Wavelets, ridgelets, and curvelets for Poisson noise removal.

PubMed

Zhang, Bo; Fadili, Jalal M; Starck, Jean-Luc

2008-07-01

In order to denoise Poisson count data, we introduce a variance stabilizing transform (VST) applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic constant variance. This new transform, which can be deemed as an extension of the Anscombe transform to filtered data, is simple, fast, and efficient in (very) low-count situations. We combine this VST with the filter banks of wavelets, ridgelets and curvelets, leading to multiscale VSTs (MS-VSTs) and nonlinear decomposition schemes. By doing so, the noise-contaminated coefficients of these MS-VST-modified transforms are asymptotically normally distributed with known variances. A classical hypothesis-testing framework is adopted to detect the significant coefficients, and a sparsity-driven iterative scheme reconstructs properly the final estimate. A range of examples show the power of this MS-VST approach for recovering important structures of various morphologies in (very) low-count images. These results also demonstrate that the MS-VST approach is competitive relative to many existing denoising methods.

Determining the 13C(α, n)16O absolute cross section through the concurrent application of ANC and THM and astrophysical consequences for the s-process in AGB-LMSs.

NASA Astrophysics Data System (ADS)

Trippella, Oscar; La Cognata, Marco

2018-01-01

The 13C(α, n)16O reaction is considered to be the most important neutron source for the s-process main component in low-mass asymptotic giant branch stars. No direct experimental data exist at very low energies and measurements performed through direct techniques show inconsistent results, mostly in their absolute values. In this context, we reversed the usual normalization procedure combining two indirect approaches, the asymptotic normalization coefficient and the Trojan Horse Method, to unambiguously determine the absolute value of the 13C(α, n)16O astrophysical S(E)-factor in the most relevant energy-region for astrophysics. Adopting the new reaction rate for the n-source in the NEWTON s-process nucleosynthesis code, astrophysical calculations show only limited variations, less than 1%, for those nuclei whose production is considered to be totally due to slow neutron captures.

Statistical models of power-combining circuits for O-type traveling-wave tube amplifiers

NASA Astrophysics Data System (ADS)

Kats, A. M.; Klinaev, Iu. V.; Gleizer, V. V.

1982-11-01

The design outlined here allows for imbalances in the power of the devices being combined and for differences in phase. It is shown that the coefficient of combination is described by a beta distribution of the first type when a small number of devices are being combined and that the coefficient is asymptotically normal in relation to both the number of devices and the phase variance of the tube's output signals. Relations are derived that make it possible to calculate the efficiency of a power-combining circuit and the reproducibility of the design parameters when standard devices are used.

Local polynomial estimation of heteroscedasticity in a multivariate linear regression model and its applications in economics.

PubMed

Su, Liyun; Zhao, Yanyong; Yan, Tianshun; Li, Fenglan

2012-01-01

Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.

Persistent-random-walk approach to anomalous transport of self-propelled particles

NASA Astrophysics Data System (ADS)

Sadjadi, Zeinab; Shaebani, M. Reza; Rieger, Heiko; Santen, Ludger

2015-06-01

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

Nuclear States with Abnormally Large Radii (size Isomers)

NASA Astrophysics Data System (ADS)

Ogloblin, A. A.; Demyanova, A. S.; Danilov, A. N.; Belyaeva, T. L.; Goncharov, S. A.

2015-06-01

Application of the methods of measuring the radii of the short-lived excited states (Modified diffraction model MDM, Inelastic nuclear rainbow scattering method INRS, Asymptotic normalization coefficients method ANC) to the analysis of some nuclear reactions provide evidence of existing in 9Be, 11B, 12C, 13C the excited states whose radii exceed those of the corresponding ground states by ~ 30%. Two types of structure of these "size isomers" were identified: neutron halo an α-clusters.

Rheological equations in asymptotic regimes of granular flow

USGS Publications Warehouse

Chen, C.-L.; Ling, C.-H.

1998-01-01

This paper assesses the validity of the generalized viscoplastic fluid (GVF) model in light of the established constitutive relations in two asymptotic flow regimes, namely, the macroviscous and grain-inertia regimes. A comprehensive review of the literature on constitutive relations in both regimes reveals that except for some material constants, such as the coefficient of restitution, the normalized shear stress in both regimes varies only with the grain concentration, C. It is found that Krieger-Dougherty's relative viscosity, ??*(C), is sufficiently coherent among the monotonically nondecreasing functions of C used in describing the variation of the shear stress with C in both regimes. It not only accurately represents the C-dependent relative viscosity of a suspension in the macroviscous regime, but also plays a role of the radial distribution function that describes the statistics of particle collisions in the grain-inertia regime. Use of ??*(C) alone, however, cannot link the two regimes. Another parameter, the shear-rate number, N, is needed in modelling the rheology of neutrally buoyant granular flows in transition between the two asymptotic regimes. The GVF model proves compatible with most established relations in both regimes.

New astrophysical S factor for the {sup 15}N(p,{gamma}){sup 16}O reaction via the asymptotic normalization coefficient (ANC) method

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

Mukhamedzhanov, A. M.; Gagliardi, C. A.; Goldberg, V. Z.

