measurements, and identify the most reproducible and reliable measurements. Manual measurements were performed by three observers, who identified on two occasions the distinctive anatomical landmarks required to evaluate SVI by six measurement methods, i.e. the superior tangents, inferior tangents, anterior tangents, posterior tangents, mid-endplate lines and mid-wall lines. Computerized measurements were performed by automatically evaluating SVI from the symmetry of vertebral anatomical structures in two-dimensional (2D) sagittal cross-sections and in three-dimensional (3D) volumetric images. The mid-wall lines and posterior tangents proved to be the manual measurements with the lowest intra-observer (standard deviation, SD, of 1.4° and 1.7°, respectively) and inter-observer variability (SD of 1.9° and 2.4°, respectively). The strongest inter-method agreement was found between the mid-wall lines and posterior tangents (SD of 2.0°). Computerized measurements in 2D and in 3D resulted in intra-observer (SD of 2.8° and 3.1°, respectively) and inter-observer variability (SD of 3.8° and 5.2°, respectively) that were comparable to those of the superior tangents (SD of 2.6° and 3.7°) and inferior tangents (SD of 3.2° and 4.5°), which represent standard Cobb angle measurements. It can be concluded that computerized measurements of SVI should be based on the inclination of vertebral body walls. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

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

Semenova, N.; Anishchenko, V.; Zakharova, A.

2016-06-08

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

Experimentally reducing clutch size reveals a fixed upper limit to egg size in snakes, evidence from the king ratsnake, Elaphe carinata.

PubMed

Ji, Xiang; Du, Wei-Guo; Li, Hong; Lin, Long-Hui

2006-08-01

Snakes are free of the pelvic girdle's constraint on maximum offspring size, and therefore present an opportunity to investigate the upper limit to offspring size without the limit imposed by the pelvic girdle dimension. We used the king ratsnake (Elaphe carinata) as a model animal to examine whether follicle ablation may result in enlargement of egg size in snakes and, if so, whether there is a fixed upper limit to egg size. Females with small sized yolking follicles were assigned to three manipulated, one sham-manipulated and one control treatments in mid-May, and two, four or six yolking follicles in the manipulated females were then ablated. Females undergoing follicle ablation produced fewer, but larger as well as more elongated, eggs than control females primarily by increasing egg length. This finding suggests that follicle ablation may result in enlargement of egg size in E. carinata. Mean values for egg width remained almost unchanged across the five treatments, suggesting that egg width is more likely to be shaped by the morphological feature of the oviduct. Clutch mass dropped dramatically in four- and six-follicle ablated females. The function describing the relationship between size and number of eggs reveals that egg size increases with decreasing clutch size at an ever-decreasing rate, with the tangent slope of the function for the six-follicle ablation treatment being -0.04. According to the function describing instantaneous variation in tangent slope, the maximum value of tangent slope should converge towards zero. This result provides evidence that there is a fixed upper limit to egg size in E. carinata.

Tangent Lines without Derivatives for Quadratic and Cubic Equations

ERIC Educational Resources Information Center

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

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 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.

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.

Characterization of a Quadratic Function in Rn

ERIC Educational Resources Information Center

Xu, Conway

2010-01-01

It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

Contracting singular horseshoe

NASA Astrophysics Data System (ADS)

Morales, C. A.; San Martín, B.

2017-11-01

We suggest a notion of hyperbolicity adapted to the geometric Rovella attractor (Robinson 2012 An Introduction to Dynamical Systems—Continuous and Discrete (Pure and Applied Undergraduate Texts vol 19) 2nd edn (Providence, RI: American Mathematical Society)) . More precisely, we call a partially hyperbolic set asymptotically sectional-hyperbolic if its singularities are hyperbolic and if its central subbundle is asymptotically sectional expanding outside the stable manifolds of the singularities. We prove that there are highly chaotic flows with Rovella-like singularities exhibiting this kind of hyperbolicity. We shall call them contracting singular horseshoes.

Can One Take the Logarithm or the Sine of a Dimensioned Quantity or a Unit? Dimensional Analysis Involving Transcendental Functions

ERIC Educational Resources Information Center

Matta, Cherif F.; Massa, Lou; Gubskaya, Anna V.; Knoll, Eva

2011-01-01

The fate of dimensions of dimensioned quantities that are inserted into the argument of transcendental functions such as logarithms, exponentiation, trigonometric, and hyperbolic functions is discussed. Emphasis is placed on common misconceptions that are not often systematically examined in undergraduate courses of physical sciences. The argument…

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.

Designing worked examples for learning tangent lines to circles

NASA Astrophysics Data System (ADS)

Retnowati, E.; Marissa

2018-03-01

Geometry is a branch of mathematics that deals with shape and space, including the circle. A difficult topic in the circle may be the tangent line to circle. This is considered a complex material since students have to simultaneously apply several principles to solve the problems, these are the property of circle, definition of the tangent, measurement and Pythagorean theorem. This paper discusses designs of worked examples for learning tangent line to circles and how to apply this design to an effective and efficient instructional activity. When students do not have sufficient prior knowledge, solving tangent problems might be clumsy, and as a consequence, the problem-solving activity hinders learning. According to a Cognitive Load Theory, learning occurs when students can construct new knowledge based on the relevant knowledge previously learned. When the relevant knowledge is unavailable, providing students with the worked example is suggested. Worked example may reduce unproductive process during learning that causes extraneous cognitive load. Nevertheless, worked examples must be created in such a way facilitate learning.

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.

Application of the Double-Tangent Construction of Coexisting Phases to Any Type of Phase Equilibrium for Binary Systems Modeled with the Gamma-Phi Approach

ERIC Educational Resources Information Center

Jaubert, Jean-Noël; Privat, Romain

2014-01-01

The double-tangent construction of coexisting phases is an elegant approach to visualize all the multiphase binary systems that satisfy the equality of chemical potentials and to select the stable state. In this paper, we show how to perform the double-tangent construction of coexisting phases for binary systems modeled with the gamma-phi…

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.

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.

Continuation of SAGE and MLS High-Resolution Ozone Profiles with the Suomi NPP OMPS Limb Profiler

NASA Astrophysics Data System (ADS)

Kramarova, N. A.; Bhartia, P. K.; Moy, L.; Chen, Z.; Frith, S. M.

2015-12-01

The Ozone Mapper and Profiler Suite (OMPS) Limb Profiler (LP) onboard the Suomi NPP satellite is design to measure ozone profiles with a high vertical resolution (~2 km) and dense spatial sampling (~1° latitude). The LP sensor represents a new generation of the US ozone profile instruments with the plan for a follow-up limb instrument onboard the Joint Polar Satellite System 2 (JPSS-2) in 2021. In this study we will examine the suitability of using LP profiles to continue the EOS climate ozone profile record from the SAGE and MLS datasets. First of all, we evaluate the accuracy in determining the LP tangent height by analyzing measured and calculated radiances. The accurate estimation of the tangent height is critical for limb observations. Several methods were explored to estimate the uncertainties in the LP tangent height registration, and the results will be briefly summarized in this presentation. Version 2 of LP data, released in May 2014, includes a static adjustment of ~1.5 km and a dynamic tangent height adjustment within each orbit. A recent analysis of Version 2 Level 1 radiances revealed a 100 m step in the tangent height that occurred on 26 April 2013, due to a switch to two star trackers in determining spacecraft position. In addition, a ~200 m shift in the tangent height along each orbit was detected. These uncertainties in tangent height registrations can affect the stability of the LP ozone record. Therefore, the second step in our study includes a validation of LP ozone profiles against correlative satellite ozone measurements (Aura MLS, ACE-FTS, OSIRIS, and SBUV) with the focus on time-dependent changes. We estimate relative drifts between OMPS LP and correlative ozone records to evaluate stability of the LP measurements. We also test the tangent height corrections found in the internal analysis of Version 2 measurements to determine their effect on the long-term stability of the LP ozone record.

Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

PubMed

Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

2016-12-01

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low-dimensional one appears to be illuminating.

Tangent function transformation of the Abbreviated Injury Scale improves accuracy and simplifies scoring.

PubMed

Wang, Muding; Qiu, Wusi; Qiu, Fang; Mo, Yinan; Fan, Wenhui

2015-03-16

The Injury Severity Score (ISS) and the New Injury Severity Score (NISS) are widely used for anatomic severity assessments after trauma. We present here the Tangent Injury Severity Score (TISS), which transforms the Abbreviated Injury Scale (AIS) as a predictor of mortality. The TISS is defined as the sum of the tangent function of AIS/6 to the power 3.04 multiplied by 18.67 of a patient's three most severe AIS injuries regardless of body regions. TISS values were calculated for every patient in two large independent data sets: 3,908 and 4,171 patients treated during a 6-year period at level-3 first-class comprehensive hospitals: the Affiliated Hospital of Hangzhou Normal University and Fengtian Hospital Affiliated to Shenyang Medical College, China. The power of TISS to predict mortality was compared with previously calculated NISS values for the same patients in each data set. The TISS is more predictive of survival than NISS (Hangzhou: receiver operating characteristic (ROC): NISS = 0.929, TISS = 0.949; p = 0.002; Shenyang: ROC: NISS = 0.924, TISS = 0.942; p = 0.008). Moreover, TISS provides a better fit throughout its entire range of prediction (Hosmer Lemeshow statistic for Hangzhou NISS = 29.71; p < 0.001, TISS = 19.59; p = 0.003; Hosmer Lemeshow statistic for Shenyang NISS = 33.49; p < 0.001, TISS = 21.19; p = 0.002). The TISS shows more accurate prediction of prognosis and a linear relation to mortality. The TISS might be a better injury scoring tool with simple computation.

Without derivatives or limits: from visual and geometrical points of view to algebraic methods for identifying tangent lines

NASA Astrophysics Data System (ADS)

Vivier, L.

2013-07-01

Usually, the tangent line is considered to be a calculus notion. However, it is also a graphical and an algebraic notion. The graphical frame, where our primary conceptions are conceived, could give rise to algebraic methods to obtain the tangent line to a curve. In this pre-calculus perspective, two methods are described and discussed according to their potential for secondary students and teacher training.

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.

Drift ion acoustic shock waves in an inhomogeneous two-dimensional quantum magnetoplasma

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

Masood, W.; Siddiq, M.; Karim, S.

2009-04-15

Linear and nonlinear propagation characteristics of drift ion acoustic waves are investigated in an inhomogeneous quantum plasma with neutrals in the background employing the quantum hydrodynamics (QHD) model. In this regard, a quantum Kadomtsev-Petviashvili-Burgers (KPB) equation is derived for the first time. It is shown that the ion acoustic wave couples with the drift wave if the parallel motion of ions is taken into account. Discrepancies in the earlier works on drift solitons and shocks in inhomogeneous plasmas are also pointed out and a correct theoretical framework is presented to study the one-dimensional as well as the two-dimensional propagation ofmore » shock waves in an inhomogeneous quantum plasma. Furthermore, the solution of KPB equation is presented using the tangent hyperbolic (tanh) method. The variation of the shock profile with the quantum Bohm potential, collision frequency, and ratio of drift to shock velocity in the comoving frame, v{sub *}/u, are also investigated. It is found that increasing the number density and collision frequency enhances the strength of the shock. It is also shown that the fast drift shock (i.e., v{sub *}/u>0) increases, whereas the slow drift shock (i.e., v{sub *}/u<0) decreases the strength of the shock. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.« less

Effect of density gradients in confined supersonic shear layers, part 1

NASA Astrophysics Data System (ADS)

Peroomian, Oshin; Kelly, R. E.

1994-11-01

The effect of density gradients on the supersonic wall modes (acoustic modes) of a 2-D confined compressible shear layer were investigated using linear analysis. Due to the inadequacies of the hyperbolic tangent profile, the boundary layer basic profiles were used. First a test case was taken with the same parameters as in Tam and Hu's analysis with convective Mach number M(sub c) = 1.836 and density ratio of 1.398. Three generalized inflection points were found giving rise to three modes. The first two show similar properties to the Class A and B modes, and the third is an 'inner mode' which will be called a Class C mode. As the density ratio is increased, the smallest of the three neutral phase speeds tends towards the speed of the lower velocity stream, and the other two eventually coalesce and then disappear. These two effects lead to a linear resonance between the Class B modes which increases the cutoff frequency and growth rate of the lowest mode. In fact, growth rates of 2-4 times the test case were found as the density ratio was increased to 7. A similar trend is observed for the Class A modes when the density ratio is decreased from the test case, but the growth rate is not changed by much from the test case.

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.

Laws of trigonometry on SU(3)

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

Aslaksen, H.

1988-01-01

In this paper we will study triangles in SU(3). The orbit space of congruence classes of triangles in SU(3) has dimension 8. Each corner is made up of a pair of tangent vectors (X,Y), and we consider the 8 functions trX{sup 2}, i trX{sup 3}, trY{sup 2}, i trY{sup 3}, trXY, i trY{sup 2}Y, i trXY{sup 2}, trX{sup 2}Y{sup 2} which are invariant under the full isometry group of SU(3). We show that these 8 corner invariants determine the isometry class of the triangle. We give relations (laws of trigonometry) between the invariants at the different corners, enabling us tomore » determine the invariants at the remaining corners, including the values of the remaining side and angles, if we know one set of corner invariants. The invariants that only depend on one tangent vector we will call side invariants, while those that depend on two tangent vectors will be called angular invariants. For each triangle we then have 6 side invariants and 12 angular invariants. Hence we need 18 {minus} 8 = 10 laws of trigonometry. The basic tool for deriving these laws is a formula expressing tr(exp X exp Y) in terms of the corner invariants.« less

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.

"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.

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.

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.

Two-dimensional shape recognition using sparse distributed memory

NASA Technical Reports Server (NTRS)

Kanerva, Pentti; Olshausen, Bruno

1990-01-01

Researchers propose a method for recognizing two-dimensional shapes (hand-drawn characters, for example) with an associative memory. The method consists of two stages: first, the image is preprocessed to extract tangents to the contour of the shape; second, the set of tangents is converted to a long bit string for recognition with sparse distributed memory (SDM). SDM provides a simple, massively parallel architecture for an associative memory. Long bit vectors (256 to 1000 bits, for example) serve as both data and addresses to the memory, and patterns are grouped or classified according to similarity in Hamming distance. At the moment, tangents are extracted in a simple manner by progressively blurring the image and then using a Canny-type edge detector (Canny, 1986) to find edges at each stage of blurring. This results in a grid of tangents. While the technique used for obtaining the tangents is at present rather ad hoc, researchers plan to adopt an existing framework for extracting edge orientation information over a variety of resolutions, such as suggested by Watson (1987, 1983), Marr and Hildreth (1980), or Canny (1986).

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.

How concept images affect students' interpretations of Newton's method

NASA Astrophysics Data System (ADS)

Engelke Infante, Nicole; Murphy, Kristen; Glenn, Celeste; Sealey, Vicki

2018-07-01

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus students, we determined how evoked concept images of tangent lines and roots contributed to students' interpretation and application of Newton's method. Results show that some students' concept images of root and tangent line developed throughout the interview process, and most students were able to adequately interpret the text on Newton's method. However, students with insufficient concept images of tangent line and students who were unwilling or unable to modify their concept images of tangent line after reading the text were not successful in interpreting Newton's method.

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.

Short-term Slow Slip Events at the Southcentral Alaska Subduction Zone

NASA Astrophysics Data System (ADS)

McGuire, J. L.; Fu, Y.; Freymueller, J. T.

