Recurrence formulas for fully exponentially correlated four-body wave functions
NASA Astrophysics Data System (ADS)
Harris, Frank E.
2009-03-01
Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (≥-1) of all the interparticle distances rij , multiplied by an exponential containing an arbitrary linear combination of all the rij . These integrals are generalizations of those encountered using Hylleraas basis functions and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill plus some easily evaluated three-body “boundary” integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.
Exponential Decay of Correlations Implies Area Law
NASA Astrophysics Data System (ADS)
Brandão, Fernando G. S. L.; Horodecki, Michał
2015-01-01
We prove that a finite correlation length, i.e., exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the state, thus reproducing as a particular case Hastings's proof of an area law for groundstates of 1D gapped Hamiltonians. As a consequence, we show that 1D quantum states with exponential decay of correlations have an efficient classical approximate description as a matrix product state of polynomial bond dimension, thus giving an equivalence between injective matrix product states and states with a finite correlation length. The result can be seen as a rigorous justification, in one dimension, of the intuition that states with exponential decay of correlations, usually associated with non-critical phases of matter, are simple to describe. It also has implications for quantum computing: it shows that unless a pure state quantum computation involves states with long-range correlations, decaying at most algebraically with the distance, it can be efficiently simulated classically. The proof relies on several previous tools from quantum information theory—including entanglement distillation protocols achieving the hashing bound, properties of single-shot smooth entropies, and the quantum substate theorem—and also on some newly developed ones. In particular we derive a new bound on correlations established by local random measurements, and we give a generalization to the max-entropy of a result of Hastings concerning the saturation of mutual information in multiparticle systems. The proof can also be interpreted as providing a limitation on the phenomenon of data hiding in quantum states.
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…
Wave Propagation in Exponentially Varying Cross-Section Rods and Vibration Analysis
Nikkhah-Bahrami, Mansour; Loghmani, Masih; Pooyanfar, Mostafa
2008-09-01
In this paper vibration as propagating waves is used to calculate frequencies of exponentially varying cross-section rods with various boundary conditions. From wave standpoint, vibrations propagate, reflect and transmit in structures. The propagation and reflection matrices are combined to provide a concise and systematic approach to free longitudinal vibration analysis of exponentially varying cross-section rods. The results are compared with another method.
NASA Astrophysics Data System (ADS)
Lyakh, Dmitry I.; Bartlett, Rodney J.
2014-01-01
The fundamentality of the exponential representation of a second-quantised correlated wave function is emphasised with an accent on the physical sense of cluster amplitudes as cumulants of the correlated ansatz. Three main wave function formalisms, namely, the configuration-interaction theory, the coupled-cluster approach, and the many-body perturbation theory (as well as their extensions, e.g. the equation-of-motion coupled-cluster method, multireference schemes, etc.), are represented in an exponential form, leading to a formulation of the working equations in terms of cluster amplitudes. By expressing the corresponding many-body tensor equations in terms of cluster amplitudes, we could unambiguously check connectivity types and the asymptotic behaviour of all tensors/scalars involved (in the formal limit of an infinite number of correlated particles). In particular, the appearance of disconnected cluster amplitudes corresponds to unphysical correlations. Besides, we demonstrate that the equation-of-motion coupled-cluster approach, as well as certain excited-state configuration-interaction methods, can be recast in a fully connected (exponential) form, thus breaking the common belief that all truncated configuration-interaction methods violate connectivity. Our work is based on the recently developed algebraic framework which can be viewed as a complement to the classical diagrammatic analysis.
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.
Surface waves with simple exponential transverse decay at a biaxial bicrystalline interface.
Nelatury, Sudarshan R; Polo, John A; Lakhtakia, Akhlesh
2007-03-01
The dispersion equation for surface waves--with simple transverse exponential decay at the interface of identical biaxial crystals with a relative twist about the axis normal to the interface and propagating along a bisector of the angle between the crystallographic configurations on either side of the interface--has several solutions of which only one is physical. The selected type of surface wave is possible only for a restricted range of the twist angle, which depends on the ratio of the maximum and the minimum of the principal refractive indexes and the angle between the optic ray axes.
Steady internal waves in an exponentially stratified two-layer fluid
NASA Astrophysics Data System (ADS)
Makarenko, Nikolay; Maltseva, Janna; Ivanova, Kseniya
2016-04-01
The problem on internal waves in a weakly stratified two-layered fluid is studied analytically. We suppose that the fluid possess exponential stratification in both the layers, and the fluid density has discontinuity jump at the interface. By that, we take into account the influence of weak continuous stratification outside of sharp pycnocline. The model equation of strongly nonlinear interfacial waves propagating along the pycnocline is considered. This equation extends approximate models [1-3] suggested for a two-layer fluid with one homogeneous layer. The derivation method uses asymptotic analysis of fully nonlinear Euler equations. The perturbation scheme involves the long wave procedure with a pair of the Boussinesq parameters. First of these parameters characterizes small density slope outside of pycnocline and the second one defines small density jump at the interface. Parametric range of solitary wave solutions is characterized, including extreme regimes such as plateau-shape solitary waves. This work was supported by RFBR (grant No 15-01-03942). References [1] N. Makarenko, J. Maltseva. Asymptotic models of internal stationary waves, J. Appl. Mech. Techn. Phys, 2008, 49(4), 646-654. [2] N. Makarenko, J. Maltseva. Phase velocity spectrum of internal waves in a weakly-stratified two-layer fluid, Fluid Dynamics, 2009, 44(2), 278-294. [3] N. Makarenko, J. Maltseva. An analytical model of large amplitude internal solitary waves, Extreme Ocean Waves, 2nd ed. Springer 2015, E.Pelinovsky and C.Kharif (Eds), 191-201.
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).
NASA Astrophysics Data System (ADS)
Araújo, Vitor; Melbourne, Ian
2016-11-01
We prove exponential decay of correlations for a class of $C^{1+\\alpha}$ uniformly hyperbolic skew product flows, subject to a uniform nonintegrability condition. In particular, this establishes exponential decay of correlations for an open set of geometric Lorenz attractors. As a special case, we show that the classical Lorenz attractor is robustly exponentially mixing.
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. PMID:23767617
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. PMID:27475213
NASA Astrophysics Data System (ADS)
Nath, Gorakh
2016-07-01
The propagation of a strong cylindrical shock wave in a self-gravitating and rotational axisymmetric dusty gas, having variable azimuthal and axial fluid velocities is investigated. 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. The density of the mixture and the fluid velocities in the ambient medium are 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. Non-similarity solutions are obtained and the effects of variation of the mass concentration of solid particles in the mixture, the ratio of the density of solid particles to the initial density of the gas, and the gravitational parameter on the flow variables in the region behind the shock are investigated at a given time. Also, a comparison between the isothermal and adiabatic flow is made.
Nath, G; Sahu, P K
2016-01-01
A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere. The ambient medium is assumed to possess radial, axial and azimuthal component of fluid velocities. The initial density, the fluid velocities and magnetic field of the ambient medium are assumed to be varying with time according to an exponential law. The gas is taken to be non-viscous having infinite electrical conductivity. 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. The effects of the variation of the initial density index, adiabatic exponent of the gas and the Alfven-Mach number on the flow-field behind the shock wave are investigated. It is found that the presence of the magnetic field have decaying effects on the shock wave. Also, it is observed that the effect of an increase in the magnetic field strength is more impressive in the case of adiabatic flow than in the case of isothermal flow. The assumption of zero temperature gradient brings a profound change in the density, non-dimensional azimuthal and axial components of vorticity vector distributions in comparison to those in the case of adiabatic flow. A comparison is made between isothermal and adiabatic flows. It is obtained that an increase in the initial density variation index, adiabatic exponent and strength of the magnetic field decrease the shock strength. PMID:27652082
Nath, G; Sahu, P K
2016-01-01
A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere. The ambient medium is assumed to possess radial, axial and azimuthal component of fluid velocities. The initial density, the fluid velocities and magnetic field of the ambient medium are assumed to be varying with time according to an exponential law. The gas is taken to be non-viscous having infinite electrical conductivity. 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. The effects of the variation of the initial density index, adiabatic exponent of the gas and the Alfven-Mach number on the flow-field behind the shock wave are investigated. It is found that the presence of the magnetic field have decaying effects on the shock wave. Also, it is observed that the effect of an increase in the magnetic field strength is more impressive in the case of adiabatic flow than in the case of isothermal flow. The assumption of zero temperature gradient brings a profound change in the density, non-dimensional azimuthal and axial components of vorticity vector distributions in comparison to those in the case of adiabatic flow. A comparison is made between isothermal and adiabatic flows. It is obtained that an increase in the initial density variation index, adiabatic exponent and strength of the magnetic field decrease the shock strength.
NASA Astrophysics Data System (ADS)
Ghosal, Amit; Ash, Biswarup; Chakrabarti, Jaydeb
2015-03-01
We investigate the dynamics of Coulomb-interacting confined particles over a range of temperatures capturing the crossover from a Wigner molecule to a liquid-like phase. Dynamical signatures, derived from the Van-Hove correlations, develop pivotal understanding of the phases as well as the intervening crossover, which are inaccessible from the study of static correlations alone. The motion of the particles shows frustrations, produces heterogeneities depending on the observation time-scales and temperatures and results into a non-Gaussian behavior. The extent and nature of the departure of the behavior of spatio-temporal correlations from the conventional wisdom depends crucially on the symmetry of the confinements. In particular, we find that the decay of correlations follow a stretched-exponential form in traps that lack any symmetry. Our data offers a broad support to a theoretical model that integrates the non-Gaussian behavior arising from the convolution of Gaussian fluctuations weighted by appropriate diffusivities, consistent with local dynamics. The richness of information from the dynamic correlation will be shown to improve the understanding of melting in confined systems in a powerful manner.
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.
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
Spontaneous symmetry breaking in correlated wave functions
NASA Astrophysics Data System (ADS)
Kaneko, Ryui; Tocchio, Luca F.; Valenti, Roser; Becca, Federico; Gros, Claudius
We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is mainly related to the presence of a sufficiently strong Jastrow term (also including the case of full Gutzwiller projection, suitable for describing spin models). Selected examples are reported, including the spawning of Néel order and dimerization in spin systems, and the stabilization of density and orbital order in itinerant electronic systems
Spontaneous symmetry breaking in correlated wave functions
NASA Astrophysics Data System (ADS)
Kaneko, Ryui; Tocchio, Luca F.; Valentí, Roser; Becca, Federico; Gros, Claudius
2016-03-01
We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is mainly related to the presence of a sufficiently strong Jastrow term (also including the case of full Gutzwiller projection, suitable for describing spin models). Selected examples are reported, including the spawning of Néel order and dimerization in spin systems, and the stabilization of charge and orbital order in itinerant electronic systems.
McKellar, Robin C
2008-01-15
Developing accurate mathematical models to describe the pre-exponential lag phase in food-borne pathogens presents a considerable challenge to food microbiologists. While the growth rate is influenced by current environmental conditions, the lag phase is affected in addition by the history of the inoculum. A deeper understanding of physiological changes taking place during the lag phase would improve accuracy of models, and in earlier studies a strain of Pseudomonas fluorescens containing the Tn7-luxCDABE gene cassette regulated by the rRNA promoter rrnB P2 was used to measure the influence of starvation, growth temperature and sub-lethal heating on promoter expression and subsequent growth. The present study expands the models developed earlier to include a model which describes the change from exponential to linear increase in promoter expression with time when the exponential phase of growth commences. A two-phase linear model with Poisson weighting was used to estimate the lag (LPDLin) and the rate (RLin) for this linear increase in bioluminescence. The Spearman rank correlation coefficient (r=0.830) between the LPDLin and the growth lag phase (LPDOD) was extremely significant (P
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.
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.
Clustering correlations and limits on cosmological gravitational waves
NASA Technical Reports Server (NTRS)
Linder, Eric V.
1988-01-01
A cosmological background of gravitational waves induces angular deviations in the propagation of light traversing it. All observed astrophysical sources might therefore have varying apparent positions, with the time dependence set by the wave period. Wavelengths greater than a kiloparsec are examined, so the positions are frozen but in general correlated. Comparison with observed galaxy-galaxy n-point correlation functions provide a spectrum-independent limit on the energy density of gravitational waves with wavelengths between a few tens of kiloparsecs and a few hundred megaparsecs of Omega(GW) less than 0.001.
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.
Fertil, B.; Deschavanne, P.J.; Debieu, D.; Malaise, E.P.
1988-10-01
Published data on the in vitro radiosensitivity of 46 nontransformed fibroblasts of different genetic origins studied in plateau phase with immediate or delayed plating were used to investigate to what extent potentially lethal damage repair capacity is related to intrinsic radiosensitivity (i.e., irradiated in exponential growth phase). While most of the survival curve analysis is conducted in terms of D0, Dq, and the mean inactivation dose D, some of the data are also discussed in terms of the linear-quadratic model parameter alpha. Using D it is shown that: (i) the radiosensitivity of human fibroblasts in exponential growth phase does not significantly differ from that of plateau-phase fibroblasts with immediate plating; (ii) the radiosensitivity of plateau-phase cells with delayed plating is correlated to the radiosensitivity of cells with immediate plating: the more radioresistant the cell strain in exponential growth phase, the higher its repair capacity; (iii) the repair capacity of the cell strains is related to their genetic origin. In conclusion, we suggest that the survival curve of growing cells depends on the repair capacity of the cells.
Shear wave arrival time estimates correlate with local speckle pattern.
Mcaleavey, Stephen A; Osapoetra, Laurentius O; Langdon, Jonathan
2015-12-01
We present simulation and phantom studies demonstrating a strong correlation between errors in shear wave arrival time estimates and the lateral position of the local speckle pattern in targets with fully developed speckle. We hypothesize that the observed arrival time variations are largely due to the underlying speckle pattern, and call the effect speckle bias. Arrival time estimation is a key step in quantitative shear wave elastography, performed by tracking tissue motion via cross-correlation of RF ultrasound echoes or similar methods. Variations in scatterer strength and interference of echoes from scatterers within the tracking beam result in an echo that does not necessarily describe the average motion within the beam, but one favoring areas of constructive interference and strong scattering. A swept-receive image, formed by fixing the transmit beam and sweeping the receive aperture over the region of interest, is used to estimate the local speckle pattern. Metrics for the lateral position of the speckle are found to correlate strongly (r > 0.7) with the estimated shear wave arrival times both in simulations and in phantoms. Lateral weighting of the swept-receive pattern improved the correlation between arrival time estimates and speckle position. The simulations indicate that high RF echo correlation does not equate to an accurate shear wave arrival time estimate-a high correlation coefficient indicates that motion is being tracked with high precision, but the location tracked is uncertain within the tracking beam width. The presence of a strong on-axis speckle is seen to imply high RF correlation and low bias. The converse does not appear to be true-highly correlated RF echoes can still produce biased arrival time estimates. The shear wave arrival time bias is relatively stable with variations in shear wave amplitude and sign (-20 μm to 20 μm simulated) compared with the variation with different speckle realizations obtained along a given tracking
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.
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.
Langmuir wave growth and electron bunching: Results from a wave-particle correlator
Ergun, R.E.; Carlson, C.W.; McFadden, J.P.; Clemmons, J.H. ); Boehm, M.H. )
1991-01-01
Recent measurements of auroral electrons and intense Langmuir waves on a high-altitude sounding rocket show that these waves were produced by dispersive bursts of low-energy electrons. The sounding rocket was launched northward into the evening auroral zone during a substorm expansion and crossed several discrete auroral arcs having electron energy peaks greater than 25 keV. The large-amplitude Langmuir waves, which appeared in {approximately}100-ms bursts and had amplitudes greater than 200 mV/m, were seen only during periods of enhanced low-energy (0.3-3.0 keV), field-aligned electron precipitation. The enhanced electron flux displayed a dispersive signature in which the higher-energy electrons arrived before the lower-energy electrons. A wave-particle correlator, a new instrument that performed a direct correlation of the arrival times of electrons with the phase of the high-frequency wave field, detected electron bunching at the wave frequency during the bursts of intense Langmuir waves. The electron bunching events, which had amplitudes of a few percent, provided a direct identification of the energy (velocity) of the resonant electrons and therefore established the parallel wavelength ({approximately}15 m). The electron bunching events were detected at or near the energy at which a positive slope in the electron distribution function was seen. During a dispersive burst, the phase velocity (or wavelength) of the Langmuir waves changed in response to the changing velocity at which the positive slope occured. The authors conclude that the velocity dispersion in the low-energy, field-aligned electrons created the unstable electron distribution that was responsible for Langmuir wave growth. The proposed growth mechanism is similar to that suggested for Langmuir wave growth during solar type III radio bursts.
Correlations of πN 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 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
Correlations of π N partial waves for multireaction analyses
NASA Astrophysics Data System (ADS)
Döring, M.; Revier, J.; Rönchen, D.; Workman, R. L.
2016-06-01
In the search for missing baryonic resonances, many analyses include data from a variety of pion- and photon-induced reactions. For elastic π N 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. The influence of systematic errors is also considered.
Searching for Correlated Radio Transients & Gravitational Wave Bursts
NASA Astrophysics Data System (ADS)
Kavic, Michael; Shawhan, P. S.; Yancey, C.; Cutchin, S.; Simonetti, J. H.; Bear, B.; Tsai, J.
2013-01-01
We will discuss an ongoing multi-messenger search for transient radio pulses and gravitational wave bursts. This work is being conducted jointly by the Long Wavelength Array (LWA) and the LIGO Scientific Collaboration (LSC). A variety of astrophysical sources can produce simultaneous emission of gravitational waves and coherent low-frequency electromagnetic radiation. The primary common source motivating this work is the merger of neutron star binaries for which the LWA and LSC instruments have comparable sensitivity. Additional common sources include supernovae, long timescale GRBs and cosmic string cusp events. Data taken by both instruments can be compared to search for correlated signals. Identification of correlated signals can be used to increase the sensitivity of both instruments. We will summarize the coincident observations which have already been conducted and outline plans for future work. We will describe the process being used for synthesizing these data set and present preliminary results.
On correlation measurements of electron Bernstein wave emission
NASA Astrophysics Data System (ADS)
Popov, A.; Irzak, M.
2014-02-01
A systematic study of the electron Bernstein wave (EBW) emission from either overdense plasmas or plasmas with moderate electron temperatures is presented. Starting from description of the bare electrons microscopic thermal radiation we finally arrive at the macroscopic expression for the radiation temperature. The latter is shown to be a sum of the electron temperature and a fluctuating piece caused by the fluctuations of both the EBW emission source and the EBW damping rate within the ECR layer. It is shown that the correlation measurements of the EBW emission at two separate frequencies reveal information on the correlation length of the low frequency turbulence.
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. PMID:12162352
Charge density waves in strongly correlated electron systems.
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. PMID:27376547
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 dust magnetosonic waves with spin and exchange correlation effects
NASA Astrophysics Data System (ADS)
Maroof, R.; Mushtaq, A.; Qamar, A.
2016-01-01
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.).
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
Electrographic Correlates of Plateau Waves in Patients With Leptomeningeal Metastases
Gold, C. A.; Odom, N.; Srinivasan, S.; Schaff, L.; Haggiagi, A.
2016-01-01
We describe video electroencephalography (video-EEG) correlates of transient neurological attacks due to plateau waves—paroxysmal elevations in intracranial pressure—in patients with leptomeningeal metastases. We identified 3 patients with leptomeningeal metastases, intracranial hypertension, and transient neurological attacks captured on video-EEG without evidence of seizures or epileptiform activity. We identified all clinical events on video and reviewed the corresponding EEG data for evidence of abnormalities. All 3 patients had mild to moderate slowing and 2 had frontal intermittent rhythmic delta activity during background EEG recording. There were 33 clinical events recorded and stereotyped for each patient. All 33 events were associated with an increase in delta range slowing of ≥30% compared to the background. This abnormality started ≤2 minutes before the onset of clinical symptoms and persisted for minutes after clinical resolution. This study is the first to carefully describe the electrographic correlates of transient neurological attacks due to plateau waves in patients with leptomeningeal metastasis. Clinical attacks were consistently associated with a possible EEG signature of diffuse delta range slowing. Future studies can validate the sensitivity and specificity of these EEG changes as a prognostic and/or response biomarker in patients with leptomeningeal metastases with or without intracranial hypertension. PMID:27695598
NASA Astrophysics Data System (ADS)
Chou, Chung-Pin; Lee, T. K.; Ho, Chang-Ming
2009-03-01
We examine the strong correlation effects of the d-wave superconducting state by including the Gutzwiller projection for no electron double occupancy at each lattice site. The spectral weights (SW's) for adding and removing an electon on the projected superconducting state, the ground state of the 2-dimensional t-t'-t"-J model with moderate doped holes describing the high Tc cuprates, are studied numerically on finite lattices and compared with the observation made by low-temperature tunneling (particle asymmetry of tunneling conductance) and angle-resolved photoemission (SW transfer from the projected Fermi liquid tate) spectoscopies. The contast with the dwave case without projection is alo presented.
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.
Absence of localized acoustic waves in a scale-free correlated random system.
Costa, A E B; de Moura, F A B F
2011-02-16
We numerically study the propagation of acoustic waves in a one-dimensional medium with a scale-free long-range correlated elasticity distribution. The random elasticity distribution is assumed to have a power spectrum S(k) ∼ 1/k(α). By using a transfer-matrix method we solve the discrete version of the scalar wave equation and compute the localization length. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicate the presence of extended acoustic waves for a high degree of correlations. In contrast with local correlations, we numerically demonstrate that scale-free correlations promote a stable phase of free acoustic waves in the thermodynamic limit. PMID:21406919
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…
Decrease in serum cortisol during yoga exercise is correlated with alpha wave activation.
Kamei, T; Toriumi, Y; Kimura, H; Ohno, S; Kumano, H; Kimura, K
2000-06-01
We examined changes in brain waves and blood levels of serum cortisol during yoga exercise in 7 yoga instructors and found that alpha waves increased and serum cortisol decreased. These two measures were negatively correlated (r = -.83). Comparison with a control group of nonpractitioners is desirable.
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.
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).
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.
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.
NASA Astrophysics Data System (ADS)
Puchkov, V. A.
2016-09-01
Aspect sensitive scattering of multi-frequency probe signals by artificial, magnetic field aligned density irregularities (with transverse size ∼ 1- 10 m) generated in the ionosphere by powerful radio waves is considered. Fluctuations of received signals depending on stochastic properties of the irregularities are calculated. It is shown that in the case of HF probe waves two mechanisms may contribute to the scattered signal fluctuations. The first one is due to the propagation of probe waves in the ionospheric plasma as in a randomly inhomogeneous medium. The second one lies in non-stationary stochastic behavior of irregularities which satisfy the Bragg conditions for the scattering geometry and therefore constitute centers of scattering. In the probe wave frequency band of the order of 10-100 MHz the second mechanism dominates which delivers opportunity to recover some properties of artificial irregularities from received signals. Correlation function of backscattered probe waves with close frequencies is calculated, and it is shown that detailed spatial distribution of irregularities along the scattering vector can be found experimentally from observations of this correlation function.
Correlation of Sub-Aerial Beach Change with Numerical Model Derived Nearshore Wave Conditions
NASA Astrophysics Data System (ADS)
Hansen, J. E.; Erikson, L.; Barnard, P. L.; Eshleman, J. L.
2007-12-01
Wave-induced sediment transport on and off of beaches is difficult to understand and predict without thorough knowledge of the nearshore wave conditions. Wave data is commonly provided by a buoy located offshore in deep water that measures waves prior to shoaling and refraction. Irregular bathymetry causes dissimilar refraction and shoaling and can lead to variable wave conditions in the nearshore environment. To account for wave propagation over varying bathymetry, numerical wave models are good tools for estimating the nearshore wave climate from offshore wave data. Ocean Beach in San Francisco, CA is an energetic, intermediately sloping beach that was the subject of frequent sub-aerial topographic surveys in 2005 and 2006, with some surveys being as close as two days apart. Sediment volume change derived from these surveys was correlated to nearshore wave heights estimated from offshore buoy measurements and the application of the numerical wave model SWAN (Simulating WAves Nearshore). The SWAN model was used to create a "look-up" table of nearshore wave heights from over 4500 combinations of offshore wave heights, periods, and directions. The model was run using a nested grid scheme using three separate spatial resolutions, with the finest being closest to shore. Correlations between the sub-aerial beach volume data at five morphologically different reaches of Ocean Beach and the SWAN derived wave heights from just outside of the surf zone (in 5, 7.5, or 10 m of water depending on wave height) are generally low, with R2 values less than 0.5, with the highest being 0.61. Although the coefficients of determination are low in most instances the significance exceeds 90%. The reason for the low coefficients of determination is not known but is currently being investigated; some possible reasons are improper characterization of the lengthy time series of wave data between surveys (up to 28 days), or the ignored effect of strong along-shore directed tidal currents (O
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.
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. PMID:17624388
Exponentially Enhanced Quantum Metrology
Roy, S. M.; Braunstein, Samuel L.
2008-06-06
We show that when a suitable entanglement-generating unitary operator depending on a parameter is applied on N qubits in parallel, a precision of the order of 2{sup -N} in estimating the parameter may be achieved. This exponentially improves the precision achievable in classical and in quantum nonentangling strategies.
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.
Automatic determination of important mode-mode correlations in many-mode vibrational wave functions
NASA Astrophysics Data System (ADS)
König, Carolin; Christiansen, Ove
2015-04-01
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.
Yi, W J; Park, K S; Lee, C H; Rhee, C S
2003-07-01
Ciliary beating and metachronal waves are fundamental to effective mucociliary transport. The ciliary beat frequencies (CBFs) and metachronal wave directions of multiple cilia beating in culture media were measured simultaneously using digital microscopic images. The degree of synchronisation between ciliary beats was determined by the correlation between ciliary signals at two different locations. The wave propagation directions of cilia were determined from a two-dimensional correlation map by a principal axis method. The standard deviation of measured wave directions in a region of interest was defined as a measure of metachronal wave disorder (MWD). Considerable variation was found in the beat frequencies and metachronal wave directions of cilia beating on epithelium. The pooled mean of MWDs was 23.4 +/- 8.8 degrees, and the pooled mean of CBFs was 10.1 +/- 1.9 Hz on 120 cells from five healthy subjects. The means of the MWD and the CBF from subjects were highly correlated (correlation = -0.83). The higher the CBF, the lower the level of the MWD.
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.
NASA Astrophysics Data System (ADS)
Boué, Pierre; Roux, Philippe; Campillo, Michel; Briand, Xavier
2014-01-01
Continuous recordings of ambient seismic noise across large seismic arrays allows a new type of processing using the cross-correlation technique on broadband data. We propose to apply double beamforming (DBF) to cross correlations to extract a particular wave component of the reconstructed signals. We focus here on the extraction of the surface waves to measure phase velocity variations with great accuracy. DBF acts as a spatial filter between two distant subarrays after cross correlation of the wavefield between each single receiver pair. During the DBF process, horizontal slowness and azimuth are used to select the wavefront on both subarray sides. DBF increases the signal-to-noise ratio, which improves the extraction of the dispersive wave packets. This combination of cross correlation and DBF is used on the Transportable Array (USArray), for the central U.S. region. A standard model of surface wave propagation is constructed from a combination of the DBF and cross correlations at different offsets and for different frequency bands. The perturbation (phase shift) between each beam and the standard model is inverted. High-resolution maps of the phase velocity of Rayleigh and Love waves are then constructed. Finally, the addition of azimuthal information provided by DBF is discussed, to construct curved rays that replace the classical great-circle path assumption.
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.
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.
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. PMID:26892203
NASA Astrophysics Data System (ADS)
Casanova, David; Krylov, Anna I.
2016-01-01
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.
Correlated Monte Carlo wave functions for the atoms He through Ne
Schmidt, K.E. ); Moskowitz, J.W. )
1990-09-15
We apply the variational Monte Carlo method to the atoms He through Ne. Our trial wave function is of the form introduced by Boys and Handy. We use the Monte Carlo method to calculate the first and second derivatives of an unreweighted variance and apply Newton's method to minimize this variance. We motivate the form of the correlation function using the local current conservation arguments of Feynman and Cohen. Using a self-consistent field wave function multiplied by a Boys and Handy correlation function, we recover a large fraction of the correlation energy of these atoms. We give the value of all variational parameters necessary to reproduce our wave functions. The method can be extended easily to other atoms and to molecules.
Van Raemdonck, Mario; Alcoba, Diego R; Poelmans, Ward; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Van Neck, Dimitri; Bultinck, Patrick
2015-09-14
A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.
Correlation-driven d -wave superconductivity in Anderson lattice model: Two gaps
NASA Astrophysics Data System (ADS)
Wysokiński, Marcin M.; Kaczmarczyk, Jan; Spałek, Józef
2016-07-01
Superconductivity in heavy-fermion systems has an unconventional nature and is considered to originate from the universal features of the electronic structure. Here, the Anderson lattice model is studied by means of the full variational Gutzwiller wave function incorporating nonlocal effects of the on-site interaction. We show that the d -wave superconducting ground state can be driven solely by interelectronic correlations. The proposed microscopic mechanism leads to a multigap superconductivity with the dominant contribution due to f electrons and in the dx2-y2-wave channel. Our results rationalize several important observations for CeCoIn5.
