Exponential Correlation of IQ and the Wealth of Nations
ERIC Educational Resources Information Center
Dickerson, Richard E.
2006-01-01
Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…
Method for numerical simulation of two-term exponentially correlated colored noise
Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.
2006-04-15
A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications.
Wave Propagation by Way of Exponential B-Spline Galerkin Method
NASA Astrophysics Data System (ADS)
Zorsahin Gorgulu, M.; Dag, I.; Irk, D.
2016-10-01
In this paper, the exponential B-spline Galerkin method is set up for getting the numerical solution of the Burgers’ equation. Two numerical examples related to shock wave propagation and travelling wave are studied to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.
Exponential wave-packet spreading via self-interaction time modulation
NASA Astrophysics Data System (ADS)
Zhao, Wen-Lei; Gong, Jiangbin; Wang, Wen-Ge; Casati, Giulio; Liu, Jie; Fu, Li-Bin
2016-11-01
The time-periodic modulation of the self-interaction of a Bose-Einstein condensate or a nonlinear optics system has been recognized as an exciting tool to explore interesting physics that was previously unavailable. This tool is exploited here to examine the exotic dynamics of a nonlinear system described by the Gross-Pitaevskii equation. We observe three remarkable and closely related dynamical phenomena, exponentially localized profile of wave functions in momentum space with localization length exponentially increasing in time, exponential wave-packet spreading, and exponential sensitivity to initial conditions. A hybrid quantum-classical theory is developed to partly explain these findings. Time-periodic self-interaction modulation is seen to be a robust method to achieve superfast spreading and induce genuine chaos even in the absence of any external potential.
H2SOLV: Fortran solver for diatomic molecules in explicitly correlated exponential basis
NASA Astrophysics Data System (ADS)
Pachucki, K.; Zientkiewicz, M.; Yerokhin, V. A.
2016-11-01
We present the Fortran package H2SOLV for an efficient computation of the nonrelativistic energy levels and the wave functions of diatomic two-electron molecules within the Born-Oppenheimer approximation. The wave function is obtained as a linear combination of the explicitly correlated exponential (Kołos-Wolniewicz) functions. The computations of H2SOLV are performed within the arbitrary-precision arithmetics, where the number of working digits can be adjusted by the user. The key part of H2SOLV is the implementation of the algorithm of an efficient computation of the two-center two-electron integrals for arbitrary values of internuclear distances developed by one of us (Pachucki, 2013). This have been one of the long-standing problems of quantum chemistry. The code is parallelized, suitable for large-scale computations limited only by the computer resources available and can produce highly accurate results. As an example, we report several benchmark results obtained with H2SOLV, including the energy value accurate to 18 decimal digits.
On the interaction of deep water waves and exponential shear currents
NASA Astrophysics Data System (ADS)
Cheng, Jun; Cang, Jie; Liao, Shi-Jun
2009-05-01
A train of periodic deep-water waves propagating on a steady shear current with a vertical distribution of vorticity is investigated by an analytic method, namely the homotopy analysis method (HAM). The magnitude of the vorticity varies exponentially with the magnitude of the stream function, while remaining constant on a particular streamline. The so-called Dubreil-Jacotin transformation is used to transfer the original exponentially nonlinear boundary-value problem in an unknown domain into an algebraically nonlinear boundary-value problem in a known domain. Convergent series solutions are obtained not only for small amplitude water waves on a weak current but also for large amplitude waves on a strong current. The nonlinear wave-current interaction is studied in detail. It is found that an aiding shear current tends to enlarge the wave phase speed, sharpen the wave crest, but shorten the maximum wave height, while an opposing shear current has the opposite effect. Besides, the amplitude of waves and fluid velocity decay over the depth more quickly on an aiding shear current but more slowly on an opposing shear current than that of waves on still water. Furthermore, it is found that Stokes criteria of wave breaking is still valid for waves on a shear current: a train of propagating waves on a shear current breaks as the fiuid velocity at crest equals the wave phase speed. Especially, it is found that the highest waves on an opposing shear current are even higher and steeper than that of waves on still water. Mathematically, this analytic method is rather general in principle and can be employed to solve many types of nonlinear partial differential equations with variable coefficients in science, finance and engineering.
Hao, Qing-Yi; Jiang, Rui; Hu, Mao-Bin; Jia, Bin; Wang, Wen-Xu
2016-01-01
Driven diffusive systems have been a paradigm for modelling many physical, chemical, and biological transport processes. In the systems, spatial correlation plays an important role in the emergence of a variety of nonequilibrium phenomena and exhibits rich features such as pronounced oscillations. However, the lack of analytical results of spatial correlation precludes us from fully understanding the effect of spatial correlation on the dynamics of the system. Here we offer precise analytical predictions of the spatial correlation in a typical driven diffusive system, namely facilitated asymmetric exclusion process. We find theoretically that the correlation between two sites decays exponentially as their distance increases, which is in good agreement with numerical simulations. Furthermore, we find the exponential decay is a universal property of macroscopic homogeneous state in a broad class of 1D driven diffusive systems. Our findings deepen the understanding of many nonequilibrium phenomena resulting from spatial correlation in driven diffusive systems. PMID:26804770
Hao, Qing-Yi; Jiang, Rui; Hu, Mao-Bin; Jia, Bin; Wang, Wen-Xu
2016-01-25
Driven diffusive systems have been a paradigm for modelling many physical, chemical, and biological transport processes. In the systems, spatial correlation plays an important role in the emergence of a variety of nonequilibrium phenomena and exhibits rich features such as pronounced oscillations. However, the lack of analytical results of spatial correlation precludes us from fully understanding the effect of spatial correlation on the dynamics of the system. Here we offer precise analytical predictions of the spatial correlation in a typical driven diffusive system, namely facilitated asymmetric exclusion process. We find theoretically that the correlation between two sites decays exponentially as their distance increases, which is in good agreement with numerical simulations. Furthermore, we find the exponential decay is a universal property of macroscopic homogeneous state in a broad class of 1D driven diffusive systems. Our findings deepen the understanding of many nonequilibrium phenomena resulting from spatial correlation in driven diffusive systems.
Few-parameter exponentially correlated wavefunctions for the ground state of lithium
NASA Astrophysics Data System (ADS)
Albert, Victor V.; Guevara, Nicolais L.; Sabin, John R.; Harris, Frank E.
Compact, but relatively accurate wavefunctions for the ground state of the Li atom were obtained through the use of a limited basis of exponentially correlated functions with optimized nonlinear parameters. In contrast to our earlier work, the basis contains pre-exponential factors that improve the rate of convergence of the basis-set expansion. The matrix elements needed in the present work were evaluated analytically using recursive methods reported recently by one of us; a check on the programming was provided by comparison with numerical evaluations carried out by Turbiner and Guevara. The rate of convergence of the expansion is compared with those of Hylleraas-basis computations, and a comparison is also made with exponentially correlated studies of He-like systems.
Propagation of exponential shock wave in an axisymmetric rotating non-ideal dusty gas
NASA Astrophysics Data System (ADS)
Nath, G.
2016-09-01
One-dimensional unsteady isothermal and adiabatic flow behind a strong exponential shock wave propagating in a rotational axisymmetric mixture of non-ideal gas and small solid particles, which has variable azimuthal and axial fluid velocities, is analyzed. The shock wave is driven out by a piston moving with time according to exponential law. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to be varying and obeying exponential laws. In the present work, small solid particles are considered as pseudo-fluid with the assumption that the equilibrium flow-conditions are maintained in the flow-field, and the viscous-stress and heat conduction of the mixture are negligible. Solutions are obtained in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector and compressibility. It is found that the assumption of zero temperature gradient brings a profound change in the density, axial component of vorticity vector and compressibility distributions as compared to that of the adiabatic case. To investigate the behavior of the flow variables and the influence on the shock wave propagation by the parameter of non-idealness of the gas overline{b} in the mixture as well as by the mass concentration of solid particles in the mixture Kp and by the ratio of the density of solid particles to the initial density of the gas G1 are worked out in detail. It is interesting to note that the shock strength increases with an increase in G1 ; whereas it decreases with an increase in overline{b} . Also, a comparison between the solutions in the cases of isothermal and adiabatic flows is made.
NASA Astrophysics Data System (ADS)
Gabriel, Jan; Blochowicz, Thomas; Stühn, Bernd
2015-03-01
In a wide range of soft materials, correlation experiments using laser light or partially coherent X-rays report the so called compressed exponential correlation functions, i. e., decays c(t) ∝ exp(-(t/τ)β) with β > 1. In many cases, this is related to the relaxation of inner stresses, but in some systems, the source of such a phenomenon is still poorly understood. We performed multi speckle-dynamic light scattering experiments in a system of polystyrene spheres in supercooled propanediol. At low temperatures, compressed exponential decays are observed in a multispeckle experiment, in agreement with the literature findings in similar systems. At the same time, due to the particular geometry of our setup, the speckle pattern shows indication for convection in the sample due to a slight temperature gradient across the sample cuvette mounted in a cold finger cryostat. These effects increase with decreasing temperature and after a temperature jump. In some cases it can be corrected for by assuming convective flow at constant velocity. Such corrections reduce or remove compressed exponential behavior in our experiment.
NASA Astrophysics Data System (ADS)
Pace, David Carl
An experimental study of plasma turbulence and transport is performed in the fundamental geometry of a narrow pressure filament in a magnetized plasma. An electron beam is used to heat a cold background plasma in a linear device, the Large Plasma Device (LAPD-U) [W. Gekelman et al. Rev. Sci. Instrum. 62, 2875 (1991)] operated by the Basic Plasma Science Facility at the University of California, Los Angeles. This results in the generation of a filamentary structure 1000 cm in length and 1 cm in diameter) exhibiting a controllable radial temperature gradient embedded in a large plasma. The filament serves as a resonance cavity for a thermal (diffusive) wave manifested by large amplitude, coherent oscillations in electron temperature. Properties of this wave are used to determine the electron collision time of the plasma and suggest that a diagnostic method for studying plasma transport can be designed in a similar manner. For short times and low heating powers the filament conducts away thermal energy through particle collisions, consistent with classical theory. Experiments performed with longer heating times or greater injected power feature a transition from the classical transport regime to a regime of enhanced transport levels. During the anomalous transport regime, fluctuations exhibit an exponential power spectrum for frequencies below the ion cyclotron frequency. The exponential feature has been traced to the presence of solitary pulses having a Lorentzian temporal signature. These pulses arise from nonlinear interactions of drift-Alfven waves driven by the pressure gradients. The temporal width of the pulses is measured to be a fraction of a period of the drift-Alfven waves. A second experiment involves a macroscopic (3.5 cm gradient length) limiter-edge geometry in which a density gradient is established by inserting a metallic plate at the edge of the nominal plasma column of the LAPD-U. In both experiments the width of the pulses is narrowly distributed
Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay
NASA Astrophysics Data System (ADS)
Dai, Qiuyi; Yang, Zhifeng
2014-10-01
In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ 1 and μ 2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561-1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011) by removing the restriction imposed on μ 1 and μ 2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ 1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011).
Head wave correlations in ambient noise.
Gebbie, John; Siderius, Martin
2016-07-01
Ambient ocean noise is processed with a vertical line array to reveal coherent time-separated arrivals suggesting the presence of head wave multipath propagation. Head waves, which are critically propagating water waves created by seabed waves traveling parallel to the water-sediment interface, can propagate faster than water-only waves. Such eigenrays are much weaker than water-only eigenrays, and are often completely overshadowed by them. Surface-generated noise is different whereby it amplifies the coherence between head waves and critically propagating water-only waves, which is measured by cross-correlating critically steered beams. This phenomenon is demonstrated both experimentally and with a full wave simulation.
Almost Exponential Decay of Periodic Viscous Surface Waves without Surface Tension
NASA Astrophysics Data System (ADS)
Guo, Yan; Tice, Ian
2013-02-01
We consider a viscous fluid of finite depth below the air, occupying a three-dimensional domain bounded below by a fixed solid boundary and above by a free moving boundary. The fluid dynamics are governed by the gravity-driven incompressible Navier-Stokes equations, and the effect of surface tension is neglected on the free surface. The long time behavior of solutions near equilibrium has been an intriguing question since the work of Beale (Commun Pure Appl Math 34(3):359-392, 1981). This paper is the third in a series of three (Guo in Local well-posedness of the viscous surface wave problem without surface tension, Anal PDE 2012, to appear; in Decay of viscous surface waves without surface tension in horizontally infinite domains, Preprint, 2011) that answers this question. Here we consider the case in which the free interface is horizontally periodic; we prove that the problem is globally well-posed and that solutions decay to equilibrium at an almost exponential rate. In particular, the free interface decays to a flat surface. Our framework contains several novel techniques, which include: (1) a priori estimates that utilize a "geometric" reformulation of the equations; (2) a two-tier energy method that couples the boundedness of high-order energy to the decay of low-order energy, the latter of which is necessary to balance out the growth of the highest derivatives of the free interface; (3) a localization procedure that is compatible with the energy method and allows for curved lower surface geometry. Our decay estimates lead to the construction of global-in-time solutions to the surface wave problem.
Phase sorting wave-particle correlator
NASA Astrophysics Data System (ADS)
Kletzing, C. A.; LaBelle, J.; Bounds, S. R.; Dolan, J.; Kaeppler, S. R.; Dombrowski, M.
2017-02-01
Wave-particle correlations, particularly of Langmuir waves and electrons, have been the subject of significant interest extending back to the 1970s. Often, these correlations have been simply observing modulation of the electrons at the plasma frequency with no phase resolution. The first phase-resolving correlators were developed at UC Berkeley in the late 1980s and reported by Ergun in the early 1990s. A design is presented which further improves on phase resolution in correlations of Langmuir waves and electrons with phase resolution of 22.5°. In this technique, a phase-locked loop (PLL) is used to lock onto the wave and subdivide the phase. Electrons are sorted on-the-fly as they arrive into the phase bins. Discussed are details of accurate timing, testing, and calibration of this system as well as results from rocket flights in which statistically significant phase correlations have been observed.
NASA Astrophysics Data System (ADS)
Taller, Daniel; Go, David B.; Chang, Hsueh-Chia
2013-05-01
The exponentially decaying acoustic pressure of scattered surface acoustic waves (SAWs) at the contact line of a liquid film pinned to filter paper is shown to sustain a high curvature conic tip with micron-sized modulations whose dimension grows exponentially from the tip. The large negative capillary pressure in the film, necessary for offsetting the large positive acoustic pressure at the contact line, also creates significant negative hydrodynamic pressure and robust wicking action through the paper. An asymptotic analysis of this intricate pressure matching between the quasistatic conic film and bulk drop shows that the necessary SAW power to pump liquid from the filter paper and aerosolize, expressed in terms of the acoustic pressure scaled by the drop capillary pressure, grows exponentially with respect to twice the acoustic decay constant multiplied by the drop length, with a universal preexponential coefficient. Global rapid aerosolization occurs at a SAW power twice as high, beyond which the wicking rate saturates.
Taller, Daniel; Go, David B; Chang, Hsueh-Chia
2013-05-01
The exponentially decaying acoustic pressure of scattered surface acoustic waves (SAWs) at the contact line of a liquid film pinned to filter paper is shown to sustain a high curvature conic tip with micron-sized modulations whose dimension grows exponentially from the tip. The large negative capillary pressure in the film, necessary for offsetting the large positive acoustic pressure at the contact line, also creates significant negative hydrodynamic pressure and robust wicking action through the paper. An asymptotic analysis of this intricate pressure matching between the quasistatic conic film and bulk drop shows that the necessary SAW power to pump liquid from the filter paper and aerosolize, expressed in terms of the acoustic pressure scaled by the drop capillary pressure, grows exponentially with respect to twice the acoustic decay constant multiplied by the drop length, with a universal preexponential coefficient. Global rapid aerosolization occurs at a SAW power twice as high, beyond which the wicking rate saturates.
NASA Astrophysics Data System (ADS)
Daqaq, Mohammed F.
2011-05-01
In this theoretical study, the response of an inductive power generator with a bistable symmetric potential to stationary random environmental excitations is investigated. Both white and Ornstein-Uhlenbeck-type excitations are considered. In the white noise limit, the stationary Fokker-Plank-Kolmagorov equation is solved for the exact joint probability density function (PDF) of the response. The PDF is then used to obtain analytical expressions for the response statistics. It is shown that the expected value of the generator's output power is independent of the potential shape leading to the conclusion that under white noise excitations, bistabilities in the potential do not provide any enhancement over the traditional linear resonant generators which have a single-well potential. In the case of Ornstein-Uhlenbeck (exponentially correlated) noise, an approximate expression for the mean power of the generator which depends on the potential shape, the generator's design parameters and the noise bandwidth and intensity is obtained. It is shown that there exists an optimal potential shape which maximizes the output power. This optimal shape guarantees an optimal escapement frequency between the potential wells which remains constant even as the noise intensity is varied.
Propagating wave correlations in complex systems
NASA Astrophysics Data System (ADS)
Creagh, Stephen C.; Gradoni, Gabriele; Hartmann, Timo; Tanner, Gregor
2017-01-01
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on Poincaré sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures.
Wave propagation of myocardial stretch: correlation with myocardial stiffness.
Pislaru, Cristina; Pellikka, Patricia A; Pislaru, Sorin V
2014-01-01
The mechanism of flow propagation during diastole in the left ventricle (LV) has been well described. Little is known about the associated waves propagating along the heart walls. These waves may have a mechanism similar to pulse wave propagation in arteries. The major goal of the study was to evaluate the effect of myocardial stiffness and preload on this wave transmission. Longitudinal late diastolic deformation and wave speed (Vp) of myocardial stretch in the anterior LV wall were measured using sonomicrometry in 16 pigs. Animals with normal and altered myocardial stiffness (acute myocardial infarction) were studied with and without preload alterations. Elastic modulus estimated from Vp (E VP; Moens-Korteweg equation) was compared to incremental elastic modulus obtained from exponential end-diastolic stress-strain relation (E SS). Myocardial distensibility and α- and β-coefficients of stress-strain relations were calculated. Vp was higher at reperfusion compared to baseline (2.6 ± 1.3 vs. 1.3 ± 0.4 m/s; p = 0.005) and best correlated with E SS (r2 = 0.80, p < 0.0001), β-coefficient (r2 = 0.78, p < 0.0001), distensibility (r2 = 0.47, p = 0.005), and wall thickness/diameter ratio (r2 = 0.42, p = 0.009). Elastic moduli (E VP and E SS) were strongly correlated (r2 = 0.83, p < 0.0001). Increasing preload increased Vp and E VP and decreased distensibility. At multivariate analysis, E SS, wall thickness, and end-diastolic and systolic LV pressures were independent predictors of Vp (r2 model = 0.83, p < 0.0001). In conclusion, the main determinants of wave propagation of longitudinal myocardial stretch were myocardial stiffness and LV geometry and pressure. This local wave speed could potentially be measured noninvasively by echocardiography.
NASA Astrophysics Data System (ADS)
Nath, G.; Sinha, A. K.
2017-01-01
The propagation of a cylindrical shock wave in an ideal gas in the presence of a constant azimuthal magnetic field with consideration for the axisymmetric rotational effects is investigated. The ambient medium is assumed to have the radial, axial, and azimuthal velocity components. The fluid velocities and density of the ambient medium are assumed to vary according to an exponential law. Nonsimilar solutions are obtained by taking into account the vorticity vector and its components. The dependences of the characteristics of the problem on the Alfven-Mach number and time are obtained. It is shown that the presence of a magnetic field has a decaying effect on the shock wave. The pressure and density are shown to vanish at the inner surface (piston), and hence a vacuum forms at the line of symmetry.
NASA Astrophysics Data System (ADS)
Grobbelaar-Van Dalsen, Marié
2015-08-01
This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.
Peng, Bo; Kowalski, Karol
2016-12-23
In this paper we derive basic properties of the Green’s function matrix elements stemming from the exponential coupled cluster (CC) parametrization of the ground-state wave function. We demon- strate that all intermediates used to express retarded (or equivalently, ionized) part of the Green’s function in the ω-representation can be expressed through connected diagrams only. Similar proper- ties are also shared by the first order ω-derivatives of the retarded part of the CC Green’s function. This property can be extended to any order ω-derivatives of the Green’s function. Through the Dyson equation of CC Green’s function, the derivatives of corresponding CC self-energy can be evaluated analytically. In analogy to the CC Green’s function, the corresponding CC self-energy is expressed in terms of connected diagrams only. Moreover, the ionized part of the CC Green’s func- tion satisfies the non-homogeneous linear system of ordinary differential equations, whose solution may be represented in the exponential form. Our analysis can be easily generalized to the advanced part of the CC Green’s function.
NASA Astrophysics Data System (ADS)
Peng, Bo; Kowalski, Karol
2016-12-01
In this paper we derive basic properties of the Green's-function matrix elements stemming from the exponential coupled-cluster (CC) parametrization of the ground-state wave function. We demonstrate that all intermediates used to express the retarded (or, equivalently, ionized) part of the Green's function in the ω representation can be expressed only through connected diagrams. Similar properties are also shared by the first-order ω derivative of the retarded part of the CC Green's function. Moreover, the first-order ω derivative of the CC Green's function can be evaluated analytically. This result can be generalized to any order of ω derivatives. Through the Dyson equation, derivatives of the corresponding CC self-energy operator can be evaluated analytically. In analogy to the CC Green's function, the corresponding CC self-energy operator can be represented by connected terms. Our analysis can easily be generalized to the advanced part of the CC Green's function.
NASA Astrophysics Data System (ADS)
Nath, G.
2014-06-01
The propagation of spherical (or cylindrical) shock wave in an ideal gas with or without gravitational effects in the presence of a constant azimuthal magnetic field is investigated. Non-similarity solutions are obtained for isothermal flow between the shock and the piston. The numerical solutions are obtained using the Runge-Kutta method of the fourth order. The density of the gas is assumed to be varying and obeying an exponential law. The shock wave moves with variable velocity, and the total energy of the wave is non-constant and varies with time. The effects of variation of the Alfven-Mach number, gravitational parameter and time are obtained. It is investigated that the presence of gravitational field reduces the effect of the magnetic field. Also, the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and, therefore, the distance between the inner contact surface and the shock surface is reduced. The shock waves in conducting perfect gas can be important for description of shocks in supernova explosions, in the study of central part of star burst galaxies, nuclear explosion, rupture of a pressurized vessel and explosion in the ionosphere. Other potential applications of this study include analysis of data from exploding wire experiments and cylindrically symmetric hypersonic flow problems associated with meteors or re-entry vehicles etc. A comparison is made between the solutions in the cases of the gravitating and the non-gravitating medium with or without magnetic field. The obtained solutions are applicable for arbitrary values of time.
Intensity correlation of orthogonally crossed speckle waves
NASA Astrophysics Data System (ADS)
Okamoto, Takashi
2006-05-01
The statistical properties of three-dimensional laser speckles formed with orthogonally crossed multiple speckle waves are studied theoretically. The analytical expressions for the first and second order statistics of the crossed speckle fields are derived, and the theoretical results are verified by means of computer simulations. In the simulations, fractal speckles are also analyzed to examine the self-similar properties of the resulting field. The correlation properties of clipped speckles are investigated to explore the possibility of fabricating fractal random media by means of photopolymerization for three-dimensional patterning of micro structures.
Law, Yingyu; Ni, Bing-Jie; Lant, Paul; Yuan, Zhiguo
2012-06-15
The relationship between the ammonia oxidation rate (AOR) and nitrous oxide production rate (N(2)OR) of an enriched ammonia-oxidising bacteria (AOB) culture was investigated. The AOB culture was enriched in a nitritation system fed with synthetic anaerobic digester liquor. The AOR was controlled by adjusting the dissolved oxygen (DO) and pH levels and also by varying the initial ammonium (NH(4)(+)) concentration in batch experiments. Tests were also performed directly on the parent reactor where a stepwise decrease/increase in DO was implemented to alter AOR. The experimental data indicated a clear exponential relationship between the biomass specific N(2)OR and AOR. Four metabolic models were used to analyse the experimental data. The metabolic model formulated based on aerobic N(2)O production from the decomposition of nitrosyl radical (NOH) predicted the exponential correlation observed experimentally. The experimental data could not be reproduced by models developed on the basis of N(2)O production through nitrite (NO(2)(-)) and nitric oxide (NO) reduction by AOB.
Gentilini, Davide; Garagnani, Paolo; Pisoni, Serena; Bacalini, Maria Giulia; Calzari, Luciano; Mari, Daniela; Vitale, Giovanni; Franceschi, Claudio; Di Blasio, Anna Maria
2015-08-01
In this study we applied a new analytical strategy to investigate the relations between stochastic epigenetic mutations (SEMs) and aging. We analysed methylation levels through the Infinium HumanMethylation27 and HumanMethylation450 BeadChips in a population of 178 subjects ranging from 3 to 106 years. For each CpG probe, epimutated subjects were identified as the extreme outliers with methylation level exceeding three times interquartile ranges the first quartile (Q1-(3 x IQR)) or the third quartile (Q3+(3 x IQR)). We demonstrated that the number of SEMs was low in childhood and increased exponentially during aging. Using the HUMARA method, skewing of X chromosome inactivation (XCI) was evaluated in heterozygotes women. Multivariate analysis indicated a significant correlation between log(SEMs) and degree of XCI skewing after adjustment for age (β = 0.41; confidence interval: 0.14, 0.68; p-value = 0.0053). The PATH analysis tested the complete model containing the variables: skewing of XCI, age, log(SEMs) and overall CpG methylation. After adjusting for the number of epimutations we failed to confirm the well reported correlation between skewing of XCI and aging. This evidence might suggest that the known correlation between XCI skewing and aging could not be a direct association but mediated by the number of SEMs.
NASA Astrophysics Data System (ADS)
Nath, G.; Vishwakarma, J. P.
2016-06-01
The propagation of a strong spherical shock wave in a dusty gas with or without self-gravitational effects is investigated in the case of isothermal and adiabatic flows. The dusty gas is assumed to be a mixture of small solid particles and perfect gas. The equilibrium flow conditions are assumed to be maintained, and the density of the mixture is assumed to be varying and obeying an exponential law. Non-similarity solutions are obtained and the effects of variations of the mass concentration of solid particles in the mixture and the ratio of the density of solid particles to the initial density of the gas, and the presence of self-gravitational field on the flow variables are investigated at given times. Our analysis reveals that after inclusion of gravitational field effects surprisingly the shock strength increases and remarkable differences are found in the distribution of flow variables. An increase in time also, increases the shock strength. Further, it is investigated that the consideration of isothermal flow increases the shock strength, and removes the singularity in the density distribution. Also, the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and therefore the distance between the inner contact surface and the shock surface is reduced. The shock waves in self-gravitating dusty gas can be important for description of shocks in supernova explosions, in the study of central part of star burst galaxies, star formation and shocks in stellar explosion, nuclear explosion, in industry, rupture of a pressurized vessel and explosion in the ionosphere. Other potential applications of this study include analysis of data from exploding wire experiments and cylindrically symmetric hypersonic flow problems associated with meteors or re-entry of vehicles etc. A comparison is made between the solutions in the cases of the gravitating and the non-gravitating media. The obtained solutions are applicable for
NASA Astrophysics Data System (ADS)
Aleiner, Igor L.; Faoro, Lara; Ioffe, Lev B.
2016-12-01
We extend the Keldysh technique to enable the computation of out-of-time order correlators such as < O(t) O ˜ (0) O(t) O ˜ (0) > . We show that the behavior of these correlators is described by equations that display initially an exponential instability which is followed by a linear propagation of the decoherence between two initially identically copies of the quantum many body systems with interactions. At large times the decoherence propagation (quantum butterfly effect) is described by a diffusion equation with non-linear dissipation known in the theory of combustion waves. The solution of this equation is a propagating non-linear wave moving with constant velocity despite the diffusive character of the underlying dynamics. Our general conclusions are illustrated by the detailed computations for the specific models describing the electrons interacting with bosonic degrees of freedom (phonons, two-level-systems etc.) or with each other.
Quench-induced correlation waves, and quantum grenades
NASA Astrophysics Data System (ADS)
Corson, John; Bohn, John
2016-05-01
We investigate the wave packet dynamics of a pair of particles that undergoes a rapid change of scattering length. Such quenches have recently become experimentally feasible with fast magnetic-field ramps and optical switching in the vicinity of a Feshbach resonance. The short-range interactions are modelled in the zero-range limit, where the quench is accomplished by switching the boundary condition of the wave function at vanishing particle separation. This generates a correlation wave that propagates rapidly to nonzero particle separations. We have derived universal, analytic results for this process that lead to a simple phase-space picture of quench-induced scattering. Intuitively, the strength of the correlation wave relates to the initial contact of the system. A natural consequence is that the waves are significant when the quench dissociates, at least partially, a bound state. These waves can propagate with high energy from one lattice site to another, potentially triggering highly non-equilibrium dynamics.
Correlation equation for the marine drag coefficient and wave steepness
NASA Astrophysics Data System (ADS)
Foreman, Richard J.; Emeis, Stefan
2012-09-01
This work questions, starting from dimensional considerations, the generality of the belief that the marine drag coefficient levels off with increasing wind speed. Dimensional analysis shows that the drag coefficient scales with the wave steepness as opposed to a wave-age scaling. A correlation equation is employed here that uses wave steepness scaling at low aspect ratios (inverse wave steepnesses) and a constant drag coefficient at high aspect ratios. Invoked in support of the correlation are measurements sourced from the literature and at the FINO1 platform in the North Sea. The correlation equation is then applied to measurements recorded from buoys during the passage of hurricanes Rita, Katrina (2005) and Ike (2008). Results show that the correlation equation anticipates the expected levelling off in deeper water, but a drag coefficient more consistent with a Charnock type relation is also possible in more shallower water. Some suggestions are made for proceeding with a higher-order analysis than that conducted here.
Correlation techniques and measurements of wave-height statistics
NASA Technical Reports Server (NTRS)
Guthart, H.; Taylor, W. C.; Graf, K. A.; Douglas, D. G.
1972-01-01
Statistical measurements of wave height fluctuations have been made in a wind wave tank. The power spectral density function of temporal wave height fluctuations evidenced second-harmonic components and an f to the minus 5th power law decay beyond the second harmonic. The observations of second harmonic effects agreed very well with a theoretical prediction. From the wave statistics, surface drift currents were inferred and compared to experimental measurements with satisfactory agreement. Measurements were made of the two dimensional correlation coefficient at 15 deg increments in angle with respect to the wind vector. An estimate of the two-dimensional spatial power spectral density function was also made.
NASA Astrophysics Data System (ADS)
Xaplanteris, C. L.; Xaplanteris, L. C.; Leousis, D. P.
2014-03-01
Many physical phenomena that concern the research these days are basically complicated because of being multi-parametric. Thus, their study and understanding meets with big if not unsolved obstacles. Such complicated and multi-parametric is the plasmatic state as well, where the plasma and the physical quantities that appear along with it have chaotic behavior. Many of those physical quantities change exponentially and at most times they are stabilized by presenting wavy behavior. Mostly in the transitive state rather than the steady state, the exponentially changing quantities (Growth, Damping etc) depend on each other in most cases. Thus, it is difficult to distinguish the cause from the result. The present paper attempts to help this difficult study and understanding by proposing mathematical exponential models that could relate with the study and understanding of the plasmatic wavy instability behavior. Such instabilities are already detected, understood and presented in previous publications of our laboratory. In other words, our new contribution is the study of the already known plasmatic quantities by using mathematical models (modeling and simulation). These methods are both useful and applicable in the chaotic theory. In addition, our ambition is to also conduct a list of models useful for the study of chaotic problems, such as those that appear into the plasma, starting with this paper's examples.
Xaplanteris, C. L.; Xaplanteris, L. C.; Leousis, D. P.
2014-03-15
Many physical phenomena that concern the research these days are basically complicated because of being multi-parametric. Thus, their study and understanding meets with big if not unsolved obstacles. Such complicated and multi-parametric is the plasmatic state as well, where the plasma and the physical quantities that appear along with it have chaotic behavior. Many of those physical quantities change exponentially and at most times they are stabilized by presenting wavy behavior. Mostly in the transitive state rather than the steady state, the exponentially changing quantities (Growth, Damping etc) depend on each other in most cases. Thus, it is difficult to distinguish the cause from the result. The present paper attempts to help this difficult study and understanding by proposing mathematical exponential models that could relate with the study and understanding of the plasmatic wavy instability behavior. Such instabilities are already detected, understood and presented in previous publications of our laboratory. In other words, our new contribution is the study of the already known plasmatic quantities by using mathematical models (modeling and simulation). These methods are both useful and applicable in the chaotic theory. In addition, our ambition is to also conduct a list of models useful for the study of chaotic problems, such as those that appear into the plasma, starting with this paper's examples.
Cross-correlation search for periodic gravitational waves
Dhurandhar, Sanjeev; Mukhopadhyay, Himan; Krishnan, Badri; Whelan, John T.
2008-04-15
In this paper we study the use of cross correlations between multiple gravitational wave (GW) data streams for detecting long-lived periodic signals. Cross-correlation searches between data from multiple detectors have traditionally been used to search for stochastic GW signals, but recently they have also been used in directed searches for periodic GWs. Here we further adapt the cross-correlation statistic for periodic GW searches by taking into account both the nonstationarity and the long-term-phase coherence of the signal. We study the statistical properties and sensitivity of this search and its relation to existing periodic wave searches, and describe the precise way in which the cross-correlation statistic interpolates between semicoherent and fully coherent methods. Depending on the maximum duration over which we wish to preserve phase coherence, the cross-correlation statistic can be tuned to go from a standard cross-correlation statistic using data from distinct detectors, to the semicoherent time-frequency methods with increasing coherent time baselines, and all the way to a full coherent search. This leads to a unified framework for studying periodic wave searches and can be used to make informed trade-offs between computational cost, sensitivity, and robustness against signal uncertainties.
Strong correlations generically protect d -wave superconductivity against disorder
NASA Astrophysics Data System (ADS)
Tang, Shao; Dobrosavljević, V.; Miranda, E.
2016-05-01
We address the question of why strongly correlated d -wave superconductors, such as the cuprates, prove to be surprisingly robust against the introduction of nonmagnetic impurities. We show that, very generally, both the pair-breaking and the normal state transport scattering rates are significantly suppressed by strong correlations effects arising in the proximity to a Mott insulating state. We also show that the correlation-renormalized scattering amplitude is generically enhanced in the forward direction, an effect which was previously often ascribed to the specific scattering by charged impurities outside the copper-oxide planes.
Ballistic quench-induced correlation waves in ultracold gases
NASA Astrophysics Data System (ADS)
Corson, John P.; Bohn, John L.
2016-08-01
We investigate the wave-packet dynamics of a pair of particles that undergoes a rapid change of scattering length. The short-range interactions are modeled in the zero-range limit, where the quench is accomplished by switching the boundary condition of the wave function at vanishing particle separation. This generates a correlation wave that propagates rapidly to nonzero particle separations. We have derived universal, analytic results for this process that lead to a simple phase-space picture of the quench-induced scattering. Intuitively, the strength of the correlation wave relates to the initial contact of the system. We find that, in one spatial dimension, the k-4 tail of the momentum distribution contains a ballistic contribution that does not originate from short-range pair correlations, and a similar conclusion can hold in other dimensionalities depending on the quench protocol. We examine the resultant quench-induced transport in an optical lattice in one dimension, and a semiclassical treatment is found to give quantitatively accurate estimates for the transport probabilities.
Correlations of πN partial waves for multireaction analyses
Doring, M.; Revier, J.; Ronchen, D.; ...
2016-06-15
In the search for missing baryonic resonances, many analyses include data from a variety of pion- and photon-induced reactions. For elastic πN scattering, however, usually the partial waves of the SAID (Scattering Analysis Interactive Database) or other groups are fitted, instead of data. We provide the partial-wave covariance matrices needed to perform correlated χ2 fits, in which the obtained χ2 equals the actual χ2 up to nonlinear and normalization corrections. For any analysis relying on partial waves extracted from elastic pion scattering, this is a prerequisite to assess the significance of resonance signals and to assign any uncertainty on results.more » Lastly, the influence of systematic errors is also considered.« less
Optimization of Quantum Correlation in Cascaded Four-Wave Mixing
NASA Astrophysics Data System (ADS)
Feng, Jingliang; Jing, Jietai
2016-12-01
We propose a measurement strategy that can be used to optimize quantum correlation for a cascaded four-wave mixing (FWM) structure. By calculating the covariance matrix of a cascaded FWM structure, we can get all the correlations between any two parties in the outputs. We then calculate the eigenvalues and corresponding eigenmodes of the covariance matrix to find the squeezing degrees of the squeezed modes. Our theoretical model can explain our previous experimental results very well and is useful to optimize the squeezing degree in the cascaded FWM structure.
Optimization of Quantum Correlation in Cascaded Four-Wave Mixing
NASA Astrophysics Data System (ADS)
Feng, Jingliang; Jing, Jietai
2017-03-01
We propose a measurement strategy that can be used to optimize quantum correlation for a cascaded four-wave mixing (FWM) structure. By calculating the covariance matrix of a cascaded FWM structure, we can get all the correlations between any two parties in the outputs. We then calculate the eigenvalues and corresponding eigenmodes of the covariance matrix to find the squeezing degrees of the squeezed modes. Our theoretical model can explain our previous experimental results very well and is useful to optimize the squeezing degree in the cascaded FWM structure.
Hydrodynamic Waves and Correlation Functions in Dusty Plasmas
NASA Astrophysics Data System (ADS)
Bhattacharjee, A.; Wang, Xiaogang
1997-11-01
A hydrodynamic description of strongly coupled dusty plasmas is given when physical quantities vary slowly in space and time and the system can be assumed to be in local thermodynamic equilibrium. The linear waves in such a system are analyzed. In particular, a dispersion equation is derived for low-frequency dust acoustic waves, including collisional damping effects, and compared with experimental results. The linear response of the system is calculated from the fluctuation-dissipation theorem and the hydrodynamic equations. The requirement that these two calculations coincide constrains the particle correlation function for slowly varying perturbations [L. P. Kadanoff and P. C. Martin, Ann. Phys. 24, 419 (1963)]. It is shown that in the presence of the slow dust-acoustic waves, the dust auto-correlation function is of the Debye-Hekel form and the shielding distance is the dust Debye length. In the short-wavelength regime, an integral equation is derived from kinetic theory and solved numerically to yield particle correlation functions that display ``liquid-like'' behavior and have been observed experimentally [R. A.. Quinn, C. Cui, J. Goree, J. B. Pieper, H. Thomas and G. E. Morfill, Phys. Rev. E 53, R2049 (1996)].
Sizemore, F G; Barbato, G F
2002-07-01
Chicks divergently selected for 14-d (14H and 14L) or 42-d (42H and 42L) exponential growth rate (EGR) over five generations were used to determine correlated responses between growth at different ages and body composition. Regression coefficient estimates across five generations of selection were not significant for any line at either age for percentage total body water or protein. Genetic correlations between EGR from hatching to 14 d of age (EGR14) and 42-d percentage carcass fat were -0.18, -0.57, 0.63, and -0.79 among the 14H, 14L, 42H, and 42L lines, respectively. Genetic correlations between EGR from hatching to 42 d of age (EGR42) and 42-d percentage carcass fat were 0.09, -0.67,0.50, and -0.75 among the 14H, 14L, 42H, and 42L lines, respectively. During the short-term selection experiment, selection for fast EGR14 or EGR42 increased fat at the age of selection. However, selection for fast EGR42 increased body weight and percentage fat at 42 d of age (DOA), whereas selection for fast EGR14 increased body weight but not fat at 42 DOA. Therefore, it is possible to simultaneously select for high body weight at, or near, the inflection point of the growth curve without increasing fat deposition or obesity by taking advantage of the lack of a genetic correlation between EGR14 and body fat percentage at later ages.
Charge density waves in strongly correlated electron systems
NASA Astrophysics Data System (ADS)
Chen, Chih-Wei; Choe, Jesse; Morosan, E.
2016-08-01
Strong electron correlations are at the heart of many physical phenomena of current interest to the condensed matter community. Here we present a survey of the mechanisms underlying such correlations in charge density wave (CDW) systems, including the current theoretical understanding and experimental evidence for CDW transitions. The focus is on emergent phenomena that result as CDWs interact with other charge or spin states, such as magnetism and superconductivity. In addition to reviewing the CDW mechanisms in 1D, 2D, and 3D systems, we pay particular attention to the prevalence of this state in two particular classes of compounds, the high temperature superconductors (cuprates) and the layered transition metal dichalcogenides. The possibilities for quantum criticality resulting from the competition between magnetic fluctuations and electronic instabilities (CDW, unconventional superconductivity) are also discussed.
Quantum properties of exponential states
Luis, Alfredo
2007-05-15
The use of Renyi entropy as an uncertainty measure alternative to variance leads to the study of states with quantum fluctuations below the levels established by Gaussian states, which are the position-momentum minimum uncertainty states according to variance. We examine the quantum properties of states with exponential wave functions, which combine reduced fluctuations with practical feasibility.
Quantum dust magnetosonic waves with spin and exchange correlation effects
Maroof, R.; Qamar, A.; Mushtaq, A.
2016-01-15
Dust magnetosonic waves are studied in degenerate dusty plasmas with spin and exchange correlation effects. Using the fluid equations of magnetoplasma with quantum corrections due to the Bohm potential, temperature degeneracy, spin magnetization energy, and exchange correlation, a generalized dispersion relation is derived. Spin effects are incorporated via spin force and macroscopic spin magnetization current. The exchange-correlation potentials are used, based on the adiabatic local-density approximation, and can be described as a function of the electron density. For three different values of angle, the dispersion relation is reduced to three different modes under the low frequency magnetohydrodynamic assumptions. It is found that the effects of quantum corrections in the presence of dust concentration significantly modify the dispersive properties of these modes. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects (e.g., the cores of white dwarf stars and giant planets) and in plasma-assisted nanotechnology (e.g., quantum diodes, quantum free-electron lasers, etc.)
NASA Technical Reports Server (NTRS)
Huang, K.-N.
1977-01-01
A computational procedure for calculating correlated wave functions is proposed for three-particle systems interacting through Coulomb forces. Calculations are carried out for the muonic helium atom. Variational wave functions which explicitly contain interparticle coordinates are presented for the ground and excited states. General Hylleraas-type trial functions are used as the basis for the correlated wave functions. Excited-state energies of the muonic helium atom computed from 1- and 35-term wave functions are listed for four states.
Merrill, Stephen J; Ashrafi, Samira; Subramanian, Madhan; Godar, Dianne E
2015-01-01
For several decades the incidence of cutaneous malignant melanoma (CMM) steadily increased in fair-skinned, indoor-working people around the world. Scientists think poor tanning ability resulting in sunburns initiate CMM, but they do not understand why the incidence continues to increase despite the increased use of sunscreens and formulations offering more protection. This paradox, along with lower incidences of CMM in outdoor workers, although they have significantly higher annual UV doses than indoor workers have, perplexes scientists. We found a temporal exponential increase in the CMM incidence indicating second-order reaction kinetics revealing the existence of 2 major risk factors. From epidemiology studies, we know one major risk factor for getting CMM is poor tanning ability and we now propose the other major risk factor may be the Human Papilloma Virus (HPV) because clinicians find β HPVs in over half the biopsies. Moreover, we uncovered yet another paradox; the increasing CMM incidences significantly correlate with decreasing personal annual UV dose, a proxy for low vitamin D3 levels. We also discovered the incidence of CMM significantly increased with decreasing personal annual UV dose from 1960, when it was almost insignificant, to 2000. UV and other DNA-damaging agents can activate viruses, and UV-induced cytokines can hide HPV from immune surveillance, which may explain why CMM also occurs in anatomical locations where the sun does not shine. Thus, we propose the 2 major risk factors for getting CMM are intermittent UV exposures that result in low cutaneous levels of vitamin D3 and possibly viral infection. PMID:26413188
Correlated wave functions for the ground and some excited states of the iron atom.
Buendía, E; Gálvez, F J; Sarsa, A
2006-04-21
We study the states arising from the [Ar]4s(2)3d6 and [Ar]4s(1)3d7 configurations of iron atom with explicitly correlated wave functions. The variational wave function is the product of the Jastrow correlation factor times a model function obtained within the parametrized optimized effective potential framework. A systematic analysis of the dependence of both the effective potential and the correlation factor on the configuration and on the term is carried out. The ground state of both, the cation, Fe+, and anion, Fe-, are calculated with correlated wave functions and the ionization potential and the electron affinity are obtained.
Waves in a bounded quantum plasma with electron exchange-correlation effects
Ma Yutng; Mao Shenghng; Xue Juji
2011-10-15
Within a quantum hydrodynamic model, the collective excitations of the quantum plasma with electron exchange-correlation effects in a nano-cylindrical wave guide are studied both analytically and numerically. The influences of the electron exchange-correlation potential, the radius of the wave guide, and the quantum effect on the dispersion properties of the bounded quantum plasma are discussed. Significant frequency-shift induced by the electron exchange-correlation effect, the radius of the wave guide and the quantum correction are observed. It is found that the influence of the electron exchange-correlation, the radius of the wave guide and the quantum correction on the wave modes in a bounded nano-waveguide are strongly coupled.
An Exceptional Exponential Function
ERIC Educational Resources Information Center
Curgus, Branko
2006-01-01
We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…
NASA Astrophysics Data System (ADS)
Schaefer, Bradley E.; Dyson, Samuel E.
1996-08-01
A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.
McCartin, B.J.
1996-12-31
Herein, we discuss a generalization of the semiclassical cubic spline known in the literature as the exponential spline. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain {open_quotes}tension{close_quotes} parameters. We first outline the theoretical underpinnings of the exponential spline. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. We next discuss the numerical computation of the exponential spline. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines. We conclude with a consideration of the broad spectrum of possible uses of exponential splines in the applications. Our primary emphasis is on computational fluid dynamics although the imaginative reader will recognize the wider generality of the techniques developed.
Four-body correlation embedded in antisymmetrized geminal power wave function.
Kawasaki, Airi; Sugino, Osamu
2016-12-28
We extend the Coleman's antisymmetrized geminal power (AGP) to develop a wave function theory that can incorporate up to four-body correlation in a region of strong correlation. To facilitate the variational determination of the wave function, the total energy is rewritten in terms of the traces of geminals. This novel trace formula is applied to a simple model system consisting of one dimensional Hubbard ring with a site of strong correlation. Our scheme significantly improves the result obtained by the AGP-configuration interaction scheme of Uemura et al. and also achieves more efficient compression of the degrees of freedom of the wave function. We regard the result as a step toward a first-principles wave function theory for a strongly correlated point defect or adsorbate embedded in an AGP-based mean-field medium.
Spatial correlation of shear-wave velocity in the San Francisco Bay Area sediments
Thompson, E.M.; Baise, L.G.; Kayen, R.E.
2007-01-01
Ground motions recorded within sedimentary basins are variable over short distances. One important cause of the variability is that local soil properties are variable at all scales. Regional hazard maps developed for predicting site effects are generally derived from maps of surficial geology; however, recent studies have shown that mapped geologic units do not correlate well with the average shear-wave velocity of the upper 30 m, Vs(30). We model the horizontal variability of near-surface soil shear-wave velocity in the San Francisco Bay Area to estimate values in unsampled locations in order to account for site effects in a continuous manner. Previous geostatistical studies of soil properties have shown horizontal correlations at the scale of meters to tens of meters while the vertical correlations are on the order of centimeters. In this paper we analyze shear-wave velocity data over regional distances and find that surface shear-wave velocity is correlated at horizontal distances up to 4 km based on data from seismic cone penetration tests and the spectral analysis of surface waves. We propose a method to map site effects by using geostatistical methods based on the shear-wave velocity correlation structure within a sedimentary basin. If used in conjunction with densely spaced shear-wave velocity profiles in regions of high seismic risk, geostatistical methods can produce reliable continuous maps of site effects. ?? 2006 Elsevier Ltd. All rights reserved.
Haney, Matthew M.; Mikesell, T. Dylan; van Wijk, Kasper; Nakahara, Hisashi
2012-01-01
Using ambient seismic noise for imaging subsurface structure dates back to the development of the spatial autocorrelation (SPAC) method in the 1950s. We present a theoretical analysis of the SPAC method for multicomponent recordings of surface waves to determine the complete 3 × 3 matrix of correlations between all pairs of three-component motions, called the correlation matrix. In the case of isotropic incidence, when either Rayleigh or Love waves arrive from all directions with equal power, the only non-zero off-diagonal terms in the matrix are the vertical–radial (ZR) and radial–vertical (RZ) correlations in the presence of Rayleigh waves. Such combinations were not considered in the development of the SPAC method. The method originally addressed the vertical–vertical (ZZ), RR and TT correlations, hence the name spatial autocorrelation. The theoretical expressions we derive for the ZR and RZ correlations offer additional ways to measure Rayleigh wave dispersion within the SPAC framework. Expanding on the results for isotropic incidence, we derive the complete correlation matrix in the case of generally anisotropic incidence. We show that the ZR and RZ correlations have advantageous properties in the presence of an out-of-plane directional wavefield compared to ZZ and RR correlations. We apply the results for mixed-component correlations to a data set from Akutan Volcano, Alaska and find consistent estimates of Rayleigh wave phase velocity from ZR compared to ZZ correlations. This work together with the recently discovered connections between the SPAC method and time-domain correlations of ambient noise provide further insights into the retrieval of surface wave Green’s functions from seismic noise.
ERIC Educational Resources Information Center
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Spatial correlation of shear-wave velocity within San Francisco Bay Sediments
Thompson, E.M.; Baise, L.G.; Kayen, R.E.
2006-01-01
Sediment properties are spatially variable at all scales, and this variability at smaller scales influences high frequency ground motions. We show that surface shear-wave velocity is highly correlated within San Francisco Bay Area sediments using shear-wave velocity measurements from 210 seismic cone penetration tests. We use this correlation to estimate the surface sediment velocity structure using geostatistics. We find that the variance of the estimated shear-wave velocity is reduced using ordinary kriging, and that including this velocity structure in 2D ground motion simulations of a moderate sized earthquake improves the accuracy of the synthetics. Copyright ASCE 2006.
Wang, Hailong; Cao, Leiming; Jing, Jietai
2017-01-01
We theoretically characterize the performance of the pairwise correlations (PCs) from multiple quantum correlated beams based on the cascaded four-wave mixing (FWM) processes. The presence of the PCs with quantum corre- lation in these systems can be verified by calculating the degree of intensity difference squeezing for any pair of all the output fields. The quantum correlation characteristics of all the PCs under different cascaded schemes are also discussed in detail and the repulsion effect between PCs in these cascaded FWM processes is theoretically predicted. Our results open the way for the classification and application of quantum states generated from the cascaded FWM processes. PMID:28071759
NASA Astrophysics Data System (ADS)
Smith, Clint; Edwards, Jarrod; Fisher, Andmorgan
2010-04-01
Rapid detection of biological material is critical for determining presence/absence of bacterial endospores within various investigative programs. Even more critical is that if select material tests positive for bacillus endospores then tests should provide data at the species level. Optical detection of microbial endospore formers such as Bacillus sp. can be heavy, cumbersome, and may only identify at the genus level. Data provided from this study will aid in characterization needed by future detection systems for further rapid breakdown analysis to gain insight into a more positive signature collection of Bacillus sp. Literature has shown that fluorescence spectroscopy of endospores could be statistically separated from other vegetative genera, but could not be separated among one another. Results of this study showed endospore species separation is possible using laser-induce fluorescence with lifetime decay analysis for Bacillus endospores. Lifetime decays of B. subtilis, B. megaterium, B. coagulans, and B. anthracis Sterne strain were investigated. Using the Multi-Exponential fit method data showed three distinct lifetimes for each species within the following ranges, 0.2-1.3 ns; 2.5-7.0 ns; 7.5-15.0 ns, when laser induced at 307 nm. The four endospore species were individually separated using principle component analysis (95% CI).
Correlation coefficient measurement of the mode-locked laser tones using four-wave mixing.
Anthur, Aravind P; Panapakkam, Vivek; Vujicic, Vidak; Merghem, Kamel; Lelarge, Francois; Ramdane, Abderrahim; Barry, Liam P
2016-06-01
We use four-wave mixing to measure the correlation coefficient of comb tones in a quantum-dash mode-locked laser under passive and active locked regimes. We study the uncertainty in the measurement of the correlation coefficient of the proposed method.
The correlations between the saturated and dry P-wave velocity of rocks.