2017-12-01

The Pacific Plate is subducting beneath the North American Plate along the Aleutian Trench. The Alaska subduction zone is among the most tectonically active areas on Earth and is home to some of the largest earthquakes on record, including the second largest earthquake ever recorded, the M9.2 Prince William Sound earthquake of 1964. With the increasing availability of continuous GPS observations, studying time-dependent crustal movements in this area has become possible. Previous studies have analyzed the presence of long-term slow slip events (SSEs) in the region. Two long-term SSEs occurred from 1998-2001 and from 2010-2014 with durations of 3-4 years. These two long-term events occurred down-dip of the main asperity of the 1964 Prince William Sound earthquake. In addition to these long-term SSEs, there are also short-term SSEs evident in the GPS time series, which have durations of approximately two months. We have adequate data to study three short-term slow slip events, in 2005, 2006 and 2007. We fit the GPS time series data with the combination of a linear trend, a hyperbolic tangent function, and seasonal variations to derive the crustal displacements of all three short-term SSEs at each station in the north, east, and vertical directions. Then, an inversion model using the Green's functions for slip on the plate interface was employed to estimate the location and amplitude of slip and to calculate the magnitude of these slow slip events. Our results show Mw 6.09 for the 2005 event, Mw 6.40 for the 2006 event, and Mw 6.30 for the 2007 event. Our results indicate that both long-term SSEs and short-term SSEs occurred in the same location, down-dip of the rupture asperity of 1964 M9.2 earthquake. We use this information to relate the short-term slow slip events to the long-term events that have occurred in the region and to look for the implications on the slip budget of both short-term and long-term SSEs during the earthquake cycle at Southcentral Alaska subduction zone.

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.

S-EMG signal compression based on domain transformation and spectral shape dynamic bit allocation

PubMed Central

2014-01-01

Background Surface electromyographic (S-EMG) signal processing has been emerging in the past few years due to its non-invasive assessment of muscle function and structure and because of the fast growing rate of digital technology which brings about new solutions and applications. Factors such as sampling rate, quantization word length, number of channels and experiment duration can lead to a potentially large volume of data. Efficient transmission and/or storage of S-EMG signals are actually a research issue. That is the aim of this work. Methods This paper presents an algorithm for the data compression of surface electromyographic (S-EMG) signals recorded during isometric contractions protocol and during dynamic experimental protocols such as the cycling activity. The proposed algorithm is based on discrete wavelet transform to proceed spectral decomposition and de-correlation, on a dynamic bit allocation procedure to code the wavelets transformed coefficients, and on an entropy coding to minimize the remaining redundancy and to pack all data. The bit allocation scheme is based on mathematical decreasing spectral shape models, which indicates a shorter digital word length to code high frequency wavelets transformed coefficients. Four bit allocation spectral shape methods were implemented and compared: decreasing exponential spectral shape, decreasing linear spectral shape, decreasing square-root spectral shape and rotated hyperbolic tangent spectral shape. Results The proposed method is demonstrated and evaluated for an isometric protocol and for a dynamic protocol using a real S-EMG signal data bank. Objective performance evaluations metrics are presented. In addition, comparisons with other encoders proposed in scientific literature are shown. Conclusions The decreasing bit allocation shape applied to the quantized wavelet coefficients combined with arithmetic coding results is an efficient procedure. The performance comparisons of the proposed S-EMG data compression algorithm with the established techniques found in scientific literature have shown promising results. PMID:24571620

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.

Tangent-ogive nose cones

NASA Technical Reports Server (NTRS)

Wing, L. D.

1976-01-01

Program calculates aerodynamic heating and shear stresses at wall for tangent-ogive noses that are slender enough to maintain an attached nose shock during portion of flight when heat transfer from boundary layer to wall is significant.

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.

CMOS-based Stochastically Spiking Neural Network for Optimization under Uncertainties

DTIC Science & Technology

2017-03-01

inverse tangent characteristics at varying input voltage (VIN) [Fig. 3], thereby it is suitable for Kernel function implementation. By varying bias...cost function/constraint variables are generated based on inverse transform on CDF. In Fig. 5, F-1(u) for uniformly distributed random number u [0, 1...extracts random samples of x varying with CDF of F(x). In Fig. 6, we present a successive approximation (SA) circuit to evaluate inverse

Examination of humidity effects on measured thickness and interfacial phenomena of exfoliated graphene on silicon dioxide via amplitude modulation atomic force microscopy

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

Jinkins, K.; Farina, L.; Wu, Y., E-mail: wuy@uwplatt.edu

2015-12-14

The properties of Few-Layer Graphene (FLG) change with the number of layers and Amplitude Modulation (AM) Atomic Force Microscopy (AFM) is commonly used to determine the thickness of FLG. However, AFM measurements have been shown to be sensitive to environmental conditions such as relative humidity (RH). In the present study, AM-AFM is used to measure the thickness and loss tangent of exfoliated graphene on silicon dioxide (SiO{sub 2}) as RH is increased from 10% to 80%. We show that the measured thickness of graphene is dependent on RH. The loss tangent values of the graphene and oxide regions are bothmore » affected by humidity, with generally higher loss tangent for graphene than SiO{sub 2}. As RH increases, we observe the loss tangent of both materials approaches the same value. We hypothesize that there is a layer of water trapped between the graphene and SiO{sub 2} substrate to explain this observation. Using this interpretation, the loss tangent images also indicate movement and change in this trapped water layer as RH increases, which impacts the measured thickness of graphene using AM-AFM.« less

Study of complex permittivity spectra of binary mixtures of 2-chloroaniline and methanol in frequency range 10 KHz to 2 MHz at different temperatures

NASA Astrophysics Data System (ADS)

Shah, N. S.; Vankar, H. P.; Rana, V. A.

2017-05-01

The complex relative dielectric function ɛ*(ω)=ɛ'-jɛ″ of the binary mixture of 2-chloroaniline(2-CA) and methanol (MeOH) were measured using precision LCR meter in the frequency range of 10 KHz to 2 MHz The measurements were carried out at eight different temperatures and five different concentrations of 2-CA and MeOH. The loss tangent peaks were observed in the studied frequency range for all the binary mixtures. From the loss tangent peaks electrode polarization relaxation time were evaluated. In the plot of real part of complex permittivity against frequency, at different temperatures for 2-CA (54.54%) + MeOH (45.45%) and 2-CA (27.27%) + MeOH (72.72%)and 100% MeOH systems permittivity inversion effect was observed.

Double axis, two-crystal x-ray spectrometer.

PubMed

Erez, G; Kimhi, D; Livnat, A

1978-05-01

A two-crystal double axis x-ray spectrometer, capable of goniometric accuracy on the order of 0.1", has been developed. Some of its unique design features are presented. These include (1) a modified commercial thrust bearing which furnishes a precise, full circle theta:2theta coupling, (2) a new tangent drive system design in which a considerable reduction of the lead screw effective pitch is achieved, and (3) an automatic step scanning control which eliminates most of the mechanical deficiencies of the tangent drive by directly reading the tangent arm displacement.

Variation of parameters using Battin's universal functions

NASA Astrophysics Data System (ADS)

Burton, James R., III; Melton, Robert G.

This paper presents a variation of parameters analysis, suitable for use in situations involving small perturbations to the two-body problem, using Battin's universal functions. Unlike the universal variable formulation, this approach avoids the need to switch among different functional representations if the orbit transitions from elliptical, through parabolic, to hyperbolic state, making it attractive for use in simulating low-thrust trajectories ascending to escape or capturing into orbit.

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).

Generic Equations for Constructing Smooth Paths Along Circles and Tangent Lines With Application to Airport Ground Paths

NASA Technical Reports Server (NTRS)

Barker, L. Keith

1998-01-01

The primary purpose of this publication is to develop a mathematical model to describe smooth paths along any combination of circles and tangent lines. Two consecutive circles in a path are either tangent (externally or internally) or they appear on the same (lateral) or opposite (transverse) sides of a connecting tangent line. A path may start or end on either a segment or circle. The approach is to use mathematics common to robotics to design the path as a multilink manipulator. This approach allows a hierarchical view of the problem and keeps the notation manageable. A user simply specifies a few parameters to configure a path. Necessary and sufficient conditions automatically ensure the consistency of the inputs for a smooth path. Two example runway exit paths are given, and an angle to go assists in knowing when to switch from one path element to the next.

Mathematics Textbooks and Their Potential Role in Supporting Misconceptions

ERIC Educational Resources Information Center

Kajander, Ann; Lovric, Miroslav

2009-01-01

As a fundamental resource, textbooks shape the way we teach and learn mathematics. Based on examination of secondary school and university textbooks, we describe to what extent, and how, the presentation of mathematics material--in our case study, the concept of the line tangent to the graph of a function--could contribute to creation and…

Backscattering from targets residing in caustics resulting from ocean boundary interactions

NASA Astrophysics Data System (ADS)

Dzikowicz, Benjamin R.; Marston, Philip L.

2005-04-01

Detection of targets by backscatter in shallow water can be enhanced by interactions with ocean boundaries. A laboratory experiment is performed where a spherical target passes through an Airy caustic formed by a curved surface. When the target resides in the insonified region of the caustic there are two sets of multi-path rays: two pairs reflecting once off the surface (either to or from the target), and three reflecting twice off the surface (to and from the target). When a target moves across the caustic the singly reflected rays merge, as do the doubly reflected. With a longer tone burst the rays in each set overlap and the backscatter is greatly enhanced as the target moves into the insonified region. For a point target the singly reflected backscatter scales as an Airy function [B. R. Dzikowicz and P. L. Marston, J. Acoust. Soc. Am. 116, 2751-2757 (2004)], and the doubly reflected as the square of an Airy function. For a finite target the doubly reflected backscatter unfolds into a hyperbolic umbilic function. The arguments of the Airy and Hyperbolic Umbilic functions are calculated using the relative echo times of transient pulses. [Work supported by ONR.

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.

Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution

PubMed Central

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. PMID:29123436

Symbolic integration of a class of algebraic functions. [by an algorithmic approach

NASA Technical Reports Server (NTRS)

Ng, E. W.

1974-01-01

An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

"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).

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

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

Khmelnytskaya, Kira V., E-mail: khmel@uaq.edu.mx; Kravchenko, Vladislav V., E-mail: vkravchenko@math.cinvestav.edu.mx; Torba, Sergii M., E-mail: storba@math.cinvestav.edu.mx

2016-05-15

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

Photocopy of photograph (digital image located in LBNL Photo Lab ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Photocopy of photograph (digital image located in LBNL Photo Lab Collection, XBD200503-00117-026). March 2005. MOUSE AT EAST TANGENT, LOOKING TOWARD EAST TANGENT, BEVATRON - University of California Radiation Laboratory, Bevatron, 1 Cyclotron Road, Berkeley, Alameda County, CA

Explicit robust schemes for implementation of general principal value-based constitutive models

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Saleeb, A. F.; Tan, H. Q.; Zhang, Y.

1993-01-01

The issue of developing effective and robust schemes to implement general hyperelastic constitutive models is addressed. To this end, special purpose functions are used to symbolically derive, evaluate, and automatically generate the associated FORTRAN code for the explicit forms of the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid for the entire deformation range. The analytical form of these explicit expressions is given here for the case in which the strain-energy potential is taken as a nonseparable polynomial function of the principle stretches.

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.

Effects of Mean Flow Profiles on Instability of a Low-Density Gas Jet Injected into a High-Density Gas

NASA Technical Reports Server (NTRS)

Vedantam, Nanda Kishore

2003-01-01

The objective of this study was to investigate the effects of the mean flow profiles on the instability characteristics in the near-injector region of low-density gas jets injected into high-density ambient gas mediums. To achieve this, a linear temporal stability analysis and a spatio-temporal stability analysis of a low-density round gas jet injected vertically upwards into a high-density ambient gas were performed by assuming three different sets of mean velocity and density profiles. The flow was assumed to be isothermal and locally parallel. Viscous and diffusive effects were ignored. The mean flow parameters were represented as the sum of the mean value and a small normal-mode fluctuation. A second order differential equation governing the pressure disturbance amplitude was derived from the basic conservation equations. The first set of mean velocity and density profiles assumed were those used by Monkewitz and Sohn for investigating absolute instability in hot jets. The second set of velocity and density profiles assumed for this study were the ones used by Lawson. And the third set of mean profiles included a parabolic velocity profile and a hyperbolic tangent density profile. The effects of the inhomogeneous shear layer and the Froude number (signifying the effects of gravity) on the temporal and spatio-temporal results for each set of mean profiles were delineated. Additional information is included in the original extended abstract.

Development of kinks in car-following models

NASA Astrophysics Data System (ADS)

Kurtze, Douglas A.

2017-03-01

Many car-following models of traffic flow admit the possibility of absolute stability, a situation in which uniform traffic flow at any spacing is linearly stable. Near the threshold of absolute stability, these models can often be reduced to a modified Korteweg-deVries (mKdV) equation plus small corrections. The hyperbolic-tangent "kink" solutions of the mKdV equation are usually of particular interest, as they represent transition zones between regions of different traffic spacings. Solvability analysis is believed to show that only a single member of the one-parameter family of kink solutions is preserved by the correction terms, and this is interpreted as a kind of selection. We show, however, that the usual solvability calculation rests on an unstated, unjustified assumption, and that without this assumption it merely gives a first-order correction to the relation between the traffic spacings far behind and far ahead of the kink, rather than any kind of "selection" criterion for the family of kink solutions. On the other hand, we display a two-parameter family of traveling wave solutions of the mKdV equation, which describe regions of one traffic spacing embedded in traffic of a different spacing; this family includes the kink solutions as a limiting case. We carry out a multiple-time-scales calculation and find conditions under which the inclusions decay, conditions that lead to a selected inclusion, and conditions for which the inclusion evolves into a pair of kinks.

The direct simulation of high-speed mixing-layers without and with chemical heat release

NASA Technical Reports Server (NTRS)

Sekar, B.; Mukunda, H. S.; Carpenter, M. H.

1991-01-01

A direct numerical simulation of high speed reacting and non-reacting flows for H2-air systems is presented. The calculations are made for a convective Mach number of 0.38 with hyperbolic tangent initial profile and finite rate chemical reactions. A higher-order numerical method is used in time accurate mode to time advance the solution to a statistical steady state. About 600 time slices of all the variables are then stored for statistical analysis. It is shown that most of the problems of high-speed combustion with air are characterized by relatively weak heat release. The present study shows that: (1) the convective speed is reduced by heat release by about 10 percent at this convective Mach number M(sub c) = 0.38; (2) the variation of the mean and rms fluctuation of temperature can be explained on the basis of temperature fluctuation between the flame temperature and the ambient; (3) the growth rate with heat release is reduced by 7 percent; and (4) the entrainment is reduced by 25 percent with heat release. These differences are small in comparison with incompressible flow dynamics, and are argued to be due to the reduced importance of heat release in comparison with the large enthalpy gradients resulting from the large-scale vortex dynamics. It is finally suggested that the problems of reduced mixing in high-speed flows are not severely complicated by heat release.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Spectral collocation methods

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.

1987-01-01

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.

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.

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.

Contralateral Breast Dose After Whole-Breast Irradiation: An Analysis by Treatment Technique

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

Williams, Terence M.; Moran, Jean M., E-mail: jmmoran@med.umich.edu; Hsu, Shu-Hui

2012-04-01

Purpose: To investigate the contralateral breast dose (CBD) across a continuum of breast-conservation therapy techniques. Methods and Materials: An anthropomorphic phantom was CT-simulated, and six treatment plans were generated: open tangents, tangents with an external wedge on the lateral beam, tangents with lateral and medial external wedges, a simple segment plan (three segments per tangent), a complex segmental intensity-modulated radiotherapy (IMRT) plan (five segments per tangent), and a beamlet IMRT plan (>100 segments). For all techniques, the breast on the phantom was irradiated to 5000 cGy. Contralateral breast dose was measured at a uniform depth at the center and eachmore » quadrant using thermoluminescent detectors. Results: Contralateral breast dose varied with position and was 50 {+-} 7.3 cGy in the inner half, 24 {+-} 4.1 cGy at the center, and 16 {+-} 2.2 cGy in the outer half for the open tangential plan. Compared with an average dose of 31 cGy across all points for the open field, the average doses were simple segment 32 cGy (range, 99-105% compared with open technique), complex segment 34 cGy (range, 103-117% compared with open technique), beamlet IMRT 34 cGy (range, 103-124% compared with open technique), lateral wedge only 46 cGy (range, 133-175% compared with open technique), and medial and lateral wedge 96 cGy (range, 282-370% compared with open technique). Conclusions: Single or dual wedge techniques resulted in the highest CBD increases compared with open tangents. To obtain the desired homogeneity to the treated breast while minimizing CBD, segmental and IMRT techniques should be encouraged over external physical compensators.« less

Two-dimensional potential flow past a smooth wall with partly constant curvature

NASA Technical Reports Server (NTRS)

Koppenfels, Werner Von

1941-01-01

The speed of a two-dimensional flow potential flow past a smooth wall, which evinces a finite curvature jump at a certain point and approximates to two arcs in the surrounding area, has a vertical tangent of inflection in the critical point as a function of the arc length of the boundary curve. This report looks at a general theorem of the local character of the conformal function at the critical point as well as the case of the finite curvature jump.