Space-time correlations in inflationary spectra: A wave-packet analysis
Campo, David; Parentani, Renaud
2004-11-15
The inflationary mechanism of mode amplification predicts that the state of each mode with a given wave vector is correlated to that of its partner mode with the opposite vector. This implies nonlocal correlations which leave their imprint on temperature anisotropies in the cosmic microwave background. Their spatial properties are best revealed by using local wave packets. This analysis shows that all density fluctuations giving rise to the large scale structures originate in pairs which are born near the reheating. In fact each local density fluctuation is paired with an oppositely moving partner with opposite amplitude. To obtain these results we first apply a 'wave packet transformation' with respect to one argument of the two-point correlation function. A finer understanding of the correlations is then reached by making use of coherent states. A knowledge of the velocity field is required to extract the contribution of a single pair of wave packets. Otherwise, there is a two-folded degeneracy which gives three aligned wave packets arising from two pairs. The applicability of these methods to observational data is briefly discussed.
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.
Rearranging the exponential wall for large N-body systems.
Watson, Deborah K; Dunn, Martin
2010-07-01
The work required to solve for the fully interacting N boson wave function, which is widely believed to scale exponentially with N, is rearranged so the problem scales order by order in a perturbation series as N0. The exponential complexity reappears in an exponential scaling with the order of our perturbation series allowing exact analytical calculations for very large N systems through low order. PMID:20867687
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.
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.
Directional disorder of ciliary metachronal waves using two-dimensional correlation map.
Yi, Won-Jin; Park, Kwang-Suk; Lee, Chul-Hee; Rhee, Chae-Seo; Nam, Sang-Won
2002-03-01
The interrelationship of cilia and the order of wave directions are important factors that determine the effectiveness of cilia to transport materials in mucociliary systems of the respiratory tract. The interrelationship of cilia and the directional disorder of ciliary metachronal wave were analyzed using digital microscopic images. The degree of synchronization between ciliary beats was determined by the correlation factor between two different spots. To find out the uniphase directions of beating cilia, principal axes of inertia were applied to the two-dimensional correlation map calculated from sequential ciliary images. The standard deviation of determined wave directions in a region of interest (ROI) was defined as a measure of metachronal wave disorder. The pooled mean of metachronal wave disorder was 23.4 +/- 8.79 degrees in ROIs of 8 microm x 8 microm and 25.4 +/- 6.46 degrees in 32 microm x 24 microm from the sphenoid sinus mucosa of five normal subjects. Our result shows that there is a considerable variation in metachronal wave directions of cilia beating on the epithelium.
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.
NASA Technical Reports Server (NTRS)
Kimura, I.; Hashimoto, K.; Matsumoto, H.; Mukai, T.; Bell, T. F.; Inan, U. S.; Helliwell, R. A.; Katsufrakis, J. P.
1983-01-01
The EXOS-B/Siple Station joint experiment on the triggering of VLF emissions by man-made signals causing some form of wave-particle interactions in the magnetosphere is presented, and results concerning wave-particle correlations are reported. In situ measurements of both energetic electron flux and VLF waves were made near the meridian connecting Siple Station, Antarctica with Roberval, Quebec, Canada in campaigns during July through September, 1979 and December 1979 through January 1980 at times of VLF transmission from Siple. Strong observed signals were found to be well correlated with a pancake pitch angle distribution of 0.3 to 6.9-keV electrons, and to exhibit a positive linear growth rate. Artificially stimulated emissions were observed to be accompanied by large electron fluxes in all energy channels in the equatorial interaction region, although the measured pitch angle distribution was not highly anisotropic. Results may be interpreted by the amplification of Siple signals by the cyclotron instability due to high pitch angle anisotropy (pancake distribution) and the triggering of emissions in the presence of high electron fluxes with some anisotropy and a sufficiently strong signal.
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.
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.
Correlation dimension analysis and capillary wave turbulence in Dragon-Wash phenomena
NASA Astrophysics Data System (ADS)
Peng, Huai-Wu; Li, Rui-Qu; Chen, Song-Ze; Li, Cun-Biao
2008-02-01
This paper describes the evolution of surface capillary waves of deep water excited by gradually increasing the lateral external force at a single frequency. The vertical velocities of the water surface are measured by using a Polytec Laser Vibrometer with a thin layer of aluminium powder scattering on the surface to reflect the laser beam. Nonlinear interaction processes result in a stationary Fourier spectrum of the vertical surface velocities (the same as the surface elevation), i.e. Iω ~ ω-3.5. The observed spectrum can be interpreted as a wave-turbulent Kolmogorov spectrum for the case of 'narrowband pumping' for a direct cascade of energy. Correlation dimension analysis of the whole development process reveals four distinct stages during the wave structure development and identifies the wave turbulence stage.
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
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.
Phase Correlations at Neighboring Intensity Critical Points in Gaussian Random Wave Fields
NASA Astrophysics Data System (ADS)
Freund, Isaac
1998-11-01
Phase correlations are studied for neighboring critical points of the intensity in an isotropic Gaussian random wave field. Significant correlations and anticorrelations are found that extend out to at least the fifth nearest neighbors. A theoretical interpretation of the empirical data is attempted within the framework of the phase autocorrelation and the probability-density functions of extended two-dimensional random phase fields. It is found, however, that adaptations of these theoretical models are unable to account satisfactorily, or even qualitatively, for the extensive phase correlations that are present in these fields.
NASA Astrophysics Data System (ADS)
Sarsa, A.; Buendía, E.; Gálvez, F. J.
2016-07-01
Explicitly correlated wave functions to study confined atoms under impenetrable spherical walls have been obtained. Configuration mixing and a correlation factor are included in the variational ansatz. The behaviors of the ground state and some low-lying excited states of He, Be, B and C atoms with the confinement size are analyzed. Level crossing with confinement is found for some cases. This effect is analyzed in terms of the single particle energy of the occupied orbitals. The multi-configuration parameterized optimized effective potential method is employed with a cut-off factor to account for Dirichlet boundary conditions. The variational Monte Carlo method is used to deal with explicitly correlated wave functions.
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.
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.
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
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
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.
From plane waves to local Gaussians for the simulation of correlated periodic systems.
Booth, George H; Tsatsoulis, Theodoros; Chan, Garnet Kin-Lic; Grüneis, Andreas
2016-08-28
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.
From plane waves to local Gaussians for the simulation of correlated periodic systems.
Booth, George H; Tsatsoulis, Theodoros; Chan, Garnet Kin-Lic; Grüneis, Andreas
2016-08-28
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. PMID:27586908
Calculations of properties of screened He-like systems using correlated wave functions.
Dai, S T; Solovyova, A; Winkler, P
2001-07-01
The purpose of the present study is twofold. First, the techniques of correlated wave functions for two-electron systems have been extended to obtain results for P and D states in a screening environment, and in particular for Debye screening. In these calculations, the satisfaction of both the quantum virial theorem and a related sum rule has been enforced and found to provide a high degree of stability of the solutions. Second, in order to facilitate the general use of correlated wave functions in combination with sum rule stability criteria, a rather systematic computational approach to this notoriously cumbersome method has been developed and thoroughly discussed here. Accurate calculations for few-electron systems are of interest to plasma diagnostics; in particular, when inaccuracies in binding energies are drastically magnified as they occur in exponents of Boltzmann factors.
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.
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.
Calculations of properties of screened He-like systems using correlated wave functions.
Dai, S T; Solovyova, A; Winkler, P
2001-07-01
The purpose of the present study is twofold. First, the techniques of correlated wave functions for two-electron systems have been extended to obtain results for P and D states in a screening environment, and in particular for Debye screening. In these calculations, the satisfaction of both the quantum virial theorem and a related sum rule has been enforced and found to provide a high degree of stability of the solutions. Second, in order to facilitate the general use of correlated wave functions in combination with sum rule stability criteria, a rather systematic computational approach to this notoriously cumbersome method has been developed and thoroughly discussed here. Accurate calculations for few-electron systems are of interest to plasma diagnostics; in particular, when inaccuracies in binding energies are drastically magnified as they occur in exponents of Boltzmann factors. PMID:11461411
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.
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.
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. PMID:19813796
Effects of dust correlations on the marginal stability of ion stream driven dust acoustic waves
NASA Astrophysics Data System (ADS)
Shukla, Manish K.; Avinash, K.
2016-06-01
The effect of dust–dust correlations on the marginal stability of dust acoustic waves excited by ion drift is studied. The ion drift is driven by the electric field {E}0 which is generally present in the discharge. Correlation effects on marginal stability are studied using augmented Debye–Hückel approximation. The marginal stability boundary is calculated in {E}0-{P}0 (P 0 is the pressure of the neutral gas) space with correlated dust grains. We show that due to dust-dust correlation the stability boundary moves into the unstable region thereby stabilizing the DAW. The effects are significant for smaller values of κ (=a/{λ }d) below unity (a is the mean particle distance and {λ }d is Debye length).
Position-momentum correlations in matter waves double-slit experiment
NASA Astrophysics Data System (ADS)
Neto, J. S. M.; Cabral, L. A.; da Paz, I. G.
2015-05-01
We present a treatment of the double-slit interference of matter-waves represented by Gaussian wavepackets. The interference pattern is modelled with Green's function propagator which emphasizes the coordinate correlations and phases. We explore the connection between phases and position-momentum correlations in the intensity, visibility and predictability of the wavepacket interference. This formulation will indicate some aspects that can be useful for theoretical and experimental treatment of particle, atom or molecule interferometry and can be discussed in introductory quantum mechanics courses.
Statistical correlations of shear wave velocity and penetration resistance for soils
NASA Astrophysics Data System (ADS)
Dikmen, Ünal
2009-03-01
In this paper, the correlation between shear wave velocity and standard penetration test blow counts (SPT-N) is investigated. The study focused primarily on the correlation of SPT-N and shear wave velocity (Vs) for several soil categories: all soils, sand, silt and clay-type soils. New empirical formulae are suggested to correlate SPT-N and Vs, based on a dataset collected in a part of Eskişehir settlement in the western central Anatolia region of Turkey. The formulae are based on geotechnical soundings and active and passive seismic experiments. The new and previously suggested formulae showing correlations between uncorrected SPT-N and Vs have been compared and evaluated by using the same dataset. The results suggest that better correlations in estimation of Vs are acquired when the uncorrected blow counts are used. The blow count is a major parameter and the soil type has no significant influence on the results. In cohesive soils, the plasticity contents and, in non-cohesive soils except for gravels, the graded contents have no significant effect on the estimation of Vs. The results support most of the conclusions of earlier studies. These practical relationships developed between SPT-N and Vs should be used with caution in geotechnical engineering and should be checked against measured Vs.
Nonlocal density-functional description constructed from a correlated many-body wave function
NASA Astrophysics Data System (ADS)
Umezawa, Naoto; Tsuneyuki, Shinji
2004-03-01
We suggest a new approach to the nonlocal density-functional theory. In our method, the nonlocal correlation functional is derived from a correlated many-body wave function using the transcorrelated similarity transformation [1,2]. Our formalism is rigorous in principle if the v-representable density is assumed. In practice, Jastrow-Slater-type wave function is adopted and the correlation functional consists of many-body interactions originated from the Jastrow factor. Instead of struggling with these higher order interactions, we retain only 2-body interactions multiplying an adjusting parameter so that it can reproduce the exact correlation energy for the homogeneous electron gas. Therefore, the computational cost is comparable to the exact exchange method. Moreover, parameters in the Jastrow factor are determined by the two conditions: the cusp conditions and the random-phase approximation without empirical fitting. We found that our correlation functional gives fairly good results for small atoms and ions (He, Li^+, Be^2+, Li, and Be). [1]S. F. Boys and N. C. Handy, Proc. Roy. Soc. A, 309, 209; 310, 43; 310, 63; 311, 309. [2] N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003).
Correlation of densities with shear wave velocities and SPT N values
NASA Astrophysics Data System (ADS)
Anbazhagan, P.; Uday, Anjali; Moustafa, Sayed S. R.; Al-Arifi, Nassir S. N.
2016-06-01
Site effects primarily depend on the shear modulus of subsurface layers, and this is generally estimated from the measured shear wave velocity (V s) and assumed density. Very rarely, densities are measured for amplification estimation because drilling and sampling processes are time consuming and expensive. In this study, an attempt has been made to derive the correlation between the density (dry and wet density) and V s/SPT (standard penetration test) N values using measured data. A total of 354 measured V s and density data sets and 364 SPT N value and density data sets from 23 boreholes have been used in the study. Separate relations have been developed for all soil types as well as fine-grained and coarse-grained soil types. The correlations developed for bulk density were compared with the available data and it was found that the proposed relation matched well with the existing data. A graphical comparison and validation based on the consistency ratio and cumulative frequency curves was performed and the newly developed relations were found to demonstrate good prediction performance. An attempt has also been made to propose a relation between the bulk density and shear wave velocity applicable for a wide range of soil and rock by considering data from this study as well as that of previous studies. These correlations will be useful for predicting the density (bulk and dry) of sites having measured the shear wave velocity and SPT N values.
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.
Ezhov, Vasily
2012-11-20
The architectures of classical analog coherent optical (ACO) spectrum analyzers and correlators are not designed to process the wave signal as a whole, i.e., simultaneously in three dimensions. In this paper, the theory of ACO three-dimensional direct spectrum-correlation processing of spatial-temporal optical replicas (copies) of wave signals is discussed. In the single-stage and two-stage ACO systems, the spatial power spectrum and spatial correlation function of the wave signal (envelope) are obtained on the basis of space-time integration. The geometry of the final compressed signal in the output plane of either optical system allows one to evaluate the angle of wave arrival. The wave signal to be processed can theoretically have any form (due to autocorrelation properties of the systems) and an unlimited duration (due to time integration of wave energy and possibility of electronic subtraction of the intermediate bias terms of the time integration).
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.
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.
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.
Parameter-space correlations of the optimal statistic for continuous gravitational-wave detection
Pletsch, Holger J.
2008-11-15
The phase parameters of matched-filtering searches for continuous gravitational-wave signals are sky position, frequency, and frequency time-derivatives. The space of these parameters features strong global correlations in the optimal detection statistic. For observation times smaller than 1 yr, the orbital motion of the Earth leads to a family of global-correlation equations which describes the 'global maximum structure' of the detection statistic. The solution to each of these equations is a different hypersurface in parameter space. The expected detection statistic is maximal at the intersection of these hypersurfaces. The global maximum structure of the detection statistic from stationary instrumental-noise artifacts is also described by the global-correlation equations. This permits the construction of a veto method which excludes false candidate events.
Time Reversal Mirrors and Cross Correlation Functions in Acoustic Wave Propagation
NASA Astrophysics Data System (ADS)
Fishman, Louis; Jonsson, B. Lars G.; de Hoop, Maarten V.
2009-03-01
In time reversal acoustics (TRA), a signal is recorded by an array of transducers, time reversed, and then retransmitted into the configuration. The retransmitted signal propagates back through the same medium and retrofocuses on the source that generated the signal. If the transducer array is a single, planar (flat) surface, then this configuration is referred to as a planar, one-sided, time reversal mirror (TRM). In signal processing, for example, in active-source seismic interferometry, the measurement of the wave field at two distinct receivers, generated by a common source, is considered. Cross correlating these two observations and integrating the result over the sources yield the cross correlation function (CCF). Adopting the TRM experiments as the basic starting point and identifying the kinematically correct correspondences, it is established that the associated CCF signal processing constructions follow in a specific, infinite recording time limit. This perspective also provides for a natural rationale for selecting the Green's function components in the TRM and CCF expressions. For a planar, one-sided, TRM experiment and the corresponding CCF signal processing construction, in a three-dimensional homogeneous medium, the exact expressions are explicitly calculated, and the connecting limiting relationship verified. Finally, the TRM and CCF results are understood in terms of the underlying, governing, two-way wave equation, its corresponding time reversal invariance (TRI) symmetry, and the absence of TRI symmetry in the associated one-way wave equations, highlighting the role played by the evanescent modal contributions.
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.
NASA Astrophysics Data System (ADS)
Ostashev, Vladimir E.; Wilson, D. Keith; Goedecke, George H.
2004-01-01
Inhomogeneity and anisotropy are intrinsic characteristics of daytime and nighttime turbulence in the atmospheric boundary layer. In the present paper, line-of-sight sound propagation through inhomogeneous, anisotropic turbulence with temperature and velocity fluctuations is considered. Starting from a parabolic equation and using the Markov approximation, formulas are derived for the correlation functions and variances of log-amplitude and phase fluctuations of a spherical sound wave. These statistical moments of a sound field are important for many practical applications in atmospheric acoustics. The derived formulas for the correlation functions and variances generalize those already known in the literature for two limiting cases: (a) homogeneous, isotropic turbulence, and (b) inhomogeneous, anisotropic turbulence with temperature fluctuations only. Furthermore, the formulas differ from those for the case of plane wave propagation. Using the derived formulas and Mann's spectral tensor of velocity fluctuations for shear-driven turbulence, the correlation functions and variances of log-amplitude and phase fluctuations are studied numerically. The results obtained clearly show that turbulence inhomogeneity and anisotropy significantly affect sound propagation in the atmosphere.
Prediction of shear wave velocity using empirical correlations and artificial intelligence methods
NASA Astrophysics Data System (ADS)
Maleki, Shahoo; Moradzadeh, Ali; Riabi, Reza Ghavami; Gholami, Raoof; Sadeghzadeh, Farhad
2014-06-01
Good understanding of mechanical properties of rock formations is essential during the development and production phases of a hydrocarbon reservoir. Conventionally, these properties are estimated from the petrophysical logs with compression and shear sonic data being the main input to the correlations. This is while in many cases the shear sonic data are not acquired during well logging, which may be for cost saving purposes. In this case, shear wave velocity is estimated using available empirical correlations or artificial intelligent methods proposed during the last few decades. In this paper, petrophysical logs corresponding to a well drilled in southern part of Iran were used to estimate the shear wave velocity using empirical correlations as well as two robust artificial intelligence methods knows as Support Vector Regression (SVR) and Back-Propagation Neural Network (BPNN). Although the results obtained by SVR seem to be reliable, the estimated values are not very precise and considering the importance of shear sonic data as the input into different models, this study suggests acquiring shear sonic data during well logging. It is important to note that the benefits of having reliable shear sonic data for estimation of rock formation mechanical properties will compensate the possible additional costs for acquiring a shear log.
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.
Tagoshi, Hideyuki; Mukhopadhyay, Himan; Dhurandhar, Sanjeev; Sago, Norichika; Takahashi, Hirotaka; Kanda, Nobuyuki
2007-04-15
We discuss the coherent search strategy to detect gravitational waves from inspiraling compact binaries by a network of correlated laser interferometric detectors. From the maximum likelihood ratio statistic, we obtain a coherent statistic which is slightly different from and generally better than what we obtained in our previous work. In the special case when the cross spectrum of two detectors normalized by the power spectrum density is constant, the new statistic agrees with the old one. The quantitative difference of the detection probability for a given false alarm rate is also evaluated in a simple case.
High-energy spin-density-wave correlated fluctuations in paramagnetic Cr + 5 at. % V
Werner, S.A.; Fawcett, E.; Elmiger, M.W.; Shirane, G.
1992-11-01
Measurements of the magnetic fluctuations, termed spin-density-wave (SDW) paramagnons, in the nearly antiferromagnetic alloy Cr + 5 at.%V are extended up in energy to about 80 MeV. These fluctuating spin-spin correlations occur at incommensurate positions, corresponding to the SDW wavevector Q. Their characteristic energy is at least an order of magnitude larger than that of the magnetic fluctuations seen in the paramagnetic phase of pure Cr, but their intensity is more than two orders of magnitude smaller. We find that the dynamic susceptibility decreases by about 50% between temperature T = 10K and 300K.
High-energy spin-density-wave correlated fluctuations in paramagnetic Cr + 5 at. % V
Werner, S.A. . Dept. of Physics); Fawcett, E. . Dept. of Physics); Elmiger, M.W.; Shirane, G. )
1992-01-01
Measurements of the magnetic fluctuations, termed spin-density-wave (SDW) paramagnons, in the nearly antiferromagnetic alloy Cr + 5 at.%V are extended up in energy to about 80 MeV. These fluctuating spin-spin correlations occur at incommensurate positions, corresponding to the SDW wavevector Q. Their characteristic energy is at least an order of magnitude larger than that of the magnetic fluctuations seen in the paramagnetic phase of pure Cr, but their intensity is more than two orders of magnitude smaller. We find that the dynamic susceptibility decreases by about 50% between temperature T = 10K and 300K.
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. (c) 2000 The American Physical Society.
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
NASA Astrophysics Data System (ADS)
Casula, Michele; Marchi, Mariapia; Azadi, Sam; Sorella, Sandro
2009-08-01
We study the iron dimer by using an accurate ansatz for quantum chemical calculations based on a simple variational wave function, defined by a single geminal expanded in molecular orbitals and combined with a real space correlation factor. By means of this approach we predict that, contrary to previous expectations, the neutral ground state is 7Δ while the ground state of the anion is 8Σg-, hence explaining in a simple way a long standing controversy in the interpretation of the experiments. Moreover, we characterize consistently the states seen in the photoemission spectroscopy by Leopold and Lineberger [D.G. Leopold, W.C. Lineberger, J. Chem. Phys. 85 (1) (1986) 51]. It is shown that the non-dynamical correlations included in the geminal expansion are relevant to correctly reproduce the energy ordering of the low-lying spin states.
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.
The Poisson and Exponential Models
ERIC Educational Resources Information Center
Richards, Winston A.
1978-01-01
The students in a basic course on probability and statistics in Trinidad demonstrated that the number of fatal highway accidents appeared to follow a Poisson distribution while the length of time between deaths followed exponential distribution. (MN)
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.
Impact of wave polarization on long-range intensity correlations in a disordered medium.
Gorodnichev, E E; Kuzovlev, A I; Rogozkin, D B
2016-01-01
We present a theory of long-range intensity correlations in phase-coherent transport of polarized light through a disordered medium. Diagrammatic calculations of the intensity correlation function are performed beyond the scalar wave approximation. The correlations between the cross-polarized fields are shown to result in the dependence of mesoscopic intensity fluctuations on the polarization of the incident light. The intensity correlation function is represented as a sum of the contributions from the scalar mode and the basic modes of circular and linear polarization. The calculations, as applied to media with large scattering inhomogeneities, are carried out for diffusive transport and for small-angle multiple scattering of light. Each polarization contribution to the variance of relative transmission fluctuations is shown not to be a self-averaging quantity and tends to a nonvanishing value as the sample thickness increases. This value is proportional to the length of polarization decay in the medium and can be measured by varying the initial polarization of light.
Local perturbations perturb—exponentially-locally
NASA Astrophysics Data System (ADS)
De Roeck, W.; Schütz, M.
2015-06-01
We elaborate on the principle that for gapped quantum spin systems with local interaction, "local perturbations [in the Hamiltonian] perturb locally [the groundstate]." This principle was established by Bachmann et al. [Commun. Math. Phys. 309, 835-871 (2012)], relying on the "spectral flow technique" or "quasi-adiabatic continuation" [M. B. Hastings, Phys. Rev. B 69, 104431 (2004)] to obtain locality estimates with sub-exponential decay in the distance to the spatial support of the perturbation. We use ideas of Hamza et al. [J. Math. Phys. 50, 095213 (2009)] to obtain similarly a transformation between gapped eigenvectors and their perturbations that is local with exponential decay. This allows to improve locality bounds on the effect of perturbations on the low lying states in certain gapped models with a unique "bulk ground state" or "topological quantum order." We also give some estimate on the exponential decay of correlations in models with impurities where some relevant correlations decay faster than one would naively infer from the global gap of the system, as one also expects in disordered systems with a localized groundstate.
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
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. PMID:19667205
NASA Astrophysics Data System (ADS)
Spica, Z. J.; Perton, M.; Calo, M.; Cordoba-Montiel, F.; Legrand, D.; Iglesias, A.
2015-12-01
Standard application of the seismic ambient noise tomography considers the existence of synchronous records at stations for green's functions retrieval. More recent theoretical and experimental observations showed the possibility to apply correlation of coda of noise correlation (C3) to obtain green's functions between stations of asynchronous seismic networks making possible to dramatically increase databases for imagining the Earth's interior. However, this possibility has not been fully exploited yet, and right now the data C3 are not included into tomographic inversions to refine seismic structures. Here we show for the first time how to incorporate the data of C1 and C3 to calculate dispersion maps of Rayleigh waves in the range period of 10-120s, and how the merging of these datasets improves the resolution of the structures imaged. Tomographic images are obtained for an area covering Mexico, the Gulf of Mexico and the southern U.S. We show dispersion maps calculated using both data of C1 and the complete dataset (C1+C3). The latter provide new details of the seismic structure of the region allowing a better understanding of their role on the geodynamics of the study area. The resolving power obtained in our study is several times higher than in previous studies based on ambient noise. This demonstrates the new possibilities for imaging the Earth's crust and upper mantle using this enlarged database.
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.
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 Astrophysics Data System (ADS)
Wang, W.; Ni, S.; Wang, B.
2013-12-01
The noise cross correlation technique is a breakthrough in imaging the earth's structure and monitoring temporal variation using continuous seismic records. Compared to the fundamental mode surface waves which show up coherently in most noise correlation functions (NCF), body waves are difficult to retrieve but provide essential information of Earth's deep interior. By cross correlating five year continuous seismic records at 88 stations located in southwest China, strong signals with high apparent velocities are observed in the NCF(Noise Cross-correlation Function)) in the secondary microseism frequency band. Polarization analysis of these signals using three component NCFs indicates that these signals are P waves and they originate from coherent teleseismic body wave type noise. Moreover, these P type signals have positive or negative arrival time at specified paths in different seasons, from which we hypothesize that these P wave signals are generated from different source locations in different seasons. The locations of these sources may be related to the ocean activity and its interaction with local bathymetry. Further work on locating these sources will help to understand its generation mechanism and to retrieve P wave Green's Function which will improve deep Earth imaging substantially.
Lymphangiogenesis in Breast Cancer Correlates with Matrix Stiffness on Shear-Wave Elastography
Cha, Yoon Jin; Youk, Ji Hyun; Kim, Baek Gil; Jung, Woo Hee
2016-01-01
Purpose To correlate tumor stiffness and lymphangiogenesis in breast cancer and to find its clinical implications. Materials and Methods A total of 140 breast cancer patients were evaluated. Tumor stiffness was quantitatively measured by shear-wave elastography in preoperative ultrasound examination, calculated as mean elasticity value (kPa). Slides of resected breast cancer specimens were reviewed for most fibrotic area associated with tumor. D2-40 immunohistochemical staining was applied for fibrotic areas to detect the lymphatic spaces. Microlymphatic density, tumor stiffness, and clinicopathologic data were analyzed. Results Higher elasticity value was associated with invasive size of tumor, microlymphatic density, histologic grade 3, absence of extensive intraductal component, presence of axillary lymph node metastasis, and Ki-67 labeling index (LI) in univariate regression analysis, and associated with Ki-67 LI and axillary lymph node metastasis in multivariate regression analysis. Microlymphatic density was associated histologic grade 3, mean elasticity value, and Ki-67 LI in univariate regression analysis. In multivariate regression analysis, microlymphatic density was correlated with mean elasticity value. Conclusion In breast cancer, tumor stiffness correlates with lymphangiogenesis and poor prognostic factors. PMID:26996557
Estienne, B; Regnault, N; Bernevig, B A
2015-05-01
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.
Interferometric surface-wave acousto-optic time-integrating correlators
NASA Technical Reports Server (NTRS)
Berg, N. J.; Abramovitz, I. J.; Casseday, M. W.
1981-01-01
A structure for a coherent-interferometric acousto-optic (AO) time-integrating correlator was implemented by using a single surface acoustic wave (SAW) device with tilted transducers to reduce intermodulation terms. The SAW device was fabricated on Y-Z LiNbO3 with a center frequency of 175 MHz, a bandwidth of 60 MHz, and a time aperture of about 10 micros. The density of the photodetector array, with a potential of 120 MHz. Typical integration times are 30 to 40 ms, providing processing gains in excess of 10 to the 6th power. Such a device is useful in providing fast synchronization of communication links and in demodulating to base band and simultaneously acting as a synchronization lock monitor for moderate data rates. Where processing may be limited by Doppler shifts, a two dimensional architecture was implemented to allow full processing gain. Two one-dimensional, SAW AO time-integrating correlators and a two dimensional correlator are evaluated.
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.