Kahraman, S
2007-11-01
Sometimes engineers need to estimate the wet-rock P-wave velocity from the dry-rock P-wave velocity. An estimation equation embracing all rock classes will be useful for the rock engineers. To investigate the predictability of wet-rock P-wave velocity from the dry-rock P-wave velocity, P-wave velocity measurements were performed on 41 different rock types, 11 of which were igneous, 15 of which were sedimentary and 15 of which was metamorphic. In addition to the dry- and wet-rock P-wave velocity measurements, the P-wave velocity changing as a function of saturation degree was studied. Moreover, dry-rock S-wave velocity measurements were conducted. The test results were modeled using Gassmann's and Wood's theory and it was seen that the measured data did not fit the theories. The unconformity is due to the fact that the theories are valid for high-porosity unconsolidated sediments at low frequencies. Gassmann's equation was modified for the rocks except high-porosity unconsolidated sediments. The dry- and wet-rock P-wave velocity values were evaluated using regression analysis. A strong linear correlation between the dry- and wet-rock P-wave velocities was found. Regression analyses were repeated for the rock classes and it was shown that correlation coefficients were increased. Concluding remark is that the derived equations can be used for the prediction of wet-rock P-wave velocity from the dry-rock P-wave velocity.
Phase correlator reduces mm-wave radar cost
NASA Astrophysics Data System (ADS)
Weiss, R., Sr.; Hobbs, P.; Locatelli, J.
1986-03-01
A technique involving the IC storage of magnetron phase for reference has been developed to make possible the use of the low-cost efficient magnetron in obtaining phase coherent signals for pulse Doppler radar. In the new external coherence method, the recorded random midpulse-region phase is compared with the frequency of the echo allowing Doppler information, free of phase noise, to be extracted. The gated magnetron was tested at Ka-band in a 35-GHz radar, and good agreement with the CP-4 5.5 GHz radar was shown. With good accuracy down to 10 cm/s, the present system, especially in the mm-wave region, has important applications to meteorological and military radar.
Correlated electron-nuclear dynamics with conditional wave functions.
Albareda, Guillermo; Appel, Heiko; Franco, Ignacio; Abedi, Ali; Rubio, Angel
2014-08-22
The molecular Schrödinger equation is rewritten in terms of nonunitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear) trajectories. This scheme is exact and does not rely on the tracing out of degrees of freedom. Hence, the use of trajectory-based statistical techniques can be exploited to circumvent the calculation of the computationally demanding Born-Oppenheimer potential-energy surfaces and nonadiabatic coupling elements. The concept of the potential-energy surface is restored by establishing a formal connection with the exact factorization of the full wave function. This connection is used to gain insight from a simplified form of the exact propagation scheme.
Automatic determination of important mode-mode correlations in many-mode vibrational wave functions.
König, Carolin; Christiansen, Ove
2015-04-14
We introduce new automatic procedures for parameterizing vibrational coupled cluster (VCC) and vibrational configuration interaction wave functions. Importance measures for individual mode combinations in the wave function are derived based on upper bounds to Hamiltonian matrix elements and/or the size of perturbative corrections derived in the framework of VCC. With a threshold, this enables an automatic, system-adapted way of choosing which mode-mode correlations are explicitly parameterized in the many-mode wave function. The effect of different importance measures and thresholds is investigated for zero-point energies and infrared spectra for formaldehyde and furan. Furthermore, the direct link between important mode-mode correlations and coordinates is illustrated employing water clusters as examples: Using optimized coordinates, a larger number of mode combinations can be neglected in the correlated many-mode vibrational wave function than with normal coordinates for the same accuracy. Moreover, the fraction of important mode-mode correlations compared to the total number of correlations decreases with system size. This underlines the potential gain in efficiency when using optimized coordinates in combination with a flexible scheme for choosing the mode-mode correlations included in the parameterization of the correlated many-mode vibrational wave function. All in all, it is found that the introduced schemes for parameterizing correlated many-mode vibrational wave functions lead to at least as systematic and accurate calculations as those using more standard and straightforward excitation level definitions. This new way of defining approximate calculations offers potential for future calculations on larger systems.
Shear wave velocities from noise correlation at local scale
De Nisco, G.; Nunziata, C.; Vaccari, F.; Panza, G. F.
2008-07-08
Cross correlations of ambient seismic noise recordings have been studied to infer shear seismic velocities with depth. Experiments have been done in the crowded and noisy historical centre of Napoli over inter-station distances from 50 m to about 400 m, whereas active seismic spreadings are prohibitive, even for just one receiver. Group velocity dispersion curves have been extracted with FTAN method from the noise cross correlations and then the non linear inversion of them has resulted in Vs profiles with depth. The information of near by stratigraphies and the range of Vs variability for samples of Neapolitan soils and rocks confirms the validity of results obtained with our expeditious procedure. Moreover, the good comparison of noise H/V frequency of the first main peak with 1D and 2D spectral amplifications encourages to continue experiments of noise cross-correlation. If confirmed in other geological settings, the proposed approach could reveal a low cost methodology to obtain reliable and detailed Vs velocity profiles.
Exponentially fitted symplectic integrator
NASA Astrophysics Data System (ADS)
Simos, T. E.; Vigo-Aguiar, Jesus
2003-01-01
In this paper a procedure for constructing efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the exponential fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge-Kutta-Nyström second-order algebraic exponentially fitted method is developed. We give explicitly the symplecticness conditions for the modified Runge-Kutta-Nyström method. We also give the exponential fitting and trigonometric fitting conditions. Numerical results indicate that the present method is much more efficient than the “classical” symplectic Runge-Kutta-Nyström second-order algebraic method introduced by M.P. Calvo and J.M. Sanz-Serna [J. Sci. Comput. (USA) 14, 1237 (1993)]. We note that the present procedure is appropriate for all near-unimodal systems.
NASA Astrophysics Data System (ADS)
Yuzurihara, Hirotaka; Hayama, Kazuhiro; Mano, Shuhei; Verkindt, Didier; Kanda, Nobuyuki
2016-08-01
Noise hunting is a critical requirement for realizing design sensitivity of a detector, and consequently, noise origins and its features have been revealed partially. Among the noise sources to be hunted, sources of nonlinearly correlated noise, such up-conversion noise, are hard to find and can limit the sensitivity of gravitational wave searches with advanced detectors. We propose using a correlation analysis method called maximal information coefficient (MIC) to find both nonlinear and linear correlations. We apply MIC to the scattered light noise correlated between the seismic activity and the strain signal, which limited the sensitivity of the Virgo detector during the first science run. The results show that MIC can find nonlinearly correlated noise more efficiently than the Pearson correlation method. When the data is linearly correlated, the efficiency of the Pearson method and MIC is comparable. On the other hand, when the data is known to be nonlinearly correlated, MIC finds the correlation while the Pearson method fails completely.
Wave Correlation Effects in Active Microwave Remote Sensing of the Environment.
NASA Astrophysics Data System (ADS)
Khadr, Nagi Mahmoud
This study examines the wave correlation effects that arise in active microwave remote sensing of the environment. These correlation effects, or coherent interference effects, are not accounted for by the regular phenomenological transport and radar equations, in which intensities, as a rule, are added incoherently. In particular, two types of correlation effects are examined: those associated with the medium and those associated with the source. The study method is the analytical wave approach to propagation and scattering from random media. This entails using Maxwell's equations to arrive at expressions for the first and second moments of the field. Unlike previous studies, however, in which plane wave incidence is assumed, here the radar is directly incorporated into the analytical wave formulation, and the antenna fields replaced via their plane wave representations. In this way, analysis of both the medium and source correlation effects on a per plane wave basis becomes a straightforward matter. The medium correlation effects are responsible for backscatter enhancement. Although the enhancement effect has been studied before on numerous occasions, careful characterization of the enhancement for microwave scattering from environmental scenes, such as vegetation canopies, has been lacking. The study at hand therefore fills this void and, in addition, quantifies the influence of this enhancement on phase difference statistics, a new and potentially important environmental remote sensing tool. The source correlation effects arise as a result of both the nature of the source and the geometry of the particular problem. By including these effects, a more general expression than the radar equation is obtained analytically. Quantitative examples show that, under certain circumstances, the results of this general expression deviate substantially from the results provided by the radar equation. This finding verifies the importance of considering source correlation
Wave energy level and geographic setting correlate with Florida beach water quality.
Feng, Zhixuan; Reniers, Ad; Haus, Brian K; Solo-Gabriele, Helena M; Kelly, Elizabeth A
2016-03-15
Many recreational beaches suffer from elevated levels of microorganisms, resulting in beach advisories and closures due to lack of compliance with Environmental Protection Agency guidelines. We conducted the first statewide beach water quality assessment by analyzing decadal records of fecal indicator bacteria (enterococci and fecal coliform) levels at 262 Florida beaches. The objectives were to depict synoptic patterns of beach water quality exceedance along the entire Florida shoreline and to evaluate their relationships with wave condition and geographic location. Percent exceedances based on enterococci and fecal coliform were negatively correlated with both long-term mean wave energy and beach slope. Also, Gulf of Mexico beaches exceeded the thresholds significantly more than Atlantic Ocean ones, perhaps partially due to the lower wave energy. A possible linkage between wave energy level and water quality is beach sand, a pervasive nonpoint source that tends to harbor more bacteria in the low-wave-energy environment.
Dynamic cross correlation studies of wave particle interactions in ULF phenomena
NASA Technical Reports Server (NTRS)
Mcpherron, R. L.
1979-01-01
Magnetic field observations made by satellites in the earth's magnetic field reveal a wide variety of ULF waves. These waves interact with the ambient particle populations in complex ways, causing modulation of the observed particle fluxes. This modulation is found to be a function of species, pitch angle, energy and time. The characteristics of this modulation provide information concerning the wave mode and interaction process. One important characteristic of wave-particle interactions is the phase of the particle flux modulation relative to the magnetic field variations. To display this phase as a function of time a dynamic cross spectrum program has been developed. The program produces contour maps in the frequency time plane of the cross correlation coefficient between any particle flux time series and the magnetic field vector. This program has been utilized in several studies of ULF wave-particle interactions at synchronous orbit.
Exponential Localization of Photons
NASA Astrophysics Data System (ADS)
Bialynicki-Birula, Iwo
1998-06-01
It is shown that photons can be localized in space with an exponential falloff of the energy density and photodetection rates. The limits of localization are determined by the fundamental Paley-Wiener theorem. A direct mathematical connection between the spatial localization of photons and the decay in time of quantum mechanical systems is established.
Surface waves on quantum plasma half-space with electron exchange-correlation effects
Khalilpour, H.
2015-12-15
The propagation of surface waves on a quantum plasma half-space is investigated, taking into account the electron exchange-correlation effect. Using the modified quantum hydrodynamic model in conjunction with the Poisson equation, the dispersion relation of surface waves is obtained. It is found that due to the presence of electron exchange-correlation effect the wave frequency is shifted to lower frequencies. For different ranges of Brueckner parameter r{sub s}, the effect of electron exchange-correlation is investigated. It is indicated that for weak coupling region with r{sub s} < 0.1, the wave frequency remains unchanged and in this region the effect of electron exchange-correlation is negligible. For moderate coupling region, i.e., (0.1 < r{sub s} < 1), the influence of electron exchange-correlation is important and as r{sub s} increases, the electron exchange-correlation effect also increases.
Li, Jia; Chen, Feinan; Chang, Liping
2016-10-17
Within the validity of the first-order Born approximation, expressions are derived for the correlation between intensity fluctuations (CIF) of an electromagnetic plane wave scattered from a spatially quasi-homogeneous (QH), anisotropic medium. Upon establishing the correlation matrix of the scattering potential of the medium, we show that the CIF is the summation of Fourier transforms of the strengths and normalized correlation coefficients (NCCs) of the scattering potential matrix. Numerical results reveal that the CIF is susceptible to the effective width and correlation length of the medium, and degree of polarization of the incident electromagnetic wave. Our study not only extends the current knowledge of the CIF of a scattered field but also provides an important reference to the study of high-order intensity correlations of light scattered from a spatially anisotropic medium.
NASA Astrophysics Data System (ADS)
Gough, M.; Buckley, A.; Carozzi, T.; Beloff, N.
The technique of particle correlation measures directly electron modulations that result from naturally occurring and actively stimulated wave-particle interactions in space plasmas. In the past this technique has been used for studies of beam-plasma interactions, caused by both natural auroral electron beams via sounding rockets and by artificially generated electron beams on Shuttle missions: TSS-1/-TSS-1R. It has also been applied to studies of how electrons become energised by waves injected from in-situ transmitters (OEDIPUS-C). All four ESA Cluster-II spacecraft launched in 2000 to study the outer magnetosphere, cusp, and bow shock were implemented with electron correlators. Here the prevalent broader band wave-particle interactions have been more difficult to extract. However, the application of new statistical algorithms has permitted these correlators to provide a novel insight into turbulence occurring and also provided an independent means whereby electron count rates can be corrected for detector saturation effects.
Casanova, David; Krylov, Anna I.
2016-01-07
A new method for quantifying the contributions of local excitation, charge resonance, and multiexciton configurations in correlated wave functions of multichromophoric systems is presented. The approach relies on fragment-localized orbitals and employs spin correlators. Its utility is illustrated by calculations on model clusters of hydrogen, ethylene, and tetracene molecules using adiabatic restricted-active-space configuration interaction wave functions. In addition to the wave function analysis, this approach provides a basis for a simple state-specific energy correction accounting for insufficient description of electron correlation. The decomposition scheme also allows one to compute energies of the diabatic states of the local excitonic, charge-resonance, and multi-excitonic character. The new method provides insight into electronic structure of multichromophoric systems and delivers valuable reference data for validating excitonic models.
Salvi, Paolo; Palombo, Carlo; Salvi, Giovanni Matteo; Labat, Carlos; Parati, Gianfranco; Benetos, Athanase
2013-12-01
Several studies showed a positive association between heart rate and pulse wave velocity, a sensitive marker of arterial stiffness. However, no study involving a large population has specifically addressed the dependence of pulse wave velocity on different components of the cardiac cycle. The aim of this study was to explore in subjects of different age the link between pulse wave velocity with heart period (the reciprocal of heart rate) and the temporal components of the cardiac cycle such as left ventricular ejection time and diastolic time. Carotid-femoral pulse wave velocity was assessed in 3,020 untreated subjects (1,107 men). Heart period, left ventricular ejection time, diastolic time, and early-systolic dP/dt were determined by carotid pulse wave analysis with high-fidelity applanation tonometry. An inverse association was found between pulse wave velocity and left ventricular ejection time at all ages (<25 years, r(2) = 0.043; 25-44 years, r(2) = 0.103; 45-64 years, r(2) = 0.079; 65-84 years, r(2) = 0.044; ≥ 85 years, r(2) = 0.022; P < 0.0001 for all). A significant (P < 0.0001) negative but always weaker correlation between pulse wave velocity and heart period was also found, with the exception of the youngest subjects (P = 0.20). A significant positive correlation was also found between pulse wave velocity and dP/dt (P < 0.0001). With multiple stepwise regression analysis, left ventricular ejection time and dP/dt remained the only determinant of pulse wave velocity at all ages, whereas the contribution of heart period no longer became significant. Our data demonstrate that pulse wave velocity is more closely related to left ventricular systolic function than to heart period. This may have methodological and pathophysiological implications.
Ambient Noise Cross-correlation Surface Wave Tomography of the Continental United States and Alaska.
NASA Astrophysics Data System (ADS)
Bensen, G. D.; McCoy, C.; Ritzwoller, M. H.; Levshin, A. L.; Barmin, M. P.; Shapiro, N. M.
2006-12-01
The recent development of surface wave tomography based on ambient noise cross-correlations has provided good results on regional scales and relatively short periods less than 40 seconds. This technique however is viable at longer periods and on the continental scale. We present dispersion maps from ambient noise cross- correlation surface-wave tomography for the continental United States and Alaska between 10 and 60 seconds period. Using up to 2 years of data from over 250 permanent and temporary stations obtained from the IRIS DMC and the Canadian National Seismic Network we compute cross-correlations for all station pairs. An automated dispersion analysis technique is applied to obtain Rayleigh wave group and phase speed curves and unacceptable measurements are removed. Dispersion curves from over 12,500 paths are retained in the continental US and about 1,000 cross-correlation and earthquake paths result in Alaska. We obtain isotropic Rayleigh wave group and phase speed maps on a one half degree grid using a damped ray theoretical inversion. Compared to previous teleseismic earthquake techniques, the short period maps provide better resolution of smaller scale features, especially those in the crust. The improved path coverage also enhances resolution at longer periods compared to previous maps with better delineation of tectonic provinces. In Alaska, limited station coverage and earthquake distribution confine the results to the south-central part of the state. Preliminary azimuthally anisotropic Rayleigh wave tomography maps are also presented together with an assessment of their robustness.
The correlation of VLF propagation variations with atmospheric planetary-scale waves
NASA Technical Reports Server (NTRS)
Cavalieri, D. J.; Deland, R. J.; Potemra, T. A.; Gavin, R. F.
1973-01-01
Variations in the received daytime phase of long distance, cesium-controlled, VLF transmission were compared to the height variations of the 10-mb isobaric surface during the first three months of 1965 and 1969. The VLF phase values are also compared to height variations of constant electron densities in the E-region and to variations of f-min which have been shown to be well correlated with planetary-scale variations in the stratosphere by Deland and Cavalieri (1973). The VLF phase variations show good correlation with these previous ionospheric measurements and with the 10-mb surfaces. The planetary scale waves in the stratosphere are shown to be travelling on the average eastward in 1965 and westward in 1969. These correlations are interpreted as due to the propagation of travelling planetary scale waves with westward tilted wave fronts. Upward energy transport due to the vertical structure of those waves is also discussed. These correlations provide further evidence for the coupling between the lower ionosphere at about 70 km altitude (the daytime VLF reflection height and the stratosphere, and they demonstrate the importance of planetary wave phenomena to VLF propagation.
Small-scale seismic inversion using surface waves extracted from noise cross correlation.
Gouédard, Pierre; Roux, Philippe; Campillo, Michel
2008-03-01
Green's functions can be retrieved between receivers from the correlation of ambient seismic noise or with an appropriate set of randomly distributed sources. This principle is demonstrated in small-scale geophysics using noise sources generated by human steps during a 10-min walk in the alignment of a 14-m-long accelerometer line array. The time-domain correlation of the records yields two surface wave modes extracted from the Green's function between each pair of accelerometers. A frequency-wave-number Fourier analysis yields each mode contribution and their dispersion curve. These dispersion curves are then inverted to provide the one-dimensional shear velocity of the near surface.
Mapping Global and Regional Correlations Between MORB Helium Isotopes and Seismic Wave Speeds
NASA Astrophysics Data System (ADS)
Williams, C. D.; Mukhopadhyay, S.; Romanowicz, B. A.
2015-12-01
The global mid-ocean ridge system stretches over 65,000 km and randomly samples the Earth's mantle. Compositional variations observed in mid-ocean ridge basalts reflect complex relationships between the thermal, compositional, and dynamical state of the mantle. In this study, we compare globally distributed ridge segment averaged helium isotopic compositions with shear-wave velocities, at both the global and regional scale. Our goal is to understand how temperature, composition and mantle flow control the distribution of helium isotopic compositions in basalts erupted at mid-ocean ridges. The global dataset displays a strong correlation between helium isotopes and the underlying shear-wave velocities in the upper mantle with the most prominent correlations corresponding to depths between ~200 to 700 km. A similar, but less pronounced feature, is observed in the mid-mantle at depths of ~1000 to 1500 km. The exclusion of MORBs influenced by hotspots slightly reduces the magnitude of the global correlations observed between helium isotopes and shear-wave velocities in the upper mantle (though a statistically significant correlation still remains), while slightly intensifying the correlation at mid-mantle depths. Data grouped by individual ocean basin exhibit distinct geochemical-seismological correlations. Mid-ocean ridge basalts from the Atlantic and Indian oceans display similar features as the global correlation and dominate the global upper mantle correlations. However, in the Pacific ocean, the most dominant feature is a correlation between helium isotopes and shear-wave velocities at depths between ~750 to 1500 km. In the Atlantic, temperature appears to be the primary driver of helium isotope variability, even when influence from hotspots is removed. However, it still remains unclear what controls helium isotope variability in the Pacific.
Perring, S; Jones, E
2009-11-01
We have implemented the technique of rolling correlation coefficient as proposed by Buttfield and Bolton (2005 Real time measurement of RR intervals using a digital signal processor J. Med. Eng. Technol. 29 8-13) for ECG R-wave detection in the detection and timing of oesophageal peristalsis. 43 sequential patients attending for oesophageal manometry were retrospectively reviewed. Two expert reviewers visually assessed each swallow for normality of peristaltic amplitude and propagation speed. Automatic assessment was performed using rolling correlation, maximum amplitude, threshold and maximum gradient techniques of identifying onset of peristalsis. Rolling correlation was comparable with the maximum amplitude technique at identifying peristaltic pressure waves visually identified as present. Rolling correlation was most effective at correctly identifying propagation velocity as normal (698 out of 845 normally propagating waves) and highest correlation with expert visual assessment of percentage abnormal propagation for each patient (R value 0.918). In a sub-group of 11 studies assessed as displaying normal motility, rolling correlation gave lowest variation of propagation speed and highest consistency with visual assessment. The rolling correlation technique is effective and accurate at identifying oesophageal peristalsis and characterizing peristaltic propagation in manometric studies even in the presence of abnormally weak peristalsis and other confounding pressure perturbations.
Correlation between opposite-helicity gravitons: Imprints on gravity-wave and microwave backgrounds
NASA Astrophysics Data System (ADS)
Gubitosi, Giulia; Magueijo, João
2017-01-01
We examine some of the roots of parity violation for gravitons and uncover a closely related new effect: correlations between right- and left-handed gravitons. Such correlators have spin 4 if they involve gravitons moving along the same direction and spin zero for gravitons moving with opposite directions. In the first case, the most immediate implication would be a degree of linear polarization for the tensor vacuum fluctuations, which could be seen by gravity-wave detectors sensitive enough to probe the primordial background, its degree of polarization and anisotropies. Looking at the anisotropy of the gravity waves linear polarization, we identify the parity respecting and violating components of the effect. The imprint on the cosmic microwave background temperature and polarization would be more elusive, since it averages to zero in the two-point functions, appearing only in their cosmic variance or in fourth-order correlators. In contrast, spin-zero correlations would have an effect on the two-point function of the cosmic microwave background temperature and polarization, enhancing the B B component if they were anticorrelations. Such correlations represent an amplitude for the production of standing waves, as first envisaged by Grishchuk, and could also leave an interesting signature for gravity-wave detectors.
NASA Astrophysics Data System (ADS)
Gough, M. P.; Buckley, A. M.; Carozzi, T.; Beloff, N.
The technique of particle correlation measures directly electron modulations that result from naturally occurring and actively stimulated wave-particle interactions in space plasmas. In the past this technique has been used for studies of beam-plasma interactions, caused by both natural auroral electron beams via sounding rockets and by artificially generated electron beams on Space Shuttle missions (STS-46, STS-75). It has also been applied to studies of how electrons become energised by waves injected from in-situ transmitters (e.g OEDIPUS-C sounding rocket). All four ESA Cluster-II spacecraft launched in 2000 to study the outer magnetosphere, cusp, and bow shock were implemented with electron correlators. Here the prevalent weaker wave-particle interactions have been more difficult to extract, however, the application of new statistical algorithms has permitted these correlators to provide a novel insight into the plasma turbulence that occurs. Present work involves technical improvements to both sensor design and correlator implementation that enable many electron energy-angle combinations to be simultaneously monitored for wave-particle interactions. A broad energy-angle range spectrograph connected to a multi-channel, multi-frequency range FPGA implemented array of correlators is scheduled to fly early 2004. Neural network techniques previously flown on STS-46 and STS-75, and statistical tests developed for Cluster-II will be used on-board to select data to be transmitted.
NASA Astrophysics Data System (ADS)
Gough, M.; Buckley, A.; Carozzi, T.; Beloff, N.
The technique of particle correlation measures directly electron modulations that result from naturally occurring and actively stimulated wave-particle interactions in space plasmas. In the past this technique has been used for studies of beam-plasma interactions, caused by both natural auroral electron beams via sounding rockets and by artificially generated electron beams on Shuttle missions: TSS-1/-TSS -1R. It has also been applied to studies of how electrons become energised by waves injected from in-situ transmitters (OEDIPUS-C). All four ESA Cluster-II spacecraft launched in 2000 to study the outer magnetosphere, cusp, and bow shock were implemented with electron correlators. Here the prevalent broader band wave-particle interactions have been more difficult to extract. However, the application of new statistical algorithms has permitted these correlators to provide a novel insight into turbulence occurring and also provided an independent means whereby electron count rates can be corrected for detector saturation effects. Present work involves technical improvements to both sensor design and correlator implementation that enable many electron energy-angle combinations to be simultaneously monitored for wave-particle interactions. A b oad energy -angler range spectrograph connected to a multi-channel, multi-frequency range FPGA implemented array of correlators is scheduled to fly early 2004. Neural network techniques previously flown on TSS -1 , TSS-1R, and statistical tests developed for Cluster-II will be used on-board to select data to be transmitted.
Controlling correlations in the Rydberg-dressing six-wave mixing process
NASA Astrophysics Data System (ADS)
Zhang, Zhaoyang; Ma, Danmeng; Liu, Junfeng; Ahmed, Irfan; Tian, Hao; Che, Junling; Tang, Haijun; Raza, Faizan; Zhang, Yanpeng
2017-01-01
We report the experimental observation of intensity noise correlation between six-wave mixing (SWM), fluorescence and probe transmission signal in a coherently prepared Rydberg atomic ensemble. With the assistance of the electromagnetically induced transparency (EIT) technique, the Rydberg SWM is generated with high efficiency. Then the correlation between the probe transmission and SWM, the anti-correlation between the probe and fluorescence, and the anti-correlation between SWM and fluorescence occur, with these being caused by the enhanced dispersion and nonlinearity in the Rydberg-EIT medium. Such intensity correlation can be effectively controlled by the strong Rydberg-dressing effect. This investigation can potentially contribute to the further study of multi-field quantum correlations and anti-correlations via atomic spin coherence.
Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons
NASA Astrophysics Data System (ADS)
Ma, Tianxing; Yang, Fan; Huang, Zhongbing; Lin, Hai-Qing
2017-02-01
We reveal an edge spin triplet p–wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.
Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons
Ma, Tianxing; Yang, Fan; Huang, Zhongbing; Lin, Hai-Qing
2017-01-01
We reveal an edge spin triplet p–wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling. PMID:28186185
Viscosity, Shear Waves, and Atomic-Level Stress-Stress Correlations
NASA Astrophysics Data System (ADS)
Levashov, V. A.; Morris, J. R.; Egami, T.
2011-03-01
The Green-Kubo equation relates the macroscopic stress-stress correlation function to a liquid’s viscosity. The concept of the atomic-level stresses allows the macroscopic stress-stress correlation function in the equation to be expressed in terms of the space-time correlations among the atomic-level stresses. Molecular dynamics studies show surprisingly long spatial extension of stress-stress correlations and also longitudinal and transverse waves propagating in liquids over ranges which could exceed the system size. The results reveal that the range of propagation of shear waves corresponds to the range of distances relevant for viscosity. Thus our results show that viscosity is a fundamentally nonlocal quantity. We also show that the periodic boundary conditions play a nontrivial role in molecular dynamics simulations, effectively masking the long-range nature of viscosity.
NASA Technical Reports Server (NTRS)
Shertzer, Janine; Temkin, Aaron
2007-01-01
In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.
Kinetic correlation in the final-state wave function in photo-double-ionization of He
Otranto, S.; Garibotti, C. R.
2003-06-01
We evaluate the triply differential cross section (TDCS) for photo-double-ionization of helium. We use a final continuum wave function which correlates the motion of the three particles, through an expansion in products of two-body Coulomb functions. This function satisfies a set of appropriate physical conditions in the coalescence points, in addition to the correct asymptotic behavior condition. We analyze the effect of this correlation in the TDCS and compare our results with experimental data.
NASA Astrophysics Data System (ADS)
Nakata, Nori; Boué, Pierre; Brenguier, Florent; Roux, Philippe; Ferrazzini, Valérie; Campillo, Michel
2016-02-01
Body wave reconstruction from ambient seismic noise correlations is an important step toward improving volcano imaging and monitoring. Here we extract body and surface waves that propagate in Piton de la Fournaise volcano on La Réunion island using ambient noise cross correlation and array-processing techniques. Ambient noise was continuously recorded at three dense arrays, each comprising 49 geophones. To identify and enhance the Green's function from the ambient noise correlation, we apply a double beamforming (DBF) technique between the array pairs. The DBF allows us to separate surface and body waves, direct and reflected waves, and multipathing waves. Based on their azimuths and slownesses, we successfully extract body waves between all the combinations of arrays, including the wave that propagates through the active magmatic system of the volcano. Additionally, we identify the effects of uneven noise source distribution and interpret the surface wave reflections.
Empirical Synthesis of Green functions from the correlation of diffuse waves
NASA Astrophysics Data System (ADS)
Campillo, M.; Larose, E.; Margerin, L.; Paul, A.; van Tiggelen, B.; Derode, A.; Abers, G.
2003-12-01
We show the existence of long range field correlations in the seismic coda of regional records in both Mexico and Alaska. The cross-correlation tensor between the coda records at two points is measured for a set of distant earthquakes. Remarkably, while individual correlations have a random character, the source- averaged correlations exhibit deterministic arrivals that obey the same symmetry rules as the Green tensor between the two points. In addition, the arrival times of these waves coincide with propagating surface waves between the two stations. Thus, we propose to identify the averaged correlation signals with the surface wave part of the Green tensor. However, while time reversal symmetry theoretically imposes that the Green function appears at both negative and positive times, we find experimentally this symmetry to be broken when the distribution of earthquakes is not isotropic around the stations. We explain this observation by the long lasting anisotropy of the diffuse field. This point is further discussed in a companion paper where we prove both experimentally and theoretically that a dominant flux of energy coming from the source can persist in the late coda. Finally, we show that averaged cross-correlations of ambient noise enable the reconstruction of some coherent arrivals. These examples illustrate a novel empirical method that provides synthetic seismograms between two stations, without the knowledge of the precise location and origin times of the sources.
Correlation of stress-wave-emission characteristics with fracture aluminum alloys
NASA Technical Reports Server (NTRS)
Hartbower, C. E.; Reuter, W. G.; Morais, C. F.; Crimmins, P. P.
1972-01-01
A study to correlate stress wave emission characteristics with fracture in welded and unwelded aluminum alloys tested at room and cryogenic temperature is reported. The stress wave emission characteristics investigated were those which serve to presage crack instability; viz., a marked increase in:(1) signal amplitude; (2) signal repetition rate; and (3) the slope of cumulative count plotted versus load. The alloys were 7075-T73, 2219-T87 and 2014-T651, welded with MIG and TIG using 2319 and 4043 filler wire. The testing was done with both unnotched and part-through-crack (PTC) tension specimens and with 18-in.-dia subscale pressure vessels. In the latter testing, a real time, acoustic emission, triangulation system was used to locate the source of each stress wave emission. With such a system, multiple emissions from a given location were correlated with defects found by conventional nondestructive inspection.
NASA Astrophysics Data System (ADS)
Burston, Robert; Astin, Ivan; Mitchell, Cathryn; Alfonsi, Lucilla; Pedersen, Todd; Skone, Susan
2009-07-01
A model is developed of the gradient drift instability growth rate in the north polar cap ionosphere, utilizing a novel approach employing an ionospheric imaging algorithm. The growth rate values calculated by this model are in turn used to estimate how the amplitudes of actual gradient drift waves vary over time as the plasma drifts and the growth rates change with time. Ionospheric imaging is again used in order to determine plasma drift velocities. The final output from the model is in turn used to assess the linear correlation between the scintillation indices S4 and σ $\\phi$ recorded by several GPS L1 band scintillation receivers stationed in the north polar cap and mean gradient drift wave amplitudes. Four separate magnetic storm periods, totaling 13 days, are analyzed in this way. The results show weak but significant linear correlations between the mean wave amplitudes calculated and the observed scintillation indices at F layer altitudes.
A correlative investigation of the propagation of ULF wave power through the dayside magnetosphere
NASA Technical Reports Server (NTRS)
Engebretson, Mark J.
1992-01-01
Work performed from 1 Jan. - 30 Jun. 1992 is reported. The topics covered include the following: the radial pulsation study, the wave polarization study; radial boundaries of Pc 3-4 pulsations in the dayside magnetosphere; and source regions for correlated ULF-VLF pulsations.
Comments on 'Square-wave correlation phase detector with VLF atmospheric noise'
NASA Astrophysics Data System (ADS)
Kroenert, J. T.
1980-11-01
Calculated sine wave response data from Raab's paper (1979) are used to develop an algorithm for converting the outputs of a squarewave correlator into estimates of signal phase that is valid for all signal-to-noise ratios. The proposed algorithm is considerably simpler than three separate schemes suggested for low, intermediate, and high signal-to-noise ratio regions.
Correlated noise in networks of gravitational-wave detectors: Subtraction and mitigation
NASA Astrophysics Data System (ADS)
Thrane, E.; Christensen, N.; Schofield, R. M. S.; Effler, A.
2014-07-01
One of the key science goals of advanced gravitational-wave detectors is to observe a stochastic gravitational-wave background. However, recent work demonstrates that correlated magnetic fields from Schumann resonances can produce correlated strain noise over global distances, potentially limiting the sensitivity of stochastic background searches with advanced detectors. In this paper, we estimate the correlated noise budget for the worldwide advanced detector network and conclude that correlated noise may affect upcoming measurements. We investigate the possibility of a Wiener filtering scheme to subtract correlated noise from Advanced LIGO searches, and estimate the required specifications. We also consider the possibility that residual correlated noise remains following subtraction, and we devise an optimal strategy for measuring astronomical parameters in the presence of correlated noise. Using this new formalism, we estimate the loss of sensitivity for a broadband, isotropic stochastic background search using 1 yr of LIGO data at design sensitivity. Given our current noise budget, the uncertainty with which LIGO can estimate energy density will likely increase by a factor of ≈12—if it is impossible to achieve significant subtraction. Additionally, narrow band cross-correlation searches may be severely affected at low frequencies f ≲70 Hz without effective subtraction.
Qin, Zhongzhong; Cao, Leiming; Jing, Jietai
2015-05-25
Quantum correlations and entanglement shared among multiple modes are fundamental ingredients of most continuous-variable quantum technologies. Recently, a method used to generate multiple quantum correlated beams using cascaded four-wave mixing (FWM) processes was theoretically proposed and experimentally realized by our group [Z. Qin et al., Phys. Rev. Lett. 113, 023602 (2014)]. Our study of triple-beam quantum correlation paves the way to showing the tripartite entanglement in our system. Our system also promises to find applications in quantum information and precision measurement such as the controlled quantum communications, the generation of multiple quantum correlated images, and the realization of a multiport nonlinear interferometer. For its applications, the degree of quantum correlation is a crucial figure of merit. In this letter, we experimentally study how various parameters, such as the cell temperatures, one-photon, and two-photon detunings, influence the degree of quantum correlation between the triple beams generated from the cascaded two-FWM configuration.
NASA Astrophysics Data System (ADS)
Rontani, Massimo; Molinari, Elisa; Maruccio, Giuseppe; Janson, Martin; Schramm, Andreas; Meyer, Christian; Matsui, Tomohiro; Heyn, Christian; Hansen, Wolfgang; Wiesendanger, Roland
2007-04-01
We show both theoretically and experimentally that scanning tunneling spectroscopy (STS) images of semiconductor quantum dots may display clear signatures of electron-electron correlation. We apply many-body tunneling theory to a realistic model, which fully takes into account correlation effects and dot anisotropy. Comparing measured STS images of freestanding InAs quantum dots with those calculated by the full configuration interaction method, we explain the wave-function sequence in terms of images of one- and two-electron states. The STS map corresponding to double charging is significantly distorted by electron correlation with respect to the noninteracting case.
New analysis for the correlation between gravitational wave and neutrino detectors during SN1987A
NASA Astrophysics Data System (ADS)
Galeotti, P.; Pizzella, G.
2016-08-01
Two major problems, still associated with the SN1987A, are: (a) the signals observed with the gravitational waves detectors, (b) the duration of the collapse. Indeed, (a) the sensitivity of the gravitational wave detectors seems to be small for detecting gravitational waves and, (b) while some experimental data indicate a duration of order of hours, most theories assume that the collapse develops in a few seconds. Since recent data of the X-ray NuSTAR satellite show a clear evidence of an asymmetric collapse, we have revisited the experimental data recorded by the underground and gravitational wave detectors running during the SN1987A. New evidence is shown that confirms previous results, namely that the data recorded by the gravitational wave detectors running in Rome and in Maryland are strongly correlated with the data of both the Mont Blanc and the Kamiokande detectors, and that the correlation extends over a long period of time (1 or 2 h) centered at the Mont Blanc time. This result indicates that also Kamiokande detected neutrinos at the Mont Blanc time, and these interactions were not identified because not grouped in a burst.
Garashchuk, Sophya
2007-04-21
The de Broglie-Bohm formulation of the Schrodinger equation implies conservation of the wave function probability density associated with each quantum trajectory in closed systems. This conservation property greatly simplifies numerical implementations of the quantum trajectory dynamics and increases its accuracy. The reconstruction of a wave function, however, becomes expensive or inaccurate as it requires fitting or interpolation procedures. In this paper we present a method of computing wave packet correlation functions and wave function projections, which typically contain all the desired information about dynamics, without the full knowledge of the wave function by making quadratic expansions of the wave function phase and amplitude near each trajectory similar to expansions used in semiclassical methods. Computation of the quantities of interest in this procedure is linear with respect to the number of trajectories. The introduced approximations are consistent with approximate quantum potential dynamics method. The projection technique is applied to model chemical systems and to the H+H(2) exchange reaction in three dimensions.
NASA Astrophysics Data System (ADS)
Yao, H.; Gouedard, P.; Gerstoft, P.; McGuire, J. J.; Collins, J. A.; van der Hilst, R. D.
2010-12-01
Noise cross-correlation has been used to recover surface wave Green’s functions between receivers. However, most noise cross-correlation studies are restricted to land seismic stations and few studies have observed higher-mode surface waves. We apply noise cross-correlation on three-component broadband data recorded by 30 ocean bottom seismometers (OBSs) around the Gofar/Discovery/Quebrada transform faults on the Eastern Pacific Rise. On the vertical component, the cross-correlation functions (CFs) reveal clear Rayleigh wave propagation between each station pair for both the fundamental mode in the 2-30s period band and the first-higher mode in the 2-10 s band. However, on the radial component CFs, the first-higher mode Rayleigh waves dominate within 2-10s band and the fundamental mode Rayleigh waves appear mainly in 10-20s band. On the transverse component CFs, Love waves are observed within 2-10s band. The directionality of CFs is different for the fundamental mode and the first higher-mode surface waves, and is also frequency dependent. This infers different mechanisms for each mode, probably due to ocean wave activities and ocean bottom scattering. The dispersion characteristics of the vertical component CFs are analyzed using the time-frequency analysis for group velocities and a time-variable filter technique for phase velocities. We obtain inter-station dispersion curves within 2-30s period for the fundamental mode and within 2-8s period for the first higher-mode. These dispersion curves are averaged over station pairs and used to invert for the 1-D shear wavespeed structure in the crust and uppermost mantle in the study region. The obtained 1-D velocity model shows very low shear wavespeed in the uppermost mantle (4.25 and 4.0 km/s within 10-25 km and 25-45 km depth ranges, respectively), consistent with the local geology with hot upper mantle material upwelling to the surface through the ridges of the Eastern Pacific Rise.
Exponentiated power Lindley distribution.
Ashour, Samir K; Eltehiwy, Mahmoud A
2015-11-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data.
Exponentiated power Lindley distribution
Ashour, Samir K.; Eltehiwy, Mahmoud A.
2014-01-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data. PMID:26644927
Correlations between personality traits and specific groups of alpha waves in the human EEG.
Johannisson, Tomas
2016-01-01
Background. Different individuals have alpha waves with different wavelengths. The distribution of the wavelengths is assumed to be bell-shaped and smooth. Although this view is generally accepted, it is still just an assumption and has never been critically tested. When exploring the relationship between alpha waves and personality traits, it makes a huge difference if the distribution of the alpha waves is smooth or if specific groups of alpha waves can be demonstrated. Previous studies have not considered the possibility that specific groups of alpha waves may exist. Methods. Computerized EEGs have become standard, but wavelength measurements are problematic when based on averaging procedures using the Fourier transformation because such procedures cause a large systematic error. If the actual wavelength is of interest, it is necessary to go back to basic physiology and use raw EEG signals. In the present study, measurements were made directly from sequences of alpha waves where every wave could be identified. Personality dimensions were measured using an inventory derived from the International Personality Item Pool. Results. Recordings from 200 healthy individuals revealed that there are three main groups of alpha waves. These groups had frequencies around 8, 10, and 12 waves per second. The middle group had a bimodal distribution, and a subdivision gave a total of four alpha groups. In the center of each group, the degree of extraversion was high and the degree of neuroticism was low. Many small differences in personality traits were found when the centers were compared with one another. This gave four personality profiles that resemble the four classical temperaments. When people in the surrounding zones were compared with those in the centers, relatively large differences in personality traits were found. Conclusions. Specific groups of alpha waves exist, and these groups have to be taken into account when correlations are made to personality dimensions and
Correlations between personality traits and specific groups of alpha waves in the human EEG
2016-01-01
Background. Different individuals have alpha waves with different wavelengths. The distribution of the wavelengths is assumed to be bell-shaped and smooth. Although this view is generally accepted, it is still just an assumption and has never been critically tested. When exploring the relationship between alpha waves and personality traits, it makes a huge difference if the distribution of the alpha waves is smooth or if specific groups of alpha waves can be demonstrated. Previous studies have not considered the possibility that specific groups of alpha waves may exist. Methods. Computerized EEGs have become standard, but wavelength measurements are problematic when based on averaging procedures using the Fourier transformation because such procedures cause a large systematic error. If the actual wavelength is of interest, it is necessary to go back to basic physiology and use raw EEG signals. In the present study, measurements were made directly from sequences of alpha waves where every wave could be identified. Personality dimensions were measured using an inventory derived from the International Personality Item Pool. Results. Recordings from 200 healthy individuals revealed that there are three main groups of alpha waves. These groups had frequencies around 8, 10, and 12 waves per second. The middle group had a bimodal distribution, and a subdivision gave a total of four alpha groups. In the center of each group, the degree of extraversion was high and the degree of neuroticism was low. Many small differences in personality traits were found when the centers were compared with one another. This gave four personality profiles that resemble the four classical temperaments. When people in the surrounding zones were compared with those in the centers, relatively large differences in personality traits were found. Conclusions. Specific groups of alpha waves exist, and these groups have to be taken into account when correlations are made to personality dimensions and
[Wave-type time series variation of the correlation between NDVI and climatic factors].
Bi, Xiaoli; Wang, Hui; Ge, Jianping
2005-02-01
Based on the 1992-1996 data of 1 km monthly NDVI and those of the monthly precipitation and mean temperature collected by 400 standard meteorological stations in China, this paper analyzed the temporal and spatial dynamic changes of the correlation between NDVI and climatic factors in different climate districts of this country. The results showed that there was a significant correlation between monthly precipitations and NDVI. The wave-type time series model could simulate well the temporal dynamic changes of the correlation between NDVI and climatic factors, and the simulated results of the correlation between NDVI and precipitation was better than that between NDVI and temperature. The correlation coefficients (R2) were 0.91 and 0.86, respectively for the whole country.
A wave field synthesis approach to reproduction of spatially correlated sound fields.
Berry, Alain; Dia, Rokhiya; Robin, Olivier
2012-02-01
This article discusses an open-loop wave field synthesis (WFS) approach for the reproduction of spatially correlated sound fields. The main application concerns laboratory reproduction of turbulent boundary layer wall pressure on aircraft fuselages and measurement of their sound transmission loss. The problem configuration involves reconstruction of random sound pressure distributions on a planar reproduction surface using a planar array of reproduction monopoles parallel to the reproduction plane. In this paper, the WFS formulation is extended to sound fields with imposed time and spatial correlation properties (or equivalently imposed cross-spectral density in the frequency and wave number domains). Numerical examples are presented for the reproduction of a propagating plane wave, diffuse acoustic field and wall pressure in subsonic or supersonic turbulent boundary layers. The reproduction accuracy is examined in terms of the size of the source plane and reproduction plane, their separation, and the number of reproduction sources required per acoustic wavelength. While the reproduction approach cannot reconstruct sub-wavelength correlation scales of subsonic turbulent boundary layers, it effectively reconstructs correlation scales larger than the acoustic wavelength, making it appropriate for diffuse acoustic field and supersonic turbulent layers.
Shankar, R; Vishwanath, Ashvin
2011-09-02
For certain systems, the N-particle ground-state wave functions of the bulk happen to be exactly equal to the N-point spacetime correlation functions at the edge, in the infrared limit. We show why this had to be so for a class of topological superconductors, beginning with the p+ip state in D=2+1. Varying the chemical potential as a function of Euclidean time between weak and strong pairing states is shown to extract the wave function. Then a Euclidean rotation that exchanges time and space and approximate Lorentz invariance lead to the edge connection. This framework readily generalizes to other dimensions. We illustrate it with a D=3+1 example, superfluid 3He- B, and a p-wave superfluid in D=1+1. Our method works only when the particle number is not conserved, as in superconductors.
Surface wave phase-velocity tomography based on multichannel cross-correlation
NASA Astrophysics Data System (ADS)
Jin, Ge; Gaherty, James B.
2015-06-01
We have developed a new method to retrieve seismic surface wave phase velocity using dense seismic arrays. The method measures phase variations between nearby stations based on waveform cross-correlation. The coherence in waveforms between adjacent stations results in highly precise relative phase estimates. Frequency-dependent phase variations are then inverted for spatial variations in apparent phase velocity via the Eikonal equation. Frequency-dependent surface wave amplitudes measured on individual stations are used to correct the apparent phase velocity to account for multipathing via the Helmholtz equation. By using coherence and other data selection criteria, we construct an automated system that retrieves structural phase-velocity maps directly from raw seismic waveforms for individual earthquakes without human intervention. The system is applied to broad-band seismic data from over 800 events recorded on EarthScope's USArray from 2006 to 2014, systematically building up Rayleigh-wave phase-velocity maps between the periods of 20 and 100 s for the entire continental United States. At the highest frequencies, the resulting maps are highly correlated with phase-velocity maps derived from ambient noise tomography. At all frequencies, we observe a significant contrast in Rayleigh-wave phase velocity between the tectonically active western US and the stable eastern US, with the phase velocity variations in the western US being 1-2 times greater. The Love wave phase-velocity maps are also calculated. We find that overtone contamination may produce systemic bias for the Love-wave phase-velocity measurements.
From plane waves to local Gaussians for the simulation of correlated periodic systems
NASA Astrophysics Data System (ADS)
Booth, George H.; Tsatsoulis, Theodoros; Chan, Garnet Kin-Lic; Grüneis, Andreas
2016-08-01
We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller-Plesset perturbation theory.
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Wright, Charles; Henry, Jon; Burov, Stas; Lin, Yihan; Crosson, Sean; Dinner, Aaron; Scherer, Norbert
2013-03-01
The interplay between growth and division of cells is has been studied in the context of exponential growth of bacterial cells (in suitable conditions) for decades. However, bulk culture studies obscure phenomena that manifest in single cells over many generations. We introduce a unique technology combining microfluidics, single-cell imaging, and quantitative analysis. This enables us to track the growth of single Caulobacter crescentus stalked cells over hundreds of generations. The statistics that we extract indicate a size thresholding mechanism for cell division and a non-trivial scaling collapse of division time distributions at different temperatures. In this talk I shall discuss these observations and a stochastic model of growth and division that captures all our observations with no free parameters.
Correlating P-wave Velocity with the Physico-Mechanical Properties of Different Rocks
NASA Astrophysics Data System (ADS)
Khandelwal, Manoj
2013-04-01
In mining and civil engineering projects, physico-mechanical properties of the rock affect both the project design and the construction operation. Determination of various physico-mechanical properties of rocks is expensive and time consuming, and sometimes it is very difficult to get cores to perform direct tests to evaluate the rock mass. The purpose of this work is to investigate the relationships between the different physico-mechanical properties of the various rock types with the P-wave velocity. Measurement of P-wave velocity is relatively cheap, non-destructive and easy to carry out. In this study, representative rock mass samples of igneous, sedimentary, and metamorphic rocks were collected from the different locations of India to obtain an empirical relation between P-wave velocity and uniaxial compressive strength, tensile strength, punch shear, density, slake durability index, Young's modulus, Poisson's ratio, impact strength index and Schmidt hammer rebound number. A very strong correlation was found between the P-wave velocity and different physico-mechanical properties of various rock types with very high coefficients of determination. To check the sensitivity of the empirical equations, Students t test was also performed, which confirmed the validity of the proposed correlations.
Studying propagation of seismic waves across the Valley of Mexico from correlations of seismic noise
NASA Astrophysics Data System (ADS)
Rivet, D. N.; Campillo, M.; Shapiro, N. M.; Singh, S.; Cruz Atienza, V. M.; Quintanar, L.; Valdés, C.
2009-12-01
We reconstruct Rayleigh and Love waves from cross-correlations of ambient seismic noise recorded at 22 broad-band stations of the MesoAmerica Seismic Experiment (MASE) and Valley of Mexico Experiment (VMEX). The cross-correlations are computed over 2 years of noise data for the 9 MASE stations and over 1 year for the 13 VMEX stations. Surface waves with sufficient signal-to-noise ratio are then used in the group velocity dispersion analysis. We use the reconstructed waveforms to measure group velocity dispersion curves at period of 0.5 to 5 seconds. For traveling path inside the lake-bed zone, the maximum energy is observed at velocity higher than expected for the fundamental mode. This indicates that the propagation within the Mexico basin is dominated by higher modes of surface waves that propagate deeper in the basin. We identify the propagation modes by comparing observations with theoretical dispersion curves and eigenfunctions calculated for Rayleigh and Loves waves associated with a given model of the upper crust. The fundamental mode shows a very low group velocity, <100m/s, which is consistent with previous studies. The domination of the higher modes in the Valley of Mexico may be a determining factor in the long duration of the seismic signal. A better velocity constraint on the deeper structure of the basin is thus needed to fully understand this phenomenon.
Optical Measurement of In-plane Waves in Mechanical Metamaterials Through Digital Image Correlation
NASA Astrophysics Data System (ADS)
Schaeffer, Marshall; Trainiti, Giuseppe; Ruzzene, Massimo
2017-02-01
We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields.
On the correlation of non-isotropically distributed ballistic scalar diffuse waves.
Weaver, Richard; Froment, Berenice; Campillo, Michel
2009-10-01
Theorems indicating that a fully equipartitioned random wave field will have correlations equivalent to the Green's function that would be obtained in an active measurement are now legion. Studies with seismic waves, ocean acoustics, and laboratory ultrasound have confirmed them. So motivated, seismologists have evaluated apparent seismic travel times in correlations of ambient seismic noise and tomographically constructed impressive maps of seismic wave velocity. Inasmuch as the random seismic waves used in these evaluations are usually not fully equipartitioned, it seems right to ask why it works so well, or even if the results are trustworthy. The error, in apparent travel time, due to non-isotropic specific intensity is evaluated here in a limit of large receiver-receiver separation and for the case in which the source of the noise is in the far field of both receivers. It is shown that the effect is small, even for cases in which one might have considered the anisotropy to be significant, and even for station pairs separated by as little as one or two wavelengths. A formula is derived that permits estimations of error and corrections to apparent travel time. It is successfully compared to errors seen in synthetic waveforms.
Optical Measurement of In-plane Waves in Mechanical Metamaterials Through Digital Image Correlation
Schaeffer, Marshall; Trainiti, Giuseppe; Ruzzene, Massimo
2017-01-01
We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields. PMID:28205589
Optical Measurement of In-plane Waves in Mechanical Metamaterials Through Digital Image Correlation.
Schaeffer, Marshall; Trainiti, Giuseppe; Ruzzene, Massimo
2017-02-13
We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields.
Optical imaging through turbid media with a degenerate four-wave mixing correlation time gate
Sappey, Andrew D.