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.

NEMOTAM: tangent and adjoint models for the ocean modelling platform NEMO

NASA Astrophysics Data System (ADS)

Vidard, A.; Bouttier, P.-A.; Vigilant, F.

2015-04-01

Tangent linear and adjoint models (TAMs) are efficient tools to analyse and to control dynamical systems such as NEMO. They can be involved in a large range of applications such as sensitivity analysis, parameter estimation or the computation of characteristic vectors. A TAM is also required by the 4D-Var algorithm, which is one of the major methods in data assimilation. This paper describes the development and the validation of the tangent linear and adjoint model for the NEMO ocean modelling platform (NEMOTAM). The diagnostic tools that are available alongside NEMOTAM are detailed and discussed, and several applications are also presented.

NEMOTAM: tangent and adjoint models for the ocean modelling platform NEMO

NASA Astrophysics Data System (ADS)

Vidard, A.; Bouttier, P.-A.; Vigilant, F.

2014-10-01

The tangent linear and adjoint model (TAM) are efficient tools to analyse and to control dynamical systems such as NEMO. They can be involved in a large range of applications such as sensitivity analysis, parameter estimation or the computation of characteristics vectors. TAM is also required by the 4-D-VAR algorithm which is one of the major method in Data Assimilation. This paper describes the development and the validation of the Tangent linear and Adjoint Model for the NEMO ocean modelling platform (NEMOTAM). The diagnostic tools that are available alongside NEMOTAM are detailed and discussed and several applications are also presented.

Measurements of Wheel/Rail Loads on Class 5 Track

DOT National Transportation Integrated Search

1980-02-01

Measurements have been made on two tangent test sections and a curved test section to characterize the wheel/rail load environment on Class 5 track. The tangent-track test sections included a 3-mile length of bolted-joint rail under a 3-mile length o...

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.

A dosimetric study of cardiac dose sparing using the reverse semi-decubitus technique for left breast and internal mammary chain irradiation.

PubMed

Niglas, Mark; McCann, Claire; Keller, Brian M; Makhani, Nadiya; Presutti, Joseph; Vesprini, Danny; Rakovitch, Eileen; Elzibak, Alyaa; Mashouf, Shahram; Lee, Justin

2016-01-01

Breath-hold techniques can reduce cardiac dose in breast radiotherapy. The reverse semi-decubitus (RSD) technique is an alternative free-breathing method used at our centre. This study compares the dosimetry of free-breathing supine, RSD and moderate deep inspiration breath-hold (mDIBH) techniques. Twelve patients with left-sided breast cancer who were simulated using standard supine, RSD and mDIBH techniques were identified retrospectively. New plans using standard breast tangents and techniques for internal mammary chain (IMC) nodal coverage were assessed. Using standard tangents, mean heart dose, heart V25Gy and mean left anterior descending artery (LAD) dose were found to be significantly lower for RSD and mDIBH when compared to free-breathing supine (p ⩽ 0.03). Using wide-tangents, the maximum LAD point dose was also lower for RSD and mDIBH (p ⩽ 0.02). There were no statistically significant dosimetric differences found between the RSD and mDIBH simulation techniques for standard breast-tangent plans, though organ-at-risk doses were lower for mDIBH in wide-tangent plans. There was no improvement in cardiac dosimetry between RSD and free-breathing supine when using an electron field IMC plan. For patients unable to tolerate breath-hold, the RSD technique is an alternative approach that can reduce cardiac dose. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

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…

Kernel functions and Baecklund transformations for relativistic Calogero-Moser and Toda systems

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

Hallnaes, Martin; Ruijsenaars, Simon

We obtain kernel functions associated with the quantum relativistic Toda systems, both for the periodic version and for the nonperiodic version with its dual. This involves taking limits of previously known results concerning kernel functions for the elliptic and hyperbolic relativistic Calogero-Moser systems. We show that the special kernel functions at issue admit a limit that yields generating functions of Baecklund transformations for the classical relativistic Calogero-Moser and Toda systems. We also obtain the nonrelativistic counterparts of our results, which tie in with previous results in the literature.

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 surface-induced spatial-temporal structures in confined binary alloys

NASA Astrophysics Data System (ADS)

Krasnyuk, Igor B.; Taranets, Roman M.; Chugunova, Marina

2014-12-01

This paper examines surface-induced ordering in confined binary alloys. The hyperbolic initial boundary value problem (IBVP) is used to describe a scenario of spatiotemporal ordering in a disordered phase for concentration of one component of binary alloy and order parameter with non-linear dynamic boundary conditions. This hyperbolic model consists of two coupled second order differential equations for order parameter and concentration. It also takes into account effects of the “memory” on the ordering of atoms and their densities in the alloy. The boundary conditions characterize surface velocities of order parameter and concentration changing which is due to surface (super)cooling on walls confining the binary alloy. It is shown that for large times there are three classes of dynamic non-linear boundary conditions which lead to three different types of attractor’s elements for the IBVP. Namely, the elements of attractor are the limit periodic simple shock waves with fronts of “discontinuities” Γ. If Γ is finite, then the attractor contains spatiotemporal functions of relaxation type. If Γ is infinite and countable then we observe the functions of pre-turbulent type. If Γ is infinite and uncountable then we obtain the functions of turbulent type.

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.

Teachers' Conceptions of Tangent Line

ERIC Educational Resources Information Center

Paez Murillo, Rosa Elvira; Vivier, Laurent

2013-01-01

In order to study the conceptions, and their evolutions, of the tangent line to a curve an updating workshop which took place in Mexico was designed for upper secondary school teachers. This workshop was planned using the methodology of cooperative learning, scientific debate and auto reflection (ACODESA) and the conception-knowing-concept model…

Stiffness optimization of non-linear elastic structures

DOE PAGES

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

2017-11-13

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Stiffness optimization of non-linear elastic structures

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

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Dielectric properties of highly resistive GaN crystals grown by ammonothermal method at microwave frequencies

NASA Astrophysics Data System (ADS)

Krupka, Jerzy; Zajåc, Marcin; Kucharski, Robert; Gryglewski, Daniel

2016-03-01

Permittivity, the dielectric loss tangent and conductivity of semi-insulating Gallium Nitride crystals have been measured as functions of frequency from 10 GHz to 50 GHz and temperature from 295 to 560 K employing quasi TE0np mode dielectric resonator technique. Crystals were grown using ammonothermal method. Two kinds of doping were used to obtain high resistivity crystals; one with deep acceptors in form of transition metal ions, and the other with shallow Mg acceptors. The sample compensated with transition metal ions exhibited semi-insulating behavior in the whole temperature range. The sample doped with Mg acceptors remained semi-insulating up to 390 K. At temperatures exceeding 390 K the conductivity term in the total dielectric loss tangent of Mg compensated sample becomes dominant and it increases exponentially with activation energy of 1.14 eV. It has been proved that ammonothermal method with appropriate doping allows growth of high quality, temperature stable semi-insulating GaN crystals.

Dielectric properties and the monoclinictriclinic inversion in albite

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

Ho, P.; Duba, A.; Piwinskii, A.J.

1976-12-01

Dielectric properties (epsilon', real part of complex permittivity; epsilon'', imaginary part of complex permittivity; tan delta, loss tangent = epsilon''/epsilon') of single crystal Amelia albite have been measured parallel to the b-axis under controlled oxygen fugacity near the QFM buffer in the temperature range 1000 to 1373/sup 0/K at frequencies (..nu..) of 0.2 to 10 kHz. Plots of epsilon' and epsilon'' as a function of temperature exhibit minima which depend on time and ..nu.. in this albite. In addition, plots of tan delta as a function of temperature develop maxima which are also time-dependent. When epsilon', epsilon'', and tan deltamore » were investigated between 1220 and 1320/sup 0/K as a function of time, a break in these dielectric parameters with temperature was found. Epsilon' and epsilon'' increased with time above this break, while they decreased with time below the break. Values of loss tangent were also non-linear functions of temperature. Epsilon' and epsilon'' minima, tan delta maxima, and the temperature break in these dielectric properties were found to converge at approximately 1283/sup 0/K as time increases. Assuming that the epsilon' and epsilon'' increase and the tan delta decrease are the result of increasing disorder in this albite, these experimental data suggest that 1283 +- 20/sup 0/K is the temperature of the monoclinic-triclinic transition in this albite. This agrees well with electrical conductivity results which indicate 1253 +- 30/sup 0/K.« less

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.

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.

A Family of Ellipse Methods for Solving Non-Linear Equations

ERIC Educational Resources Information Center

Gupta, K. C.; Kanwar, V.; Kumar, Sanjeev

2009-01-01

This note presents a method for the numerical approximation of simple zeros of a non-linear equation in one variable. In order to do so, the method uses an ellipse rather than a tangent approach. The main advantage of our method is that it does not fail even if the derivative of the function is either zero or very small in the vicinity of the…

REMOTE RECORDING ANNULAR VANE ASSEMBLY

DOEpatents

Wehmann, G.

1963-06-25

A weather vane apparatus is described which is capable of movement in horizontal and vertical planes. Associated with the vane are tangent potentiometers, commutators, and other electrical apparatus for deriving electrical output voltages as a function of the wind direction. The apparatus is particularly adapted for use with an anemometer to provide an electrical output indicating the amount and direction of an up or down draft. (AEC)

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

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.

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

Dielectric response of high permittivity polymer ceramic composite with low loss tangent

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

Subodh, G.; 1.Physikalisches Institut, Universitat Stuttgart, Pfaffenwaldring 57, Stuttgart 70550; Deepu, V.

2009-08-10

The present communication investigates the dielectric response of the Sr{sub 9}Ce{sub 2}Ti{sub 12}O{sub 36} ceramics loaded high density polyethylene and epoxy resin. Sr{sub 9}Ce{sub 2}Ti{sub 12}O{sub 36} ceramic filled polyethylene and epoxy composites were prepared using hot blending and mechanical mixing, respectively. 40 vol % ceramic loaded polyethylene has relative permittivity of 12.1 and loss tangent of 0.004 at 8 GHz, whereas the corresponding composite using epoxy as matrix has permittivity and loss tangent of 14.1 and 0.022, respectively. The effective medium theory fits relatively well for the observed permittivity of these composites.

A derivation of the Cramer-Rao lower bound of euclidean parameters under equality constraints via score function

NASA Astrophysics Data System (ADS)

Susyanto, Nanang

2017-12-01

We propose a simple derivation of the Cramer-Rao Lower Bound (CRLB) of parameters under equality constraints from the CRLB without constraints in regular parametric models. When a regular parametric model and an equality constraint of the parameter are given, a parametric submodel can be defined by restricting the parameter under that constraint. The tangent space of this submodel is then computed with the help of the implicit function theorem. Finally, the score function of the restricted parameter is obtained by projecting the efficient influence function of the unrestricted parameter on the appropriate inner product spaces.

Toward more accurate loss tangent measurements in reentrant cavities

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

Moyer, R. D.

1980-05-01

Karpova has described an absolute method for measurement of dielectric properties of a solid in a coaxial reentrant cavity. His cavity resonance equation yields very accurate results for dielectric constants. However, he presented only approximate expressions for the loss tangent. This report presents more exact expressions for that quantity and summarizes some experimental results.

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

Special ergodic theorems and dynamical large deviations

NASA Astrophysics Data System (ADS)

Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav

2012-11-01

Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.

Lateralization of the Huggins pitch

NASA Astrophysics Data System (ADS)

Zhang, Peter Xinya; Hartmann, William M.

2004-05-01

The lateralization of the Huggins pitch (HP) was measured using a direct estimation method. The background noise was initially N0 or Nπ, and then the laterality of the entire stimulus was varied with a frequency-independent interaural delay, ranging from -1 to +1 ms. Two versions of the HP boundary region were used, stepped phase and linear phase. When presented in isolation, without the broadband background, the stepped boundary can be lateralized on its own but the linear boundary cannot. Nevertheless, the lateralizations of both forms of HP were found to be almost identical functions both of the interaural delay and of the boundary frequency over a two-octave range. In a third experiment, the same listeners lateralized sine tones in quiet as a function of interaural delay. Good agreement was found between lateralizations of the HP and of the corresponding sine tones. The lateralization judgments depended on the boundary frequency according to the expected hyperbolic law except when the frequency-independent delay was zero. For the latter case, the dependence on boundary frequency was much slower than hyperbolic. [Work supported by the NIDCD grant DC 00181.

Reversible dielectric property degradation in moisture-contaminated fiber-reinforced laminates

NASA Astrophysics Data System (ADS)

Rodriguez, Luis A.; García, Carla; Fittipaldi, Mauro; Grace, Landon R.

2016-03-01

The potential for recovery of dielectric properties of three water-contaminated fiber-reinforced laminates is investigated using a split-post dielectric resonant technique at X-band (10 GHz). The three material systems investigated are bismaleimide (BMI) reinforced with an eight-harness satin weave quartz fabric, an epoxy resin reinforced with an eight- harness satin weave glass fabric (style 7781), and the same epoxy reinforced with a four-harness woven glass fabric (style 4180). A direct correlation between moisture content, dielectric constant, and loss tangent was observed during moisture absorption by immersion in distilled water at 25 °C for five equivalent samples of each material system. This trend is observed through at least 0.72% water content by weight for all three systems. The absorption of water into the BMI, 7781 epoxy, and 4180 epoxy laminates resulted in a 4.66%, 3.35%, and 4.01% increase in dielectric constant for a 0.679%, 0.608%, and 0.719% increase in water content by weight, respectively. Likewise, a significant increase was noticed in loss tangent for each material. The same water content is responsible for a 228%, 71.4%, and 64.1% increase in loss tangent, respectively. Subsequent to full desorption through drying at elevated temperature, the dielectric constant and loss tangent of each laminate exhibited minimal change from the dry, pre-absorption state. The dielectric constant and loss tangent change after the absorption and desorption cycle, relative to the initial state, was 0.144 % and 2.63% in the BMI, 0.084% and 1.71% in the style 7781 epoxy, and 0.003% and 4.51% in the style 4180 epoxy at near-zero moisture content. The similarity of dielectric constant and loss tangent in samples prior to absorption and after desorption suggests that any chemical or morphological changes induced by the presence of water have not caused irreversible changes in the dielectric properties of the laminates.

Where We Look When We Drive with or without Active Steering Wheel Control

PubMed Central

Mars, Franck; Navarro, Jordan

2012-01-01

Current theories on the role of visuomotor coordination in driving agree that active sampling of the road by the driver informs the arm-motor system in charge of performing actions on the steering wheel. Still under debate, however, is the nature of visual cues and gaze strategies used by drivers. In particular, the tangent point hypothesis, which states that drivers look at a specific point on the inside edge line, has recently become the object of controversy. An alternative hypothesis proposes that drivers orient gaze toward the desired future path, which happens to be often situated in the vicinity of the tangent point. The present study contributed to this debate through the analyses of the distribution of gaze orientation with respect to the tangent point. The results revealed that drivers sampled the roadway in the close vicinity of the tangent point rather than the tangent point proper. This supports the idea that drivers look at the boundary of a safe trajectory envelop near the inside edge line. Furthermore, the study investigated for the first time the reciprocal influence of manual control on gaze control in the context of driving. This was achieved through the comparison of gaze behavior when drivers actively steered the vehicle or when steering was performed by an automatic controller. The results showed an increase in look-ahead fixations in the direction of the bend exit and a small but consistent reduction in the time spent looking in the area of the tangent point when steering was passive. This may be the consequence of a change in the balance between cognitive and sensorimotor anticipatory gaze strategies. It might also reflect bidirectional coordination control between the eye and arm-motor systems, which goes beyond the common assumption that the eyes lead the hands when driving. PMID:22928043

The representation of spacetime through steep time functions

NASA Astrophysics Data System (ADS)

Minguzzi, Ettore

2018-02-01

In a recent work I showed that the family of smooth steep time functions can be used to recover the order, the topology and the (Lorentz-Finsler) distance of spacetime. In this work I present the main ideas entering the proof of the (smooth) distance formula, particularly the product trick which converts metric statements into causal ones. The paper ends with a second proof of the distance formula valid for globally hyperbolic Lorentzian spacetimes.