NASA Astrophysics Data System (ADS)
Luo, Hongjun; Kolb, Dietmar; Flad, Heinz-Jurgen; Hackbusch, Wolfgang; Koprucki, Thomas
2002-08-01
We have studied various aspects concerning the use of hyperbolic wavelets and adaptive approximation schemes for wavelet expansions of correlated wave functions. In order to analyze the consequences of reduced regularity of the wave function at the electron-electron cusp, we first considered a realistic exactly solvable many-particle model in one dimension. Convergence rates of wavelet expansions, with respect to L2 and H1 norms and the energy, were established for this model. We compare the performance of hyperbolic wavelets and their extensions through adaptive refinement in the cusp region, to a fully adaptive treatment based on the energy contribution of individual wavelets. Although hyperbolic wavelets show an inferior convergence behavior, they can be easily refined in the cusp region yielding an optimal convergence rate for the energy. Preliminary results for the helium atom are presented, which demonstrate the transferability of our observations to more realistic systems. We propose a contraction scheme for wavelets in the cusp region, which reduces the number of degrees of freedom and yields a favorable cost to benefit ratio for the evaluation of matrix elements.
NASA Astrophysics Data System (ADS)
Makarov, S. V.; Plotnikov, V. A.; Potekaev, A. I.; Grinkevich, L. S.
2015-04-01
A discrete pattern of the low-frequency acoustic emission spectrum under conditions of high-temperature plastic deformation of aluminum is analyzed. It is attributed to re-distribution of vibrational energy of the primary acoustic signal over resonant vibrations of standing waves of the resonators. In a low-stability crystal medium, standing-wave oscillations initiate elementary deformation displacements in a certain material volume. The linear dimensions of this volume are related to the length of the standing wave, thus determining the macroscopic scale of correlation. The correlated deformation displacements in turn generate acoustic signals, whose interference results in the formation of a single acoustic signal of abnormally high amplitude. In a low-stability state of the crystal lattice, activation of the elementary plastic shears could result from a combined action of static forces, thermal fluctuations and dynamic forces of standing acoustic waves.
Gudimetla, V S Rao; Holmes, Richard B; Riker, Jim F
2014-01-01
An analytical expression for the log-amplitude correlation function based on the Rytov approximation is derived for spherical wave propagation through an anisotropic non-Kolmogorov refractive turbulent atmosphere. The expression reduces correctly to the previously published analytic expressions for the case of spherical wave propagation through isotropic Kolmogorov turbulence. These results agree well with a wave-optics simulation based on the more general Fresnel approximation, as well as with numerical evaluations, for low-to-moderate strengths of turbulence. These results are useful for understanding the potential impact of deviations from the standard isotropic Kolmogorov spectrum.
Gudimetla, V S Rao; Holmes, Richard B; Riker, Jim F
2012-12-01
An analytical expression for the log-amplitude correlation function for plane wave propagation through anisotropic non-Kolmogorov turbulent atmosphere is derived. The closed-form analytic results are based on the Rytov approximation. These results agree well with wave optics simulation based on the more general Fresnel approximation as well as with numerical evaluations, for low-to-moderate strengths of turbulence. The new expression reduces correctly to the previously published analytic expressions for the cases of plane wave propagation through both nonisotropic Kolmogorov turbulence and isotropic non-Kolmogorov turbulence cases. These results are useful for understanding the potential impact of deviations from the standard isotropic Kolmogorov spectrum.
Robust clustering using exponential power mixtures.
Zhang, Jian; Liang, Faming
2010-12-01
Clustering is a widely used method in extracting useful information from gene expression data, where unknown correlation structures in genes are believed to persist even after normalization. Such correlation structures pose a great challenge on the conventional clustering methods, such as the Gaussian mixture (GM) model, k-means (KM), and partitioning around medoids (PAM), which are not robust against general dependence within data. Here we use the exponential power mixture model to increase the robustness of clustering against general dependence and nonnormality of the data. An expectation-conditional maximization algorithm is developed to calculate the maximum likelihood estimators (MLEs) of the unknown parameters in these mixtures. The Bayesian information criterion is then employed to determine the numbers of components of the mixture. The MLEs are shown to be consistent under sparse dependence. Our numerical results indicate that the proposed procedure outperforms GM, KM, and PAM when there are strong correlations or non-Gaussian components in the data. PMID:20163406
Wang, Qin; Monahan, E.C.; Asher, W.E.
1995-07-01
Bubbles and bubble plumes generated by wind-induced breaking waves significantly enhance the gas exchange across the interface between the ocean and atmosphere under high-wind conditions. Whitcaps, or active spilling wave crests, are the sea-surface manifestation of the bubbles and bubble plumes in the subsurface mixed layer, and the fractional area of the sea surface covered by which has been proposed to correlate linearly with the air-sea gas transfer velocity. The presence of whitecaps substantially increases the microwave brightness temperature of the sea surface. It could be possible to estimate the whitecap coverage from the sea-surface microwave brightness temperature would also be very helpful in developing a remote-sensing model for predicting air-sea gas transfer velocities from microwave brightness temperatures. As a part of an air-water gas exchange experiment conducted in an outdoor surf pool, measurements were made that were designed to investigate the correlation between whitecap coverage and microwave brightness temperature. A mechanical wave maker was located at the deep end of the pool and the generated waves propagate and break towards the shallow end of the pool. Two wave patterns characteristic of plunging and spilling breaking waves at four wave heights from 0.3 m to 1.2 m were produced.
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"…
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 than linear,…
Cross-correlation search for a hot spot of gravitational waves
Dhurandhar, Sanjeev; Tagoshi, Hideyuki; Okada, Yuta; Kanda, Nobuyuki; Takahashi, Hirotaka
2011-10-15
The cross-correlation search has been previously applied to map the gravitational wave (GW) stochastic background in the sky and also to target GW from rotating neutron stars/pulsars. Here we investigate how the cross-correlation method can be used to target a small region in the sky spanning at most a few pixels, where a pixel in the sky is determined by the diffraction limit which depends on the (i) baseline joining a pair of detectors and (ii) detector bandwidth. Here as one of the promising targets, we consider the Virgo cluster--a ''hot spot'' spanning few pixels--which could contain, as estimates suggest {approx}10{sup 11} neutron stars, of which a small fraction would continuously emit GW in the bandwidth of the detectors. For the detector baselines, we consider advanced detector pairs among LCGT, LIGO, Virgo, ET, etc. Our results show that sufficient signal to noise can be accumulated with integration times of the order of a year if the ellipticity of neutron stars is larger than 10{sup -6}. The results improve for the multibaseline search. This analysis could as well be applied to other likely hot spots in the sky and other possible pairs of detectors.
Carotid-femoral pulse wave velocity is negatively correlated with aortic diameter.
Bailey, Marc A; Davies, Jennifer M; Griffin, Kathryn J; Bridge, Katherine I; Johnson, Anne B; Sohrabi, Soroush; Baxter, Paul D; Scott, D Julian A
2014-10-01
Cardiovascular events pose significant morbidity and mortality burden to abdominal aortic aneurysm (AAA) patients. Arterial stiffness as measured by pulse wave velocity (PWV) is an independent predictor of cardiovascular risk. We investigated the relationship between aortic diameter and PWV. Consecutive patients with AAA were invited to participate. Patients completed a health questionnaire, received aortic ultrasound and carotid-femoral PWV (cfPWV) recordings with a Vicorder. Thirty patients were used for reproducibility assessment. A linear regression model was used to identify significant predictors of cfPWV. Observer variation was assessed using Bland and Altman analysis and the intraclass correlation coefficient. Three hundred and nine patients were included-148 with AAA and 161 controls. The mean difference for repeated cfPWV between observers was 0.11 ms(-1). cfPWV was positively correlated with age (r=0.24, P<0.001) and systolic blood pressure (r=0.29, P<0.001) and negatively correlated with aortic diameter (r=-0.15, P=0.008). There was no difference in cfPWV between AAA and control groups (9.75±2.3 ms(-1) vs. 9.55±2.3 ms(-1), P=0.43). Aortic diameter (P=0.003) and systolic blood pressure (P<0.001) were significant predictors of cfPWV independent of age, aspirin usage and a history of myocardial infarction. Patients with large AAA (>5 cm) had decreased cfPWV compared with patients with small AAA (P=0.02) or normal diameter aorta (P=0.02). Vicorder measurements of cfPWV are repeatable. cfPWV is negatively associated with infra-renal aortic diameter and reduced in large AAA. cfPWV is likely invalid for accurate arterial stiffness assessment in patients with AAA owing to the apparent confounding effect of aortic size.
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
NASA Astrophysics Data System (ADS)
Zapata, I.; Sols, F.; Demler, E.
2012-10-01
We show that antiparallel triplet pairing correlations are generated in superfluids with purely s-wave interactions whenever population imbalance enforces anisotropic Fulde-Ferrell (FF) or inhomogeneous Larkin-Ovchinikov (LO) states. These triplet correlations appear in the Cooper pair wave function, while the triplet part of the gap remains zero. The same set of quasiparticle states contributes to the triplet component and to the polarization, thus spatially correlating them. In the LO case, this set forms a narrow band of Andreev states centered on the nodes of the s-wave order parameter. This picture naturally provides a unifying explanation of previous findings that attractive p-wave interaction stabilizes FFLO states. We also study a similar triplet mixing which occurs when a balanced two-component system displays FFLO-type oscillations due to a spin-dependent optical lattice. We discuss how this triplet component can be measured in systems of ultracold atoms using a rapid ramp across a p-wave Feshbach resonance. This should provide a smoking gun signature of FFLO states.
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
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.
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.
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
Poynee, L A
2003-05-06
Shack-Hartmann based Adaptive Optics system with a point-source reference normally use a wave-front sensing algorithm that estimates the centroid (center of mass) of the point-source image 'spot' to determine the wave-front slope. The centroiding algorithm suffers for several weaknesses. For a small number of pixels, the algorithm gain is dependent on spot size. The use of many pixels on the detector leads to significant propagation of read noise. Finally, background light or spot halo aberrations can skew results. In this paper an alternative algorithm that suffers from none of these problems is proposed: correlation of the spot with a ideal reference spot. The correlation method is derived and a theoretical analysis evaluates its performance in comparison with centroiding. Both simulation and data from real AO systems are used to illustrate the results. The correlation algorithm is more robust than centroiding, but requires more computation.
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
NASA Astrophysics Data System (ADS)
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.
Transient superdiffusion in random walks with a q-exponentially decaying memory profile
NASA Astrophysics Data System (ADS)
Moura, Thiago R. S.; Viswanathan, G. M.; da Silva, M. A. A.; Cressoni, J. C.; da Silva, L. R.
2016-07-01
We propose a random walk model with q-exponentially decaying memory profile. The q-exponential function is a generalization of the ordinary exponential function. In the limit q → 1, the q-exponential becomes the ordinary exponential function. This model presents a Markovian diffusive regime that is characterized by finite memory correlations. It is well known, that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. In this problem we report the outcome of a transient superdiffusion for finite sized walks.
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).
Interpolation via symmetric exponential functions
NASA Astrophysics Data System (ADS)
Bezubik, Agata; Pošta, Severin
2013-11-01
Complex valued functions on the Euclidean space Bbb Rn, symmetric or antisymmetric with respect to the permutation group Sn, are often dealt with in various branches of physics, such as quantum theory or theory of integrable systems. One often needs to approximate such functions with series consisting of various special functions which satisfy nice properties. Questions of uniform convergence of such approximations are crucial for applications. In this article a family of special functions called the symmetric exponential functions are used for such approximation and the uniform convergence of their sums is considered.
Cosmological evolution in exponential gravity
Bamba, Kazuharu; Geng, Chao-Qiang; Lee, Chung-Chi E-mail: geng@phys.nthu.edu.tw
2010-08-01
We explore the cosmological evolution in the exponential gravity f(R) = R+c{sub 1}(1−e{sup −c{sub 2}R}) (c{sub 1,2} = constant). We summarize various viability conditions and explicitly demonstrate that the late-time cosmic acceleration following the matter-dominated stage can be realized. We also study the equation of state for dark energy and confirm that the crossing of the phantom divide from the phantom phase to the non-phantom (quintessence) one can occur. Furthermore, we illustrate that the cosmological horizon entropy globally increases with time.
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.
Walker, S C
2012-03-01
Broadband noise correlation methods for the passive extraction of information about the propagation of waves between distant sensor locations have received considerable attention in the literature. For the case of an isotropic ambient field distribution, there is a well-defined relationship between the expectation value of the wave coherence over the sensors and point-to-point wave propagation. Experimental applications, however, must contend with ambient field anisotropy as well as the performance limitations associated with stochastic fluctuations. This paper explores the influence of ambient field directionality on both (1) the connection between the measured wave coherence and sensor-to-sensor propagation and on (2) the rate at which measurements stochastically converge to the expectation value of the underlying wave coherence. Due to diffraction, the relationship between the measured wave coherence and sensor-to-sensor propagation is shown to be robust to even highly directional ambient field features. While the fluctuations of a stochastic system are generally known to depend on bandwidth and measurement duration, the rate of stochastic convergence depends additionally on the cross-spectral power density (coherent power) relative to the power-spectral density (total incident power). Practical experimental implications of these results are discussed.
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.
Cometary kilometric radio waves and plasma waves correlated with ion pick-up effect at Comet Halley
NASA Astrophysics Data System (ADS)
Oya, H.; Morioka, A.; Miyake, W.; Smith, E. J.; Tsurutani, B. T.
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.
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.
Universal stretched exponential relaxation in nanoconfined water
NASA Astrophysics Data System (ADS)
Shekhar, Adarsh; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya; Alm, Camilla K.; Malthe-Sørenssen, Anders
2014-10-01
Understanding the behavior of water confined at the nanometer scale is a fundamental problem not only in physics but also in life sciences, geosciences, and atmospheric sciences. Here, we examine spatial and dynamic heterogeneities in water confined in nanoporous silica using molecular dynamics (MD) simulations. The simulations reveal intermixed low-density water and high-density water with distinct local structures in nanopores of silica. The MD simulations also show dynamic heterogeneities in nanoconfined water. The temporal decay of cage correlation functions for room temperature and supercooled, nanoconfined water is very well described by stretched exponential relaxation, exp(-(t/τ)β). The exponent β has a unique value, d/(d + 2), which agrees with an exact result for diffusion in systems with static, random traps in d = 3 dimensions.
NASA Astrophysics Data System (ADS)
AlTheyab, A.; Workman, E. J.; Lin, F. C.; Schuster, G. T.
2014-12-01
Correlation of ambient seismic noise gives traces that are an approximation to the time-derivative of the Green's function between two recording stations. These empirical Greens functions often contain the incident surface-waves and backscattered waves, which can be migrated to image near-surface discontinuities and scatterers. Traditional migration approaches require an approximation of the near-surface velocity field and proper modeling of elastic waves to estimate the Green's functions from the source and receiver positions to every image-point. With dense passive seismic array acquisition and ambient noise cross-correlations, each station can be considered as both a virtual source and a receiver and near-surface scatterers can be imaged across the array using only the empirical Green's functions. This new imaging approach is referred to as natural migration because the Green's functions needed for migration are naturally estimated from the crosscorrelograms of recorded traces. The advantages of natural migration are that it does not require estimation of the near-surface velocity or modeling of elastic waves. In addition, natural migration simultaneously images both low- and higher-order scattering and mode converted waves. The disadvantage is that the image resolution is dependent on the distribution of seismic receivers. To validate this concept, natural migration is applied to crosscorrelograms of passive data recorded by the Long Beach array and the USArray. The resulting migration images highlight known discontinuities from tomography and correlate to prominent geological boundaries at two very different scales: (1) tectonic scale such as the edge of the Atlantic Plain Province in southeastern US and (2) regional scale structure in Long Beach, California. The migration images can be used along with tomography methods to improve structure sharpness in a model construction.
Gudimetla, V S Rao; Holmes, Richard B; Smith, Carey; Needham, Gregory
2012-05-01
The effect of anisotropic Kolmogorov turbulence on the log-amplitude correlation function for plane-wave fields is investigated using analysis, numerical integration, and simulation. A new analytical expression for the log-amplitude correlation function is derived for anisotropic Kolmogorov turbulence. The analytic results, based on the Rytov approximation, agree well with a more general wave-optics simulation based on the Fresnel approximation as well as with numerical evaluations, for low and moderate strengths of turbulence. The new expression reduces correctly to previously published analytic expressions for isotropic turbulence. The final results indicate that, as asymmetry becomes greater, the Rytov variance deviates from that given by the standard formula. This deviation becomes greater with stronger turbulence, up to moderate turbulence strengths. The anisotropic effects on the log-amplitude correlation function are dominant when the separation of the points is within the Fresnel length. In the direction of stronger turbulence, there is an enhanced dip in the correlation function at a separation close to the Fresnel length. The dip is diminished in the weak-turbulence axis, suggesting that energy redistribution via focusing and defocusing is dominated by the strong-turbulence axis. The new analytical expression is useful when anisotropy is observed in relevant experiments.
Electronic structure and correlated wave functions of a few electron quantum dots
Sako, Tokuei; Ishida, Hiroshi; Fujikawa, Kazuo
2015-01-22
The energy spectra and wave functions of a few electrons confined by a quasi-one-dimensional harmonic and anharmonic potentials have been studied by using a full configuration interaction method employing a Cartesian anisotropic Gaussian basis set. The energy spectra are classified into three regimes of the strength of confinement, namely, large, medium and small. The polyad quantum number defined by a total number of nodes in the wave functions is shown to be a key ingredient to interpret the energy spectra for the whole range of the confinement strength. The nodal pattern of the wave functions exhibits normal modes for the harmonic confining potential, indicating collective motions of electrons. These normal modes are shown to undergo a transition to local modes for an anharmonic potential with large anharmonicity.
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.
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.
De Caprio, L; Adamo, B; Bellotti, P; Cuomo, S; Meccariello, P; Romano, M; Vigorito, C; Rengo, F
1980-01-01
The Authors studied correlations between angiocardiography and changes of R wave amplitude (delta R) during effort in 113 patients. They showed coronarographic evidence: 69 with stenosis greater than or equal to 70% of at least one major coronary vessel and 44 with no significant lesions. delta R values greater or equal than 0 were considered as pathologic. delta R appeared greater than or equal to 0 in 8 of 14 patients (57%) with single stenosis, 4 (28%) with abnormal wall motion (AWM). delta R increase or unchanged in 26 of 31 (84%) patients with double stenoses, 25 of them (81%) with AWM. delta R was greater than or equal to 0 in 22 of 24 (92%) with triple stenoses. In subjects with milk coronary artery disease (CAD) R wave increased or unchanged in 47% (19/44). Pathologic changes of R wave are highly frequent in CAD patients, especially in those with severe impairment. These changes, however, are not specific or costant because they appeared enough frequently in subjects with normal doronary vessels, and, moreover, R wave may decrease also in CAD patients with severe impairment. The Authors consider that evidence of delta R values greater than or equal to 0 may not be considered as a sign of CAD, but it must be evaluated with the other data showed by ergometric tests. PMID:7372032
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.
NASA Astrophysics Data System (ADS)
Spica, Zack; Perton, Mathieu; Calò, Marco; Legrand, Denis; Córdoba Montiel, Francisco; Iglesias, Arturo
2016-07-01
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 travel times 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)
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.
Midlife Decline in Declarative Memory Consolidation Is Correlated with a Decline in Slow Wave Sleep
ERIC Educational Resources Information Center
Backhaus, Jutta; Born, Jan; Hoeckesfeld, Ralf; Fokuhl, Sylvia; Hohagen, Fritz; Junghanns, Klaus
2007-01-01
Sleep architecture as well as memory function are strongly age dependent. Slow wave sleep (SWS), in particular, decreases dramatically with increasing age, starting already beyond the age of 30. SWS normally predominates during early nocturnal sleep and is implicated in declarative memory consolidation. However, the consequences of changes in…
Effects of source correlation on the spectral shift of light waves on scattering.
Wang, Tao; Zhao, Daomu
2013-05-01
The far-zone scattered spectrum has been investigated for the scattering of two correlated sources from a deterministic medium. It is shown that red shift or blue shift can be produced in the far-zone scattered spectrum, and the spectral shift is influenced by the source correlation.
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.
Leonard, Mary B.; Townsend, Raymond R.; Appel, Lawrence; Wolf, Myles; Budoff, Matt J.; Chen, Jing; Lustigova, Eva; Gadegbeku, Crystal A.; Glenn, Melanie; Hanish, Asaf; Raj, Dominic; Rosas, Sylvia E.; Seliger, Stephen L.; Weir, Matthew R.; Parekh, Rulan S.
2011-01-01
Summary Background and objectives Osteoprotegerin (OPG), a cytokine that regulates bone resorption, has been implicated in the process of vascular calcification and stiffness. Design, setting, participants, & measurements Serum OPG was measured in 351 participants with chronic kidney disease (CKD) from one site of the Chronic Renal Insufficiency Cohort Study. Cortical bone mineral content (BMC) was measured by quantitative computed tomography in the tibia. Multivariable linear regression was used to test the association between serum OPG and traditional cardiovascular risk factors, measures of abnormal bone and mineral metabolism, and pulse wave velocity. Results Higher serum OPG levels were associated with older age, female gender, greater systolic BP, lower estimated GFR, and lower serum albumin. OPG was not associated with measures of abnormal bone or mineral metabolism including serum phosphorus, albumin-corrected serum calcium, intact parathyroid hormone, bone-specific alkaline phosphatase, or cortical BMC. Among 226 participants with concurrent aortic pulse wave velocity measurements, increasing tertiles of serum OPG were associated with higher aortic pulse wave velocity after adjustment for demographics, traditional vascular risk factors, and nontraditional risk factors such as estimated GFR, albuminuria, serum phosphate, corrected serum calcium, presence of secondary hyperparathyroidism, serum albumin, and C-reactive protein or after additional adjustment for cortical BMC in a subset (n = 161). Conclusions These data support a strong relationship between serum OPG and arterial stiffness independent of many potential confounders including traditional cardiovascular risk factors, abnormal bone and mineral metabolism, and inflammation. PMID:21940840
Method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1972-01-01
Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.
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 Technical Reports Server (NTRS)
Carpenter, D. L.; Fraser-Smith, A. C.; Unwin, R. S.; Hones, E. W., Jr.; Heacock, R. R.
1971-01-01
Correlation of several magnetoionospheric wave and particle phenomena previously linked observationally to magnetospheric substorms and inferred to involve convection electric fields with whistler measurements of convection activity during two relatively isolated substorms. The events occurred at about 0600 UT on July 15, 1965, and about 0500 UT on Oct. 13, 1965. The correlated phenomena include cross-L inward plasma drifts near midnight within the plasmaphere, diffuse auroral radar echoes observed near the dusk meridian, IPDP micropulsations (intervals of pulsations of diminishing period) in the premidnight sector, apparent contractions and expansions of the plasma sheet at about 20 earth radii in the magnetotail, and Pc 1/Pi 1 micropulsation events near or before midnight. Two new vlf phenomena occurred during the October 13 event - a noise band within the plasmasphere associated with a convecting whistler path, and ?hisslers,' falling-tone auroral-hiss forms repeated at intervals of about 2 sec.
Surface wave imaging of the Mas d'Avignonet landslide with ambient noise cross-correlation analysis
NASA Astrophysics Data System (ADS)
Renalier, F.; Jongmans, D.; Bard, P. Y.; Campillo, M.
2009-04-01
The Mas d'Avignonet landslide is a 2*2 km slide affecting clayey deposits in the Trièves area (Isère, France). Its sliding velocity is comprised between a few cm/y at the top of the landslide, to 15 cm/y in the most deformed areas. Previous studies enlighted the fact that on this landslide, the shear wave velocity (Vs) is spatially related to the displacement rate: the fastest the slide, the lowest Vs. The present study analyses the possibility to use the ambient noise cross-correlation method to derive a 3D surface wave group velocity image of the landslide, strongly related to Vs. This method was developped at larger scales to image geological objects such as volcanoes or continental crust below the Alps. With this aim in mind, ambient noise was recorded during 10 days with eleven 3-component stations on the southern part of the landslide. The frequency spectrum of the signal shows two main frequency bands : 1-10 Hz and 30-60 Hz. We computed the cross-correlation of the sign of the signals whitened in the 1-10 Hz frequency band. The evolution of the signal to noise ratio with correlation time shows that the recording time was sufficient to saturate the cross-correlated signals. Resulting waveforms are in good agreement with direct signals generated with explosive shots. In order to check the hypothesis of sources uniformly distributed around the area, we both look at beamforming analysis and azimuthal dependance of slowness, showing that for frequencies above 1.5 Hz, the correct propagation times are retrievd for all azimuths. Finally, using an S-transform, we compute the slowness-frequency image of the cross-correlations, determining the group velocity dispersion curve of surface waves from 1.5 to 5 Hz for about half pairs of stations. A group velocity image of the basement of the landslide is derived from these dispersion curves.
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
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.
A correlated study of ELF waves and electron precipitation on Ogo 6
NASA Technical Reports Server (NTRS)
Holzer, R. E.; Farley, T. A.; Burton, R. K.; Chapman, M. C.
1974-01-01
The Ogo 6 ELF chorus records from the search coil magnetometer have been compared with simultaneous electron precipitation records. The chorus signals observed in the vicinity of field lines passing through the outer magnetosphere were characteristically accompanied by electron precipitation in the same region. Both the chorus and the precipitation records consisted of a series of sharp peaks. Although in some cases chorus and precipitation peaks appeared to be associated, the observed peaks did not in general coincide. Comparison of the chorus measurements on Ogo 6 and Ogo 5 suggests a model in which the chorus is ducted along field lines to within less than 1 earth radius above the Ogo 6 orbit after which it diverges from the field lines and is deflected toward the local vertical. The result is equatorward skewing of the average wave pattern with respect to the precipitation pattern.
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.
Fate of disorder-induced inhomogeneities in strongly correlated d-wave superconductors
NASA Astrophysics Data System (ADS)
Chakraborty, Debmalya; Ghosal, Amit
2014-10-01
We analyze the complex interplay of the strong correlations and impurities in a high temperature superconductor and show that both the nature and degree of the inhomogeneities at zero temperature in the local-order parameters change drastically from those obtained in a simple Hartree-Fock-Bogoliubov theory. Although both the strong electronic repulsions and disorder contribute to the nanoscale inhomogeneity in the population of charge-carriers, we find they compete with each other, leading to a relatively smooth variation of the local density. Our self-consistent calculations modify the spatial fluctuations in the pairing amplitude by suppressing all the double occupancy within a Gutzwiller formalism and prohibit the formation of distinct superconducting ‘islands’. In contrast, presence of such ‘islands’ controls the outcome if strong correlations are neglected. The reorganization of the spatial structures in the Gutzwiller method makes these superconductors surprisingly insensitive to the impurities. This is illustrated by a very weak decay of superfluid stiffness, off-diagonal long-range order and local density of states up to a large disorder strength. Exploring the origin of such a robustness, we conclude that the underlying one-particle normal states reshape in a rich manner, such that the superconductor formed by pairing these states experiences a weaker but spatially correlated effective disorder. Such a route to superconductivity is evocative of Anderson's theorem. Our results capture the key experimental trends in the cuprates.
Inhomogeneities in a strongly correlated d-wave superconductors in the limit of strong disorder
NASA Astrophysics Data System (ADS)
Chakraborty, Debmalya; Sensarma, Rajdeep; Ghosal, Amit
2015-03-01
The complex interplay of the strong correlations and impurities in a high temperature superconductor is analyzed within a Hartree-Fock-Bogoliubov theory, augmented with Gutzwiller approximation for taking care of the strong electronic repulsion. The inclusion of such correlations is found to play a crucial role in reducing inhomogeneities in both qualitative and quantitative manner. This difference is comprehended by investigating the underlying one-particle ``normal states'' that includes the order parameters in the Hartree and Fock channels in the absence of superconductivity. This amounts to the renormalization of disorder both on the lattice sites and also on links. These two components of disorder turn out to be spatially anti-correlated through self-consistency. Interestingly, a simple pairing theory in terms of these normal states is found to describe the complex behaviors of dirty cuprates with reasonable accuracy. However, this framework needs modifications in the limit where disorder strengths are comparable to the band width. We will discuss appropriate updates in the formalism to describe physics of inhomogeneities with strong disorder.
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)
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.
NASA Astrophysics Data System (ADS)
Dunn, M.; Watson, D. K.; Loeser, J. G.
2006-08-01
In this paper, we develop an analytic N-body wave function for identical particles under quantum confinement with a general two-body interaction. A systematic approach to correlation is developed by combining three theoretical methods: dimensional perturbation theory, the FG method of Wilson et. al., and the group theory of the symmetric group. Analytic results are achieved for a completely general interaction potential. Unlike conventional perturbation methods which are applicable only for weakly interacting systems, this analytic approach is applicable to both weakly and strongly interacting systems. This method directly accounts for each two-body interaction, rather than an average interaction so even lowest-order results include beyond-mean-field effects. One major advantage is that N appears as a parameter in the analytical expressions for the energy so results for different N are easy to obtain.
Exponential Orthogonality Catastrophe at the Anderson Metal-Insulator Transition
NASA Astrophysics Data System (ADS)
Kettemann, S.