1998-04-14
Optical imaging through turbid media is demonstrated using a degenerate four-wave mixing correlation time gate. An apparatus and method for detecting ballistic and/or snake light while rejecting unwanted diffusive light for imaging structures within highly scattering media are described. Degenerate four-wave mixing (DFWM) of a doubled YAG laser in rhodamine 590 is used to provide an ultrafast correlation time gate to discriminate against light that has undergone multiple scattering and therefore has lost memory of the structures within the scattering medium. Images have been obtained of a test cross-hair pattern through highly turbid suspensions of whole milk in water that are opaque to the naked eye, which demonstrates the utility of DFWM for imaging through turbid media. Use of DFWM as an ultrafast time gate for the detection of ballistic and/or snake light in optical mammography is discussed.
Subtraction of correlated noise in global networks of gravitational-wave interferometers
NASA Astrophysics Data System (ADS)
Coughlin, Michael W.; Christensen, Nelson L.; De Rosa, Rosario; Fiori, Irene; Gołkowski, Mark; Guidry, Melissa; Harms, Jan; Kubisz, Jerzy; Kulak, Andrzej; Mlynarczyk, Janusz; Paoletti, Federico; Thrane, Eric
2016-11-01
The recent discovery of merging black holes suggests that a stochastic gravitational-wave background is within reach of the advanced detector network operating at design sensitivity. However, correlated magnetic noise from Schumann resonances threatens to contaminate observation of a stochastic background. In this paper, we report on the first effort to eliminate intercontinental correlated noise from Schumann resonances using Wiener filtering. Using magnetometers as proxies for gravitational-wave detectors, we demonstrate as much as a factor of two reduction in the coherence between magnetometers on different continents. While much work remains to be done, our results constitute a proof-of-principle and motivate follow-up studies with a dedicated array of magnetometers.
NASA Astrophysics Data System (ADS)
Cao, Leiming; Qi, Jian; Du, Jinjian; Jing, Jietai
2017-02-01
Multimode quantum states, such as multipartite quantum entanglement or quantum correlations, are important for both fundamental science and the future development of quantum technologies. Here we theoretically propose and experimentally realize a scheme that can fully exploit the multi-spatial-mode nature of the four-wave-mixing (FWM) process, i.e., spatial multiplexing, and thus integrates multiple FWM processes into a single cell at each stage of the cascaded process. The number of generated quantum-correlated beams 2n is exponentially dependent on the number of vapor cells n . In addition, the quantum correlations between the multiple beams also increase as the number of vapor cell increases. For the case of n =2 , we experimentally show that the degree of intensity-difference squeezing between the four quantum-correlated beams in our scheme is enhanced to -8.2 ±0.2 dB from -5.6 ±0.3 and -6.5 ±0.2 dB of squeezing obtained with a single FWM process. Our system may find applications in quantum information and precision measurement.
Collective modes in strongly correlated yukawa liquids: waves in dusty plasmas.
Kalman, G; Rosenberg, M; DeWitt, H E
2000-06-26
We determine the collective mode structure of a strongly correlated Yukawa fluid, with the purpose of analyzing wave propagation in a strongly coupled dusty plasma. We identify a longitudinal plasmon and a transverse shear mode. The dispersion is characterized by a low- k acoustic behavior, a frequency maximum well below the plasma frequency, and a high- k merging of the two modes around the Einstein frequency of localized oscillations. The damping effect of collisions between neutrals and dust grains is estimated.
Correlation of scanning-tunneling-microscope image profiles and charge-density-wave amplitudes
NASA Astrophysics Data System (ADS)
Giambattista, B.; Johnson, A.; McNairy, W. W.; Slough, C. G.; Coleman, R. V.
1988-08-01
Scanning-tunneling-microscope (STM) studies of 4Hb-TaS2 and 4Hb-TaSe2 at 4.2 K show systematic correlation between the charge-density-wave (CDW) amplitude and the STM deflection. The 4Hb phases have both weak and strong CDW's in the trigonal prismatic and octahedral sandwiches, respectively. Scans on opposite faces of the same cleave allow a comparison of the STM response to the two types of CDW.
Baseline-free fatigue crack detection based on spectral correlation and nonlinear wave modulation
NASA Astrophysics Data System (ADS)
Liu, Peipei; Sohn, Hoon; Yang, Suyoung; Lim, Hyung Jin
2016-12-01
By generating ultrasonic waves at two different frequencies onto a cracked structure, modulations due to crack-induced nonlinearity can be observed in the corresponding ultrasonic response. This nonlinear wave modulation phenomenon has been widely studied and proven capable of detecting a fatigue crack at a very early stage. However, under field conditions, other exogenous vibrations exist and the modulation components can be buried under ambient noises, making it difficult to extract the modulation components simply by using a spectral density function. In this study, the nonlinear modulation components in the ultrasonic response were extracted using a spectral correlation function (the double Fourier transform) with respect to time and time lag of a signal’s autocorrelation. Using spectral correlation, noise or interference, which is spectrally overlapped with the nonlinear modulation components in the ultrasonic response, can be effectively removed or reduced. Only the nonlinear modulation components are accentuated at specific coordinates of the spectral correlation plot. A damage feature is defined by comparing the spectral correlation value between nonlinear modulation components with other spectral correlation values among randomly selected frequencies. Then, by analyzing the statistical characteristics of the multiple damage feature values obtained from different input frequency combinations, fatigue cracks can be detected without relying on baseline data obtained from the pristine condition of the target structure. In the end, an experimental test was conducted on aluminum plates with a real fatigue crack and the test signals were contaminated by simulated noises with varying signal-to-noise ratios. The results validated the proposed technique.
Spin correlations and spin-wave excitations in Dirac-Weyl semimetals
NASA Astrophysics Data System (ADS)
Araki, Yasufumi; Nomura, Kentaro
We study correlations among magnetic dopants in three-dimensional Dirac and Weyl semimetals. Effective field theory for localized magnetic moments is derived by integrating out the itinerant electron degrees of freedom. We find that spin correlation in the spatial direction parallel to local magnetization is more rigid than that in the perpendicular direction, reflecting spin-momentum locking nature of the Dirac Hamiltonian. Such an anisotropy becomes stronger for Fermi level close to the Dirac points, due to Van Vleck paramagnetism triggered by spin-orbit coupling. One can expect topologically nontrivial spin textures under this anisotropy, such as a hedgehog around a single point, or a radial vortex around an axis, as well as a uniform ferromagnetic order. We further investigate the characteristics of spin waves in the ferromagnetic state. Spin-wave dispersion also shows a spatial anisotropy, which is less dispersed in the direction transverse to the magnetization than that in the longitudinal direction. The spin-wave dispersion anisotropy can be traced back to the rigidity and flexibility of spin correlations discussed above. This work was supported by Grant-in-Aid for Scientific Research (Grants No.15H05854, No.26107505, and No.26400308) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
Increased neural correlations in primate auditory cortex during slow-wave sleep.
Issa, Elias B; Wang, Xiaoqin
2013-06-01
During sleep, changes in brain rhythms and neuromodulator levels in cortex modify the properties of individual neurons and the network as a whole. In principle, network-level interactions during sleep can be studied by observing covariation in spontaneous activity between neurons. Spontaneous activity, however, reflects only a portion of the effective functional connectivity that is activated by external and internal inputs (e.g., sensory stimulation, motor behavior, and mental activity), and it has been shown that neural responses are less correlated during external sensory stimulation than during spontaneous activity. Here, we took advantage of the unique property that the auditory cortex continues to respond to sounds during sleep and used external acoustic stimuli to activate cortical networks for studying neural interactions during sleep. We found that during slow-wave sleep (SWS), local (neuron-neuron) correlations are not reduced by acoustic stimulation remaining higher than in wakefulness and rapid eye movement sleep and remaining similar to spontaneous activity correlations. This high level of correlations during SWS complements previous work finding elevated global (local field potential-local field potential) correlations during sleep. Contrary to the prediction that slow oscillations in SWS would increase neural correlations during spontaneous activity, we found little change in neural correlations outside of periods of acoustic stimulation. Rather, these findings suggest that functional connections recruited in sound processing are modified during SWS and that slow rhythms, which in general are suppressed by sensory stimulation, are not the sole mechanism leading to elevated network correlations during sleep.
Hoffman, Joseph J; Nelson, Amber M; Holland, Mark R; Miller, James G
2012-09-01
A Bayesian probability theory approach for separating overlapping ultrasonic fast and slow waves in cancellous bone has been previously introduced. The goals of this study were to investigate whether the fast and slow waves obtained from Bayesian separation of an apparently single mode signal individually correlate with porosity and to isolate the fast and slow waves from medial-lateral insonification of the calcaneus. The Bayesian technique was applied to trabecular bone data from eight human calcanei insonified in the medial-lateral direction. The phase velocity, slope of attenuation (nBUA), and amplitude were determined for both the fast and slow waves. The porosity was assessed by micro-computed tomography (microCT) and ranged from 78.7% to 94.1%. The method successfully separated the fast and slow waves from medial-lateral insonification of the calcaneus. The phase velocity for both the fast and slow wave modes showed an inverse correlation with porosity (R(2) = 0.73 and R(2) = 0.86, respectively). The slope of attenuation for both wave modes also had a negative correlation with porosity (fast wave: R(2) = 0.73, slow wave: R(2) = 0.53). The fast wave amplitude decreased with increasing porosity (R(2) = 0.66). Conversely, the slow wave amplitude modestly increased with increasing porosity (R(2) = 0.39).
NASA Astrophysics Data System (ADS)
Fermi, Enrico
The Patent contains an extremely detailed description of an atomic pile employing natural uranium as fissile material and graphite as moderator. It starts with the discussion of the theory of the intervening phenomena, in particular the evaluation of the reproduction or multiplication factor, K, that is the ratio of the number of fast neutrons produced in one generation by the fissions to the original number of fast neutrons, in a system of infinite size. The possibility of having a self-maintaining chain reaction in a system of finite size depends both on the facts that K is greater than unity and the overall size of the system is sufficiently large to minimize the percentage of neutrons escaping from the system. After the description of a possible realization of such a pile (with many detailed drawings), the various kinds of neutron losses in a pile are depicted. Particularly relevant is the reported "invention" of the exponential experiment: since theoretical calculations can determine whether or not a chain reaction will occur in a give system, but can be invalidated by uncertainties in the parameters of the problem, an experimental test of the pile is proposed, aimed at ascertaining if the pile under construction would be divergent (i.e. with a neutron multiplication factor K greater than 1) by making measurements on a smaller pile. The idea is to measure, by a detector containing an indium foil, the exponential decrease of the neutron density along the length of a column of uranium-graphite lattice, where a neutron source is placed near its base. Such an exponential decrease is greater or less than that expected due to leakage, according to whether the K factor is less or greater than 1, so that this experiment is able to test the criticality of the pile, its accuracy increasing with the size of the column. In order to perform this measure a mathematical description of the effect of neutron production, diffusion, and absorption on the neutron density in the
Zhao, X. H.; Feng, X. S.; Jiang, C. W.; Wu, S. T.; Wang, A. H.; Vourlidas, A. E-mail: wus@uah.edu
2011-12-01
An EIT wave, which typically appears as a diffuse brightening that propagates across the solar disk, is one of the major discoveries of the Extreme ultraviolet Imaging Telescope on board the Solar and Heliospheric Observatory. However, the physical nature of the so-called EIT wave continues to be debated. In order to understand the relationship between an EIT wave and its associated coronal wave front, we investigate the morphology and kinematics of the coronal mass ejection (CME)-EIT wave event that occurred on 2010 January 17. Using the observations of the SECCHI EUVI, COR1, and COR2 instruments on board the Solar Terrestrial Relations Observation-B, we track the shape and movements of the CME fronts along different radial directions to a distance of about 15 solar radii (R{sub s} ); for the EIT wave, we determine the propagation of the wave front on the solar surface along different propagating paths. The relation between the EIT wave speed, the CME speed, and the local fast-mode characteristic speed is also investigated. Our results demonstrate that the propagation of the CME front is much faster than that of the EIT wave on the solar surface, and that both the CME front and the EIT wave propagate faster than the fast-mode speed in their local environments. Specifically, we show a significant positive correlation between the EIT wave speed and the local fast-mode wave speed in the propagation paths of the EIT wave. Our findings support that the EIT wave under study is a fast-mode magnetohydrodynamic wave.
OPINION: Safe exponential manufacturing
NASA Astrophysics Data System (ADS)
Phoenix, Chris; Drexler, Eric
2004-08-01
In 1959, Richard Feynman pointed out that nanometre-scale machines could be built and operated, and that the precision inherent in molecular construction would make it easy to build multiple identical copies. This raised the possibility of exponential manufacturing, in which production systems could rapidly and cheaply increase their productive capacity, which in turn suggested the possibility of destructive runaway self-replication. Early proposals for artificial nanomachinery focused on small self-replicating machines, discussing their potential productivity and their potential destructiveness if abused. In the light of controversy regarding scenarios based on runaway replication (so-called 'grey goo'), a review of current thinking regarding nanotechnology-based manufacturing is in order. Nanotechnology-based fabrication can be thoroughly non-biological and inherently safe: such systems need have no ability to move about, use natural resources, or undergo incremental mutation. Moreover, self-replication is unnecessary: the development and use of highly productive systems of nanomachinery (nanofactories) need not involve the construction of autonomous self-replicating nanomachines. Accordingly, the construction of anything resembling a dangerous self-replicating nanomachine can and should be prohibited. Although advanced nanotechnologies could (with great difficulty and little incentive) be used to build such devices, other concerns present greater problems. Since weapon systems will be both easier to build and more likely to draw investment, the potential for dangerous systems is best considered in the context of military competition and arms control.
NASA Astrophysics Data System (ADS)
Dombrowski, M. P.; Labelle, J. W.; Kletzing, C.; Bounds, S. R.; Kaeppler, S. R.
2014-12-01
Langmuir-mode electron plasma waves are frequently observed by spacecraft in active plasma environments such as the ionosphere. Ionospheric Langmuir waves may be excited by the bump-on-tail instability generated by impinging beams of electrons traveling parallel to the background magnetic field (B). The Correlation of High-frequencies and Auroral Roar Measurement (CHARM II) sounding rocket was launched into a substorm at 9:49 UT on 17 February 2010, from the Poker Flat Research Range in Alaska. The primary instruments included the University of Iowa Wave-Particle Correlator (WPC), the Dartmouth High-Frequency Experiment (HFE), several charged particle detectors, low-frequency wave instruments, and a magnetometer. The HFE is a receiver system which effectively yields continuous (100% duty cycle) electric-field waveform measurements from 100 kHz to 5 MHz, and which had its detection axis aligned nominally parallel to B. The HFE output was fed on-payload to the WPC, which uses a phase-locked loop to track the incoming wave frequency with the most power, then sorting incoming electrons at eight energy levels into sixteen wave-phase bins. CHARM II encountered several regions of strong Langmuir wave activity throughout its 15-minute flight, and the WPC showed wave-lock and statistically significant particle correlation distributions during several time periods. We show results of an in-depth analysis of the CHARM II WPC data for the entire flight, including statistical analysis of correlations which show evidence of direct interaction with the Langmuir waves, indicating (at various times) trapping of particles and both driving and damping of Langmuir waves by particles. In particular, the sign of the gradient in particle flux appears to correlate with the phase relation between the electrons and the wave field, with possible implications for the wave physics.
NASA Technical Reports Server (NTRS)
Ohlson, J. E.
1976-01-01
Optimum estimation (tracking) of the polarization plane of a linearly polarized electromagnetic wave is determined when the signal is a narrow-band Gaussian random process with a polarization plane angle which is also a Gaussian random process. This model is compared to previous work and is applicable to space communication. The estimator performs a correlation operation similar to an amplitude-comparison monopulse angle tracker, giving the name correlation polarimeter. Under large signal-to-noise ratio (SNR), the estimator is causal. Performance of the causal correlation polarimeter is evaluated for arbitrary SNR. Optimum precorrelation filtering is determined. With low SNR, the performance of this system is far better than that of previously developed systems. Practical implementation is discussed. A scheme is given to reduce the effect of linearly polarized noise.
Excited states of boron isoelectronic series from explicitly correlated wave functions.
Gálvez, F J; Buendía, E; Sarsa, A
2005-04-15
The ground state and some low-lying excited states arising from the 1s2 2s2p2 configuration of the boron isoelectronic series are studied starting from explicitly correlated multideterminant wave functions. One- and two-body densities in position space have been calculated and different expectation values such as
Lewis, Philip M; Smielewski, Peter; Rosenfeld, Jeffrey V; Pickard, John D; Czosnyka, Marek
2016-01-01
We previously showed that the flow-ICP index (Fix), a moving correlation coefficient between intracranial pressure (ICP) and cerebral blood flow velocity (CBFV), had marginally greater prognostic value for patients with traumatic brain injury (TBI) than an index of cerebral autoregulation (mean index, Mx). The aim of this study was to further examine the clinical and physiological relevance of Fix by studying its behaviour during ICP plateau waves in patients with TBI. Twenty-nine recordings of CBFV made during ICP plateau waves were analysed. Both Mx and Fix at baseline and peak ICP were significantly different, although the magnitude of Fix change was slightly greater. The correlation between Fix and cerebral perfusion pressure (CPP) was stronger than that between Mx and CPP. Unlike in our previous study, plotting Fix against CPP revealed a peak value in the range of "optimal" CPP, as indicated by the Mx versus CPP plot. The findings suggest that during periods of reduced CPP caused by plateau waves, the dynamic behaviour of Fix is similar to that of a measure of cerebral autoregulation. This conclusion needs to be verified against similar results obtained during episodes of supranormal CPP.
Xu, Zhen J; Song, Xiaodong
2009-08-25
Detecting temporal changes of the medium associated with major earthquakes has implications for understanding earthquake genesis. Here we report temporal changes of surface wave velocity over a large area associated with 3 major Sumatra earthquakes in 2004, 2005, and 2007. We use ambient noise correlation to retrieve empirical Green's function (EGF) of surface waves between stations. Because the process is completely repeatable, the technique is powerful in detecting possible temporal change of medium. We find that 1 excellent station pair (PSI in Indonesia and CHTO in Thailand) shows significant time shifts (up to 1.44 s) after the 2004 and 2005 events in the Rayleigh waves at 10-20 s but not in the Love waves, suggesting that the Rayleigh time shifts are not from clock error. The time shifts are frequency dependent with the largest shifts at the period band of 11-16 s. We also observe an unusual excursion approximately 1 month before the 2004 event. We obtain a total of 17 pairs for June, 2007 to June, 2008, which allow us to examine the temporal and spatial variation of the time shifts. We observed strong anomalies (up to 0.68 s) near the epicenter after the 2007 event, but not in the region further away from the source or before the event or 3 months after the event. The observations are interpreted as stress changes and subsequent relaxation in upper-mid crust in the immediate vicinity of the rupture and the broad area near the fault zone.
Seismic Body-Wave Interferometry Using Noise Auto-correlations for Crustal Structure
NASA Astrophysics Data System (ADS)
Oren, Can; Nowack, Robert L.
2016-10-01
In this study, we use ambient seismic noise recorded at selected broadband USArray Earthscope Transportable Array (TA) stations to obtain effective reflection seismograms using noise auto-correlations. In order to best retrieve the body-wave component of the Green's function beneath a station from ambient seismic noise, a number of processing steps are used, including temporal sign-bit normalization, spectral whitening, and band-pass filtering. Hourly auto-correlations are stacked for different time periods including one day, one month, and one year. On the final stack, different amplitude gain functions are applied, including automatic gain control (AGC), to equalize the correlation amplitudes. The robustness of the resulting ambient noise auto-correlations is first tested on a TA station in Nevada where we are able to identify arrivals similar to those found in an earlier study. We then investigated noise auto-correlations applied to several USArray TA stations in the central U.S., and the results were then compared with reflectivity synthetics for an average crustal model based on CRUST 1.0 where an AGC was used to enhance the later arrivals. Different stacking periods are also investigated in order to find stable correlation stacks.
Cerebral correlates of delta waves during non-REM sleep revisited.
Dang-Vu, Thien Thanh; Desseilles, Martin; Laureys, Steven; Degueldre, Christian; Perrin, Fabien; Phillips, Christophe; Maquet, Pierre; Peigneux, Philippe
2005-10-15
We aimed at characterizing the neural correlates of delta activity during Non Rapid Eye Movement (NREM) sleep in non-sleep-deprived normal young adults, based on the statistical analysis of a positron emission tomography (PET) sleep data set. One hundred fifteen PET scans were obtained using H(2)(15)O under continuous polygraphic monitoring during stages 2-4 of NREM sleep. Correlations between regional cerebral blood flow (rCBF) and delta power (1.5-4 Hz) spectral density were analyzed using statistical parametric mapping (SPM2). Delta power values obtained at central scalp locations negatively correlated during NREM sleep with rCBF in the ventromedial prefrontal cortex, the basal forebrain, the striatum, the anterior insula, and the precuneus. These regions embrace the set of brain areas in which rCBF decreases during slow wave sleep (SWS) as compared to Rapid Eye Movement (REM) sleep and wakefulness (Maquet, P., Degueldre, C., Delfiore, G., Aerts, J., Peters, J.M., Luxen, A., Franck, G., 1997. Functional neuroanatomy of human slow wave sleep. J. Neurosci. 17, 2807-S2812), supporting the notion that delta activity is a valuable prominent feature of NREM sleep. A strong association was observed between rCBF in the ventromedial prefrontal regions and delta power, in agreement with electrophysiological studies. In contrast to the results of a previous PET study investigating the brain correlates of delta activity (Hofle, N., Paus, T., Reutens, D., Fiset, P., Gotman, J., Evans, A.C., Jones, B.E., 1997. Regional cerebral blood flow changes as a function of delta and spindle activity during slow wave sleep in humans. J. Neurosci. 17, 4800-4808), in which waking scans were mixed with NREM sleep scans, no correlation was found with thalamus activity. This latter result stresses the importance of an extra-thalamic delta rhythm among the synchronous NREM sleep oscillations. Consequently, this rCBF distribution might preferentially reflect a particular modulation of the
Multi-channel analysis of passive surface waves based on cross-correlations
NASA Astrophysics Data System (ADS)
Cheng, F.; Xia, J.; Xu, Z.; Hu, Y.
2015-12-01
Traditional active seismic survey can no longer be properly applied in highly populated urban areas due to restrictions in modern civilian life styles. Passive seismic methods, however, have gained much more attention from the engineering geophysics community because of their environmental friendly and deeper investigation depth. Due to extracting signal from noise has never been as comfortable as that in active seismic survey, how to make it more efficiently and accurately has been emphasized. We propose a multi-channel analysis of passive surface waves (MAPW) based on long noise sequences cross-correlations to meet the demand for increasing investigation depth by acquiring surface-wave data at a relative low-frequency range (1 Hz ≤ f ≤ 10 Hz) in urban areas. We utilize seismic interferometry to produce common virtual source gathers from one-hour-long noise records and do dispersion measurements by using the classic passive multi-channel analysis of surface waves (PMASW). We used synthetic tests to demonstrate the advantages of MAPW for various noise distributions. Results show that our method has the superiority of maximizing the analysis accuracy. Finally, we used two field data applications to demonstrate the advantages of our MAPW over the classic PMASW on isolating azimuth of the predominant noise sources and the effectivity of combined survey of active multi-channel analysis of surface waves (MASW) and MAPW. We suggest, for the field operation using MAPW, that a parallel receiver line which is close to a main road or river, if any, with one or two hours noise observation will be an effective means for an unbiased dispersion image. Keywords: passive seismic method, MAPW, MASW, cross-correlation, directional noise source, spatial-aliasing effects, inversion
Dossmann, Yvan; Paci, Alexandre; Auclair, Francis; Lepilliez, Mathieu; Cid, Emmanuel
2014-05-15
Internal solitary waves (ISWs) are large amplitude stable waves propagating in regions of high density gradients such as the ocean pycnocline. Their dynamics has often been investigated in two-dimensional approaches, however, their three-dimensional evolution is still poorly known. Experiments have been conducted in the large stratified water tank of CNRM-GAME to study the generation of ISWs in two academic configurations inspired by oceanic regimes. First, ultrasonic probes are used to measure the interfacial displacement in the two configurations. In the primary generation case for which the two layers are of constant density, the generation of ISWs is investigated in two series of experiments with varying amplitude and forcing frequency. In the secondary generation case for which the lower layer is stratified, the generation of ISWs from the impact of an internal wave beam on the pycnocline and their subsequent dynamics is studied. The dynamics of ISWs in these two regimes accords well with analytical approaches and numerical simulations performed in analogous configurations. Then, recent developments of a stereo correlation technique are used to describe the three-dimensional structure of propagating ISWs. In the primary generation configuration, small transverse effects are observed in the course of the ISW propagation. In the secondary generation configuration, larger transverse structures are observed in the interfacial waves dynamics. The interaction between interfacial troughs and internal waves propagating in the lower stratified layer are a possible cause for the generation of these structures. The magnitude of these transverse structures is quantified with a nondimensional parameter in the two configurations. They are twice as large in the secondary generation case as in the primary generation case.
On the Matrix Exponential Function
ERIC Educational Resources Information Center
Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai
2006-01-01
A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.
Radio-wave emission due to hypervelocity impacts and its correlation with optical observations
NASA Astrophysics Data System (ADS)
Takano, T.; Maki, K.; Yamori, A.
This paper describes the most interesting phenomena of radio-wave emission due to hypervelocity impacts. A projectile of polycarbonate with 1.1 g weight was accelerated by a rail gun to 3.8 km/sec, and hit two targets which are a 2 mm thick aluminum plate upstream and a 45 mm diameter aluminum column downstream, respectively. The projectile first breaks wires to give a triggering signal to a data recorder, then penetrates the aluminum plate, and finally hit the column, The emitted radio-waves propagate through the chamber window, and are received by antennas at each frequency band. The receivers in 22 GHz- and 2 GHz-bands consist of a low noise amplifier, a mixer, a local oscillator and an IF amplifier , respectively. The receiver in 1 MHz-band is a simple RF amplifier. The outputs of all receivers are fed to a data recorder which is actually a high-speed digital oscilloscope with a large amount of memory. The radio-waves were successfully recorded in 22 GHz-band with 500 MHz bandwidth, in 2 GHz-band with 300 MHz bandwidth, and in 1MHz-band. The waveforms in 22 GHz- and 2 GHz-bands coincide well each other, and are composed of two groups of sharp impulses with a separation of about 20 micro seconds. The width of an impulse is less than 2 n sec. which is the resolution limit of the data recorder. We carried out optical observations using an ultra-high speed camera simultaneously through another window of the chamber. The time interval between scenes is 2 micro sec. We can see a faint light of the projectile before the first impact to the plate, and then a brilliant gas exploding backward from the plate and forward to the column. After hitting the column target, the brilliant gas flows to the chamber wall and is reflected back to make a mixture with dark gas in the chamber. Excellent correlation between radio-wave emission and the observed optical phenomena was obtained in the experiment. It is easily conceived that the radio-waves consist of quite a wide frequency
Phase-sensitive cascaded four-wave-mixing processes for generating three quantum correlated beams
NASA Astrophysics Data System (ADS)
Wang, Li; Wang, Hailong; Li, Sijin; Wang, Yaxian; Jing, Jietai
2017-01-01
Theoretical studies and experimental implementations of quantum correlation are the important contents of continuous variables quantum optics and quantum information science. There are various systems for the study of quantum correlation. Here, we study an experimental scheme for generating three quantum correlated beams based on phase-sensitive cascaded four-wave-mixing (FWM) processes in rubidium vapor. Quantum correlation including intensity difference or sum squeezing, two other combinatorial squeezing, and quantum entanglement among the three output light fields are theoretically analyzed in this paper. Also, the comparison of the quantum correlations have been made between the phase-sensitive cascaded FWM processes and the phase-insensitive cascaded FWM processes. By changing the phases and intensities of the input beams, it is interesting to find that the maximum degrees of various combinatorial squeezing are equal when the two FWM processes share a common intensity gain. When the common intensity gain of the two FWM processes changes, the maximum degrees of different combinatorial squeezing will be synchronously controlled. At last we discuss the genuine tripartite entanglement and steering in our phase-sensitive cascaded scheme, and compare them with the cases of the phase-insensitive cascaded scheme.
NASA Astrophysics Data System (ADS)
Sun, Chang-Guk; Cho, Chang-Soo; Son, Minkyung; Shin, Jin Soo
2013-03-01
Shear wave velocity ( V S) can be obtained using seismic tests, and is viewed as a fundamental geotechnical characteristic for seismic design and seismic performance evaluation in the field of earthquake engineering. To apply conventional geotechnical site investigation techniques to geotechnical earthquake engineering, standard penetration tests (SPT) and piezocone penetration tests (CPTu) were undertaken together with a variety of borehole seismic tests for a range of sites in Korea. Statistical modeling of the in-situ testing data identified correlations between V S and geotechnical in-situ penetration data, such as blow counts ( N value) from SPT and CPTu data including tip resistance ( q t), sleeve friction ( f s), and pore pressure ratio ( B q). Despite the difference in strain levels between conventional geotechnical penetration tests and borehole seismic tests, it is shown that the suggested correlations in this study is applicable to the preliminary determination of V S for soil deposits.
Photoionization of helium by attosecond pulses: Extraction of spectra from correlated wave functions
NASA Astrophysics Data System (ADS)
Argenti, Luca; Pazourek, Renate; Feist, Johannes; Nagele, Stefan; Liertzer, Matthias; Persson, Emil; Burgdörfer, Joachim; Lindroth, Eva
2013-05-01
We investigate the photoionization spectrum of helium by attosecond XUV pulses both in the spectral region of doubly excited resonances as well as above the double ionization threshold. In order to probe for convergence, we compare three techniques to extract photoelectron spectra from the wave packet resulting from the integration of the time-dependent Schrödinger equation in a finite-element discrete variable representation basis. These techniques are projection on products of hydrogenic bound and continuum states, projection onto multichannel scattering states computed in a B-spline close-coupling basis, and a technique based on exterior complex scaling implemented in the same basis used for the time propagation. These methods allow one to monitor the population of continuum states in wave packets created with ultrashort pulses in different regimes. Applications include photo cross sections and anisotropy parameters in the spectral region of doubly excited resonances, time-resolved photoexcitation of autoionizing resonances in an attosecond pump-probe setting, and the energy and angular distribution of correlated wave packets for two-photon double ionization.
A cross-correlation search for intermediate-duration gravitational waves from GRB magnetars
NASA Astrophysics Data System (ADS)
Coyne, Robert
2015-04-01
Since the discovery of the afterglow in 1997, the progress made in our understanding of gamma-ray bursts (GRBs) has been spectacular. Yet a direct proof of GRB progenitors is still missing. In the last few years, evidence for a long-lived and sustained central engine in GRBs has mounted. This has called attention to the so-called millisecond-magnetar model, which proposes that a highly magnetized, rapidly-rotating neutron star may exist at the heart of some of these events. The advent of advanced gravitational wave detectors such as LIGO and Virgo may enable us to probe directly, for the first time, the nature of GRB progenitors and their byproducts. In this context, we describe a novel application of a generalized cross-correlation technique optimized for the detection of long-duration gravitational wave signals that may be associated with bar-like deformations of GRB magnetars. The detection of these signals would allow us to answer some of the most intriguing questions on the nature of GRB progenitors, and serve as a starting point for a new class of intermediate-duration gravitational wave searches.
Capillary waves and the decay of density correlations at liquid surfaces.
Hernández-Muñoz, Jose; Chacón, Enrique; Tarazona, Pedro
2016-12-01
Wertheim predicted strong density-density correlations at free liquid surfaces, produced by capillary wave fluctuations of the interface [M. S. Wertheim, J. Chem. Phys. 65, 2377 (1976)JCPSA60021-960610.1063/1.433352]. That prediction has been used to search for a link between capillary wave (CW) theory and density functional (DF) formalism for classical fluids. In particular, Parry et al. have recently analyzed the decaying tails of these CW effects moving away from the interface as a clue for the extended CW theory [A. O. Parry et al., J. Phys.: Condens. Matter 28, 244013 (2016)JCOMEL0953-898410.1088/0953-8984/28/24/244013], beyond the strict long-wavelength limit studied by Wertheim. Some apparently fundamental inconsistencies between the CW and the DF theoretical views of the fluid interfaces arose from the asymptotic analysis of the CW signal. In this paper we revisit the problem of the CW asymptotic decay with a separation of local non-CW surface correlation effects from those that are a truly nonlocal propagation of the CW fluctuations from the surface towards the liquid bulk.
Capillary waves and the decay of density correlations at liquid surfaces
NASA Astrophysics Data System (ADS)
Hernández-Muñoz, Jose; Chacón, Enrique; Tarazona, Pedro
2016-12-01
Wertheim predicted strong density-density correlations at free liquid surfaces, produced by capillary wave fluctuations of the interface [M. S. Wertheim, J. Chem. Phys. 65, 2377 (1976), 10.1063/1.433352]. That prediction has been used to search for a link between capillary wave (CW) theory and density functional (DF) formalism for classical fluids. In particular, Parry et al. have recently analyzed the decaying tails of these CW effects moving away from the interface as a clue for the extended CW theory [A. O. Parry et al., J. Phys.: Condens. Matter 28, 244013 (2016), 10.1088/0953-8984/28/24/244013], beyond the strict long-wavelength limit studied by Wertheim. Some apparently fundamental inconsistencies between the CW and the DF theoretical views of the fluid interfaces arose from the asymptotic analysis of the CW signal. In this paper we revisit the problem of the CW asymptotic decay with a separation of local non-CW surface correlation effects from those that are a truly nonlocal propagation of the CW fluctuations from the surface towards the liquid bulk.
Xu, Zhen J.; Song, Xiaodong
2009-01-01
Detecting temporal changes of the medium associated with major earthquakes has implications for understanding earthquake genesis. Here we report temporal changes of surface wave velocity over a large area associated with 3 major Sumatra earthquakes in 2004, 2005, and 2007. We use ambient noise correlation to retrieve empirical Green's function (EGF) of surface waves between stations. Because the process is completely repeatable, the technique is powerful in detecting possible temporal change of medium. We find that 1 excellent station pair (PSI in Indonesia and CHTO in Thailand) shows significant time shifts (up to 1.44 s) after the 2004 and 2005 events in the Rayleigh waves at 10–20 s but not in the Love waves, suggesting that the Rayleigh time shifts are not from clock error. The time shifts are frequency dependent with the largest shifts at the period band of 11–16 s. We also observe an unusual excursion ∼1 month before the 2004 event. We obtain a total of 17 pairs for June, 2007 to June, 2008, which allow us to examine the temporal and spatial variation of the time shifts. We observed strong anomalies (up to 0.68 s) near the epicenter after the 2007 event, but not in the region further away from the source or before the event or 3 months after the event. The observations are interpreted as stress changes and subsequent relaxation in upper-mid crust in the immediate vicinity of the rupture and the broad area near the fault zone. PMID:19667205
Glorieux, Quentin; Guidoni, Luca; Guibal, Samuel; Likforman, Jean-Pierre; Coudreau, Thomas
2011-11-15
We study the generation of intensity quantum correlations using four-wave mixing in a rubidium vapor. The absence of cavities in these experiments allows to deal with several spatial modes simultaneously. In the standard amplifying configuration, we measure relative intensity squeezing up to 9.2 dB below the standard quantum limit. We also theoretically identify and experimentally demonstrate an original regime where, despite no overall amplification, quantum correlations are generated. In this regime, a four-wave mixing setup can play the role of a photonic beam splitter with nonclassical properties, that is, a device that splits a coherent state input into two quantum-correlated beams.
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Is radioactive decay really exponential?
NASA Astrophysics Data System (ADS)
Aston, P. J.
2012-03-01
Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of 14C can be calibrated over a period of 12550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that radiocarbon dates of over 3000 years are in error, which is generally attributed to past variation in atmospheric levels of 14C. We note that predicted atmospheric variation (assuming exponential decay) does not agree with results from modelling, and that theoretical quantum mechanics does not predict exact exponential decay. We give mathematical arguments that non-exponential decay should be expected for slowly decaying isotopes and explore the consequences of non-exponential decay. We propose an experimental test of this prediction of non-exponential decay for 14C. If confirmed, a foundation stone of current dating methods will have been removed, requiring a radical reappraisal both of radioisotope dating methods and of currently predicted dates obtained using these methods.
NASA Astrophysics Data System (ADS)
Sabutis, J. L.; Turco, R. P.; Kar, S. K.
1997-09-01
This study examines temporal and spatial correlations between TOMS total ozone and MSU4 brightness temperature data for the seven-years 1980-1986. These data sets are separated into monthly mean and transient time series, and a Monte Carlo method is used to determine the statistical significance of the observed correlations. Monthly mean data have large areas of positive correlations during NH summer months, and during SH springtime months. Both the NH and SH have smaller areas of monthly mean positive correlations during winter. The NH has large areas of transient correlations during October, November and April, and the SH during September, October and November. One result of this analysis is that monthly mean and transient total ozone and brightness temperature show little correlation in the NH during January and the SH during July. To examine the role that planetary waves play in these correlations during January, LIMS data are used to calculate the wave activity. It is found that the NH regions of significant total ozone-temperature positive correlations correspond to regions (corridors) in the stratosphere where large vertical planetary wave propagation takes place. Monthly mean correlations are found in the corridors over north central Asia, northeastern Pacific and northern Atlantic Oceans. Transient correlations are found over northern Canada. The northern Atlantic Ocean region is characterized by downward, and the remaining three regions are dominated by upward propagating wave activity. Trajectory calculations are used to examine the observed LIMS temperature and ozone trends. This analysis shows that as air parcels pass through the corridor over the northern Atlantic Ocean, they rise and cool. This unique region of downward wave activity and subsequent upward trajectory motion may be important when considering the processing of air by polar stratospheric clouds.
Universal bulk charge-density-wave (CDW) correlations in the cuprate superconductors
NASA Astrophysics Data System (ADS)
Tabis, Wojciech
2014-03-01
The recent observation of bulk CDW order in YBa2Cu3O8+δ(YBCO) in competition with superconductivity is a significant development. Using Cu L-edge resonant X-ray scattering, we also observe bulk CDW order in HgBa2CuO4+δ(Hg1201 Tc = 72K). The correlations appear below TCDW ~ 200K, well below the pseudogap temperature T* ~ 320K associated with unusual magnetism, but coincident with the onset of Fermi-liquid-like charge transport. In contrast to YBCO, we observe no decrease of the CDW amplitude below Tc, and the correlation length is short and temperature independent. CDW correlations therefore are a universal property of underdoped cuprates, enhanced by low structural symmetry and a magnetic field, but fundamentally not in significant competition with superconductivity. We also discuss the relationship between the CDW modulation wave vector and the Fermi surface area extracted from QO experiments. Work supported by DOE-BES. In collaboration with Y. Li, M. Le Tacon, L. Braicovich, A. Kreyssig, M. Minola, G. Dellea, E. Weschke, M. Veit, A. Goldman, T. Schmitt, G. Ghiringhelli, N. Barisic, M.K. Chan, C. Dorow, G. Yu, X. Zhao, B. Keimer, M. Greven.
Estienne, B; Regnault, N; Bernevig, B A
2015-05-08
Using the newly developed matrix product state formalism for non-Abelian fractional quantum Hall (FQH) states, we address the question of whether a FQH trial wave function written as a correlation function in a nonunitary conformal field theory (CFT) can describe the bulk of a gapped FQH phase. We show that the nonunitary Gaffnian state exhibits clear signatures of a pathological behavior. As a benchmark we compute the correlation length of a Moore-Read state and find it to be finite in the thermodynamic limit. By contrast, the Gaffnian state has an infinite correlation length in (at least) the non-Abelian sector, and is therefore gapless. We also compute the topological entanglement entropy of several non-Abelian states with and without quasiholes. For the first time in the FQH effect the results are in excellent agreement in all topological sectors with the CFT prediction for unitary states. For the nonunitary Gaffnian state in finite size systems, the topological entanglement entropy seems to behave like that of the composite fermion Jain state at equal filling.
A seismic waves velocity model for Gran Canaria Island from ambient noise correlations
NASA Astrophysics Data System (ADS)
García-Jerez, Antonio; Almendros, Javier; Martínez-Arévalo, Carmen; de Lis Mancilla, Flor; Luzón, Francisco; Carmona, Enrique; Martín, Rosa; Sánchez, Nieves
2014-05-01
We have analysed continuous ambient seismic noise recorded by a temporary array in Gran Canaria (Canary Islands, Spain) in order to find a velocity model for the top few kilometers. The SISTEVOTENCAN-IGN seismic array consisted of five broadband stations surrounding a sixth central one placed close to Pico de las Nieves, at the center of the island. The array had a radius of 12-14 km, with interstation distances ranging from 10 to 27 km. This network was operative from December 2009 to November 2011. The Green's functions between the 15 pairs of stations have been estimated in the time domain by stacking cross-correlations of 60-s time windows for the whole recording period (~2 years). The effects of several processing adjustments such as 1-bit normalization and spectral whitening are discussed. We observe significant differences (mainly in amplitude) between causal and acausal parts of the estimated Green's functions, which can be associated to an uneven distribution of the seismic noise sources. The application of a phase-matched filter based on an average dispersion curve allowed the effective reduction of some spurious early arrivals and the selection of fundamental-mode Rayleigh wave pulses, making possible an automatic extraction of their group velocities. Then, Rayleigh-wave dispersion curves were retrieved for the set of paths by using frequency-time analysis (FTAN) as well as by following the procedure described by Herrin and Goforth (1977, BSSA) based on the iterative fitting of a phase-matched filter which optimally undisperses the signal. Reliable curves were obtained from 1 s to 6-7 s with group velocities ranging between 1.5 and 2.2 km/s. Some lateral variations in velocity have been detected in spite of the limited spatial coverage and path density, which substantially restricted the resolution. A mean S-wave velocity model has been inverted for this area down to ~3 km.
Minimum variance imaging based on correlation analysis of Lamb wave signals.
Hua, Jiadong; Lin, Jing; Zeng, Liang; Luo, Zhi
2016-08-01
In Lamb wave imaging, MVDR (minimum variance distortionless response) is a promising approach for the detection and monitoring of large areas with sparse transducer network. Previous studies in MVDR use signal amplitude as the input damage feature, and the imaging performance is closely related to the evaluation accuracy of the scattering characteristic. However, scattering characteristic is highly dependent on damage parameters (e.g. type, orientation and size), which are unknown beforehand. The evaluation error can degrade imaging performance severely. In this study, a more reliable damage feature, LSCC (local signal correlation coefficient), is established to replace signal amplitude. In comparison with signal amplitude, one attractive feature of LSCC is its independence of damage parameters. Therefore, LSCC model in the transducer network could be accurately evaluated, the imaging performance is improved subsequently. Both theoretical analysis and experimental investigation are given to validate the effectiveness of the LSCC-based MVDR algorithm in improving imaging performance.
NASA Astrophysics Data System (ADS)
Oguri, Masamune
2016-04-01
Gravitational waves from inspiraling compact binaries are known to be an excellent absolute distance indicator, yet it is unclear whether electromagnetic counterparts of these events are securely identified for measuring their redshifts, especially in the case of black hole-black hole mergers such as the one recently observed with the Advanced LIGO. We propose to use the cross-correlation between spatial distributions of gravitational wave sources and galaxies with known redshifts as an alternative means of constraining the distance-redshift relation from gravitational waves. In our analysis, we explicitly include the modulation of the distribution of gravitational wave sources due to weak gravitational lensing. We show that the cross-correlation analysis in next-generation observations will be able to tightly constrain the relation between the absolute distance and the redshift and therefore constrain the Hubble constant as well as dark energy parameters.
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Universality in Stochastic Exponential Growth
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.
2014-07-01
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
NASA Technical Reports Server (NTRS)
Fritts, David C.
1996-01-01
The goals of this research effort have been to use MF radar and UARS/HRDI wind measurements for correlative studies of large-scale atmospheric dynamics, focusing specifically on the tidal and various planetary wave structures occurring in the middle atmosphere. We believed that the two data sets together would provide the potential for much more comprehensive studies than either by itself, since they jointly would allow the removal of ambiguities in wave structure that are difficult to resolve with either data set alone. The joint data were to be used for studies of wave structure, variability, and the coupling of these motions to mean and higher-frequency motions.
Derivation of stretched exponential tap density equations of granular powders.
Hao, Tian
2015-04-21
The tap density of granular powders was found to be better fitted with the stretched exponential law. In our previous work, the stretched exponential tap density equations were derived with the rate process theory and free volume concept, under the assumption that the particle packing rate during the tapping process obeys the stretched Arrhenius equation, which, however, has an empirical origin. In this article, the above assumption is eliminated and attempts are made to obtain the stretched exponential tap density equations from very fundamental bases. In a vertical tapping process, the probability of particles attaining certain energy states is assumed to obey the Boltzmann distribution and particles traveling from one site to another are assumed to follow a very common memoryless random exponential law. The stretched exponential tap density equations are thus derived and all parameters acquire clear physical meanings. The most important parameter, the stretched exponential, is demonstrated to correlate with the interparticle forces: a small value may indicate a strong adhesive or cohesive interaction. Therefore, the stretched exponential could be a better indicator for powder flowability correlated with particle interactions as well.
NASA Astrophysics Data System (ADS)
Li, Jia; Chang, Liping; Chen, Feinan
2016-12-01
Based on the first-order Born approximation, the correlation between intensity fluctuations is derived for a partially coherent, electromagnetic plane wave scattering from a spatially quasi-homogeneous medium. Young's pinholes are utilized to control the degree of coherence of the incident field. For the electromagnetic scattering case, it is shown that the CIF of the scattered field strongly depends on the degree of polarization of the incident wave, Young's pinhole parameter, effective radius and correlation length of the medium. The influences of these parameters on the CIF distributions are revealed by numerical calculations.
Model-based cross-correlation search for gravitational waves from Scorpius X-1
NASA Astrophysics Data System (ADS)
Whelan, John T.; Sundaresan, Santosh; Zhang, Yuanhao; Peiris, Prabath
2015-05-01
We consider the cross-correlation search for periodic gravitational waves and its potential application to the low-mass x-ray binary Sco X-1. This method coherently combines data not only from different detectors at the same time, but also data taken at different times from the same or different detectors. By adjusting the maximum allowed time offset between a pair of data segments to be coherently combined, one can tune the method to trade off sensitivity and computing costs. In particular, the detectable signal amplitude scales as the inverse fourth root of this coherence time. The improvement in amplitude sensitivity for a search with a maximum time offset of one hour, compared with a directed stochastic background search with 0.25-Hz-wide bins, is about a factor of 5.4. We show that a search of one year of data from the Advanced LIGO and Advanced Virgo detectors with a coherence time of one hour would be able to detect gravitational waves from Sco X-1 at the level predicted by torque balance over a range of signal frequencies from 30 to 300 Hz; if the coherence time could be increased to ten hours, the range would be 20 to 500 Hz. In addition, we consider several technical aspects of the cross-correlation method: We quantify the effects of spectral leakage and show that nearly rectangular windows still lead to the most sensitive search. We produce an explicit parameter-space metric for the cross-correlation search, in general, and as applied to a neutron star in a circular binary system. We consider the effects of using a signal template averaged over unknown amplitude parameters: The quantity to which the search is sensitive is a given function of the intrinsic signal amplitude and the inclination of the neutron-star rotation axis to the line of sight, and the peak of the expected detection statistic is systematically offset from the true signal parameters. Finally, we describe the potential loss of signal-to-noise ratio due to unmodeled effects such as signal
Halland, M; Ravi, K; Barlow, J; Arora, A
2016-01-01
Barium esophagrams are a frequently performed test, and radiological observations about potential abnormal esophageal motility, such as tertiary contractions, are commonly reported. We sought to assess the correlation between tertiary waves, and in particular isolated tertiary waves, on esophagrams and findings on non-synchronous high-resolution esophageal manometry. We retrospectively reviewed reports of esophagrams performed at a tertiary referral center and identified patients in whom tertiary waves were observed and a high-resolution esophageal manometry had been performed. We defined two groups; group 1 was defined as patients with isolated tertiary waves, whereas group 2 had tertiary waves and evidence of achalasia or an obstructing structural abnormality on the esophagram. We collected data on demographics, dysphagia score, associated findings on esophagram, and need for intervention. We reviewed the reports of 2100 esophagrams of which tertiary waves were noted as an isolated abnormality in 92, and in association with achalasia or a structural obstruction in 61. High-resolution manometry was performed in 17 patients in group 1, and five had evidence of a significant esophageal motility disorder and 4 required any intervention. Twenty-one patients in group 2 underwent manometry, and 18 had a significant esophageal motility disorder. An isolated finding of tertiary waves on an esophagram is rarely associated with a significant esophageal motility disorder that requires intervention. All patients with isolated tertiary waves who required intervention had a dysphagia to liquids. Tertiary contractions, in the absence of dysphagia to liquids, indicate no significant esophageal motility disorder.
Shear wave elastography results correlate with liver fibrosis histology and liver function reserve
Feng, Yan-Hong; Hu, Xiang-Dong; Zhai, Lin; Liu, Ji-Bin; Qiu, Lan-Yan; Zu, Yuan; Liang, Si; Gui, Yu; Qian, Lin-Xue
2016-01-01
AIM: To evaluate the correlation of shear wave elastography (SWE) results with liver fibrosis histology and quantitative function reserve. METHODS: Weekly subcutaneous injection of 60% carbon tetrachloride (1.5 mL/kg) was given to 12 canines for 24 wk to induce experimental liver fibrosis, with olive oil given to 2 control canines. At 24 wk, liver condition was evaluated using clinical biochemistry assays, SWE imaging, lidocaine metabolite monoethylglycine-xylidide (MEGX) test, and histologic fibrosis grading. Clinical biochemistry assays were performed at the institutional central laboratory for routine liver function evaluation. Liver stiffness was measured in triplicate from three different intercostal spaces and expressed as mean liver stiffness modulus (LSM). Plasma concentrations of lidocaine and its metabolite MEGX were determined using high-performance liquid chromatography repeated in duplicate. Liver biopsy samples were fixed in 10% formaldehyde, and liver fibrosis was graded using the modified histological activity index Knodell score (F0-F4). Correlations among histologic grading, LSM, and MEGX measures were analyzed with the Pearson linear correlation coefficient. RESULTS: At 24 wk liver fibrosis histologic grading was as follows: F0, n = 2 (control); F1, n = 0; F2, n = 3; F3, n = 7; and F4, n = 2. SWE LSM was positively correlated with histologic grading (r = 0.835, P < 0.001). Specifically, the F4 group had a significantly higher elastic modulus than the F3, F2, and F0 groups (P = 0.002, P = 0.003, and P = 0.006, respectively), and the F3 group also had a significantly higher modulus than the control F0 group (P = 0.039). LSM was negatively associated with plasma MEGX concentrations at 30 min (r = -0.642; P = 0.013) and 60 min (r = -0.651; P = 0.012), time to ½ of the maximum concentration (r = -0.538; P = 0.047), and the area under the curve (r = -0.636; P = 0.014). Multiple comparisons showed identical differences in these three measures
Linear or Exponential Number Lines
ERIC Educational Resources Information Center
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather…
Approximating Functions with Exponential Functions
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2005-01-01
The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…
Holz, Johannes; Piosczyk, Hannah; Feige, Bernd; Spiegelhalder, Kai; Baglioni, Chiara; Riemann, Dieter; Nissen, Christoph
2012-12-01
Previous studies suggest that sleep-specific brain activity patterns such as sleep spindles and electroencephalographic slow-wave activity contribute to the consolidation of novel memories. The generation of both sleep spindles and slow-wave activity relies on synchronized oscillations in a thalamo-cortical network that might be implicated in synaptic strengthening (spindles) and downscaling (slow-wave activity) during sleep. This study further examined the association between electroencephalographic power during non-rapid eye movement sleep in the spindle (sigma, 12-16 Hz) and slow-wave frequency range (0.1-3.5 Hz) and overnight memory consolidation in 20 healthy subjects (10 men, 27.1 ± 4.6 years). We found that both electroencephalographic sigma power and slow-wave activity were positively correlated with the pre-post-sleep consolidation of declarative (word list) and procedural (mirror-tracing) memories. These results, although only correlative in nature, are consistent with the view that processes of synaptic strengthening (sleep spindles) and synaptic downscaling (slow-wave activity) might act in concert to promote synaptic plasticity and the consolidation of both declarative and procedural memories during sleep.