Machine-learning the string landscape

NASA Astrophysics Data System (ADS)

He, Yang-Hui

2017-11-01

We propose a paradigm to apply machine learning various databases which have emerged in the study of the string landscape. In particular, we establish neural networks as both classifiers and predictors and train them with a host of available data ranging from Calabi-Yau manifolds and vector bundles, to quiver representations for gauge theories, using a novel framework of recasting geometrical and physical data as pixelated images. We find that even a relatively simple neural network can learn many significant quantities to astounding accuracy in a matter of minutes and can also predict hithertofore unencountered results, whereby rendering the paradigm a valuable tool in physics as well as pure mathematics. Of course, this paradigm is useful not only to physicists but to also to mathematicians; for instance, could our NN be trained well enough to approximate bundle cohomology calculations? This, and a host of other examples, we will now examine.Methodology  Neural networks are known for their complexity, involving usually a complicated directed graph each node of which is a ;perceptron; (an activation function imitating a neuron) and amongst the multitude of which there are many arrows encoding input/output. Throughout this letter, we will use a rather simple multi-layer perceptron (MLP) consisting of 5 layers, three of which are hidden, with activation functions typically of the form of a logistic sigmoid or a hyperbolic tangent. The input layer is a linear layer of 100 to 1000 nodes, recognizing a tensor (as we will soon see, algebro-geometric objects such as Calabi-Yau manifolds or polytopes are generically configurations of integer tensors) and the output layer is a summation layer giving a number corresponding to a Hodge number, or to rank of a cohomology group, etc. Such an MLP can be implemented, for instance, on the latest versions of Wolfram Mathematica. With 500-1000 training rounds, the running time is merely about 5-20 minutes on an ordinary laptop. It is reassuring and pleasantly surprising that even such a relatively simple NN can achieve the level of accuracy shortly to be presented.This letter is a companion summary of the longer paper[42]where the interested reader can find more details of the computations and the data.

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

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

Aging Mechanisms and Nondestructive Aging Indicator of Filled Cross-linked Polyethylene (XLPE) Exposed to Simultaneous Thermal and Gamma Radiation

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

Liu, Shuaishuai; Fifield, Leonard S.; Bowler, Nicola

Aging mechanisms and a nondestructive aging indicator of filled cross-linked polyethylene (XLPE) cable insulation material used in nuclear power plants (NPPs) are studied. Using various material characterization techniques, likely candidates and functions for the main additives in a commercial filled-XLPE insulation material have been identified. These include decabromodiphenyl ether and Sb2O3 as flame retardants, ZnS as white pigment and polymerized 1,2-dihydro-2,2,4-trimethylquinoline as antioxidant. Gas chromatography-mass spectrometry, differential scanning calorimetry, oxidation induction time and measurements of dielectric loss tangent are utilized to monitor property changes as a function of thermal and radiation exposure of the cable material. Small-molecular-weight hydrocarbons are evolvemore » with gamma radiation aging at 90 °C. The level of antioxidant decreases with aging by volatilization and chemical reaction with free radicals. Thermal aging at 90 °C for 25 days or less causes no observable change to the cross-linked polymer structure. Gamma radiation causes damage to crystalline polymer regions and introduces defects. Dielectric loss tangent is shown to be an effective and reliable nondestructive indicator of the aging severity of the filled-XLPE insulation material.« less

Horizontal visibility graphs generated by type-I intermittency

NASA Astrophysics Data System (ADS)

Núñez, Ángel M.; Luque, Bartolo; Lacasa, Lucas; Gómez, Jose Patricio; Robledo, Alberto

2013-05-01

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

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

Explicit blow-up solutions to the Schroedinger maps from R{sup 2} to the hyperbolic 2-space H{sup 2}

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

Ding Qing

2009-10-15

In this article, we prove that the equation of the Schroedinger maps from R{sup 2} to the hyperbolic 2-space H{sup 2} is SU(1,1)-gauge equivalent to the following 1+2 dimensional nonlinear Schroedinger-type system of three unknown complex functions p, q, r, and a real function u: iq{sub t}+q{sub zz}-2uq+2(pq){sub z}-2pq{sub z}-4|p|{sup 2}q=0, ir{sub t}-r{sub zz}+2ur+2(pr){sub z}-2pr{sub z}+4|p|{sup 2}r=0, ip{sub t}+(qr){sub z}-u{sub z}=0, p{sub z}+p{sub z}=-|q|{sup 2}+|r|{sup 2}, -r{sub z}+q{sub z}=-2(pr+pq), where z is a complex coordinate of the plane R{sup 2} and z is the complex conjugate of z. Although this nonlinear Schroedinger-type system looks complicated, it admits a class ofmore » explicit blow-up smooth solutions: p=0, q=(e{sup i(bzz/2(a+bt))}/a+bt){alpha}z, r=e{sup -i(bzz/2(a+bt))}/(a+bt){alpha}z, u=2{alpha}{sup 2}zz/(a+bt){sup 2}, where a and b are real numbers with ab<0 and {alpha} satisfies {alpha}{sup 2}=b{sup 2}/16. From these facts, we explicitly construct smooth solutions to the Schroedinger maps from R{sup 2} to the hyperbolic 2-space H{sup 2} by using the gauge transformations such that the absolute values of their gradients blow up in finite time. This reveals some blow-up phenomenon of Schroedinger maps.« less

Transformation formulas relating geodetic coordinates to a tangent to Earth, plane coordinate system

NASA Technical Reports Server (NTRS)

Credeur, L.

1981-01-01

Formulas and their approximation were developed to map geodetic position to an Earth tangent plane with an airport centered rectangular coordinate system. The transformations were developed for use in a terminal area air traffic model with deterministic aircraft traffic. The exact configured vehicle's approximation equations used in their precision microwave landing system navigation experiments.

Closed Circular Chains

ERIC Educational Resources Information Center

Caglayan, Günhan

2016-01-01

A Steiner chain is defined as the sequence of n circles that are all tangent to two given non-intersecting circles. A closed chain, in particular, is one in which every circle in the sequence is tangent to the previous and next circles of the chain. In a closed Steiner chain the first and the "n"th circles of the chain are also tangent…

Linear approximations of nonlinear systems

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Su, R.

1983-01-01

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

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.

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.

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.

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

Applications of Random Differential Equations to Engineering Science. Wave Propagation in Turbulent Media and Random Linear Hyperbolic Systems.

DTIC Science & Technology

1981-11-10

1976), 745-754. 4. (with W. C. Tam) Periodic and traveling wave solutions to Volterra - Lotka equation with diffusion. Bull. Math. Biol. 38 (1976), 643...with applications [17,19,20). (5) A general method for reconstructing the mutual coherent function of a static or moving source from the random

Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations.

PubMed

Gu, Yongyi; Qi, Jianming

2017-01-01

In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the [Formula: see text]-expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Larson, Mats G.; Barth, Timothy J.

1999-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Universal analytical scattering form factor for shell-, core-shell, or homogeneous particles with continuously variable density profile shape.

PubMed

Foster, Tobias

2011-09-01

A novel analytical and continuous density distribution function with a widely variable shape is reported and used to derive an analytical scattering form factor that allows us to universally describe the scattering from particles with the radial density profile of homogeneous spheres, shells, or core-shell particles. Composed by the sum of two Fermi-Dirac distribution functions, the shape of the density profile can be altered continuously from step-like via Gaussian-like or parabolic to asymptotically hyperbolic by varying a single "shape parameter", d. Using this density profile, the scattering form factor can be calculated numerically. An analytical form factor can be derived using an approximate expression for the original Fermi-Dirac distribution function. This approximation is accurate for sufficiently small rescaled shape parameters, d/R (R being the particle radius), up to values of d/R ≈ 0.1, and thus captures step-like, Gaussian-like, and parabolic as well as asymptotically hyperbolic profile shapes. It is expected that this form factor is particularly useful in a model-dependent analysis of small-angle scattering data since the applied continuous and analytical function for the particle density profile can be compared directly with the density profile extracted from the data by model-free approaches like the generalized inverse Fourier transform method. © 2011 American Chemical Society

Measurement of corneal tangent modulus using ultrasound indentation.

PubMed

Wang, Li-Ke; Huang, Yan-Ping; Tian, Lei; Kee, Chea-Su; Zheng, Yong-Ping

2016-09-01

Biomechanical properties are potential information for the diagnosis of corneal pathologies. An ultrasound indentation probe consisting of a load cell and a miniature ultrasound transducer as indenter was developed to detect the force-indentation relationship of the cornea. The key idea was to utilize the ultrasound transducer to compress the cornea and to ultrasonically measure the corneal deformation with the eyeball overall displacement compensated. Twelve corneal silicone phantoms were fabricated with different stiffness for the validation of measurement with reference to an extension test. In addition, fifteen fresh porcine eyes were measured by the developed system in vitro. The tangent moduli of the corneal phantoms calculated using the ultrasound indentation data agreed well with the results from the tensile test of the corresponding phantom strips (R(2)=0.96). The mean tangent moduli of the porcine corneas measured by the proposed method were 0.089±0.026MPa at intraocular pressure (IOP) of 15mmHg and 0.220±0.053MPa at IOP of 30mmHg, respectively. The coefficient of variation (CV) and intraclass correlation coefficient (ICC) of tangent modulus were 14.4% and 0.765 at 15mmHg, and 8.6% and 0.870 at 30mmHg, respectively. The preliminary study showed that ultrasound indentation could be applied to the measurement of corneal tangent modulus with good repeatability and improved measurement accuracy compared to conventional surface displacement-based measurement method. The ultrasound indentation can be a potential tool for the corneal biomechanical properties measurement in vivo. Copyright © 2016 Elsevier B.V. All rights reserved.

Three filters for visualization of phase objects with large variations of phase gradients

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

Sagan, Arkadiusz; Antosiewicz, Tomasz J.; Szoplik, Tomasz

2009-02-20

We propose three amplitude filters for visualization of phase objects. They interact with the spectra of pure-phase objects in the frequency plane and are based on tangent and error functions as well as antisymmetric combination of square roots. The error function is a normalized form of the Gaussian function. The antisymmetric square-root filter is composed of two square-root filters to widen its spatial frequency spectral range. Their advantage over other known amplitude frequency-domain filters, such as linear or square-root graded ones, is that they allow high-contrast visualization of objects with large variations of phase gradients.

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.

Conic Sections and the Discovery of a Novel Curve Using Differential Equations

ERIC Educational Resources Information Center

de Alwis, Amal

2013-01-01

We began by observing a variety of properties related to the tangent and normal lines of three conic sections: a parabola, an ellipse, and a hyperbola. Some of these properties include specific relationships between the x- and y-intercepts of the tangent and normal lines. Using these properties, we were able to form several differential equations.…

An improved tree height measurement technique tested on mature southern pines

Treesearch

Don C. Bragg

2008-01-01

Virtually all techniques for tree height determination follow one of two principles: similar triangles or the tangent method. Most people apply the latter approach, which uses the tangents of the angles to the top and bottom and a true horizontal distance to the subject tree. However, few adjust this method for ground slope, tree lean, crown shape, and crown...

Influence of high temperature annealing on the dielectric properties of alumina films prepared by the aerosol deposition method

NASA Astrophysics Data System (ADS)

Leupold, Nico; Schubert, Michael; Kita, Jaroslaw; Moos, Ralf

The aerosol deposition method (ADM) is a novel coating technique that allows to fabricate dense and nanocrystalline ceramic films at room temperature. To investigate the dielectric properties of aerosol deposited alumina films at high temperatures and the influence of annealing on them, the temperature was increased in steps of 100∘C from 200∘C to 900∘C and subsequently cooled down stepwise again. At each step, the dielectric properties were measured by impedance spectroscopy between 50mHz and 200kHz. During the heating steps, the relative permittivity and also the loss tangent showed a disordered behavior with various maxima in the loss tangent. After reaching 900∘C, during cooling, the behavior was more ordered, and the loss tangent exhibited only one maximum that appeared at lower frequencies. Overall, the annealing reduces the loss tangent at low frequencies and low temperatures. The origin of this behavior could lie in the annealing of defects, which are incorporated into the layer when the particles hit the surface of the substrate and crack while being deposited via ADM following the room temperature impact consolidation mechanism (RTIC).

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

NASA Astrophysics Data System (ADS)

Bacigalupo, Andrea; Gambarotta, Luigi

2017-05-01

Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units, having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected with each other through homogeneous linear interfaces, have been analyzed. The acoustic behavior of the resulting discrete Lagrangian model has been obtained through a Floquet-Bloch approach. From the resulting eigenproblem derived by the Euler-Lagrange equations for harmonic wave propagation, two acoustic branches and an optical branch are obtained in the frequency spectrum. A micropolar continuum model to approximate the Lagrangian model has been derived based on a second-order Taylor expansion of the generalized macro-displacement field. The constitutive equations of the equivalent micropolar continuum have been obtained, with the peculiarity that the positive definiteness of the second-order symmetric tensor associated to the curvature vector is not guaranteed and depends both on the ratio between the local tangent and normal stiffness and on the block shape. The same results have been obtained through an extended Hamiltonian derivation of the equations of motion for the equivalent continuum that is related to the Hill-Mandel macro homogeneity condition. Moreover, it is shown that the hermitian matrix governing the eigenproblem of harmonic wave propagation in the micropolar model is exact up to the second order in the norm of the wave vector with respect to the same matrix from the discrete model. To appreciate the acoustic behavior of some relevant blocky materials and to understand the reliability and the validity limits of the micropolar continuum model, some blocky patterns have been analyzed: rhombic and hexagonal assemblages and running bond masonry. From the results obtained in the examples, the obtained micropolar model turns out to be particularly accurate to describe dispersive functions for wavelengths greater than 3-4 times the characteristic dimension of the block. Finally, in consideration that the positive definiteness of the second order elastic tensor of the micropolar model is not guaranteed, the hyperbolicity of the equation of motion has been investigated by considering the Legendre-Hadamard ellipticity conditions requiring real values for the wave velocity.

Toward a 3D dynamic model of a faulty duplex ball bearing

NASA Astrophysics Data System (ADS)

Kogan, Gideon; Klein, Renata; Kushnirsky, Alex; Bortman, Jacob

2015-03-01

Bearings are vital components for safe and proper operation of machinery. Increasing efficiency of bearing diagnostics usually requires training of health and usage monitoring systems via expensive and time-consuming ground calibration tests. The main goal of this research, therefore, is to improve bearing dynamics modeling tools in order to reduce the time and budget needed to implement the health and usage monitoring approach. The proposed three-dimensional ball bearing dynamic model is based on the classic dynamic and kinematic equations. Interactions between the bodies are simulated using non-linear springs combined with dampers described by Hertz-type contact relation. The force friction is simulated using the hyperbolic-tangent function. The model allows simulation of a wide range of mechanical faults. It is validated by comparison to known bearing behavior and to experimental results. The model results are verified by demonstrating numerical convergence. The model results for the two cases of single and duplex angular ball bearings with axial deformation in the outer ring are presented. The qualitative investigation provides insight into bearing dynamics, the sensitivity study generalizes the qualitative findings for similar cases, and the comparison to the test results validates model reliability. The article demonstrates the variety of the cases that the 3D bearing model can simulate and the findings to which it may lead. The research allowed the identification of new patterns generated by single and duplex bearings with axially deformed outer race. It also enlightened the difference between single and duplex bearing manifestation. In the current research the dynamic model enabled better understanding of the physical behavior of the faulted bearings. Therefore, it is expected that the modeling approach has the potential to simplify and improve the development process of diagnostic algorithms. • A deformed outer race of a single axially loaded bearing is simulated. • The model results are subjected to a sensitivity study. • Duplex bearing with deformed outer race is simulated as well as tested. • The simulation results are in a good agreement with the experimental results.

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.