2016-09-01
We consider the orthogonality catastrophe at the Anderson metal-insulator transition (AMIT). The typical overlap F between the ground state of a Fermi liquid and the one of the same system with an added potential impurity is found to decay at the AMIT exponentially with system size L as F ˜exp (-c Lη) , where η is the power of multifractal intensity correlations. Thus, strong disorder typically increases the sensitivity of a system to an added impurity exponentially. We recover, on the metallic side of the transition, Anderson's result that the fidelity F decays with a power law F ˜L-q (EF) with system size L . Its power increases as the Fermi energy EF approaches the mobility edge EM as q (EF)˜[(EF-EM )/EM]-ν η , where ν is the critical exponent of the correlation length ξc. On the insulating side of the transition, F is constant for system sizes exceeding the localization length ξ . While these results are obtained for the typical fidelity F , we find that log F is widely, log normally, distributed with a width diverging at the AMIT. As a consequence, the mean value of the fidelity F converges to one at the AMIT, in strong contrast to its typical value which converges to zero exponentially fast with system size L . This counterintuitive behavior is explained as a manifestation of multifractality at the AMIT.
Twofold PT symmetry in doubly exponential optical lattices
NASA Astrophysics Data System (ADS)
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
2016-01-01
We introduce a family of non-Hermitian optical potentials that are given in terms of double-exponential periodic functions. The center of PT symmetry is not around zero and the potential satisfies a shifted PT -symmetry relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum, and exceptional points in the band structure are examined in detail. In addition, the nonlinear properties of wave propagation in Kerr nonlinearity media are studied. In particular, coherent structures such as lattice solitons are numerically identified by applying the spectral renormalization method. The spatial symmetries of such lattice solitons follow the shifted PT -symmetric relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stabilities are critically dependent on their spatial symmetry point.
Del Ben, Mauro; Hutter, Jürg; VandeVondele, Joost
2013-06-11
The second-order Møller-Plesset perturbation energy (MP2) and the Random Phase Approximation (RPA) correlation energy are increasingly popular post-Kohn-Sham correlation methods. Here, a novel algorithm based on a hybrid Gaussian and Plane Waves (GPW) approach with the resolution-of-identity (RI) approximation is developed for MP2, scaled opposite-spin MP2 (SOS-MP2), and direct-RPA (dRPA) correlation energies of finite and extended system. The key feature of the method is that the three center electron repulsion integrals (μν|P) necessary for the RI approximation are computed by direct integration between the products of Gaussian basis functions μν and the electrostatic potential arising from the RI fitting densities P. The electrostatic potential is obtained in a plane waves basis set after solving the Poisson equation in Fourier space. This scheme is highly efficient for condensed phase systems and offers a particularly easy way for parallel implementation. The RI approximation allows to speed up the MP2 energy calculations by a factor 10 to 15 compared to the canonical implementation but still requires O(N(5)) operations. On the other hand, the combination of RI with a Laplace approach in SOS-MP2 and an imaginary frequency integration in dRPA reduces the computational effort to O(N(4)) in both cases. In addition to that, our implementations have low memory requirements and display excellent parallel scalability up to tens of thousands of processes. Furthermore, exploiting graphics processing units (GPU), a further speedup by a factor ∼2 is observed compared to the standard only CPU implementations. In this way, RI-MP2, RI-SOS-MP2, and RI-dRPA calculations for condensed phase systems containing hundreds of atoms and thousands of basis functions can be performed within minutes employing a few hundred hybrid nodes. In order to validate the presented methods, various molecular crystals have been employed as benchmark systems to assess the performance, while
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
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.
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.
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.
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.
Time correlation of two γ rays resulting from positronium annihilation
NASA Astrophysics Data System (ADS)
Saito, Haruo; Shibuya, Kengo
2012-04-01
We have obtained the wave function and time correlation of two γ rays resulting from the annihilation of a spin-singlet positronium. We have modified the calculations made by Gauthier and Hawton [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.81.062121 81, 062121 (2010)] in consideration of the real experimental conditions. It has been found that the time correlation is determined by the center-of-mass motion of the positronium, and that the exponential decay component shown by Gauthier and Hawton does not appear in the time-correlation function. We have also conducted an experiment focused on the exponential component in the time-correlation function. The experimental results are consistent with our calculation.
NASA Astrophysics Data System (ADS)
Krehl, P.; Engemann, S.; Schwenkel, D.
During whip cracking the whip-tip reaches a supersonic velocity for a period of about 1.2 ms, thereby emitting a head wave with a parabolic-shaped geometry. A detailed study of this mechanism which encompasses the motion analysis of the whip-tip as well as the determination of the local origin of the shock emission requires a sophisticated recording technique. A pre-trigger framing high-speed video camera system was used which was triggered by an acoustical sensor and synchronized with a pulsed copper-vapour laser. The phenomena were visualized by the direct shadowgraph method and recorded cinematographically as digital images at a frame rate of 9 kHz using a CCD-matrix with 256(H)× 128(V) pixels. The resulting series of frames allowed, for the first time, (i) a reconstruction of the whip-tip trajectory, (ii) a determination of the tuft velocity and acceleration, (iii) a correlation of whip-tip kinematics with shock wave emission, and (iv) a motion analysis of the turning and unfolding mechanism of the tuft. The tuft at the whip-tip was accelerated within a distance of about 45 cm from a Mach number of M=1 to a maximum of M=2.19, thereby reaching a maximum acceleration of 50,000 g. The shock is emitted at the moment when the cracker, arriving at the turning point of the lash, is rapidly turned around. After emission of the shock wav M<1 within a short distance of only 20 cm.
NASA Astrophysics Data System (ADS)
Milota, F.; Sperling, J.; Szöcs, V.; Tortschanoff, A.; Kauffmann, H. F.
2004-05-01
Probing electronic femtosecond (fs) coherence among segmental sites that are congested by static and dynamic site disorder and subject to structural relaxation is a big, experimental challenge in the study of photophysics of poly(p-phenylenevinylene). In this work, fs-wave-packet fluorescence interferometry experiments are presented that measure macroscopic coherent kernels and their phase-relaxation in the low-temperature, bottom-state regime of the density-of-states below the migrational threshold energy where downhill site-to-site transfer is marginal. By using freely propagating and tunable 70 fs excitation/probing pulses and employing narrow-band spectral filtering of wave packets, fluorescence interferograms with strongly damped beatings can be observed. The coherences formally follow the in-phase superpositions of two site-optical free-induction-decays and originate from distinct pairs of coherent doorway-states, different in energy and space, each of them being targeted, by two discrete quantum-arrival-states 1α and 1β, via independent, isoenergetic 0→1 fluorescence transitions. The coherent transients are explained as site-to-site polarization beatings, caused by the interference of two fluorescence correlation signals. The numerical analysis of the damping regime, based upon second-order perturbational solutions, reveals the lower limit value of homogeneous dephasing in the range from T2≃100 fs to T2≃200 fs depending on the site-excitation energy of the bottom-states. The experiments enable to look into the formation of the relaxed state as a special molecular process of electron-phonon coupling and hence open-up a quite new perspective in the puzzle of multichromophore optical dynamics and structural relaxation in conjugated polymers.
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.
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)
Pérez, Alberto T.
2011-10-01
When one end of a transmission line is connected to a broadband noise generator, sharp peaks are visible in the cross-correlation function of the signals at both ends of the line. The speed of the electromagnetic waves can be deduced from the time when the peaks appear. The method is suitable for introducing the concepts of cross-correlation functions and noise analysis in an undergraduate physics laboratory.
NASA Astrophysics Data System (ADS)
Nakahara, Hisashi
2015-02-01
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. Use of coda waves requires earthquakes resulting in decreased time resolution for monitoring. Nonetheless, it may be possible to monitor subsurface structures in sufficient time resolutions in regions with high seismicity. In studying the 2011 Tohoku-Oki, Japan earthquake (Mw 9.0), for which velocity changes have been previously reported, I try to validate the method. KiK-net stations in northern Honshu are used in this analysis. For each moderate earthquake normalized auto correlation functions of surface records are stacked with respect to time windows in the S-wave coda. Aligning the stacked, normalized auto correlation functions with time, I search for changes in phases arrival times. The phases at lag times of <1 s are studied because changes at shallow depths are focused. Temporal variations in the arrival times are measured at the stations based on the stretching method. Clear phase delays are found to be associated with the mainshock and to gradually recover with time. The amounts of the phase delays are 10 % on average with the maximum of about 50 % at some stations. The deconvolution analysis using surface and subsurface records at the same stations is conducted for validation. The results show 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 percent, which is much larger than methods using earthquake doublets and borehole array data. So this analysis might be applicable in detecting larger changes. In spite of these disadvantages, this analysis is still attractive because it can
Stretched Exponential Relaxation of Glasses at Low Temperature
NASA Astrophysics Data System (ADS)
Yu, Yingtian; Wang, Mengyi; Zhang, Dawei; Wang, Bu; Sant, Gaurav; Bauchy, Mathieu
2015-10-01
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.
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
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…
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 asymptotics of the Voigt functions
NASA Astrophysics Data System (ADS)
Paris, R. B.
2015-06-01
We obtain the asymptotic expansion of the Voigt functionss K( x, y) and L( x, y) for large (real) values of the variables x and y, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered as with x > 0 fixed. Numerical examples are presented to demonstrate the accuracy of these new expansions.
Kovalevskaya exponents of systems with exponential interaction
Emel'yanov, K V; Tsygvintsev, A V
2000-10-31
The Kovalevskaya exponents are calculated for a class of systems generalizing Toda chains: systems with exponential interaction. It is shown that the known cases of algebraic integrability have no direct analogues in the case of spaces with pseudo-Euclidean metrics because the full-parameter expansions of the general solution contain complex powers of the independent variable.
Kovalevskaya exponents of systems with exponential interaction
NASA Astrophysics Data System (ADS)
Emel'yanov, K. V.; Tsygvintsev, A. V.
2000-10-01
The Kovalevskaya exponents are calculated for a class of systems generalizing Toda chains: systems with exponential interaction. It is shown that the known cases of algebraic integrability have no direct analogues in the case of spaces with pseudo-Euclidean metrics because the full-parameter expansions of the general solution contain complex powers of the independent variable.
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.
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. PMID:27300977
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)
Lin, C. D.; Macek, J. H.
1984-05-01
Doubly-excited-state basis (DESB) functions of Herrick and Sinanoǧlu are compared with the large-scale configuration-interaction (CI) wave functions of Lipsky et al., and with the adiabatic channel functions in hyperspherical coordinates. It is shown that DESB functions will represent those states where the mean value of θ12 is large. Owing to the absence of intershell correlations, and a consequent underestimation of radial correlations, the DESB functions give excessive concentrations near θ12=0 for other, less sharply correlated in angle, states.
Yu, Siyuan; Ma, Zhongtian; Ma, Jing; Wu, Feng; Tan, Liying
2015-03-23
In some applications of optical communication systems, such as inter-satellites optical communication, the correlation of the bidirectional tracking beams changes in far-field as a result of wave-front deformation. Far-field correlation model with wave-front deformation on tracking stability is established. Far-field correlation function and factor have been obtained. Combining with parameters of typical laser communication systems, the model is corrected. It shows that deformation pointing-tracking errors θ(A) and θ(B), far-field correlation factor δ depend on RMS of deformation error rms, which decline with a increasing rms including Tilt and Coma. The principle of adjusting far-field correlation factor with wave-front deformation to compensate deformation pointing-tracking errors has been given, through which the deformation pointing-tracking error is reduced to 18.12″ (Azimuth) and 17.65″ (Elevation). Work above possesses significant reference value on optimization design in inter-satellites optical communication.
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).
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.; Ali, A. F.; Malaspina, D. M.; Michell, R. G.; Spanswick, E. L.; Baker, D. N.; Blake, J. B.; Cully, C.; et al
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
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.
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)
Jacobs, C. M. J.; Makin, V. K.; van Oort, C.; Worrel, E. H. W.
Continuous flux measurements performed at the stable research platform Meetpost Noordwijk are described. For interpretation of these data, meteorological and hydro- graphic data at the platform are extracted from the operational observation network over the Northsea. A subset of the eddy-correlation stress data is analysed and inter- preted in the framework of an advanced wind-over-waves coupling model. The model uses the wind speed and the phase speed at the spectral peak to compute the stress and accounts for the stress contribution due to the air flow separation from breaking waves.
Först, M.; Frano, A.; Kaiser, S.; Mankowsky, R.; Hunt, C. R.; Turner, J. J.; Dakovski, G. L.; Minitti, M. P.; Robinson, J.; Loew, T.; et al
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.
Exponential Boundary Observers for Pressurized Water Pipe
NASA Astrophysics Data System (ADS)
Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel
2015-11-01
This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.
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.
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}.
Parallel and perpendicular turbulence correlation length in the TJ-II Stellarator
NASA Astrophysics Data System (ADS)
van Milligen, B. Ph.; Lopez Fraguas, A.; Pedrosa, M. A.; Hidalgo, C.; Martín de Aguilera, A.; Ascasíbar, E.
2013-09-01
Long-range correlations were measured using two remote reciprocating Langmuir probe systems at TJ-II. The influence of the rotational transform on the correlation was studied by scanning the magnetic configuration. A simple drift-wave correlation model, assuming an exponential decay of the correlation with different correlation lengths in the directions parallel and perpendicular to the field lines, was found to describe the observations well at low densities. The experiment was repeated at gradually higher densities, and an additional correlation was detected at a critical value of the density. In accordance with previous work, this additional correlation was ascribed to zonal flows associated with a confinement transition. Thus, the total long-range correlation is found to be a sum of the drift wave and zonal flow contributions.
NASA Astrophysics Data System (ADS)
Karakul, Hasan; Ulusay, Resat
2013-09-01
Determination of P-wave velocity ( V p), which is closely related to intact rock properties both in laboratory and in situ conditions, is a non-destructive, easy and less complicated procedure. Due to these advantages, there is an increasing trend to predict the physico-mechanical properties of rocks from V p. By considering that no attempt on the estimation of mechanical properties of rocks from V p under different degrees of saturation has been made, in this study, it was aimed to correlate strength properties (uniaxial compressive and tensile strengths) with V p of various rock types under different degrees of saturation. For this purpose, fourteen different rock types were collected from several parts of Turkey and a comprehensive laboratory testing program was conducted. Experimental results indicated that strength and deformability properties of the rocks decreased with increasing degree of saturation, while V p showed increasing and decreasing trends depending on degree of saturation. Simple regression analysis results indicated that although prediction of the strength properties of rocks directly from V p at different degrees of saturation was possible, the equations developed would yield some under- or over-predictions. In the second stage of statistical analyses, a series of different prediction relationships were developed by using independent variables such as V p, degree of saturation and effective clay content (ECC). The statistical tests suggested that the resultant multivariate equations had very high prediction performances and were very useful tools to estimate the strength properties from V p determined at any degree of saturation. In addition, the comparisons between the theoretical Gassmann-Biot velocities, which were calculated at different degrees of saturation, and the experimental results suggest that the theoretical Gassmann-Biot velocities show inconsistencies with the experimental results obtained from the investigated rock types with
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.
Analytical solution of the Klein Gordon equation for a quadratic exponential-type potential
NASA Astrophysics Data System (ADS)
Ezzatpour, Somayyeh; Akbarieh, Amin Rezaei
2016-07-01
In this research study, analytical solutions of the Klein Gordon equation by considering the potential as a quadratic exponential will be presented. However, the potential is assumed to be within the framework of an approximation for the centrifugal potential in any state. The Nikiforov-Uvarov method is used to calculate the wave function, as well as corresponding exact energy equation, in bound states. We finally concluded that the quadratic exponential-type potential under which the results were deduced, led to outcomes that were comparable to the results obtained from the well-known potentials in some special cases.
On the origin of exponential galaxy discs
NASA Astrophysics Data System (ADS)
Dutton, Aaron A.
2009-06-01
One of the most important unresolved issues for galaxy formation theory is to understand the origin of exponential galaxy discs. We use a disc galaxy evolution model to investigate whether galaxies with exponential surface brightness profiles can be produced in a cosmologically motivated framework for disc galaxy formation. Our model follows the accretion, cooling and ejection of baryonic mass, as a function of radius, inside growing dark matter haloes. The surface density profile of the disc is determined by detailed angular momentum conservation, starting from the distribution of specific angular momentum as found in cosmological simulations. Exponential and quasi-exponential discs can be produced by our model through a combination of supernova-driven galactic outflows (which preferentially remove low angular momentum material), intrinsic variation in the angular momentum distribution of the halo gas and the inefficiency of star formation at large radii. We use observations from the Sloan Digital Sky Survey (SDSS) New York University Value Added Catalog (NYU-VAGC) to show that the median Sérsic index of late-type galaxies is a strong function of stellar mass. For blue galaxies, low-mass galaxies have n ~= 1.3, while high-mass galaxies have n ~= 4, with a transition mass of Mstar ~= 2.5 × 1010Msolar. Our model with energy-driven outflows correctly reproduces this trend, whereas our models with momentum-driven outflows and no outflows overpredict the Sérsic indices in low-mass galaxies. We show that the observed fraction of `bulge-less' exponential galaxies is a strong function of stellar mass. For Milky Way mass galaxies (Vrot ~= 220kms-1, Mstar ~= 1011Msolar), less than 0.1 per cent of blue galaxies are bulge-less, whereas for M33 mass galaxies (Vrot ~= 120kms-1, Mstar ~= 1010Msolar) bulge-less and quasi-bulge-less galaxies are more common, with 45 per cent of blue galaxies having the Sérsic index n < 1.5. These results suggest that the difficulty of
NASA Astrophysics Data System (ADS)
Yanagisawa, Takashi
2016-11-01
The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the ground-state energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction U increases. The antiferromagnetic correlation induced by U is reduced for hole doping when U is large, being greater than the bandwidth, thus increasing the kinetic energy gain. The spin and charge fluctuations are induced in the strongly correlated region. These antiferromagnetic and kinetic charge fluctuations induce electron pairings, which results in high-temperature superconductivity.
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 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.
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.
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.
Rounded stretched exponential for time relaxation functions.
Powles, J G; Heyes, D M; Rickayzen, G; Evans, W A B
2009-12-01
A rounded stretched exponential function is introduced, C(t)=exp{(tau(0)/tau(E))(beta)[1-(1+(t/tau(0))(2))(beta/2)]}, where t is time, and tau(0) and tau(E) are two relaxation times. This expression can be used to represent the relaxation function of many real dynamical processes, as at long times, t>tau(0), the function converges to a stretched exponential with normalizing relaxation time, tau(E), yet its expansion is even or symmetric in time, which is a statistical mechanical requirement. This expression fits well the shear stress relaxation function for model soft soft-sphere fluids near coexistence, with tau(E)
Exponential evolution: implications for intelligent extraterrestrial life.
Russell, D A
1983-01-01
Some measures of biologic complexity, including maximal levels of brain development, are exponential functions of time through intervals of 10(6) to 10(9) yrs. Biological interactions apparently stimulate evolution but physical conditions determine the time required to achieve a given level of complexity. Trends in brain evolution suggest that other organisms could attain human levels within approximately 10(7) yrs. The number (N) and longevity (L) terms in appropriate modifications of the Drake Equation, together with trends in the evolution of biological complexity on Earth, could provide rough estimates of the prevalence of life forms at specified levels of complexity within the Galaxy. If life occurs throughout the cosmos, exponential evolutionary processes imply that higher intelligence will soon (10(9) yrs) become more prevalent than it now is. Changes in the physical universe become less rapid as time increases from the Big Bang. Changes in biological complexity may be most rapid at such later times. This lends a unique and symmetrical importance to early and late universal times. PMID:11542467
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.
An Exponentiation Method for XML Element Retrieval
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. PMID:24696643
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.
Poissonian renormalizations, exponentials, and power laws
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Poissonian renormalizations, exponentials, and power laws.
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
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.
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. PMID:24696643
Modified OMP Algorithm for Exponentially Decaying Signals
Kazimierczuk, Krzysztof; Kasprzak, Paweł
2015-01-01
A group of signal reconstruction methods, referred to as compressed sensing (CS), has recently found a variety of applications in numerous branches of science and technology. However, the condition of the applicability of standard CS algorithms (e.g., orthogonal matching pursuit, OMP), i.e., the existence of the strictly sparse representation of a signal, is rarely met. Thus, dedicated algorithms for solving particular problems have to be developed. In this paper, we introduce a modification of OMP motivated by nuclear magnetic resonance (NMR) application of CS. The algorithm is based on the fact that the NMR spectrum consists of Lorentzian peaks and matches a single Lorentzian peak in each of its iterations. Thus, we propose the name Lorentzian peak matching pursuit (LPMP). We also consider certain modification of the algorithm by introducing the allowed positions of the Lorentzian peaks' centers. Our results show that the LPMP algorithm outperforms other CS algorithms when applied to exponentially decaying signals. PMID:25609044
Monitoring medical procedures by exponential smoothing.
Spliid, Henrik
2007-01-15
A new exponentially weighted moving average (EWMA) control chart well suited for 'online' routine surveillance of medical procedures is introduced. The chart is based on inter-event counts for failures recorded when the failures occur. The method can be used for many types of hospital procedures and activities, such as problems or errors in surgery, hospital-acquired infections, erroneous handling or prescription of medicine, deviations from scheduled treatments causing inconveniences for patients. The construction, the use and the effectiveness of the control chart are demonstrated by two well-known examples about wound infection in orthopaedic surgery and neonatal arterial switch surgery. The method is easy to implement and apply, it illustrates, estimates and tests the current failure rate. Comparisons with two examples from the literature indicate that its ability to quickly detect an increased failure rate is comparable to that of other well-established methods.
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.
Radiating stars with exponential Lie symmetries
NASA Astrophysics Data System (ADS)
Mohanlal, R.; Maharaj, S. D.; Tiwari, Ajey K.; Narain, R.
2016-07-01
We analyze the general model of a radiating star in general relativity. A group analysis of the under determined, nonlinear partial differential equation governing the model's gravitational potentials is performed. This analysis is an extension of previous group analyses carried out and produces new group invariant solutions. We find that the gravitational potentials depend on exponential functions owing to the choice of the Lie symmetry generator. The fundamental boundary equation to be solved is in general a Riccati equation. Several new exact families of solutions to the boundary condition are generated. Earlier models of Euclidean stars and generalized Euclidean stellar models are regained as special cases. Linear equations of state can be found for shear-free and shearing spacetimes.
Vortex structures in exponentially shaped Josephson junctions
NASA Astrophysics Data System (ADS)
Shukrinov, Yu. M.; Semerdjieva, E. G.; Boyadjiev, T. L.
2005-04-01
We report the numerical calculations of the static vortex structure and critical curves in exponentially shaped long Josephson junctions for in-line and overlap geometries. Stability of the static solutions is investigated by checking the sign of the smallest eigenvalue of the associated Sturm-Liouville problem. The change in the junction width leads to the renormalization of the magnetic flux in comparison with the case of a linear one-dimensional model. We study the influence of the model's parameters, and particularly, the shape parameter on the stability of the states of the magnetic flux. We compare the vortex structure and critical curves for the in-line and overlap geometries. Our numerically constructed critical curve of the Josephson junction matches well with the experimental one.
Exponential Disks from Stellar Scattering. III. Stochastic Models
NASA Astrophysics Data System (ADS)
Elmegreen, Bruce G.; Struck, Curtis
2016-10-01
Stellar scattering off irregularities in a galaxy disk has been shown to make an exponential radial profile, but no fundamental reason for this has been suggested. Here, we show that exponentials are mathematically expected from random scattering in a disk when there is a slight inward bias in the scattering probability. Such a bias was present in our previous scattering experiments that formed exponential profiles. Double exponentials can arise when the bias varies with radius. This is a fundamental property of scattering and may explain why piece-wise exponential profiles are ubiquitous in galaxies, even after minor mergers and other disruptive events.
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)
Zhao, W.; Baskaran, D.; Grishchuk, L. P.
2009-01-01
The detection of primordial gravitational waves is one of the biggest challenges of the present time. The existing (Wilkinson Microwave Anisotropy Probe) observations are helpful in achieving this goal, and the forthcoming experiments (Planck) are likely to complete this mission. We show that the 5-year Wilkinson Microwave Anisotropy Probe TE data contain a hint of the presence of the gravitational wave contribution. In terms of the parameter R, which gives the ratio of contributions from gravitational waves and density perturbations to the temperature quadrupole, the best-fit model produced R=0.24. Because of large residual noises, the uncertainty of this determination is still large, and it easily includes the R=0 hypothesis. However, the uncertainty will be strongly reduced in the forthcoming observations which are more sensitive. We numerically simulated the Planck data and concluded that the relic gravitational waves with R=0.24 will be present at a better than 3σ level in the TE observational channel, and at a better than 2σ level in the “realistic” BB channel. The balloon-borne and ground-based observations may provide healthy competition for Planck in some parts of the lower-ℓ spectrum.
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
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)
Rolland, Joran; Domeisen, Daniela I. V.
2016-04-01
Many geophysical waves in the atmosphere or in the ocean have a three dimensional structure and contain a range of scales. This is for instance the case of planetary waves in the stratosphere connected to baroclinic eddies in the troposphere [1]. In the study of such waves from reanalysis data or output of numerical simulations, Empirical Orthogonal Functions (EOF) obtained as a Proper Orthogonal Decomposition of the data sets have been of great help. However, most of these computations rely on the diagonalisation of space correlation matrices: this means that the considered data set can only have a limited number of gridpoints. The main consequence is that such analyses are often only performed in planes (as function of height and latitude, or longitude and latitude for instance), which makes the educing of the three dimensional structure of the wave quite difficult. In the case of the afore mentionned waves, the matter of the longitudinal dependence or the proper correlation between modes through the tropopause is an open question. An elegant manner to circumvent this problem is to consider the output of the Orthogonal Decomposition as a whole. Indeed, it has been shown that the normalised time series of the amplitude of each EOF, far from just being decorrelated from one another, are actually another set of orthogonal functions. These can actually be computed through the diagonlisation of the time correlation matrix of the data set, just like the EOF were the result of the diagonalisation of the space correlation matrix. The signal is then fully decomposed in the framework of the Bi-Orthogonal Decomposition as the sum of the nth explained variance, time the nth eigenmode of the time correlation times the nth eigenmode of the spacial correlations [2,3]. A practical consequence of this result is that the EOF can be reconstructed from the projection of the dataset onto the eigenmodes of the time correlation matrix in the so-called snapshot method [4]. This is very
NASA Astrophysics Data System (ADS)
Rolland, Joran; Domeisen, Daniela I. V.
2016-04-01
Many geophysical waves in the atmosphere or in the ocean have a three dimensional structure and contain a range of scales. This is for instance the case of planetary waves in the stratosphere connected to baroclinic eddies in the troposphere [1]. In the study of such waves from reanalysis data or output of numerical simulations, Empirical Orthogonal Functions (EOF) obtained as a Proper Orthogonal Decomposition of the data sets have been of great help. However, most of these computations rely on the diagonalisation of space correlation matrices: this means that the considered data set can only have a limited number of gridpoints. The main consequence is that such analyses are often only performed in planes (as function of height and latitude, or longitude and latitude for instance), which makes the educing of the three dimensional structure of the wave quite difficult. In the case of the afore mentionned waves, the matter of the longitudinal dependence or the proper correlation between modes through the tropopause is an open question. An elegant manner to circumvent this problem is to consider the output of the Orthogonal Decomposition as a whole. Indeed, it has been shown that the normalised time series of the amplitude of each EOF, far from just being decorrelated from one another, are actually another set of orthogonal functions. These can actually be computed through the diagonlisation of the time correlation matrix of the data set, just like the EOF were the result of the diagonalisation of the space correlation matrix. The signal is then fully decomposed in the framework of the Bi-Orthogonal Decomposition as the sum of the nth explained variance, time the nth eigenmode of the time correlation times the nth eigenmode of the spacial correlations [2,3]. A practical consequence of this result is that the EOF can be reconstructed from the projection of the dataset onto the eigenmodes of the time correlation matrix in the so-called snapshot method [4]. This is very
NASA Astrophysics Data System (ADS)
Zhang, G.; Katz, A.; Alfano, R. R.; Kofinas, A. D.; Kofinas, D. A.; Stubblefield, P. G.; Rosenfeld, W.; Beyer, D.; Maulik, D.; Stankovic, M. R.
2000-11-01
The newborn piglet brain model was used to correlate continuous-wave (CW) and frequency-domain (FD) near-infrared spectroscopy. Six ventilated and instrumented newborn piglets were subjected to a series of manipulations in blood oxygenation with the effects on brain perfusion known to be associated with brain hypoxia-ischaemia. An excellent agreement between the CW and FD was demonstrated. This agreement improved when the scattering properties (determined by the FD device) were employed to calculate the differential pathlength factor, an important step in CW data processing.
An Exponential Decay Model for Mediation
Fritz, Matthew S.
2013-01-01
Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, addresses many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed. PMID:23625557
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.
Acoustic wave propagation in heterogeneous two-dimensional fractured porous media.