Lin, Chun-I; Lu, Yan; He, Cunfu; Song, Guorong; Lee, Yung-Chun
2015-11-01
This paper presents a method for measuring circumferential Lamb waves propagating on a cylindrically curved thin plate. The measurement is carried out using a wideband and line-focused poly(vinylidene fluoride) transducer along with a defocusing waveform measurement method. After synthesizing the acquired waveforms, interference patterns can be obtained and a cross correlation method is developed to accurately extract the wave velocity as a function of wave frequency. Using three stainless steel thin plates of different thicknesses (100, 150, and 300 μm) and a radius of curvature of 10 mm, dispersion curves for several fundamental and higher order modes of circumferential Lamb waves are simultaneously determined. Theoretical dispersion curves are also calculated and compared with their experimental counterparts. Very good agreements are observed, which concludes the measurement accuracy of this measurement method.
NASA Astrophysics Data System (ADS)
Fritts, David C.; Pautet, P.-Dominique; Bossert, Katrina; Taylor, Michael J.; Williams, Bifford P.; Iimura, Hiroyuki; Yuan, Tao; Mitchell, Nicholas J.; Stober, Gunter
2014-12-01
An Advanced Mesosphere Temperature Mapper and other instruments at the Arctic Lidar Observatory for Middle Atmosphere Research in Norway (69.3°N) and at Logan and Bear Lake Observatory in Utah (42°N) are used to demonstrate a new method for quantifying gravity wave (GW) pseudo-momentum fluxes accompanying spatially and temporally localized GW packets. The method improves on previous airglow techniques by employing direct characterization of the GW temperature perturbations averaged over the OH airglow layer and correlative wind and temperature measurements to define the intrinsic GW properties with high confidence. These methods are applied to two events, each of which involves superpositions of GWs having various scales and character. In each case, small-scale GWs were found to achieve transient, but very large, momentum fluxes with magnitudes varying from ~60 to 940 m2 s-2, which are ~1-2 decades larger than mean values. Quantification of the spatial and temporal variations of GW amplitudes and pseudo-momentum fluxes may also enable assessments of the total pseudo-momentum accompanying individual GW packets and of the potential for secondary GW generation that arises from GW localization. We expect that the use of this method will yield key insights into the statistical forcing of the mesosphere and lower thermosphere by GWs, the importance of infrequent large-amplitude events, and their effects on GW spectral evolution with altitude.
NASA Astrophysics Data System (ADS)
Xueju, Shen; Chao, Lin; Xiao, Zou; Jianjun, Cai
2015-05-01
We present a nonlinear optical cryptosystem with multi-dimensional keys including phase, polarization and diffraction distance. To make full use of the degrees of freedom that optical processing offers, an elaborately designed vector wave with both a space-variant phase and locally linear polarization is generated with a common-path interferometer for illumination. The joint transform correlator in the Fresnel domain, implemented with a double optical wedge, is utilized as the encryption framework which provides an additional key known as the Fresnel diffraction distance. Two nonlinear operations imposed on the recorded joint Fresnel power distribution (JFPD) by a charge coupled device (CCD) are adopted. The first one is the division of power distribution of the reference window random function which is previously proposed by researchers and can improve the quality of the decrypted image. The second one is the recording of a hybrid JFPD using a micro-polarizers array with orthogonal and random transmissive axes attached to the CCD. Then the hybrid JFPD is further scrambled by substituting random noise for partial power distribution. The two nonlinear operations break the linearity of this cryptosystem and provide ultra security. We verify our proposal using a quick response code for noise-free recovery.
Weak values, quantum trajectories, and the cavity-QED experiment on wave-particle correlation
NASA Astrophysics Data System (ADS)
Wiseman, H. M.
2002-03-01
Weak values as introduced by Aharonov, Albert, and Vaidman (AAV) are ensemble-average values for the results of weak measurements. They are interesting when the ensemble is preselected on a particular initial state and postselected on a particular final measurement result. It is shown that weak values arise naturally in quantum optics, as weak measurements occur whenever an open system is monitored (as by a photodetector). The quantum-trajectory theory is used to derive a generalization of AAV's formula to include (a) mixed initial conditions, (b) nonunitary evolution, (c) a generalized (nonprojective) final measurement, and (d) a non-back-action-evading weak measurement. This theory is applied to the recent cavity-QED experiment demonstrating wave particle duality [G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000)]. It is shown that the ``fractional-order'' correlation function measured in that experiment can be recast as a weak value in a form as simple as that introduced by AAV.
Optical imaging through turbid media with a degenerate four wave mixing correlation time gate
Sappey, A.D. )
1994-12-20
A novel method for detection of ballistic light and rejection of unwanted diffusive light to image structures inside highly scattering media is demonstrated. Degenerate four wave mixing (DFWM) of a doubled YAG laser in Rhodamine 6G is used to provide an ultrafast correlation time gate to discriminate against light that has undergone multiple scattering and therefore lost memory of the structures inside the scattering medium. We present preliminary results that determine the nature of the DFWM grating, confirm the coherence time of the laser, prove the phase-conjugate nature of the signal beam, and determine the dependence of the signal (reflectivity) on dye concentration and laser intensity. Finally, we have obtained images of a test cross-hair pattern through highly turbid suspensions of whole milk in water that are opaque to the naked eye. These imaging experiments demonstrate the utility of DFWM for imaging through turbid media. Based on our results, the use of DFWM as an ultrafast time gate for the detection of ballistic light in optical mammography appears to hold great promise for improving the current state of the art.
NASA Astrophysics Data System (ADS)
Lee, Dongyeon; Tippur, Hareesh V.
2010-03-01
In this work, fracture behavior of unidirectional graphite/epoxy composite materials is optically investigated. Single-edge notched coupons are studied under geometrically symmetric impact loading. The notch orientation parallel to or at an angle relative to the fiber orientation is considered to produce mode-I as well as mixed-mode fracture. Stress-wave induced crack initiation and rapid crack growth events are studied using a digital correlation technique and high-speed photography. Surface deformations histories in the crack-tip vicinity are obtained by analyzing decorated speckle recordings. Measured deformation fields are used to extract fracture parameters and examine the effect of fiber orientation on crack initiation and growth behaviors. The maximum crack speed observed is the highest for mode-I dominant conditions and decreases with increasing fiber orientation angle. With increasing fiber orientation angle, crack takes longer to attain the maximum speed upon initiation. The crack initiation toughness values decrease with increasing degree-of-anisotropy.
NASA Astrophysics Data System (ADS)
Lee, Dongyeon; Tippur, Hareesh V.
2009-12-01
In this work, fracture behavior of unidirectional graphite/epoxy composite materials is optically investigated. Single-edge notched coupons are studied under geometrically symmetric impact loading. The notch orientation parallel to or at an angle relative to the fiber orientation is considered to produce mode-I as well as mixed-mode fracture. Stress-wave induced crack initiation and rapid crack growth events are studied using a digital correlation technique and high-speed photography. Surface deformations histories in the crack-tip vicinity are obtained by analyzing decorated speckle recordings. Measured deformation fields are used to extract fracture parameters and examine the effect of fiber orientation on crack initiation and growth behaviors. The maximum crack speed observed is the highest for mode-I dominant conditions and decreases with increasing fiber orientation angle. With increasing fiber orientation angle, crack takes longer to attain the maximum speed upon initiation. The crack initiation toughness values decrease with increasing degree-of-anisotropy.
Correlation of wave propagation modes in helicon plasma with source tube lengths
NASA Astrophysics Data System (ADS)
Niu, Chen; Zhao, Gao; Wang, Yu; Liu, Zhongwei; Chen, Qiang
2017-01-01
Helicon wave plasma demonstrates lots of advantages in high coupling efficiency, high density, and low magnetic field. However, the helicon wave plasma still meets challenges in applications of material deposition, surface treatment, and electromagnetic thrusters owing to the changeable coupled efficiency and the remarkable non-uniformity. In this paper, we explore the wave propagation characterization by the B-dot probe in various lengths of source tubes. We find that in a long source tube the standing wave appears under the antenna zone, while the traveling wave is formed out of the antenna region. The apparent modulation of wave amplitude is formed in upstream rather than in downstream of the antenna. In a short source tube, however, there is only standing wave propagation.
Exponential Size Distribution of von Willebrand Factor
Lippok, Svenja; Obser, Tobias; Müller, Jochen P.; Stierle, Valentin K.; Benoit, Martin; Budde, Ulrich; Schneppenheim, Reinhard; Rädler, Joachim O.
2013-01-01
Von Willebrand Factor (VWF) is a multimeric protein crucial for hemostasis. Under shear flow, it acts as a mechanosensor responding with a size-dependent globule-stretch transition to increasing shear rates. Here, we quantify for the first time, to our knowledge, the size distribution of recombinant VWF and VWF-eGFP using a multilateral approach that involves quantitative gel analysis, fluorescence correlation spectroscopy, and total internal reflection fluorescence microscopy. We find an exponentially decaying size distribution of multimers for recombinant VWF as well as for VWF derived from blood samples in accordance with the notion of a step-growth polymerization process during VWF biosynthesis. The distribution is solely described by the extent of polymerization, which was found to be reduced in the case of the pathologically relevant mutant VWF-IIC. The VWF-specific protease ADAMTS13 systematically shifts the VWF size distribution toward smaller sizes. This dynamic evolution is monitored using fluorescence correlation spectroscopy and compared to a computer simulation of a random cleavage process relating ADAMTS13 concentration to the degree of VWF breakdown. Quantitative assessment of VWF size distribution in terms of an exponential might prove to be useful both as a valuable biophysical characterization and as a possible disease indicator for clinical applications. PMID:24010664
Continuous-wave quasi-phase-matched waveguide correlated photon pair source on a III–V chip
Sarrafi, Peyman Zhu, Eric Y.; Dolgaleva, Ksenia; Aitchison, J. Stewart; Qian, Li; Holmes, Barry M.; Hutchings, David C.
2013-12-16
We report on the demonstration of correlated photon pair generation in a quasi-phase-matched superlattice GaAs/AlGaAs waveguide using a continuous-wave pump. Our photon pair source has a low noise level and achieves a high coincidence-to-accidental ratio greater than 100, which is the highest value reported in III–V chips so far. This correlated photon pair source has the potential to be monolithically integrated with on-chip pump laser sources fabricated on the same superlattice wafer structure, enabling direct correlated/entangled photon pair production from a compact electrically powered chip.
Grassani, Davide; Simbula, Angelica; Pirotta, Stefano; Galli, Matteo; Menotti, Matteo; Harris, Nicholas C; Baehr-Jones, Tom; Hochberg, Michael; Galland, Christophe; Liscidini, Marco; Bajoni, Daniele
2016-04-01
Compact silicon integrated devices, such as micro-ring resonators, have recently been demonstrated as efficient sources of quantum correlated photon pairs. The mass production of integrated devices demands the implementation of fast and reliable techniques to monitor the device performances. In the case of time-energy correlations, this is particularly challenging, as it requires high spectral resolution that is not currently achievable in coincidence measurements. Here we reconstruct the joint spectral density of photons pairs generated by spontaneous four-wave mixing in a silicon ring resonator by studying the corresponding stimulated process, namely stimulated four wave mixing. We show that this approach, featuring high spectral resolution and short measurement times, allows one to discriminate between nearly-uncorrelated and highly-correlated photon pairs.
Grassani, Davide; Simbula, Angelica; Pirotta, Stefano; Galli, Matteo; Menotti, Matteo; Harris, Nicholas C.; Baehr-Jones, Tom; Hochberg, Michael; Galland, Christophe; Liscidini, Marco; Bajoni, Daniele
2016-01-01
Compact silicon integrated devices, such as micro-ring resonators, have recently been demonstrated as efficient sources of quantum correlated photon pairs. The mass production of integrated devices demands the implementation of fast and reliable techniques to monitor the device performances. In the case of time-energy correlations, this is particularly challenging, as it requires high spectral resolution that is not currently achievable in coincidence measurements. Here we reconstruct the joint spectral density of photons pairs generated by spontaneous four-wave mixing in a silicon ring resonator by studying the corresponding stimulated process, namely stimulated four wave mixing. We show that this approach, featuring high spectral resolution and short measurement times, allows one to discriminate between nearly-uncorrelated and highly-correlated photon pairs. PMID:27032688
Exponentially Stabilizing Robot Control Laws
NASA Technical Reports Server (NTRS)
Wen, John T.; Bayard, David S.
1990-01-01
New class of exponentially stabilizing laws for joint-level control of robotic manipulators introduced. In case of set-point control, approach offers simplicity of proportion/derivative control architecture. In case of tracking control, approach provides several important alternatives to completed-torque method, as far as computational requirements and convergence. New control laws modified in simple fashion to obtain asymptotically stable adaptive control, when robot model and/or payload mass properties unknown.
Amsler, C D; Cho, M; Matsumura, P
1993-01-01
Motility and chemotaxis allow cells to move away from stressful microenvironments. Motility of Escherichia coli in batch cultures, as measured by cell swimming speed, was low in early-exponential-phase cells, peaked as the cells entered post-exponential phase, and declined into early stationary phase. Transcription from the flhB operon and synthesis of flagellin protein similarly peaked in late exponential and early post-exponential phases, respectively. The increase in swimming speed between early-exponential and post-exponential phases was correlated with twofold increases in both flagellar length and flagellar density per cell volume. This increased investment in flagella probably reflects the increased adaptive value of motility in less favorable environments. The decrease in speed between post-exponential and stationary phases was correlated with a threefold decrease in torque produced by the flagellar motors and presumably reflects decreased proton motive force available to stationary-phase cells. Images PMID:8407796
Fine structure of transient waves in a random medium: The correlation and spectral density functions
NASA Technical Reports Server (NTRS)
Wenzel, Alan R.
1994-01-01
This is essentially a progress report on a theoretical investigation of the propagation of transient waves in a random medium. The emphasis in this study is on applications to sonic-boom propagation, particularly as regards the effect of atmospheric turbulence on the sonic-boom waveform. The analysis is general, however, and is applicable to other types of waves besides sonic-boom waves. The phenomenon of primary concern in this investigation is the fine structure of the wave. A figure is used to illustrate what is meant by finestructure.
Cometary kilometric radio waves and plasma waves correlated with ion pick-up effect at Comet Halley
NASA Technical Reports Server (NTRS)
Oya, H.; Morioka, A.; Miyake, W.; Smith, E. J.; Tsurutani, B. T.
1985-01-01
Bow-shock movements at Comet Halley are inferred from the discrete spectra of the cometary kilometric radiation (30-195 kHz); the observed emissions can be interpreted as being generated and propagating from the moving shock. The shock motion is possibly associated with the time variation of the solar wind and cometary outgassing. It is concluded that these plasma wave phenomena are manifestations of ion pick-up processes, which occur even in a remote region 7 million to 10 million km from the cometary nucleus.
Cheng, Jin; Yu, Kuang; Libisch, Florian; Dieterich, Johannes M; Carter, Emily A
2017-03-14
Quantum mechanical embedding theories partition a complex system into multiple spatial regions that can use different electronic structure methods within each, to optimize trade-offs between accuracy and cost. The present work incorporates accurate but expensive correlated wave function (CW) methods for a subsystem containing the phenomenon or feature of greatest interest, while self-consistently capturing quantum effects of the surroundings using fast but less accurate density functional theory (DFT) approximations. We recently proposed two embedding methods [for a review, see: Acc. Chem. Res. 2014 , 47 , 2768 ]: density functional embedding theory (DFET) and potential functional embedding theory (PFET). DFET provides a fast but non-self-consistent density-based embedding scheme, whereas PFET offers a more rigorous theoretical framework to perform fully self-consistent, variational CW/DFT calculations [as defined in part 1, CW/DFT means subsystem 1(2) is treated with CW(DFT) methods]. When originally presented, PFET was only tested at the DFT/DFT level of theory as a proof of principle within a planewave (PW) basis. Part 1 of this two-part series demonstrated that PFET can be made to work well with mixed Gaussian type orbital (GTO)/PW bases, as long as optimized GTO bases and consistent electron-ion potentials are employed throughout. Here in part 2 we conduct the first PFET calculations at the CW/DFT level and compare them to DFET and full CW benchmarks. We test the performance of PFET at the CW/DFT level for a variety of types of interactions (hydrogen bonding, metallic, and ionic). By introducing an intermediate CW/DFT embedding scheme denoted DFET/PFET, we show how PFET remedies different types of errors in DFET, serving as a more robust type of embedding theory.
Correlations of $\pi N$ partial waves for multireaction analyses
Doring, M.; Revier, J.; Ronchen, D.; Workman, R. L.
2016-06-15
In the search for missing baryonic resonances, many analyses include data from a variety of pion- and photon-induced reactions. For elastic πN scattering, however, usually the partial waves of the SAID (Scattering Analysis Interactive Database) or other groups are fitted, instead of data. We provide the partial-wave covariance matrices needed to perform correlated χ^{2} fits, in which the obtained χ^{2} equals the actual χ^{2} up to nonlinear and normalization corrections. For any analysis relying on partial waves extracted from elastic pion scattering, this is a prerequisite to assess the significance of resonance signals and to assign any uncertainty on results. Lastly, the influence of systematic errors is also considered.
NASA Astrophysics Data System (ADS)
Immler, F.; Krüger, K.; Fujiwara, M.; Verver, G.; Rex, M.; Schrems, O.
2008-07-01
A number of field-campaigns in the tropics have been conducted in recent years with two different LIDAR systems at Paramaribo (5.8° N, 55.2° W), Suriname. The lidars detect particles in the atmosphere with high vertical and temporal resolution and are capable of detecting extremely thin cloud layers which frequently occur in the tropical tropopause layer (TTL). Radiosonde as well as operational ECMWF analysis showed that equatorial Kelvin waves propagated in the TTL and greatly modulated its temperature structure. We found a clear correlation between the temperature anomalies introduced by these waves and the occurrence of thin cirrus in the TTL. In particular we found that extremely thin ice clouds form regularly where cold anomalies shift the tropopause to high altitudes. These findings suggest an influence of Kelvin wave activity on the dehydration in the TTL and thus on the global stratospheric water vapour concentration.
NASA Astrophysics Data System (ADS)
Immler, F.; Krüger, K.; Fujiwara, M.; Verver, G.; Rex, M.; Schrems, O.
2008-02-01
A number of field-campaigns in the tropics have been conducted in the recent years with two different LIDAR systems at Paramaribo in Suriname (5.8° N, 55.2° W). The lidars detect particles in the atmosphere with high vertical and temporal resolution and are capable of detecting extremely thin cloud layers which frequently occur in the tropical tropopause layer (TTL). Radiosonde as well as operational ECMWF analysis show that temperature anomalies caused by equatorial Kelvin waves propagate downward, well below the cold point tropopause (CPT). We find a clear correlation between the temperature anomalies introduced by these waves and the occurrence of thin cirrus in the TTL. In particular we found that extremely thin ice clouds form regularly where cold anomalies shift the tropopause to high altitudes. This finding suggests an influence of Kelvin wave activity on the dehydration in the TTL and thus on the global stratospheric water vapour concentration.
Exponential Formulae and Effective Operations
NASA Technical Reports Server (NTRS)
Mielnik, Bogdan; Fernandez, David J. C.
1996-01-01
One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).
NASA Astrophysics Data System (ADS)
Ochi, Masayuki; Arita, Ryotaro; Tsuneyuki, Shinji
2017-01-01
Obtaining accurate band structures of correlated solids has been one of the most important and challenging problems in first-principles electronic structure calculation. There have been promising recent active developments of wave function theory for condensed matter, but its application to band-structure calculation remains computationally expensive. In this Letter, we report the first application of the biorthogonal transcorrelated (BITC) method: self-consistent, free from adjustable parameters, and systematically improvable many-body wave function theory, to solid-state calculations with d electrons: wurtzite ZnO. We find that the BITC band structure better reproduces the experimental values of the gaps between the bands with different characters than several other conventional methods. This study paves the way for reliable first-principles calculations of the properties of strongly correlated materials.
Teaching about Exponential Growth in Social Studies.
ERIC Educational Resources Information Center
Allen, Rodney F.; LaHart, David E.
1984-01-01
Characteristics of exponential growth which should be taught in social studies classes are listed, and learning activities dealing with exponential growth which can be used in secondary social studies classes are provided. (RM)
Non-exponential and oscillatory decays in quantum mechanics
Peshkin, Murray; Volya, Alexander; Zelevinsky, Vladimir
2014-08-07
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.
Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles
Warshaw, S I
2001-07-15
In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resulted from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.
Kwiek, Piotr
2015-03-01
The phenomenon of collinear correlated photon pairs diffraction by an ultrasonic wave is investigated within Raman-Nath and intermediate region. The numbers of single photons and photon pairs counts in discrete diffraction orders were measured as functions of the Raman-Nath parameter. Similarly, the number of coincidence photon counts in separate diffraction orders was also investigated. It was shown experimentally that the phenomenon of photon pairs diffraction by an ultrasonic wave happens at angles identical to those corresponding to single photons diffraction. It was also demonstrated that in case of Raman-Nath diffraction the number of photon pairs in a selected, n(th), diffraction order varies with the Raman-Nath parameter changes as an n(th) order Bessel function of the first kind, raised to the fourth power. Whilst in the so-called intermediate diffraction zone, the number of diffracted photon pairs varies as squared intensity of a diffracted light beam consisting of single photons. Moreover, it was revealed that correlations between photons in selected diffraction orders change with the Raman-Nath parameter variation as products of relevant intensities of light in the considered diffraction orders. Finally, it should be emphasized that the presented formulae describing diffraction of collinear correlated proton pairs by an ultrasonic wave are in a very good agreement with corresponding experimental data, for both Raman-Nath and intermediate diffraction.
NASA Technical Reports Server (NTRS)
Krupp, N.; Tsurutani, B. T.; Lanzerotti, L. J.; Maclennan, C. G.
1996-01-01
We report on measurements of energetic particle modulations observed by the HI-SCALE instrument aboard the Ulysses Spacecraft that were associated with the only hydromagnetic wave event measured inside the Jovian magnetosphere by the Ulysses magnetometer investigation.
NASA Astrophysics Data System (ADS)
Menietti, J. D.; Lin, C. S.; Wong, H. K.
Using the High Altitude Plasma Instrument on board the Dynamics Explorer 1 satellite, an example of electron conics associated with ring (trapped) distributions of warm electrons is shown. Using an electrostatic P-I-C code, numerical simulations of the generation of upper hybrid waves with ring distributions as the free energy source are performed. These waves heat the electrons perpendicular to the magnetic field, and thus provide a very efficient mechanism for the production of electron conics.
Observational constraints on exponential gravity
Yang, Louis; Lee, Chung-Chi; Luo, Ling-Wei; Geng, Chao-Qiang
2010-11-15
We study the observational constraints on the exponential gravity model of f(R)=-{beta}R{sub s}(1-e{sup -R/R}{sub s}). We use the latest observational data including Supernova Cosmology Project Union2 compilation, Two-Degree Field Galaxy Redshift Survey, Sloan Digital Sky Survey Data Release 7, and Seven-Year Wilkinson Microwave Anisotropy Probe in our analysis. From these observations, we obtain a lower bound on the model parameter {beta} at 1.27 (95% C.L.) but no appreciable upper bound. The constraint on the present matter density parameter is 0.245<{Omega}{sub m}{sup 0}<0.311 (95% C.L.). We also find out the best-fit value of model parameters on several cases.
Correlation of Fiber Composite Tensile Strength with the Ultrasonic Stress Wave Factor
NASA Technical Reports Server (NTRS)
Vary, A.; Lark, R. F.
1978-01-01
An ultrasonic-acoustic technique was used to indicate the strength variations of tensile specimens of a graphite-epoxy composite. A stress wave factor was determined and its value was found to depend on variations of the fiber-resin bonding as well as fiber orientation. The fiber orientations studied were 0 deg (longitudinal), 10 deg (off-axis), 90 deg (transverse), 0 deg + or - 45 deg/0 deg symmetrical, and + or - 45 deg] symmetrical. The stress wave factor can indicate variations of the tensile and shear strengths of composite materials. The stress wave factor was also found to be sensitive to strength variations associated with microporosity and differences in fiber-resin ratio.
Correlation of fiber composite tensile strength with the ultrasonic stress wave factor
NASA Technical Reports Server (NTRS)
Vary, A.; Lark, R. F.
1978-01-01
An ultrasonic-acoustic technique was used to indicate the strength variations of tensile specimens of a graphite-epoxy composite. A 'stress wave factor' was determined and its value was found to depend on variations of the fiber-resin bonding as well as fiber orientation. The fiber orientations studied were 0 deg (longitudinal), 10 deg (off-axis), 90 deg (transverse), (0 deg/+ or - 45 deg/0) symmetrical, and (+ or - 45 deg) symmetrical. The stress wave factor can indicate variations of the tensile and shear strengths of composite materials. The stress wave factor was also found to be sensitive to strength variations associated with microporosity and differences in fiber-resin ratio.
Müller, Markus Franziskus; Rummel, Christian; Goodfellow, Marc; Schindler, Kaspar
2014-03-01
Cerebral electrical activity is highly nonstationary because the brain reacts to ever changing external stimuli and continuously monitors internal control circuits. However, a large amount of energy is spent to maintain remarkably stationary activity patterns and functional inter-relations between different brain regions. Here we examine linear EEG correlations in the peri-ictal transition of focal onset seizures, which are typically understood to be manifestations of dramatically changing inter-relations. Contrary to expectations we find stable correlation patterns with a high similarity across different patients and different frequency bands. This skeleton of spatial correlations may be interpreted as a signature of standing waves of electrical brain activity constituting a dynamical ground state. Such a state could promote the formation of spatiotemporal neuronal assemblies and may be important for the integration of information stemming from different local circuits of the functional brain network.
NASA Astrophysics Data System (ADS)
Leroy, Valentin; Strybulevych, Anatoliy; Page, John H.; Scanlon, Martin G.
2011-04-01
We present experimental results on a model system for studying wave propagation in a complex medium exhibiting low-frequency resonances. These experiments enable us to investigate a fundamental question that is relevant for many materials, such as metamaterials, where low-frequency scattering resonances strongly influence the effective medium properties. This question concerns the effect of correlations in the positions of the scatterers on the coupling between their resonances, and hence on wave transport through the medium. To examine this question experimentally, we measure the effective medium wavenumber of acoustic waves in a sample made of bubbles embedded in an elastic matrix over a frequency range that includes the resonance frequency of the bubbles. The effective medium is highly dispersive, showing peaks in the attenuation and the phase velocity as functions of the frequency, which cannot be accurately described using the independent scattering approximation (ISA). This discrepancy may be explained by the effects of the positional correlations of the scatterers, which we show to be dependent on the size of the scatterers. We propose a self-consistent approach for taking this “polydisperse correlation” into account and show that our model better describes the experimental results than the ISA.
NASA Astrophysics Data System (ADS)
Angilella, G. G.; March, N. H.; Pucci, R.
2002-03-01
Following earlier work on electron or hole liquids flowing through assemblies with magnetic fluctuations, we have recently exposed a marked correlation of the superconducting temperature Tc, for non-s-wave pairing materials, with coherence length ξ and effective mass m*. The very recent study of Abanov et al. [Europhys. Lett. 54, 488 (2001)] and the prior investigation of Monthoux and Lonzarich [Phys. Rev. B 59, 14 598 (1999)] have each focused on the concept of a spin-fluctuation temperature Tsf, which again is intimately related to Tc. For the d-wave pairing via antiferromagnetic spin fluctuations in the cuprates, these studies are brought into close contact with our own work, and the result is that kBTsf~ħ2/m*ξ2. This demonstrates that ξ is also determined by such antiferromagnetic spin-fluctuation mediated pair interaction. The coherence length in units of the lattice spacing is then essentially given in the cuprates as the square root of the ratio of two characteristic energies, namely, the kinetic energy of localization of a charge carrier of mass m* in a specified magnetic correlation length to the hopping energy. The quasi-two-dimensional ruthenate Sr2RuO4, with Tc~1.3 K, has p-wave spin-triplet pairing and so is also briefly discussed here.
A correlative investigation of the propagation of ULF wave power through the dayside magnetosphere
NASA Technical Reports Server (NTRS)
Engebretson, Mark J.
1990-01-01
Three different ULF wave phenomena (azimuthally polarized Pc 3 pulsations, radially polarized Pc 4 pulsations, and solitary Pc 5 pulsations related to solar wind pressure pulses) were studied. The main problems covered are: (1) how do magnetospheric Pc 3-4 pulsations, which appear to originate in the solar wind, enter the magnetosphere, and how is this wave energy transported throughout the magnetosphere once it enters; (2) what is the ULF response of the outer dayside magnetosphere to solar wind pressure pulses; and (3) how do Pc 3-4 pulsations modulate ELF-VLF emissions in the dayside magnetosphere.
NASA Astrophysics Data System (ADS)
Spica, Zack; Perton, Mathieu; Calò, Marco; Legrand, Denis; Córdoba-Montiel, Francisco; Iglesias, Arturo
2016-09-01
This work presents an innovative strategy to enhance the resolution of surface wave tomography obtained from ambient noise cross-correlation (C1) by bridging asynchronous seismic networks through the correlation of coda of correlations (C3). Rayleigh wave group dispersion curves show consistent results between synchronous and asynchronous stations. Rayleigh wave group traveltimes are inverted to construct velocity-period maps with unprecedented resolution for a region covering Mexico and the southern United States. The resulting period maps are then used to regionalize dispersion curves in order to obtain local 1-D shear velocity models (VS) of the crust and uppermost mantle in every cell of a grid of 0.4°. The 1-D structures are obtained by iteratively adding layers until reaching a given misfit, and a global tomography model is considered as an input for depths below 150 km. Finally, a high-resolution 3-D VS model is obtained from these inversions. The major structures observed in the 3-D model are in agreement with the tectonic-geodynamic features and with previous regional and local studies. It also offers new insights to understand the present and past tectonic evolution of the region.
NASA Astrophysics Data System (ADS)
Hoggan, Philip E.
2009-03-01
Slater-type orbitals (STO) are rarely used as atomic basis sets for molecular structure and property calculations, since integrals are expensive to evaluate, reliable basis sets are scarce and exact properties such as Kato's cusp condition and the correct exponential decay of the electron density are not significantly better described numerically than with commonly used Gaussian basis sets. We adopt the systematic parallelized development of integration routines for multi-centre integrals, and high-quality basis sets over STOs, useful for modern electron correlation calculations via compact low-variance trial wave-functions for QMC (Quantum Monte Carlo). Molecular QMC applications are also rare, because the method is comparatively complicated to use, however it is extremely precise and can be made to include nearly all the correlation energy. It also scales well for large numbers of processors (1000 s at nearly 100 percent efficiency). Applications need to be carried out on a large scale, to determine electronic structure and properties of large (about 100 atoms) molecules of chemical interest, including intermolecular interactions, best described using Slater trial wave-functions for QMC. Such functions combined as hydrogen-like atomic orbitals possess the correct nodal structure for the high precision FN-MC (Fixed Node Monte Carlo) methods, which include more than 95 percent of the electron correlation energy.
Shats, M; Punzmann, H; Xia, H
2010-03-12
We report the first observation of extreme wave events (rogue waves) in parametrically driven capillary waves. Rogue waves are observed above a certain threshold in forcing. Above this threshold, frequency spectra broaden and develop exponential tails. For the first time we present evidence of strong four-wave coupling in nonlinear waves (high tricoherence), which points to modulation instability as the main mechanism in rogue waves. The generation of rogue waves is identified as the onset of a distinct tail in the probability density function of the wave heights. Their probability is higher than expected from the measured wave background.
NASA Astrophysics Data System (ADS)
Tanimoto, T.; Okamoto, T.
2013-12-01
Modeling high-frequency (>1 Hz) seismic waves is known to be difficult but it is extremely important for earthquake hazard mitigation as many buildings have resonant frequencies above 1 Hz. In this study, we examine high-frequency waves at 1.64 Hz, generated by building-shaking experiments in California. The specific data we will examine are seismic data generated by shaking experiments of the Millikan Library between 2000 and 2002, located on the campus of California Institute of Technology in Pasadena, California. The excited wavefields were recorded by the broadband seismic network in the region (~150 stations), Southern California Seismic Network (SCSN). There were about 60 stations with good signal-to-noise ratios among SCSN stations. The maximum distance for signal detection was 323 km (station GRA). Based on numerical calculations for a regional seismic structure model (SCEC Community Velocity Model 11.9), we can show that the signals are dominated by surface waves (at 1.11 Hz and 1.64 Hz), whose energy is confined to shallow depths. The focus of this report will be on the cross-correlated signals between a station in the building (station MIK) and other stations. This cross-correlation may be viewed as a source deconvolution process and will let us focus on propagation in the medium. This cross-correlated phase can be expressed as a line integral of wavenumber along a propagation path for a direct (ballistic) phase, although it may contain complexity from the caustics (the Maslov index). Somewhat to our surprise, despite the fact that we are dealing with high frequency waves (1.64 Hz), we observe well-defined constant phase in many cross-correlated seismograms. If we knew the number of cycles between the source (Millikan) and a station, we could estimate phase velocity in principle but this is not possible and seems extremely hard because the number of cycles is about 50-100 or more. However, our signals do show frequency-dependence within a narrow (signal
NASA Astrophysics Data System (ADS)
Oren, C.; Nowack, R. L.
2015-12-01
It is known that the positive lags of the auto-correlation for the seismic transmission response of a layered medium correspond to the reflection seismogram (Claerbout, 1968). In this study, we investigate the use of ambient seismic noise recorded at selected broadband USArray EarthScope Transportable Array (TA) stations to obtain effective reflection seismograms for frequencies up to 1 Hz. The goal is to determine the most suitable parameters used for the processing of ambient seismic noise for the identification of crustal and upper mantle reflections and to minimize unwanted artifacts in the noise correlations. In order to best retrieve the body-wave components of the Green's function beneath a station, a number of processing steps are required. We first remove the instrument response and apply a temporal normalization to remove the effects of the most energetic sources. Next we implement spectral whitening. We test several operators for the spectral whitening where the undulations of the power spectrum are related to the strengths of later arrivals in the auto-correlation. Different filters are then applied to the auto-correlation functions, including Gaussian and zero phase Butterworth filters, in order to reduce the effect of side lobes. Hourly auto-correlations are then stacked for up to one year. On the final stack, Automatic Gain Control (AGC) is applied to equalize the correlation amplitudes in the time domain. The robustness of the resulting ambient noise auto-correlation is first tested on selected TA stations in Nevada, where we are able to identify PmP and SmS arrivals similar to those found by Tibuleac and von Seggern (2012). We then investigate noise auto-correlations applied to selected USArray TA stations in the central US.
Long-range correlations induced by the self-regulation of zonal flows and drift-wave turbulence
Manz, P.; Ramisch, M.; Stroth, U.
2010-11-15
By means of a unique probe array, the interaction between zonal flows and broad-band drift-wave turbulence has been investigated experimentally in a magnetized toroidal plasma. Homogeneous potential fluctuations on a magnetic flux surface, previously reported as long range correlations, could be traced back to a predator-prey-like interaction between the turbulence and the zonal flow. At higher frequency the nonlocal transfer of energy to the zonal flow is dominant and the low-frequency oscillations are shown to result from the reduced turbulence activity due to this energy loss. This self-regulation process turns out to be enhanced with increased background shear flows.
EXPONENTIAL GALAXY DISKS FROM STELLAR SCATTERING
Elmegreen, Bruce G.; Struck, Curtis E-mail: curt@iastate.edu
2013-10-01
Stellar scattering off of orbiting or transient clumps is shown to lead to the formation of exponential profiles in both surface density and velocity dispersion in a two-dimensional non-self gravitating stellar disk with a fixed halo potential. The exponential forms for both nearly flat rotation curves and near-solid-body rotation curves. The exponential does not depend on initial conditions, spiral arms, bars, viscosity, star formation, or strong shear. After a rapid initial development, the exponential saturates to an approximately fixed scale length. The inner exponential in a two-component profile has a break radius comparable to the initial disk radius; the outer exponential is primarily scattered stars.
Theory, computation, and application of exponential splines
NASA Technical Reports Server (NTRS)
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Surface Wave Dispersion Measurements and Tomography from Ambient Seismic Noise Correlation in China
2008-09-30
30 Sep 2008 REPRINT 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER SURFACE WAVE DISPERSION MEASUREMENTS AND TOMOGRAPHY FROM FA8718-07-C-0006 C AMIBIENT...25 September 2008, Portsmouth, VA, Volume I pp 268 - 278. 14. ABSTRACT We perform ambient noise tomography of China using the data from the China...National Seismic Network and global and PASSCAL stations. The results so far are summarized below. (I) Dispersion measurements and tomography . For most of
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.
Long-time correlation for the chaotic orbit in the two-wave Hamiltonian
NASA Astrophysics Data System (ADS)
Hatori, Tadatsugu; Irie, Haruyuki
1987-03-01
The time correlation function of velocity is found to decay with the power law for the orbit governed by a Hamiltonian, H=v sup 2/2 - Mcosx - Pcos (k(x-t)). The renormalization group technique can predict the power of decay for the correlation function defined by the ensemble average. The power spectrum becomes the 1/f-type for a special case.
NASA Astrophysics Data System (ADS)
Aglietta, M.; Castellina, A.; Fulgione, W.; Trinchero, G.; Vernetto, S.; Astone, P.; Badino, G.; Bologna, G.; Bassan, M.; Coccia, E.; Modena, I.; Bonifazi, P.; Castellano, M. G.; Visco, M.; Castagnoli, C.; Galeotti, P.; Saavedra, O.; Cosmelli, C.; Frasca, S.; Pallottino, G. V.; Pizzella, G.; Rapagnani, P.; Ricci, F.; Majorana, E.; Gretz, D.; Weber, J.; Wilmot, G.
1991-11-01
Following a previously found correlation between the gravitational-wave detectors and the Mont Blanc particle detector, the authors have searched for a similar correlation between the data of the experiments mentioned in the title. They have found that both the Kamioka and the IMB data have a correlation with the gravitational-wave data that occurs with the same characteristics and at the same time of that already found with Mont Blanc. This correlation extends for a period of one or two hours centred at the hour 2:45 UT of 23 February 1987. It shows that the particle detector signals are delayed with respect to the gravitational-wave detector signals by (1.2±0.5)s. The probability that the additional correlation due to Kamioka and IMB is only accidental is estimated of the order of 10-3 or 10-4.
Ground state and resonant states of helium in exponential cosine screened Coulomb potential
NASA Astrophysics Data System (ADS)
Ghoshal, Arijit; Ho, Y. K.
2009-05-01
We have investigated the ground state and a resonance state of normal helium atom in exponential cosine screened Coulomb potential (ECSCP) with screening parameterλ: V(r),,,1r,^-λr(λr) (in a.u.), where r denotes the inter-particle distance. Within the framework of Ritz's variational principle and making use of a highly correlated wave function, we have determined the ground state energies and wave functions of the helium atom for different values of the screening parameterλ. Furthermore, we have shown that the ground state energy of helium for a particular value of λ does converge with increasing number of terms in the wave function. In addition, using the stabilization method, we have investigated the doubly excited 2s^2 ^1S^e resonance state in helium with ECSCP. Resonance energy and width for various λ values are calculated. Our present work will play a useful role in the investigations of atomic structures in quantum plasmas [1]. [1]. P.K. Shukla and B. Eliasson, Phys. Lett. A 372, 2899 (2008).
Optical imaging through turbid media using a degenerate-four-wave mixing correlation time gate
Bigio, I.J.; Strauss, C.E.M.; Zerkle, D.K.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors have demonstrated the use of a degenerate-four-wave-mixing time gate to allow imaging through turbid media, with potential application to tissue imaging. A near infrared (NIR), long-pulse Cr{sup +3}:Li{sub 2}SrAlF{sub 6} laser was used as the light source (during most the project) for imaging through clear and turbid media. Preliminary experiments were also carried out with a continuous diode laser.
Yalcin, E; Keskin Akca, A; Selcuk, B; Kurtaran, A; Akyuz, M
2012-02-01
Plantar heel pain, a chronic and disabling foot alignment, occurs in the adult population. Extracorporal shock wave therapy (ESWT) offers a nonsurgical option in addition to stretching exercises, heel cups, NSAI, and corticosteroid injections. This study aimed to investigate the effects of ESWT on calcaneal bone spurs and the correlation between clinical outcomes and radiologic changes. The study involved 108 patients with heel pain and radiologically diagnosed heel spurs. All patients underwent ESWT once a week for 5 weeks at the clinic. Each patient received 2,000 impulses of shock waves, starting with 0.05 mJ/mm2 (1.8 bar) and increasing to 0.4 mJ/mm2 (4.0 bar). Standard radiographies of the affected heels were obtained before and after the therapy. Clinical results demonstrated excellent (no pain) in 66.7% of the cases, good (50% of pain reduced) in 15.7% of the cases, and unsatisfactory (no reduction in pain) in 17.6%. After five ESWT treatments, no patients who received shock wave applications had significant spur reductions, but 19 patients (17.6%) had a decrease in the angle of the spur, 23 patients (21.3%) had a decrease in the dimensions of the spur, and one patient had a broken spur. Therefore, results showed no correlation between clinical outcome and radiologic changes. The present study supports the finding that even with no radiologic change after ESWT therapy, the therapy produces significant effects in reducing patients' complaints about heel spurs.
Wave breaking and turbulence at a tidal inlet
NASA Astrophysics Data System (ADS)
Zippel, Seth; Thomson, Jim
2015-02-01
Field measurements collected with surface drifters at New River Inlet (NC, USA) are used to characterize wave breaking and turbulence in the presence of currents. Shoreward wave evolution is affected by currents, and breaking is observed in deeper water with opposing currents (ebb tides) relative to the following currents (flood tides). Wave dissipation models are evaluated with observed cross-shore gradients in wave energy flux. Wave dissipation models that include the effects of currents are better correlated with the observations than the depth-only models. Turbulent dissipation rates measured in the breaking regions are used to evaluate two existing scaling models for the vertical structure and magnitude of turbulent dissipation relative to wave dissipation. Although both describe the rapid decay of turbulence beneath the surface, exponential vertical scaling by water depth is superior to power law vertical scaling by wave height.
Giving Exponential Functions a Fair Shake
ERIC Educational Resources Information Center
Wanko, Jeffrey J.
2005-01-01
This article details an exploration of exponential decay and growth relationships using M&M's and dice. Students collect data for mathematical models and use graphing calculators to make sense of the general form of the exponential functions. (Contains 10 figures and 2 tables.)
NASA Astrophysics Data System (ADS)
Shi, F.; Lowe, M. J. S.; Craster, R. V.
2017-02-01
We propose an ultrasonic methodology to reconstruct the height correlation function of remotely inaccessible random rough surfaces in solids. The inverse method is based on the Kirchhoff approximation(KA), and it requires measuring the angular distribution of diffuse scattering intensities by sending in a narrow band incident pulse. Near field scattering effects are also included by considering the Fresnel assumption. The proposed approach is successfully verified by simulating the scattering from multiple realizations of rough surfaces whose correlation function is known, calculating the mean scattering intensities from these received signals, and then deploying the inverse method on these to reconstruct the original correlation function. Very good agreement between the reconstructed correlation function and the original is found, for a wide range of roughness parameters. In addition, the effect of reducing the number of realizations to approximate the mean intensity are investigated, providing confidence bounds for the experiment. An experiment on a corrugated rough surface is performed with a limited number of scans using a phased array, which further validates the proposed inversion algorithm.
Correlation of bow shock plasma wave turbulence with solar wind parameters
NASA Technical Reports Server (NTRS)
Rodriguez, P.; Gurnett, D. A.
1975-01-01
The r.m.s. field strengths of electrostatic and electromagnetic turbulence in the earth's bow shock, measured in the frequency range 20 Hz to 200 kHz with IMP-6 satellite, are found to correlate with specific solar wind parameters measured upstream of the bow shock.
The matrix exponential in transient structural analysis
NASA Technical Reports Server (NTRS)
Minnetyan, Levon
1987-01-01
The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.
NASA Astrophysics Data System (ADS)
Li, Jia; Chen, Feinan
2016-11-01
Based on the first-order Born approximation, formulas are derived for the correlation between intensity fluctuations (CIF) of light generated by a Young’s diffractive electromagnetic wave scattered by a spatially quasi-homogeneous (QH), anisotropic medium. It is shown that the CIF of the scattered field can be written as the summation of the Fourier transforms of the strengths and normalized correlation coefficients (NCCs) of the scattering potentials. The differences between our results and those obtained in the previous literature are discussed. Our results might be important in investigating the high-order intensity correlation of an electromagnetic wave scattered from a 3D anisotropic object.
NASA Astrophysics Data System (ADS)
Scheffold, Frank
2014-08-01
To characterize the structural and dynamic properties of soft materials and small particles, information on the relevant mesoscopic length scales is required. Such information is often obtained from traditional static and dynamic light scattering (SLS/DLS) experiments in the single scattering regime. In many dense systems, however, these powerful techniques frequently fail due to strong multiple scattering of light. Here I will discuss some experimental innovations that have emerged over the last decade. New methods such as 3D static and dynamic light scattering (3D LS) as well as diffusing wave spectroscopy (DWS) can cover a much extended range of experimental parameters ranging from dilute polymer solutions, colloidal suspensions to extremely opaque viscoelastic emulsions.
Stretched Exponential relaxation in pure Se glass
NASA Astrophysics Data System (ADS)
Dash, S.; Ravindren, S.; Boolchand, P.
A universal feature of glasses is the stretched exponential relaxation, f (t) = exp[ - t / τ ] β . The model of diffusion of excitations to randomly distributed traps in a glass by Phillips1 yields the stretched exponent β = d[d +2] where d, the effective dimensionality. We have measured the enthalpy of relaxation ΔHnr (tw) at Tg of Se glass in modulated DSC experiments as glasses age at 300K and find β = 0.43(2) for tw in the 0
Three & Four Product Surface-Wave Acousto-Optic Time Integrating Correlators.
four product correlated signals. A laser beam is split and shaped into first and second sheet beams. The first beam is directed to a first acousto - optic medium...where it is doubly diffracted by first and second signals. The second beam is directed to a second acousto - optic medium which is spatially...rotated 90 degs relative to the first acousto - optic medium where the second sheet beam is either singly diffracted by a third signal or doubly diffracted
NASA Astrophysics Data System (ADS)
Taylor, S. R.; Lentati, L.; Babak, S.; Brem, P.; Gair, J. R.; Sesana, A.; Vecchio, A.
2017-02-01
We present two methods for determining the significance of a stochastic gravitational-wave (GW) background affecting a pulsar-timing array, where detection is based on evidence for quadrupolar spatial correlations between pulsars. Rather than constructing noise simulations, we eliminate the GWB spatial correlations in the true data sets to assess detection significance with all real data features intact. In our first method, we perform random phase shifts in the signal-model basis functions. This phase shifting eliminates signal phase coherence between pulsars, while keeping the statistical properties of the pulsar timing residuals intact. We then explore a method to null correlations between pulsars by using a "scrambled" overlap-reduction function in the signal model for the array. This scrambled function is orthogonal to what we expect of a real GW background signal. We demonstrate the efficacy of these methods using Bayesian model selection on a set of simulated data sets that contain a stochastic GW signal, timing noise, undiagnosed glitches, and uncertainties in the Solar system ephemeris. Finally, we introduce an overarching formalism under which these two techniques are naturally linked. These methods are immediately applicable to all current pulsar-timing array data sets, and should become standard tools for future analyses.
Peterson, K.A. ); Dunning, T.H. Jr. )
1995-02-01
The hydrogen bond energy and geometry of the HF dimer have been investigated using the series of correlation consistent basis sets from aug-cc-pVDZ to aug-cc-pVQZ and several theoretical methods including Moller--Plesset perturbation and coupled cluster theories. Estimates of the complete basis set (CBS) limit have been derived for the binding energy of (HF)[sub 2] at each level of theory by utilizing the regular convergence characteristics of the correlation consistent basis sets. CBS limit hydrogen bond energies of 3.72, 4.53, 4.55, and 4.60 kcal/mol are estimated at the SCF, MP2, MP4, and CCSD(T) levels of theory, respectively. CBS limits for the intermolecular F--F distance are estimated to be 2.82, 2.74, 2.73, and 2.73 A, respectively, for the same correlation methods. The effects of basis set superposition error (BSSE) on both the binding energies and structures have also been investigated for each basis set using the standard function counterpoise (CP) method. While BSSE has a negligible effect on the intramolecular geometries, the CP-corrected F--F distance and binding energy differ significantly from the uncorrected values for the aug-cc-pVDZ basis set; these differences decrease regularly with increasing basis set size, yielding the same limits in the CBS limit. Best estimates for the equilibrium properties of the HF dimer from CCSD(T) calculations are [ital D][sub [ital e
Double ionization of neon by electron impact: use of correlated wave functions*
NASA Astrophysics Data System (ADS)
Kada, Imene; Cappello, Claude Dal; Mansouri, Abdelaziz
2017-02-01
A model including correlation both in the initial state and in the final state is applied to the case of the double ionization of neon. The results of our model are compared to the available experimental data performed at high incident energy. Fully (fivefold) differential cross sections (FDCS) have been studied by applying the first Born approximation. Four ion states of Ne++, which are not resolved in the experiments, have been included in our calculation. Contribution to the Topical Issue "Many Particle Spectroscopy of Atoms, Molecules, Clusters and Surfaces", edited by A.N. Grum-Grzhimailo, E.V. Gryzlova, Yu V. Popov, and A.V. Solov'yov.
The Correlation Radiometer - A New Application in MM-Wave Total Power Radiometry
NASA Technical Reports Server (NTRS)
Gaier, Todd; Tanner, Alan; Kangaslahti, Pekka; Lim, Boon
2013-01-01
We describe the design and performance of a 180 GHz correlation radiometer suitable for remote sensing. The radiometer provides continuous comparisons between a the observed signal and a reference load to provide stable radiometric baselines. The radiometer was assembled and tested using parts from the GeoSTAR-II instrument and is fully compatible with operation in a synthetic aperture radiometer or as a standalone technology for use in microwave sounding and imaging. This new radiometer was tested over several days easily demonstrating the required 6 hour stability requirement for observations of mean brightness temperature for a geostationary instrument.
Correlated input-port, matter-wave interferometer: Quantum-noise limits to the atom-laser gyroscope
NASA Astrophysics Data System (ADS)
Dowling, Jonathan P.
1998-06-01
I derive the quantum phase-noise limit to the sensitivity of a Mach-Zehnder interferometer in which the incident quantum particles enter via both input ports. I show that if the incident particles are entangled and correlated properly, then the phase sensitivity scales asymptotically like the Heisenberg-limited Δφ=O(1/N), for large N, where N is the number of particles incident per unit time. (In a one-input-port device, the sensitivity can be at best Δφ=1/N.) My calculation applies to bosons or fermions of arbitrary integer or half-integer spin. Applications to optical, atom-beam, and atom-laser gyroscopes are discussed-in particular, an atom-laser can be used to obtain the required entanglements for achieving this Heisenberg-limited sensitivity with atomic matter waves.
Correlated dynamics of the motion of proton-hole wave packets in a photoionized water cluster.
Li, Zheng; Madjet, Mohamed El-Amine; Vendrell, Oriol; Santra, Robin
2013-01-18
We explore the correlated dynamics of an electron hole and a proton after ionization of a protonated water cluster by extreme ultraviolet light. An ultrafast decay mechanism is found in which the proton-hole dynamics after the ionization are driven by electrostatic repulsion and involve a strong coupling between the nuclear and electronic degrees of freedom. We describe the system by a quantum-dynamical approach and show that nonadiabatic effects are a key element of the mechanism by which electron and proton repel each other and become localized at opposite sides of the cluster. Based on the generality of the decay mechanism, similar effects may be expected for other ionized systems featuring hydrogen bonds.
A Simulation To Model Exponential Growth.
ERIC Educational Resources Information Center
Appelbaum, Elizabeth Berman
2000-01-01
Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)
NASA Astrophysics Data System (ADS)
Taira, T.; Kato, A.