Development of Metamaterial Composites for Compact High Power Microwave Systems and Antennas

DTIC Science & Technology

2016-05-01

for the eddy currents to decay and thus the reverse magnetizing field becomes significant at the surface of the material. This reverse field shields ...76 Appendix A: Ceramic Magnetics , Inc. Ferrite Data Sheets…………………………………81 Appendix B: Conference Presentations and Journal...Figure 21: Magnetic loss tangent as a function of frequency for each of the five ferrite composites

Scars of the Wigner Function.

PubMed

Toscano; de Aguiar MA; Ozorio De Almeida AM

2001-01-01

We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical hyperbolic orbit of a Hamiltonian system with 2 degrees of freedom. The stationary wave functions are the familiar mixture of scarred and random waves, but the spectral average of the Wigner functions in part of the plane is nearly that of a harmonic oscillator and individual states are also remarkably regular. These results are interpreted in terms of the semiclassical picture of chords and centers.

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.

Improving GPR image resolution in lossy ground using dispersive migration

USGS Publications Warehouse

Oden, C.P.; Powers, M.H.; Wright, D.L.; Olhoeft, G.R.

2007-01-01

As a compact wave packet travels through a dispersive medium, it becomes dilated and distorted. As a result, ground-penetrating radar (GPR) surveys over conductive and/or lossy soils often result in poor image resolution. A dispersive migration method is presented that combines an inverse dispersion filter with frequency-domain migration. The method requires a fully characterized GPR system including the antenna response, which is a function of the local soil properties for ground-coupled antennas. The GPR system response spectrum is used to stabilize the inverse dispersion filter. Dispersive migration restores attenuated spectral components when the signal-to-noise ratio is adequate. Applying the algorithm to simulated data shows that the improved spatial resolution is significant when data are acquired with a GPR system having 120 dB or more of dynamic range, and when the medium has a loss tangent of 0.3 or more. Results also show that dispersive migration provides no significant advantage over conventional migration when the loss tangent is less than 0.3, or when using a GPR system with a small dynamic range. ?? 2007 IEEE.

The Regularity of Optimal Irrigation Patterns

NASA Astrophysics Data System (ADS)

Morel, Jean-Michel; Santambrogio, Filippo

2010-02-01

A branched structure is observable in draining and irrigation systems, in electric power supply systems, and in natural objects like blood vessels, the river basins or the trees. Recent approaches of these networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow s in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s α with 0 < α < 1. The aim of this paper is to prove the regularity of paths (rivers, branches,...) when the irrigated measure is the Lebesgue density on a smooth open set and the irrigating measure is a single source. In that case we prove that all branches of optimal irrigation trees satisfy an elliptic equation and that their curvature is a bounded measure. In consequence all branching points in the network have a tangent cone made of a finite number of segments, and all other points have a tangent. An explicit counterexample disproves these regularity properties for non-Lebesgue irrigated measures.

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 \

Morera-type theorems in the hyperbolic disc

NASA Astrophysics Data System (ADS)

Volchkov, V. V.; Volchkov, V. V.

2018-02-01

Let G be the group of conformal automorphisms of the unit disc {D}=\\{z\\in{C}\\colon \\vert z\\vert<1\\}. We study the problem of the holomorphicity of functions f on {D} satisfying the equation where γ\\varrho=\\{z\\in{C}\\colon \\vert z\\vert=\\varrho\\} and ρ\\in(0,1) is fixed. We find exact conditions for holomorphicity in terms of the boundary behaviour of such functions. A by-product of our work is a new proof of the Berenstein-Pascuas two-radii theorem.

Explicit robust schemes for implementation of a class of principal value-based constitutive models: Symbolic and numeric implementation

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Saleeb, A. F.; Tan, H. Q.; Zhang, Y.

1993-01-01

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal-stretch values have been theoretically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.

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.

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.

Corrigendum to “A new hyperbolic auxiliary function method and exact solutions of the mBBM equation” [Commun Nonlinear Sci Numer Simul 2010;15:135-138

NASA Astrophysics Data System (ADS)

Layeni, Olawanle P.; Akinola, Ade P.

2010-09-01

The symbols w and ω were abused in article [1]. Replacing ξ + ω with ξ throughout the article (that is in Eqs. (5) and (13)-(23)) and afterwards taking w and ω to denote the (same) frequency of the traveling wave(s) set this right.

Multiresolution and Explicit Methods for Vector Field Analysis and Visualization

NASA Technical Reports Server (NTRS)

1996-01-01

We first report on our current progress in the area of explicit methods for tangent curve computation. The basic idea of this method is to decompose the domain into a collection of triangles (or tetrahedra) and assume linear variation of the vector field over each cell. With this assumption, the equations which define a tangent curve become a system of linear, constant coefficient ODE's which can be solved explicitly. There are five different representation of the solution depending on the eigenvalues of the Jacobian. The analysis of these five cases is somewhat similar to the phase plane analysis often associate with critical point classification within the context of topological methods, but it is not exactly the same. There are some critical differences. Moving from one cell to the next as a tangent curve is tracked, requires the computation of the exit point which is an intersection of the solution of the constant coefficient ODE and the edge of a triangle. There are two possible approaches to this root computation problem. We can express the tangent curve into parametric form and substitute into an implicit form for the edge or we can express the edge in parametric form and substitute in an implicit form of the tangent curve. Normally the solution of a system of ODE's is given in parametric form and so the first approach is the most accessible and straightforward. The second approach requires the 'implicitization' of these parametric curves. The implicitization of parametric curves can often be rather difficult, but in this case we have been successful and have been able to develop algorithms and subsequent computer programs for both approaches. We will give these details along with some comparisons in a forthcoming research paper on this topic.

Validation of UARS Microwave Limb Sounder Temperature and Pressure Measurements

NASA Technical Reports Server (NTRS)

Fishbein, E. F.; Cofield, R. E.; Froidevaux, L.; Jarnot, R. F.; Lungu, T.; Read, W. G.; Shippony, Z.; Waters, J. W.; McDermid, I. S.; McGee, T. J.;

Development of the WRF-CO2 4D-Var assimilation system v1.0

NASA Astrophysics Data System (ADS)

Zheng, Tao; French, Nancy H. F.; Baxter, Martin

2018-05-01

Regional atmospheric CO2 inversions commonly use Lagrangian particle trajectory model simulations to calculate the required influence function, which quantifies the sensitivity of a receptor to flux sources. In this paper, an adjoint-based four-dimensional variational (4D-Var) assimilation system, WRF-CO2 4D-Var, is developed to provide an alternative approach. This system is developed based on the Weather Research and Forecasting (WRF) modeling system, including the system coupled to chemistry (WRF-Chem), with tangent linear and adjoint codes (WRFPLUS), and with data assimilation (WRFDA), all in version 3.6. In WRF-CO2 4D-Var, CO2 is modeled as a tracer and its feedback to meteorology is ignored. This configuration allows most WRF physical parameterizations to be used in the assimilation system without incurring a large amount of code development. WRF-CO2 4D-Var solves for the optimized CO2 flux scaling factors in a Bayesian framework. Two variational optimization schemes are implemented for the system: the first uses the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization algorithm (L-BFGS-B) and the second uses the Lanczos conjugate gradient (CG) in an incremental approach. WRFPLUS forward, tangent linear, and adjoint models are modified to include the physical and dynamical processes involved in the atmospheric transport of CO2. The system is tested by simulations over a domain covering the continental United States at 48 km × 48 km grid spacing. The accuracy of the tangent linear and adjoint models is assessed by comparing against finite difference sensitivity. The system's effectiveness for CO2 inverse modeling is tested using pseudo-observation data. The results of the sensitivity and inverse modeling tests demonstrate the potential usefulness of WRF-CO2 4D-Var for regional CO2 inversions.

The effect of in-service aerospace contaminants on X-band dielectric properties of a bismaleimide/quartz composite

NASA Astrophysics Data System (ADS)

Rodriguez, Luis A.; García, Carla; Grace, Landon R.

2015-05-01

The impact of three common aerospace in-service liquid contaminants on the X-band dielectric properties of a polymer composite radar protecting structure (radome) is investigated and quantified. The dielectric properties of the composite laminate are critical to radar transparency, and thus performance, of the radome structure. Further, polymer composites are highly susceptible to absorption of liquids. As such, the effect of common aerospace contaminants on the dielectric properties of composite laminates is crucial. Measurement of relative permittivity and loss tangent via a split-post dielectric resonant technique at 10 GHz is used to determine the effect of water, deicing fluid, and propylene glycol absorption in a three-ply quartz-reinforced bismaleimide laminate. Additionally, fluid uptake kinetics are investigated as a function of liquid type. An approximately linear relationship between fluid content and relative permittivity is observed for all three contaminant types. A 1% increase in contaminant content by weight results in a 7.8%, 4.5%, and 2.5% increase in relative permittivity of the material due to water, deicing fluid, and propylene glycol, respectively. A more significant impact is seen in material loss tangent, where a 1% increase in contaminant content by weight is responsible for a 378.5%, 593.0%, and 441.5% increase in loss tangent due to the aforementioned fluids, respectively. A fluid uptake weight content of 1.31%, 3.41%, and 4.28% is achieved for water, deicing fluid, and propylene glycol respectively, at approximately 1300 hours exposure. Based on the reported observations, the dielectric property degradation of composite laminates due to these commonly used fluids is of significant concern for in-service aircraft radar systems routinely exposed to these contaminants.

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.

Local Subspace Classifier with Transform-Invariance for Image Classification

NASA Astrophysics Data System (ADS)

Hotta, Seiji

A family of linear subspace classifiers called local subspace classifier (LSC) outperforms the k-nearest neighbor rule (kNN) and conventional subspace classifiers in handwritten digit classification. However, LSC suffers very high sensitivity to image transformations because it uses projection and the Euclidean distances for classification. In this paper, I present a combination of a local subspace classifier (LSC) and a tangent distance (TD) for improving accuracy of handwritten digit recognition. In this classification rule, we can deal with transform-invariance easily because we are able to use tangent vectors for approximation of transformations. However, we cannot use tangent vectors in other type of images such as color images. Hence, kernel LSC (KLSC) is proposed for incorporating transform-invariance into LSC via kernel mapping. The performance of the proposed methods is verified with the experiments on handwritten digit and color image classification.

Reverse-Tangent Injection in a Centrifugal Compressor

NASA Technical Reports Server (NTRS)

Skoch, Gary J.

2007-01-01

Injection of working fluid into a centrifugal compressor in the reverse tangent direction has been invented as a way of preventing flow instabilities (stall and surge) or restoring stability when stall or surge has already commenced. The invention applies, in particular, to a centrifugal compressor, the diffuser of which contains vanes that divide the flow into channels oriented partly radially and partly tangentially. In reverse-tangent injection, a stream or jet of the working fluid (the fluid that is compressed) is injected into the vaneless annular region between the blades of the impeller and the vanes of the diffuser. As used here, "reverse" signifies that the injected flow opposes (and thereby reduces) the tangential component of the velocity of the impeller discharge. At the same time, the injected jet acts to increase the radial component of the velocity of the impeller discharge.

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...

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

The isotropic-nematic phase transition of tangent hard-sphere chain fluids—Pure components

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J. H.; Gross, Joachim

2013-07-01

An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under- and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition.

Boundary Layer Studies on a Spinning Tangent-Ogive-Cylinder Model

DTIC Science & Technology

1975-07-01

ca) An experimental investigation of the Magnus effect on a seven caliber tangent-I ;’ ogive- cylinder model in supersonic flow is reported. The...necessary and Identify by block number) Three-Dimiensional Boundary Layer Compressible Flow Body of Revolution Magnus Effects Boundary Layer...factors have resulted in renewed interest in the study of the Magnus effect . This report describes an experimental study of the effects of spin on

Multiband tangent space mapping and feature selection for classification of EEG during motor imagery.

PubMed

Islam, Md Rabiul; Tanaka, Toshihisa; Molla, Md Khademul Islam

2018-05-08

When designing multiclass motor imagery-based brain-computer interface (MI-BCI), a so-called tangent space mapping (TSM) method utilizing the geometric structure of covariance matrices is an effective technique. This paper aims to introduce a method using TSM for finding accurate operational frequency bands related brain activities associated with MI tasks. A multichannel electroencephalogram (EEG) signal is decomposed into multiple subbands, and tangent features are then estimated on each subband. A mutual information analysis-based effective algorithm is implemented to select subbands containing features capable of improving motor imagery classification accuracy. Thus obtained features of selected subbands are combined to get feature space. A principal component analysis-based approach is employed to reduce the features dimension and then the classification is accomplished by a support vector machine (SVM). Offline analysis demonstrates the proposed multiband tangent space mapping with subband selection (MTSMS) approach outperforms state-of-the-art methods. It acheives the highest average classification accuracy for all datasets (BCI competition dataset 2a, IIIa, IIIb, and dataset JK-HH1). The increased classification accuracy of MI tasks with the proposed MTSMS approach can yield effective implementation of BCI. The mutual information-based subband selection method is implemented to tune operation frequency bands to represent actual motor imagery tasks.

Application of the Artificial Neural Network model for prediction of monthly Standardized Precipitation and Evapotranspiration Index using hydrometeorological parameters and climate indices in eastern Australia

NASA Astrophysics Data System (ADS)

Deo, Ravinesh C.; Şahin, Mehmet

2015-07-01

The forecasting of drought based on cumulative influence of rainfall, temperature and evaporation is greatly beneficial for mitigating adverse consequences on water-sensitive sectors such as agriculture, ecosystems, wildlife, tourism, recreation, crop health and hydrologic engineering. Predictive models of drought indices help in assessing water scarcity situations, drought identification and severity characterization. In this paper, we tested the feasibility of the Artificial Neural Network (ANN) as a data-driven model for predicting the monthly Standardized Precipitation and Evapotranspiration Index (SPEI) for eight candidate stations in eastern Australia using predictive variable data from 1915 to 2005 (training) and simulated data for the period 2006-2012. The predictive variables were: monthly rainfall totals, mean temperature, minimum temperature, maximum temperature and evapotranspiration, which were supplemented by large-scale climate indices (Southern Oscillation Index, Pacific Decadal Oscillation, Southern Annular Mode and Indian Ocean Dipole) and the Sea Surface Temperatures (Nino 3.0, 3.4 and 4.0). A total of 30 ANN models were developed with 3-layer ANN networks. To determine the best combination of learning algorithms, hidden transfer and output functions of the optimum model, the Levenberg-Marquardt and Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton backpropagation algorithms were utilized to train the network, tangent and logarithmic sigmoid equations used as the activation functions and the linear, logarithmic and tangent sigmoid equations used as the output function. The best ANN architecture had 18 input neurons, 43 hidden neurons and 1 output neuron, trained using the Levenberg-Marquardt learning algorithm using tangent sigmoid equation as the activation and output functions. An evaluation of the model performance based on statistical rules yielded time-averaged Coefficient of Determination, Root Mean Squared Error and the Mean Absolute Error ranging from 0.9945-0.9990, 0.0466-0.1117, and 0.0013-0.0130, respectively for individual stations. Also, the Willmott's Index of Agreement and the Nash-Sutcliffe Coefficient of Efficiency were between 0.932-0.959 and 0.977-0.998, respectively. When checked for the severity (S), duration (D) and peak intensity (I) of drought events determined from the simulated and observed SPEI, differences in drought parameters ranged from - 1.41-0.64%, - 2.17-1.92% and - 3.21-1.21%, respectively. Based on performance evaluation measures, we aver that the Artificial Neural Network model is a useful data-driven tool for forecasting monthly SPEI and its drought-related properties in the region of study.

Real-Time Adaptive Color Segmentation by Neural Networks

NASA Technical Reports Server (NTRS)

Duong, Tuan A.