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)PLEEE81539-375510.1103/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. PMID:27415385
Himemoto, Yoshiaki; Hiramatsu, Takashi; Taruya, Atsushi; Kudoh, Hideaki
2007-01-15
We discuss a robust data analysis method to detect a stochastic background of gravitational waves in the presence of non-Gaussian noise. In contrast to the standard cross-correlation (SCC) statistic frequently used in the stochastic background searches, we consider a generalized cross-correlation (GCC) statistic, which is nearly optimal even in the presence of non-Gaussian noise. The detection efficiency of the GCC statistic is investigated analytically, particularly focusing on the statistical relation between the false-alarm and the false-dismissal probabilities, and the minimum detectable amplitude of gravitational-wave signals. We derive simple analytic formulas for these statistical quantities. The robustness of the GCC statistic is clarified based on these formulas, and one finds that the detection efficiency of the GCC statistic roughly corresponds to the one of the SCC statistic neglecting the contribution of non-Gaussian tails. This remarkable property is checked by performing the Monte Carlo simulations and successful agreement between analytic and simulation results was found.
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.
Exponential Orthogonality Catastrophe in Single-Particle and Many-Body Localized Systems
NASA Astrophysics Data System (ADS)
Deng, Dong-Ling; Pixley, J. H.; Li, Xiaopeng
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 post-quench 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. We show that in a many-body localized phase, this non-local 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. We thank S.-T. Wang, Z.-X. Gong, Y.-L. Wu, J. D. Sau, and Z. Ovadyahu for discussions. This work is supported by LPS-MPO-CMTC, JQI-NSF-PFC, and ARO-Atomtronics-MURI. The authors acknowledge the University of Maryland supercomputing resources.
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.
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.
Stretched exponential relaxation in molecular and electronic glasses
NASA Astrophysics Data System (ADS)
Phillips, J. C.
1996-09-01
Stretched exponential relaxation, 0034-4885/59/9/003/img1, fits many relaxation processes in disordered and quenched electronic and molecular systems, but it is widely believed that this function has no microscopic basis, especially in the case of molecular relaxation. For electronic relaxation the appearance of the stretched exponential is often described in the context of dispersive transport, where 0034-4885/59/9/003/img2 is treated as an adjustable parameter, but in almost all cases it is generally assumed that no microscopic meaning can be assigned to 0034-4885/59/9/003/img3 even at 0034-4885/59/9/003/img4, a glass transition temperature. We show that for molecular relaxation 0034-4885/59/9/003/img5 can be understood, providing that one separates extrinsic and intrinsic effects, and that the intrinsic effects are dominated by two magic numbers, 0034-4885/59/9/003/img6 for short-range forces, and 0034-4885/59/9/003/img7 for long-range Coulomb forces, as originally observed by Kohlrausch for the decay of residual charge on a Leyden jar. Our mathematical model treats relaxation kinetics using the Lifshitz - Kac - Luttinger diffusion to traps depletion model in a configuration space of effective dimensionality, the latter being determined using axiomatic set theory and Phillips - Thorpe constraint theory. The experiments discussed include ns neutron scattering experiments, particularly those based on neutron spin echoes which measure S( Q,t) directly, and the traditional linear response measurements which span the range from 0034-4885/59/9/003/img8 to s, as collected and analysed phenomenologically by Angell, Ngai, Böhmer and others. The electronic materials discussed include a-Si:H, granular 0034-4885/59/9/003/img9, semiconductor nanocrystallites, charge density waves in 0034-4885/59/9/003/img10, spin glasses, and vortex glasses in high-temperature semiconductors. The molecular materials discussed include polymers, network glasses, electrolytes and alcohols, Van
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.
Lack of exponential stability to Timoshenko system with viscoelastic Kelvin-Voigt type
NASA Astrophysics Data System (ADS)
Malacarne, Andréia; Muñoz Rivera, Jaime Edilberto
2016-06-01
We study the Timoshenko systems with a viscoelastic dissipative mechanism of Kelvin-Voigt type. We prove that the model is analytical if and only if the viscoelastic damping is present in both the shear stress and the bending moment. Otherwise, the corresponding semigroup is not exponentially stable no matter the choice of the coefficients. This result is different to all others related to Timoshenko model with partial dissipation, which establish that the system is exponentially stable if and only if the wave speeds are equal. Finally, we show that the solution decays polynomially to zero as {t^{-1/2}} , no matter where the viscoelastic mechanism is effective and that the rate is optimal whenever the initial data are taken on the domain of the infinitesimal operator.
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…
101 Ways to Teach About Exponential Growth and Its Consequences.
ERIC Educational Resources Information Center
Allen, Rodney F., Ed.
Exponential growth is a mega-concept which has many applications. It is fundamental to understanding how and why systems work and fail, be they natural or man-made systems. Lessons/activities in this booklet are designed for Florida teachers to help provide their students with an understanding of the nature and implications of exponential growth.…
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.
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.
COMMUNICATION: Neuron network activity scales exponentially with synapse density
NASA Astrophysics Data System (ADS)
Brewer, G. J.; Boehler, M. D.; Pearson, R. A.; DeMaris, A. A.; Ide, A. N.; Wheeler, B. C.
2009-02-01
Neuronal network output in the cortex as a function of synapse density during development has not been explicitly determined. Synaptic scaling in cortical brain networks seems to alter excitatory and inhibitory synaptic inputs to produce a representative rate of synaptic output. Here, we cultured rat hippocampal neurons over a three-week period to correlate synapse density with the increase in spontaneous spiking activity. We followed the network development as synapse formation and spike rate in two serum-free media optimized for either (a) neuron survival (Neurobasal/B27) or (b) spike rate (NbActiv4). We found that while synaptophysin synapse density increased linearly with development, spike rates increased exponentially in developing neuronal networks. Synaptic receptor components NR1, GluR1 and GABA-A also increase linearly but with more excitatory receptors than inhibitory. These results suggest that the brain's information processing capability gains more from increasing connectivity of the processing units than increasing processing units, much as Internet information flow increases much faster than the linear number of nodes and connections.
Neuron network activity scales exponentially with synapse density.
Brewer, G J; Boehler, M D; Pearson, R A; DeMaris, A A; Ide, A N; Wheeler, B C
2009-02-01
Neuronal network output in the cortex as a function of synapse density during development has not been explicitly determined. Synaptic scaling in cortical brain networks seems to alter excitatory and inhibitory synaptic inputs to produce a representative rate of synaptic output. Here, we cultured rat hippocampal neurons over a three-week period to correlate synapse density with the increase in spontaneous spiking activity. We followed the network development as synapse formation and spike rate in two serum-free media optimized for either (a) neuron survival (Neurobasal/B27) or (b) spike rate (NbActiv4). We found that while synaptophysin synapse density increased linearly with development, spike rates increased exponentially in developing neuronal networks. Synaptic receptor components NR1, GluR1 and GABA-A also increase linearly but with more excitatory receptors than inhibitory. These results suggest that the brain's information processing capability gains more from increasing connectivity of the processing units than increasing processing units, much as Internet information flow increases much faster than the linear number of nodes and connections. PMID:19104141
Hack, S N; Eichling, J O; Bergmann, S R; Welch, M J; Sobel, B E
1980-11-01
A technique was developed and evaluated using the exponential infusion of positron-emitting diffusible tracers to quantitate myocardial perfusion. The approach employs a parameter that rapidly reaches a constant value as a function of tracer delivery rate, isotope decay constant, and the monotonically increasing tissue radioactivity. Isolated rabbit hearts with controlled flow were used to evaluate the approach, because tracer kinetics in such preparations mimic those in vivo. Accordingly, exponential infusions of H2 15O and [11C]butanol were administered to 25 isolated rabbit hearts perfused with Krebs-Henseleit solution (KH) alone or KH enriched with erythrocytes (KH-RBC, hematocrit = 40). With flow varied from 1.2 to 5 ml/g per min in eight KH hearts infused with H2 15O, actual and estimated flow correlated closely (r = 0.95, n = 52 determinations). For the KH-RBC hearts, flow was varied from 0.3 to 1.5 ml/g per min. Actual and estimated flow correlated significantly for both the 14 KH-RBC hearts infused with H2 15O (r = 0.90, n = 89 determinations) and the 3 KH-RBC hearts infused with [11C]butanol (r = 0.93, n = 13 determinations). In addition, the required exponentially increasing arterial tracer concentrations were shown to be attainable in vivo in dogs and rhesus monkeys after intravenous exponential administrations of tracer. The results suggest that the approach developed employing exponential tracer infusion permits accurate measurement of myocardial perfusion and that it should prove useful in the noninvasive measurement of regional myocardial perfusion in vivo by positron emission tomography.
NASA Astrophysics Data System (ADS)
Jiang, Shenghan; Mesaros, Andrej; Ran, Ying
2014-07-01
Recently, two interesting candidate quantum phases—the chiral spin-density wave state featuring anomalous quantum Hall effect and the d+id superconductor—were proposed for the Hubbard model on the honeycomb lattice at 1/4 doping. Using a combination of exact diagonalization, density matrix renormalization group, the variational Monte Carlo method, and quantum field theories, we study the quantum phase diagrams of both the Hubbard model and the t-J model on the honeycomb lattice at 1/4 doping. The main advantage of our approach is the use of symmetry quantum numbers of ground-state wave functions on finite-size systems (up to 32 sites) to sharply distinguish different quantum phases. Our results show that for 1≲U/t<40 in the Hubbard model and for 0.1
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.
NASA Astrophysics Data System (ADS)
Sun, Shih-Jye; Chung, Chung-Hou; Chang, Yung-Yeh; Tsai, Wei-Feng; Zhang, Fu-Chun
2016-04-01
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 -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.
Robb Swan, Ashley; Nichols, Sharon; Drake, Angela; Angeles, AnneMarie; Diwakar, Mithun; Song, Tao; Lee, Roland R; Huang, Ming-Xiong
2015-10-01
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.
Sun, Shih-Jye; Chung, Chung-Hou; Chang, Yung-Yeh; Tsai, Wei-Feng; Zhang, Fu-Chun
2016-01-01
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. PMID:27064108
Sun, Shih-Jye; Chung, Chung-Hou; Chang, Yung-Yeh; Tsai, Wei-Feng; Zhang, Fu-Chun
2016-01-01
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 -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. PMID:27064108
NASA Astrophysics Data System (ADS)
Martellini, Lionel; Regimbau, Tania
2015-11-01
Under standard assumptions including stationary and serially uncorrelated Gaussian gravitational wave stochastic background signal and noise distributions, as well as homogenous detector sensitivities, the standard cross-correlation detection statistic is known to be optimal in the sense of minimizing the probability of a false dismissal at a fixed value of the probability of a false alarm. The focus of this paper is to analyze the comparative efficiency of this statistic, vs a simple alternative statistic obtained by cross-correlating the squared measurements, in situations that deviate from such standard assumptions. We find that differences in detector sensitivities have a large impact on the comparative efficiency of the cross-correlation detection statistic, which is dominated by the alternative statistic when these differences reach 1 order of magnitude. This effect holds even when both the signal and noise distributions are Gaussian. While the presence of non-Gaussian signals has no material impact for reasonable parameter values, the relative inefficiency of the cross-correlation statistic is less prominent for fat-tailed noise distributions, but it is magnified in case noise distributions have skewness parameters of opposite signs. Our results suggest that introducing an alternative detection statistic can lead to noticeable sensitivity gains when noise distributions are possibly non-Gaussian and/or when detector sensitivities exhibit substantial differences, a situation that is expected to hold in joint detections from Advanced LIGO and Advanced Virgo, in particular in the early phases of development of the detectors, or in joint detections from Advanced LIGO and the Einstein Telescope.
Tripathi, Dharmendra; Pandey, S K; Siddiqui, Abdul; Bég, O Anwar
2014-01-01
A theoretical study is presented for transient peristaltic flow of an incompressible fluid with variable viscosity in a finite length cylindrical tube as a simulation of transport in physiological vessels and biomimetic peristaltic pumps. The current axisymmetric analysis is qualitatively similar to two-dimensional analysis but exhibits quantitative variations. The current analysis is motivated towards further elucidating the physiological migration of gastric suspensions (food bolus) in the human digestive system. It also applies to variable viscosity industrial fluid (waste) peristaltic pumping systems. First, an axisymmetric model is analysed in the limit of large wavelength ([Formula: see text]) and low Reynolds number ([Formula: see text]) for axial velocity, radial velocity, pressure, hydromechanical efficiency and stream function in terms of radial vibration of the wall ([Formula: see text]), amplitude of the wave ([Formula: see text]), averaged flow rate ([Formula: see text]) and variable viscosity ([Formula: see text]). Subsequently, the peristaltic flow of a fluid with an exponential viscosity model is examined, which is based on the analytical solutions for pressure, wall shear stress, hydromechanical efficiency and streamline patterns in the finite length tube. The results are found to correlate well with earlier studies using a constant viscosity formulation. This study reveals some important features in the flow characteristics including the observation that pressure as well as both number and size of lower trapped bolus increases. Furthermore, the study indicates that hydromechanical efficiency reduces with increasing magnitude of viscosity parameter.
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
A Stochastic Super-Exponential Growth Model for Population Dynamics
NASA Astrophysics Data System (ADS)
Avila, P.; Rekker, A.
2010-11-01
A super-exponential growth model with environmental noise has been studied analytically. Super-exponential growth rate is a property of dynamical systems exhibiting endogenous nonlinear positive feedback, i.e., of self-reinforcing systems. Environmental noise acts on the growth rate multiplicatively and is assumed to be Gaussian white noise in the Stratonovich interpretation. An analysis of the stochastic super-exponential growth model with derivations of exact analytical formulae for the conditional probability density and the mean value of the population abundance are presented. Interpretations and various applications of the results are discussed.
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
Exponential temperature dependence of the penetration depth in single crystal MgB2.
Manzano, F; Carrington, A; Hussey, N E; Lee, S; Yamamoto, A; Tajima, S
2002-01-28
The temperature dependence of the London penetration depth, lambda(T), was measured in both single crystal and polycrystalline MgB2 samples by a high-resolution, radio frequency technique. A clear exponential temperature dependence of lambda(T) was observed at low temperature, indicating s-wave pairing. A BCS fit to the lowest temperature data gives an in-plane energy gap Delta of 30+/-2 K (2Delta/T(c) = 1.5+/-0.1), which is significantly smaller than the standard BCS weak coupling value of 3.5. We find that the data are best described by a two-gap model.
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.
Dixit, Anant; Ángyán, János G; Rocca, Dario
2016-09-14
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. PMID:27634249
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
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.
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…
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.
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.
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
Bayesian estimation of generalized exponential distribution under noninformative priors
NASA Astrophysics Data System (ADS)
Moala, Fernando Antonio; Achcar, Jorge Alberto; Tomazella, Vera Lúcia Damasceno
2012-10-01
The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional noninformative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.
Exponential filtering of singular values improves photoacoustic image reconstruction.
Bhatt, Manish; Gutta, Sreedevi; Yalavarthy, Phaneendra K
2016-09-01
Model-based image reconstruction techniques yield better quantitative accuracy in photoacoustic image reconstruction. In this work, an exponential filtering of singular values was proposed for carrying out the image reconstruction in photoacoustic tomography. The results were compared with widely popular Tikhonov regularization, time reversal, and the state of the art least-squares QR-based reconstruction algorithms for three digital phantom cases with varying signal-to-noise ratios of data. It was shown that exponential filtering provides superior photoacoustic images of better quantitative accuracy. Moreover, the proposed filtering approach was observed to be less biased toward the regularization parameter and did not come with any additional computational burden as it was implemented within the Tikhonov filtering framework. It was also shown that the standard Tikhonov filtering becomes an approximation to the proposed exponential filtering. PMID:27607501
Exponential convergence through linear finite element discretization of stratified subdomains
NASA Astrophysics Data System (ADS)
Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali
2016-10-01
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.
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 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
Event-based exponential synchronization of complex networks.
Zhou, Bo; Liao, Xiaofeng; Huang, Tingwen
2016-10-01
In this paper, we consider exponential synchronization of complex networks. The information diffusions between nodes are driven by properly defined events. By employing the M-matrix theory, algebraic graph theory and the Lyapunov method, two kinds of distributed event-triggering laws are designed, which avoid continuous communications between nodes. Then, several criteria that ensure the event-based exponential synchronization are presented, and the exponential convergence rates are obtained as well. Furthermore, we prove that Zeno behavior of the event-triggering laws can be excluded before synchronization being achieved, that is, the lower bounds of inter-event times are strictly positive. Finally, a simulation example is provided to illustrate the effectiveness of theoretical analysis.
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.
Event-based exponential synchronization of complex networks.
Zhou, Bo; Liao, Xiaofeng; Huang, Tingwen
2016-10-01
In this paper, we consider exponential synchronization of complex networks. The information diffusions between nodes are driven by properly defined events. By employing the M-matrix theory, algebraic graph theory and the Lyapunov method, two kinds of distributed event-triggering laws are designed, which avoid continuous communications between nodes. Then, several criteria that ensure the event-based exponential synchronization are presented, and the exponential convergence rates are obtained as well. Furthermore, we prove that Zeno behavior of the event-triggering laws can be excluded before synchronization being achieved, that is, the lower bounds of inter-event times are strictly positive. Finally, a simulation example is provided to illustrate the effectiveness of theoretical analysis. PMID:27668021
Kullback-Leibler divergence and the Pareto-Exponential approximation.
Weinberg, G V
2016-01-01
Recent radar research interests in the Pareto distribution as a model for X-band maritime surveillance radar clutter returns have resulted in analysis of the asymptotic behaviour of this clutter model. In particular, it is of interest to understand when the Pareto distribution is well approximated by an Exponential distribution. The justification for this is that under the latter clutter model assumption, simpler radar detection schemes can be applied. An information theory approach is introduced to investigate the Pareto-Exponential approximation. By analysing the Kullback-Leibler divergence between the two distributions it is possible to not only assess when the approximation is valid, but to determine, for a given Pareto model, the optimal Exponential approximation.
Stretched versus compressed exponential kinetics in α-helix folding
NASA Astrophysics Data System (ADS)
Hamm, Peter; Helbing, Jan; Bredenbeck, Jens
2006-03-01
In a recent paper (J. Bredenbeck, J. Helbing, J.R. Kumita, G.A. Woolley, P. Hamm, α-helix formation in a photoswitchable peptide tracked from picoseconds to microseconds by time resolved IR spectroscopy, Proc. Natl. Acad. Sci USA 102 (2005) 2379), we have investigated the folding of a photo-switchable α-helix with a kinetics that could be fit by a stretched exponential function exp(-( t/ τ) β). The stretching factor β became smaller as the temperature was lowered, a result which has been interpreted in terms of activated diffusion on a rugged energy surface. In the present paper, we discuss under which conditions diffusion problems occur with stretched exponential kinetics ( β < 1) and under which compressed exponential kinetics is obtained ( β > 1). We show that diffusion problems do have a strong tendency to yield stretched exponential kinetics, yet, that there are conditions (strong perturbation from equilibrium, performing the experiment in the folding direction) under which compressed exponential kinetics would be expected instead. We discuss the kinetics on free energy surfaces predicted by simple initiation-propagation models (zipper models) of α-helix folding, as well as by folding funnel models. We show that our recent experiment has been performed under condition for which models with strong downhill driving force, such as the zipper model, would predict compressed, rather than stretched exponential kinetics, in disagreement with the experimental observation. We therefore propose that the free energy surface along a reaction coordinate that governs the folding kinetics must be relatively flat and has a shape similar to a 1D golf course. We discuss how this conclusion can be unified with the thermodynamically well established zipper model by introducing an additional kinetic reaction coordinate.
Linear superposition solutions to nonlinear wave equations
NASA Astrophysics Data System (ADS)
Liu, Yu
2012-11-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed.
Expansivity properties and rigidity for non-recurrent exponential maps
NASA Astrophysics Data System (ADS)
Benini, Anna Miriam
2015-07-01
We show that an exponential map fc(z) = ez + c whose singular value c is combinatorially non-recurrent and non-escaping is uniquely determined by its combinatorics, i.e. the pattern in which its periodic dynamic rays land together. We do this by constructing puzzles and parapuzzles in the exponential family. We also prove that f is expanding on the postsingular set with respect to the Euclidean metric in the case that the singular value is non-recurrent. Finally, we show that boundedness of the postsingular set implies combinatorial non-recurrence if c is in the Julia set.
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.
Application of Krylov exponential propagation to fluid dynamics equations
NASA Technical Reports Server (NTRS)
Saad, Y.; Semeraro, B. D.
1991-01-01
This paper presents an application of matrix exponentiation via Krylov subspace projection, to the solution of fluid dynamics problems. The main idea is to approximate the operation exp(A)v by means of a projection-like process onto a Krylov subspace. This results in a computation of an exponential matrix vector product similar to the one above but of a much smaller size. Time integration schemes can then be devised to exploit this basic computational kernel. The motivation of this approach is to provide time-integration schemes that are essentially of an explicit nature but which have good stability properties.
Application of Krylov exponential propagation to fluid dynamics equations
NASA Technical Reports Server (NTRS)
Saad, Youcef; Semeraro, David
1991-01-01
An application of matrix exponentiation via Krylov subspace projection to the solution of fluid dynamics problems is presented. The main idea is to approximate the operation exp(A)v by means of a projection-like process onto a krylov subspace. This results in a computation of an exponential matrix vector product similar to the one above but of a much smaller size. Time integration schemes can then be devised to exploit this basic computational kernel. The motivation of this approach is to provide time-integration schemes that are essentially of an explicit nature but which have good stability properties.
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.
Exponential velocity profile of granular flows down a confined heap.
Martínez, E; González-Lezcano, A; Batista-Leyva, A J; Altshuler, E
2016-06-01
Thick granular flows are essential to many natural and industrial phenomena. Experimentally, it has been well established that the grain velocity profile is linear from the free surface to a certain depth, after which it decreases exponentially in the so-called "creep region". In this paper we obtain an exponential velocity profile based on the force balance of a grain near a wall, where the Janssen effect and the non-locality of interactions between grains are considered. When experimental parameters such as flow angles and friction coefficients are introduced in our model, it is able to reproduce experimental creep velocity profiles previously reported in the literature. PMID:27415346
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.
Derivatives of Siegel modular forms and exponential functions
NASA Astrophysics Data System (ADS)
Bertrand, D.; Zudilin, W. W.
2001-08-01
We show that the differential field generated by Siegel modular forms and the differential field generated by exponentials of polynomials are linearly disjoint over \\mathbb C. Combined with our previous work [3], this provides a complete multidimensional extension of Mahler's theorem on the transcendence degree of the field generated by the exponential function and the derivatives of a modular function. We give two proofs of our result, one purely algebraic, the other analytic, but both based on arguments from differential algebra and on the stability under the action of the symplectic group of the differential field generated by rational and modular functions.
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.
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.
NASA Astrophysics Data System (ADS)
Dembele, S.; Lima, K. L. M.; Wen, J. X.
2011-11-01
For radiative transfer in complex geometries, Sakami and his co-workers have developed a discrete ordinates method (DOM) exponential scheme for unstructured meshes which was mainly applied to gray media. The present study investigates the application of the unstructured exponential scheme to a wider range of non-gray scenarios found in fire and combustion applications, with the goal to implement it in an in-house Computational Fluid Dynamics (CFD) code for fire simulations. The original unstructured gray exponential scheme is adapted to non-gray applications by employing a statistical narrow-band/correlated-k (SNB-CK) gas model and meshes generated using the authors' own mesh generator. Different non-gray scenarios involving spectral gas absorption by H2O and CO2 are investigated and a comparative analysis is carried out between heat flux and radiative source terms predicted and literature data based on ray-tracing and Monte Carlo methods. The maximum discrepancies for total radiative heat flux do not typically exceed 5%.
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.
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.
Grant, Bridget F.; Chou, S. Patricia; Goldstein, Risë B.; Huang, Boji; Stinson, Frederick S.; Saha, Tulshi D.; Smith, Sharon M.; Dawson, Deborah A.; Pulay, Attila J.; Pickering, Roger P.; Ruan, W. June
2009-01-01
Objectives To present nationally representative findings on prevalence, sociodemographic correlates, disability, and comorbidity of BPD among men and women. Methods Face-to-face interviews with 34,653 adults participating in the Wave 2 National Epidemiologic Survey on Alcohol and Related Conditions. Results Prevalence of lifetime BPD was 5.9% (99% CI: 5.4–6.4). There were no differences in the rates of BPD among men (5.6%, 99% CI: 5.0–6.2) and women (6.2%, 99% CI: 5.6–6.9). BPD was more prevalent among Native American men, younger and separated/divorced/widowed adults, and those with lower incomes and education, and less prevalent among Hispanic men and women and Asian women. BPD was associated with substantial mental and physical disability, especially among women. High co-occurrence rates of mood and anxiety disorders with BPD were similar. With additional comorbidity controlled, associations with bipolar disorder and schizotypal and narcissistic PDs remained strong and significant. Associations of BPD with other specific disorders were no longer significant or were considerably weakened. Conclusions Prevalence of BPD in the general population is much greater than previously recognized, equal prevalent among men and women, and associated with considerable mental and physical disability, especially among women. Unique and common factors may differentially contribute to disorder-specific comorbidity with BPD and some of these associations appear to be sex-specific. There is a need for future epidemiologic, clinical and genetically-informed studies to identify unique and common factors that underlie disorder-specific comorbidity with BPD. Important sex differences observed in rates of and associations with BPD can inform more focused, hypothesis-driven investigations of these factors. PMID:18426259
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.
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)
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)
Using Logarithms to Explore Power and Exponential Functions.
ERIC Educational Resources Information Center
Rahn, James R.; Berndes, Barry A.
1994-01-01
Discusses activities to help students make visual generalizations about power and exponential functions, methods to determine an approximate function represented by data using logarithms, hands-on activities, and student activity sheets. Includes a Pascal Turbo computer program which generates random numbers. (MKR)
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…
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.
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…
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.…
Imperfect Geometric Control and Overdamping for The Damped Wave Equation
NASA Astrophysics Data System (ADS)
Burq, Nicolas; Christianson, Hans
2015-05-01
We consider the damped wave equation on a manifold with imperfect geometric control. We show the sub-exponential energy decay estimate in (Christianson, J Funct Anal 258(3):1060-1065, 2010) is optimal in the case of one hyperbolic periodic geodesic. We show if the equation is overdamped, then the energy decays exponentially. Finally we show if the equation is overdamped but geometric control fails for one hyperbolic periodic geodesic, then nevertheless the energy decays exponentially.
Analysis of Small-Scale Atmospheric Gravity Waves Using UARS MLS Radiance Measurements
NASA Technical Reports Server (NTRS)
Wu, Dong L.
1999-01-01
Gravity waves play an important role in determining atmospheric circulation and small-scale mixing. Upper Atmosphere Research Satellite (UARS) Microwave Limb Sounder (MLS) 63-GHz radiances can be used to calculate small-scale wave variances at 30-80 km altitudes. The major results from this new data set are summarized in the following: (1) MLS radiance fluctuations are contributed mostly by gravity waves of small (about 100 km) horizontal and large (>10 km) vertical scales. (2) MLS observations show that variance enhancements are strongly correlated with the stratospheric polar vortices, tropospheric deep convection zones, and surface topography. (3) As expected for gravity wave propagation, the normalized wave variances grow exponentially with height in the stratosphere but saturate in the mesosphere. (4) The long-term variations of the wave variance are dominated by an annual cycle in the stratosphere and a semiannual cycle in the mesosphere. (5) Separate analyses of the ascending and descending measurements show that the variances are sensitive to wave propagation directions. The subtropical variances, which are associated with deep convection, are likely caused by the gravity waves that propagate upward and eastward in the westward background wind. Additional information contained in the original.
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.
New Analysis Methods In Photon Correlation Spectroscopy
NASA Astrophysics Data System (ADS)
Nash, P. J.; King, T. A.
1983-06-01
This paper describes the analysis of photon correlation spectroscopy decay curves by a significant new method based on the fitting of sums of positive exponentials by the S-exponential sum fitting method. The method fits a positive exponential sum to a given data set providing a best weighted least squares fit. No initial setting of any of the parameters is required and the number of exponential coefficients does not have to be preset in the program but is determined by the number of components apparent above the noise level. Results will be discussed for application in scattering systems which may be single or multiple component. Systems generating single, double or multiple exponential decay functions derived from computer simulation or photon correlation exneriments are considered and fitting analysis with varying noise levels.
Asymptotic Linear Stability of Solitary Water Waves
NASA Astrophysics Data System (ADS)
Pego, Robert L.; Sun, Shu-Ming
2016-06-01
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.
Stacked-Bloch-wave electron diffraction simulations using GPU acceleration.
Pennington, Robert S; Wang, Feng; Koch, Christoph T
2014-06-01
In this paper, we discuss the advantages for Bloch-wave simulations performed using graphics processing units (GPUs), based on approximating the matrix exponential directly instead of performing a matrix diagonalization. Our direct matrix-exponential algorithm yields a functionally identical electron scattering matrix to that generated with matrix diagonalization. Using the matrix-exponential scaling-and-squaring method with a Padé approximation, direct GPU-based matrix-exponential double-precision calculations are up to 20× faster than CPU-based calculations and up to approximately 70× faster than matrix diagonalization. We compare precision and runtime of scaling and squaring methods with either the Padé approximation or a Taylor expansion. We also discuss the stacked-Bloch-wave method, and show that our stacked-Bloch-wave implementation yields the same electron scattering matrix as traditional Bloch-wave matrix diagonalization.
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.