2013-12-01
A high-resolution Vp/Vs ratio estimate is one of the key parameters to understand spatial variations of composition and physical state within the Earth. Lin and Shearer (2007, BSSA) recently developed a methodology to obtain local Vp/Vs ratios in individual similar earthquake clusters, based on P- and S-wave differential times. A waveform cross-correlation approach is typically employed to measure those differential times for pairs of seismograms from similar earthquakes clusters, at narrow time windows around the direct P and S waves. This approach effectively collects P- and S-wave differential times and however requires the robust P- and S-wave time windows that are extracted based on either manually or automatically picked P- and S-phases. We present another technique to estimate P- and S-wave differential times by exploiting temporal properties of delayed time as a function of elapsed time on the seismograms with a moving-window cross-correlation analysis (e.g., Snieder, 2002, Phys. Rev. E; Niu et al. 2003, Nature). Our approach is based on the principle that the delayed time for the direct S wave differs from that for the direct P wave. Two seismograms aligned by the direct P waves from a pair of similar earthquakes yield that delayed times become zero around the direct P wave. In contrast, delayed times obtained from time windows including the direct S wave have non-zero value. Our approach, in principle, is capable of measuring both P- and S-wave differential times from single-component seismograms. In an ideal case, the temporal evolution of delayed time becomes a step function with its discontinuity at the onset of the direct S wave. The offset in the resulting step function would be the S-wave differential time, relative to the P-wave differential time as the two waveforms are aligned by the direct P wave. We apply our moving-window cross-correlation technique to the two different data sets collected at: 1) the Wakayama district, Japan and 2) the Geysers
Matsuda, Satoru; Miura, Michio; Matsuda, Takashi; Ueda, Masanori; Satoh, Yoshio; Hashimoto, Ken-Ya
2013-05-01
The correlation between the propagation loss and SiO2 film properties has been studied for temperature-compensated SAW devices using the SiO2/LiNbO3 structure. The SAW devices were prepared under different deposition temperatures for SiO2 film. Although they possessed excellent temperature coefficient of elasticity characteristics, devices prepared at lower temperature showed lower Q-factors. The SiO2 films were also deposited on a Si substrate under the same deposition conditions used for the SAW device preparation. Optical characterization was performed with Fourier transform infrared spectroscopy (FT-IR), spectrometer measurement, and Raman spectroscopy. IR absorbance spectra were almost same in the FT-IR measurement. However, optical attenuation in the UV region decreased with the deposition temperature in the spectrometer measurement. The optical attenuation is caused by the increase of the extinction coefficient in the SiO2 layer, and its optical wavelength dependence indicated that observed excess attenuation is caused by Rayleigh scattering. The Raman scattering also decreased with the deposition temperature in the Raman spectroscopy. The scattering is caused by the distortion of the SiO2 network. These results indicate that the Rayleigh scattering caused by the distortion of the SiO2 network is the main contributor to the excess SAW propagation loss in this case.
Di Lascio, Nicole; Kusmic, Claudia; Stea, Francesco; Faita, Francesco
2016-11-03
Mouse models are increasingly employed in the comprehension of cardiovascular disease. Wave Intensity Analysis (WIA) can provide information about the interaction between the vascular and the cardiac system. We investigate age-associated changes in WIA-derived parameters in mice and correlate them with biomarkers of cardiac function. Sixteen wild-type male mice were imaged with high-resolution ultrasound (US) at 8 weeks (T 0) and 25 weeks (T 1) of age. Carotid pulse wave velocity (PWV) was calculated from US images using the diameter-velocity loop and employed to evaluate WIA. Amplitudes of the first (W 1) and the second (W 2) local maxima, local minimum (W b) and the reflection index (RI = W b/W 1) were assessed. Cardiac output (CO), ejection fraction (EF), fractional shortening (FS) and stroke volume (SV) were evaluated; longitudinal, radial and circumferential strain and strain rate values (LS, LSR, RS, RSR, CS, CSR) were obtained through strain analysis. W 1 (T 0: 4.42e-07 ± 2.32e-07 m(2)/s; T 1: 2.21e-07 ± 9.77 m(2)/s), W 2 (T 0: 2.45e-08 ± 9.63e-09 m(2)/s; T 1: 1.78e-08 ± 7.82 m(2)/s), W b (T 0: -8.75e-08 ± 5.45e-08 m(2)/s; T 1: -4.28e-08 ± 2.22e-08 m(2)/s), CO (T 0: 19.27 ± 4.33 ml/min; T 1: 16.71 ± 2.88 ml/min), LS (T 0: 17.55 ± 3.67%; T 1: 15.05 ± 2.89%), LSR (T 0: 6.02 ± 1.39 s(-1); T 1: 5.02 ± 1.25 s(-1)), CS (T 0: 27.5 ± 5.18%; T 1: 22.66 ± 3.09%) and CSR (T 0: 10.03 ± 2.55 s(-1); T 1: 7.50 ± 1.84 s(-1)) significantly reduced with age. W 1 was significantly correlated with CO (R = 0.58), EF (R = 0.72), LS (R = 0.65), LSR (R = 0.89), CS (R = 0.61), CSR (R = 0.70) at T 0; correlations were lost at T 1. The decrease in W 1 and W 2 suggests a cardiac performance reduction, while that in Wb, considering unchanged RI, might indicate a wave energy decrease. The loss of correlation between WIA-derived and cardiac parameters might reflect an alteration in cardiovascular interaction.
Youk, Ji Hyun; Gweon, Hye Mi; Son, Eun Ju; Kim, Jeong-Ah; Jeong, Joon
2013-02-01
To compare the mean elasticity value, as measured by shear-wave elastography (SWE), with immunohistochemical profile of invasive breast cancer. This was an institutional review board-approved retrospective study, with a waiver of informed consent. A total of 166 invasive breast cancers in 152 women undergoing preoperative SWE and surgery were included. Quantitative mean elasticity values in kPa were measured for each lesion by using SWE. Medical records were reviewed to determine palpability, invasive size, lymphovascular invasion, histologic grade, and axillary lymph node status. Based on the immunohistochemical profiles, tumor subtypes were categorized as triple-negative (TN), luminal A and B, or human epidermal growth factor receptor 2-enriched cancer. The mean elasticity value was correlated with clinicopathological features using univariate regression models and multivariate linear regression analysis. Palpability (P < 0.0001), larger size (P = 0.013), lymphovascular invasion (P < 0.0001), higher histologic grade (P < 0.0001), and lymph node involvement (P = 0.018) were significantly associated with the mean elasticity value. For the immunohistochemical profiles and tumor subtypes, the estrogen receptor (P = 0.015), progesterone receptor (P = 0.002), Ki-67 (P = 0.009), and the TN (P = 0.009) tumor subtype were correlated with the mean elasticity value. Multivariate logistic regression analysis showed that the following variables were significantly associated with the mean elasticity value: palpable abnormality, histologic grade, and lymphovascular invasion. No immunohistochemical profile of the cancers was independently correlated with the mean elasticity value. For invasive breast cancers, clinicopathological features of poor prognosis showed higher mean elasticity values than those of good prognosis. However, the immunohistochemical profile showed no independent association with the mean elasticity value.
NASA Astrophysics Data System (ADS)
Yamashita, C.; Chu, X.; Huang, W.; Nott, G. J.; Espy, P. J.
2007-12-01
Gravity waves (GWs) play an important role in the dynamics of global middle and upper atmosphere. However, quantitative characterization of GWs in the upper stratosphere is still rare in Antarctica. Here we present a study of stratospheric GW parameters and seasonal variations using the data obtained with the University of Illinois Fe Boltzmann/Rayleigh lidar at the South Pole (90°S) from December 1999 to January 2001 and at Rothera (67.5°S, 68.0°W) from December 2002 to March 2005. Through analyzing the Rayleigh lidar density data in 30-60 km, GW parameters are derived for the South Pole and Rothera, and the results are comparable. The annual mean GW vertical wavelength is 4.3 +/- 1.5 km, vertical phase speed is 0.33 +/- 0.15 m/s, and the period is 245 +/- 110 min. We characterize the stratospheric GW strength with the root- mean-square (RMS) relative density perturbation. The seasonal variation of GW strength is clear at Rothera, with the maximum in winter and the minimum in summer. No significant seasonal variations are observed at the South Pole. The data also show that the GW period is shorter in summer than in winter at Rothera. In addition, the stratospheric GW strength is negatively correlated with PMC brightness at Rothera but no significant correlation at the South Pole. Two important factors, i.e., the wind filtering effect and topographical GW source difference, are investigated in order to explain the GW seasonal variations. We then apply a GW ray-tracing model to analyze the GW source and propagation. The correlation between GW strength and PMC brightness also provides a clue of GW propagation from the stratosphere to the mesosphere.
Exponential frequency spectrum and Lorentzian pulses in magnetized plasmas
Pace, D. C.; Shi, M.; Maggs, J. E.; Morales, G. J.; Carter, T. A.
2008-12-15
Two different experiments involving pressure gradients across the confinement magnetic field in a large plasma column are found to exhibit a broadband turbulence that displays an exponential frequency spectrum for frequencies below the ion cyclotron frequency. The exponential feature has been traced to the presence of solitary pulses having a Lorentzian temporal signature. These pulses arise from nonlinear interactions of drift-Alfven waves driven by the pressure gradients. In both experiments the width of the pulses is narrowly distributed resulting in exponential spectra with a single characteristic time scale. The temporal width of the pulses is measured to be a fraction of a period of the drift-Alfven waves. The experiments are performed in the Large Plasma Device (LAPD-U) [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] operated by the Basic Plasma Science Facility at the University of California, Los Angeles. One experiment involves a controlled, pure electron temperature gradient associated with a microscopic (6 mm gradient length) hot electron temperature filament created by the injection a small electron beam embedded in the center of a large, cold magnetized plasma. The other experiment is a macroscopic (3.5 cm gradient length) limiter-edge experiment in which a density gradient is established by inserting a metallic plate at the edge of the nominal plasma column of the LAPD-U. The temperature filament experiment permits a detailed study of the transition from coherent to turbulent behavior and the concomitant change from classical to anomalous transport. In the limiter experiment the turbulence sampled is always fully developed. The similarity of the results in the two experiments strongly suggests a universal feature of pressure-gradient driven turbulence in magnetized plasmas that results in nondiffusive cross-field transport. This may explain previous observations in helical confinement devices, research tokamaks, and arc plasmas.
Exponential orthogonality catastrophe in single-particle and many-body localized systems
NASA Astrophysics Data System (ADS)
Deng, Dong-Ling; Pixley, J. H.; Li, Xiaopeng; Das Sarma, S.
2015-12-01
We investigate the statistical orthogonality catastrophe (STOC) in single-particle and many-body localized systems by studying the response of the many-body ground state to a local quench. Using scaling arguments and exact numerical calculations, we establish that the STOC gives rise to a wave function overlap between the pre- and postquench ground states that has an exponential decay with the system size, in sharp contrast to the well-known power law Anderson orthogonality catastrophe in metallic systems. This exponential decay arises from a statistical charge transfer process where a particle can be effectively "transported" to an arbitrary lattice site. In a many-body localized phase, this nonlocal transport and the associated exponential STOC phenomenon persist in the presence of interactions. We study the possible experimental consequences of the exponential STOC on the Loschmidt echo and spectral function, establishing that this phenomenon might be observable in cold atomic experiments through Ramsey interference and radio-frequency spectroscopy.
Phylogenetic Stochastic Mapping Without Matrix Exponentiation
Irvahn, Jan; Minin, Vladimir N.
2014-01-01
Abstract Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), because current methodology relies on exponentiating CTMC infinitesimal rate matrices—an operation whose computational complexity grows as the size of the CTMC state space cubed. In this work, we introduce a new approach, based on a CTMC technique called uniformization, which does not use matrix exponentiation for phylogenetic stochastic mapping. Our method is based on a new Markov chain Monte Carlo (MCMC) algorithm that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared. Moreover, in contrast to competing matrix exponentiation methods, if the rate matrix is sparse, we can leverage this sparsity and increase the computational efficiency of our algorithm further. Using simulated data, we illustrate advantages of our MCMC algorithm and investigate how large the state space needs to be for our method to outperform matrix exponentiation approaches. We show that even on the moderately large state space of codons our MCMC method can be significantly faster than currently used matrix exponentiation methods. PMID:24918812
Decoherence and Exponential Law: A Solvable Model
NASA Technical Reports Server (NTRS)
Pascazio, Saverio; Namiki, Mikio
1996-01-01
We analyze a modified version of the 'AgBr' Hamiltonian, solve exactly the equations of motion in terms of SU(2) coherent states, and study the weak-coupling, macroscopic limit of the model, obtaining an exponential behavior at all times. The asymptotic dominance of the exponential behavior is representative of a purely stochastic evolution and can be derived quantum mechanically in the so-called van Hove's limit (which is a weak-coupling, macroscopic limit). At the same time, a temporal behavior of the exponential type, yielding a 'probability dissipation' is closely related to dephasing ('decoherence') effects and one can expect a close connection with a dissipative and irreversible behavior. We stress the central relevance of the problem of dissipation to the quantum measurement theory and to the general topic of decoherence.
Method for exponentiating in cryptographic systems
Brickell, Ernest F.; Gordon, Daniel M.; McCurley, Kevin S.
1994-01-01
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computi The United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.
Modeling aftershocks as a stretched exponential relaxation
NASA Astrophysics Data System (ADS)
Mignan, A.
2015-11-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.
The Exponential Decay Law, Bell's Inequality, and Nonlinear Dynamics
NASA Astrophysics Data System (ADS)
McHarris, Wm. C.
2002-10-01
What do the exponential decay law and Bell's inequality have in common? And with nonlinear dynamics? Simply that they both are among the puzzles at the heart of quantum mechanics, puzzles which can have parallel explanations in terms of chaos or nonlinear dynamics. The statistical nature of the exponential decay law, which at first glance is incompatible with the quantum mechanical concept of indistinguishabe particles, can be mocked up by the extreme sensitivity of chaotic systems to initial conditions. In accord with Ockham's Razor, iteration of a simple unimodal (e.g., quadratic) map in its chaotic region and keeping track of the number of iterations required for a trajectory starting from a point chosen at random within a small interval to escape into another small small interval reproduces the observed exponential behavior. Similarly, Bell's inequality derived using classical mechanics (with an underlying assumption of classical statistics) places an upper limit on numbers derived from measurements on entangled states, whereas quantum mechanics implies that this upper limit no longer holds. Experiments have shown the inequality to be violated, upholding quantum mechanics. However, nonlinear dynamics, with its correlated statistics, can yield results overlapping with the quantum mechanical predictions. Whether or not the experiments rule out "local realism" is thus a moot point. Nonlinear determinism just might exist within quantum mechanics.
A method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
Phase correlation between four-wave mixing and optical fields in double Λ-type atomic system.
Jeong, Taek; Moon, Han Seb
2016-12-12
We study the spectral features and phase of four-wave mixing (FWM) light according to the relative phase-noise of the optical fields coupled to a double Λ-type atomic system of the 5S_{1/2}-5P_{1/2} transition of ^{87}Rb atoms. We observe that the spectral shape of the FWM spectrum is identical to that of the two-photon absorption (TPA) spectrum due to two-photon coherence and that it is independent of the relative phase-noise of the pump light. From these results, we clarify that the two-photon coherence plays a very important role in the FWM process. Furthermore, we measure the relative linewidth of the FWM signal to the probe and pump lasers by means of a beat interferometer. We confirmed that the phase of the FWM signal is strongly correlated with that of the pump laser under the condition of phase-locked probe and coupling lasers for two-photon coherence.
Bussonnière, A; Baudoin, M; Brunet, P; Matar, O Bou
2016-05-01
When sessile droplets are excited by ultrasonic traveling surface acoustic waves (SAWs), they undergo complex dynamics with both oscillations and translational motion. While the nature of the Rayleigh-Lamb quadrupolar drop oscillations has been identified, their origin and their influence on the drop mobility remains unexplained. Indeed, the physics behind this peculiar dynamics is complex with nonlinearities involved both at the excitation level (acoustic streaming and radiation pressure) and in the droplet response (nonlinear oscillations and contact line dynamics). In this paper, we investigate the dynamics of sessile and pendant drops excited by SAWs. For pendant drops, so-far unreported dynamics are observed close to the drop detachment threshold with the suppression of the translational motion. Away from this threshold, the comparison between pendant and sessile drop dynamics allows us to identify the role played by gravity or, more generally, by an initial or dynamically induced stretching of the drop. In turn, we elucidate the origin of the resonance frequency shift, as well as the origin of the strong correlation between oscillatory and translational motion. We show that for sessile drops, the velocity is mainly determined by the amplitude of oscillation and that the saturation observed is due to the nonlinear dependence of the drop response frequency on the dynamically induced stretching.
NASA Astrophysics Data System (ADS)
Bussonnière, A.; Baudoin, M.; Brunet, P.; Matar, O. Bou
2016-05-01
When sessile droplets are excited by ultrasonic traveling surface acoustic waves (SAWs), they undergo complex dynamics with both oscillations and translational motion. While the nature of the Rayleigh-Lamb quadrupolar drop oscillations has been identified, their origin and their influence on the drop mobility remains unexplained. Indeed, the physics behind this peculiar dynamics is complex with nonlinearities involved both at the excitation level (acoustic streaming and radiation pressure) and in the droplet response (nonlinear oscillations and contact line dynamics). In this paper, we investigate the dynamics of sessile and pendant drops excited by SAWs. For pendant drops, so-far unreported dynamics are observed close to the drop detachment threshold with the suppression of the translational motion. Away from this threshold, the comparison between pendant and sessile drop dynamics allows us to identify the role played by gravity or, more generally, by an initial or dynamically induced stretching of the drop. In turn, we elucidate the origin of the resonance frequency shift, as well as the origin of the strong correlation between oscillatory and translational motion. We show that for sessile drops, the velocity is mainly determined by the amplitude of oscillation and that the saturation observed is due to the nonlinear dependence of the drop response frequency on the dynamically induced stretching.
ERIC Educational Resources Information Center
Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel
2016-01-01
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…
NASA Astrophysics Data System (ADS)
Ohta, Mitsuo; Ogawa, Hitoshi; Ikuta, Akira
2005-08-01
A probabilistic signal processing method, with which is possible to get some methodological suggestion to the measurement method of correlative and/or accumulative effects in the compound environment of sound, light and electromagnetic (EM) waves is discussed. In order to extract various types of latent interrelation characteristics among wave environmental factors leaked from an actually operating video display terminal (VDT), an extended regression system model, hierarchically reflecting not only linear correlation information but also nonlinear correlation information, is first introduced, especially from a viewpoint of 'relationism-first'. Then, through estimating each regression parameter of this model, some original evaluation methods for predicting a whole probability distribution form, from one another, are proposed. Finally, the effectiveness of the methods is experimentally confirmed, by applying them to the actual observed data leaked by a VDT with some television games. To cite this article: M. Ohta et al., C. R. Mecanique 333 (2005).
Stretched Exponential Relaxation of Glasses at Low Temperature.
Yu, Yingtian; Wang, Mengyi; Zhang, Dawei; Wang, Bu; Sant, Gaurav; Bauchy, Mathieu
2015-10-16
The question of whether glass continues to relax at low temperature is of fundamental and practical interest. Here, we report a novel atomistic simulation method allowing us to directly access the long-term dynamics of glass relaxation at room temperature. We find that the potential energy relaxation follows a stretched exponential decay, with a stretching exponent β=3/5, as predicted by Phillips's diffusion-trap model. Interestingly, volume relaxation is also found. However, it is not correlated to the energy relaxation, but it is rather a manifestation of the mixed alkali effect.
Graphical Models via Univariate Exponential Family Distributions
Yang, Eunho; Ravikumar, Pradeep; Allen, Genevera I.; Liu, Zhandong
2016-01-01
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a general sub-class of graphical models where the node-wise conditional distributions arise from exponential families. This allows us to derive multivariate graphical model distributions from univariate exponential family distributions, such as the Poisson, negative binomial, and exponential distributions. Our key contributions include a class of M-estimators to fit these graphical model distributions; and rigorous statistical analysis showing that these M-estimators recover the true graphical model structure exactly, with high probability. We provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from Poisson and exponential distributions. PMID:27570498
A Simple Mechanical Experiment on Exponential Growth
ERIC Educational Resources Information Center
McGrew, Ralph
2015-01-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…
Exponential lifetime improvement in topological quantum memories
NASA Astrophysics Data System (ADS)
Bardyn, Charles-Edouard; Karzig, Torsten
2016-09-01
We propose a simple yet efficient mechanism for passive error correction in topological quantum memories. Our scheme relies on driven-dissipative ancilla systems which couple to local excitations (anyons) and make them "sink" in energy, with no required interaction among ancillae or anyons. Through this process, anyons created by some thermal environment end up trapped in potential "trenches" that they themselves generate, which can be interpreted as a "memory foam" for anyons. This self-trapping mechanism provides an energy barrier for anyon propagation and removes entropy from the memory by favoring anyon recombination over anyon separation (responsible for memory errors). We demonstrate that our scheme leads to an exponential increase of the memory-coherence time with system size L , up to an upper bound Lmax, which can increase exponentially with Δ /T , where T is the temperature and Δ is some energy scale defined by potential trenches. This results in a double exponential increase of the memory time with Δ /T , which greatly improves over the Arrhenius (single-exponential) scaling found in typical quantum memories.
A note on the Jackson exponentiality test
NASA Astrophysics Data System (ADS)
Caeiro, Frederico; Marques, Filipe J.; Mateus, Ayana; Atal, Serra
2016-12-01
In this paper we revisit the Jackson exponentiality test. We study and provide functions in R language to compute theoretical moments, the distribution function and quantiles of the statistic test. Approximations to the exact distribution function and quantiles are also provided and their precision discussed. In addition, we provide an application of the Jackson test to real data.
Intersection of the Exponential and Logarithmic Curves
ERIC Educational Resources Information Center
Boukas, Andreas; Valahas, Theodoros
2009-01-01
The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…
Exponential examples of solving parity games
NASA Astrophysics Data System (ADS)
Lebedev, V. N.
2016-04-01
This paper is devoted to solving certain problems on the computational complexity of deciding the winner in cyclic games. The main result is the proof of the fact that the nondeterministic potential transformation algorithm designed for solving parity games is exponential in terms of computation time.
NASA Astrophysics Data System (ADS)
Jaynes, A. N.; Lessard, M.; Takahashi, K.; Ali, A.; Malaspina, D.; Michell, R.; Spanswick, E.; Baker, D. N.; Blake, J. B.; Cully, C. M.; Donovan, E.; Kletzing, C.; Reeves, G. D.; Samara, M.; Spence, H. E.; Wygant, J. R.
2015-12-01
Theory and observations have linked equatorial VLF waves with pulsating aurora for decades, invoking the process of pitch-angle scattering of 10's keV electrons in the equatorial magnetosphere. Recently published satellite studies have strengthened this argument, by showing strong correlation between pulsating auroral patches and both lower-band chorus and 10's keV electron modulation in the vicinity of geosynchronous orbit. Additionally, a previous link has been made between Pc4-5 compressional pulsations and modulation of whistler-mode chorus using THEMIS. In the current study, we present simultaneous in-situ observations of structured chorus waves and an apparent field line resonance (in the Pc4-5 range) as a result of a substorm injection, observed by Van Allen Probes, along with ground-based observations of pulsating aurora. We demonstrate the likely scenario being one of substorm-driven Pc4-5 ULF pulsations modulating chorus waves, and thus providing the driver for pulsating particle precipitation into the Earth's atmosphere. Interestingly, the modulated chorus wave and ULF wave periods are well correlated, with chorus occurring at half the periodicity of the ULF waves. We also show, for the first time, a particular few-Hz modulation of individual chorus elements that coincides with the same modulation in a nearby pulsating aurora patch. Such modulation has been noticed as a high-frequency component in ground-based camera data of pulsating aurora for decades, and may be a result of nonlinear chorus wave interactions in the equatorial region. This work illustrates the significant understanding of magnetospheric processes that can be gained through use of conjunctive ground- and space-based observations.
Jaynes, A. N.; Lessard, M. R.; Takahashi, K.; Ali, A. F.; Malaspina, D. M.; Michell, R. G.; Spanswick, E. L.; Baker, D. N.; Blake, J. B.; Cully, C.; Donovan, E. F.; Kletzing, C. A.; Reeves, G. D.; Samara, M.; Spence, H. E.; Wygant, J. R.
2015-10-28
Theory and observations have linked equatorial VLF waves with pulsating aurora for decades, invoking the process of pitch angle scattering of tens of keV electrons in the equatorial magnetosphere. Recently published satellite studies have strengthened this argument, by showing strong correlation between pulsating auroral patches and both lower-band chorus and tens of keV electron modulation in the vicinity of geosynchronous orbit. Additionally, a previous link has been made between Pc4–5 compressional pulsations and modulation of whistler-mode chorus using Time History of Events and Macroscale Interactions during Substorms. In the current study, we present simultaneous in situ observations of structured chorus waves and an apparent field line resonance (in the Pc4–5 range) as a result of a substorm injection, observed by Van Allen Probes, along with ground-based observations of pulsating aurora. We demonstrate the likely scenario being one of substorm-driven Pc4–5 ULF pulsations modulating chorus waves, and thus providing the driver for pulsating particle precipitation into the Earth's atmosphere. Interestingly, the modulated chorus wave and ULF wave periods are well correlated, with chorus occurring at half the periodicity of the ULF waves. We also show, for the first time, a particular few-Hz modulation of individual chorus elements that coincides with the same modulation in a nearby pulsating aurora patch. As a result, such modulation has been noticed as a high-frequency component in ground-based camera data of pulsating aurora for decades and may be a result of nonlinear chorus wave interactions in the equatorial region.
Jaynes, A. N.; Lessard, M. R.; Takahashi, K.; ...
2015-10-28
Theory and observations have linked equatorial VLF waves with pulsating aurora for decades, invoking the process of pitch angle scattering of tens of keV electrons in the equatorial magnetosphere. Recently published satellite studies have strengthened this argument, by showing strong correlation between pulsating auroral patches and both lower-band chorus and tens of keV electron modulation in the vicinity of geosynchronous orbit. Additionally, a previous link has been made between Pc4–5 compressional pulsations and modulation of whistler-mode chorus using Time History of Events and Macroscale Interactions during Substorms. In the current study, we present simultaneous in situ observations of structured chorusmore » waves and an apparent field line resonance (in the Pc4–5 range) as a result of a substorm injection, observed by Van Allen Probes, along with ground-based observations of pulsating aurora. We demonstrate the likely scenario being one of substorm-driven Pc4–5 ULF pulsations modulating chorus waves, and thus providing the driver for pulsating particle precipitation into the Earth's atmosphere. Interestingly, the modulated chorus wave and ULF wave periods are well correlated, with chorus occurring at half the periodicity of the ULF waves. We also show, for the first time, a particular few-Hz modulation of individual chorus elements that coincides with the same modulation in a nearby pulsating aurora patch. As a result, such modulation has been noticed as a high-frequency component in ground-based camera data of pulsating aurora for decades and may be a result of nonlinear chorus wave interactions in the equatorial region.« less
Först, M.; Frano, A.; Kaiser, S.; ...
2014-11-17
In this study, we use femtosecond resonant soft x-ray diffraction to measure the optically stimulated ultrafast changes of charge density wave correlations in underdoped YBa₂Cu₃O₆.₆. We find that when coherent interlayer transport is enhanced by optical excitation of the apical oxygen distortions, at least 50% of the in-plane charge density wave order is melted. These results indicate that charge ordering and superconductivity may be competing up to the charge ordering transition temperature, with the latter becoming a hidden phase that is accessible only by nonlinear phonon excitation.
Fumal, Thomas E.
1978-01-01
To identify geologic units with distinctly different seismic responses for the purposes of seismic zonation, compressional and shear wave velocities have been measured in boreholes at 59 sites in the San Francisco Bay region in a wide range of near-surface (0-30m) geologic materials. Several physical parameters, which can be readily determined in the field, were found to correlate with the shear wave velocities and were used to define seismically distinct groups. For the unconsolidated to semiconsolidated sediments, texture, standard penetration resistance and depth were used to define eight seismically distinct groups. For the bedrock materials, fracture spacing and hardness were used to differentiate ten distinct categories. The correlation obtained between shear wave velocity and the physical parameters were used to regroup the map units defined for the San Francisco Bay region into seismically distinct units. The map units for the younger unconsolidated sediments can be really differentiated seismically. In contrast, the older semiconsolidated sedimentary deposits and bedrock units, which have experienced significant variations in post-depositial changes, show wider and overlapping velocity ranges. The map units for the sedimentary deposits have been regrouped into eight seismically distinct geotechnical units. The bedrock map units have been broadly regrouped into five distinct categories. Compressional wave velocities were not found to be well correlated with the physical parameters dependent on the soil or rock structure. For materials above the water table, the wide velocity variations found for each geotechnical group can be attributed to differences in degree of saturation. The strong correlations observed between shear wave velocity and other readily determine physical properties suggest that geologic maps which incorporate these parameters are most useful for seismic zonation.
NASA Astrophysics Data System (ADS)
Vicuña-Hernández, Verónica; Santiago, José T.; Jerónimo-Moreno, Yasser; Ramírez-Alarcón, Roberto; Cruz-Ramírez, Héctor; U'Ren, Alfred B.; Jáuregui-Renaud, Rocio
2016-12-01
We present an experimental and theoretical study of type I, frequency-degenerate spontaneous parametric down-conversion (SPDC) with a Bessel-Gauss pump in which we include both paraxial and nonparaxial pump beam configurations. We present measurements of the SPDC angular spectrum (AS), of the conditional angular spectrum (CAS) of signal-mode single photons as heralded by the detection of an idler photon, and of the transverse wave-vector signal-idler correlations (TWC). We show that as the pump is made increasingly nonparaxial, the AS acquires a nonconcentric double-cone structure, with the CAS shape depending on the azimuthal location of the heralding detector, while the signal-idler wave-vector correlation region splits into characteristic doublet stripes, representing as yet unexplored nontrivial, nonlocal quantum correlations between the signal and idler photons. Our work provides further understanding of SPDC with a particular class of structured pump beams, and we believe that the controlled presence of double wave-vector correlations represents an interesting resource for photon-pair quantum-state engineering.
Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2013-07-28
We propose here fast antisymmetrization procedures for the partially correlated wave functions that appear in the free complement-local Schrödinger equation (FC-LSE) method. Pre-analysis of the correlation diagram, referred to as dot analysis, combined with the determinant update technique based on the Laplace expansion, drastically reduces the orders of the antisymmetrization computations. When the complement functions include only up to single-correlated terms, the order of computations is O(N{sup 3}), which is the same as the non-correlated case. Similar acceleration is obtained for general correlated functions as a result of dot analysis. This algorithm has been successfully used in our laboratory in actual FC-LSE calculations for accurately solving the many-electron Schrödinger equations of atoms and molecules. The proposed method is general and applicable to the sampling-type methodology of other partially correlated wave functions like those in the quantum Monte Carlo and modern Hylleraas-type methods.
Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2013-07-28
We propose here fast antisymmetrization procedures for the partially correlated wave functions that appear in the free complement-local Schrödinger equation (FC-LSE) method. Pre-analysis of the correlation diagram, referred to as dot analysis, combined with the determinant update technique based on the Laplace expansion, drastically reduces the orders of the antisymmetrization computations. When the complement functions include only up to single-correlated terms, the order of computations is O(N(3)), which is the same as the non-correlated case. Similar acceleration is obtained for general correlated functions as a result of dot analysis. This algorithm has been successfully used in our laboratory in actual FC-LSE calculations for accurately solving the many-electron Schrödinger equations of atoms and molecules. The proposed method is general and applicable to the sampling-type methodology of other partially correlated wave functions like those in the quantum Monte Carlo and modern Hylleraas-type methods.
Atomic shell structure from the Single-Exponential Decay Detector
Silva, Piotr de; Korchowiec, Jacek; Wesolowski, Tomasz A.
2014-04-28
The density of atomic systems is analysed via the Single-Exponential Decay Detector (SEDD). SEDD is a scalar field designed to explore mathematical, rather than physical, properties of electron density. Nevertheless, it has been shown that SEDD can serve as a descriptor of bonding patterns in molecules as well as an indicator of atomic shells [P. de Silva, J. Korchowiec, and T. A. Wesolowski, ChemPhysChem 13, 3462 (2012)]. In this work, a more detailed analysis of atomic shells is done for atoms in the Li–Xe series. Shell populations based on SEDD agree with the Aufbau principle even better than those obtained from the Electron Localization Function, which is a popular indicator of electron localization. A link between SEDD and the local wave vector is given, which provides a physical interpretation of SEDD.
A Simple Mechanical Experiment on Exponential Growth
NASA Astrophysics Data System (ADS)
McGrew, Ralph
2015-04-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the activity are accessible to students in physical science and environmental science courses.
Exponential integration algorithms applied to viscoplasticity
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Walker, Kevin P.
1991-01-01
Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.
Likelihood Estimation for Generalized Mixed Exponential Distributions.
1984-07-01
specified beforehand. 23 S. . ... .- ~T§777 ~"~~ 7’.7 . -- ." F0 * 0 REFERENCES L. Armijo, "Minimization of Functions Having Lipschitz Continuous...and F. W. Fairman, Exponential Approximation via a Closed Form Gauss-Newton Method, IEEE Trans. Circuit Theory, CT-20 (1973), pp. 361-369. A. R...engineering disciplines of Chemical, Civil, Electrical , and Mechanical and Aerospace to newer, more specialized fields of Biomedical Engineering
Exponential DNA Replication by Laminar Convection
NASA Astrophysics Data System (ADS)
Braun, Dieter; Goddard, Noel L.; Libchaber, Albert
2003-10-01
It is shown that laminar thermal convection can drive a chain reaction of DNA replication. The convection is triggered by a constant horizontal temperature gradient, moving molecules along stationary paths between hot and cold regions. This implements the temperature cycling for the classical polymerase chain reaction (PCR). The amplification is shown to be exponential and reaches 100 000-fold gains within 25min. Besides direct applications, the mechanism might have implications for the molecular evolution of life.
Predicting jet radius in electrospinning by superpositioning exponential functions
NASA Astrophysics Data System (ADS)
Widartiningsih, P. M.; Iskandar, F.; Munir, M. M.; Viridi, S.
2016-08-01
This paper presents an analytical study of the correlation between viscosity and fiber diameter in electrospinning. Control over fiber diameter in electrospinning process was important since it will determine the performance of resulting nanofiber. Theoretically, fiber diameter was determined by surface tension, solution concentration, flow rate, and electric current. But experimentally it had been proven that significantly viscosity had an influence to fiber diameter. Jet radius equation in electrospinning process was divided into three areas: near the nozzle, far from the nozzle, and at jet terminal. There was no correlation between these equations. Superposition of exponential series model provides the equations combined into one, thus the entire of working parameters on electrospinning take a contribution to fiber diameter. This method yields the value of solution viscosity has a linear relation to jet radius. However, this method works only for low viscosity.
Dynamo theory, vorticity generation, and exponential stretching.
Friedlander, Susan; Vishik, Misha M.
1991-08-01
A discussion is given of the analogy between the dynamo equation for the generation of a magnetic field by the motion of an electrically conducting fluid and the equation for the evolution of vorticity of a viscous fluid. In both cases exponential stretching is an important feature of the underlying instability problem. For the "fast" dynamo problem, the existence of exponential stretching (i.e., the positivity of the Lyapunov exponent) somewhere in the flow is a necessary condition when the flow is smooth. An example is presented of a flow with exponential stretching (an Anosov flow) that supports fast dynamo action. A parallel treatment is described for the linearized Navier-Stokes equations for the motion of a viscous fluid. In this problem the analogous necessary condition for "fast vorticity generation" is the existence of some instability in the corresponding Euler (i.e., inviscid) equation. Dynamo theory methods give a second related result, namely a universal geometric estimate from below on the growth rate of a small perturbation in an inviscid fluid. This bound gives an effective sufficient condition for local instability for Eulers equations. In particular, it is proved that a steady flow with a hyperbolic stagnation point is unstable. The growth rate of an infinitesimal perturbation in a metric with derivatives depends on this metric. This dependence is completely described.
Method for exponentiating in cryptographic systems
Brickell, E.F.; Gordon, D.M.; McCurley, K.S.
1992-12-31
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a pre-approved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g{sup e}; transmitting the value g{sup e} to a remote facility by a communications network; receiving the value g{sup e} at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g{sup xi}, computing a{sub i} representations for a integer base b, where a{sub i} represents the weighing factor of the ith digit of the integer e; computing the individual values of c{sub d} according to the rule: c{sub d}={product}a{sub i}=d g{sup x {sub i}}; and computing the product of {product}{sup h}/{sub d=1} c{sub d}{sup d} from the stored values of from the plurality of memory locations so as to determine a value for g{sup e}.
Turbulent Structure Under Short Fetch Wind Waves
2015-12-01
partitioned into wave growth , wave breaking, and wave forcing of the ocean surface layer. The purpose of this study was to support the ONR Coupled Boundary...complicated by the presence of surface waves. Wind momentum and energy are partitioned into wave growth , wave breaking, and wave forcing of the ocean surface...subrange, beyond which will display a rapid exponential decay through the dissipation range as shown in Figure 1. There are six properties that best
Gálvez, F J; Buendía, E; Sarsa, A
2006-01-28
The (3)P ground state and both the (1)D and (1)S excited states arising from the low-lying 1s(2)2s(2)2p(2) configuration of the carbon isoelectronic series are studied starting from explicitly correlated multiconfigurational wave functions. One- and two-body densities in position space have been calculated and different one- and two-body expectation values have been obtained. The effects of electronic correlations have been systematically studied. All the calculations have been done by means of variational Monte Carlo.
Feng, Shechao Charles
1995-02-01
This is the final report on the grant, entitled `applications of mesoscopic physics to novel correlations and fluctuations of speckle patterns: imaging and tomography with multiply scattered classical waves`, which expired on September 14, 1994. The author summarizes the highlights of this research program, and lists the publications supported by this grant. The report is divided into sections, titled: application of mesoscopic fluctuations theory to correlations and fluctuations of multiply scattered light; quantum transport in localized electronic systems; electron-phonon inelastic scattering rate and the temperature scaling exponent in integer quantum Hall effect; high frequency quantum transport in quantum well devices.
NASA Astrophysics Data System (ADS)
Nakahara, H.
2013-12-01
For monitoring temporal changes in subsurface structures, I propose to use auto correlation functions of coda waves from local earthquakes recorded at surface receivers, which probably contain more body waves than surface waves. Because the use of coda waves requires earthquakes, time resolution for monitoring decreases. But at regions with high seismicity, it may be possible to monitor subsurface structures in sufficient time resolutions. Studying the 2011 Tohoku-Oki (Mw 9.0), Japan, earthquake for which velocity changes have been already reported by previous studies, I try to validate the method. KiK-net stations in northern Honshu are used in the analysis. For each moderate earthquake, normalized auto correlation functions of surface records are stacked with respect to time windows in S-wave coda. Aligning the stacked normalized auto correlation functions with time, I search for changes in arrival times of phases. The phases at lag times of less than 1s are studied because changes at shallow depths are focused. Based on the stretching method, temporal variations in the arrival times are measured at the stations. Clear phase delays are found to be associated with the mainshock and to gradually recover with time. Amounts of the phase delays are in the order of 10% on average with the maximum of about 50% at some stations. For validation, the deconvolution analysis using surface and subsurface records at the same stations are conducted. The results show that the phase delays from the deconvolution analysis are slightly smaller than those from the auto correlation analysis, which implies that the phases on the auto correlations are caused by larger velocity changes at shallower depths. The auto correlation analysis seems to have an accuracy of about several percents, which is much larger than methods using earthquake doublets and borehole array data. So this analysis might be applicable to detect larger changes. In spite of these disadvantages, this analysis is
NASA Technical Reports Server (NTRS)
Wang, C. R.; Hingst, W. R.; Porro, A. R.
1991-01-01
The properties of 2-D shock wave/turbulent boundary layer interaction flows were calculated by using a compressible turbulent Navier-Stokes numerical computational code. Interaction flows caused by oblique shock wave impingement on the turbulent boundary layer flow were considered. The oblique shock waves were induced with shock generators at angles of attack less than 10 degs in supersonic flows. The surface temperatures were kept at near-adiabatic (ratio of wall static temperature to free stream total temperature) and cold wall (ratio of wall static temperature to free stream total temperature) conditions. The computational results were studied for the surface heat transfer, velocity temperature correlation, and turbulent shear stress in the interaction flow fields. Comparisons of the computational results with existing measurements indicated that (1) the surface heat transfer rates and surface pressures could be correlated with Holden's relationship, (2) the mean flow streamwise velocity components and static temperatures could be correlated with Crocco's relationship if flow separation did not occur, and (3) the Baldwin-Lomax turbulence model should be modified for turbulent shear stress computations in the interaction flows.
NASA Technical Reports Server (NTRS)
Freeman, Frederick G.
1993-01-01
presented target stimulus. In addition to the task requirements, irrelevant tones were presented in the background. Research has shown that even though these stimuli are not attended, ERP's to them can still be elicited. The amplitude of the ERP waves has been shown to change as a function of a person's level of alertness. ERP's were also collected and analyzed for the target stimuli for each task. Brain maps were produced based on the ERP voltages for the different stimuli. In addition to the ERP's, a quantitative EEG (QEEG) was performed on the data using a fast Fourier technique to produce a power spectral analysis of the EEG. This analysis was conducted on the continuous EEG while the subjects were performing the tasks. Finally, a QEEG was performed on periods during the task when subjects indicated that they were in an altered state of awareness. During the tasks, subjects were asked to indicate by pressing a button when they realized their level of task awareness had changed. EEG epochs were collected for times just before and just after subjects made this reponse. The purpose of this final analysis was to determine whether or not subjective indices of level of awareness could be correlated with different patterns of EEG.
Absence of exponential clustering in quantum Coulomb fluids
NASA Astrophysics Data System (ADS)
Alastuey, A.; Martin, Ph. A.
1989-12-01
We show that the quantum corrections to the classical correlations of a Coulomb fluid do not decay exponentially fast for all values of the thermodynamical parameters. Specifically, the ħ4 term in the Wigner-Kirkwood expansion of the equilibrium charge-charge correlations of the quantum one-component plasma is found to decay like ||r||-10. More generally, using functional integration, we present a diagrammatic representation of the ħ expansion of the correlations in a multicomponent fluid with a locally regularized Coulomb potential and Maxwell-Boltzmann statistics. The ħ2n terms are found to decay algebraically for all n>=2. Furthermore, an analysis of the hierarchy equations for the correlations provides upper bounds that are compatible with the findings of the perturbative expansion. Except for the monopole, all higher-order multipole sum rules do not hold, in general, in the quantum system. This violation of the multipole sum rules as well as the related algebraic tails are due to the intrinsic quantum fluctuations that prevent a perfect organization of the screening clouds. This phenomenon is illustrated in a simpler model where the large-distance correlations between two quantum particles embedded in a classical plasma can be exactly computed.
Exponential expansion: galactic destiny or technological hubris?
NASA Astrophysics Data System (ADS)
Finney, B. R.
Is it our destiny to expand exponentially to populate the galaxy, or is such a vision but an extreme example of technological hubris? The overall record of human evolution and dispersion over the Earth can be cited to support the view that we are a uniquely expansionary and technological animal bound for the stars, yet an examination of the fate of individual migrations and exploratory initiatives raises doubts. Although it may be in keeping with our hubristic nature to predict ultimate galactic expansion, there is no way to specify how far expansionary urges may drive our spacefaring descendants.
Applications of an exponential finite difference technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.; Keith, Theo G., Jr.
1988-01-01
An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.
Hyperbolic neighborhoods as organizers of finite-time exponential stretching
NASA Astrophysics Data System (ADS)
Balasuriya, Sanjeeva; Ouellette, Nicholas
2016-11-01
Hyperbolic points and their unsteady generalization, hyperbolic trajectories, drive the exponential stretching that is the hallmark of nonlinear and chaotic flow. Typical experimental and observational velocity data is unsteady and available only over a finite time interval, and in such situations hyperbolic trajectories will move around in the flow, and may lose their hyperbolicity at times. Here we introduce a way to determine their region of influence, which we term a hyperbolic neighborhood, which marks fluid elements whose dynamics are instantaneously dominated by the hyperbolic trajectory. We establish, using both theoretical arguments and numerical verification from model and experimental data, that the hyperbolic neighborhoods profoundly impact Lagrangian stretching experienced by fluid elements. In particular, we show that fluid elements traversing a flow experience exponential boosts in stretching while within these time-varying regions, that greater residence time within hyperbolic neighborhoods is directly correlated to larger Finite-Time Lyapunov Exponent (FTLE) values, and that FTLE diagnostics are reliable only when the hyperbolic neighborhoods have a geometrical structure which is regular in a specific sense. Future Fellowship Grant FT130100484 from the Australian Research Council (SB), and a Terman Faculty Fellowship from Stanford University (NO).
Mourik, Van Tonja; Wilson, Angela K.; Dunning, Thomas H.
1999-02-20
The potential energy curves of the rare gas dimers He2, Ne2, and Ar2 have been computed using correlation consistent basis sets ranging from singly augmented aug-cc-pVDZ sets through triply augmented t-aug-cc-pV6Z sets, with the augmented sextuple basis sets being reported herein. Several methods for including electron correlation were investigated, namely Moller Plesset perturbation theory (MP2, MP3 and MP4) and coupled cluster theory [CCSD and CCSD(T)].
On the use of the exponential window method in the space domain
NASA Astrophysics Data System (ADS)
Liu, Li
Wave propagation in unbounded media is a topic widely studied in different science and engineering fields. Global and local absorbing boundary conditions combined with the finite element method or the finite difference method are the usual numerical treatments. In this dissertation, an alternative is investigated based on the dynamic stiffness and the exponential window method in the space-wave number domain. Applying the exponential window in the space-wave number domain is equivalent to introducing fictitious damping into the system. The Discrete Fourier Transform employed in the dynamic stiffness can be properly performed in a damped system. An open boundary in space is thus created. Since the equation is solved by the finite difference formula in the time domain, this approach is in the time-wave number domain, which provides a complement for the original dynamic stiffness method, which is in the frequency-wave number domain. The approach is tested through different elasto-dynamic models that cover one-, two- and three-dimensional problems. The results from the proposed approach are compared with those from either analytical solutions or the finite element method. The comparison demonstrates the effectiveness of the approach. The incident waves can be efficiently absorbed regardless of incident angles and frequency contents. The approach proposed in this dissertation can be widely applied to the dynamics of railways, dams, tunnels, building and machine foundations, layered soil and composite materials.
NASA Astrophysics Data System (ADS)
Aranda, Alfredo; Amigo, Nicolás; Ihle, Christian; Tamburrino, Aldo
2016-06-01
A method based on digital image correlation (DIC) is implemented for measuring the height of the roll waves developed in a non-Newtonian fluid flowing on an inclined channel. A projector and a high-resolution digital camera, placed vertically above the fluid surface, are used to project and record a random speckle pattern located on the free liquid surface, where the pattern is deformed due to the developed roll waves. According to the experimental geometry, the height of the roll waves associated to the out-of-plane deformation of the dots is obtained through a quantitative relationship between the experimental parameters and the in-plane displacement field in the flow direction. In terms of this, the out-of-plane deformation is found using a DIC criterion based on the speckle comparison between a reference image without the deformed pattern and an image with a deformed pattern. The maximum height of the roll waves computed with this technique is compared with the height measured using a lateral camera, with both results differing by <10% over the set of experimental instances.
Preconditioned implicit-exponential integrators (IMEXP) for stiff PDEs
NASA Astrophysics Data System (ADS)
Luan, Vu Thai; Tokman, Mayya; Rainwater, Greg
2017-04-01
We propose two new classes of time integrators for stiff DEs: the implicit exponential (IMEXP) and the hybrid exponential methods. In contrast to the existing exponential schemes, the new methods offer significant computational advantages when used with preconditioners. Any preconditioner can be used with any of these new schemes. This leads to a broader applicability of exponential methods. The proof of convergence of these integrators and numerical demonstration of their efficiency are presented.
The LEM exponential integrator for advection-diffusion-reaction equations
NASA Astrophysics Data System (ADS)
Caliari, Marco; Vianello, Marco; Bergamaschi, Luca
2007-12-01
We implement a second-order exponential integrator for semidiscretized advection-diffusion-reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja-Euler-Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.
Measuring Entanglement Spectrum via Density Matrix Exponentiation
NASA Astrophysics Data System (ADS)
Zhu, Guanyu; Seif, Alireza; Pichler, Hannes; Zoller, Peter; Hafezi, Mohammad
Entanglement spectrum (ES), the eigenvalues of the reduced density matrix of a subsystem, serves as a powerful theoretical tool to study many-body systems. For example, the gap and degeneracies of the entanglement spectrum have been used to identify various topological phases. However, the usefulness of such a concept in real experiments has been debated, since it is believed that obtaining the ES requires full state tomography, at a cost which exponentially grows with the systems size. Inspired by a recent density matrix exponentiation technique, we propose a scheme to measure ES by evolving the system with a Hamiltonian that is the subsystem's own reduced density matrix. Such a time evolution can be induced by an ancilla photon that is coupled to multiple qubits at the same time. The phase associated with the time evolution can be detected and converted into ES through either a digital or an analogue scheme. The digital scheme involves a modified quantum phase estimation algorithm based on random time evolution, while the analogue scheme is in the spirit of Ramsey interferometry. Both schemes are not limited by the size of the system, and are especially sensitive to the gap and degeneracies. We also discuss the implementation in cavity/circuit-QED and ion trap systems.
Human-chimpanzee alignment: ortholog exponentials and paralog power laws.
Gao, Kun; Miller, Jonathan
2014-12-01
Genomic subsequences conserved between closely related species such as human and chimpanzee exhibit an exponential length distribution, in contrast to the algebraic length distribution observed for sequences shared between distantly related genomes. We find that the former exponential can be further decomposed into an exponential component primarily composed of orthologous sequences, and a truncated algebraic component primarily composed of paralogous sequences.
Williams, R.A.; Stephenson, W.J.; Frankel, A.D.; Cranswick, E.; Meremonte, M.E.; Odum, J.K.
2000-01-01
Resonances observed in earthquake seismograms recorded in Seattle, Washington, the central United States and Sherman Oaks, California, are correlated with each site's respective near-surface seismic velocity profile and reflectivity determined from shallow seismic-reflection/refraction surveys. In all of these cases the resonance accounts for the highest amplitude shaking at the site above 1 Hz. These results show that imaging near-surface reflections from the ground surface can locate impedance structures that are important contributors to earthquake ground shaking. A high-amplitude S-wave reflection, recorded 250-m northeast and 300-m east of the Seattle Kingdome earthquake-recording station, with a two-way travel time of about 0.23 to 0.27 sec (about 18- to 22-m depth) marks the boundary between overlying alluvium (VS < 180 m/sec) and a higher velocity material (VS about 400 m/sec). This reflector probably causes a strong 2-Hz resonance that is observed in the earthquake data for the site near the Kingdome. In the central United States, S-wave reflections from a high-impedance boundary (an S-wave velocity increase from about 200 m/sec to 2000 m/sec) at about 40-m depth corresponds to a strong fundamental resonance at about 1.5 Hz. In Sherman Oaks, strong resonances at about 1.0 and 4 Hz are consistently observed on earthquake seismograms. A strong S-wave reflector at about 40-m depth may cause the 1.0 Hz resonance. The 4.0-Hz resonance is possibly explained by constructive interference between the first overtone of the 1.0-Hz resonance and a 3.25- to 3.9-Hz resonance calculated from an areally consistent impedance boundary at about 10-m depth as determined by S-wave refraction data.