2004-01-01

Artificial neural networks that would utilize the cascade error projection (CEP) algorithm have been proposed as means of autonomous, real-time, adaptive color segmentation of images that change with time. In the original intended application, such a neural network would be used to analyze digitized color video images of terrain on a remote planet as viewed from an uninhabited spacecraft approaching the planet. During descent toward the surface of the planet, information on the segmentation of the images into differently colored areas would be updated adaptively in real time to capture changes in contrast, brightness, and resolution, all in an effort to identify a safe and scientifically productive landing site and provide control feedback to steer the spacecraft toward that site. Potential terrestrial applications include monitoring images of crops to detect insect invasions and monitoring of buildings and other facilities to detect intruders. The CEP algorithm is reliable and is well suited to implementation in very-large-scale integrated (VLSI) circuitry. It was chosen over other neural-network learning algorithms because it is better suited to realtime learning: It provides a self-evolving neural-network structure, requires fewer iterations to converge and is more tolerant to low resolution (that is, fewer bits) in the quantization of neural-network synaptic weights. Consequently, a CEP neural network learns relatively quickly, and the circuitry needed to implement it is relatively simple. Like other neural networks, a CEP neural network includes an input layer, hidden units, and output units (see figure). As in other neural networks, a CEP network is presented with a succession of input training patterns, giving rise to a set of outputs that are compared with the desired outputs. Also as in other neural networks, the synaptic weights are updated iteratively in an effort to bring the outputs closer to target values. A distinctive feature of the CEP neural network and algorithm is that each update of synaptic weights takes place in conjunction with the addition of another hidden unit, which then remains in place as still other hidden units are added on subsequent iterations. For a given training pattern, the synaptic weight between (1) the inputs and the previously added hidden units and (2) the newly added hidden unit is updated by an amount proportional to the partial derivative of a quadratic error function with respect to the synaptic weight. The synaptic weight between the newly added hidden unit and each output unit is given by a more complex function that involves the errors between the outputs and their target values, the transfer functions (hyperbolic tangents) of the neural units, and the derivatives of the transfer functions.

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

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.

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.

Bathymetry and composition of Titan's Ontario Lacus derived from Monte Carlo-based waveform inversion of Cassini RADAR altimetry data

NASA Astrophysics Data System (ADS)

Mastrogiuseppe, M.; Hayes, A. G.; Poggiali, V.; Lunine, J. I.; Lorenz, R. D.; Seu, R.; Le Gall, A.; Notarnicola, C.; Mitchell, K. L.; Malaska, M.; Birch, S. P. D.

2018-01-01

Recently, the Cassini RADAR was used to sound hydrocarbon lakes and seas on Saturn's moon Titan. Since the initial discovery of echoes from the seabed of Ligeia Mare, the second largest liquid body on Titan, a dedicated radar processing chain has been developed to retrieve liquid depth and microwave absorptivity information from RADAR altimetry of Titan's lakes and seas. Herein, we apply this processing chain to altimetry data acquired over southern Ontario Lacus during Titan fly-by T49 in December 2008. The new signal processing chain adopts super resolution techniques and dedicated taper functions to reveal the presence of reflection from Ontario's lakebed. Unfortunately, the extracted waveforms from T49 are often distorted due to signal saturation, owing to the extraordinarily strong specular reflections from the smooth lake surface. This distortion is a function of the saturation level and can introduce artifacts, such as signal precursors, which complicate data interpretation. We use a radar altimetry simulator to retrieve information from the saturated bursts and determine the liquid depth and loss tangent of Ontario Lacus. Received waveforms are represented using a two-layer model, where Cassini raw radar data are simulated in order to reproduce the effects of receiver saturation. A Monte Carlo based approach along with a simulated waveform look-up table is used to retrieve parameters that are given as inputs to a parametric model which constrains radio absorption of Ontario Lacus and retrieves information about the dielectric properties of the liquid. We retrieve a maximum depth of 50 m along the radar transect and a best-fit specific attenuation of the liquid equal to 0.2 ± 0.09 dB m-1 that, when converted into loss tangent, gives tanδ = 7 ± 3 × 10-5. When combined with laboratory measured cryogenic liquid alkane dielectric properties and the variable solubility of nitrogen in ethane-methane mixtures, the best-fit loss tangent is consistent with a ternary mixture of 51% methane, 38% ethane and 11% nitrogen by volume.

Semiclassical propagator of the Wigner function.

PubMed

Dittrich, Thomas; Viviescas, Carlos; Sandoval, Luis

2006-02-24

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.

Equivalences between nonuniform exponential dichotomy and admissibility

NASA Astrophysics Data System (ADS)

Zhou, Linfeng; Lu, Kening; Zhang, Weinian

2017-01-01

Relationship between exponential dichotomies and admissibility of function classes is a significant problem for hyperbolic dynamical systems. It was proved that a nonuniform exponential dichotomy implies several admissible pairs of function classes and conversely some admissible pairs were found to imply a nonuniform exponential dichotomy. In this paper we find an appropriate admissible pair of classes of Lyapunov bounded functions which is equivalent to the existence of nonuniform exponential dichotomy on half-lines R± separately, on both half-lines R± simultaneously, and on the whole line R. Additionally, the maximal admissibility is proved in the case on both half-lines R± simultaneously.

Study of analytical method to seek for exact solutions of variant Boussinesq equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali

2014-01-01

In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G'/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function solutions of this equation. 35 K99; 35P05; 35P99.

Exact and Approximate Solutions for the Decades-Old Michaelis-Menten Equation: Progress-Curve Analysis through Integrated Rate Equations

ERIC Educational Resources Information Center

Golicnik, Marko

2011-01-01

The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate "V", and the Michaelis constant "K"[subscript M]) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to…

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.

Global Modeling and Data Assimilation. Volume 11; Documentation of the Tangent Linear and Adjoint Models of the Relaxed Arakawa-Schubert Moisture Parameterization of the NASA GEOS-1 GCM; 5.2

NASA Technical Reports Server (NTRS)

Suarez, Max J. (Editor); Yang, Wei-Yu; Todling, Ricardo; Navon, I. Michael

1997-01-01

A detailed description of the development of the tangent linear model (TLM) and its adjoint model of the Relaxed Arakawa-Schubert moisture parameterization package used in the NASA GEOS-1 C-Grid GCM (Version 5.2) is presented. The notational conventions used in the TLM and its adjoint codes are described in detail.

The influence of NO and ClO variations at twilight on the interpretation of solar occultation measurements

NASA Technical Reports Server (NTRS)

Boughner, R.; Larsen, J. C.; Natarajan, M.

1980-01-01

Measurement of short-lived photochemically-produced species in the stratosphere by solar occultation is difficult because the rapid variation of such species near the terminator introduces ambiguities in interpreting the measured absorption in terms of meaningful atmospheric abundances. These variations produce tangent path concentrations that are asymmetric relative to the tangent point, as opposed to the symmetrical distribution usually assumed in most inversion algorithms. Neglect of this asymmetry may yield an inverted profile that deviates significantly from the true sunset/sunrise profile. In the present paper, the influence of this effect on solar occultation measurements of ClO and NO is examined. The results show that average inhomogeneity factors, which measure the concentration variation along the tangent path and which can be calculated from a photochemical model, can indicate which species require more careful data analysis.

Optical properties of transiently-excited semiconductor hyperbolic metamaterials

DOE PAGES

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

2015-10-02

Ultrafast optical excitation of photocarriers has the potential to transform undoped semiconductor superlattices into semiconductor hyperbolic metamaterials (SHMs). In this paper, we investigate the optical properties associated with such ultrafast topological transitions. We first show reflectance, transmittance, and absorption under TE and TM plane wave incidence. In the unpumped state, the superlattice exhibits a frequency region with high reflectance (>80%) and a region with low reflectance (<1%) for both TE and TM polarizations over a wide range of incidence angles. In contrast, in the photopumped state, the reflectance for both frequencies and polarizations is very low (<1%) for a similarmore » range of angles. Interestingly, this system can function as an all-optical reflection switch on ultrafast timescales. Furthermore, for TM incidence and close to the epsilon-near-zero point of the longitudinal permittivity, directional perfect absorption on ultrafast timescales may also be achieved. Lastly, we discuss the onset of negative refraction in the photopumped state.« less

On oscillatory convection with the Cattaneo–Christov hyperbolic heat-flow model

PubMed Central

Bissell, J. J.

2015-01-01

Adoption of the hyperbolic Cattaneo–Christov heat-flow model in place of the more usual parabolic Fourier law is shown to raise the possibility of oscillatory convection in the classic Bénard problem of a Boussinesq fluid heated from below. By comparing the critical Rayleigh numbers for stationary and oscillatory convection, Rc and RS respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value CT≥8/27π2≈0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number P1, which—in contrast to the classical stationary scenario—can impact on oscillatory modes significantly owing to the non-zero frequency of convection. Numerical investigation indicates that the behaviour found analytically for free boundaries applies in a qualitatively similar fashion for fixed boundaries, while the threshold Cattaneo number CT is computed as a function of P1∈[10−2,10+2] for both boundary regimes. PMID:25792960

Humans Can Adopt Optimal Discounting Strategy under Real-Time Constraints

PubMed Central

Schweighofer, N; Shishida, K; Han, C. E; Okamoto, Y; Tanaka, S. C; Yamawaki, S; Doya, K

2006-01-01

Critical to our many daily choices between larger delayed rewards, and smaller more immediate rewards, are the shape and the steepness of the function that discounts rewards with time. Although research in artificial intelligence favors exponential discounting in uncertain environments, studies with humans and animals have consistently shown hyperbolic discounting. We investigated how humans perform in a reward decision task with temporal constraints, in which each choice affects the time remaining for later trials, and in which the delays vary at each trial. We demonstrated that most of our subjects adopted exponential discounting in this experiment. Further, we confirmed analytically that exponential discounting, with a decay rate comparable to that used by our subjects, maximized the total reward gain in our task. Our results suggest that the particular shape and steepness of temporal discounting is determined by the task that the subject is facing, and question the notion of hyperbolic reward discounting as a universal principle. PMID:17096592

Definition of (so MIScalled) ''Complexity'' as UTTER-SIMPLICITY!!! Versus Deviations From it as Complicatedness-Measure

NASA Astrophysics Data System (ADS)

Young, F.; Siegel, Edward Carl-Ludwig

2011-03-01

(so MIScalled) "complexity" with INHERENT BOTH SCALE-Invariance Symmetry-RESTORING, AND 1 / w (1.000..) "pink" Zipf-law Archimedes-HYPERBOLICITY INEVITABILITY power-spectrum power-law decay algebraicity. Their CONNECTION is via simple-calculus SCALE-Invariance Symmetry-RESTORING logarithm-function derivative: (d/ d ω) ln(ω) = 1 / ω , i.e. (d/ d ω) [SCALE-Invariance Symmetry-RESTORING](ω) = 1/ ω . Via Noether-theorem continuous-symmetries relation to conservation-laws: (d/ d ω) [inter-scale 4-current 4-div-ergence} = 0](ω) = 1 / ω . Hence (so MIScalled) "complexity" is information inter-scale conservation, in agreement with Anderson-Mandell [Fractals of Brain/Mind, G. Stamov ed.(1994)] experimental-psychology!!!], i.e. (so MIScalled) "complexity" is UTTER-SIMPLICITY!!! Versus COMPLICATEDNESS either PLUS (Additive) VS. TIMES (Multiplicative) COMPLICATIONS of various system-specifics. COMPLICATEDNESS-MEASURE DEVIATIONS FROM complexity's UTTER-SIMPLICITY!!!: EITHER [SCALE-Invariance Symmetry-BREAKING] MINUS [SCALE-Invariance Symmetry-RESTORING] via power-spectrum power-law algebraicity decays DIFFERENCES: ["red"-Pareto] MINUS ["pink"-Zipf Archimedes-HYPERBOLICITY INEVITABILITY]!!!

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.

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

Quantum quenches in a holographic Kondo model

NASA Astrophysics Data System (ADS)

Erdmenger, Johanna; Flory, Mario; Newrzella, Max-Niklas; Strydom, Migael; Wu, Jackson M. S.

2017-04-01

We study non-equilibrium dynamics and quantum quenches in a recent gauge/gravity duality model for a strongly coupled system interacting with a magnetic impurity with SU( N ) spin. At large N , it is convenient to write the impurity spin as a bilinear in Abrikosov fermions. The model describes an RG flow triggered by the marginally relevant Kondo operator. There is a phase transition at a critical temperature, below which an operator condenses which involves both an electron and an Abrikosov fermion field. This corresponds to a holographic superconductor in AdS2 and models the impurity screening. We quench the Kondo coupling either by a Gaussian pulse or by a hyperbolic tangent, the latter taking the system from the condensed to the uncondensed phase or vice-versa. We study the time dependence of the condensate induced by this quench. The timescale for equilibration is generically given by the leading quasinormal mode of the dual gravity model. This mode also governs the formation of the screening cloud, which is obtained as the decrease of impurity degrees of freedom with time. In the condensed phase, the leading quasinormal mode is imaginary and the relaxation of the condensate is over-damped. For quenches whose final state is close to the critical point of the large N phase transition, we study the critical slowing down and obtain the combination of critical exponents zν = 1. When the final state is exactly at the phase transition, we find that the exponential ringing of the quasinormal modes is replaced by a power-law behaviour of the form ˜ t - a sin( b log t). This indicates the emergence of a discrete scale invariance.

An Improved Perturb and Observe Algorithm for Photovoltaic Motion Carriers

NASA Astrophysics Data System (ADS)

Peng, Lele; Xu, Wei; Li, Liming; Zheng, Shubin

2018-03-01

An improved perturbation and observation algorithm for photovoltaic motion carriers is proposed in this paper. The model of the proposed algorithm is given by using Lambert W function and tangent error method. Moreover, by using matlab and experiment of photovoltaic system, the tracking performance of the proposed algorithm is tested. And the results demonstrate that the improved algorithm has fast tracking speed and high efficiency. Furthermore, the energy conversion efficiency by the improved method has increased by nearly 8.2%.

More Toda-like (0,2) mirrors

NASA Astrophysics Data System (ADS)

Chen, Zhuo; Guo, Jirui; Sharpe, Eric; Wu, Ruoxu

2017-08-01

In this paper, we extend our previous work to construct (0 , 2) Toda-like mirrors to A/2-twisted theories on more general spaces, as part of a program of understanding (0,2) mirror symmetry. Specifically, we propose (0 , 2) mirrors to GLSMs on toric del Pezzo surfaces and Hirzebruch surfaces with deformations of the tangent bundle. We check the results by comparing correlation functions, global symmetries, as well as geometric blowdowns with the corresponding (0 , 2) Toda-like mirrors. We also briefly discuss Grassmannian manifolds.

Local electron tomography using angular variations of surface tangents: Stomo version 2

NASA Astrophysics Data System (ADS)

Petersen, T. C.; Ringer, S. P.