Fractional Noether Theorem Based on Extended Exponentially Fractional Integral
NASA Astrophysics Data System (ADS)
Long, Zi-Xuan; Zhang, Yi
2013-10-01
Based on the new type of fractional integral definition, namely extended exponentially fractional integral introduced by EI-Nabulsi, we study the fractional Noether symmetries and conserved quantities for both holonomic system and nonholonomic system. First, the fractional variational problem under the sense of extended exponentially fractional integral is established, the fractional d'Alembert-Lagrange principle is deduced, then the fractional Euler-Lagrange equations of holonomic system and the fractional Routh equations of nonholonomic system are given; secondly, the invariance of fractional Hamilton action under infinitesimal transformations of group is also discussed, the corresponding definitions and criteria of fractional Noether symmetric transformations and quasi-symmetric transformations are established; finally, the fractional Noether theorems for both holonomic system and nonholonomic system are explored. What's more, the relationship between the fractional Noether symmetry and conserved quantity are revealed.
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].
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.
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.
Least Squ Fit of Lin Combination of Exponential Decay
2001-07-06
This program fits by least squares a function which is a linear combination of real exponential decay functions. The function is y(k) = summation over j of a(j) * exp(-lambda(j) * k). Values of the independent variable (k) and the dependent variable y(k) are specified as input data. Weights may be specified as input information or set by the program (w(k) = 1/y(k) ).
Exponential growth of publications on carbon nanodots by Chinese authors
Wang, Junqing; Choi, Hak Soo
2015-01-01
Publication statistics was retrieved on carbon nanodots (C-dots) from 2004 up till 2014 using the web of ScienceTM search engine. The number of publications from Chinese authors increased exponentially during this period. Till 2014 China mainland authors contributed 47% of the total publications. Publications on pharmacology and toxicology lagged far behind the publications on chemistry and material science, indicating that research is not solidly moving toward the direction of application. PMID:26380753
Pricing turbo warrants under mixed-exponential jump diffusion model
NASA Astrophysics Data System (ADS)
Yu, Jianfeng; Xu, Weidong
2016-06-01
Turbo warrant is a special type of barrier options in which the rebate is calculated as another exotic option. In this paper, using Laplace transforms we obtain the valuation of turbo warrant under the mixed-exponential jump diffusion model, which is able to approximate any jump size distribution. The numerical Laplace inversion examples verify that the analytical solutions are accurate. The results of simulation confirm the argument that jump risk should not be ignored in the valuation of turbo warrants.
Linearized traveling wave amplifier with hard limiter characteristics
NASA Technical Reports Server (NTRS)
Kosmahl, H. G. (Inventor)
1986-01-01
A dynamic velocity taper is provided for a traveling wave tube with increased linearity to avoid intermodulation of signals being amplified. In a traveling wave tube, the slow wave structure is a helix including a sever. A dynamic velocity taper is provided by gradually reducing the spacing between the repeating elements of the slow wave structure which are the windings of the helix. The reduction which takes place coincides with the ouput point of helix. The spacing between the repeating elements of the slow wave structure is ideally at an exponential rate because the curve increases the point of maximum efficiency and power, at an exponential rate. A coupled cavity traveling wave tube having cavities is shown. The space between apertured discs is gradually reduced from 0.1% to 5% at an exponential rate. Output power (or efficiency) versus input power for a commercial tube is shown.
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."
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
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.
Chest wall velocity as a predictor of nonauditory blast injury in a complex wave environment.
Axelsson, H; Yelverton, J T
1996-03-01
Previous blast injury prediction criteria have been based on exposure to classic Friedlander or ideal blast waves. An ideal waveform is characterized by an instantaneous rise to a peak overpressure that decays exponentially to ambient pressure followed by a negative phase. The prediction criteria did not address injuries resulting from exposure to complex blast waves. It was difficult to establish a simple relationship between the two because complex blast waves typically consist of multiple shocks with variable frequency content and intensity that may be superimposed on a slow rising quasistatic pressure pulse. This paper deals with the application of a single degree of freedom mathematical model, originally developed to measure the response of the thorax to Friedlander waves, to calculate chest wall velocities resulting from various complex blast loads. Experimental results with sheep, exposed to complex blast waves in enclosures, demonstrated that there was a good relationship between the Adjusted Severity of Injury Index (which includes injury to the lungs, upper respiratory tract, gastrointestinal tract and solid intraabdominal organs) and the calculated peak inward chest wall velocity. In addition, there was a good correlation between these results and previously established Friedlander injury prediction curves. The velocity of complex blast waves was nearly the same as that of Friedlander waves for a given degree of injury: 3-4.5 meters/second for threshold injury, 8-12 meters/second for an LD1, and 12-17 meters/second for an LD50. PMID:8606417
NASA Astrophysics Data System (ADS)
Tan, Lun C.; Shao, X.; Sharma, A. S.; Fung, Shing F.
2011-07-01
Simultaneous observations by Cluster and Los Alamos National Laboratory (LANL) spacecraft and Canadian Array for Real-Time Investigations of Magnetic Activity and International Monitor for Auroral Geomagnetic Effects magnetometer arrays during a sudden storm commencement on 25 September 2001 show evidence of relativistic electron acceleration by compressional-mode ULF waves. The waves are driven by the quasiperiodic solar wind dynamical pressure fluctuations that continuously buffet the magnetosphere for ˜3 h. The compressional-mode ULF waves are identified by comparing the power of magnetic field magnitude fluctuations with the total magnetic field power. The radial distribution and azimuthal propagation of both toroidal and poloidal-mode ULF waves are derived from ground-based magnetometer data. The energetic electron fluxes measured by LANL show modulation of low-energy electrons and acceleration of high-energy electrons by the compressional poloidal-mode electric field oscillations. The energy threshold of accelerated electrons at the geosynchronous orbit is ˜0.4 MeV, which is roughly consistent with drift-resonant interaction of magnetospheric electrons with compressional-mode ULF waves.
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...
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.
Optical nonlinearity of liquid nanosuspensions: Kerr versus exponential model
NASA Astrophysics Data System (ADS)
Wright, E. M.; Lee, W. M.; Dholakia, K.; El-Ganainy, R.; Christodoulides, D. N.
2009-08-01
We report our experimental and theoretical progress towards elucidating the nonlinear optical response of nanosuspensions. To date, we have devised a fiber-optic variant of the Z-scan method to accurately measure the nonlinearity of liquid nanosuspensions. Furthermore, we shall show that the optical nonlinearity may be properly accounted theoretically by including both the virial coefficients for the soft-condensed matter system in addition to the exponential term, which does not account for particleparticle interactions, yielding an effective or renormalized Kerr effect in many cases.
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.
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.
Evidence for the exponential distribution of income in the USA
NASA Astrophysics Data System (ADS)
Drăgulescu, A.; Yakovenko, V. M.
2001-04-01
Using tax and census data, we demonstrate that the distribution of individual income in the USA is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data. From the individual income distribution, we derive the distribution function of income for families with two earners and show that it also agrees well with the data. The family data for the period 1947-1994 fit the Lorenz curve and Gini coefficient 3/8 = 0.375 calculated for two-earners families.
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
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.
Exponentially Slow Heating in Periodically Driven Many-Body Systems.
Abanin, Dmitry A; De Roeck, Wojciech; Huveneers, François
2015-12-18
We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that, for systems with local interactions, the energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including the decay of highly energetic excitations in cold atomic and solid-state systems. PMID:26722939
A Detailed Investigation into Near Degenerate Exponential Random Graphs
NASA Astrophysics Data System (ADS)
Yin, Mei
2016-07-01
The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better understand how phases transition between one another as tuning parameters vary. As the parameters cross certain lines, the model asymptotically transitions from a very sparse graph to a very dense graph, completely skipping all intermediate structures. We delve deeper into this near degenerate tendency and give an explicit characterization of the asymptotic graph structure as a function of the parameters.
Power-exponential velocity distributions in disordered porous media
NASA Astrophysics Data System (ADS)
Matyka, Maciej; Gołembiewski, Jarosław; Koza, Zbigniew
2016-01-01
Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power-exponential law controlled by an exponent γ and a shift parameter u0 and examine how these parameters depend on the porosity. We find that γ has a universal value 1 /2 at the percolation threshold and grows with the porosity, but never exceeds 2.
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.
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.
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.
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.
Freddi: Fast Rise Exponential Decay accretion Disk model Implementation
NASA Astrophysics Data System (ADS)
Lipunova, G. V.; Malanchev, K. L.
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.
Analytic comparison of Monte Carlo geometry splitting and exponential transform
Booth, T.E.
1991-01-01
Modern Monte Carlo particle transport codes such as MCNP offer the user a wide variety of variance reduction techniques. These techniques change the score distribution from the physical distribution. For example, if one counts the number of physical neutrons penetrating a (nonmultiplying) shield, then for each incident neutron, either one neutron penetrates the shield with probability p or zero neutrons penetrate with probability 1 {minus} p. The natural variance of this binomial process is p {minus} p{sup 2}. One may not know the value of p, but one knows the form of the score distribution. However, when variance reduction techniques are used, the form of the score distribution usually is not known. This is a significant problem when confidence intervals are desired. This paper considers a simple two-state transport problem and derives the score distribution when geometry splitting/Russian roulette is used and the score distribution when the exponential transform is used. The results provide a theoretical framework for understanding the sometime ill-behaved exponential transform results.
Beneficial Fitness Effects Are Not Exponential for Two Viruses
Rokyta, Darin R.; Beisel, Craig J.; Joyce, Paul; Ferris, Martin T.; Burch, Christina L.; Wichman, Holly A.
2008-01-01
The distribution of fitness effects for beneficial mutations is of paramount importance in determining the outcome of adaptation. It is generally assumed that fitness effects of beneficial mutations follow an exponential distribution, for example, in theoretical treatments of quantitative genetics, clonal interference, experimental evolution, and the adaptation of DNA sequences. This assumption has been justified by the statistical theory of extreme values, because the fitnesses conferred by beneficial mutations should represent samples from the extreme right tail of the fitness distribution. Yet in extreme value theory, there are three different limiting forms for right tails of distributions, and the exponential describes only those of distributions in the Gumbel domain of attraction. Using beneficial mutations from two viruses, we show for the first time that the Gumbel domain can be rejected in favor of a distribution with a right-truncated tail, thus providing evidence for an upper bound on fitness effects. Our data also violate the common assumption that small-effect beneficial mutations greatly outnumber those of large effect, as they are consistent with a uniform distribution of beneficial effects. PMID:18779988
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.
CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS
Shalizi, Cosma Rohilla; Rinaldo, Alessandro
2015-01-01
The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM’s expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses. PMID:26166910
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).
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.
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.
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)
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.
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…
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
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.
Exponential Clogging Time for a One Dimensional DLA
NASA Astrophysics Data System (ADS)
Benjamini, Itai; Hoffman, Christopher
2008-06-01
In this paper a simple DLA type model is analyzed. In (Benjamini and Yadin in Commun. Math. Phys. 279:187-223, [2008]) the standard DLA model from (Witten and Sander in Phys. Rev. B 27:5686-5697, [1983]) was considered on a cylinder and the arm growing phenomena was established, provided that the section of the cylinder has sufficiently fast mixing rate. When considering DLA on a cylinder it is natural to ask how many particles it takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we formulate a very simple DLA clogging model and establish an exponential lower bound on the number of particles arriving before clogging appears. In particular we possibly shed some light on why it takes so long to reach the bypass operation.
Exponential approximation for one-component Yukawa plasma
Hlushak, Stepan
2014-11-28
A theory based on the exponential approximation of the liquid-state theory is applied to study properties of several models of one-component Yukawa plasma characterized by different values of the screening parameter z. The results of the new theory are compared to the results of a conventional theory, which is based on the first-order mean spherical approximation, and to the results of a Monte Carlo simulation. The new theory shows improvements in the predictions for the thermodynamic and structural properties of Yukawa plasmas with high and intermediate values of the screening parameter, z, and coupling parameter, Γ. For low values of z and Γ, the new theory is comparable in accuracy to the conventional theory, which in turn agrees well with the results of the Monte Carlo simulation.
Green s Function Expansion for Exponentially Graded Elasticity
Abd El Azzim Mohamed, Omar M; Gray, Leonard J
2010-01-01
New computational forms are derived for the Green s function of an exponentially graded elastic material in three dimensions. By suitably expanding a term in the defining inverse Fourier integral, the displacement tensor can be written as a relatively simple analytic term, plus a single double integral that must be evaluated numerically. The integration is over a fixed finite domain, the integrand involves only elementary functions, and only low order Gauss quadrature is required for an accurate answer. Moreover, it is expected that this approach will allow a far simpler procedure for obtaining the first and second order derivatives needed in a boundary integral analysis. The new Green s function expressions have been tested by comparing with results from an earlier algorithm
Iterative exponential growth of stereo- and sequence-controlled polymers.
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.
Type II Hermite-Pade approximation to the exponential function
NASA Astrophysics Data System (ADS)
Kuijlaars, A. B. J.; Stahl, H.; van Assche, W.; Wielonsky, F.
2007-10-01
We obtain strong and uniform asymptotics in every domain of the complex plane for the scaled polynomials a(3nz), b(3nz), and c(3nz) where a, b, and c are the type II Hermite-Pade approximants to the exponential function of respective degrees 2n+2, 2n and 2n, defined by and as z-->0. Our analysis relies on a characterization of these polynomials in terms of a 3x3 matrix Riemann-Hilbert problem which, as a consequence of the famous Mahler relations, corresponds by a simple transformation to a similar Riemann-Hilbert problem for type I Hermite-Pade approximants. Due to this relation, the study that was performed in previous work, based on the Deift-Zhou steepest descent method for Riemann-Hilbert problems, can be reused to establish our present results.
Exponential and power laws in public procurement markets
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav; Skuhrovec, Jiri
2012-07-01
We analyze for the first time a unique public procurement database, which includes information about a number of bidders for a contract, a final price, an identification of a winner and an identification of a contracting authority for each of more than 40000 public procurements in the Czech Republic between 2006 and 2011, focusing on the distributional properties of the variables of interest. We uncover several scaling laws —the exponential law for the number of bidders, and the power laws for the total revenues and total spendings of the participating companies, which even follows Zipf's law for the 100 most spending institutions. We propose an analogy between extensive and non-extensive systems in physics and the public procurement market situations. Through an entropy maximization, such analogy yields some interesting results and policy implications with respect to the Maxwell-Boltzmann and Pareto distributions in the analyzed quantities.
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.
Coexistence of exponentially many chaotic spin-glass attractors.
Peleg, Y; Zigzag, M; Kinzel, W; Kanter, I
2011-12-01
A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N < 1, where P stands for the number of stored patterns, the chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.
On the role of exponential smoothing in circadian dosimetry.
Price, Luke L A
2014-01-01
The effects lighting has on health through modulation of circadian rhythms are becoming increasingly well documented. Data are still needed to show how light exposures are influenced by architecture and lighting design and circadian dosimetry analyses should provide duration, phase and amplitude measures of 24 h exposure profiles. Exponential smoothing is used to derive suitable metrics from 24 h light measurements collected from private dwellings. A further application of these modified exposure time series as physiological models of the light drive is discussed. Unlike previous light drive models, the dose rate persists into periods of darkness following exposures. Comparisons to long duration exposure studies suggest this type of persistent light drive model could be incorporated into contemporary physiological models of the human circadian oscillator. PMID:24749696
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.
The Unreasonable Effectiveness of Exponentially Suppressed Corrections in Preserving Information
NASA Astrophysics Data System (ADS)
Papadodimas, Kyriakos; Raju, Suvrat
2013-11-01
We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.
Static vortices in long Josephson junctions of exponentially varying width
NASA Astrophysics Data System (ADS)
Semerdjieva, E. G.; Boyadjiev, T. L.; Shukrinov, Yu. M.
2004-06-01
A numerical simulation is carried out for static vortices in a long Josephson junction with an exponentially varying width. At specified values of the parameters the corresponding boundary-value problem admits more than one solution. Each solution (distribution of the magnetic flux in the junction) is associated to a Sturm-Liouville problem, the smallest eigenvalue of which can be used, in a first approximation, to assess the stability of the vortex against relatively small spatiotemporal perturbations. The change in width of the junction leads to a renormalization of the magnetic flux in comparison with the case of a linear one-dimensional model. The influence of the model parameters on the stability of the states of the magnetic flux is investigated in detail, particularly that of the shape parameter. The critical curve of the junction is constructed from pieces of the critical curves for the different magnetic flux distributions having the highest critical currents for the given magnetic field.
Rational approximations to linear forms of exponentials and binomials
Chudnovsky, G. V.
1983-01-01
Mahler proved the following quantitative result supplementing the Lindemann-Weierstrass theorem: ǀΣi=0nCieriǀ > H-n-ε for any distinct rational numbers r0,r1,..., rn and rational integers C0,C1,...,Cn with H = max0≤i≤n ǀCiǀ. We improve Mahler's estimate by replacing exponentials eri by linearly independent linear forms Li = Σ Lijesij with rational Lij,siji = 0,1,...,n. Similar results are obtained for binomials (a/b)ri or Σ Lij(a/b)sij with integers a,b and logǀbǀ/logǀaǀ > 1 - ε. The simplest examples of new numbers with the irrationality exponent “2 + ε” are sinh 1 or sin 1. PMID:16593320
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. PMID:26961654
NASA Astrophysics Data System (ADS)
Kharazova, Yu. V.; Pavlenko, O. V.; Dudinskii, K. A.
2016-05-01
The relationship between the characteristics of seismic waves in the Western Caucasus and the geological-tectonic structure of the region is studied for identifying the specificity of seismic propagation in the mountainous regions with a complicated geological structure and forecasting the characteristics of the propagation from the geological and tectonic data. The interpretation is presented for the estimates of the Q-factor of the medium ( Q( f) ~ 55 f 0.9 in the region of Sochi and Q( f) ~ 90 f 0.7 in the region of Anapa), seismic wave enhancement in the upper crustal layers ( A( f) ~ 1), and peak ground acceleration residuals, which were previously determined from the records of the local earthquakes and show the distributions of local variations in the parameters of seismic wave radiation and propagation. The obtained characteristics are interpreted in the context of the up-to-date information about the tectonic, geological, and deep structure of the epicentral zones in the Western Caucasus and neighboring territory of the Black Sea. The discrepancies revealed in the low-frequency behavior of the Q-factor in the vicinities of Sochi and Anapa is accounted for by the spatial scale and character of tectonic dislocations of the rocks in these regions. The local variations in the parameters of seismic radiation and propagation are probably related to the geological features of the region such as the fault structures, including the thrusts, shatter zones, oblique seismic boundaries, variations in the thickness and consolidation of the sedimentary cover, as well as the peculiarities in the structure and material composition of the basement.
Photoelectron wave function in photoionization: plane wave or Coulomb wave?
Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I
2015-11-19
The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.
Photoelectron wave function in photoionization: plane wave or Coulomb wave?
Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I
2015-11-19
The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion. PMID:26509428
Eli Piasetzky
2012-09-01
The combination of inclusive and exclusive electron scattering data from JLab in kinematic regimes that were not reachable before, together with the analysis and interpretation of older data from hadronic reactions at BNL is finally revealing the details of short-range nucleon-nucleon correlations in nuclei. The most significant result is the demonstration of the dominance of correlated np pairs over pp and nn pairs. I will review these results, discuss them in terms of short-range tensor-force dominance and also discuss the connection to the EMC effect.
NASA Astrophysics Data System (ADS)
Nembach, Hans; Shaw, Justin; Boone, Carl; McMichael, Robert; Silva, Tom
2014-03-01
It was recently shown that modes localized at the edges are sensitive to presumed defects. We measured localized spin-wave modes of individual Ni80Fe20 nanomagnets (NMs) with sizes ranging from 100 nm to 400 nm via heterodyne magneto-optical microwave microscopy. Comparison of field-swept spectra with micromagnetic simulations allows for identification of the observed spin-wave modes. One of the modes, the ``center-mode'', extends throughout the NM. The lowest order (highest resonance field) ``end-modes'' are localized at the ends of the nanomagnet. As such, it is expected that the end modes are more susceptible to edge defects. Spectra from nominally identical nanomagnets show that the resonance fields of the two end-modes vary substantially between nanomagnets.. We measured the lateral shape of the NMs with scanning electron microscopy, and then used the measured shapes to simulate the mode-spectra, but shape distortions cannot explain the observed mode distortions. Sidewall angle, re-deposition, and mill-induced edge-damage might also be important to accurately model end-mode distortions.
NASA Technical Reports Server (NTRS)
Klemin, Alexander
1937-01-01
An airplane in steady rectilinear flight was assumed to experience an initial disturbance in rolling or yawing velocity. The equations of motion were solved to see if it was possible to hasten recovery of a stable airplane or to secure recovery of an unstable airplane by the application of a single lateral control following an exponential law. The sample computations indicate that, for initial disturbances complex in character, it would be difficult to secure correlation with any type of exponential control. The possibility is visualized that the two-control operation may seriously impair the ability to hasten recovery or counteract instability.
Vikulina, Anna S; Anissimov, Yuri G; Singh, Prateek; Prokopović, Vladimir Z; Uhlig, Katja; Jaeger, Magnus S; von Klitzing, Regine; Duschl, Claus; Volodkin, Dmitry
2016-03-21
In this study, the effect of temperature on the build-up of exponentially growing polyelectrolyte multilayer films was investigated. It aims at understanding the multilayer growth mechanism as crucially important for the fabrication of tailor-made multilayer films. Model poly(L-lysine)/hyaluronic acid (PLL/HA) multilayers were assembled in the temperature range of 25-85 °C by layer-by-layer deposition using a dipping method. The film growth switches from the exponential to the linear regime at the transition point as a result of limited polymer diffusion into the film. With the increase of the build-up temperature the film growth rate is enhanced in both regimes; the position of the transition point shifts to a higher number of deposition steps confirming the diffusion-mediated growth mechanism. Not only the faster polymer diffusion into the film but also more porous/permeable film structure are responsible for faster film growth at higher preparation temperature. The latter mechanism is assumed from analysis of the film growth rate upon switching of the preparation temperature during the film growth. Interestingly, the as-prepared films are equilibrated and remain intact (no swelling or shrinking) during temperature variation in the range of 25-45 °C. The average activation energy for complexation between PLL and HA in the multilayers calculated from the Arrhenius plot has been found to be about 0.3 kJ mol(-1) for monomers of PLL. Finally, the following processes known to be dependent on temperature are discussed with respect to the multilayer growth: (i) polymer diffusion, (ii) polymer conformational changes, and (iii) inter-polymer interactions. PMID:26911320
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.
Weathers, P J; Allen, M M
1978-03-01
Aphanocapsa 6308 metabolizes both NaHCO3 and Na2CO3. The short term incorporation (5-s) metabolic pattern and the patterns of incorporation of bicarbonate for exponential versus stationary phase cultures differ, however. Cells were equilibrated for 10 min in air and distilled water prior to injection of either NaH14CO3 at pH 8.0, or Na214CO3 at pH 11.0. Hot ethanol extracts were analyzed via paper chromatography and autoradiography for products of CO2 fixation. At 5 s, malate (51.5%) predominates slightly as a primary bicarbonate fixation product over 3-phosphoglycerate (40.3%); 3-phosphoglycerate is the primary product of carbonate fixation. At 60 s, the carbonate and bicarbonate labelling patterns are similar. Cells in stationary phase fix in 5 s a greater proportion of bicarbonate into malate (36% vs. 14% for 3-phosphoglycerate) than do cells in exponential growth. Likewise, 60 s incorporations show a large amount of bicarbonate fixed into aspartate (30.9%) in stationary phase cells over that of exponential phase (11.6%). These data suggest an operative C4 pathway for purposes not related to carbohydrate synthesis but rather as compensation for the incomplete tricarboxylic acid cycle in cyanobacteria. The enhancement of both aspartate fixation and CO2 fixation into citrulline in stationary phase correlates with an increase in cyanophycin granule production which requires both aspartate and arginine. PMID:417691
NASA Astrophysics Data System (ADS)
Kądzielawa, Andrzej P.; Bielas, Agata; Acquarone, Marcello; Biborski, Andrzej; Maśka, Maciej M.; Spałek, Józef
2014-12-01
The hydrogen molecules H2 and {{≤ft( {{H}2} \\right)}2} are analyzed with electronic correlations taken into account between the 1s electrons in an exact manner. The optimal single-particle Slater orbitals are evaluated in the correlated state of H2 by combining their variational determination with the diagonalization of the full Hamiltonian in the second-quantization language. All electron-ion coupling constants are determined explicitly and their relative importance is discussed. Sizable zero-point motion amplitude and the corresponding energy are then evaluated by taking into account the anharmonic contributions up to the ninth order in the relative displacement of the ions from their static equilibrium value. The applicability of the model to solid molecular hydrogen is briefly analyzed by calculating intermolecular microscopic parameters for the 2× {{H}2} rectangular configuration, as well its ground state energy.
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.
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.
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.
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
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
Stretched exponential relaxation of piezovoltages in wet bovine bone.
Xu, Lianyun; Hou, Zhende; Fu, Donghui; Qin, Qing-Hua; Wang, Yihan
2015-01-01
It is important to determine the amplitude and variation characteristics of piezovoltage in wet bone, which can, in turn, be taken as a basis for studying whether electrical signals induced by external forces can affect the growth of bone cells. This work measured the characteristics of piezoelectric effects under dynamic and static loading. The results show that the variations of piezovoltage in wet bone in both loading and load holding periods follow a stretched exponential relaxation law, and the relaxation time constants of the piezovoltages are much larger than those of dry bone. This finding means that the active time of piezovoltage in wet bone is much longer than that of dry bone. Regardless of the loading and load holding processes, continuously increasing deformation in wet bone caused piezoelectric charges to be continuously induced and increased the dielectric constant of wet bone along with the deformation process. In general, compared with piezovoltage in dry bone, that in wet bone had lower amplitude and could exist for a longer duration. It can be inferred, therefore, that piezoelectricity might create coupling with the streaming potential in bone by changing the thickness of the double electrode layer.
Exponential depression as a test of estimated decay parameters
NASA Astrophysics Data System (ADS)
Isenberg, Irvin; Small, Enoch W.
1982-09-01
A new test for judging the goodness of estimated decay parameters is presented. The test is based on the fact that a convolution is invariant under exponential depression. In the absence of significant error the estimated parameters will then remain constant as the degree of depression is varied over a finite range. In the presence of error, the parameters will vary. Up to now, no test has existed to see if moment index displacement corrects errors to a satisfactory extent in any given analysis. It has always been necessary to have some a priori knowledge of the type of error that limited the analysis. The test presented here removes that requirement. In addition, it is shown that the test performs better than a visual inspection of residual and autocorrelation plots in judging analyses when decays are closely spaced, even in the absence of nonrandom errors. The test is useful in accepting or rejecting analyses, with or without automatic error correction, in helping to discriminate between different models of sample decay, and in tuning pulse fluorometers for optimal performance. The test is, in principle, independent of the method of moments; it may be used with any method which needs only a small amount of computer time, and which is a statistically resistant procedure.
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.
Exponential repulsion improves structural predictability of molecular docking.
Bazgier, Václav; Berka, Karel; Otyepka, Michal; Banáš, Pavel
2016-10-30
Molecular docking is a powerful tool for theoretical prediction of the preferred conformation and orientation of small molecules within protein active sites. The obtained poses can be used for estimation of binding energies, which indicate the inhibition effect of designed inhibitors, and therefore might be used for in silico drug design. However, the evaluation of ligand binding affinity critically depends on successful prediction of the native binding mode. Contemporary docking methods are often based on scoring functions derived from molecular mechanical potentials. In such potentials, nonbonded interactions are typically represented by electrostatic interactions between atom-centered partial charges and standard 6-12 Lennard-Jones potential. Here, we present implementation and testing of a scoring function based on more physically justified exponential repulsion instead of the standard Lennard-Jones potential. We found that this scoring function significantly improved prediction of the native binding modes in proteins bearing narrow active sites such as serine proteases and kinases. © 2016 Wiley Periodicals, Inc. PMID:27620738
Stretched exponential relaxation of piezovoltages in wet bovine bone.
Xu, Lianyun; Hou, Zhende; Fu, Donghui; Qin, Qing-Hua; Wang, Yihan
2015-01-01
It is important to determine the amplitude and variation characteristics of piezovoltage in wet bone, which can, in turn, be taken as a basis for studying whether electrical signals induced by external forces can affect the growth of bone cells. This work measured the characteristics of piezoelectric effects under dynamic and static loading. The results show that the variations of piezovoltage in wet bone in both loading and load holding periods follow a stretched exponential relaxation law, and the relaxation time constants of the piezovoltages are much larger than those of dry bone. This finding means that the active time of piezovoltage in wet bone is much longer than that of dry bone. Regardless of the loading and load holding processes, continuously increasing deformation in wet bone caused piezoelectric charges to be continuously induced and increased the dielectric constant of wet bone along with the deformation process. In general, compared with piezovoltage in dry bone, that in wet bone had lower amplitude and could exist for a longer duration. It can be inferred, therefore, that piezoelectricity might create coupling with the streaming potential in bone by changing the thickness of the double electrode layer. PMID:25460408
NASA Astrophysics Data System (ADS)
Andreeva, Tatiana A.; Durgin, William W.