NASA Astrophysics Data System (ADS)
Meigas, Kalju; Lass, Jaanus; Kattai, Rain; Karai, Deniss; Kaik, Juri
2004-07-01
This paper is a part of research to develop convenient method for continuous monitoring of arterial blood pressure by non-invasive and non-oscillometric way. A simple optical method, using self-mixing in a diode laser, is used for detection of skin surface vibrations near the artery. These vibrations, which can reveal the pulsate propagation of blood pressure waves along the vasculature, are used for pulse wave registration. The registration of the Pulse Wave Transit Time (PWTT) is based on computing the time delay in different regions of the human body using an ECG as a reference signal. In this study, the comparison of method of optical self-mixing with other methods as photoplethysmographic (PPG) and bioimpedance (BI) for PWTT is done. Also correlation of PWTT, obtained with different methods, with arterial blood pressure is calculated. In our study, we used a group of volunteers (34 persons) who made the bicycle exercise test. The test consisted of cycling sessions of increasing workloads during which the HR changed from 60 to 180 beats per minute. In addition, a blood pressure (NIBP) was registered with standard sphygmomanometer once per minute during the test and all NIBP measurement values were synchronized to other signals to find exact time moments where the systolic blood pressure was detected (Korotkoff sounds starting point). Computer later interpolated the blood pressure signal in order to get individual value for every heart cycle. The other signals were measured continuously during all tests. At the end of every session, a recovery period was included until person's NIBP and heart rate (HR) normalized. As a result of our study it turned out that time intervals that were calculated from plethysmographic (PPG) waveforms were in the best correlation with systolic blood pressure. The diastolic pressure does not correlate with any of the parameters representing PWTT. The pulse wave signals measured by laser and piezoelectric transducer are very similar
Exponential-Krylov methods for ordinary differential equations
NASA Astrophysics Data System (ADS)
Tranquilli, Paul; Sandu, Adrian
2014-12-01
This paper develops a new family of exponential time discretization methods called exponential-Krylov (EXPK). The new schemes treat the time discretization and the Krylov-based approximation of exponential matrix-vector products as a single computational process. The classical order conditions theory developed herein accounts for both the temporal and the Krylov approximation errors. Unlike traditional exponential schemes, EXPK methods require the construction of only a single Krylov space at each timestep. The number of basis vectors that guarantee the temporal order of accuracy does not depend on the application at hand. Numerical results show favorable properties of EXPK methods when compared to current exponential schemes.
Fluctuation Bounds in the Exponential Bricklayers Process
NASA Astrophysics Data System (ADS)
Balázs, Márton; Komjáthy, Júlia; Seppäläinen, Timo
2012-04-01
This paper is the continuation of our earlier paper (Balázs et al. in Ann. Inst. Henri Poincaré Probab. Stat. 48(1):151-187, 2012), where we proved t 1/3-order of current fluctuations across the characteristics in a class of one dimensional interacting systems with one conserved quantity. We also claimed two models with concave hydrodynamic flux which satisfied the assumptions which made our proof work. In the present note we show that the totally asymmetric exponential bricklayers process also satisfies these assumptions. Hence this is the first example with convex hydrodynamics of a model with t 1/3-order current fluctuations across the characteristics. As such, it further supports the idea of universality regarding this scaling.
Arsenic for the fool: an exponential connection.
Dani, Sergio U
2010-03-15
Anthropogenic arsenic is insidiously building up together with natural arsenic to a level unprecedented in the history of mankind. Arsenopyrite (FeAsS) is the principal ore of arsenic and gold in hard rock mines; it is formed by a coupled substitution of sulphur by arsenic in the structure of pyrite (FeS(2)) - nicknamed "fool's gold". Other important sources of anthropogenic arsenic are fossil fuels such as coal and oil. Here I report on the first indication that the environmental concentration of total arsenic in topsoils - in the 7-18ppm range - is exponentially related to the prevalence and mortality of Alzheimer's disease and other dementias in European countries. This evidence defies the imputed absence of verified cases of human morbidity or mortality resulting from exposure to low-level arsenic in topsoils.
An exponentiation method for XML element retrieval.
Wichaiwong, Tanakorn
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP.
Generalized exponential function and discrete growth models
NASA Astrophysics Data System (ADS)
Souto Martinez, Alexandre; Silva González, Rodrigo; Lauri Espíndola, Aquino
2009-07-01
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.
Frank, R; Fontaine, G; Guiraudon, G; Cabrol, C; Grosgogeat, Y; Facquet, J
1977-05-01
A comparison between the epicardial siting of the zone of pre-excitation of the ventricle in Wolff-Parkinson-White syndrome and the ECG has allowed us to distinguish 6 topographical types, according to the orientation of the delta wave in the horizontal plane, and especially in the frontal plane which is often ignored: right anterior, left lateral, right of left anterior paraseptal, and right or left posterior paraseptal. The association of a heart defect with ventricular hypertrophy, or the coexistence of several associated accessory pathways prevents such correlation and makes it imperative to carry out intracavitary investigation and epicardial mapping to localise the accessory pathway if surgery is contemplated.
NASA Astrophysics Data System (ADS)
Pallottino, G. V.
The author reports the analysis of gravitational wave and neutrino detectors over a period of 18 hours that includes the Mont Blanc 5 neutrino burst time. There is statistical evidence for correlations during a period of about two hours, centered on the 5 neutrino burst: the effect is mainly due to a dozen of large amplitude Maryland and Rome events. The interpretation of these events as due to gravitational radiation from SN1987A should be rejected, according to the standard theory of the cross-section of g.w. detectors, since it would imply an emission of energy too large by a factor of about 104.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
NASA Astrophysics Data System (ADS)
Barbier, M.; Zaquine, I.; Delaye, P.
2015-05-01
We experimentally demonstrate, for the first time to our knowledge, the generation of correlated photon pairs in a liquid-core photonic crystal fiber. Moreover, we show that, thanks to the specific Raman properties of liquids, the Raman noise (which is the main limitation of the performance of silica-core fiber-based correlated photon pair sources) is highly reduced. With a demonstrated coincident-to-accidental ratio equal to 63 and a pair generation efficiency of about 10-4 per pump pulse, this work contributes to the development of high-quality correlated photon pair sources for quantum communications.
NASA Astrophysics Data System (ADS)
Pallottino, G. V.
1990-02-01
The paper describes the analysis of data obtained in the period 12 h of February 22, 1987 to 6 h of February 23, 1987, that includes the time of neutrino observation with the Mont Blanc detector during SN 1987 A. A very significant correlation has been observed among the data of the above detectors in a period of one or two hours which includes the time of the Mont Blanc 5-neutrino observation. The correlation between the gravitational wave detector data and the Kamiokande data is found if a time of 7.8 s is added to the Kamioka recorded time; this is very close to the time difference, 6.2 s, between the IMB and Kamioka large neutrino bursts observed at about 7 h 35 min.
Acoustic wave propagation in heterogeneous two-dimensional fractured porous media
NASA Astrophysics Data System (ADS)
Hamzehpour, Hossein; Asgari, Mojgan; Sahimi, Muhammad
2016-06-01
This paper addresses an important fundamental question: the differences between wave propagation in fractured porous media with a uniform matrix (constant bulk modulus) and those in which the matrix is heterogeneous with its bulk modulus distributed spatially. The analysis of extensive experimental data [Phys. Rev. E 71, 046301 (2005), 10.1103/PhysRevE.71.046301] indicated that such distributions are self-affine and induce correlations at all the relevant length scales. The comparison is important from a practical view point because in many of the traditional models of fractured rock, particularly those that are used to study wave propagation or fit some data, the matrix is assumed to be uniform. Using extensive numerical simulation of propagation of acoustic waves, we present strong evidence indicating that the waves' amplitude in a fractured porous medium with a heterogeneous matrix decays exponentially with the distance from the source. This is in sharp contrast with a fractured porous medium with a uniform matrix in which not only the waves' amplitude decays with the distance as a stretched exponential function, but the exponent that characterizes the function is also dependent upon the fracture density. The localization length depends on the correlations in the spatial distribution of the bulk modulus, as well as the fracture density. The mean speed of the waves varies linearly with the fractures' mean orientation.
NASA Astrophysics Data System (ADS)
Bertaux, Jean-Loup; Khatunstsev, Igor; Hauchecorne, Alain; Markiewicz, Wojtek; Emmanuel, Marcq; Sébastien, Lebonnois; Marina, Patsaeva; Alex, Turin; Anna, Fedorova
2016-04-01
Based on the analysis of UV images (at 365 nm) of Venus cloud top (altitude 67±2 km) collected with VMC (Venus Monitoring Camera) on board Venus Express (VEX), it is found that the zonal wind speed south of the equator (from 5°S to 15°s) shows a conspicuous variation (from -101 to -83 m/s) with geographic longitude of Venus, correlated with the underlying relief of Aphrodite Terra. We interpret this pattern as the result of stationary gravity waves produced at ground level by the up lift of air when the horizontal wind encounters a mountain slope. These waves can propagate up to cloud top level, break there and transfer their momentum to the zonal flow. Such upward propagation of gravity waves and influence on the wind speed vertical profile was shown to play an important role in the middle atmosphere of the Earth by Lindzen [1981], but is not reproduced in a current GCM of Venus atmosphere. Consistent with present findings, the two VEGA mission balloons experienced a small, but significant, difference of westward velocity, at their 53 km floating altitude. The albedo at 365 nm varies also with longitude and latitude in a pattern strikingly similar in the low latitude regions to a recent map of cloud top H2O [Fedorova et al., 2015], in which a lower UV albedo is correlated with increased H2O. We argue that H2O enhancement is the sign of upwelling, suggesting that the UV absorber is also brought to cloud top by upwelling.
Bell, Iris R.; Howerter, Amy; Jackson, Nicholas; Aickin, Mikel; Bootzin, Richard R.; Brooks, Audrey J.
2012-01-01
Background Investigators of homeopathy have proposed that nonlinear dynamical systems (NDS) and complex systems science offer conceptual and analytic tools for evaluating homeopathic remedy effects. Previous animal studies demonstrate that homeopathic medicines alter delta electroencephalographic (EEG) slow wave sleep. The present study extended findings of remedy-related sleep stage alterations in human subjects by testing the feasibility of using two different NDS analytic approaches to assess remedy effects on human slow wave sleep EEG. Methods Subjects (N=54) were young adult male and female college students with a history of coffee-related insomnia who participated in a larger 4-week study of the polysomnographic effects of homeopathic medicines on home-based all-night sleep recordings. Subjects took one bedtime dose of a homeopathic remedy (Coffea cruda or Nux vomica 30c). We computed multiscale entropy (MSE) and the correlation dimension (Mekler-D2) for stage 3 and 4 slow wave sleep EEG sampled in artifact-free 2-minute segments during the first two rapid-eye-movement (REM) cycles for remedy and post-remedy nights, controlling for placebo and post-placebo night effects. Results MSE results indicate significant, remedy-specific directional effects, especially later in the night (REM cycle 2) (CC: remedy night increases and post-remedy night decreases in MSE at multiple sites for both stages 3 and 4 in both REM cycles; NV: remedy night decreases and post-remedy night increases, mainly in stage 3 REM cycle 2 MSE). D2 analyses yielded more sporadic and inconsistent findings. Conclusions Homeopathic medicines Coffea cruda and Nux vomica in 30c potencies alter short-term nonlinear dynamic parameters of slow wave sleep EEG in healthy young adults. MSE may provide a more sensitive NDS analytic method than D2 for evaluating homeopathic remedy effects on human sleep EEG patterns. PMID:22818237
Motion-correlated flow distortion and wave-induced biases in air-sea flux measurements from ships
NASA Astrophysics Data System (ADS)
Prytherch, J.; Yelland, M. J.; Brooks, I. M.; Tupman, D. J.; Pascal, R. W.; Moat, B. I.; Norris, S. J.
2015-09-01
Direct measurements of the turbulent air-sea fluxes of momentum, heat, moisture and gases are often made using sensors mounted on ships. Ship-based turbulent wind measurements are corrected for platform motion using well established techniques, but biases at scales associated with wave and platform motion are often still apparent in the flux measurements. It has been uncertain whether this signal is due to time-varying distortion of the air flow over the platform or to wind-wave interactions impacting the turbulence. Methods for removing such motion-scale biases from scalar measurements have previously been published but their application to momentum flux measurements remains controversial. Here we show that the measured motion-scale bias has a dependence on the horizontal ship velocity and that a correction for it reduces the dependence of the measured momentum flux on the orientation of the ship to the wind. We conclude that the bias is due to experimental error and that time-varying motion-dependent flow distortion is the likely source.
Motion-correlated flow distortion and wave-induced biases in air-sea flux measurements from ships
NASA Astrophysics Data System (ADS)
Prytherch, J.; Yelland, M. J.; Brooks, I. M.; Tupman, D. J.; Pascal, R. W.; Moat, B. I.; Norris, S. J.
2015-06-01
Direct measurements of the turbulent air-sea fluxes of momentum, heat, moisture and gases. are often made using sensors mounted on ships. Ship-based turbulent wind measurements are corrected for platform motion using well established techniques, but biases at scales associated with wave and platform motion are often still apparent in the flux measurements. It has been uncertain whether this signal is due to time-varying distortion of the air flow over the platform, or to wind-wave interactions impacting the turbulence. Methods for removing such motion-scale biases from scalar measurements have previously been published but their application to momentum flux measurements remains controversial. Here we show that the measured motion-scale bias has a dependence on the horizontal ship velocity, and that a correction for it reduces the dependence of the measured momentum flux on the orientation of the ship to the wind. We conclude that the bias is due to experimental error, and that time-varying motion-dependent flow distortion is the likely source.
NASA Technical Reports Server (NTRS)
Smarr, L. L.; Vessot, R. F. C.; Lundquist, C. A.; Decher, R.; Piran, T.
1983-01-01
A two-step satellite mission for improving the accuracy of gravitational wave detection and for observing actual gravity waveforms is proposed. The spacecraft would carry both a highly stable hydrogen maser, which would control a transmitter sending signals to earth, and a Doppler transponder operating in the two-way mode. The use of simultaneous one- and two-way Doppler transmissions offers four time records of frequency pulsations, which can reveal gravitational radiation at 1-10 MHz with an amplitude accuracy of a factor of six. The first mission phase would consist of a Shuttle launch into a highly eccentric orbit to obtain measurements of the gravitational redshift using gravitational potentials of different earth regions to establish that gravity is describable by a metric theory. Then, after a boost into a heliocentric orbit at 6 AU, the earth-satellite system could detect gravitational waves in the solar system, as well as bursts emitted by the collisions of supermassive black holes.
Easton, D M
1978-01-01
The conductance changes, gK(t) and gNa(t), of squid giant axon under voltage clamp (Hodgkin and Huxley, 1952) may be modeled by exponentiated exponential functions (Gompertz kinetics) from any holding potential VO to any membrane clamp potential V. The equation constants are set by the membrane potential V, and include, for any voltage step in the case of gK, the initial conductance, gO, the asymptote conductance g, and rate constant k: gK = g exp(-be-kt) where b = 1n g/gO. Equations of similar form relate g and k to the voltage V, and govern the corresponding parameters of the gNa system. For the gNa, the fast phase y = y exp (-be-kt) is cut down in proportion to a slow process p = (1 - p)e-k't + p, and thus gNa = py. The expo-exponential functions involve fewer constants than the Hodgkin-Huxley model. In particular, the role of the n, m, h parameters appears to be filled largely by 1n (g/gO) in the case of gK and by 1n (y/yO) in the case of gNa. Membrane action potentials during current clamp may be computed from the conductances generated by use of the appropriate differential forms of the equations; diverse other membrane behaviors may be predicted. PMID:638223
NASA Astrophysics Data System (ADS)
Sil, Arjun; Sitharam, T. G.
2014-08-01
the city is susceptible to site effects and liquefaction. Further, the different data set combinations between V s and SPT-N (corrected and uncorrected) values have been used to develop site-specific correlation equations by statistical regression, as ` V s' is a function of SPT- N value (corrected and uncorrected), considered with or without depth. However, after considering the data set pairs, a probabilistic approach has also been presented to develop a correlation using a quantile-quantile (Q-Q) plot. A comparison has also been made with the well known published correlations (for all soils) available in the literature. The present correlations closely agree with the other equations, but, comparatively, the correlation of shear wave velocity with the variation of depth and uncorrected SPT-N values provides a more suitable predicting model. Also the Q-Q plot agrees with all the other equations. In the absence of in situ measurements, the present correlations could be used to measure V s profiles of the study area for site response studies.
Exponential and power-law contact distributions represent different atmospheric conditions.
Reynolds, A M
2011-12-01
It is well known that the dynamics of plant disease epidemics are very sensitive to the functional form of the contact distribution?the probability distribution function for the distance of viable fungal spore movement until deposition. Epidemics can take the form of a constant-velocity travelling wave when the contact distribution is exponentially bounded. Fat-tailed contact distributions, on the other hand, lead to epidemic spreads that accelerate over time. Some empirical data for contact distributions can be well represented by negative exponentials while other data are better represented by fat-tailed inverse power laws. Here we present data from numerical simulations that suggest that negative exponentials and inverse power laws are not competing candidate forms of the contact distribution but are instead representative of different atmospheric conditions. Contact distributions for atmospheric boundary-layers with stabilities ranging from strongly convective (a hot windless day time scenario) to stable stratification (a cold windy night time scenario) but without precipitation events are calculated using well-established state-of-the-art Lagrangian stochastic (particle tracking) dispersal models. Contact distributions are found to be well represented by exponentials for strongly convective conditions; a -3/2 inverse power law for convective boundary-layers with wind shear; and by a -2/3 inverse power law for stably stratified conditions.
Bulanov, Sergei V.; Esirkepov, Timur Zh.; Kando, Masaki; Koga, James K.; Pirozhkov, Alexander S.; Nakamura, Tatsufumi; Bulanov, Stepan S.; Schroeder, Carl B.; Esarey, Eric; Califano, Francesco; Pegoraro, Francesco
2012-11-15
In thermal plasma, the structure of the density singularity formed in a relativistically large amplitude plasma wave close to the wavebreaking limit leads to a refraction coefficient with discontinuous spatial derivatives. This results in a non-exponentially small above-barrier reflection of an electromagnetic wave interacting with the nonlinear plasma wave.
Exponential convergence rates for weighted sums in noncommutative probability space
NASA Astrophysics Data System (ADS)
Choi, Byoung Jin; Ji, Un Cig
2016-11-01
We study exponential convergence rates for weighted sums of successive independent random variables in a noncommutative probability space of which the weights are in a von Neumann algebra. Then we prove a noncommutative extension of the result for the exponential convergence rate by Baum, Katz and Read. As applications, we first study a large deviation type inequality for weighted sums in a noncommutative probability space, and secondly we study exponential convergence rates for weighted free additive convolution sums of probability measures.
Density Estimation of Simulation Output Using Exponential EPI-Splines
2013-12-01
ak+1,1, k = 1, 2, ..., N − 1. Pointwise Fisher information. We define the pointwise Fisher information of an exponential epi-spline density h at x to...are required to obtain meaningful results. All exponential epi-splines are computed under the assumptions of continuity, smoothness, pointwise Fisher...Kernel 0.4310 0.3536 In the exponential epi-spline estimates, we include continuity, differentiability, and pointwise Fisher information constraints with
Using Differentials to Differentiate Trigonometric and Exponential Functions
ERIC Educational Resources Information Center
Dray, Tevian
2013-01-01
Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.
Trout, Andrew T; Dillman, Jonathan R; Xanthakos, Stavra; Kohli, Rohit; Sprague, Garrett; Serai, Suraj; Mahley, Alana D; Podberesky, Daniel J
2016-11-01
Purpose To evaluate the correlation between ultrasonographic (US) point shear-wave elastography (SWE) and magnetic resonance (MR) elastography liver shear-wave speed (SWS) measurements in a pediatric population and to determine if US data dispersion affects this relationship. Materials and Methods Institutional review board approval was obtained for this HIPAA-compliant investigation; informed consent and patient assent (as indicated) were obtained. Patients (age range, 0-21 years) undergoing clinical liver MR elastography between July 2014 and November 2015 were prospectively enrolled. Patients underwent two-dimensional gradient-recalled-echo 1.5-T MR elastography with point SWE performed immediately before or immediately after MR elastography. Spearman rank correlation coefficients were calculated to assess the relationship and agreement between point SWE and MR elastography SWS measurements. Uni- and multivariate logistic regression were performed to identify predictors of US data dispersion, with the best multivariate model selected based on Akaike information criterion. Results A total of 55 patients (24 female) were enrolled (mean age, 14.0 years ± 3.9 (standard deviation) (range, 3.5-21.4 years). There was fair correlation between point SWE and MR elastography SWS values for all patients (ρ = 0.33, P = .016). Correlation was substantial, however, when including only patients with minimal US data dispersion (n = 26, ρ = 0.61, P = .001). Mean body mass index (BMI) was significantly lower in patients with minimal US data dispersion than in those with substantial US data dispersion (25.4 kg/m(2) ± 7.8 vs 32.3 kg/m(2) ± 8.3, P = .003). At univariate analysis, BMI (odds ratio, 1.12; 95% confidence interval [CI]: 1.03, 1.21; P = .006) and abdominal wall thickness (odds ratio, 2.50; 95% CI: 1.32, 4.74; P = .005) were significant predictors of US data dispersion. In the best multivariate model, BMI was the only significant predictor (odds ratio, 1.11; 95% CI: 1
Robust Variable Selection with Exponential Squared Loss.
Wang, Xueqin; Jiang, Yunlu; Huang, Mian; Zhang, Heping
2013-04-01
Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness that has not been done for the existing procedures, while its performance is near optimal and superior to some recently developed methods. Specifically, under defined regularity conditions, our estimators are [Formula: see text] and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed method with some recent methods, using the oracle method as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error and the positive selection rate even in the presence of influential points. In contrast, other existing procedures have a much lower non-causal selection rate. Furthermore, we re-analyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Dataset that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods.
NASA Astrophysics Data System (ADS)
Chung, Chung-Hou; Sun, Shih-Jye; Chang, Yung-Yeh; Tsai, Wei-Feng; Zhang, Fuchun
Large Hubbard U limit of the Kane-Mele model on a zigzag ribbon of honeycomb lattice near half-filling is studied via a renormalized mean-field theory. The ground state exhibits time-reversal symmetry (TRS) breaking dx2 -y2 + idxy -wave superconductivity. At large spin-orbit coupling, the Z2 topological phase with non-trivial spin Chern number in the pure Kane-Mele model is persistent into the TRS broken state (called ``spin-Chern phase''), and has two pairs of counter-propagating helical Majorana modes at the edges. As the spin-orbit coupling is reduced, the system undergoes a topological quantum phase transition from the spin-Chern to chiral superconducting states. Possible relevance of our results to adatom-doped graphene and irridate compounds is discussed.Ref.:Shih-Jye Sun, Chung-Hou Chung, Yung-Yeh Chang, Wei-Feng Tsai, and Fu-Chun Zhang, arXiv:1506.02584. CHC acknowledges support from NSC Grant No. 98-2918-I-009-06, No. 98-2112-M-009-010-MY3, the NCTU-CTS, the MOE-ATU program, the NCTS of Taiwan, R.O.C.
Study of B and Bs mesons with a Coulomb plus exponential type potential
NASA Astrophysics Data System (ADS)
Yazarloo, B. H.; Mehraban, H.
2016-11-01
In this paper, we have studied the B and B s mesons spectra and their decays within the framework of nonrelativistic potential model. We have considered a new potential model for the interaction of mesonic systems, the Coulomb plus exponential type potential. We have applied the perturbation approach and reported the total wave function. We have used the Nikiforov-Uvarov (NU) technique to calculate the parent wave function and thereby obtained a series solution for the perturbative wave function. Besides the decay constant and leptonic decay width, we have considered the semileptonic decay width which is related to the Isgur-Wise function. The obtained results are compared with the available experimental and theoretical data.
Wehbe, Ali; Youssef, Wael
2010-10-15
In this paper, we study the energy decay rate for the elastic Bresse system in one-dimensional bounded domain. The physical system consists of three wave equations. The two wave equations about the rotation angle and the longitudinal displacement are damped by two locally distributed feedbacks at the neighborhood of the boundary. Then indirect damping is applied to the equation for the transverse displacement of the beam through the coupling terms. We will establish the exponential stability for this system in the case of the same speed of propagation in the equation for the vertical displacement and the equation for the rotation angle of the system. When the wave speeds are different, nonexponential decay rate is proved and a polynomial-type decay rate is obtained. The frequency domain method and the multiplier technique are applied.
Seislet-based morphological component analysis using scale-dependent exponential shrinkage
NASA Astrophysics Data System (ADS)
Yang, Pengliang; Fomel, Sergey
2015-07-01
Morphological component analysis (MCA) is a powerful tool used in image processing to separate different geometrical components (cartoons and textures, curves and points etc.). MCA is based on the observation that many complex signals may not be sparsely represented using only one dictionary/transform, however can have sparse representation by combining several over-complete dictionaries/transforms. In this paper we propose seislet-based MCA for seismic data processing. MCA algorithm is reformulated in the shaping-regularization framework. Successful seislet-based MCA depends on reliable slope estimation of seismic events, which is done by plane-wave destruction (PWD) filters. An exponential shrinkage operator unifies many existing thresholding operators and is adopted in scale-dependent shaping regularization to promote sparsity. Numerical examples demonstrate a superior performance of the proposed exponential shrinkage operator and the potential of seislet-based MCA in application to trace interpolation and multiple removal.
Entanglement effects in capillary waves on liquid polymer films.
Jiang, Zhang; Mukhopadhyay, Mrinmay K; Song, Sanghoon; Narayanan, Suresh; Lurio, L B; Kim, Hyunjung; Sinha, Sunil K
2008-12-12
Overdamped surface capillary wave relaxations on molten polymer films were measured using x-ray photon correlation spectroscopy. We found a transition from a single through a stretched to another single exponential regime as the temperature is decreased from well above to near the bulk glass transition temperature. A universal scaling of the dynamics was discovered over a wide range of film thicknesses, temperatures, and molecular weights (except in the multiple relaxation regime). These observations are justified by hydrodynamic theory and the time-temperature superposition principle by considering an effective viscosity instead of the bulk zero shear viscosity.
Robb Swan, Ashley; Nichols, Sharon; Drake, Angela; Angeles, AnneMarie; Diwakar, Mithun; Song, Tao; Lee, Roland R.
2015-01-01
Abstract Mild traumatic brain injury (mTBI) is common in the United States, accounting for as many as 75–80% of all TBIs. It is recognized as a significant public health concern, but there are ongoing controversies regarding the etiology of persistent symptoms post-mTBI. This constellation of nonspecific symptoms is referred to as postconcussive syndrome (PCS). The present study combined results from magnetoencephalography (MEG) and cognitive assessment to examine group differences and relationships between brain activity and cognitive performance in 31 military and civilian individuals with a history of mTBI+PCS and 33 matched healthy control subjects. An operator-free analysis was used for MEG data to increase reliability of the technique. Subjects completed a comprehensive neuropsychological assessment, and measures of abnormal slow-wave activity from MEG were collected. Results demonstrated significant group differences on measures of executive functioning and processing speed. In addition, significant correlations between slow-wave activity on MEG and patterns of cognitive functioning were found in cortical areas, consistent with cognitive impairments on exams. Results provide more objective evidence that there may be subtle changes to the neurobiological integrity of the brain that can be detected by MEG. Further, these findings suggest that these abnormalities are associated with cognitive outcomes and may account, at least in part, for long-term PCS in those who have sustained an mTBI. PMID:25808909
Sun, Shih-Jye; Chung, Chung-Hou; Chang, Yung-Yeh; Tsai, Wei-Feng; Zhang, Fu-Chun
2016-04-11
There has been growing interest in searching for exotic self-conjugate, charge-neutral low-energy fermionic quasi-particles, known as Majorana fermions (MFs) in solid state systems. Their signatures have been proposed and potentially observed at edges of topological superconcuctors with non-trivial topological invariant in the bulk electronic band structure. Much effort have been focused on realizing MFs in odd-parity superconductors made of strong spin-orbit coupled materials in proximity to conventional superconductors. In this paper, we propose a novel mechanism for realizing MFs in 2D spin-singlet topological superconducting state induced by doping a correlated quantum spin Hall (Kane-Mele) insulator. Via a renormalized mean-field approach, the system is found to exhibits time-reversal symmetry (TRS) breaking d(x2-y2) + id(xy)-wave (chiral d-wave) superconductivity near half-filling in the limit of large on-site repulsion. Surprisingly, however, at large spin-orbit coupling, the system undergoes a topological phase transition and enter into a new topological phase protected by a pseudo-spin Chern number, which can be viewed as a persistent extension of the quantum spin Hall phase upon doping. From bulk-edge correspondence, this phase is featured by the presence of two pairs of counter-propagating helical Majorana modes per edge, instead of two chiral propagating edge modes in the d + id' superconductors.
Review of "Going Exponential: Growing the Charter School Sector's Best"
ERIC Educational Resources Information Center
Garcia, David
2011-01-01
This Progressive Policy Institute report argues that charter schools should be expanded rapidly and exponentially. Citing exponential growth organizations, such as Starbucks and Apple, as well as the rapid growth of molds, viruses and cancers, the report advocates for similar growth models for charter schools. However, there is no explanation of…
A Learning Cycle on Exponential Growth and the Energy Crises.
ERIC Educational Resources Information Center
Dykstra, D. I., Jr.
1982-01-01
Describes nature and logistics of a learning cycle approach to teaching exponential growth and the energy crisis. Used with both science and nonscience majors, the cycle uses no algebra, never mentions the terms exponential or logarithmic, and requires a calculator. Instructions for obtaining student and instructor materials are provided.…
Flows induced by exponential stretching and shearing plate motions
NASA Astrophysics Data System (ADS)
Weidman, Patrick
2016-11-01
Boundary-layer solutions for the flow induced by an exponentially stretching surface also sheared in its own plane are given. Prior to this study no similarity solutions have been reported for flows generated by exponentially sheared surfaces concomitant with surface stretching in any form. The method of solution is self-similarity. The results found here are intimately related to those of Magyari and Keller ["Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface," J. Phys. D: Appl. Phys. 32, 577-585 (1999)] who studied the motion and heat transfer induced by an exponentially stretching plate. In addition to two particular cases reported here, a third situation is found where an exponentially stretching surface admits a concomitant arbitrary streamwise shearing motion.
NASA Technical Reports Server (NTRS)
Weatherford, C. A.; Brown, F. B.; Temkin, A.
1987-01-01
In a recent calculation, an exact exchange method was developed for use in the partial-differential-equation approach to electron-molecule scattering and was applied to e-N2 scattering in the fixed-nuclei approximation with an adiabatic polarization potential at low energies (0-10 eV). Integrated elastic cross sections were calculated and found to be lower than experiment at energies both below and above the Pi(g) resonance. It was speculated at that time that improved experimental agreement could be obtained if a correlated target representation were used in place of the uncorrelated one. The present paper implements this suggestion and demonstrates the improved agreement. These calculations are also extended to higher energies (0-30 eV) so asd to include the Sigma(u) resonance. Some discrepancies among the experiments and between experiment and the various calculations at very low energy are noted.
NASA Astrophysics Data System (ADS)
Tamma, Vincenzo
2016-12-01
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring" interferograms measured at the output of an analogue computer that allows the selection of the factors of each integer. At the present stage, the algorithm manifests an exponential scaling which may be overcome by an extension of this method to correlated qubits emerging from n-order quantum correlations measurements. We describe the conditions for a generic physical system to compute such an analogue algorithm. A particular example given by an "optical computer" based on optical interference will be addressed in the second paper of this series (Tamma in Quantum Inf Process 11128:1189, 2015).
NASA Astrophysics Data System (ADS)
Anbazhagan, P.; Kumar, Abhishek; Sitharam, T. G.
2013-03-01
Subsurface lithology and seismic site classification of Lucknow urban center located in the central part of the Indo-Gangetic Basin (IGB) are presented based on detailed shallow subsurface investigations and borehole analysis. These are done by carrying out 47 seismic surface wave tests using multichannel analysis of surface waves (MASW) and 23 boreholes drilled up to 30 m with standard penetration test (SPT) N values. Subsurface lithology profiles drawn from the drilled boreholes show low- to medium-compressibility clay and silty to poorly graded sand available till depth of 30 m. In addition, deeper boreholes (depth >150 m) were collected from the Lucknow Jal Nigam (Water Corporation), Government of Uttar Pradesh to understand deeper subsoil stratification. Deeper boreholes in this paper refer to those with depth over 150 m. These reports show the presence of clay mix with sand and Kankar at some locations till a depth of 150 m, followed by layers of sand, clay, and Kankar up to 400 m. Based on the available details, shallow and deeper cross-sections through Lucknow are presented. Shear wave velocity (SWV) and N-SPT values were measured for the study area using MASW and SPT testing. Measured SWV and N-SPT values for the same locations were found to be comparable. These values were used to estimate 30 m average values of N-SPT ( N 30) and SWV ( V {s/30}) for seismic site classification of the study area as per the National Earthquake Hazards Reduction Program (NEHRP) soil classification system. Based on the NEHRP classification, the entire study area is classified into site class C and D based on V {s/30} and site class D and E based on N 30. The issue of larger amplification during future seismic events is highlighted for a major part of the study area which comes under site class D and E. Also, the mismatch of site classes based on N 30 and V {s/30} raises the question of the suitability of the NEHRP classification system for the study region. Further, 17 sets
NASA Astrophysics Data System (ADS)
Elward, Jennifer Mary
Semiconductor nanoparticles, or quantum dots (QDs), are well known to have very unique optical and electronic properties. These properties can be controlled and tailored as a function of several influential factors, including but not limited to the particle size and shape, effect of composition and heterojunction as well as the effect of ligand on the particle surface. This customizable nature leads to extensive experimental and theoretical research on the capabilities of these quantum dots for many application purposes. However, in order to be able to understand and thus further the development of these materials, one must first understand the fundamental interaction within these nanoparticles. In this thesis, I have developed a theoretical method which is called electron-hole explicitly correlated Hartee-Fock (eh-XCHF). It is a variational method for solving the electron-hole Schrodinger equation and has been used in this work to study electron-hole interaction in semiconductor quantum dots. The method was benchmarked with respect to a parabolic quantum dot system, and ground state energy and electron-hole recombination probability were computed. Both of these properties were found to be in good agreement with expected results. Upon successful benchmarking, I have applied the eh-XCHF method to study optical properties of several quantum dot systems including the effect of dot size on exciton binding energy and recombination probability in a CdSe quantum dot, the effect of shape on a CdSe quantum dot, the effect of heterojunction on a CdSe/ZnS quantum dot and the effect of quantum dot-biomolecule interaction within a CdSe-firefly Luciferase protein conjugate system. As metrics for assessing the effect of these influencers on the electron-hole interaction, the exciton binding energy, electron-hole recombination probability and the average electron-hole separation distance have been computed. These excitonic properties have been found to be strongly infuenced by the
Gálvez, F J; Buendía, E; Sarsa, A
2005-07-15
For some members of the boron isoelectronic series and starting from explicitly correlated wave functions, six low-lying excited states have been studied. Three of them arise from the 1s(2)2p(3) configuration, and the other three from the 1s(2)2s(2)3l, l = s,p,d, configurations. This work follows a previous one on both the 1s(2)2s(2)2p-(2)P ground state and the four excited states coming from the 1s(2)2s2p(2) configuration. Energies, one- and two-body densities in position space and some other two-body properties in position and momentum spaces have been obtained. A systematic analysis of the energetic ordering of the states as a function of the total orbital angular momentum and spin is performed in terms of the electron-nucleus and electron-electron potential energies and the role of the angular correlation is discussed. All calculations have been carried out by using the Monte Carlo algorithm.
NASA Astrophysics Data System (ADS)
Dixit, Anant; Ángyán, János G.; Rocca, Dario
2016-09-01
A new formalism was recently proposed to improve random phase approximation (RPA) correlation energies by including approximate exchange effects [B. Mussard et al., J. Chem. Theory Comput. 12, 2191 (2016)]. Within this framework, by keeping only the electron-hole contributions to the exchange kernel, two approximations can be obtained: An adiabatic connection analog of the second order screened exchange (AC-SOSEX) and an approximate electron-hole time-dependent Hartree-Fock (eh-TDHF). Here we show how this formalism is suitable for an efficient implementation within the plane-wave basis set. The response functions involved in the AC-SOSEX and eh-TDHF equations can indeed be compactly represented by an auxiliary basis set obtained from the diagonalization of an approximate dielectric matrix. Additionally, the explicit calculation of unoccupied states can be avoided by using density functional perturbation theory techniques and the matrix elements of dynamical response functions can be efficiently computed by applying the Lanczos algorithm. As shown by several applications to reaction energies and weakly bound dimers, the inclusion of the electron-hole kernel significantly improves the accuracy of ground-state correlation energies with respect to RPA and semi-local functionals.
NASA Astrophysics Data System (ADS)
Witek, M.; Kang, T. S.; van der Lee, S.
2015-12-01
We have collected three-component data from 122 Korean accelerometer stations for the month of December in 2014. We apply similar techniques described by Zha et al. (2013) to retrieve accurate station orientation angles, in order to rotate the horizontal component data into the radial and transverse frame of reference, and for subsequent measurement of Love wave group velocity dispersion. We simultaneously normalize all three components of a daily noise record via the frequency-time normalization (FTN) method. Each component is divided by the average signal envelope in an effort to retain relative amplitude information between all three components. Station orientations are found by a grid search for the orientation azimuth which maximizes the coherency between the radial-vertical cross-correlation and the Hilbert transformed vertical-vertical cross-correlation. After measuring orientation angles, we cross-correlate and rotate the data. Typically, the group velocity dispersion curves are measured using the frequency time analysis technique (FTAN), effectively producing spectrograms with significant uncertainty in the time-frequency plane. The spectrogram approach retains only the amplitude information of the short-time Fourier transform (STFT). However, Kodera et al (1976) show that by taking into account the phase information, the concepts of instantaneous frequency and group-time delay can be used to compute the first moment of the signal power in the frequency and time domains. During energy reassignment, the signal power calculated using the STFT at a point (t0,f0t_0, f_0) is reassigned to the location of the first moment (t^g,f^ihat{t}_g,hat{f}_i), where t^ghat{t}_g is the group-time delay and f^ihat{f}_i is the instantaneous frequency. We apply the method of energy reassignment to produce precise Rayleigh and Love wave group velocity measurements in the frequency range 0.1 - 1.0 Hz. Tests on synthetic data show more accurate retrieval of group velocities at
NASA Astrophysics Data System (ADS)
Arroucau, P.; Rawlinson, N.; Sambridge, M.; Reading, A. M.
2009-12-01
Ambient noise cross-correlation is now a well established and powerful tool for studying the structure of the crust and upper mantle. In the past decade, it has given rise to a new class of seismic tomography which has been successfully applied at different scales and in various regions of the world. In this work, we exploit the ambient noise data from WOMBAT, an extensive program of temporary seismic array deployments in southeast Australia and Tasmania. With an interstation distance of a few tens of kilometers, and a cumulative total of approximately 500 sites occupied over the past decade, this dataset provides a unique opportunity to help address fundamental questions regarding the structure and tectonic evolution of the Lachlan and Delamarian orogens, which underpin the southern half of Palaeozoic eastern Australia. We computed the cross-correlation of the vertical component of the ambient noise for all simultaneously recording station pairs. Rayleigh wave group traveltimes were determined from the obtained cross-correlograms in a two-stage approach. In the first stage, preliminary dispersion curves for periods ranging from 1 to 20 s were constructed and averaged in order to build a phase-matched filter which was subsequently applied to the seismograms prior to a second round of traveltime picking. Theoretical studies have shown that the negative time derivative of the average noise correlation function provides an estimate of the Green's function of the intervening medium. Yet some studies have been successfully carried out using the correlation function without differentiation, assuming that results would not be significantly affected when dealing with group velocity only. In this work, traveltimes were picked on both and an average value was calculated for each period and station pair after some consistency check. Time picking uncertainties were assigned by determining the half-width of the time interval during which the amplitude of the envelope was 50% of
On long-time algebraic and exponential instabilities found in linear dispersive flows
NASA Astrophysics Data System (ADS)
Barlow, Nathaniel; King, Kristina; Zaretzky, Paula; Cromer, Michael; Weinstein, Steven
2016-11-01
A physically-motivated class of partial differential equations that describes the response of a system to disturbances is examined. Morphological differences are identified between system responses that exhibit algebraic growth and the more typical case of exponential growth. Specifically, the propagation characteristics of the response are examined in the context of spatio-temporal hydrodynamic stability theory. One key attribute of predicted algebraically growing solutions is the prevalence of transient growth in almost all of the response, with the long-time growth occurring asymptotically at precisely one wave speed.
NASA Astrophysics Data System (ADS)
Costanzo, M. R.; Nunziata, C.
2014-09-01
Cross-correlation functions of long noise recordings with two broadband stations and earthquake recordings in the Campanian Plain have been processed with frequency time analysis to extract the fundamental mode of Rayleigh waves. Group velocities have been combined with regional group and phase velocity data in the non-linear inversion, with Hedgehog method, in order to get average shear wave velocity models for lithospheric structures extending to 73 km of depth. The structural model below the central part of the Campanian Plain is characterized by a covering of pyroclastics and alluvial sediments, about 2 km thick, on the carbonate platform with VS ranging from 2.30-2.40 to 2.85-3.15 km/s. However, the presence of lava bodies within the carbonates cannot be excluded in the light of the same density and seismic velocities. At greater depths, a main feature is represented by a sharp increment of velocity around 8-9 km of depth (VS of 3.85 km/s), which can be attributed to the presence of metamorphic rocks, overlying a low VS layer (5% velocity reduction), at about 14-15 km of depth. Such structural model resembles those found below the quiescent Roccamonfina and Colli Albani volcanoes, and can be interpreted as the signature of a cooling magma chamber. Moreover, a low VS layer is detected at 8-9 km of depth towards the Apennines and at 6 km of depth in the southernmost part of the Campanian Plain, nearby Mt. Vesuvius. Such low velocity layer seems to be a regional feature since it has been found below Roccamonfina in the North, Campi Flegrei, bay of Napoli and Mt. Vesuvius in the South, and can be explained by the widespread presence of partially melted material below the whole Campanian area.
On the role of exponential splines in image interpolation.
Kirshner, Hagai; Porat, Moshe
2009-10-01
A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks.
Exponential Functions, Rates of Change, and the Multiplicative Unit.
ERIC Educational Resources Information Center
Confrey, Jere; Smith, Erick
1994-01-01
Describes a covariational, rather than correspondence, approach to functions that emphasizes rate of change. Proposes three ways of understanding rate of change in relation to exponential functions. (Contains 41 references.) (Author/MKR)
Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent
NASA Astrophysics Data System (ADS)
Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T.
2016-10-01
In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.
Dynamic controller design for exponential synchronization of Chen chaotic system
NASA Astrophysics Data System (ADS)
Park, Ju H.; Lee, S. M.; Kwon, O. M.
2007-07-01
The Letter considers synchronization of Chen chaotic system. The problems of determining the exponential stability and estimating the exponential convergence rate for the synchronization are investigated by employing the Lyapunov functional method and linear matrix inequality (LMI) technique. For this end, a dynamic controller is proposed for the first time and a criterion for existence of the controller is given in terms of LMIs. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1985-01-01
Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1986-01-01
Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Demonstration of the exponential decay law using beer froth
NASA Astrophysics Data System (ADS)
Leike, A.
2002-01-01
The volume of beer froth decays exponentially with time. This property is used to demonstrate the exponential decay law in the classroom. The decay constant depends on the type of beer and can be used to differentiate between different beers. The analysis shows in a transparent way the techniques of data analysis commonly used in science - consistency checks of theoretical models with the data, parameter estimation and determination of confidence intervals.
Fast Modular Exponentiation and Elliptic Curve Group Operation in Maple
ERIC Educational Resources Information Center
Yan, S. Y.; James, G.
2006-01-01
The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…
NASA Astrophysics Data System (ADS)
Cárdenas-Soto, M.; Valdes, J. E.; Escobedo-Zenil, D.
2013-05-01
In June 2006, the base of the artificial lake in Chapultepec Park collapsed. 20 thousand liters of water were filtered to the ground through a crack increasing the dimensions of initial gap. Studies indicated that the collapse was due to saturated material associated with a sudden and massive water filtration process. Geological studies indicates that all the area of this section the subsoil is composed of vulcano-sedimentary materials that were economically exploited in the mid-20th century, leaving a series of underground mines that were rehabilitated for the construction of the Park. Currently, the Lake is rehabilitated and running for recreational activities. In this study we have applied two methods of seismic noise correlation; seismic interferometry (SI) in time domain and the Spatial Power Auto Correlation (SPAC) in frequency domain, in order to explore the 3D subsoil velocity structure. The aim is to highlight major variations in velocity that can be associated with irregularities in the subsoil that may pose a risk to the stability of the Lake. For this purpose we use 96 vertical geophones of 4.5 Hz with 5-m spacing that conform a semi-circular array that provide a length of 480 m around the lake zone. For both correlation methods, we extract the phase velocity associated with the dispersion characteristics between each pair of stations in the frequency range from 4 to 12 Hz. In the SPAC method the process was through the dispersion curve, and in SI method we use the time delay of the maximum amplitude in the correlation pulse, which was previously filtered in multiple frequency bands. The results of both processes were captured in 3D velocity volumes (in the case SI a process of traveltime tomography was applied). We observed that in the frequency range from 6 to 8 Hz, appear irregular structures, with high velocity contrast in relation with the shear wave velocity of surface layer (ten thick m of saturated sediments). One of these anomalies is related
Berthelot, Geoffroy; Len, Stéphane; Hellard, Philippe; Tafflet, Muriel; Guillaume, Marion; Vollmer, Jean-Claude; Gager, Bruno; Quinquis, Laurent; Marc, Andy; Toussaint, Jean-François
2012-08-01
The physiological parameters characterizing human capacities (the ability to move, reproduce or perform tasks) evolve with ageing: performance is limited at birth, increases to a maximum and then decreases back to zero at the day of death. Physical and intellectual skills follow such a pattern. Here, we investigate the development of sport and chess performances during the lifetime at two different scales: the individual athletes' careers and the world record by age class in 25 Olympic sports events and in grandmaster chess players. For all data sets, a biphasic development of growth and decline is described by a simple model that accounts for 91.7% of the variance at the individual level and 98.5% of the variance at the species one. The age of performance peak is computed at 26.1 years old for the events studied (26.0 years old for track and field, 21.0 years old for swimming and 31.4 years old for chess). The two processes (growth and decline) are exponential and start at age zero. Both were previously demonstrated to happen in other human and non-human biological functions that evolve with age. They occur at the individual and species levels with a similar pattern, suggesting a scale invariance property.
NASA Astrophysics Data System (ADS)
Kalkowski, Michał K.; Muggleton, Jen M.; Rustighi, Emiliano
2017-03-01
Whilst the dynamics of tapered structures have been extensively studied numerically and analytically, very few experimental results have been presented to date. The main aim of this paper is to derive and demonstrate an experimental method enabling both axial and flexural wavenumbers in exponentially tapered bars to be estimated. Our particular interest in this type of tapering is motivated by its occurrence in naturally grown structures such as tree roots, with an outlook towards remote root mapping. Decomposing a dynamic response into a sum of contributing waves, we propose a method in which two independent wavenumbers can be calculated from five equispaced measurements. The approach was demonstrated in an experiment on a freely suspended wooden specimen supported by theoretical modelling. For axial waves we used the well-established elementary rod theory, whereas for flexural waves we build a piecewise uniform model based on the Timoshenko beam theory. The estimates calculated from the experimental data were compared with the analytical and numerical results and showed good agreement. The limitations of the method include an appropriate choice of sensor spacing, the effect of sensor misalignments and the assumption of small wavenumber variation for flexural waves.
Design of a 9-loop quasi-exponential waveform generator.
Banerjee, Partha; Shukla, Rohit; Shyam, Anurag
2015-12-01
We know in an under-damped L-C-R series circuit, current follows a damped sinusoidal waveform. But if a number of sinusoidal waveforms of decreasing time period, generated in an L-C-R circuit, be combined in first quarter cycle of time period, then a quasi-exponential nature of output current waveform can be achieved. In an L-C-R series circuit, quasi-exponential current waveform shows a rising current derivative and thereby finds many applications in pulsed power. Here, we have described design and experiment details of a 9-loop quasi-exponential waveform generator. In that, design details of magnetic switches have also been described. In the experiment, output current of 26 kA has been achieved. It has been shown that how well the experimentally obtained output current profile matches with the numerically computed output.
Exponential rise of dynamical complexity in quantum computing through projections.
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-10-10
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.
Exponential rise of dynamical complexity in quantum computing through projections
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-01-01
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics. PMID:25300692
Exponential Sensitivity and its Cost in Quantum Physics.
Gilyén, András; Kiss, Tamás; Jex, Igor
2016-02-10
State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed.
Rotational stretched exponential relaxation in random trap-barrier model
NASA Astrophysics Data System (ADS)
Aydiner, Ekrem
2015-07-01
The relaxation behavior of complex-disordered systems, such as spin glasses, polymers, colloidal suspensions, structural glasses,and granular media, has not been clarified. Theoretical studies show that relaxation in these systems has a topological origin. In this paper, we focus on the rotational stretched exponential relaxation behavior in complex-disordered systems and introduce a simple phase space model to understand the mechanism of the non-exponential relaxation of these systems. By employing the Monte Carlo simulation method to the model, we obtain the rotational relaxation function as a function of temperature. We show that the relaxation function has a stretched exponential form under the critical temperature while it obeys the Debye law above the critical temperature. Project supported by Istanbul University (Grant Nos. 28432 and 45662).
Exponential Sensitivity and its Cost in Quantum Physics
Gilyén, András; Kiss, Tamás; Jex, Igor
2016-01-01
State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed. PMID:26861076
Woon, D.E. )
1994-02-15
Dimer interactions of helium, neon, and argon have been studied using the augmented correlation consistent basis sets of Dunning and co-workers. Two correlation methods have been employed throughout; Moller--Plesset perturbation theory through fourth-order (MP4) and single and double excitation coupled-cluster theory with perturbative treatment of triple excitations [CCSD(T)]. Full configuration interaction (FCI) calculations were performed on He[sub 2] for some basis sets. In general, only valence electrons were correlated, although some calculations which also correlated the [ital n]=2 shell of Ar[sub 2] were performed. Dimer potential energy curves were determined using the supermolecule method with and without the counterpoise correction. A series of additional basis sets beyond the augmented correlation consistent sets were explored in which the diffuse region of the radial function space has been systematically saturated. In combination with the systematic expansion across angular function space which is inherent to the correlation consistent prescription, this approach guarantees very accurate atomic polarizabilities and hyperpolarizabilities and should lead to an accurate description of dispersion forces. The best counterpoise-corrected MP4 values for the well depths of the three dimers are (in microhartrees, empirical values in parentheses) He[sub 2], 31.9 (34.6); Ne[sub 2], 123 (134); and Ar[sub 2], 430 (454). The corresponding CCSD(T) values are He[sub 2], 33.1; Ne[sub 2], 128; and Ar[sub 2], 417. Although these values are very good, the nearly exponential convergence of well depth as a function of basis quality afforded by using the various series of correlation consistent basis sets allows estimation of complete basis set (CBS) limiting values. The MP4 estimated CBS limits are He[sub 2], 32.2; Ne[sub 2], 126; and Ar[sub 2], 447.
Woon, D.E.; Peterson, K.A.; Dunning, T.H. , Jr.
1998-08-01
The interaction of Ar with H{sub 2} and HCl has been studied using Mo/ller{endash}Plesset perturbation theory (MP2, MP3, MP4) and coupled-cluster [CCSD, CCSD(T)] methods with augmented correlation consistent basis sets. Basis sets as large as triply augmented quadruple zeta quality were used to investigate the convergence trends. Interaction energies were determined using the supermolecule approach with the counterpoise correction to account for basis set superposition error. Comparison with the available empirical potentials finds excellent agreement for both binding energies and transition state. For Ar{endash}H{sub 2}, the estimated complete basis set (CBS) limits for the binding energies of the two equivalent minima and the connecting transition state (TS) are, respectively, 55 and 47thinspcm{sup {minus}1} at the MP4 level and 54 and 46thinspcm{sup {minus}1} at the CCSD(T) level, respectively [the XC(fit) empirical potential of Bissonnette {ital et al.} [J. Chem. Phys. {bold 105}, 2639 (1996)] yields 56.6 and 47.8thinspcm{sup {minus}1} for H{sub 2} (v=0)]. The estimated CBS limits for the binding energies of the two minima and transition state of Ar{endash}HCl are 185, 155, and 109thinspcm{sup {minus}1} at the MP4 level and 176, 147, and 105thinspcm{sup {minus}1} at the CCSD(T) level, respectively [the H6(4,3,0) empirical potential of Hutson [J. Phys. Chem. {bold 96}, 4237 (1992)] yields 176.0, 148.3, and 103.3thinspcm{sup {minus}1} for HCl (v=0)]. Basis sets containing diffuse functions of (dfg) symmetries were found to be essential for accurately modeling these two complexes, which are largely bound by dispersion and induction forces. Highly correlated wave functions were also required for accurate results. This was found to be particularly true for ArHCl, where significant differences in calculated binding energies were observed between MP2, MP4, and CCSD(T). {copyright} {ital 1998 American Institute of Physics.}
On the performance of exponential integrators for problems in magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Einkemmer, Lukas; Tokman, Mayya; Loffeld, John
2017-02-01
Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin-Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.