2012-03-01

In a recent publication, we investigated the prospect of measuring the outer three-dimensional (3D) shapes of nano-scale atom probe specimens from tilt-series of images collected in the transmission electron microscope. For this purpose alone, an algorithm and simplified reconstruction theory were developed to circumvent issues that arise in commercial "back-projection" computations in this context. In our approach, we give up the difficult task of computing the complete 3D continuum structure and instead seek only the 3D morphology of internal and external scattering interfaces. These interfaces can be described as embedded 2D surfaces projected onto each image in a tilt series. Curves and other features in the images are interpreted as inscribed sets of tangent lines, which intersect the scattering interfaces at unknown locations along the direction of the incident electron beam. Smooth angular variations of the tangent line abscissa are used to compute the surface tangent intersections and hence the 3D morphology as a "point cloud". We have published the explicit details of our alternative algorithm along with the source code entitled "stomo_version_1". For this work, we have further modified the code to efficiently handle rectangular image sets, perform much faster tangent-line "edge detection" and smoother tilt-axis image alignment using simple bi-linear interpolation. We have also adapted the algorithm to detect tangent lines as "ridges", based upon 2nd order partial derivatives of the image intensity; the magnitude and orientation of which is described by a Hessian matrix. Ridges are more appropriate descriptors for tangent-line curves in phase contrast images outlined by Fresnel fringes or absorption contrast data from fine-scale objects. Improved accuracy, efficiency and speed for "stomo_version_2" is demonstrated in this paper using both high resolution electron tomography data of a nano-sized atom probe tip and simulated absorption-contrast images. Program summaryProgram title: STOMO version 2 Catalogue identifier: AEFS_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFS_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2854 No. of bytes in distributed program, including test data, etc.: 23 559 Distribution format: tar.gz Programming language: C/C++ Computer: PC Operating system: Windows XP RAM: Scales as the product of experimental image dimensions multiplied by the number of points chosen by the user in polynomial fitting. Typical runs require between 50 Mb and 100 Mb of RAM. Supplementary material: Sample output files, for the test run provided, are available. Classification: 7.4, 14 Catalogue identifier of previous version: AEFS_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 676 Does the new version supersede the previous version?: Yes Nature of problem: A local electron tomography algorithm of specimens for which conventional back projection may fail and or data for which there is a limited angular range (which would otherwise cause significant 'missing-wedge' artefacts). The algorithm does not solve the tomography back projection problem but rather locally reconstructs the 3D morphology of surfaces defined by varied scattering densities. Solution method: Local reconstruction is effected using image-analysis edge and ridge detection computations on experimental tilt series to measure smooth angular variations of surface tangent-line intersections, which generate point clouds decorating the embedded and or external scattering surfaces of a specimen. Reasons for new version: The new version was coded to cater for rectangular images in experimental tilt-series, ensure smoother image rotations, provide ridge detection (suitable for sensing phase-contrast Fresnel fringes and other fine-scale structures), faster/larger kernel edge detection and also greatly reduce RAM usage. Specimen surface normals are also explicitly computed from tangent-line and edge intersections, providing new information for potential use in point cloud rendering. Hysteresis thresholding implemented in the version 1 edge-detection algorithm provided only sparse edge-linking. Version 2 now implements edge tracking using recursion to fully link the edges during hysteresis thresholding. Furthermore in version 1 the minimum number of fitted polynomial points (specified in the input file) was not correctly imposed, which has been fixed for version 2. Most of these changes increase the accuracy of 3d morphology surface-tomography reconstructions by facilitating the use of more/finer tilt angles and experimental images of increased spatial-resolution. The ridge detection was incorporated to specifically improve the reconstruction of internal specimen morphology. Summary of revisions: Included Hessian() function to compute 2nd order spatial derivatives of image intensities (operates in the same fashion as the previous and existing Sobel() function). Changed convolve_Gaussian() function to alternatively use successive 1D convolutions (rather than cumbersome 2D summations implemented in version 1), resulting in a large increase in computational speed without any loss in accuracy. The convolution kernel size was hence widened to three times the full width half maximum of the Gaussian filter to improve scale-space selection accuracy. A ridge detection option was included to compute edge maps sensitive to ridges, rather than edges, using elements from a Hessian matrix; the eigenvalues of which were used to define ridge direction for Canny-type hysteresis thresholding. Function edge_detect_Canny() was also altered to pass the gradient-direction maps (from either Hessian or Sobel based operators) in and out of scope for computation of surface normals; thereby enabling the output of both point-cloud and corresponding unstructured vector-field surface descriptors. Function rotate_imgs() was changed to incorporate basic bi-linear interpolation for improved tilt-axis alignment of the entire tilt series in exp_data.dat. Smoother and more accurate edge maps are thereby produced. Algorithm convert_point_cloud_to_tomogram() was created to output the tomogram 3d_imgs.dat in a more memory efficient manner. The function shell_sort(), adapted from numerical recipes in C, was also coded for this purpose. The new function compute_xyz() was coded to calculate point-clouds and tomogram surface normals using information from single tilt images, as opposed to the entire stack. This function is hence used iteratively throughout the reconstruction as each tilt image is analysed in succession. The new function reconstruct_local() is the heart of stomo_version_2.cpp. the main() source code in stomo_version_1.cpp has been rewritten here to process experimental images and edge maps one at a time, using a buffered 3d array of dimensions dictated solely by the number of tilt images required for the local SVD fit of the angular variations. These changes (along with similar iterative file writing) have been made to vastly reduce memory usage and hence allow higher spatial and angular resolution data sets to be analysed without recourse to high performance computing resources. The input file has been simplified by removing the 'slices' and 'channels' settings (used in version 1 for crude image binning), which are now equal to the respective numbers of image rows and columns. Every summation over image rows and columns has been checked to enable the analysis of rectangular images without error. For images of specimens with high aspect-ratios, such as narrow tips, these fixes allow significant reductions in computation time and memory usage. Some arrays in the source code were not appropriately zeroed in version 1, causing reconstruction artefacts in some cases. These problems have now been fixed. Fixed an if-statement to correctly impose the minimum number of fitted polynomial points, thereby reducing noise in the reconstructed data. Implemented proper edge linking in the hysteresis thresholding code for Canny edge detection. Restrictions: The input experimental tilt-series of images must be registered with respect to a common single tilt axis with known orientation and position. Running time: For high quality reconstruction, 2-5 min.

Lyapounov Functions of Closed Cone Fields: From Conley Theory to Time Functions

NASA Astrophysics Data System (ADS)

Bernard, Patrick; Suhr, Stefan

2018-03-01

We propose a theory "à la Conley" for cone fields using a notion of relaxed orbits based on cone enlargements, in the spirit of space time geometry. We work in the setting of closed (or equivalently semi-continuous) cone fields with singularities. This setting contains (for questions which are parametrization independent such as the existence of Lyapounov functions) the case of continuous vector-fields on manifolds, of differential inclusions, of Lorentzian metrics, and of continuous cone fields. We generalize to this setting the equivalence between stable causality and the existence of temporal functions. We also generalize the equivalence between global hyperbolicity and the existence of a steep temporal function.

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…

Solving nonlinear evolution equation system using two different methods

NASA Astrophysics Data System (ADS)

Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.

2015-12-01

This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

Tensor tomography on Cartan–Hadamard manifolds

NASA Astrophysics Data System (ADS)

Lehtonen, Jere; Railo, Jesse; Salo, Mikko

2018-04-01

We study the geodesic x-ray transform on Cartan–Hadamard manifolds, generalizing the x-ray transforms on Euclidean and hyperbolic spaces that arise in medical and seismic imaging. We prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016 arXiv:1612.04800) to dimensions n ≥slant 3 and to the case of tensor fields of any order.

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.

Observations of Al, Fe and Ca(+) in Mercury's Exosphere

NASA Technical Reports Server (NTRS)

Bida, Thomas A.; Killen, Rosemary M.

2011-01-01

We report 5-(sigma) tangent column detections of Al and Fe, and strict 3-(sigma) tangent column upper limits for Ca(+) in Mercury's exosphere obtained using the HIRES spectrometer on the Keck I telescope. These are the first direct detections of Al and Fe in Mercury's exosphere. Our Ca(-) observation is consistent with that reported by The Mercury Atmospheric and Surface Composition Spectrometer (MASCS) on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft.

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

Dielectric characteristics of Mn-doped LaTiO3+δ ceramics

NASA Astrophysics Data System (ADS)

Chen, Yan; Cui, Yimin

A series of ceramic composites of Mn-doped La1- x MnxTiO3+ δ and LaMnxTi1- x O3+ δ (x = 0.1, 0.2) were synthesized by conventional solid-state reaction method. The low-frequency complex dielectric properties of the composites were investigated as functions of temperature (77 K <= T <= 360 K) and frequency (100 Hz <= f <= 1 MHz), respectively. The dielectric constant of A-site doped samples is higher than that of B-site doped samples. The loss tangent of low doped samples is much less than that of high doped samples. The A-site doped composites exhibit intrinsic dielectric response with a dielectric constant of 40 in the temperature below 250 K. Interestingly, the dielectric constants of B-site doped ceramics increase slightly in the temperature range from 77 to 360 K. And it is clearly observed that extraordinarily high dielectric loss tangent ( 6) appear at low frequency (100 Hz) in LaMn0.2Ti0.8O3+ δ , which is 8 times larger than that of LaMn0.1Ti0.9O3+ δ , which indicates that the doped content can affect the intrinsic dielectric characteristics significantly.

Human pose tracking from monocular video by traversing an image motion mapped body pose manifold

NASA Astrophysics Data System (ADS)

Basu, Saurav; Poulin, Joshua; Acton, Scott T.

2010-01-01

Tracking human pose from monocular video sequences is a challenging problem due to the large number of independent parameters affecting image appearance and nonlinear relationships between generating parameters and the resultant images. Unlike the current practice of fitting interpolation functions to point correspondences between underlying pose parameters and image appearance, we exploit the relationship between pose parameters and image motion flow vectors in a physically meaningful way. Change in image appearance due to pose change is realized as navigating a low dimensional submanifold of the infinite dimensional Lie group of diffeomorphisms of the two dimensional sphere S2. For small changes in pose, image motion flow vectors lie on the tangent space of the submanifold. Any observed image motion flow vector field is decomposed into the basis motion vector flow fields on the tangent space and combination weights are used to update corresponding pose changes in the different dimensions of the pose parameter space. Image motion flow vectors are largely invariant to style changes in experiments with synthetic and real data where the subjects exhibit variation in appearance and clothing. The experiments demonstrate the robustness of our method (within +/-4° of ground truth) to style variance.

Off Axis Growth of Strontium Titanate Films with High Dielectric Constant Tuning and Low Loss

NASA Astrophysics Data System (ADS)

Kampangkeaw, Satreerat

2002-03-01

Using off-axis pulsed laser deposition, we have grown strontium titanate (STO) films on neodymium gallate (NGO) and lanthanum aluminate (LAO) substrates. We measured the film dielectric constant and loss tangent as a function of temperature in the 10kHz to 1 MHz frequency range. We found that the loss is less than 0.01 We also obtained a figure of merit from the relative variation of the dielectric constant divided by the loss tangent. The obtained figured of merit at 35K and 1MHz is about 1000 comparable to bulk values. The dielectric constant of these films can be changed by a factor of 4-8 in the presence of a DC electric field up to 5V/μm. The films show significant variations of dielectric properties grown on different substrates at different locations respect to the axis of the plume. The STO films on LAO having high dielectric constant and dielectric tuning were grown in region near the center of the plume. On the other hand, STO on NGO shows this effect only on the films grown far from the plume axis.

Can manipulation of orthokeratology lens parameters modify peripheral refraction?

PubMed

Kang, Pauline; Gifford, Paul; Swarbrick, Helen

2013-11-01

To investigate changes in peripheral refraction, corneal topography, and aberrations induced by changes in orthokeratology (OK) lens parameters in myopes. Subjects were fitted with standard OK lenses that were worn overnight for 2 weeks. Peripheral refraction, corneal topography, and corneal surface aberrations were measured at baseline and after 14 nights of OK lens wear. Subsequent to a 2-week washout period, subjects were refitted with another set of lenses where one eye was randomly assigned to wear an OK lens with a smaller optic zone diameter (OZD) and the other eye with a steeper peripheral tangent. Measurements were taken again at a second baseline and after 14 days of overnight wear of the second OK lens set. Standard OK lenses with a 6-mm OZD and 1/4 peripheral tangent caused significant changes in both peripheral refraction and corneal topography. Significant hyperopic shift occurred in the central visual field (VF) while a myopic shift was found at 35 degrees in the nasal VF. OK induced significant reductions in corneal power at all positions along the horizontal corneal chord except at 2.4 mm nasal where there was no significant change and at 2.8 mm nasal where there was an increase in corneal refractive power. A positive shift in spherical aberration was induced for all investigated lens designs except for the 1/2 tangent design when calculated over a 4-mm pupil. Reducing OZD and steepening the peripheral tangent did not cause significant changes in peripheral refraction or corneal topography profiles across the horizontal meridian. OK lenses caused significant changes in peripheral refraction, corneal topography, and corneal surface aberrations. Modifying OZD and peripheral tangent made no significant difference to the peripheral refraction or corneal topography profile. Attempting to customize refraction and topography changes through manipulation of OK lens parameters appears to be a difficult task.

Self-stimulation in the rat: quantitative characteristics of the reward pathway.

PubMed

Gallistel, C R

1978-12-01

Quantitative characteristics of the neural pathway that carries the reinforcing signal in electrical self-stimulation of the brain were established by finding which combinations of stimulation parameters give the same performance in a runway. The reward for each run was a train of evenly spaced monophasic cathodal pulses from a monopolar electrode. With train duration and pulse frequency held constant, the required current was a hyperbolic function of pulse duration, with chronaxie c approximately 1.5 msec. With pulse duration held constant, the required strength of the train (the charge delivered per second) was a hyperbolic function of train duration, with chronaxie C approximately 500 msec. To a first approximation, the values of c and C were independent of the choice either of train duration and pulse frequency or of pulse duration, respectively. Hence, the current intensity required by any choice of train duration, pulse frequency, and pulse duration dependent on only two basic parameters, c and C, and one quantity, Qi, the required impulse charge. These may reflect, respectively, current integration by directly excited neurons; temporal integration of neural activity by synaptic processes in a neural network; and the peak of the impulse response of the network, assuming that the network has linear dynamics and that the reward depends on the peak of the output of the network.

Measuring Impatience in Intertemporal Choice.

PubMed

Cruz Rambaud, Salvador; Muñoz Torrecillas, María José

2016-01-01

In general terms, decreasing impatience means decreasing discount rates. This property has been usually referred to as hyperbolic discounting, although there are other discount functions which also exhibit decreasing discount rates. This paper focuses on the measurement of the impatience associated with a discount function with the aim of establishing a methodology to compare this characteristic for two different discount functions. In this way, first we define the patience associated with a discount function in an interval as its corresponding discount factor and consequently we deduce that the impatience at a given moment is the corresponding instantaneous discount rate. Second we compare the degree of impatience of discount functions belonging to the same or different families, by considering the cases in which the functions do or do not intersect.

Electrical properties of lunar soil dependence on frequency, temperature and moisture.

NASA Technical Reports Server (NTRS)

Strangway, D. W.; Chapman, W. B.; Olhoeft, G. R.; Carnes, J.

1972-01-01

It was found that the dielectric constant and loss tangent of lunar soil samples in the range from 100 Hz to 1 MHz are not strongly dependent on frequency provided care is taken to avoid exposure of the sample to atmospheric air containing moisture. The loss tangent value obtained is lower by nearly a factor 10 than any previously reported value. The measurement data imply that the surface layers of the moon are probably extremely transparent to radiowaves.

Reduction of Decoherence in the Flux Qubit

DTIC Science & Technology

2014-12-08

Letters, (04 2012): 142601. doi: 10.1063/1.3700964 Nicolas Vogt, Jared Cole, Michael Marthaler, Gerd Schön. Influence of two-level fluctuators on adiabatic...a loss tangent tan δi = 1/Qi = 2.2-3×10−5 in the 4-8 GHz band. Crystalline dielectrics, such as silicon can exhibit low intrinsic loss and have been...the observed loss to the capacitive element, our measurements place and upper bound on the loss tangent of the silicon dielectric layer of tan δi = 5

Perfect gas effects in compressible rapid distortion theory

NASA Technical Reports Server (NTRS)

Kerschen, E. J.; Myers, M. R.

1987-01-01

The governing equations presented for small amplitude unsteady disturbances imposed on steady, compressible mean flows that are two-dimensional and nearly uniform have their basis in the perfect gas equations of state, and therefore generalize previous results based on tangent gas theory. While these equations are more complex, this complexity is required for adequate treatment of high frequency disturbances, especially when the base flow Mach number is large; under such circumstances, the simplifying assumptions of tangent gas theory are not applicable.

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

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

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

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.

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...

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.

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

Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

NASA Astrophysics Data System (ADS)

Nguyen, Van-Dung; Wu, Ling; Noels, Ludovic

2017-03-01

This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems. An efficient procedure is developed to enforce the multi-point linear constraints arising from the microscopic boundary condition either by the direct constraint elimination or by the Lagrange multiplier elimination methods. The macroscopic tangent operators are computed in an efficient way from a multiple right hand sides linear system whose left hand side matrix is the stiffness matrix of the microscopic linearized system at the converged solution. The number of vectors at the right hand side is equal to the number of the macroscopic kinematic variables used to formulate the microscopic boundary condition. As the resolution of the microscopic linearized system often follows a direct factorization procedure, the computation of the macroscopic tangent operators is then performed using this factorized matrix at a reduced computational time.