2011-12-01
An experimental study of the propagation of high-frequency acoustic waves through grid-generated turbulence by means of an ultrasound technique is discussed. Experimental data were obtained for ultrasonic wave propagation downstream of heated and non-heated grids in a wind tunnel. A semi-analytical acoustic propagation model that allows the determination of the spatial correlation functions of the flow field is developed based on the classical flowmeter equation and the statistics of the travel time of acoustic waves traveling through the kinematic and thermal turbulence. The basic flowmeter equation is reconsidered in order to take into account sound speed fluctuations and turbulent velocity fluctuations. It allows deriving an integral equation that relates the correlation functions of travel time, sound speed fluctuations and turbulent velocity fluctuations. Experimentally measured travel time statistics of data with and without grid heating are approximated by an exponential function and used to analytically solve the integral equation. The reconstructed correlation functions of the turbulent velocity and sound speed fluctuations are presented. The power spectral density of the turbulent velocity and sound speed fluctuations are calculated.
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
/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)
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.
ERIC Educational Resources Information Center
DeClark, Tom
2000-01-01
Presents an activity on waves that addresses the state standards and benchmarks of Michigan. Demonstrates waves and studies wave's medium, motion, and frequency. The activity is designed to address different learning styles. (YDS)
NASA Astrophysics Data System (ADS)
Chen, Bingling; Guo, Zhouyi
2008-12-01
Conventional analyses of OCT signal measurements resolve the signal decay profile in terms of single discrete exponential function with distinct exponential model. In symmetrical medium, mono-exponential decay function can appear to provide a well fit to OCT signal decay data, but the assuption of symmetrical components is essentially arbitrary and is often erroneous. Actually, the real biological samples such as tissue contained more complex components and are more heterogeneous. To avoid the shortages of mono-exponential decay function fitting to OCT signal decay data from heterogeneous biological tissues, a novel model of flexible exponential function has been developed. The main idea of the flexible exponential function modle is based on the assuption that heterogeneous biological tissue can be considered as a multi-layered tissue. Each layer is symmetric and the OCT signal decay profile in each layer obeies to a distinct single exponential function. If we can find out all the distinct single exponential function for each layer, the total flexible exponential function is determined by summing up all the single exponential functions. As pilot studies on the practical application of flexibleexponential decay model for monitoring and quantifying the diffusion of different analytes in turbid biological tissues in vivo by using OCT system, we demonstrate an experiment of monitoring of glucose diffusion in agar gel. In addition, the flexible-exponential decay model can provide a direct measure of the heterogeneity of the sample, and the analysis of turbid tissues OCT map using the flexible-exponential decay model can reveal subtle tissue differences that other models fail to show.
Zhu, Song; Shen, Yi
2013-02-01
This paper analyzes the robustness of global exponential stability of stochastic recurrent neural networks (SRNNs) subject to parameter uncertainty in connection weight matrices. Given a globally exponentially stable stochastic recurrent neural network, the problem to be addressed here is how much parameter uncertainty in the connection weight matrices that the neural network can remain to be globally exponentially stable. We characterize the upper bounds of the parameter uncertainty for the recurrent neural network to sustain global exponential stability. A numerical example is provided to illustrate the theoretical result.
NASA Astrophysics Data System (ADS)
Silenko, Alexander J.
2016-09-01
The exact exponential Foldy-Wouthuysen transformation operator applicable for a particle with an arbitrary spin is derived. It can be successfully utilized for verifying any Foldy-Wouthuysen transformation method based on the exponential operator. When a verified method is relativistic, the relativistic exponential operator should be expanded in the semirelativistic power series. The obtained exponential operator can be also used for a derivation of the Foldy-Wouthuysen Hamiltonian and its comparison with Hamiltonians found by other methods. This procedure makes it possible to check the validity of any other method of the Foldy-Wouthuysen transformation.
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. PMID:26657239
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. PMID:26657239
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.
Incompressible magnetohydrodynamic surface waves - Nonlinear aspects
NASA Technical Reports Server (NTRS)
Hollweg, Joseph V.
1987-01-01
The nonlinear properties of MHD surface waves in the solar atmosphere are investigated analytically, assuming that the fluid is incompressible and that the waves are confined to a single surface, with semiinfinite regions on both sides. The governing equations are derived in detail, and qualitative results are presented in a graph. For propagating waves, second-order terms in the wave amplitude are found to lead to wave steepening at leading or trailing edges, the steepening rate becoming very large as the threshold for the linear Kelvin-Helmholtz instability is approached. Second-order effects on standing waves include crest and trough sharpening (increasing with time), a current independent of distance on the surface but decreasing exponentially with distance from the surface, and pressure-field fluctuations of infinite extent. It is suggested that these effects could account for a large fraction of solar-atmosphere heating.
Global stability of travelling wave fronts for non-local diffusion equations with delay
NASA Astrophysics Data System (ADS)
Wang, X.; Lv, G.
2014-04-01
This paper is concerned with the global stability of travelling wave fronts for non-local diffusion equations with delay. We prove that the non-critical travelling wave fronts are globally exponentially stable under perturbations in some exponentially weighted L^\\infty-spaces. Moreover, we obtain the decay rates of \\sup_{x\\in{R}}\\vert u(x,t)-\\varphi(x+ct)\\vert using weighted energy estimates.
Standing waves along a microwave generated surface wave plasma
NASA Technical Reports Server (NTRS)
Rogers, J.; Asmussen, J.
1982-01-01
Two surface wave plasma columns, generated by microwave power in argon at gas pressures of 0.05 torr to 330 torr, interact in the same discharge tube to form standing surface waves. Radial electric field and azimuthal magnetic field outside the discharge tube are measured to be 90 deg out of phase with respect to axial position and to decay exponentially with radial distance from the tube axis. Maximum light emission occurs at the position of maximum azimuthal magnetic field and minimum radial electric field. Electron temperature and density are measured at low pressures with double probes inserted into the plasma at a null of radial electric field. Measured electron densities compare well with those predicted by Gould-Trivelpiece surface wave theory.
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.
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)
Putra, Andika; Iskandar, Alexander A.; Tjia, May-On
2011-08-01
A study is carried out to investigate the possible enhancement of photonic crystal (PC) microcavity performance induced by geometrical and permittivity variations in relation to localization of the associated evanescent Bloch wave. The study is focused on PCs of hexagonally packed dielectric rods. A numerical scheme formulated on the basis of Green's function method with multipole expansion approximation is employed to exhibit explicitly the exponential growth curves of the spontaneous emission rate (F) and quality factor (Q) of the cavity with respect to increasing number of surrounding layers (N), which are characterized by their growth rates kF. While the same exponential growth pattern is found for PCs with different rod parameters, the associated growth rates do show distinct and significant differences, implying that an appropriate choice of the rod parameters may produce a large performance enhancement for the microcavity or achieve the same performance with a largely reduced surrounding layer number. Meanwhile, the corresponding spatial decay constants of the evanescent Bloch waves, represented by its smallest Im(k) in the photonic gap, are calculated by means of the extended plane-wave expansion method. The resulting smallest values of Im(k) show their strong correlation with kF as characterized by their linear relation. The study further demonstrates that a judicious choice of the defect rod parameters may also give rise to a remarkable performance enhancement of the microcavity, even at a reduced number of surrounding rod layers. Remarkably, the [kF,Im(k)] values of all PCs considered are located on the same linear correlation line.
Preibisch, Christine; Volz, Steffen; Anti, Sandra; Deichmann, Ralf
2008-10-01
Several water content mapping techniques are based on the acquisition of multiple gradient echoes (GE) with different echo times (TE). However, in the presence of linear magnetic field gradients G(susc) the signal decay is no longer exponential but in the case of a rectangular slice profile weighted by a sinc function, giving rise to erroneous initial amplitudes S(0) in monoexponential fitting. Generally, it can be shown that the signal decay is weighted by the time profile of the excitation pulse. Thus, for an excitation pulse with an exponential time profile, i.e., a Lorentzian slice profile, the signal decay remains exponential and exponential fitting still yields the correct amplitude S(0). Multiecho GE images of a gel phantom and five human volunteers were acquired at 3 T using a sinc-shaped and an exponential excitation pulse. In addition, simulations were performed to investigate the influence of saturation effects due to distortion of the ideal Lorentzian slice profile. A considerable overestimation of S(0) when using a sinc-shaped excitation pulse was observed. Errors were greatly reduced with an exponential excitation pulse. We thus propose the use of excitation pulses with exponential time profile to obtain accurate estimates for S(0) from exponential fitting. PMID:18816811
Pu, Hao; Liu, Yanmin; Jiang, Haijun; Hu, Cheng
2015-08-01
In this paper, the globally exponential synchronization of delayed fuzzy cellular neural networks with nonlinear impulsive effects are concerned. By utilizing inequality techniques and Lyapunov functional method, some sufficient conditions on the exponential synchronization are obtained based on [Formula: see text]-norm. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.
Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth
ERIC Educational Resources Information Center
Castillo-Garsow, Carlos
2010-01-01
Both Thompson and the duo of Confrey and Smith describe how students might be taught to build "ways of thinking" about exponential behavior by coordinating the covariation of two changing quantities, however, these authors build exponential behavior from different meanings of covariation. Confrey and Smith advocate beginning with discrete additive…
An approximation theorem for entire functions of exponential type and stability of zero sequences
NASA Astrophysics Data System (ADS)
Khabibullin, B. N.
2004-02-01
Let L be an entire function of exponential type in \\mathbb C with indicator function h_L; let \\Lambda=\\{\\lambda_n\\}, n=1,2,\\dots, be a subsequence of zeros of the entire function of exponential type L\
An exact formulation of the time-ordered exponential using path-sums
Giscard, P.-L.; Lui, K.; Thwaite, S. J.; Jaksch, D.
2015-05-15
We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitude of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.
Exponential parameterization of neutrino mixing matrix with account of CP-violation data
NASA Astrophysics Data System (ADS)
Zhukovsky, Konstantin; Melazzini, Francisco
2016-08-01
The exponential parameterization of the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrinos is discussed. The exponential form allows easy factorization and separate analysis of the CP-violating and Majorana terms. Based upon the recent experimental data on the neutrino mixing, the values for the exponential parameterization matrix for neutrinos are determined. The matrix entries for the pure rotational part in charge of the mixing without CP violation are derived. The complementarity hypothesis for quarks and neutrinos is demonstrated. A comparison of the results based on most recent and on old data is presented. The CP-violating parameter value is estimated, based on the so far imprecise experimental indications, regarding CP violation for neutrinos. The unitarity of the exponential parameterization and the CP-violating term transform is confirmed. The transform of the neutrino mass state vector by the exponential matrix with account of CP violation is shown.
The importance of the pre-exponential factor in semiclassical molecular dynamics
NASA Astrophysics Data System (ADS)
Di Liberto, Giovanni; Ceotto, Michele
2016-10-01
This paper deals with the critical issue of approximating the pre-exponential factor in semiclassical molecular dynamics. The pre-exponential factor is important because it accounts for the quantum contribution to the semiclassical propagator of the classical Feynman path fluctuations. Pre-exponential factor approximations are necessary when chaotic or complex systems are simulated. We introduced pre-exponential factor approximations based either on analytical considerations or numerical regularization. The approximations are tested for power spectrum calculations of more and more chaotic model systems and on several molecules, for which exact quantum mechanical values are available. The results show that the pre-exponential factor approximations introduced are accurate enough to be safely employed for semiclassical simulations of complex systems.
Survival analysis approach to account for non-exponential decay rate effects in lifetime experiments
NASA Astrophysics Data System (ADS)
Coakley, K. J.; Dewey, M. S.; Huber, M. G.; Huffer, C. R.; Huffman, P. R.; Marley, D. E.; Mumm, H. P.; O`Shaughnessy, C. M.; Schelhammer, K. W.; Thompson, A. K.; Yue, A. T.
2016-03-01
In experiments that measure the lifetime of trapped particles, in addition to loss mechanisms with exponential survival probability functions, particles can be lost by mechanisms with non-exponential survival probability functions. Failure to account for such loss mechanisms produces systematic measurement error and associated systematic uncertainties in these measurements. In this work, we develop a general competing risks survival analysis method to account for the joint effect of loss mechanisms with either exponential or non-exponential survival probability functions, and a method to quantify the size of systematic effects and associated uncertainties for lifetime estimates. As a case study, we apply our survival analysis formalism and method to the Ultra Cold Neutron lifetime experiment at NIST. In this experiment, neutrons can escape a magnetic trap before they decay due to a wall loss mechanism with an associated non-exponential survival probability function.
Gaimster, Hannah; Summers, David
2015-01-01
During the transition from exponential to stationary phase E. coli produces a substantial quantity of the small, aromatic signalling molecule indole. In LB medium the supernatant indole concentration reaches a maximum of 0.5-1 mM. At this concentration indole has been implicated in many processes inducing acid resistance and the modulation of virulence. It has recently been shown that cell-associated indole transiently reaches a very high concentration (approx. 60 mM) during stationary phase entry, presumably because indole is being produced more rapidly than it can leave the cell. It is proposed that this indole pulse inhibits growth and cell division, causing the culture to enter stationary phase before nutrients are completely exhausted, with benefits for survival in long-term stationary phase. This study asks how E. coli cells rapidly upregulate indole production during stationary phase entry and why the indole pulse has a duration of only 10-15 min. We find that at the start of the pulse tryptophanase synthesis is triggered by glucose depletion and that this is correlates with the up-regulation of indole synthesis. The magnitude and duration of the resulting indole pulse are dependent upon the availability of exogenous tryptophan. Indole production stops when all the available tryptophan is depleted and the cell-associated indole equilibrates with the supernatant.
Gaimster, Hannah; Summers, David
2015-01-01
During the transition from exponential to stationary phase E. coli produces a substantial quantity of the small, aromatic signalling molecule indole. In LB medium the supernatant indole concentration reaches a maximum of 0.5–1 mM. At this concentration indole has been implicated in many processes inducing acid resistance and the modulation of virulence. It has recently been shown that cell-associated indole transiently reaches a very high concentration (approx. 60 mM) during stationary phase entry, presumably because indole is being produced more rapidly than it can leave the cell. It is proposed that this indole pulse inhibits growth and cell division, causing the culture to enter stationary phase before nutrients are completely exhausted, with benefits for survival in long-term stationary phase. This study asks how E. coli cells rapidly upregulate indole production during stationary phase entry and why the indole pulse has a duration of only 10–15 min. We find that at the start of the pulse tryptophanase synthesis is triggered by glucose depletion and that this is correlates with the up-regulation of indole synthesis. The magnitude and duration of the resulting indole pulse are dependent upon the availability of exogenous tryptophan. Indole production stops when all the available tryptophan is depleted and the cell-associated indole equilibrates with the supernatant. PMID:26332864
NASA Astrophysics Data System (ADS)
Lopes, Sílvia R. C.; Prass, Taiane S.
2014-05-01
Here we present a theoretical study on the main properties of Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedastic (FIEGARCH) processes. We analyze the conditions for the existence, the invertibility, the stationarity and the ergodicity of these processes. We prove that, if { is a FIEGARCH(p,d,q) process then, under mild conditions, { is an ARFIMA(q,d,0) with correlated innovations, that is, an autoregressive fractionally integrated moving average process. The convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes { and { are discussed. Expressions for the kurtosis and the asymmetry measures for any stationary FIEGARCH(p,d,q) process are also derived. The h-step ahead forecast for the processes {, { and { are given with their respective mean square error of forecast. The work also presents a Monte Carlo simulation study showing how to generate, estimate and forecast based on six different FIEGARCH models. The forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models (namely, ARCH-type models) and radial basis models is compared through an empirical application to Brazilian stock market exchange index.
Vibrational energies for HFCO using a neural network sum of exponentials potential energy surface.
Pradhan, Ekadashi; Brown, Alex
2016-05-01
A six-dimensional potential energy surface (PES) for formyl fluoride (HFCO) is fit in a sum-of-products form using neural network exponential fitting functions. The ab initio data upon which the fit is based were computed at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations [CCSD(T)-F12]/cc-pVTZ-F12 level of theory. The PES fit is accurate (RMSE = 10 cm(-1)) up to 10 000 cm(-1) above the zero point energy and covers most of the experimentally measured IR data. The PES is validated by computing vibrational energies for both HFCO and deuterated formyl fluoride (DFCO) using block improved relaxation with the multi-configuration time dependent Hartree approach. The frequencies of the fundamental modes, and all other vibrational states up to 5000 cm(-1) above the zero-point energy, are more accurate than those obtained from the previous MP2-based PES. The vibrational frequencies obtained on the PES are compared to anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory obtained using second-order vibrational perturbation theory. The new PES will be useful for quantum dynamics simulations for both HFCO and DFCO, e.g., studies of intramolecular vibrational redistribution leading to unimolecular dissociation and its laser control.
Vibrational energies for HFCO using a neural network sum of exponentials potential energy surface.
Pradhan, Ekadashi; Brown, Alex
2016-05-01
A six-dimensional potential energy surface (PES) for formyl fluoride (HFCO) is fit in a sum-of-products form using neural network exponential fitting functions. The ab initio data upon which the fit is based were computed at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations [CCSD(T)-F12]/cc-pVTZ-F12 level of theory. The PES fit is accurate (RMSE = 10 cm(-1)) up to 10 000 cm(-1) above the zero point energy and covers most of the experimentally measured IR data. The PES is validated by computing vibrational energies for both HFCO and deuterated formyl fluoride (DFCO) using block improved relaxation with the multi-configuration time dependent Hartree approach. The frequencies of the fundamental modes, and all other vibrational states up to 5000 cm(-1) above the zero-point energy, are more accurate than those obtained from the previous MP2-based PES. The vibrational frequencies obtained on the PES are compared to anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory obtained using second-order vibrational perturbation theory. The new PES will be useful for quantum dynamics simulations for both HFCO and DFCO, e.g., studies of intramolecular vibrational redistribution leading to unimolecular dissociation and its laser control. PMID:27155638
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.
Morales, Esteban; de Leon, John Mark S.; Abdollahi, Niloufar; Yu, Fei; Nouri-Mahdavi, Kouros; Caprioli, Joseph
2016-01-01
Purpose The study was conducted to evaluate threshold smoothing algorithms to enhance prediction of the rates of visual field (VF) worsening in glaucoma. Methods We studied 798 patients with primary open-angle glaucoma and 6 or more years of follow-up who underwent 8 or more VF examinations. Thresholds at each VF location for the first 4 years or first half of the follow-up time (whichever was greater) were smoothed with clusters defined by the nearest neighbor (NN), Garway-Heath, Glaucoma Hemifield Test (GHT), and weighting by the correlation of rates at all other VF locations. Thresholds were regressed with a pointwise exponential regression (PER) model and a pointwise linear regression (PLR) model. Smaller root mean square error (RMSE) values of the differences between the observed and the predicted thresholds at last two follow-ups indicated better model predictions. Results The mean (SD) follow-up times for the smoothing and prediction phase were 5.3 (1.5) and 10.5 (3.9) years. The mean RMSE values for the PER and PLR models were unsmoothed data, 6.09 and 6.55; NN, 3.40 and 3.42; Garway-Heath, 3.47 and 3.48; GHT, 3.57 and 3.74; and correlation of rates, 3.59 and 3.64. Conclusions Smoothed VF data predicted better than unsmoothed data. Nearest neighbor provided the best predictions; PER also predicted consistently more accurately than PLR. Smoothing algorithms should be used when forecasting VF results with PER or PLR. Translational Relevance The application of smoothing algorithms on VF data can improve forecasting in VF points to assist in treatment decisions. PMID:26998405
Spurious long-range entanglement and replica correlation length
NASA Astrophysics Data System (ADS)
Zou, Liujun; Haah, Jeongwan
2016-08-01
Topological entanglement entropy has been regarded as a smoking-gun signature of topological order in two dimensions, capturing the total quantum dimension of the topological particle content. An extrapolation method on cylinders has been used frequently to measure the topological entanglement entropy. Here, we show that a class of short-range entangled 2D states, when put on an infinite cylinder of circumference L , exhibits the entanglement Rényi entropy of any integer index α ≥2 that obeys Sα=a L -γ , where a ,γ >0 . Under the extrapolation method, the subleading term γ would be identified as the topological entanglement entropy, which is spurious. A nonzero γ is always present if the 2D state reduces to a certain symmetry-protected topological 1D state, upon disentangling spins that are far from the entanglement cut. The internal symmetry that stabilizes γ >0 is not necessarily a symmetry of the 2D state, but should be present after the disentangling reduction. If the symmetry is absent, γ decays exponentially in L with a characteristic length, termed as a replica correlation length, which can be arbitrarily large compared to the two-point correlation length of the 2D state. We propose a simple numerical procedure to measure the replica correlation length through replica correlation functions. We also calculate the replica correlation functions for representative wave functions of Abelian discrete gauge theories and the double semion theory in 2D, to show that they decay abruptly to zero. This supports a conjecture that the replica correlation length being small implies that the subleading term from the extrapolation method determines the total quantum dimension.
Sivakumar, Vidyashankar; Banerjee, Arindam; Ravikumar, Pradeep
2016-01-01
We consider the problem of high-dimensional structured estimation with norm-regularized estimators, such as Lasso, when the design matrix and noise are drawn from sub-exponential distributions. Existing results only consider sub-Gaussian designs and noise, and both the sample complexity and non-asymptotic estimation error have been shown to depend on the Gaussian width of suitable sets. In contrast, for the sub-exponential setting, we show that the sample complexity and the estimation error will depend on the exponential width of the corresponding sets, and the analysis holds for any norm. Further, using generic chaining, we show that the exponential width for any set will be at most logp times the Gaussian width of the set, yielding Gaussian width based results even for the sub-exponential case. Further, for certain popular estimators, viz Lasso and Group Lasso, using a VC-dimension based analysis, we show that the sample complexity will in fact be the same order as Gaussian designs. Our general analysis and results are the first in the sub-exponential setting, and are readily applicable to special sub-exponential families such as log-concave and extreme-value distributions. PMID:27563230
McNair, James N; Newbold, J Denis
2012-05-01
Most ecological studies of particle transport in streams that focus on fine particulate organic matter or benthic invertebrates use the Exponential Settling Model (ESM) to characterize the longitudinal pattern of particle settling on the bed. The ESM predicts that if particles are released into a stream, the proportion that have not yet settled will decline exponentially with transport time or distance and will be independent of the release elevation above the bed. To date, no credible basis in fluid mechanics has been established for this model, nor has it been rigorously tested against more-mechanistic alternative models. One alternative is the Local Exchange Model (LEM), which is a stochastic advection-diffusion model that includes both longitudinal and vertical spatial dimensions and is based on classical fluid mechanics. The LEM predicts that particle settling will be non-exponential in the near field but will become exponential in the far field, providing a new theoretical justification for far-field exponential settling that is based on plausible fluid mechanics. We review properties of the ESM and LEM and compare these with available empirical evidence. Most evidence supports the prediction of both models that settling will be exponential in the far field but contradicts the ESM's prediction that a single exponential distribution will hold for all transport times and distances.
A study of physician collaborations through social network and exponential random graph
2013-01-01
Background Physician collaboration, which evolves among physicians during the course of providing healthcare services to hospitalised patients, has been seen crucial to effective patient outcomes in healthcare organisations and hospitals. This study aims to explore physician collaborations using measures of social network analysis (SNA) and exponential random graph (ERG) model. Methods Based on the underlying assumption that collaborations evolve among physicians when they visit a common hospitalised patient, this study first proposes an approach to map collaboration network among physicians from the details of their visits to patients. This paper terms this network as physician collaboration network (PCN). Second, SNA measures of degree centralisation, betweenness centralisation and density are used to examine the impact of SNA measures on hospitalisation cost and readmission rate. As a control variable, the impact of patient age on the relation between network measures (i.e. degree centralisation, betweenness centralisation and density) and hospital outcome variables (i.e. hospitalisation cost and readmission rate) are also explored. Finally, ERG models are developed to identify micro-level structural properties of (i) high-cost versus low-cost PCN; and (ii) high-readmission rate versus low-readmission rate PCN. An electronic health insurance claim dataset of a very large Australian health insurance organisation is utilised to construct and explore PCN in this study. Results It is revealed that the density of PCN is positively correlated with hospitalisation cost and readmission rate. In contrast, betweenness centralisation is found negatively correlated with hospitalisation cost and readmission rate. Degree centralisation shows a negative correlation with readmission rate, but does not show any correlation with hospitalisation cost. Patient age does not have any impact for the relation of SNA measures with hospitalisation cost and hospital readmission rate. The
Movement of boulders and megagravel by storm waves
NASA Astrophysics Data System (ADS)
Cox, Rónadh; Jahn, Kalle L.; Watkins, Oona G.
2016-04-01
Coastal boulder deposits along Ireland's west coast - which include megagravel with masses in the 100s of tonnes near sea level, and boulders > 1 t at locations up to 50 m above high water (AHW) - record extreme wave events. As their scale and elevation seem inconsistent with our current understanding of storm wave hydrodynamics, and because the deposits have been largely inactive in the last decade or so (the time span over which they have been studied), there has been controversy over whether they are moved by storms or whether they are relict tsunami deposits. Recent data acquisition shows definitively that these rocks are moved during storms. Using repeat photography of sites on the Aran Islands and on the mainland (images taken before and after the severe storms of winter 2013-2014) we documented movement of >1100 clasts, 84 of which were ≥ 20 t, and 16 of which were ≥ 50 t. The highest elevation at which we recorded movement was 25 m AHW, and the largest clast moved at this elevation was ~5.5 t. Larger clasts (up to ~400 t) moved at lower elevations. Horizontal transport distances exceeded 100 m in some instances, including large dislocations of some very large clasts (e.g. a ~210 t block that moved 23 m inland). The large dataset allows us to investigate relationships between clast movements and topography. For each site, the largest clast moved represents an upper limit on the transport capacity at that site (for that set of storms). We find an inverse correlation between mass transported and height above high water, as well as a (counter-intuitive) positive correlation between boulder mass and distance inland. The strongest correlation, however, is an exponential relationship between mass and average coastal slope: the largest clasts moved over the most gently sloping terrain. We use the term "waves" quite loosely. The clasts were transported by overland flow of ocean waters activated by storm systems, but we cannot determine whether the flow was due
C.P.Oertel; J.R.Giles
2009-11-01
Characterization of radionuclide concentrations in soil profiles requires accurate evaluation of the depth distribution of the concentrations as measured by gamma emissions. An ongoing study based on 137Cs activity has shown that such concentration data generally follow an exponential trend when the fraction of radioactivity below depth is plotted against the depth. The slope of the exponential regression fit is defined as alpha/rho, the depth profile parameter. A weighted exponential regression procedure has been developed to compute a mean ??? for a group of related soil samples. Regression results from different areas or from different time periods can be used to compare representative radionuclide concentrations for the specified groupings.
Freitas, R. J.; Shimakawa, K.; Wagner, T.
2014-01-07
The article discusses the dynamics of photoinduced defect creations (PDC) in amorphous chalcogenides, which is described by the stretched exponential function (SEF), while the well known photodarkening (PD) and photoinduced volume expansion (PVE) are governed only by the exponential function. It is shown that the exponential distribution of the thermal activation barrier produces the SEF in PDC, suggesting that thermal energy, as well as photon energy, is incorporated in PDC mechanisms. The differences in dynamics among three major photoinduced effects (PD, PVE, and PDC) in amorphous chalcogenides are now well understood.
Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation. Part 1; Analysis
NASA Technical Reports Server (NTRS)
Choi, Sung R.; Nemeth, Noel N.; Gyekenyesi, John P.
2002-01-01
Extensive slow-crack-growth (SCG) analysis was made using a primary exponential crack-velocity formulation under three widely used load configurations: constant stress rate, constant stress, and cyclic stress. Although the use of the exponential formulation in determining SCG parameters of a material requires somewhat inconvenient numerical procedures, the resulting solutions presented gave almost the same degree of simplicity in both data analysis and experiments as did the power-law formulation. However, the fact that the inert strength of a material should be known in advance to determine the corresponding SCG parameters was a major drawback of the exponential formulation as compared with the power-law formulation.
Evanescent Waves Nuclear Magnetic Resonance
Halidi, El Mohamed; Nativel, Eric; Akel, Mohamad; Kenouche, Samir; Coillot, Christophe; Alibert, Eric; Jabakhanji, Bilal; Schimpf, Remy; Zanca, Michel; Stein, Paul; Goze-Bac, Christophe
2016-01-01
Nuclear Magnetic Resonance spectroscopy and imaging can be classified as inductive techniques working in the near- to far-field regimes. We investigate an alternative capacitive detection with the use of micrometer sized probes positioned at sub wavelength distances of the sample in order to characterize and model evanescent electromagnetic fields originating from NMR phenomenon. We report that in this experimental configuration the available NMR signal is one order of magnitude larger and follows an exponential decay inversely proportional to the size of the emitters. Those investigations open a new road to a better understanding of the evanescent waves component in NMR with the opportunity to perform localized spectroscopy and imaging. PMID:26751800
Evanescent Waves Nuclear Magnetic Resonance.