Chowell, Gerardo; Viboud, Cécile
2016-10-01
The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing models that capture the baseline transmission characteristics in order to generate reliable epidemic forecasts. Improved models for epidemic forecasting could be achieved by identifying signature features of epidemic growth, which could inform the design of models of disease spread and reveal important characteristics of the transmission process. In particular, it is often taken for granted that the early growth phase of different growth processes in nature follow early exponential growth dynamics. In the context of infectious disease spread, this assumption is often convenient to describe a transmission process with mass action kinetics using differential equations and generate analytic expressions and estimates of the reproduction number. In this article, we carry out a simulation study to illustrate the impact of incorrectly assuming an exponential-growth model to characterize the early phase (e.g., 3-5 disease generation intervals) of an infectious disease outbreak that follows near-exponential growth dynamics. Specifically, we assess the impact on: 1) goodness of fit, 2) bias on the growth parameter, and 3) the impact on short-term epidemic forecasts. Designing transmission models and statistical approaches that more flexibly capture the profile of epidemic growth could lead to enhanced model fit, improved estimates of key transmission parameters, and more realistic epidemic forecasts.
Modeling the Role of Dislocation Substructure During Class M and Exponential Creep. Revised
NASA Technical Reports Server (NTRS)
Raj, S. V.; Iskovitz, Ilana Seiden; Freed, A. D.
1995-01-01
The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.
Numerical Studies of Non-Exponential Decay of Wavefunctions
NASA Astrophysics Data System (ADS)
Vermedahl, Jon; Petridis, Athanasios; Luban, Marshall; Staunton, Lawrence
2002-04-01
We use the staggered-leap-frog algorithm to numerically solve the time-dependent Schrödinger equation. This algorithm is particularly accurate and stable as demonstrated in a number of cases whose solutions are analytically known. Deviations from exponential decay have been established for short times for a wavefunction initially set within finite depth potential wells. The survival probability has been fit with analytical functions that reproduce exponential decay at long times. Various time scales characterizing the decay are thus extracted.
Circuit design and exponential stabilization of memristive neural networks.
Wen, Shiping; Huang, Tingwen; Zeng, Zhigang; Chen, Yiran; Li, Peng
2015-03-01
This paper addresses the problem of circuit design and global exponential stabilization of memristive neural networks with time-varying delays and general activation functions. Based on the Lyapunov-Krasovskii functional method and free weighting matrix technique, a delay-dependent criteria for the global exponential stability and stabilization of memristive neural networks are derived in form of linear matrix inequalities (LMIs). Two numerical examples are elaborated to illustrate the characteristics of the results. It is noteworthy that the traditional assumptions on the boundness of the derivative of the time-varying delays are removed.
Real-Time Exponential Curve Fits Using Discrete Calculus
NASA Technical Reports Server (NTRS)
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
New results on robust exponential stability of integral delay systems
NASA Astrophysics Data System (ADS)
Melchor-Aguilar, Daniel
2016-06-01
The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov-Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.
Stretched-exponential Doppler spectra in underwater acoustic communication channels.
van Walree, P A; Jenserud, T; Otnes, R
2010-11-01
The theory of underwater sound interacting with the sea surface predicts a Gaussian-spread frequency spectrum in the case of a large Rayleigh parameter. However, recent channel soundings reveal more sharply peaked spectra with heavier tails. The measured Doppler spread increases with the frequency and differs between multipath arrivals. The overall Doppler spectrum of a broadband waveform is the sum of the spectra of all constituent paths and frequencies, and is phenomenologically described by a stretched or compressed exponential. The stretched exponential also fits well to the broadband spectrum of a single propagation path, and narrowband spectra summed over all paths.
Robust exponential acceleration in time-dependent billiards.
Gelfreich, Vassili; Rom-Kedar, Vered; Shah, Kushal; Turaev, Dmitry
2011-02-18
A class of nonrelativistic particle accelerators in which the majority of particles gain energy at an exponential rate is constructed. The class includes ergodic billiards with a piston that moves adiabatically and is removed adiabatically in a periodic fashion. The phenomenon is robust: deformations that keep the chaotic character of the billiard retain the exponential energy growth. The growth rate is found analytically and is, thus, controllable. Numerical simulations corroborate the analytic predictions with good precision. The acceleration mechanism has a natural thermodynamical interpretation and is applied to a hot dilute gas of repelling particles.
Exponential model for option prices: Application to the Brazilian market
NASA Astrophysics Data System (ADS)
Ramos, Antônio M. T.; Carvalho, J. A.; Vasconcelos, G. L.
2016-03-01
In this paper we report an empirical analysis of the Ibovespa index of the São Paulo Stock Exchange and its respective option contracts. We compare the empirical data on the Ibovespa options with two option pricing models, namely the standard Black-Scholes model and an empirical model that assumes that the returns are exponentially distributed. It is found that at times near the option expiration date the exponential model performs better than the Black-Scholes model, in the sense that it fits the empirical data better than does the latter model.
Green function for three-wave coupling problems
Molevich, N E
2001-07-31
The Green function is found for three-wave coupling problems. The function was used for analysis of parametric amplification in dissipative and active media. It is shown that the parametric increment in active media can become exponential. As an example, the nonstationary stimulated scattering of electromagnetic waves by sound and temperatures waves is considered. (nonlinear optical phenomena)
Asymptotic Linear Stability of Solitary Water Waves
NASA Astrophysics Data System (ADS)
Pego, Robert L.; Sun, Shu-Ming
2016-12-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
Self-organized critical phenomenon as a q-exponential decay - Avalanche epidemiology of dengue
NASA Astrophysics Data System (ADS)
Saba, H.; Miranda, J. G. V.; Moret, M. A.
2014-11-01
We studied the evolution of dengue disease in the state of Bahia. The number of epidemiological dengue cases for each city follows a Self-Organized Criticality behavior (SOC). However, the analysis of the number of cases in Bahia exhibits a q-exponential distribution. To understand this different behavior, we analyzed the distribution of the power law of SOC (γ) to all cities of Bahia. Our findings show that the distribution of γ exhibits a dependence between the exponents, which may be because of migration between cities, causing the emergence of outbreaks in different cities in a correlated and asynchronous time series.
Exponential dichotomy for hyperbolic systems with periodic boundary conditions
NASA Astrophysics Data System (ADS)
Klyuchnyk, R.; Kmit, I.; Recke, L.
2017-02-01
We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions on the coefficient functions that are sufficient for the existence of exponential dichotomies on R in the space of continuous periodic functions.
Exponentially Fitted Variants of Euler's Method for ODEs
ERIC Educational Resources Information Center
Kanwar, V.; Tomar, S. K.
2008-01-01
A new class of Euler's method for the numerical solution of ordinary differential equations is presented in this article. The methods are iterative in nature and admit their geometric derivation from an exponentially fitted osculating straight line. They are single-step methods and do not require evaluation of any derivatives. The accuracy and…
Teaching Exponential Growth and Decay: Examples from Medicine
ERIC Educational Resources Information Center
Hobbie, Russell K.
1973-01-01
A treatment of exponential growth and decay is sketched which does not require knowledge of calculus, and hence, it can be applied to many cases in the biological and medical sciences. Some examples are bacterial growth, sterilization, clearance, and drug absorption. (DF)
Min and Max Exponential Extreme Interval Values and Statistics
ERIC Educational Resources Information Center
Jance, Marsha; Thomopoulos, Nick
2009-01-01
The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…
Concept of the Exponential Law Prior to 1900
ERIC Educational Resources Information Center
Curtis, Lorenzo J.
1978-01-01
Presents the historical development of perceptions and applications of the exponential law, tracing it from its ancient origins until the year 1900. Shows that many concepts such as mean life and half life and their relationships to differential equations were known long before their application to nuclear radioactivity. (GA)
Weight Factor Selection in Double Exponential Smoothing Enrollment Forecasts.
ERIC Educational Resources Information Center
Gardner, Don E.
1981-01-01
The merits of double exponential smoothing are discussed relative to other types of pattern-based enrollment forecasting methods. The basic assumptions and formulas for its use are outlined. The difficulties associated with selecting an appropriate weight factor are discussed, and the potential effect on prediction results is illustrated.…
Extreme rainfall distribution tails: Exponential, subexponential or hyperexponential?
NASA Astrophysics Data System (ADS)
Nerantzaki, Sofia; Papalexiou, Simon Michael; Koutsoyiannis, Demetris
2013-04-01
The upper tail of a probability distribution controls the behavior of both the magnitude and the frequency of extreme events. In general, based on their tail behavior, probability distributions can be categorized into two families (with reference to the exponential distribution): subexponential and hyperexponential. The latter corresponds to milder and less frequent extremes. In order to evaluate the behavior of rainfall extremes, we examine data from 3 477 stations from all over the world with sample size over 100 years. We apply the Mean Excess Function (MEF) which is a common graphical method that results in a zero slope line when applied to exponentially distributed data and in a positive slope in the case of subexponential distributions. To implement the method, we constructed confidence intervals for the slope of the Exponential distribution as functions of the sample size. The validation of the method using Monte Carlo techniques reveals that it performs well especially for large samples. The analysis shows that subexponential distributions are generally in better agreement with rainfall extremes compared to the commonly used exponential ones.
Double Exponential Relativity Theory Coupled Theoretically with Quantum Theory?
Montero Garcia, Jose de la Luz; Novoa Blanco, Jesus Francisco
2007-04-28
Here the problem of special relativity is analyzed into the context of a new theoretical formulation: the Double Exponential Theory of Special Relativity with respect to which the current Special or Restricted Theory of Relativity (STR) turns to be a particular case only.
Modelling income data using two extensions of the exponential distribution
NASA Astrophysics Data System (ADS)
Calderín-Ojeda, Enrique; Azpitarte, Francisco; Gómez-Déniz, Emilio
2016-11-01
In this paper we propose two extensions of the Exponential model to describe income distributions. The Exponential ArcTan (EAT) and the composite EAT-Lognormal models discussed in this paper preserve key properties of the Exponential model including its capacity to model distributions with zero incomes. This is an important feature as the presence of zeros conditions the modelling of income distributions as it rules out the possibility of using many parametric models commonly used in the literature. Many researchers opt for excluding the zeros from the analysis, however, this may not be a sensible approach especially when the number of zeros is large or if one is interested in accurately describing the lower part of the distribution. We apply the EAT and the EAT-Lognormal models to study the distribution of incomes in Australia for the period 2001-2012. We find that these models in general outperform the Gamma and Exponential models while preserving the capacity of the latter to model zeros.
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
ERIC Educational Resources Information Center
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
Exponential passivity for output feedback stabilisation of nonlinear uncertain systems
NASA Astrophysics Data System (ADS)
Benabdallah, Amel
2010-11-01
In this article, we address the problem of stabilisation by output feedback for a class of uncertain systems. We consider uncertain systems with a nominal part which is affine in the control and an uncertain part which is norm bounded by a known function. We propose an output feedback such that the closed loop system is globally exponentially stable.
Looking for Connections between Linear and Exponential Functions
ERIC Educational Resources Information Center
Lo, Jane-Jane; Kratky, James L.
2012-01-01
Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…
Exponentially localized Wannier functions in periodic zero flux magnetic fields
NASA Astrophysics Data System (ADS)
De Nittis, G.; Lein, M.
2011-11-01
In this work, we investigate conditions which ensure the existence of an exponentially localized Wannier basis for a given periodic hamiltonian. We extend previous results [Panati, G., Ann. Henri Poincare 8, 995-1011 (2007), 10.1007/s00023-007-0326-8] to include periodic zero flux magnetic fields which is the setting also investigated by Kuchment [J. Phys. A: Math. Theor. 42, 025203 (2009), 10.1088/1751-8113/42/2/025203]. The new notion of magnetic symmetry plays a crucial rôle; to a large class of symmetries for a non-magnetic system, one can associate "magnetic" symmetries of the related magnetic system. Observing that the existence of an exponentially localized Wannier basis is equivalent to the triviality of the so-called Bloch bundle, a rank m hermitian vector bundle over the Brillouin zone, we prove that magnetic time-reversal symmetry is sufficient to ensure the triviality of the Bloch bundle in spatial dimension d = 1, 2, 3. For d = 4, an exponentially localized Wannier basis exists provided that the trace per unit volume of a suitable function of the Fermi projection vanishes. For d > 4 and d ⩽ 2m (stable rank regime) only the exponential localization of a subset of Wannier functions is shown; this improves part of the analysis of Kuchment [J. Phys. A: Math. Theor. 42, 025203 (2009), 10.1088/1751-8113/42/2/025203]. Finally, for d > 4 and d > 2m (unstable rank regime) we show that the mere analysis of Chern classes does not suffice in order to prove triviality and thus exponential localization.
Scattering resonance of elastic wave and low-frequency equivalent slow wave
NASA Astrophysics Data System (ADS)
Meng, X.; Liu, H.; Hu, T.; Yang, L.
2015-12-01
Transmitted wave occurs as fast p-wave and slow p-wave in certain conditions when seismic waves travel through inhomogeneous layers. Energy of slow p-waves is strongest at some frequency band, but rather weak at both high frequency band and low frequency band, called scattering resonance. For practical seismic exploration, the frequency of slow p-wave occurs is below 10Hz, which cannot be explained by Biot's theory which predicts existence of the slow p-wave at ultrasonic band in the porous media. The slow p-wave equation have been derived, but which only adapted to explaining slow p-wave in the ultrasonic band. Experimental observations exhibit that slow p-wave also exists in nonporous media but with enormous low-velocity interbeds. When vertical incidence, elastic wave is simplified as compressing wave, the generation of slow waves is independent on shear wave. In the case of flat interbed and gas bubble, Liu (2006) has studied the transmission of acoustic waves, and found that the slow waves below the 10Hz frequency band can be explained. In the case of general elastic anisotropy medium, the tiheoretical research on the generation of slow waves is insufficient. Aiming at this problem, this paper presents an exponential mapping method based on transmitted wave (Magnus 1954), which can successfully explain the generation of the slow wave transmission in that case. Using the prediction operator (Claerbout 1985) to represent the transmission wave, this can be derived as first order partial differential equation. Using expansions in the frequency domain and the wave number domain, we find that the solutions have different expressions in the case of weak scattering and strong scattering. Besides, the method of combining the prediction operator and the exponential map is needed to extend to the elastic wave equation. Using the equation (Frazer and Fryer 1984, 1987), we derive the exponential mapping solution for the prediction operator of the general elastic medium
Autowaves in an active two-wire line with exponential current-voltage characteristics
Zhuravlev, V. M.
2006-03-15
Nonlinear wave processes in two-wire lines containing an active element with an exponential current-voltage characteristic (CVC) similar to that of a p-n junction are investigated. These lines are models of systems that are encountered in various physical and biological applications, such as biological membranes and semiconductor devices. It is shown that such systems may operate in different modes each of which has different dispersion and dissipation properties and, as a consequence, is described by autowave processes of different types. The behavior of a system in all basic modes is analyzed. For each mode, exact solutions to relevant equations are found and their differential conservation laws and intrinsic symmetries are investigated. One of common properties of such equations is the presence of a special superposition principle that describes the discrete structure of excitations in a line that consist of individual elementary excitations. It is shown that autopulses may be generated in such systems.
Communication at millimeter waves
NASA Astrophysics Data System (ADS)
Kamal, A. K.; Christopher, P. F.
The advantage and disadvantages of millimeter waves for terrestrial and satellite communications are enumerated. Atmospheric attenuation is discussed in detail, with brief attention given to signal loss in particulates, sandstorms, snow, hail, and fog. Short closed forms are then found for gaseous attenuation on ground-satellite paths. An exponential rain loss probability density function is used in generating atmospheric loss at arbitrary required availability. It is pointed out that this loss (as a function of frequency) can be used to pick optimum carrier frequencies as a function of location, required availability, elevation angle, and system cost. An estimate is made of the rate-of-change of millimeter wave device availability. Special attention is given to GaAs FETs, not only because they will be useful, but because one phase of their millimeter wave performance is predictable: their noise performance as a function of frequency can be estimated with the aid of a Fukui equation.
Exponential time-dependent perturbation theory in rotationally inelastic scattering
NASA Astrophysics Data System (ADS)
Cross, R. J.
1983-08-01
An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. A phase-shift matrix is calculated as an integral in time over the anisotropic part of the potential. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final velocities and the average orbital angular momentum. The exponential of the phase-shift matrix gives the scattering matrix and the various cross sections. A special representation is used where the orbital angular momentum is either treated classically or may be frozen out to yield the orbital sudden approximation. Calculations on Ar+N2 and Ar+TIF show that the theory generally gives very good agreement with accurate calculations, even where the orbital sudden approximation (coupled-states) results are seriously in error.
Exponentials and Laplace transforms on nonuniform time scales
NASA Astrophysics Data System (ADS)
Ortigueira, Manuel D.; Torres, Delfim F. M.; Trujillo, Juan J.
2016-10-01
We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla and delta exponentials, computed. With these exponentials, two generalised discrete-time Laplace transforms are deduced and their properties studied. These transforms are compatible with the standard Laplace and Z transforms. They are used to study discrete-time linear systems defined by difference equations. These equations mimic the usual continuous-time equations that are uniformly approximated when the sampling interval becomes small. Impulse response and transfer function notions are introduced. This implies a unified mathematical framework that allows us to approximate the classic continuous-time case when the sampling rate is high or to obtain the standard discrete-time case, based on difference equations, when the time grid becomes uniform.
The scaling of human mobility by taxis is exponential
NASA Astrophysics Data System (ADS)
Liang, Xiao; Zheng, Xudong; Lv, Weifeng; Zhu, Tongyu; Xu, Ke
2012-03-01
As a significant factor in urban planning, traffic forecasting and prediction of epidemics, modeling patterns of human mobility draws intensive attention from researchers for decades. Power-law distribution and its variations are observed from quite a few real-world human mobility datasets such as the movements of banking notes, trackings of cell phone users' locations and trajectories of vehicles. In this paper, we build models for 20 million trajectories with fine granularity collected from more than 10 thousand taxis in Beijing. In contrast to most models observed in human mobility data, the taxis' traveling displacements in urban areas tend to follow an exponential distribution instead of a power-law. Similarly, the elapsed time can also be well approximated by an exponential distribution. Worth mentioning, analysis of the interevent time indicates the bursty nature of human mobility, similar to many other human activities.
Historical remarks on exponential product and quantum analysis
Suzuki, Masuo
2015-03-10
The exponential product formula [1, 2] was substantially introduced in physics by the present author [2]. Its systematic applications to quantum Monte Carlo Methods [3] were preformed [4, 5] first in 1977. Many interesting applications [6] of the quantum-classical correspondence (namely S-T transformation) have been reported. Systematic higher-order decomposition formulae were also discovered by the present author [7-11], using the recursion scheme [7, 9]. Physically speaking, these exponential product formulae play a conceptual role of separation of procedures [3,14]. Mathematical aspects of these formulae have been integrated in quantum analysis [15], in which non-commutative differential calculus is formulated and a general quantum Taylor expansion formula is given. This yields many useful operator expansion formulae such as the Feynman expansion formula and the resolvent expansion. Irreversibility and entropy production are also studied using quantum analysis [15].
Exponential fitted Gauss, Radau and Lobatto methods of low order
NASA Astrophysics Data System (ADS)
Martín-Vaquero, J.; Vigo-Aguiar, J.
2008-08-01
Several exponential fitting Runge-Kutta methods of collocation type are derived as a generalization of the Gauss, Radau and Lobatto traditional methods of two steps. The new methods are capable of the exact integration (with only round-off errors) of differential equations whose solutions are linear combinations of an exponential and ordinary polynomials. Theorems of the truncation error reveal the good behavior of the new methods for stiff problems. Plots of their absolute stability regions that include the whole of the negative real axis are provided. A different procedure to find the parameter of the method is proposed. The variable step Radau method of two stages is derived. Finally, numerical examples underscore the efficiency of the proposed codes, especially when they are integrating stiff problems.
A Spectral Lyapunov Function for Exponentially Stable LTV Systems
NASA Technical Reports Server (NTRS)
Zhu, J. Jim; Liu, Yong; Hang, Rui
2010-01-01
This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.
Tachyonic matter cosmology with exponential and hyperbolic potentials
NASA Astrophysics Data System (ADS)
Pourhassan, B.; Naji, J.
In this paper, we consider tachyonic matter in spatially flat Friedmann-Robertson-Walker (FRW) universe, and obtain behavior of some important cosmological parameters for two special cases of potentials. First, we assume the exponential potential and then consider hyperbolic cosine type potential. In both cases, we obtain behavior of the Hubble, deceleration and EoS parameters. Comparison with observational data suggest the model with hyperbolic cosine type scalar field potentials has good model to describe universe.
An exponential polynomial observer for synchronization of chaotic systems
NASA Astrophysics Data System (ADS)
Mata-Machuca, J. L.; Martínez-Guerra, R.; Aguilar-López, R.
2010-12-01
In this paper, we consider the synchronization problem via nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by means of numerical simulation.
Exponential Stability of Complex-Valued Memristive Recurrent Neural Networks.
Wang, Huamin; Duan, Shukai; Huang, Tingwen; Wang, Lidan; Li, Chuandong
2017-03-01
In this brief, we establish a novel complex-valued memristive recurrent neural network (CVMRNN) to study its stability. As a generalization of real-valued memristive neural networks, CVMRNN can be separated into real and imaginary parts. By means of M -matrix and Lyapunov function, the existence, uniqueness, and exponential stability of the equilibrium point for CVMRNNs are investigated, and sufficient conditions are presented. Finally, the effectiveness of obtained results is illustrated by two numerical examples.
Fragale, Jennifer E. C.; Beck, Kevin D.; Pang, Kevin C. H.
2017-01-01
Abnormal motivation and hedonic assessment of aversive stimuli are symptoms of anxiety and depression. Symptoms influenced by motivation and anhedonia predict treatment success or resistance. Therefore, a translational approach to the study of negatively motivated behaviors is needed. We describe a novel use of behavioral economics demand curve analysis to investigate negative reinforcement in animals that separates hedonic assessment of footshock termination (i.e., relief) from motivation to escape footshock. In outbred Sprague Dawley (SD) rats, relief increased as shock intensity increased. Likewise, motivation to escape footshock increased as shock intensity increased. To demonstrate the applicability to anxiety disorders, hedonic and motivational components of negative reinforcement were investigated in anxiety vulnerable Wistar Kyoto (WKY) rats. WKY rats demonstrated increased motivation for shock cessation with no difference in relief as compared to control SD rats, consistent with a negative bias for motivation in anxiety vulnerability. Moreover, motivation was positively correlated with relief in SD, but not in WKY. This study is the first to assess the hedonic and motivational components of negative reinforcement using behavioral economic analysis. This procedure can be used to investigate positive and negative reinforcement in humans and animals to gain a better understanding of the importance of motivated behavior in stress-related disorders. PMID:28270744
Fragale, Jennifer E C; Beck, Kevin D; Pang, Kevin C H
2017-01-01
Abnormal motivation and hedonic assessment of aversive stimuli are symptoms of anxiety and depression. Symptoms influenced by motivation and anhedonia predict treatment success or resistance. Therefore, a translational approach to the study of negatively motivated behaviors is needed. We describe a novel use of behavioral economics demand curve analysis to investigate negative reinforcement in animals that separates hedonic assessment of footshock termination (i.e., relief) from motivation to escape footshock. In outbred Sprague Dawley (SD) rats, relief increased as shock intensity increased. Likewise, motivation to escape footshock increased as shock intensity increased. To demonstrate the applicability to anxiety disorders, hedonic and motivational components of negative reinforcement were investigated in anxiety vulnerable Wistar Kyoto (WKY) rats. WKY rats demonstrated increased motivation for shock cessation with no difference in relief as compared to control SD rats, consistent with a negative bias for motivation in anxiety vulnerability. Moreover, motivation was positively correlated with relief in SD, but not in WKY. This study is the first to assess the hedonic and motivational components of negative reinforcement using behavioral economic analysis. This procedure can be used to investigate positive and negative reinforcement in humans and animals to gain a better understanding of the importance of motivated behavior in stress-related disorders.
The Exponential Function, the Human Race, and Scientists
NASA Astrophysics Data System (ADS)
Bartlett, Albert A.
2004-05-01
"The greatest shortcoming of the human race is our inability to understand the exponential function." This is the opening line of a talk I have given over 1500 times since 1969. In this context, the exponential function is used to give a quantitative description of steady growth of, for example, a population. As we all know, quantities that grow steadily, at even modest rates, quickly become impossibly large. Yet non-scientists in the business and government communities continue to fight for "sustainable growth" of the U.S. economy and population. What are scientists doing to increase public comprehension of the impossibility of "sustainable growth?" The main role of scientists seems to be to avoid calling attention to the impossibility of continued growth of populations and of rates of consumption of resources and, instead, to focus on minor aspects of the related problems. In so doing, we are complicit in making the problems worse. For scientists, this opening line should be revised to read: "The greatest shortcoming of scientists is our unwillingness to apply our knowledge of the exponential function to the great problems that are facing the human race."
A kernel representation for exponential splines with global tension
NASA Astrophysics Data System (ADS)
Barendt, Sven; Fischer, Bernd; Modersitzki, Jan
2009-02-01
Interpolation is a key ingredient in many imaging routines. In this note, we present a thorough evaluation of an interpolation method based on exponential splines in tension. They are based on so-called tension parameters, which allow for a tuning of their properties. As it turns out, these interpolants have very many nice features, which are, however, not born out in the literature. We intend to close this gap. We present for the first time an analytic representation of their kernel which enables one to come up with a space and frequency domain analysis. It is shown that the exponential splines in tension, as a function of the tension parameter, bridging the gap between linear and cubic B-Spline interpolation. For example, with a certain tension parameter, one is able to suppress ringing artefacts in the interpolant. On the other hand, the analysis in the frequency domain shows that one derives a superior signal reconstruction quality as known from the cubic B-Spline interpolation, which, however, suffers from ringing artifacts. With the ability to offer a trade-off between opposing features of interpolation methods we advocate the use of the exponential spline in tension from a practical point of view and use the new kernel representation to qualify the trade-off.
NASA Astrophysics Data System (ADS)
Ekinci, B.; Sabbağ, N.; Uyanik, O.; Öncü, Z.; Akdemir, S.; Türker, E.
2014-12-01
Determining of concrete strength can be used by destructive or non-destructive methods. Concrete strength is determined with uniaxial compressive test as destructive in laboratory and with Seismic Ultrasonic P- (Compressional) and S-wave (Shear) measurements as non-destructive in-situ or laboratory. In this study, strength of saturated concrete is investigated by using seismic P and S-wave velocities. For this, concrete samples were formed with using the cube samples in size 15x15x15cm. Different strength designs were made for obtain different strengths in these samples. The aim is to create concrete strengths of between the lowest 5MPa and the highest 100 MPa. After the end of the curing time of created the cube concrete samples Seismic P and S waves measurements were made in the laboratory by Ultrasonic test equipment. Hence, P and S wave velocities of the sample were calculated. After these, for determine the strength of the samples uniaxial compression strength test was performed. As a result, P and S wave velocities and concrete strength values of concrete samples were obtained. By correlating these values over %90 exponential relationships were determined. By using this relationship, concrete strength can be determined sensitively from P and S wave velocities. In addition, by using P and S wave velocities elastic parameters values and Poisson's ratio of concrete specimens can be calculated. Keywords: Concrete, Strength, Compressional and Shear-wave velocities, Empirical Relationship
Giesbertz, Klaas J. H.; Leeuwen, Robert van
2014-05-14
Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r{sub 12}) depending on the interelectronic distance r{sub 12}. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r{sub 12}) needs to diverge for large r{sub 12} at large internuclear distances while for shorter bond distances it increases as a function of r{sub 12} to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.
NASA Astrophysics Data System (ADS)
Guardia, Marcel; Seara, Tere M.
2012-05-01
In this paper, we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian system of one degree of freedom with a fast periodic or quasiperiodic and meromorphic in the state variables perturbation. The obtained results are different from the previous ones in the literature, which mainly assume algebraic or trigonometric polynomial dependence on the state variables. As a model, we consider the pendulum equation with several meromorphic perturbations and we show the sensitivity of the size of the splitting on the width of the analyticity strip of the perturbation with respect to the state variables. We show that the size of the splitting is exponentially small if the strip of analyticity is wide enough. Furthermore, we see that the splitting grows as the width of the analyticity strip shrinks, even becoming non-exponentially small for very narrow strips. Our results prevent use of polynomial truncations of the meromorphic perturbation to compute the size of the splitting of separatrices.
NASA Astrophysics Data System (ADS)
Williams, B. P.; Fritts, D. C.; Bossert, K.
2015-12-01
During the DEEPWAVE campaign, the NCAR Gulfstream V research aircraft flew over New Zealand, Tasmania, and the Southern Ocean with research flights covering 33° in latitude (31S to 64S) and 40° in longitude (144E to 184E) during June and July 2014. During these flights, we operated a Rayleigh lidar for middle atmosphere temperature measurements and a narrowband, 2-frequency Na lidar for sodium density and temperature measurements. This platform allows high resolution horizontal/vertical cross sections of temperature covering most of the region from the surface to 105km and up to 20° in latitude or longitude per flight. Both lidars operated during 23 flights with 130 total hours of operation split between repeated cross sections over the Southern Alps to measure mountain waves, downstream flights to look at trailing waves from mountain and island sources, upstream flights for modeling predictability, and flights to the deep Southern Ocean to measure waves from polar vortex/jets/fronts. This presentation will summarize the lidar results and present measurements of large amplitude waves starting from their tropospheric sources through the stratosphere to their dissipation in the upper mesosphere and lower thermosphere.
Technology Transfer Automated Retrieval System (TEKTRAN)
Electrical penetration graph (EPG) monitoring is a rigorous means of observing and quantifying the feeding of any piercing-sucking insect. Previous studies with aphid and leafhopper pests of agricultural crops have demonstrated the unique value of what is termed the X wave, i.e. the waveform that r...
Technology Transfer Automated Retrieval System (TEKTRAN)
Electrical penetration graph (EPG) monitoring is a rigorous means of observing and quantifying the feeding of any piercing-sucking insect. Previous studies with aphid and leafhopper pests of agricultural crops have demonstrated the unique value of what is termed the X wave, i.e. the waveform that r...
Decay of capillary wave turbulence.
Deike, Luc; Berhanu, Michael; Falcon, Eric
2012-06-01
We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent as the one found in the stationary regime, in agreement with weak turbulence predictions. The amplitude of all Fourier modes are found to decrease exponentially with time at the same damping rate. The longest wavelengths involved in the system are shown to be damped by a viscous surface boundary layer. These long waves play the role of an energy source during the decay that sustains nonlinear interactions to keep capillary waves in a wave turbulent state.
Stability of traveling waves of a diffusive susceptible-infective-removed (SIR) epidemic model
NASA Astrophysics Data System (ADS)
Li, Yan; Li, Wan-Tong; Yang, Yun-Rui
2016-04-01
This paper is concerned with the stability and uniqueness of traveling waves of a delayed diffusive susceptible-infective-removed (SIR) epidemic model. We first prove the exponential stability of traveling waves by using the weighted energy method, where the traveling waves are allowed to be non-monotone. Then we establish the exact asymptotic behavior of traveling waves at -∞ by using Ikehara's theorem. Finally, the uniqueness of traveling waves is proved by the stability result of traveling waves.
NASA Astrophysics Data System (ADS)
Amovilli, Claudio; March, Norman H.
The Hiller-Sucher-Feinberg (HSF) identity is combined with the three-parameter correlated wave function of Chandrasekhar in order to generate an alternative electron density ρ(r) for the He atom. This and the conventional "local" operator form of ρ(r) are then compared with a diffusion quantum Monte Carlo density. An exact limiting relation is also presented, via HSF identity, between the one-particle density matrix and the pair density in a many-electron atom, which transcends its Hartree-Fock counterpart and has no N-representability difficulties. For the Ne atom, the accuracy of the semiempirical correlated electron density recently obtained by Cordero et al. (Phys. Rev. A 2007, 75, 052502) using fine-tuning of Hartree-Fock theory was assessed by appealing to the ground-state density from diffusion quantum Monte Carlo. The high accuracy of the Cordero et al. density was thereby confirmed. A HSF calculation on neon, with a correlated many-body wave function as starting point, is a worthwhile future aim.
Technology Transfer Automated Retrieval System (TEKTRAN)
Surface soil moisture is an important parameter in hydrology and climate investigations. Current and future satellite missions with L-band passive microwave radiometers can provide valuable information for monitoring the global soil moisture. A factor that can play a significant role in the modeling...
Imaginary time density-density correlations for two-dimensional electron gases at high density
Motta, M.; Galli, D. E.; Moroni, S.; Vitali, E.
2015-10-28
We evaluate imaginary time density-density correlation functions for two-dimensional homogeneous electron gases of up to 42 particles in the continuum using the phaseless auxiliary field quantum Monte Carlo method. We use periodic boundary conditions and up to 300 plane waves as basis set elements. We show that such methodology, once equipped with suitable numerical stabilization techniques necessary to deal with exponentials, products, and inversions of large matrices, gives access to the calculation of imaginary time correlation functions for medium-sized systems. We discuss the numerical stabilization techniques and the computational complexity of the methodology and we present the limitations related to the size of the systems on a quantitative basis. We perform the inverse Laplace transform of the obtained density-density correlation functions, assessing the ability of the phaseless auxiliary field quantum Monte Carlo method to evaluate dynamical properties of medium-sized homogeneous fermion systems.
NASA Astrophysics Data System (ADS)
Mandrà, Salvatore; Zhu, Zheng; Katzgraber, Helmut G.
2017-02-01
We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated with a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009), 10.1088/1367-2630/11/7/073021]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.
Mandrà, Salvatore; Zhu, Zheng; Katzgraber, Helmut G
2017-02-17
We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated with a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)NJOPFM1367-263010.1088/1367-2630/11/7/073021]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.
Klein, Etienne K; Lavigne, Claire; Gouyon, Pierre-Henri
2006-01-01
Background Rare long distance dispersal events impact the demography and the genetic structure of populations. When dispersal is modelled via a dispersal kernel, one possible characterisation of long-distance dispersal is given by the shape of the tail of the kernel, i.e. its type of decay. This characteristic is known to directly act on the speed and pattern of colonization, and on the spatial structure of genetic diversity during colonization. In particular, colonization waves behave differently depending on whether the kernel decreases faster or slower than an exponential (i.e. is thin-tailed vs. fat-tailed). To interpret and extend published results on the impact of long-distance dispersal on the genetic structure of populations, we examine a classification of dispersal kernels based on the shape of their tails and formally demonstrate qualitative differences among them that can influence the predicted diversity of a propagule pool sampled far from two distinct sources. Results We show that a fat-tailed kernel leads asymptotically to a diverse propagule pool containing a balanced mixing of the propagules from the two sources, whereas a thin-tailed kernel results in all propagules originating from the closest source. We further show that these results hold for biologically relevant distances under certain circumstances, and in particular if the number of propagules is large enough, as would be the case for pollen or seeds. Conclusion To understand the impact of long-distance dispersal on the structure and dynamics of a metapopulation, it might be less important to precisely estimate an average dispersal distance than to determine if the tail of the dispersal kernel is fatter or thinner than that of an exponential function. Depending solely on this characteristic, a metapopulation will behave similarly to an island model with a diverse immigrant pool or to a stepping-stone model with migrants from closest populations. Our results further help to understand why
NASA Astrophysics Data System (ADS)
Stanke, Monika; Palikot, Ewa; Adamowicz, Ludwik
2016-05-01
Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H2 and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.
Stanke, Monika; Palikot, Ewa; Adamowicz, Ludwik
2016-05-07
Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H2 and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.
Glasser, M. L.; March, N. H.; Nieto, L. M.
2011-12-15
Here attention is first drawn to the importance of gaining insight into Fock's early proposal for expanding the ground-state wave function for He-like atomic ions in hyperspherical coordinates. We approach the problem via two solvable models, namely, (i) the s-term model put forth by Temkin [Phys. Rev. 126, 130 (1962)] and (ii) the Hookean atom model proposed by Kestner and Sinanoglu [Phys. Rev. 128, 2687 (1962)]. In both cases the local kinetic energy can be obtained explicitly in hyperspherical coordinates. Separation of variables occurs in both model wave functions, though in a different context in the two cases. Finally, a k-space formulation is proposed that should eventually result in distinctive identifying characteristics of Fock's nonanalyticities for He-like atomic ions when both electrons are close to the nucleus.
Xuan, Weipeng; He, Mei; Meng, Nan; He, Xingli; Wang, Wenbo; Chen, Jinkai; Shi, Tianjin; Hasan, Tawfique; Xu, Zhen; Xu, Yang; Luo, J. K.
2014-01-01
We report ZnO/glass surface acoustic wave (SAW) humidity sensors with high sensitivity and fast response using graphene oxide sensing layer. The frequency shift of the sensors is exponentially correlated to the humidity change, induced mainly by mass loading effect rather than the complex impedance change of the sensing layer. The SAW sensors show high sensitivity at a broad humidity range from 0.5%RH to 85%RH with < 1 sec rise time. The simple design and excellent stability of our GO-based SAW humidity sensors, complemented with full humidity range measurement, highlights their potential in a wide range of applications. PMID:25425458
NASA Astrophysics Data System (ADS)
Xuan, Weipeng; He, Mei; Meng, Nan; He, Xingli; Wang, Wenbo; Chen, Jinkai; Shi, Tianjin; Hasan, Tawfique; Xu, Zhen; Xu, Yang; Luo, J. K.
2014-11-01
We report ZnO/glass surface acoustic wave (SAW) humidity sensors with high sensitivity and fast response using graphene oxide sensing layer. The frequency shift of the sensors is exponentially correlated to the humidity change, induced mainly by mass loading effect rather than the complex impedance change of the sensing layer. The SAW sensors show high sensitivity at a broad humidity range from 0.5%RH to 85%RH with < 1 sec rise time. The simple design and excellent stability of our GO-based SAW humidity sensors, complemented with full humidity range measurement, highlights their potential in a wide range of applications.
Xuan, Weipeng; He, Mei; Meng, Nan; He, Xingli; Wang, Wenbo; Chen, Jinkai; Shi, Tianjin; Hasan, Tawfique; Xu, Zhen; Xu, Yang; Luo, J K
2014-11-26
We report ZnO/glass surface acoustic wave (SAW) humidity sensors with high sensitivity and fast response using graphene oxide sensing layer. The frequency shift of the sensors is exponentially correlated to the humidity change, induced mainly by mass loading effect rather than the complex impedance change of the sensing layer. The SAW sensors show high sensitivity at a broad humidity range from 0.5%RH to 85%RH with < 1 sec rise time. The simple design and excellent stability of our GO-based SAW humidity sensors, complemented with full humidity range measurement, highlights their potential in a wide range of applications.
Exponentially accurate approximations to piece-wise smooth periodic functions
NASA Technical Reports Server (NTRS)
Greer, James; Banerjee, Saheb
1995-01-01
A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.
Exponential Methods for the Time Integration of Schroedinger Equation
Cano, B.; Gonzalez-Pachon, A.
2010-09-30
We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.
A Mixed Exponential Time Series Model. NMEARMA(p,q).
1980-03-01
AD-AO85 316 NAVAL POSTGRADUATE SCHOOL MONTEREY CA F/G 12/1 A MIXED EXPONENTIAL TIME SERIES MODEL. NMEARMA(P,Q).(U MAR GO A .J LAWRANCE , P A LEWIS...This report was prepared by: A. J. Lawrance University of Birmingham Birmingham, England Reviewed by: Released by- Michael G. Sover’ign, Chirman...MODEL, NMEARMA(p,q) by A. J. Lawrance P. A. W. Lewis University of Birmingham Naval Postgraduate School Birmingham, England Monterey, California, USA
A conditionally exponential decay approach to scaling in finance
NASA Astrophysics Data System (ADS)
Weron, Rafal; Weron, Karina; Weron, Aleksander
We demonstrate how the basic ideas of the fractal and the heterogeneous market hypotheses lead to a rigorous mathematical model, which can be used to solve the problem of characterizing the distribution of price changes corresponding to the empirical scaling law of volatility for high-frequency data from the foreign exchange market. For this purpose, we adopt the conditionally exponential decay model, which describes asymptotic behaviour of general complex systems. We also discuss the overall rationale for why one might expect such scaling laws to hold for financial data.
An Exponential Finite Difference Technique for Solving Partial Differential Equations.
1987-06-01
density , kg/N 3 (lbm/ft 3) 91.*,e separation variables (At dimensionless timelAX) 2 vi -W sNiv W- NiW.4%1 1. INTRODUCTION Partial differential equations...competing numerical analysis were run in double precision on either the IBM-3033 or the Cray X-MP mainframes. The computer codes developed for the...is increased. - R P~p~ 15 Effect of Initial and Boundary Conditions on the Exponential Finite Difference Method In this section the effect of
Asymptotic Structure of Constrained Exponential Random Graph Models
NASA Astrophysics Data System (ADS)
Zhu, Lingjiong
2017-03-01
In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the asymptotic structure is uniform and there also exists non-trivial regions in the phase plane where the asymptotic structure is non-uniform. We will get more refined results for the star model and in particular the two-star model for which a sharp transition from uniform to non-uniform structure, a stationary point and phase transitions will be obtained.
On the function inverse to the exponential integral function
NASA Astrophysics Data System (ADS)
Pecina, P.
1986-01-01
The paper deals briefly with one integral of the basic equations of meteoric physics which includes the exponential integral function Ei(x). It is further shown that the approximation of the function inverse to Ei(x), Ei-1(x), is also required. The construction of this function, using series expansion by means of Chebyshev polynomials, is described. Computer programs, written in Fortran IV G, which serve to compute the values of Ei(x) and Ei-1(x), accurate to 13 decimal figures, are included.
Polar exponential sensor arrays unify iconic and Hough space representation
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1990-01-01
The log-polar coordinate system, inherent in both polar exponential sensor arrays and log-polar remapped video imagery, is identical to the coordinate system of its corresponding Hough transform parameter space. The resulting unification of iconic and Hough domains simplifies computation for line recognition and eliminates the slope quantization problems inherent in the classical Cartesian Hough transform. The geometric organization of the algorithm is more amenable to massively parallel architectures than that of the Cartesian version. The neural architecture of the human visual cortex meets the geometric requirements to execute 'in-place' log-Hough algorithms of the kind described here.
Curve fitting of aeroelastic transient response data with exponential functions
NASA Technical Reports Server (NTRS)
Bennett, R. M.; Desmarais, R. N.
1976-01-01
The extraction of frequency, damping, amplitude, and phase information from unforced transient response data is considered. These quantities are obtained from the parameters determined by fitting the digitized time-history data in a least-squares sense with complex exponential functions. The highlights of the method are described, and the results of several test cases are presented. The effects of noise are considered both by using analytical examples with random noise and by estimating the standard deviation of the parameters from maximum-likelihood theory.
Exponential integrators for the incompressible Navier-Stokes equations.
Newman, Christopher K.
2004-07-01
We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size. Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step. Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L{sup 2} inner product. We examine this L{sup 2} projection and an H{sup 1} projection induced by the H{sup 1} semi-inner product. The H
Stretched exponential survival statistics for microorganisms in radiation field
NASA Astrophysics Data System (ADS)
Plonka, Andrzej; Bogus, Wlodzimierz
1999-11-01
The so-called concave or tailed survival curves are reported both for multi and single species bacterial populations. Taking as an example Bacillus pumilus, frequently encountered in decontamination studies, it is shown that the tailed survival curves are adequately described by stretched (0< α<1) exponential SF=exp[-( D/ D0) α], where SF denotes the fraction of species surviving the irradiation dose D, D0 is the effective dose, and α is the dispersion parameter interpreted phenomenologically in terms of radiation sensivity distribution for single species population under the given experimental conditions.
Incomplete exponential sums and Diffie-Hellman triples
NASA Astrophysics Data System (ADS)
Banks, William D.; Friedlander, John B.; Konyagin, Sergei V.; Shparlinski, Igor E.
2006-03-01
Let p be a prime and vartheta an integer of order t in the multiplicative group modulo p. In this paper, we continue the study of the distribution of Diffie-Hellman triples (vartheta(x,) vartheta(y,) vartheta(xy) ) by considering the closely related problem of estimating exponential sums formed from linear combinations of the entries in such triples. We show that the techniques developed earlier for complete sums can be combined, modified and developed further to treat incomplete sums as well. Our bounds imply uniformity of distribution results for Diffie-Hellman triples as the pair (x,y) varies over small boxes.
Solving Point-Reactor Kinetics Equations Using Exponential Moment Methods
2013-03-21
equations of the following form: ( ) ( ) ( ) ( ) ( )i i i dn t t n t c t S t dt (2) ( ) ( ) ( )i ii i dc t c t n...presented in the function. Exponential moment functions are orderless; that is, the value of the function is invariant under permutations of its...turned into an integral equation by ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) i i i i i i i i i i i i dn
Hermite-Padé approximation of exponential functions
NASA Astrophysics Data System (ADS)
Astafyeva, A. V.; Starovoitov, A. P.
2016-06-01
The paper is concerned with diagonal Hermite-Padé polynomials of the first kind for the system of exponentials \\{eλ_jz\\}j=0^k with arbitrary distinct complex parameters \\{λ_k\\}j=0^k. An asymptotic formula for the remainder term is established and the location of the zeros is described. For real parameters the asymptotics are found and the extremal properties are described. The theorems obtained supplement the well-known results due to Borwein, Wielonsky, Saff, Varga and Stahl. Bibliography: 43 titles.
Takai, Kazuyuki
2017-01-21
Codon adaptation index (CAI) has been widely used for prediction of expression of recombinant genes in Escherichia coli and other organisms. However, CAI has no mechanistic basis that rationalizes its application to estimation of translational efficiency. Here, I propose a model based on which we could consider how codon usage is related to the level of expression during exponential growth of bacteria. In this model, translation of a gene is considered as an analog of electric current, and an analog of electric resistance corresponding to each gene is considered. "Translational resistance" is dependent on the steady-state concentration and the sequence of the mRNA species, and "translational resistivity" is dependent only on the mRNA sequence. The latter is the sum of two parts: one is the resistivity for the elongation reaction (coding sequence resistivity), and the other comes from all of the other steps of the decoding reaction. This electric circuit model clearly shows that some conditions should be met for codon composition of a coding sequence to correlate well with its expression level. On the other hand, I calculated relative frequency of each of the 61 sense codon triplets translated during exponential growth of E. coli from a proteomic dataset covering over 2600 proteins. A tentative method for estimating relative coding sequence resistivity based on the data is presented.
NASA Astrophysics Data System (ADS)
Beale, Paul
2015-03-01
We propose a new class of pseudorandom number generators based on Pohlig-Hellman exponentiation ciphers. The method generates uniform pseudorandom streams by encrypting simple sequences of short integer messages into ciphertexts by exponentiation modulo prime numbers. The advantages of the method are: the method is trivially parallelizable by parameterization with each pseudorandom number generator derived from an independent prime modulus, the method is fully scalable on massively parallel computing clusters due to the large number of primes available for each implementation, the seeding and initialization of the independent streams is simple, the method requires only a few integer multiply-mod operations per pseudorandom number, the state of each instance is defined by only a few integer values, the period of each instance is different, and the method passes a battery of intrastream and interstream correlation tests using up to 1013 pseudorandom numbers per test. We propose an implementation using 32-bit prime moduli with small exponents that require only a few 64-bit multiply-mod operations that can be executed directly in hardware. The 32-bit implementation we propose has millions of possible instances, all with periods greater than 1018. Supported by NSF CNS-082179.
He, Jing-Lin; Wu, Ping; Zhu, Shuang-Li; Li, Ting; Li, Pan-Pan; Xiang, Jian-Nan; Cao, Zhong
2015-01-01
A novel strategy of cleaved DNAzyme substrate induced enzymatic cascade has been devised for the exponential amplified detection of L-histidine. The enzyme strand carries out hydrolytic cleavage of the substrate strand in the presence of L-histidine. The cleaved DNAzyme substrates introduce the polymerase/endonuclease reaction cycles as primers. The L-histidine acts as the activator for enzymatic cascade amplification generating a distinguishable fluorescence enhancement. A good nonlinear correlation (R=0.9994) between fluorescence intensity and the logarithm of the L-histidine concentration is obtained over the range from 50 nM to 1.0 mM. The detection limit was estimated as 30 nM. This efficient amplification of the fluorescence signal is attributed to the L-histidine induced cooperation of Klenow Fragment polymerase (exo(-)) and Nb.BbvCI endonuclease reaction. The activation of such enzymatic cascades through analyte-DNAzyme interactions has a substantial impact on the development of exponential amplified DNAzyme sensors.
Magnetic correlations at graphene edges: basis for novel spintronics devices.
Yazyev, Oleg V; Katsnelson, M I
2008-02-01
Magnetic zigzag edges of graphene are considered as a basis for novel spintronics devices despite the fact that no true long-range magnetic order is possible in one dimension. We study the transverse and longitudinal fluctuations of magnetic moments at zigzag edges of graphene from first principles. We find a high value for the spin wave stiffness D=2100 meV A2 and a spin-collinear domain wall creation energy E(dw)=114 meV accompanied by low magnetic anisotropy. Above the crossover temperature T(x) approximately 10 K, the spin correlation length xi proportional, variantT(-1) limits the long-range magnetic order to approximately 1 nm at 300 K while below T(x), it grows exponentially with decreasing temperature. We discuss possible ways of increasing the range of magnetic order and effects of edge roughness on it.
Data assimilation on the exponentially accurate slow manifold.
Cotter, Colin
2013-05-28
I describe an approach to data assimilation making use of an explicit map that defines a coordinate system on the slow manifold in the semi-geostrophic scaling in Lagrangian coordinates, and apply the approach to a simple toy system that has previously been proposed as a low-dimensional model for the semi-geostrophic scaling. The method can be extended to Lagrangian particle methods such as Hamiltonian particle-mesh and smooth-particle hydrodynamics applied to the rotating shallow-water equations, and many of the properties will remain for more general Eulerian methods. Making use of Hamiltonian normal-form theory, it has previously been shown that, if initial conditions for the system are chosen as image points of the map, then the fast components of the system have exponentially small magnitude for exponentially long times as ε→0, and this property is preserved if one uses a symplectic integrator for the numerical time stepping. The map may then be used to parametrize initial conditions near the slow manifold, allowing data assimilation to be performed without introducing any fast degrees of motion (more generally, the precise amount of fast motion can be selected).
Freddi: Fast Rise Exponential Decay accretion Disk model Implementation
NASA Astrophysics Data System (ADS)
Malanchev, K. L.; Lipunova, G. V.
2016-10-01
Freddi (Fast Rise Exponential Decay: accretion Disk model Implementation) solves 1-D evolution equations of the Shakura-Sunyaev accretion disk. It simulates fast rise exponential decay (FRED) light curves of low mass X-ray binaries (LMXBs). The basic equation of the viscous evolution relates the surface density and viscous stresses and is of diffusion type; evolution of the accretion rate can be found on solving the equation. The distribution of viscous stresses defines the emission from the source. The standard model for the accretion disk is implied; the inner boundary of the disk is at the ISCO or can be explicitely set. The boundary conditions in the disk are the zero stress at the inner boundary and the zero accretion rate at the outer boundary. The conditions are suitable during the outbursts in X-ray binary transients with black holes. In a binary system, the accretion disk is radially confined. In Freddi, the outer radius of the disk can be set explicitely or calculated as the position of the tidal truncation radius.
A stochastic evolutionary model generating a mixture of exponential distributions
NASA Astrophysics Data System (ADS)
Fenner, Trevor; Levene, Mark; Loizou, George
2016-02-01
Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in [T. Fenner, M. Levene, G. Loizou, J. Stat. Mech. 2015, P08015 (2015)] so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.
Arima model and exponential smoothing method: A comparison
NASA Astrophysics Data System (ADS)
Wan Ahmad, Wan Kamarul Ariffin; Ahmad, Sabri
2013-04-01
This study shows the comparison between Autoregressive Moving Average (ARIMA) model and Exponential Smoothing Method in making a prediction. The comparison is focused on the ability of both methods in making the forecasts with the different number of data sources and the different length of forecasting period. For this purpose, the data from The Price of Crude Palm Oil (RM/tonne), Exchange Rates of Ringgit Malaysia (RM) in comparison to Great Britain Pound (GBP) and also The Price of SMR 20 Rubber Type (cents/kg) with three different time series are used in the comparison process. Then, forecasting accuracy of each model is measured by examinethe prediction error that producedby using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute deviation (MAD). The study shows that the ARIMA model can produce a better prediction for the long-term forecasting with limited data sources, butcannot produce a better prediction for time series with a narrow range of one point to another as in the time series for Exchange Rates. On the contrary, Exponential Smoothing Method can produce a better forecasting for Exchange Rates that has a narrow range of one point to another for its time series, while itcannot produce a better prediction for a longer forecasting period.