Linear strain sensor made of multi-walled carbon nanotube/epoxy composite

NASA Astrophysics Data System (ADS)

Tong, Shuying; Yuan, Weifeng; Liu, Haidong; Alamusi; Hu, Ning; Zhao, Chaoyang; Zhao, Yangzhou

2017-11-01

In this study, a fabrication process was developed to make the multi-walled carbon nanotubes/epoxy (MWCNT/EP) composite films. The electrical-strain behaviour of the films in direct and alternating current circuits were both tested. It is found that the direct current resistance and the dielectric loss tangent of the MWCNT/EP composite films are dependent on the strain and the weight fraction of the carbon nanotubes. In an alternating current circuit, the test frequency affects the impedance and the phase angle of the composite film, but it has nothing to do with the change ratio of the dielectric loss tangent of the film in tension. This phenomenon can be interpreted by a proposed equivalent circuit model. Experiment results show that the change rate of the dielectric loss tangent of the MWCNT/EP sensor is linearly proportional to the strain. The findings obtained in the present study provide a promising method to develop ultrasensitive linear strain gauges.

Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

PubMed

Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-02-01

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.

Comparison of shear wave velocity measurements assessed with two different ultrasound systems in an ex-vivo tendon strain phantom.

PubMed

Rosskopf, Andrea B; Bachmann, Elias; Snedeker, Jess G; Pfirrmann, Christian W A; Buck, Florian M

2016-11-01

The purpose of this study is to compare the reliability of SW velocity measurements of two different ultrasound systems and their correlation with the tangent traction modulus in a non-static tendon strain model. A bovine tendon was fixed in a custom-made stretching device. Force was applied increasing from 0 up to 18 Newton. During each strain state the tangent traction modulus was determined by the stretcher device, and SW velocity (m/s) measurements using a Siemens S3000 and a Supersonic Aixplorer US machine were done for shear modulus (kPa) calculation. A strong significant positive correlation was found between SW velocity assessed by the two ultrasound systems and the tangent traction modulus (r = 0.827-0.954, p < 0.001), yet all SW velocity-based calculations underestimated the reference tissue tangent modulus. Mean difference of SW velocities with the S3000 was 0.44 ± 0.3 m/s (p = 0.002) and with the Aixplorer 0.25 ± 0.3 m/s (p = 0.034). Mean difference of SW velocity between the two US-systems was 0.37 ± 0.3 m/s (p = 0.012). In conclusion, SW velocities are highly dependent on mechanical forces in the tendon tissue, but for controlled mechanical loads appear to yield reproducible and comparable measurements using different US systems.

Reliability analysis for radiographic measures of lumbar lordosis in adult scoliosis: a case–control study comparing 6 methods

PubMed Central

Hong, Jae Young; Modi, Hitesh N.; Hur, Chang Yong; Song, Hae Ryong; Park, Jong Hoon

2010-01-01

Several methods are used to measure lumbar lordosis. In adult scoliosis patients, the measurement is difficult due to degenerative changes in the vertebral endplate as well as the coronal and sagittal deformity. We did the observational study with three examiners to determine the reliability of six methods for measuring the global lumbar lordosis in adult scoliosis patients. Ninety lateral lumbar radiographs were collected for the study. The radiographs were divided into normal (Cobb < 10°), low-grade (Cobb 10°–19°), high-grade (Cobb  ≥ 20°) group to determine the reliability of Cobb L1–S1, Cobb L1–L5, centroid, posterior tangent L1–S1, posterior tangent L1–L5 and TRALL method in adult scoliosis. The 90 lateral radiographs were measured twice by each of the three examiners using the six measurement methods. The data was analyzed to determine the inter- and intra-observer reliability. In general, for the six radiographic methods, the inter- and intra-class correlation coefficients (ICCs) were all ≥0.82. A comparison of the ICCs and 95% CI for the inter- and intra-observer reliability between the groups with varying degrees of scoliosis showed that, the reliability of the lordosis measurement decreased with increasing severity of scoliosis. In Cobb L1–S1, centroid and posterior tangent L1–S1 methods, the ICCs were relatively lower in the high-grade scoliosis group (≥0.60). And, the mean absolute difference (MAD) in these methods was high in the high-grade scoliosis group (≤7.17°). However, in the Cobb L1–L5 and posterior tangent L1–L5 method, the ICCs were ≥0.86 in all groups. And, in the TRALL method, the ICCs were ≥0.76 in all groups. In addition, in the Cobb L1–L5 and posterior tangent L1–L5 method, the MAD was ≤3.63°. And, in the TRALL method, the MAD was ≤3.84° in all groups. We concluded that the Cobb L1–L5 and the posterior tangent L1–L5 methods are reliable methods for measuring the global lumbar lordosis in adult scoliosis. And the TRALL method is more reliable method than other methods which include the L5–S1 joint in lordosis measurement. PMID:20437183

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.

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

Measuring Impatience in Intertemporal Choice

PubMed Central

2016-01-01

In general terms, decreasing impatience means decreasing discount rates. This property has been usually referred to as hyperbolic discounting, although there are other discount functions which also exhibit decreasing discount rates. This paper focuses on the measurement of the impatience associated with a discount function with the aim of establishing a methodology to compare this characteristic for two different discount functions. In this way, first we define the patience associated with a discount function in an interval as its corresponding discount factor and consequently we deduce that the impatience at a given moment is the corresponding instantaneous discount rate. Second we compare the degree of impatience of discount functions belonging to the same or different families, by considering the cases in which the functions do or do not intersect. PMID:26890895

High-frequency viscoelastic shear properties of vocal fold tissues: implications for vocal fold tissue engineering.

PubMed

Teller, Sean S; Farran, Alexandra J E; Xiao, Longxi; Jiao, Tong; Duncan, Randall L; Clifton, Rodney J; Jia, Xinqiao

2012-10-01

The biomechanical function of the vocal folds (VFs) depends on their viscoelastic properties. Many conditions can lead to VF scarring that compromises voice function and quality. To identify candidate replacement materials, the structure, composition, and mechanical properties of native tissues need to be understood at phonation frequencies. Previously, the authors developed the torsional wave experiment (TWE), a stress-wave-based experiment to determine the linear viscoelastic shear properties of small, soft samples. Here, the viscoelastic properties of porcine and human VFs were measured over a frequency range of 10-200 Hz. The TWE utilizes resonance phenomena to determine viscoelastic properties; therefore, the specimen test frequency is determined by the sample size and material properties. Viscoelastic moduli are reported at resonance frequencies. Structure and composition of the tissues were determined by histology and immunochemistry. Porcine data from the TWE are separated into two groups: a young group, consisting of fetal and newborn pigs, and an adult group, consisting of 6-9-month olds and 2+-year olds. Adult tissues had an average storage modulus of 2309±1394 Pa and a loss tangent of 0.38±0.10 at frequencies of 36-200 Hz. The VFs of young pigs were significantly more compliant, with a storage modulus of 394±142 Pa and a loss tangent of 0.40±0.14 between 14 and 30 Hz. No gender dependence was observed. Histological staining showed that adult porcine tissues had a more organized, layered structure than the fetal tissues, with a thicker epithelium and a more structured lamina propria. Elastin fibers in fetal VF tissues were immature compared to those in adult tissues. Together, these structural changes in the tissues most likely contributed to the change in viscoelastic properties. Adult human VF tissues, recovered postmortem from adult patients with a history of smoking or disease, had an average storage modulus of 756±439 Pa and a loss tangent of 0.42±0.10. Contrary to the results of some other investigators, no significant frequency dependence was observed. This lack of observable frequency dependence may be due to the modest frequency range of the experiments and the wide range of stiffnesses observed within nominally similar sample types.

High-Frequency Viscoelastic Shear Properties of Vocal Fold Tissues: Implications for Vocal Fold Tissue Engineering

PubMed Central

Teller, Sean S.; Farran, Alexandra J.E.; Xiao, Longxi; Jiao, Tong; Duncan, Randall L.

2012-01-01

The biomechanical function of the vocal folds (VFs) depends on their viscoelastic properties. Many conditions can lead to VF scarring that compromises voice function and quality. To identify candidate replacement materials, the structure, composition, and mechanical properties of native tissues need to be understood at phonation frequencies. Previously, the authors developed the torsional wave experiment (TWE), a stress-wave-based experiment to determine the linear viscoelastic shear properties of small, soft samples. Here, the viscoelastic properties of porcine and human VFs were measured over a frequency range of 10–200 Hz. The TWE utilizes resonance phenomena to determine viscoelastic properties; therefore, the specimen test frequency is determined by the sample size and material properties. Viscoelastic moduli are reported at resonance frequencies. Structure and composition of the tissues were determined by histology and immunochemistry. Porcine data from the TWE are separated into two groups: a young group, consisting of fetal and newborn pigs, and an adult group, consisting of 6–9-month olds and 2+-year olds. Adult tissues had an average storage modulus of 2309±1394 Pa and a loss tangent of 0.38±0.10 at frequencies of 36–200 Hz. The VFs of young pigs were significantly more compliant, with a storage modulus of 394±142 Pa and a loss tangent of 0.40±0.14 between 14 and 30 Hz. No gender dependence was observed. Histological staining showed that adult porcine tissues had a more organized, layered structure than the fetal tissues, with a thicker epithelium and a more structured lamina propria. Elastin fibers in fetal VF tissues were immature compared to those in adult tissues. Together, these structural changes in the tissues most likely contributed to the change in viscoelastic properties. Adult human VF tissues, recovered postmortem from adult patients with a history of smoking or disease, had an average storage modulus of 756±439 Pa and a loss tangent of 0.42±0.10. Contrary to the results of some other investigators, no significant frequency dependence was observed. This lack of observable frequency dependence may be due to the modest frequency range of the experiments and the wide range of stiffnesses observed within nominally similar sample types. PMID:22741523

Full cycle trigonometric function on Intel Quartus II Verilog

NASA Astrophysics Data System (ADS)

Mustapha, Muhazam; Zulkarnain, Nur Antasha

2018-02-01

This paper discusses about an improvement of a previous research on hardware based trigonometric calculations. Tangent function will also be implemented to get a complete set. The functions have been simulated using Quartus II where the result will be compared to the previous work. The number of bits has also been extended for each trigonometric function. The design is based on RTL due to its resource efficient nature. At earlier stage, a technology independent test bench simulation was conducted on ModelSim due to its convenience in capturing simulation data so that accuracy information can be obtained. On second stage, Intel/Altera Quartus II will be used to simulate on technology dependent platform, particularly on the one belonging to Intel/Altera itself. Real data on no. logic elements used and propagation delay have also been obtained.

A computational model of selection by consequences.

PubMed

McDowell, J J

2004-05-01

Darwinian selection by consequences was instantiated in a computational model that consisted of a repertoire of behaviors undergoing selection, reproduction, and mutation over many generations. The model in effect created a digital organism that emitted behavior continuously. The behavior of this digital organism was studied in three series of computational experiments that arranged reinforcement according to random-interval (RI) schedules. The quantitative features of the model were varied over wide ranges in these experiments, and many of the qualitative features of the model also were varied. The digital organism consistently showed a hyperbolic relation between response and reinforcement rates, and this hyperbolic description of the data was consistently better than the description provided by other, similar, function forms. In addition, the parameters of the hyperbola varied systematically with the quantitative, and some of the qualitative, properties of the model in ways that were consistent with findings from biological organisms. These results suggest that the material events responsible for an organism's responding on RI schedules are computationally equivalent to Darwinian selection by consequences. They also suggest that the computational model developed here is worth pursuing further as a possible dynamic account of behavior.

Compound Poisson Law for Hitting Times to Periodic Orbits in Two-Dimensional Hyperbolic Systems

NASA Astrophysics Data System (ADS)

Carney, Meagan; Nicol, Matthew; Zhang, Hong-Kun

2017-11-01

We show that a compound Poisson distribution holds for scaled exceedances of observables φ uniquely maximized at a periodic point ζ in a variety of two-dimensional hyperbolic dynamical systems with singularities (M,T,μ ), including the billiard maps of Sinai dispersing billiards in both the finite and infinite horizon case. The observable we consider is of form φ (z)=-ln d(z,ζ ) where d is a metric defined in terms of the stable and unstable foliation. The compound Poisson process we obtain is a Pólya-Aeppli distibution of index θ . We calculate θ in terms of the derivative of the map T. Furthermore if we define M_n=\\max {φ ,\\ldots ,φ circ T^n} and u_n (τ ) by \\lim _{n→ ∞} nμ (φ >u_n (τ ) )=τ the maximal process satisfies an extreme value law of form μ (M_n ≤ u_n)=e^{-θ τ }. These results generalize to a broader class of functions maximized at ζ , though the formulas regarding the parameters in the distribution need to be modified.

SCRIBE (Stratospheric Cryogenic Interferometer Baloon Experiment) Data Survey and Validation.

DTIC Science & Technology

1987-02-16

Altitude of 27000 to 28000 m, SPIE Publ. 366, p165-172, AD-A133 472. 5 ferometer 3 𔃾 𔃿 and to point out flaws in the system which were subsequently...Tangent Height - 16.9 km * 6 j4 II’ a. WA#EUM k CM p Altitude = 31.3 km ’ / Zenith Angle = 93.7 deg.- ouTangent Height = 16.9 km I- + p ISO . .. .. 0...Height = 30.47 106 250 200 ISO ........................., .................................. ’ 65S 660 665 670 675 WAVENUMBER (CM-1) Figure 31. Comparison

Performance evaluation of MLP and RBF feed forward neural network for the recognition of off-line handwritten characters

NASA Astrophysics Data System (ADS)

Rishi, Rahul; Choudhary, Amit; Singh, Ravinder; Dhaka, Vijaypal Singh; Ahlawat, Savita; Rao, Mukta

2010-02-01

In this paper we propose a system for classification problem of handwritten text. The system is composed of preprocessing module, supervised learning module and recognition module on a very broad level. The preprocessing module digitizes the documents and extracts features (tangent values) for each character. The radial basis function network is used in the learning and recognition modules. The objective is to analyze and improve the performance of Multi Layer Perceptron (MLP) using RBF transfer functions over Logarithmic Sigmoid Function. The results of 35 experiments indicate that the Feed Forward MLP performs accurately and exhaustively with RBF. With the change in weight update mechanism and feature-drawn preprocessing module, the proposed system is competent with good recognition show.

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

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.

Navigability of Random Geometric Graphs in the Universe and Other Spacetimes.

PubMed

Cunningham, William; Zuev, Konstantin; Krioukov, Dmitri

2017-08-18

Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter. We find these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.

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.

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

The probability density function (PDF) of Lagrangian Turbulence

NASA Astrophysics Data System (ADS)

Birnir, B.

2012-12-01

The statistical theory of Lagrangian turbulence is derived from the stochastic Navier-Stokes equation. Assuming that the noise in fully-developed turbulence is a generic noise determined by the general theorems in probability, the central limit theorem and the large deviation principle, we are able to formulate and solve the Kolmogorov-Hopf equation for the invariant measure of the stochastic Navier-Stokes equations. The intermittency corrections to the scaling exponents of the structure functions require a multiplicative (multipling the fluid velocity) noise in the stochastic Navier-Stokes equation. We let this multiplicative noise, in the equation, consists of a simple (Poisson) jump process and then show how the Feynmann-Kac formula produces the log-Poissonian processes, found by She and Leveque, Waymire and Dubrulle. These log-Poissonian processes give the intermittency corrections that agree with modern direct Navier-Stokes simulations (DNS) and experiments. The probability density function (PDF) plays a key role when direct Navier-Stokes simulations or experimental results are compared to theory. The statistical theory of turbulence is determined, including the scaling of the structure functions of turbulence, by the invariant measure of the Navier-Stokes equation and the PDFs for the various statistics (one-point, two-point, N-point) can be obtained by taking the trace of the corresponding invariant measures. Hopf derived in 1952 a functional equation for the characteristic function (Fourier transform) of the invariant measure. In distinction to the nonlinear Navier-Stokes equation, this is a linear functional differential equation. The PDFs obtained from the invariant measures for the velocity differences (two-point statistics) are shown to be the four parameter generalized hyperbolic distributions, found by Barndorff-Nilsen. These PDF have heavy tails and a convex peak at the origin. A suitable projection of the Kolmogorov-Hopf equations is the differential equation determining the generalized hyperbolic distributions. Then we compare these PDFs with DNS results and experimental data.

[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.

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.