Halidi, El Mohamed; Nativel, Eric; Akel, Mohamad; Kenouche, Samir; Coillot, Christophe; Alibert, Eric; Jabakhanji, Bilal; Schimpf, Remy; Zanca, Michel; Stein, Paul; Goze-Bac, Christophe
2016-01-01
Nuclear Magnetic Resonance spectroscopy and imaging can be classified as inductive techniques working in the near- to far-field regimes. We investigate an alternative capacitive detection with the use of micrometer sized probes positioned at sub wavelength distances of the sample in order to characterize and model evanescent electromagnetic fields originating from NMR phenomenon. We report that in this experimental configuration the available NMR signal is one order of magnitude larger and follows an exponential decay inversely proportional to the size of the emitters. Those investigations open a new road to a better understanding of the evanescent waves component in NMR with the opportunity to perform localized spectroscopy and imaging.
Resolution properties of the Fourier method for discontinuous waves
NASA Technical Reports Server (NTRS)
Gottlieb, David; Shu, Chi-Wang
1992-01-01
In this paper we discuss the wave-resolution properties of the Fourier approximations of a wave function with discontinuities. It is well known that a minimum of two points per wave is needed to resolve a periodic wave function using Fourier expansions. For Chebyshev approximations of a wave function, a minimum of pi points per wave is needed. Here we obtain an estimate for the minimum number of points per wave to resolve a discontinuous wave based on its Fourier coefficients. In our recent work on overcoming the Gibbs phenomenon, we have shown that the Fourier coefficients of a discontinuous function contain enough information to reconstruct with exponential accuracy the coefficient of a rapidly converging Gegenbauer expansion. We therefore study the resolution properties of a Gegenbauer expansion where both the number of terms and the order increase.
Atmospheric Science Data Center
2013-04-19
article title: Gravity Waves Ripple over Marine Stratocumulus Clouds ... Imaging SpectroRadiometer (MISR), a fingerprint-like gravity wave feature occurs over a deck of marine stratocumulus clouds. Similar ... that occur when a pebble is thrown into a still pond, such "gravity waves" sometimes appear when the relatively stable and stratified air ...
NASA Astrophysics Data System (ADS)
Shibahara, M.; Fukuda, K.; Liu, Q. S.; Hata, K.
2016-06-01
Steady and transient heat transfer coefficients for water flowing in small tubes with exponentially increasing heat inputs were measured. Platinum tubes with inner diameters of 1.0 and 2.0 mm were used as test tubes, which were mounted vertically in the experimental water loop. In the experiment, the upward flow velocity ranged from 2 to 16 m/s, and the corresponding Reynolds numbers ranged from 4.77 × 103 to 9.16 × 104 at the inlet liquid temperatures ranged from 298 to 343 K. The heat generation rate exponentially increased with the function. The period of the heat generation rate ranged from 24 ms to 17.5 s. Experimental results indicate that steady heat transfer coefficients decreased with the increase in the inner diameter of the small tube. Moreover, the ratio of bulk viscosity to near-wall viscosity of water increased with the rise in surface temperature of the vertical tube. From the experimental data, correlations of steady-state heat transfer for inner diameters of 1.0 and 2.0 mm were obtained. The heat transfer coefficient increased with decreasing the period of the heat generation rate as the flow velocity decreased. Moreover, the Nusselt number under the transient condition was affected by the Fourier number and the Reynolds number.
Kerschensteiner, Daniel
2016-01-01
Spontaneous activity patterns propagate through many parts of the developing nervous system and shape the wiring of emerging circuits. Prior to vision, waves of activity originating in the retina propagate through the lateral geniculate nucleus (LGN) of the thalamus to primary visual cortex (V1). Retinal waves have been shown to instruct the wiring of ganglion cell axons in LGN and of thalamocortical axons in V1 via correlation-based plasticity rules. Across species, retinal waves mature in three stereotypic stages (I–III), in which distinct circuit mechanisms give rise to unique activity patterns that serve specific functions in visual system refinement. Here, I review insights into the patterns, mechanisms, and functions of stage III retinal waves, which rely on glutamatergic signaling. As glutamatergic waves spread across the retina, neighboring ganglion cells with opposite light responses (ON vs. OFF) are activated sequentially. Recent studies identified lateral excitatory networks in the inner retina that generate and propagate glutamatergic waves, and vertical inhibitory networks that desynchronize the activity of ON and OFF cells in the wavefront. Stage III wave activity patterns may help segregate axons of ON and OFF ganglion cells in the LGN, and could contribute to the emergence of orientation selectivity in V1. PMID:27242446
Sreenivasan, R; Joshi, P G; Joshi, N B
1994-11-01
Plateau phase glioblastoma (U 87MG) cells were found more photosensitive than the exponentially growing cells. In both phases of growth, the photosensitivity showed further enhancement on incubating the cells with HpD for longer duration. Plateau phase cells accumulated more HpD than exponential phase cells for shorter duration of incubation with HpD, however, for longer duration of incubation, the amount of drug uptake was almost the same in both phases of growth. Fluorescence spectra of cell bound HpD showed a difference in spectral intensity distribution in exponential and plateau phase cells. In exponential phase cells, the fluorescence maximum of cell bound HpD was at 615 nm whereas in plateau phase cells the same was at 636 nm. PMID:7896304
Traveling waves and impact-parameter correlations
Munier, S.; Salam, G. P.; Soyez, G.
2008-09-01
It is usually assumed that the high-energy evolution of partons in QCD remains local in coordinate space. In particular, fixed impact-parameter scattering is thought to be in the universality class of one-dimensional reaction-diffusion processes as if the evolutions at different points in the transverse plane became uncorrelated through rapidity evolution. We check this assumption by numerically comparing a toy model with QCD-like impact-parameter dependence to its exact counterpart with uniform evolution in impact-parameter space. We find quantitative differences, but which seem to amount to a mere rescaling of the strong coupling constant. Since the rescaling factor does not show any strong {alpha}{sub s} dependence, we conclude that locality is well verified, up to subleading terms at small {alpha}{sub s}.
Traveling waves and impact-parameter correlations
NASA Astrophysics Data System (ADS)
Munier, S.; Salam, G. P.; Soyez, G.
2008-09-01
It is usually assumed that the high-energy evolution of partons in QCD remains local in coordinate space. In particular, fixed impact-parameter scattering is thought to be in the universality class of one-dimensional reaction-diffusion processes as if the evolutions at different points in the transverse plane became uncorrelated through rapidity evolution. We check this assumption by numerically comparing a toy model with QCD-like impact-parameter dependence to its exact counterpart with uniform evolution in impact-parameter space. We find quantitative differences, but which seem to amount to a mere rescaling of the strong coupling constant. Since the rescaling factor does not show any strong αs dependence, we conclude that locality is well verified, up to subleading terms at small αs.
NASA Astrophysics Data System (ADS)
Vaninsky, Alexander
2015-04-01
Defining the logarithmic function as a definite integral with a variable upper limit, an approach used by some popular calculus textbooks, is problematic. We discuss the disadvantages of such a definition and provide a way to fix the problem. We also consider a definition-based, rigorous derivation of the derivative of the exponential function that is easier, more intuitive, and complies with the standard definitions of the number e, the logarithmic, and the exponential functions.
Neutron Flux Perturbations due to Infinite Plane Absorbers IV: The Exponential Flux Revisited
Williams, M.M.R
2002-02-15
Flux depression factors and measures of asymmetry are presented for an absorbing and scattering slab in an infinite medium in which there is an overall exponential flux. One speed transport theory is employed. The effect of the slab on the exponential flux is determined and the necessary correction factors to recover the unperturbed flux from the activation of the slab are calculated. Although this is an old problem, we present here a new formalism which highlights clearly some important physical aspects.
Exponential stability of second-order stochastic evolution equations with Poisson jumps
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Ren, Y.
2012-12-01
This paper is concerned with the exponential stability problem of second-order nonlinear stochastic evolution equations with Poisson jumps. By using the stochastic analysis theory, a set of novel sufficient conditions are derived for the exponential stability of mild solutions to the second-order nonlinear stochastic differential equations with infinite delay driven by Poisson jumps. An example is provided to demonstrate the effectiveness of the proposed result.
Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency
NASA Astrophysics Data System (ADS)
Randoux, Stéphane; Walczak, Pierre; Onorato, Miguel; Suret, Pierre
2016-10-01
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schrödinger equation. We consider random complex fields having a Gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from Gaussian statistics are observed in focusing regime while low-tailed deviations from Gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum changes with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regimes, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.
Rates of exponential decay in systems of discrete energy levels by Stieltjes imaging
Craigie, Jacob; Hammad, Ali; Cooper, Bridgette; Averbukh, Vitali
2014-07-07
An isolated bound state coupled to a continuum shows an exponential decay of its survival probability. Rates of the exponential decay occurring due to the bound-continuum coupling can be recovered from discretized continuum (L{sup 2}) calculations using a computational technique known as Stieltjes-Chebyshev moment theory or Stieltjes imaging. At the same time, some genuinely discrete level systems, e.g., Bixon-Jortner model, also show an exponential (or approximately exponential) decay of the initially populated level before the onset of quantum revivals. Here, we demonstrate numerically that Stieltjes imaging can be used for calculation of the rates of the exponential decay in such discrete level systems. We apply the Stieltjes imaging technique to the approximately exponential decay of inner-valence vacancies in trans-butadiene in order to show that the breakdown of the molecular orbital picture of ionization in the inner valence region can be physically interpreted as an energy-forbidden Coster-Kronig transition.
NASA Astrophysics Data System (ADS)
Chen, Yanguang
2015-03-01
The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).
Use of Continuous Exponential Families to Link Forms via Anchor Tests. Research Report. ETS RR-11-11
ERIC Educational Resources Information Center
Haberman, Shelby J.; Yan, Duanli
2011-01-01
Continuous exponential families are applied to linking test forms via an internal anchor. This application combines work on continuous exponential families for single-group designs and work on continuous exponential families for equivalent-group designs. Results are compared to those for kernel and equipercentile equating in the case of chained…
Decapitation in rats: latency to unconsciousness and the 'wave of death'.
van Rijn, Clementina M; Krijnen, Hans; Menting-Hermeling, Saskia; Coenen, Anton M L
2011-01-27
The question whether decapitation is a humane method of euthanasia in awake animals is being debated. To gather arguments in this debate, obsolete rats were decapitated while recording the EEG, both of awake rats and of anesthetized rats. Following decapitation a fast and global loss of power of the EEG was observed; the power in the 13-100 Hz frequency band, expressing cognitive activity, decreased according to an exponential decay function to half the initial value within 4 seconds. Whereas the pre-decapitation EEG of the anesthetized animals showed a burst suppression pattern quite different from the awake animals, the power in the postdecapitation EEG did not differ between the two groups. This might indicate that either the power of the EEG does not correlate well with consciousness or that consciousness is briefly regained in the anesthetized group after decapitation. Remarkably, after 50 seconds (awake group) or 80 seconds (anesthetized group) following decapitation, a high amplitude slow wave was observed. The EEG before this wave had more power than the signal after the wave. This wave might be due to a simultaneous massive loss of membrane potentials of the neurons. Still functioning ion channels, which keep the membrane potential intact before the wave, might explain the observed power difference. Two conclusions were drawn from this experiment. It is likely that consciousness vanishes within seconds after decapitation, implying that decapitation is a quick and not an inhumane method of euthanasia. It seems that the massive wave which can be recorded approximately one minute after decapitation reflects the ultimate border between life and death. This observation might have implications in the discussions on the appropriate time for organ donation.
Transport and Structure of Charge Density Waves
NASA Astrophysics Data System (ADS)
Dicarlo, David Anthony
Experimental studies are presented concerning the transport properties and structure of charge-density waves (CDWs) in rm NbSe_3 and rm K_{0.3}MoO_3. Transport measurements were performed to determine how charged impurities affect the CDW and how the narrow -band noise is created in sliding CDWs. Ti-doped rm NbSe_3 is shown to have a weakly pinned CDW even though Ti is incorporated as a charged impurity. The narrow-band-noise amplitude versus sample volume and impurity concentration is consistent with the narrow-band-noise being generated in the bulk by impurities and a weakly pinned CDW. X-ray scattering measurements were performed to determine how impurities, temperature, normal carriers, and electric fields affect the CDW structure. The periodic CDW scatters x-rays and the sharpness of the scattering is a reflection of the CDW structure. The CDW correlation function and its characteristic length are determined through the competition between the disordering impurity forces and the ordering elastic forces. Added impurities and high temperatures decrease the correlations by increasing the disorder forces and decreasing the CDW order parameter Delta , respectively. For rm NbSe_3, the correlation length l was much greater than the average impurity spacing and depends on impurity density n _{i} and temperature as l ~ Delta^2/n_{i}. In addition, the CDW correlation function decays exponentially in real space;
Integrable turbulence generated from modulational instability of cnoidal waves
NASA Astrophysics Data System (ADS)
Agafontsev, D. S.; Zakharov, V. E.
2016-11-01
We study numerically the nonlinear stage of the modulational instability (MI) of cnoidal waves in the framework of the focusing one-dimensional nonlinear Schrödinger (NLS) equation. Cnoidal waves are exact periodic solutions of the NLS equation which can be represented as the lattices of overlapping solitons. The MI of these lattices leads to the development of ‘integrable turbulence’ (Zakharov 2009 Stud. Appl. Math. 122 219–34). We study the major characteristics of turbulence for the dn-branch of cnoidal waves and demonstrate how these characteristics depend on the degree of ‘overlapping’ between the solitons within the cnoidal wave. Integrable turbulence, which develops from the MI of the dn-branch of cnoidal waves, asymptotically approaches its stationary state in an oscillatory way. During this process, kinetic and potential energies oscillate around their asymptotic values. The amplitudes of these oscillations decay with time as {{t}-α} , 1<α <1.5 , the phases contain nonlinear phase shift decaying as t ‑1/2, and the frequency of the oscillations is equal to the double maximal growth rate of the MI, s=2{γ\\max} . In the asymptotic stationary state, the ratio of potential to kinetic energy is equal to ‑2. The asymptotic PDF of the wave intensity is close to the exponential distribution for cnoidal waves with strong overlapping, and is significantly non-exponential for cnoidal waves with weak overlapping of the solitons. In the latter case, the dynamics of the system reduces to two-soliton collisions, which occur at an exponentially small rate and provide an up to two-fold increase in amplitude compared with the original cnoidal wave. For all cnoidal waves of the dn-branch, the rogue waves at the time of their maximal elevation have a quasi-rational profile similar to that of the Peregrine solution.
Functional methods for waves in random media
NASA Technical Reports Server (NTRS)
Chow, P. L.
1981-01-01
Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media; and a derivation of approximate moment equations from the functional integral representation.
Functional methods for waves in random media
NASA Technical Reports Server (NTRS)
Chow, P. L.
1981-01-01
Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media, and a derivation of approximate moment equations from the functional integral representation.
Three-dimensional strong Langmuir turbulence and wave collapse
NASA Technical Reports Server (NTRS)
Robinson, P. A.; Newman, D. L.; Goldman, M. V.
1988-01-01
Results from the first fully three-dimensional simulations of driven damped strong Langmuir turbulence and wave collapse are presented. Key results are that turbulence is maintained at least in part by nucleation, the cores of most collapsing objects are pancake shaped in form, and the power spectrum falls off approximately as the product of a power law and an exponential at large wave number.
Phase space correlation to improve detection accuracy.
Carroll, T L; Rachford, F J
2009-09-01
The standard method used for detecting signals in radar or sonar is cross correlation. The accuracy of the detection with cross correlation is limited by the bandwidth of the signals. We show that by calculating the cross correlation based on points that are nearby in phase space rather than points that are simultaneous in time, the detection accuracy is improved. The phase space correlation technique works for some standard radar signals, but it is especially well suited to chaotic signals because trajectories that are adjacent in phase space move apart from each other at an exponential rate.
NASA Astrophysics Data System (ADS)
Pasari, S.; Kundu, D.; Dikshit, O.
2012-12-01
Earthquake recurrence interval is one of the important ingredients towards probabilistic seismic hazard assessment (PSHA) for any location. Exponential, gamma, Weibull and lognormal distributions are quite established probability models in this recurrence interval estimation. However, they have certain shortcomings too. Thus, it is imperative to search for some alternative sophisticated distributions. In this paper, we introduce a three-parameter (location, scale and shape) exponentiated exponential distribution and investigate the scope of this distribution as an alternative of the afore-mentioned distributions in earthquake recurrence studies. This distribution is a particular member of the exponentiated Weibull distribution. Despite of its complicated form, it is widely accepted in medical and biological applications. Furthermore, it shares many physical properties with gamma and Weibull family. Unlike gamma distribution, the hazard function of generalized exponential distribution can be easily computed even if the shape parameter is not an integer. To contemplate the plausibility of this model, a complete and homogeneous earthquake catalogue of 20 events (M ≥ 7.0) spanning for the period 1846 to 1995 from North-East Himalayan region (20-32 deg N and 87-100 deg E) has been used. The model parameters are estimated using maximum likelihood estimator (MLE) and method of moment estimator (MOME). No geological or geophysical evidences have been considered in this calculation. The estimated conditional probability reaches quite high after about a decade for an elapsed time of 17 years (i.e. 2012). Moreover, this study shows that the generalized exponential distribution fits the above data events more closely compared to the conventional models and hence it is tentatively concluded that generalized exponential distribution can be effectively considered in earthquake recurrence studies.
Double Exponential Disks in Irregular Galaxies and Implications for Star Formation Thresholds
NASA Astrophysics Data System (ADS)
Hunter, D. A.; Elmegreen, B. G.; Anderson, E.
2005-12-01
V-band imaging as part of a large multi-wavelength survey of irregular (Im), Magellanic-``spiral'' (Sm), and Blue Compact Dwarf (BCD) galaxies reveals that 28% of the Im and Sm systems have complex surface brightness profiles: an exponential decline of starlight with a break followed by, usually, a steeper exponential in the outer parts. Ultra-deep imaging of two of these systems shows that the outer exponential continues without end to our detection limit of 29 mag of 1 arcsec2. Breaks like this have also been seen in the outer disks of spirals, but the breaks occur at smaller radii in Im galaxies. We reproduce the double exponential profiles with a new model of star formation that combines the Toomre large-scale gravitational instability criterion of the gas with local compression mechanisms. The inner exponential covers the regime where the average gas density is large enough for gravitational instabilities to dominate. The outer exponential occurs where the average gas density drops below the critical threshold for gravitational instabilities, but a low level of turbulence and other local processes occassionally form clouds. Star formation sputters along out there in a patchy fashion that results in a star-forming gradient that is somewhat exponential but steeper than that in the inner disk. This model also predicts that the break radius should be higher in spirals than in Im galaxies, as observed, because spirals have a larger unstable disk. Funding for this work was provided by the Lowell Research Fund and by the National Science Foundation through grants AST-0204922 to DAH and AST-0205097 to BGE.
Yonetoku, Daisuke; Sawano, Tatsuya; Toyanago, Asuka; Nakamura, Takashi; Takahashi, Keitaro E-mail: takashi@tap.scphys.kyoto-u.ac.jp
2014-07-01
Using 72 short gamma-ray bursts (SGRBs) with well determined spectral data observed by BATSE, we determine their redshift and luminosity by applying the E{sub p} -L{sub p} correlation for SGRBs found by Tsutsui et al. For 53 SGRBs with an observed flux brighter than 4 × 10{sup –6} erg cm{sup –2} s{sup –1}, the cumulative redshift distribution up to z = 1 agrees well with that of 22 Swift SGRBs. This suggests that the redshift determination by the E{sub p} -L{sub p} correlation for SGRBs works well. The minimum event rate at z = 0 is estimated as R{sub on−axis}{sup min}=6.3{sub −3.9}{sup +3.1}× 10{sup −10} events Mpc{sup −3} yr{sup −1}, so that the minimum beaming angle is 0.°6-7.°8 assuming a merging rate of 10{sup –7}- 4 × 10{sup –6} events Mpc{sup –3} yr{sup –1} suggested from the binary pulsar data. Interestingly, this angle is consistent with that for SGRB 130603B of ∼4°-8°. On the other hand, if we assume a beaming angle of ∼6° suggested from four SGRBs with the observed beaming angle value, then the minimum event rate including off-axis SGRBs is estimated as R{sub all}{sup min}=1.15{sub −0.66}{sup +0.56} × 10{sup −7} events Mpc{sup −3} yr{sup −1}. If SGRBs are induced by the coalescence of binary neutron stars (NSs) and/or black holes (BHs), then this event rate leads to a minimum gravitational-wave detection rate of 3.8{sub −2.2}{sup +1.8} (146{sub −83}{sup +71}) events yr{sup −1} for an NS-NS (NS-BH) binary, respectively, by a worldwide network with KAGRA, advanced-LIGO, advanced-VIRGO, and GEO.
Stability of imploding spherical shock waves
NASA Astrophysics Data System (ADS)
Chen, H. B.; Zhang, L.; Panarella, E.
1995-12-01
The stability of spherically imploding shock waves is systematically investigated in this letter. The basic state is Guderley and Landau's unsteady self-similar solution of the implosion of a spherical shock wave. The stability analysis is conducted by combining Chandrasekhar's approach to the stability of a viscous liquid drop with Zel'dovich's approach to the stability of spherical flames. The time-dependent amplitudes of the perturbations are obtained analytically by using perturbation method. The relative amplification and decay of the amplitudes of perturbations decides the stability/instability of the spherical imploding shock waves. It is found that the growth rate of perturbations is not in exponential form and near the collapse phase of the shocks, the spherically imploding shock waves are relatively stable.
Stability of imploding spherical shock waves
Chen, H.B.; Zhang, L.; Panarella, E.
1995-12-01
The stability of spherically imploding shock waves is systematically investigated in this letter. The basic state is Guderley and Landau`s unsteady self-similar solution of the implosion of a spherical shock wave. The stability analysis is conducted by combining Chandrasekhar`s approach to the stability of a viscous liquid drop with Zel`dovich`s approach to the stability of spherical flames. The time-dependent amplitudes of the perturbations are obtained analytically by using perturbation method. The relative amplification and decay of the amplitudes of perturbations are obtained analytically by using perturbation method. The relative amplification and decay of the amplitudes of perturbations decides the stability/instability of the spherical imploding shock waves. It is found that the growth rate of perturbations is not in exponential form and near the collapse phase of the shocks, the spherically imploding shock waves are relatively stable. 14 refs., 1 fig.
Fast wave evanescence in filamentary boundary plasmas
Myra, J. R.
2014-02-15
Radio frequency waves for heating and current drive of plasmas in tokamaks and other magnetic confinement devices must first traverse the scrape-off-layer (SOL) before they can be put to their intended use. The SOL plasma is strongly turbulent and intermittent in space and time. These turbulent properties of the SOL, which are not routinely taken into account in wave propagation codes, can have an important effect on the coupling of waves through an evanescent SOL or edge plasma region. The effective scale length for fast wave (FW) evanescence in the presence of short-scale field-aligned filamentary plasma turbulence is addressed in this paper. It is shown that although the FW wavelength or evanescent scale length is long compared with the dimensions of the turbulence, the FW does not simply average over the turbulent density; rather, the average is over the exponentiation rate. Implications for practical situations are discussed.
Brain Wave Analysis and School Achievement.
ERIC Educational Resources Information Center
Wilson, Barry; And Others
The Brain Wave Analyzer (BWA Ertl 02) was used to measure the brain potentials of 110 public school children. Resulting scores were correlated with concurrent measures of school achievement. Results indicate that certain brain wave scores have relatively low correlations with school achievement compared to traditional intelligence measures but may…
Wang, Tzu-Yin; Hall, Timothy L; Xu, Zhen; Fowlkes, J Brian; Cain, Charles A
2014-07-01
Our previous study indicated that shear waves decay and propagate at a lower speed as they propagate into a tissue volume mechanically fractionated by histotripsy. In this paper, we hypothesize that the change in the shear dynamics is related to the degree of tissue fractionation, and can be used to predict histotripsy treatment outcomes. To test this hypothesis, lesions with different degrees of tissue fractionation were created in agar-graphite tissue phantoms and ex vivo kidneys with increasing numbers of therapy pulses, from 0 to 2000 pulses per treatment location. The therapy pulses were 3-cycle 750-kHz focused ultrasound delivered at a peak negative/positive pressure of 17/108 MPa and a repetition rate of 50 Hz. The shear waves were excited by acoustic radiation force impulse (ARFI) focused at the center of the lesion. The spatial and temporal behavior of the propagating shear waves was measured with ultrasound plane wave imaging. The temporal displacement profile at a lateral location 10 mm offset to the shear excitation region was detected with M-mode imaging. The decay and delay of the shear waves were quantitatively characterized on the temporal displacement profile. Results showed significant changes in two characteristics on the temporal displacement profile: the peak-to-peak displacement decayed exponentially with increasing numbers of therapy pulses; the relative time-to-peak displacement increased with increasing numbers of therapy pulses, and appeared to saturate at higher numbers of pulses. Correspondingly, the degree of tissues fractionation, as indicated by the percentage of structurally intact cell nuclei, decreased exponentially with increasing numbers of therapy pulses. Strong linear correlations were found between the two characteristics and the degree of tissue fractionation. These results suggest that the characteristics of the shear temporal displacement profile may provide useful feedback information regarding the treatment outcomes.
Equatorial waves in the stratosphere of Uranus
NASA Technical Reports Server (NTRS)
Hinson, David P.; Magalhaes, Julio A.
1991-01-01
Analyses of radio occultation data from Voyager 2 have led to the discovery and characterization of an equatorial wave in the Uranus stratosphere. The observed quasi-periodic vertical atmospheric density variations are in close agreement with theoretical predictions for a wave that propagates vertically through the observed background structure of the stratosphere. Quantitative comparisons between measurements obtained at immersion and at emersion yielded constraints on the meridional and zonal structure of the wave; the fact that the two sets of measurements are correlated suggests a wave of planetary scale. Two equatorial wave models are proposed for the wave.
A modified exponential behavioral economic demand model to better describe consumption data.
Koffarnus, Mikhail N; Franck, Christopher T; Stein, Jeffrey S; Bickel, Warren K
2015-12-01
Behavioral economic demand analyses that quantify the relationship between the consumption of a commodity and its price have proven useful in studying the reinforcing efficacy of many commodities, including drugs of abuse. An exponential equation proposed by Hursh and Silberberg (2008) has proven useful in quantifying the dissociable components of demand intensity and demand elasticity, but is limited as an analysis technique by the inability to correctly analyze consumption values of zero. We examined an exponentiated version of this equation that retains all the beneficial features of the original Hursh and Silberberg equation, but can accommodate consumption values of zero and improves its fit to the data. In Experiment 1, we compared the modified equation with the unmodified equation under different treatments of zero values in cigarette consumption data collected online from 272 participants. We found that the unmodified equation produces different results depending on how zeros are treated, while the exponentiated version incorporates zeros into the analysis, accounts for more variance, and is better able to estimate actual unconstrained consumption as reported by participants. In Experiment 2, we simulated 1,000 datasets with demand parameters known a priori and compared the equation fits. Results indicated that the exponentiated equation was better able to replicate the true values from which the test data were simulated. We conclude that an exponentiated version of the Hursh and Silberberg equation provides better fits to the data, is able to fit all consumption values including zero, and more accurately produces true parameter values. PMID:26280591
Mathews, K.; Sjoden, G.; Minor, B. )
1994-09-01
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport in slab geometry is derived and compared with current methods. It is similar to the linear characteristic (or, in slab geometry, the linear nodal) quadrature but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx), whose parameters are root-solved to match the known (from the previous iteration) average and first moment of the source over the cell. Like the linear adaptive method, the exponential characteristic method is positive and nonlinear but more accurate and more readily extended to other cell shapes. The nonlinearity has not interfered with convergence. The authors introduce the exponential moment functions,'' a generalization of the functions used by Walters in the linear nodal method, and use them to avoid numerical ill-conditioning. The method exhibits O([Delta]x[sup 4]) truncation error on fine enough meshes; the error is insensitive to mesh size for coarse meshes. In a shielding problem, it is accurate to 10% using 16-mfp-thick cells; conventional methods err by 8 to 15 orders of magnitude. The exponential characteristic method is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems.
Inouye, David I.; Ravikumar, Pradeep; Dhillon, Inderjit S.
2016-01-01
We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models (Yang et al., 2015) did not allow positive dependencies for the exponential and Poisson generalizations. However, in many real-world datasets, variables clearly have positive dependencies. For example, the airport delay time in New York—modeled as an exponential distribution—is positively related to the delay time in Boston. With this motivation, we give an example of our model class derived from the univariate exponential distribution that allows for almost arbitrary positive and negative dependencies with only a mild condition on the parameter matrix—a condition akin to the positive definiteness of the Gaussian covariance matrix. Our Poisson generalization allows for both positive and negative dependencies without any constraints on the parameter values. We also develop parameter estimation methods using node-wise regressions with ℓ1 regularization and likelihood approximation methods using sampling. Finally, we demonstrate our exponential generalization on a synthetic dataset and a real-world dataset of airport delay times. PMID:27563373