Exponentially more precise quantum simulation of fermions in second quantization
NASA Astrophysics Data System (ADS)
Babbush, Ryan; Berry, Dominic W.; Kivlichan, Ian D.; Wei, Annie Y.; Love, Peter J.; Aspuru-Guzik, Alán
2016-03-01
We introduce novel algorithms for the quantum simulation of fermionic systems which are dramatically more efficient than those based on the Lie-Trotter-Suzuki decomposition. We present the first application of a general technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The key difficulty in applying algorithms for general sparse Hamiltonian simulation to fermionic simulation is that a query, corresponding to computation of an entry of the Hamiltonian, is costly to compute. This means that the gate complexity would be much higher than quantified by the query complexity. We solve this problem with a novel quantum algorithm for on-the-fly computation of integrals that is exponentially faster than classical sampling. While the approaches presented here are readily applicable to a wide class of fermionic models, we focus on quantum chemistry simulation in second quantization, perhaps the most studied application of Hamiltonian simulation. Our central result is an algorithm for simulating an N spin-orbital system that requires \\tilde{{ O }}({N}5t) gates. This approach is exponentially faster in the inverse precision and at least cubically faster in N than all previous approaches to chemistry simulation in the literature.
Truncated γ-exponential models for tidal stellar systems
NASA Astrophysics Data System (ADS)
Gomez-Leyton, Y. J.; Velazquez, L.
2016-05-01
We introduce a parametric family of models to characterize the properties of astrophysical systems in a quasi-stationary evolution under the incidence evaporation. We start from an one-particle distribution fγ (q, p|β,ɛs) that considers an appropriate deformation of Maxwell-Boltzmann form with inverse temperature β, in particular, a power-law truncation at the scape energy ɛs with exponent γ > 0. This deformation is implemented using a generalized γ-exponential function obtained from the fractional integration of ordinary exponential. As shown in this work, this proposal generalizes models of tidal stellar systems that predict particles distributions with isothermal cores and polytropic haloes, e.g.: Michie-King models. We perform the analysis of thermodynamic features of these models and their associated distribution profiles. A nontrivial consequence of this study is that profiles with isothermal cores and polytropic haloes are only obtained for low energies whenever deformation parameter γ < γc ≃ 2.13. This study is a first approximation to characterize a self- gravitating system, so we consider equal to all the particles that constitute the system.
Properties of branching exponential flights in bounded domains
NASA Astrophysics Data System (ADS)
Zoia, A.; Dumonteil, E.; Mazzolo, A.
2012-11-01
In a series of recent works, important results have been reported concerning the statistical properties of exponential flights evolving in bounded domains, a widely adopted model for finite-speed transport phenomena (Blanco S. and Fournier R., Europhys. Lett., 61 (2003) 168; Mazzolo A., Europhys. Lett., 68 (2004) 350; Bénichou O. et al., Europhys. Lett., 70 (2005) 42). Motivated by physical and biological systems where random spatial displacements are coupled with Galton-Watson birth-death mechanisms, such as neutron multiplication, diffusion of reproducing bacteria or spread of epidemics, in this letter we extend those results in two directions, via a Feynman-Kac formalism. First, we characterize the occupation statistics of exponential flights in the presence of absorption and branching, and give explicit moment formulas for the total length travelled by the walker and the number of performed collisions in a given domain. Then, we show that the survival and escape probability can be derived as well by resorting to a similar approach.
Facilitating Understanding of a Catch-22 Concept: Teaching Exponential Change with Logo.
ERIC Educational Resources Information Center
Weller, Herman G.; Johnson, Vivian
1992-01-01
Describes a unit for teaching exponential change in a noncalculus physics course by having students write recursive procedures in LOGO to graphically represent linear and exponential change. Summarizes the experience of implementing the unit in a segment on radioactive decay. Modifications to the unit are suggested for teaching exponential change…
NASA Astrophysics Data System (ADS)
Guarnieri, R.; Padilha, L.; Guarnieri, F.; Echer, E.; Makita, K.; Pinheiro, D.; Schuch, A.; Boeira, L.; Schuch, N.
Ultraviolet radiation type B (UV-B 280-315nm) is well known by its damage to life on Earth, including the possibility of causing skin cancer in humans. However, the atmo- spheric ozone has absorption bands in this spectral radiation, reducing its incidence on Earth's surface. Therefore, the ozone amount is one of the parameters, besides clouds, aerosols, solar zenith angles, altitude, albedo, that determine the UV-B radia- tion intensity reaching the Earth's surface. The total ozone column, in Dobson Units, determined by TOMS spectrometer on board of a NASA satellite, and UV-B radiation measurements obtained by a UV-B radiometer model MS-210W (Eko Instruments) were correlated. The measurements were obtained at the Observatório Espacial do Sul - Instituto Nacional de Pesquisas Espaciais (OES/CRSPE/INPE-MCT) coordinates: Lat. 29.44oS, Long. 53.82oW. The correlations were made using UV-B measurements in fixed solar zenith angles and only days with clear sky were selected in a period from July 1999 to December 2001. Moreover, the mathematic behavior of correlation in dif- ferent angles was observed, and correlation coefficients were determined by linear and first order exponential fits. In both fits, high correlation coefficients values were ob- tained, and the difference between linear and exponential fit can be considered small.
Relativistic Electron Wave Packets Carrying Angular Momentum
NASA Astrophysics Data System (ADS)
Bialynicki-Birula, Iwo; Bialynicka-Birula, Zofia
2017-03-01
There are important differences between the nonrelativistic and relativistic description of electron beams. In the relativistic case the orbital angular momentum quantum number cannot be used to specify the wave functions and the structure of vortex lines in these two descriptions is completely different. We introduce analytic solutions of the Dirac equation in the form of exponential wave packets and we argue that they properly describe relativistic electron beams carrying angular momentum.
Non-exponential Stabilization of Linear Time-invariant Systems by Time-varying Controllers
NASA Astrophysics Data System (ADS)
Inoue, Masaki; Wada, Teruyo; Ikeda, Masao
This paper proposes non-exponential stabilization of linear time-invariant systems by linear time-varying controllers. We consider state feedback and dynamic output feedback to make the states of the closed-loop systems decay non-exponentially. We first introduce a non-exponential stability concept that the state of a time-varying system converges to the origin with a bound provided by a desired function. Then, we give non-exponential stabilizability conditions and time-varying controllers to achieve the desired behavior of the closed-loop systems. By the proposed methods, we can realize various non-exponential behaviors, which may improve control performance.
On Using Exponential Parameter Estimators with an Adaptive Controller
NASA Technical Reports Server (NTRS)
Patre, Parag; Joshi, Suresh M.
2011-01-01
Typical adaptive controllers are restricted to using a specific update law to generate parameter estimates. This paper investigates the possibility of using any exponential parameter estimator with an adaptive controller such that the system tracks a desired trajectory. The goal is to provide flexibility in choosing any update law suitable for a given application. The development relies on a previously developed concept of controller/update law modularity in the adaptive control literature, and the use of a converse Lyapunov-like theorem. Stability analysis is presented to derive gain conditions under which this is possible, and inferences are made about the tracking error performance. The development is based on a class of Euler-Lagrange systems that are used to model various engineering systems including space robots and manipulators.
On exponential stability of gravity driven viscoelastic flows
NASA Astrophysics Data System (ADS)
Jiang, Fei; Wu, Guochun; Zhong, Xin
2016-05-01
We investigate stability of an equilibrium state to a nonhomogeneous incompressible viscoelastic fluid driven by gravity in a bounded domain Ω ⊂R3 of class C3. First, we establish a critical number κC, which depends on the equilibrium density and the gravitational constant, and is a threshold of the elasticity coefficient κ for instability and stability of the linearized perturbation problem around the equilibrium state. Then we prove that the equilibrium state is exponential stability provided that κ >κC and the initial disturbance quantities around the equilibrium state satisfy some relations. In particular, if the equilibrium density ρ bar is a Rayleigh-Taylor (RT) type and ρbar‧ is a constant, our result strictly shows that the sufficiently large elasticity coefficient can prevent the RT instability from occurrence.
Iterative exponential growth of stereo- and sequence-controlled polymers
NASA Astrophysics Data System (ADS)
Barnes, Jonathan C.; Ehrlich, Deborah J. C.; Gao, Angela X.; Leibfarth, Frank A.; Jiang, Yivan; Zhou, Erica; Jamison, Timothy F.; Johnson, Jeremiah A.
2015-10-01
Chemists have long sought sequence-controlled synthetic polymers that mimic nature's biopolymers, but a practical synthetic route that enables absolute control over polymer sequence and structure remains a key challenge. Here, we report an iterative exponential growth plus side-chain functionalization (IEG+) strategy that begins with enantiopure epoxides and facilitates the efficient synthesis of a family of uniform >3 kDa macromolecules of varying sequence and stereoconfiguration that are coupled to produce unimolecular polymers (>6 kDa) with sequences and structures that cannot be obtained using traditional polymerization techniques. Selective side-chain deprotection of three hexadecamers is also demonstrated, which imbues each compound with the ability to dissolve in water. We anticipate that these new macromolecules and the general IEG+ strategy will find broad application as a versatile platform for the scalable synthesis of sequence-controlled polymers.
Exponentially Fragile PT Symmetry in Lattices with Localized Eigenmodes
Bendix, Oliver; Fleischmann, Ragnar; Kottos, Tsampikos; Shapiro, Boris
2009-07-17
We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting deltaapproxexp{sup -N/x}i where xi is their localization length. The level 'evolution' with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous PT symmetry breaking occurs at gamma{sub PT}approxmin(delta), thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gamma{sub PT}approx1/N{sup 2} and the distribution P(gamma{sub PT}) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.
Exponential-family random graph models for valued networks
Krivitsky, Pavel N.
2013-01-01
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through choice of model terms (sufficient statistics). However, those ERGMs modeling the more complex features have, to date, been limited to binary data: presence or absence of ties. Thus, analysis of valued networks, such as those where counts, measurements, or ranks are observed, has necessitated dichotomizing them, losing information and introducing biases. In this work, we generalize ERGMs to valued networks. Focusing on modeling counts, we formulate an ERGM for networks whose ties are counts and discuss issues that arise when moving beyond the binary case. We introduce model terms that generalize and model common social network features for such data and apply these methods to a network dataset whose values are counts of interactions. PMID:24678374
Auxiliary Parameter MCMC for Exponential Random Graph Models
NASA Astrophysics Data System (ADS)
Byshkin, Maksym; Stivala, Alex; Mira, Antonietta; Krause, Rolf; Robins, Garry; Lomi, Alessandro
2016-11-01
Exponential random graph models (ERGMs) are a well-established family of statistical models for analyzing social networks. Computational complexity has so far limited the appeal of ERGMs for the analysis of large social networks. Efficient computational methods are highly desirable in order to extend the empirical scope of ERGMs. In this paper we report results of a research project on the development of snowball sampling methods for ERGMs. We propose an auxiliary parameter Markov chain Monte Carlo (MCMC) algorithm for sampling from the relevant probability distributions. The method is designed to decrease the number of allowed network states without worsening the mixing of the Markov chains, and suggests a new approach for the developments of MCMC samplers for ERGMs. We demonstrate the method on both simulated and actual (empirical) network data and show that it reduces CPU time for parameter estimation by an order of magnitude compared to current MCMC methods.
Black hole as a magnetic monopole within exponential nonlinear electrodynamics
NASA Astrophysics Data System (ADS)
Kruglov, S. I.
2017-03-01
We perform the gauge covariant quantization of the exponential model of nonlinear electrodynamics. Magnetically charged black holes, in the framework of our model are considered, and the regular black hole solution is obtained in general relativity. The asymptotic black hole solution at r → ∞ is found. We calculate the magnetic mass of the black hole and the metric function which are expressed via the parameter β of the model and the magnetic charge. The thermodynamic properties and thermal stability of regular black holes are analysed. We calculate the Hawking temperature of black holes and their heat capacity at the constant magnetic charge. We find a point where the temperature changes the sign that corresponds to the first-order phase transition. It is shown that at critical point, where the heat capacity diverges, there is a phase transition of the second-order. We obtain the parameters of the model when the black hole is stable.
Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results
NASA Astrophysics Data System (ADS)
Baldomá, Inmaculada; Fontich, Ernest; Guardia, Marcel; Seara, Tere M.
We study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a non-autonomous perturbation fast and periodic in time. We provide a result valid for general systems which are algebraic or trigonometric polynomials in the state variables. It consists on obtaining a rigorous proof of the asymptotic formula for the measure of the splitting. We obtain that the splitting has the asymptotic behavior Kɛβe, identifying the constants K, β, a in terms of the system features. We consider several cases. In some cases, assuming the perturbation is small enough, the values of K, β coincide with the classical Melnikov approach. We identify the limit size of the perturbation for which this theory holds true. However for the limit cases, which appear naturally both in averaging and bifurcation theories, we encounter that, generically, K and β are not well predicted by Melnikov theory.
Statistical modelling of agrometeorological time series by exponential smoothing
NASA Astrophysics Data System (ADS)
Murat, Małgorzata; Malinowska, Iwona; Hoffmann, Holger; Baranowski, Piotr
2016-01-01
Meteorological time series are used in modelling agrophysical processes of the soil-plant-atmosphere system which determine plant growth and yield. Additionally, long-term meteorological series are used in climate change scenarios. Such studies often require forecasting or projection of meteorological variables, eg the projection of occurrence of the extreme events. The aim of the article was to determine the most suitable exponential smoothing models to generate forecast using data on air temperature, wind speed, and precipitation time series in Jokioinen (Finland), Dikopshof (Germany), Lleida (Spain), and Lublin (Poland). These series exhibit regular additive seasonality or non-seasonality without any trend, which is confirmed by their autocorrelation functions and partial autocorrelation functions. The most suitable models were indicated by the smallest mean absolute error and the smallest root mean squared error.
Non-exponential decay of dark localized surface plasmons.
Ginzburg, Pavel; Zayats, Anatoly V
2012-03-12
It is shown that the decay of the weakly coupled to radiation (dark) modes of subwavelength plasmonic nanostructures is strongly nonexponential. Their lifetime is overestimated by conventional exponential relaxation time obtained in the standard Markovian approximation. These effects are manifestations of the strong dispersion and near-field feedback. The developed theoretical framework introduces an ensemble of local relaxation degrees of freedom coupled to plasmonic mode in order to describe its decay due to material losses. The macroscopic description of the decay process leads to the specific memory function of the system, evaluated from the modal and material dispersions of the plasmonic nanostructure. Proper knowledge of the relaxation behavior is vital for various applications relying on light-matter interactions of emitters with nanoscale objects, such as fluorescence manipulation, bio-imaging, sensing, spasers, sub-diffraction optics, Raman scattering, and quantum optics.
Income inequality in Romania: The exponential-Pareto distribution
NASA Astrophysics Data System (ADS)
Oancea, Bogdan; Andrei, Tudorel; Pirjol, Dan
2017-03-01
We present a study of the distribution of the gross personal income and income inequality in Romania, using individual tax income data, and both non-parametric and parametric methods. Comparing with official results based on household budget surveys (the Family Budgets Survey and the EU-SILC data), we find that the latter underestimate the income share of the high income region, and the overall income inequality. A parametric study shows that the income distribution is well described by an exponential distribution in the low and middle incomes region, and by a Pareto distribution in the high income region with Pareto coefficient α = 2.53. We note an anomaly in the distribution in the low incomes region (∼9,250 RON), and present a model which explains it in terms of partial income reporting.
Exponential protection of zero modes in Majorana islands
NASA Astrophysics Data System (ADS)
Albrecht, S. M.; Higginbotham, A. P.; Madsen, M.; Kuemmeth, F.; Jespersen, T. S.; Nygård, J.; Krogstrup, P.; Marcus, C. M.
2016-03-01
Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, with the departure from zero expected to be exponentially small as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced superconducting Coulomb island (a ‘Majorana island’) that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometre of increased wire length. For devices longer than about one micrometre, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.
Exponential protection of zero modes in Majorana islands.
Albrecht, S M; Higginbotham, A P; Madsen, M; Kuemmeth, F; Jespersen, T S; Nygård, J; Krogstrup, P; Marcus, C M
2016-03-10
Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, with the departure from zero expected to be exponentially small as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced superconducting Coulomb island (a 'Majorana island') that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometre of increased wire length. For devices longer than about one micrometre, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.
Exponential and power-law mass distributions in brittle fragmentation
NASA Astrophysics Data System (ADS)
Åström, J. A.; Linna, R. P.; Timonen, J.; Møller, Peder Friis; Oddershede, Lene
2004-08-01
Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size s scales as s-(2D-1)/Df1(-(2/λ)Ds)+f2(-s0-1(λ+s1/D)D) , where D is the Euclidean dimension of the space, λ is the penetration depth, and f1 and f2 can be approximated by exponential functions. Simulation results and experiments can both be described by this theoretical fragment-size distribution. The typical largest fragment size s0 was found to diverge at the minimum strain required for fragmentation as it is inversely related to the density of initially formed cracks. Our results also indicate that scaling of s0 close to this divergence depends on, e.g., loading conditions, and thus is not universal. At the same time, the density of fragment surface vanishes as L-1 , L being the linear dimension of the brittle solid. The results obtained provide an explanation as to why the fragment-size distributions found in nature can have two components, an exponential as well as a power-law component, with varying relative weights.
Subglacial bedforms reveal an exponential size-frequency distribution
NASA Astrophysics Data System (ADS)
Hillier, J. K.; Smith, M. J.; Clark, C. D.; Stokes, C. R.; Spagnolo, M.
2013-05-01
Subglacial bedforms preserved in deglaciated landscapes record characteristics of past ice-sediment flow regimes, providing insight into subglacial processes and ice sheet dynamics. Individual forms vary considerably, but they can often be grouped into coherent fields, typically called flow-sets, that reflect discrete episodes of ice flow. Within these, bedform size-frequency distributions (predominantly height, width and length) are currently described by several statistics (e.g., mean, median, and standard deviation) that, arguably, do not best capture the defining characteristics of these populations. This paper seeks to create a better description based upon semi-log plots, which reveal that the frequency distributions of bedform dimensions (drumlin, mega-scale glacial lineation, and ribbed moraine) plot as straight lines above the mode (ϕ). This indicates, by definition, an exponential distribution, for which a simple and easily calculated, yet statistically rigorous, description is designed. Three descriptive parameters are proposed: gradient (λ; the exponent, characterising bedforms likely least affected by non-glacial factors), area-normalised y-intercept (β0; quantifying spatial density), and the mode (ϕ). Below ϕ, small features are less prevalent due to i) measurement: data, sampling and mapping fidelity; ii) possible post-glacial degradation; or iii) genesis: not being created sub-glacially. This new description has the benefit of being insensitive to the impact of potentially unmapped or degraded smaller features and better captures properties relating to ice flow. Importantly, using λ, flow sets can now be more usefully compared with each other across all deglaciated regions and with the output of numerical ice sheet models. Applications may also exist for analogous fluvial and aeolian bedforms. Identifying the characteristic exponential and that it is typical of 'emergent' subglacial bedforms is a new and potentially powerful constraint on
NASA Astrophysics Data System (ADS)
Line, C. E. R.; Hobbs, R. W.; Hudson, J. A.; Snyder, D. B.
1998-01-01
Statistical parameters describing heterogeneity in the Proterozoic basement of the Baltic Shield were estimated from controlled-source seismic data, using a statistical inversion based on the theory of wave propagation through random media (WPRM), derived from the parabolic wave approximation. Synthetic plane-wave seismograms generated from models of random media show consistency with WPRM theory for forward propagation in the weak-scattering regime, whilst for two-way propagation a discrepancy exists that is due to contamination of the primary wave by backscattered energy. Inverse modelling of the real seismic data suggests that the upper crust to depths of ~ 15 km can be characterized, subject to the range of spatial resolution of the method, by a medium with an exponential spatial autocorrelation function, an rms velocity fluctuation of 1.5 +/- 0.5 per cent and a correlation length of 150 +/- 50 m. Further inversions show that scattering is predominantly occurring in the uppermost ~ 2 km of crust, where rms velocity fluctuation is 3 - 6 per cent. Although values of correlation distance are well constrained by these inversions, there is a trade-off between thickness of scattering layer and rms velocity perturbation estimates, with both being relatively poorly resolved. The higher near-surface heterogeneity is interpreted to arise from fractures in the basement rocks that close under lithostatic pressure for depths greater than 2 - 3 km.
Colman, Michael A; Aslanidi, Oleg V; Stott, Jonathan; Holden, Arun V; Zhang, Henggui
2011-10-01
Atrial arrhythmias resulting from abnormally rapid focal activity in the atria may be reflected in an altered P-wave morphology (PWM) in the ECG. Although clinically important, detailed relationships between PWM and origins of atrial focal excitations have not been established. To study such relationships, we developed computational models of the human atria and torso. The model simulation results were used to evaluate an extant clinical algorithm for locating the origin of atrial focal points from the ECG. The simulations showed that the algorithm was practical and could predict the atrial focal locations with 85% accuracy. We proposed a further refinement of the algorithm to distinguish between focal locations within the large atrial bundles.
Fault-zone attenuation of high-frequency seismic waves
NASA Astrophysics Data System (ADS)
Blakeslee, Sam; Malin, Peter; Alvarez, Marcos
1989-11-01
We have developed a technique to measure seismic attenuation within an active fault-zone at seismogenic depths. Utilizing a pair of stations and pairs of earthquakes, spectral ratios are performed to isolate attenuation produced by wave-propagation within the fault-zone. This empirical approach eliminates common source, propagation, instrument and near-surface site effects. The technique was applied to a cluster of 19 earthquakes recorded by a pair of downhole instruments located within the San Andreas fault-zone, at Parkfield California. Over the 1-40 Hz bandwidth used in this analysis, amplitudes are found to decrease exponentially with frequency. Furthermore, the fault-zone propagation distance correlates with the severity of attenuation. Assuming a constant Q attenuation operator, the S-wave quality factor within the fault-zone at a depth of 5-6 kilometers is 31 (+7,-5). If fault-zones are low-Q environments, then near-source attenuation of high-frequency seismic waves may help to explain phenomenon such as fmax. Fault-zone Q may prove to be a valuable indicator of the mechanical behavior and rheology of fault-zones. Specific asperities can be monitored for precursory changes associated with the evolving stress-field within the fault-zone. The spatial and temporal resolution of the technique is fundamentally limited by the uncertainty in earthquake location and the interval time between earthquakes.
Symmetry and decay of traveling wave solutions to the Whitham equation
NASA Astrophysics Data System (ADS)
Bruell, Gabriele; Ehrnström, Mats; Pei, Long
2017-04-01
This paper is concerned with decay and symmetry properties of solitary-wave solutions to a nonlocal shallow-water wave model. An exponential decay result for supercritical solitary-wave solutions is given. Moreover, it is shown that all such solitary-wave solutions are symmetric and monotone on either side of the crest. The proof is based on the method of moving planes. Furthermore, a close relation between symmetric and traveling-wave solutions is established.
Surface Wear Measurement Using Optical Correlation Technique
NASA Astrophysics Data System (ADS)
Acinger, Kresimir
1983-12-01
The coherent optical correlation technique was applied for measuring the surface wear of a tappet (part of car engine), worn by friction with the camshaft. It was found that maximum correlation intensity decays exponentially with the number of wear cycles (i.e. camshaft revolutions). Tappets of the same make have an identical rate of correlation decay. Tappets of different makes have different rates of correlation decay which are in agreement with observed long term wear.
Evaluation of Compressive Strength and Stiffness of Grouted Soils by Using Elastic Waves
Lee, In-Mo; Kim, Jong-Sun; Yoon, Hyung-Koo; Lee, Jong-Sub
2014-01-01
Cement grouted soils, which consist of particulate soil media and cementation agents, have been widely used for the improvement of the strength and stiffness of weak ground and for the prevention of the leakage of ground water. The strength, elastic modulus, and Poisson's ratio of grouted soils have been determined by classical destructive methods. However, the performance of grouted soils depends on several parameters such as the distribution of particle size of the particulate soil media, grouting pressure, curing time, curing method, and ground water flow. In this study, elastic wave velocities are used to estimate the strength and elastic modulus, which are generally obtained by classical strength tests. Nondestructive tests by using elastic waves at small strain are conducted before and during classical strength tests at large strain. The test results are compared to identify correlations between the elastic wave velocity measured at small strain and strength and stiffness measured at large strain. The test results show that the strength and stiffness have exponential relationship with elastic wave velocities. This study demonstrates that nondestructive methods by using elastic waves may significantly improve the strength and stiffness evaluation processes of grouted soils. PMID:25025082
NASA Astrophysics Data System (ADS)
Knudson, M. D.; Desjarlais, M. P.
2017-01-01
We present shock compression data for deuterium through the molecular-to-atomic transition along the principal Hugoniot with unprecedented precision, enabling discrimination between subtle differences in first-principle theoretical predictions. These observations, supported through reshock measurements, provide tight constraints in a regime directly relevant to planetary interiors. Our findings are in best agreement with density functional theory; however, no one exchange-correlation functional describes well both the onset of dissociation and the maximum compression along the Hugoniot.
Hennig, Thomas; Maass, Philipp; Hayano, Junichiro; Heinrichs, Stefan
2006-11-01
The statistical properties of heart beat intervals of 130 long-term surface electrocardiogram recordings during atrial fibrillation (AF) are investigated. We find that the distribution of interbeat intervals exhibits a characteristic exponential tail, which is absent during sinus rhythm, as tested in a corresponding control study with 72 healthy persons. The rate gamma of the exponential decay lies in the range 3-12 Hz and shows diurnal variations. It equals, up to statistical uncertainties, the level of the previously uncovered white noise part of the power spectrum, which is also characteristic for AF. The overall statistical features can be described by decomposing the intervals into two statistically independent times, where the first one is associated with a correlated process with 1/f noise characteristics, while the second one belongs to an uncorrelated process and is responsible for the exponential tail. It is suggested to use gamma as a further parameter for a better classification of AF and for the medical diagnosis. The relevance of the findings with respect to a general understanding of AF is discussed.
Controllable optical rogue waves in the femtosecond regime.
Dai, Chao-Qing; Zhou, Guo-Quan; Zhang, Jie-Fang
2012-01-01
We derive analytical rogue wave solutions of variable-coefficient higher-order nonlinear Schrödinger equations describing the femtosecond pulse propagation via a transformation connected with the constant-coefficient Hirota equation. Then we discuss the propagation behaviors of controllable rogue waves, including recurrence, annihilation, and sustainment in a periodic distributed fiber system and an exponential dispersion decreasing fiber. Finally, we investigate nonlinear tunneling effects for rogue waves.
NASA Astrophysics Data System (ADS)
Khalil, Adil; Humeau-Heurtier, Anne; Mahé, Guillaume; Abraham, Pierre
2015-05-01
In the cardiovascular system, the macrocirculation and microcirculation-two subsystems-can be affected by aging. Laser speckle contrast imaging (LSCI) is an emerging noninvasive optical technique that allows the monitoring of microvascular function and can help, using specific data processing, to understand the relationship between the subsystems. Using LSCI, the goals of this study are: (i) to assess the aging effect over microvascular parameters (perfusion and moving blood cells velocity, MBCV) and macrocirculation parameters (pulse-wave velocity, PWV) and (ii) to study the relationship between these parameters. In 16 healthy subjects (20 to 62 years old), perfusion and MBCV computed from LSCI are studied in three physiological states: rest, vascular occlusion, and post-occlusive reactive hyperaemia (PORH). MBCV is computed from a model of velocity distribution. During PORH, the experimental results show a relationship between perfusion and age (R2=0.67) and between MBCV and age (R2=0.72), as well as between PWV and age at rest (R2=0.91). A relationship is also found between perfusion and MBCV for all physiological states (R2=0.98). Relationships between microcirculation and macrocirculation (perfusion-PWV or MBCV-PWV) are found only during PORH with R2=0.76 and R2=0.77, respectively. This approach may prove useful for investigating dysregulation in blood flow.
The exponential eigenmodes of the carbon-climate system
NASA Astrophysics Data System (ADS)
Raupach, M. R.
2012-09-01
Several basic ratios describing the carbon-climate system are observed to adopt relatively steady values. Examples include the CO2 airborne fraction (the fraction of the total anthropogenic CO2 emission flux that accumulates in the atmosphere) and the ratio T/QE of warming (T) to cumulative total CO2 emissions (QE). This paper explores the reason for such near-constancy in the past, and its likely limitations in future. The contemporary carbon-climate system is often approximated as a first-order linear system, for example in response-function descriptions. All such linear systems have exponential eigenfunctions in time (an eigenfunction being one that, if applied to the system as a forcing, produces a response of the same shape). This implies that, if the carbon-climate system is idealised as a linear system (Lin) forced by exponentially growing CO2 emissions (Exp), then all ratios among fluxes and perturbation state variables are constant. Important cases are the CO2 airborne fraction (AF), the cumulative airborne fraction (CAF), other CO2 partition fractions and cumulative partition fractions into land and ocean stores, the CO2 sink uptake rate (kS, the combined land and ocean CO2 sink flux per unit excess atmospheric CO2), and the ratio T/QE. Further, the AF and the CAF are equal. The Lin and Exp idealisations apply approximately (but not exactly) to the carbon-climate system in the period from the start of industrialisation (nominally 1750) to the present, consistent with the observed near-constancy of the AF, CAF and T/QE in this period. A nonlinear carbon-climate model is used to explore how the likely future breakdown of both the Lin and Exp idealisations will cause the AF, CAF and kS to depart significantly from constancy, in ways that depend on CO2 emissions scenarios. However, T/QE remains approximately constant in typical scenarios, because of compensating interactions between emissions trajectories, carbon-cycle dynamics and non-CO2 gases. This theory
NASA Astrophysics Data System (ADS)
Ishizuka, Jun; Yamada, Takemi; Yanagi, Yuki; Ōno, Yoshiaki
2013-12-01
We investigate the electronic state and the superconductivity in the 5-orbital Hubbard model for iron pnictides by using the dynamical mean-field theory in conjunction with the Eliashberg equation. The renormalization factor exhibits significant orbital dependence resulting in the large change in the band dispersion as observed in recent ARPES experiments. The critical interactions towards the magnetic, orbital and superconducting instabilities are suppressed as compared with those from the random phase approximation (RPA) due to local correlation effects. Remarkably, the s++-pairing phase due to the orbital fluctuation is largely expanded relative to the RPA result, while the s+--pairing phase due to the magnetic fluctuation is reduced.
Yi, Xiang; Yao, Mingwu
2015-02-09
In this paper, we present analytical expressions for the performance of urban free-space optical (FSO) communication systems under the combined influence of atmospheric turbulence- and misalignment-induced fading (pointing errors). The atmospheric turbulence channel is modeled by the exponentiated Weibull (EW) distribution that can accurately describe the probability density function (PDF) of the irradiance fluctuations associated with a transmitted Gaussian-beam wave and a finite-sized receiving aperture. The nonzero boresight pointing error PDF model, which is recently proposed for considering the effects of both boresight and jitter, is adopted in analysis. We derive a novel expression for the composite PDF in terms of a convergent double series involving a Meijer's G-function. Based on the statistical results mentioned above, exact expressions for the average bit error rate of on-off keying modulation scheme and the outage probability are developed. To provide more insight, we also perform an asymptotic error rate analysis at high average signal-to-noise ratio. Our analytical results indicate that the diversity gain for the zero boresight case is determined only by the ratio between the equivalent beamwidth at the receiver and the jitter standard deviation, while for the nonzero boresight case, the diversity gain is related to the ratio of the equivalent beamwidth to the jitter variance as well as the parameter of the EW distribution.
Beyond Sérsic + exponential disc morphologies in the Coma Cluster
NASA Astrophysics Data System (ADS)
Head, Jacob T. C. G.; Lucey, John R.; Hudson, Michael J.
2015-11-01
Galaxies are not limited to simple spheroid or bulge + disc morphologies. We explore the diversity of internal galaxy structures in the Coma Cluster across a wide range of luminosities (-17 > Mg > -22) and cluster-centric radii (0 < rcluster < 1.3r200) through analysis of deep Canada-France-Hawaii Telescope i-band imaging. We present 2D multicomponent decomposition via GALFIT, encompassing a wide range of candidate model morphologies with up to three photometric components. Particular focus is placed on early-type galaxies with outer discs (i.e. S0s), and deviations from simple (`unbroken') exponential discs. Rigorous filtering ensures that each model component provides a statistically significant improvement to the goodness-of-fit. The majority of Coma Cluster members in our sample (478 of 631) are reliably fitted by symmetric structural models. Of these, 134 (28 per cent) are single Sérsic objects, 143 (30 per cent) are well-described by 2-component structures, while 201 (42 per cent) require more complex models. Multicomponent Sérsic galaxies resemble compact pseudo-bulges (n ˜ 2, Re ˜ 4 kpc) surrounded by extended Gaussian-like outer structures (Re > 10 kpc). 11 per cent of galaxies (N = 52) feature a break in their outer profiles, indicating `truncated' or `antitruncated' discs. Beyond the break radius, truncated galaxies are structurally consistent with exponential discs, disfavouring physical truncation as their formation mechanism. Bulge luminosity in antitruncated galaxies correlates strongly with galaxy luminosity, indicating a bulge-enhancing origin for these systems. Both types of broken disc are found overwhelmingly (>70 per cent) in `barred' galaxies, despite a low measured bar fraction for Coma (20 ± 2 per cent). Thus, galaxy bars play an important role in formation of broken disc structures. No strong variation in galaxy structure is detected with projected cluster-centric radius.
An exponential relationship exists between fatty acid uptake and myocardial blood flow
Sloof, G.W.; Comans, E.F.I.; Visser, F.C.
1997-05-01
High lineair (lin) correlations have been reported between myocardial blood flow (MBF) and uptake of various fatty acid (FA) analogues. However, the positive intercept with the Y-axis is not physiologically explainable (FA uptake without flow). This study investigates the appropriateness of an exponential (exp) model function. Methods: In 10 open-chest dogs the left anterior descending coronary artery was cannulated and extra corporally bypass perfused at reduced flow. MBF was assessed with scandium-46 labeled microspheres. 40 Minutes after iv. injection of 37 MBq 15-(p-[I-125]-iodophenyl)-3,3-dirnethylpentadecanoic acid (DMIPP), the heart was excised and cut into 120 samples. In each sample MBF (ml/g*min) and DMIPP uptake were assessed.In each dog, MBF and DMIPP uptake data were normalized to die respective means of the normally perfused myocardium. Uptake data were fitted to an exp model A[1-exp(-MBF/Fc)] by adjusting the flow constant Fc for minimal residual variance and adapting the amplitude A to obtain a zero mean residual error. The goodness of each fit was expressed by the standard error of the estimate (SEE). The mean SEE of the 10 dogs was 0.12{+-}0.04 with the exp fit and 0.24{+-}0.07 with the lin fit: p<0.001, F-test. For pooled data, the SEE was 0.15 with the exp fit and 0.26 with the lin fit (fig). Lin fit without zero intercept revealed a SEE of 0.18, which is higher than the SEE of the exp fit. The intercept was 0.54. Conclusion: In the normal to low MBF range, uptake of (methyl branched) FA analogues shows an exponential relationship, which is more appropriate than a linear relationship from a physiological point of view.
Woon, D.E.; Dunning, T.H. Jr. )
1994-11-15
Benchmark calculations employing the correlation consistent basis sets of Dunning and co-workers are reported for the following diatomic species: Al[sub 2], Si[sub 2], P[sub 2], S[sub 2], Cl[sub 2], SiS, PS, PN, PO, and SO. Internally contracted multireference configuration interaction (CMRCI) calculations (correlating valence electrons only) have been performed for each species. For Cl[sub 2], P[sub 2], and PN, calculations have also been carried out using Moller--Plesset perturbation theory (MP2, MP3, MP4) and the singles and doubles coupled-cluster method with and without perturbative triples [CCSD, CCSD(T)]. Spectroscopic constants and dissociation energies are reported for the ground state of each species. In addition, the low-lying excited states of Al[sub 2] and Si[sub 2] have been investigated. Estimated complete basis set (CBS) limits for the dissociation energies, [ital D][sub [ital e
Predictors of the peak width for networks with exponential links
Troutman, B.M.; Karlinger, M.R.
1989-01-01
We investigate optimal predictors of the peak (S) and distance to peak (T) of the width function of drainage networks under the assumption that the networks are topologically random with independent and exponentially distributed link lengths. Analytical results are derived using the fact that, under these assumptions, the width function is a homogeneous Markov birth-death process. In particular, exact expressions are derived for the asymptotic conditional expectations of S and T given network magnitude N and given mainstream length H. In addition, a simulation study is performed to examine various predictors of S and T, including N, H, and basin morphometric properties; non-asymptotic conditional expectations and variances are estimated. The best single predictor of S is N, of T is H, and of the scaled peak (S divided by the area under the width function) is H. Finally, expressions tested on a set of drainage basins from the state of Wyoming perform reasonably well in predicting S and T despite probable violations of the original assumptions. ?? 1989 Springer-Verlag.
An Exponential Luminous Efficiency Model for Hypervelocity Impact into Regolith
NASA Technical Reports Server (NTRS)
Swift, W. R.; Moser, D. E.; Suggs, R. M.; Cooke, W. J.
2011-01-01
The flash of thermal radiation produced as part of the impact-crater forming process can be used to determine the energy of the impact if the luminous efficiency is known. From this energy the mass and, ultimately, the mass flux of similar impactors can be deduced. The luminous efficiency, eta, is a unique function of velocity with an extremely large variation in the laboratory range of under 6 km/s but a necessarily small variation with velocity in the meteoric range of 20 to 70 km/s. Impacts into granular or powdery regolith, such as that on the moon, differ from impacts into solid materials in that the energy is deposited via a serial impact process which affects the rate of deposition of internal (thermal) energy. An exponential model of the process is developed which differs from the usual polynomial models of crater formation. The model is valid for the early time portion of the process and focuses on the deposition of internal energy into the regolith. The model is successfully compared with experimental luminous efficiency data from both laboratory impacts and from lunar impact observations. Further work is proposed to clarify the effects of mass and density upon the luminous efficiency scaling factors. Keywords hypervelocity impact impact flash luminous efficiency lunar impact meteoroid 1
Mutant number distribution in an exponentially growing population
NASA Astrophysics Data System (ADS)
Keller, Peter; Antal, Tibor
2015-01-01
We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.
Exponential flux-controlled memristor model and its floating emulator
NASA Astrophysics Data System (ADS)
Liu, Wei; Wang, Fa-Qiang; Ma, Xi-Kui
2015-11-01
As commercial memristors are still unavailable in the market, mathematic models and emulators which can imitate the features of the memristor are meaningful for further research. In this paper, based on the analyses of characteristics of the q-φ curve, an exponential flux-controlled model, which has the quality that its memductance (memristance) will keep monotonically increasing or decreasing unless the voltage’s polarity reverses (if not approach the boundaries), is constructed. A new approach to designing the floating emulator of the memristor is also proposed. This floating structure can flexibly meet various demands for the current through the memristor (especially the demand for a larger current). The simulations and experiments are presented to confirm the effectiveness of this model and its floating emulator. Project supported by the National Natural Science Foundation of China (Grant Nos. 51377124 and 51221005), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 201337), the Program for New Century Excellent Talents in University of China (Grant No. NCET-13-0457), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2012JQ7026).
Exponential 6 parameterization for the JCZ3-EOS
McGee, B.C.; Hobbs, M.L.; Baer, M.R.
1998-07-01
A database has been created for use with the Jacobs-Cowperthwaite-Zwisler-3 equation-of-state (JCZ3-EOS) to determine thermochemical equilibrium for detonation and expansion states of energetic materials. The JCZ3-EOS uses the exponential 6 intermolecular potential function to describe interactions between molecules. All product species are characterized by r*, the radius of the minimum pair potential energy, and {var_epsilon}/k, the well depth energy normalized by Boltzmann`s constant. These parameters constitute the JCZS (S for Sandia) EOS database describing 750 gases (including all the gases in the JANNAF tables), and have been obtained by using Lennard-Jones potential parameters, a corresponding states theory, pure liquid shock Hugoniot data, and fit values using an empirical EOS. This database can be used with the CHEETAH 1.40 or CHEETAH 2.0 interface to the TIGER computer program that predicts the equilibrium state of gas- and condensed-phase product species. The large JCZS-EOS database permits intermolecular potential based equilibrium calculations of energetic materials with complex elemental composition.
An Exponential Luminous Efficiency Model for Hypervelocity Impact into Regolith
NASA Technical Reports Server (NTRS)
Swift, Wesley R.; Moser, D.E.; Suggs, Robb M.; Cooke, W.J.
2010-01-01
The flash of thermal radiation produced as part of the impact-crater forming process can be used to determine the energy of the impact if the luminous efficiency is known. From this energy the mass and, ultimately, the mass flux of similar impactors can be deduced. The luminous efficiency, Eta is a unique function of velocity with an extremely large variation in the laboratory range of under 8 km/s but a necessarily small variation with velocity in the meteoric range of 20 to 70 km/s. Impacts into granular or powdery regolith, such as that on the moon, differ from impacts into solid materials in that the energy is deposited via a serial impact process which affects the rate of deposition of internal (thermal) energy. An exponential model of the process is developed which differs from the usual polynomial models of crater formation. The model is valid for the early time portion of the process and focuses on the deposition of internal energy into the regolith. The model is successfully compared with experimental luminous efficiency data from laboratory impacts and from astronomical determinations and scaling factors are estimated. Further work is proposed to clarify the effects of mass and density upon the luminous efficiency scaling factors
Nonstationary multistate Coulomb and multistate exponential models for nonadiabatic transitions
Ostrovsky, V. N.
2003-07-01
The nonstationary Schroedinger equation is considered in a finite basis of states. The model Hamiltonian matrix corresponds to a single diabatic potential curve with a Coulombic {approx}1/t time dependence. An arbitrary number of other diabatic potential curves are flat, i.e., time independent and have arbitrary energies. Related states are coupled by constant interactions with the Coulomb state. The resulting nonstationary Schroedinger equation is solved by the method of contour integral. Probabilities of transitions to any other state are obtained as t{yields}{infinity} in a simple analytical form for the case when the Coulomb state is populated initially (at instant of time t{yields}+0). The formulas apply both to the cases when a horizontal diabatic potential curve is crossed by the Coulomb one and to a noncrossing situation. In the limit of weak coupling, the transition probabilities are interpreted in terms of a sequence of pairwise Landau-Zener-type transitions. Mapping of the Coulomb model onto an exactly solvable exponential multistate model is established. For the special two-state case, the well-known Nikitin model is recovered.
Analysis of preloaded bolted joints under exponentially decaying pressure
Esmailzadeh, E.; Chorashi, M.; Ohadi, A.R.
1996-11-01
Dynamic properties of joints must be considered when designing complex structures. A good deal of investigation has been carried out for a better understanding of the dynamic behavior of mechanical joints. It is suitable initially to identify the parameters of a mechanical joint by using either experimental modal analysis or accurate finite element model, and then predicating the behavior of closure bolting system by means of spring-mass-damper model. The effect of bolt prestress on the maximum bolt displacement and stress has been treated. The loading is assumed to be initially peaked, exponentially decaying internal pressure pulse acting on the closure. The dependence of peak bolt stresses and deflections on the bolt prestress level and system damping is investigated. It has been shown that the derived formulas, if damping is neglected, reduce to those reported in the literature. Furthermore, the damping effect is shown to be most important, especially for large natural frequencies, longer loading duration, and lower levels of prestress. Existence of damping, which results in the reduction of maximum bolt displacement and stress, was shown to be beneficial, especially for longer loading duration. The importance of bolt displacement reduction from the viewpoint of fatigue life, vibration loosening, and sealing, especially for lower values of prestress, has been fully emphasized.
/q-exponential, Weibull, and /q-Weibull distributions: an empirical analysis
NASA Astrophysics Data System (ADS)
Picoli, S.; Mendes, R. S.; Malacarne, L. C.
2003-06-01
In a comparative study, the q-exponential and Weibull distributions are employed to investigate frequency distributions of basketball baskets, cyclone victims, brand-name drugs by retail sales, and highway length. In order to analyze the intermediate cases, a distribution, the q-Weibull one, which interpolates the q-exponential and Weibull ones, is introduced. It is verified that the basketball baskets distribution is well described by a q-exponential, whereas the cyclone victims and brand-name drugs by retail sales ones are better adjusted by a Weibull distribution. On the other hand, for highway length the q-exponential and Weibull distributions do not give satisfactory adjustment, being necessary to employ the q-Weibull distribution. Furthermore, the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law ( q-exponential with q>1) controversy.
NASA Astrophysics Data System (ADS)
Yan, Zhenya
2011-11-01
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black-Scholes option pricing model. In this Letter, we analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The vector financial rogue wave (rogon) solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of vector rogue waves in the financial markets and other related fields.
Rajchakit, G; Saravanakumar, R; Ahn, Choon Ki; Karimi, Hamid Reza
2017-02-01
This article examines the exponential stability analysis problem of generalized neural networks (GNNs) including interval time-varying delayed states. A new improved exponential stability criterion is presented by establishing a proper Lyapunov-Krasovskii functional (LKF) and employing new analysis theory. The improved reciprocally convex combination (RCC) and weighted integral inequality (WII) techniques are utilized to obtain new sufficient conditions to ascertain the exponential stability result of such delayed GNNs. The superiority of the obtained results is clearly demonstrated by numerical examples.
The transmission of Alfven waves through the Io plasma torus
NASA Astrophysics Data System (ADS)
Wright, A. N.; Schwartz, S. J.
1989-04-01
The nature of Alfven wave propagation through the Io plasma torus was investigated using a one-dimensional model with uniform magnetic field and an exponential density decrease to a constant value. The solution was interpreted in terms of a wave that is incident upon the torus, a reflected wave, and a wave that is transmitted through the torus. The results obtained indicate that Io's Alfven waves may not propagate completely through the plasma torus, and, thus, the WKB theory and ray tracing may not provide meaningful estimates of the energy transport.
NASA Astrophysics Data System (ADS)
Nonomura, Yoshihiko
2014-11-01
Nonequilibrium relaxation behaviors in the Ising model on a square lattice based on the Wolff algorithm are totally different from those based on local-update algorithms. In particular, the critical relaxation is described by the stretched-exponential decay. We propose a novel scaling procedure to connect nonequilibrium and equilibrium behaviors continuously, and find that the stretched-exponential scaling region in the Wolff algorithm is as wide as the power-law scaling region in local-update algorithms. We also find that relaxation to the spontaneous magnetization in the ordered phase is characterized by the exponential decay, not the stretched-exponential decay based on local-update algorithms.
Generalized Exponential Distribution in Flood Frequency Analysis for Polish Rivers.
Markiewicz, Iwona; Strupczewski, Witold G; Bogdanowicz, Ewa; Kochanek, Krzysztof
2015-01-01
Many distributions have been used in flood frequency analysis (FFA) for fitting the flood extremes data. However, as shown in the paper, the scatter of Polish data plotted on the moment ratio diagram shows that there is still room for a new model. In the paper, we study the usefulness of the generalized exponential (GE) distribution in flood frequency analysis for Polish Rivers. We investigate the fit of GE distribution to the Polish data of the maximum flows in comparison with the inverse Gaussian (IG) distribution, which in our previous studies showed the best fitting among several models commonly used in FFA. Since the use of a discrimination procedure without the knowledge of its performance for the considered probability density functions may lead to erroneous conclusions, we compare the probability of correct selection for the GE and IG distributions along with the analysis of the asymptotic model error in respect to the upper quantile values. As an application, both GE and IG distributions are alternatively assumed for describing the annual peak flows for several gauging stations of Polish Rivers. To find the best fitting model, four discrimination procedures are used. In turn, they are based on the maximized logarithm of the likelihood function (K procedure), on the density function of the scale transformation maximal invariant (QK procedure), on the Kolmogorov-Smirnov statistics (KS procedure) and the fourth procedure based on the differences between the ML estimate of 1% quantile and its value assessed by the method of moments and linear moments, in sequence (R procedure). Due to the uncertainty of choosing the best model, the method of aggregation is applied to estimate of the maximum flow quantiles.
Chen, Shentan; Raugei, Simone; Rousseau, Roger J.; Dupuis, Michel; Bullock, R. Morris
2010-12-09
A systematic assessment of theoretical methods applicable to the accurate characterization of catalytic cycles of homogeneous catalysts for H2 oxidation and evolution is reported. For these catalysts, H2 bond breaking or formation involve di-hydrogen, di-hydride, hydride-proton, and di-proton complexes. The key elementary steps have heterolytic character. In the context of Density Functional Theory (DFT) we investigated the use of functionals in the generalized gradient approximation (GGA) as well as hybrid functionals. We compared the results with wavefunction theories based on perturbation theory (MP2 and MP4) and on coupled-cluster expansions (CCSD and CCSD(T)). Our findings suggest that DFT results based on Perdew functionals are in semi-quantitative agreement with the CCSD(T) results, with deviations of a few kcal/mol only. On the other hand, the B3LYP functional is not even in qualitative agreement with CCSD[T]. Surprisingly the MP2 results are found to be extremely poor, a finding that we attribute to the limited treatment in MP2 theory of dynamic electron correlation effects in Ni(0) oxidation state. This material is based upon work supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences.
NASA Astrophysics Data System (ADS)
Nazarenko, Sergey
2015-07-01
Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence - Kolmogorov-Zakharov (KZ) spectra.
Localized coherence of freak waves
NASA Astrophysics Data System (ADS)
Latifah, Arnida L.; van Groesen, E.
2016-09-01
This paper investigates in detail a possible mechanism of energy convergence leading to freak waves. We give examples of a freak wave as a (weak) pseudo-maximal wave to illustrate the importance of phase coherence. Given a time signal at a certain position, we identify parts of the time signal with successive high amplitudes, so-called group events, that may lead to a freak wave using wavelet transform analysis. The local coherence of the critical group event is measured by its time spreading of the most energetic waves. Four types of signals have been investigated: dispersive focusing, normal sea condition, thunderstorm condition and an experimental irregular wave. In all cases presented in this paper, it is shown that a high correlation exists between the local coherence and the appearance of a freak wave. This makes it plausible that freak waves can be developed by local interactions of waves in a wave group and that the effect of waves that are not in the immediate vicinity is minimal. This indicates that a local coherence mechanism within a wave group can be one mechanism that leads to the appearance of a freak wave.
Bellissima, S; Neumann, M; Guarini, E; Bafile, U; Barocchi, F
2017-01-01
Extending a preceding study of the velocity autocorrelation function (VAF) in a simulated Lennard-Jones fluid [Phys. Rev. E 92, 042166 (2015)PLEEE81539-375510.1103/PhysRevE.92.042166] to cover higher-density and lower-temperature states, we show that the recently demonstrated multiexponential expansion method allows for a full account and understanding of the basic dynamical processes encompassed by a fundamental quantity as the VAF. In particular, besides obtaining evidence of a persisting long-time tail, we assign specific and unambiguous physical meanings to groups of exponential modes related to the longitudinal and transverse collective dynamics, respectively. We have made this possible by consistently introducing the interpretation of the VAF frequency spectrum as a global density of states in fluids, generalizing a solid-state concept, and by giving to specific spectral components, obtained through the VAF exponential expansion, the corresponding meaning of partial densities of states relative to specific dynamical processes. The clear identification of a high-frequency oscillation of the VAF with the near-top excitation frequency in the dispersion curve of acoustic waves is a neat example of the power of the method. As for the transverse mode contribution, its analysis turns out to be particularly important, because the multiexponential expansion reveals a transition marking the onset of propagating excitations when the density is increased beyond a threshold value. While this finding agrees with the recent literature debating the issue of dynamical crossover boundaries, such as the one identified with the Frenkel line, we can add detailed information on the modes involved in this specific process in the domains of both time and frequency. This will help obtain a still missing full account of transverse dynamics, in both its nonpropagating and propagating aspects which are linked through dynamical transitions depending on both the thermodynamic states and