2008-07-15

The {sup 15}N(p,{gamma}){sup 16}O reaction provides a path from the CN cycle to the CNO bi-cycle and CNO tri-cycle. The measured astrophysical factor for this reaction is dominated by resonant capture through two strong J{sup {pi}}=1{sup -} resonances at E{sub R}=312 and 962 keV and direct capture to the ground state. Asymptotic normalization coefficients (ANCs) for the ground and seven excited states in {sup 16}O were extracted from the comparison of experimental differential cross sections for the {sup 15}N({sup 3}He,d){sup 16}O reaction with distorted-wave Born approximation calculations. Using these ANCs and proton and {alpha} resonance widths determined from an R-matrixmore » fit to the data from the {sup 15}N(p,{alpha}){sup 12}C reaction, we carried out an R-matrix calculation to obtain the astrophysical factor for the {sup 15}N(p,{gamma}){sup 16}O reaction. The results indicate that the direct capture contribution was previously overestimated. We find the astrophysical factor to be S(0)=36.0{+-}6.0 keV b, which is about a factor of 2 lower than the presently accepted value. We conclude that for every 2200{+-}300 cycles of the main CN cycle one CN catalyst is lost due to this reaction.« less

The leading term of the Plancherel-Rotach asymptotic formula for solutions of recurrence relations

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

Aptekarev, A I; Tulyakov, D N

Recurrence relations generating Padé and Hermite-Padé polynomials are considered. Their coefficients increase with the index of the relation, but after dividing by an appropriate power of the scaling function they tend to a finite limit. As a result, after scaling the polynomials 'stabilize' for large indices; this type of asymptotic behaviour is called Plancherel-Rotach asymptotics. An explicit expression for the leading term of the asymptotic formula, which is valid outside sets containing the zeros of the polynomials, is obtained for wide classes of three- and four-term relations. For three-term recurrence relations this result generalizes a theorem Van Assche obtained for recurrence relations withmore » 'regularly' growing coefficients. Bibliography: 19 titles.« less

Rupture Dynamics along Thrust Dipping Fault: Inertia Effects due to Free Surface Wave Interactions

NASA Astrophysics Data System (ADS)

Vilotte, J. P.; Scala, A.; Festa, G.

2017-12-01

We numerically investigate the dynamic interaction between free surface and up-dip, in-plane rupture propagation along thrust faults, under linear slip-weakening friction. With reference to shallow along-dip rupture propagation during large subduction earthquakes, we consider here low dip-angle fault configurations with fixed strength excess and depth-increasing initial stress. In this configuration, the rupture undergoes a break of symmetry with slip-induced normal stress perturbations triggered by the interaction with reflected waves from the free surface. We found that both body-waves - behind the crack front - and surface waves - at the crack front - can trigger inertial effects. When waves interact with the rupture before this latter reaches its asymptotic speed, the rupture can accelerate toward the asymptotic speed faster than in the unbounded symmetric case, as a result of these inertial effects. Moreover, wave interaction at the crack front also affects the slip rate generating large ground motion on the hanging wall. Imposing the same initial normal stress, frictional strength and stress drop while varying the static friction coefficient we found that the break of symmetry makes the rupture dynamics dependent on the absolute value of friction. The higher the friction the stronger the inertial effect both in terms of rupture acceleration and slip amount. When the contact condition allows the fault interface to open close to the free surface, the length of the opening zone is shown to depend on the propagation length, the initial normal stress and the static friction coefficient. These new results are shown to agree with analytical results of rupture propagation in bounded media, and open new perspectives for understanding the shallow rupture of large subduction earthquakes and tsunami sources.

Multiple imputation for cure rate quantile regression with censored data.

PubMed

Wu, Yuanshan; Yin, Guosheng

2017-03-01

The main challenge in the context of cure rate analysis is that one never knows whether censored subjects are cured or uncured, or whether they are susceptible or insusceptible to the event of interest. Considering the susceptible indicator as missing data, we propose a multiple imputation approach to cure rate quantile regression for censored data with a survival fraction. We develop an iterative algorithm to estimate the conditionally uncured probability for each subject. By utilizing this estimated probability and Bernoulli sample imputation, we can classify each subject as cured or uncured, and then employ the locally weighted method to estimate the quantile regression coefficients with only the uncured subjects. Repeating the imputation procedure multiple times and taking an average over the resultant estimators, we obtain consistent estimators for the quantile regression coefficients. Our approach relaxes the usual global linearity assumption, so that we can apply quantile regression to any particular quantile of interest. We establish asymptotic properties for the proposed estimators, including both consistency and asymptotic normality. We conduct simulation studies to assess the finite-sample performance of the proposed multiple imputation method and apply it to a lung cancer study as an illustration. © 2016, The International Biometric Society.

Absorption spectra and light penetration depth of normal and pathologically altered human skin

NASA Astrophysics Data System (ADS)

Barun, V. V.; Ivanov, A. P.; Volotovskaya, A. V.; Ulashchik, V. S.

2007-05-01

A three-layered skin model (stratum corneum, epidermis, and dermis) and engineering formulas for radiative transfer theory are used to study absorption spectra and light penetration depths of normal and pathologically altered skin. The formulas include small-angle and asymptotic approximations and a layer-addition method. These characteristics are calculated for wavelengths used for low-intensity laser therapy. We examined several pathologies such as vitiligo, edema, erythematosus lupus, and subcutaneous wound, for which the bulk concentrations of melanin and blood vessels or tissue structure (for subcutaneous wound) change compared with normal skin. The penetration depth spectrum is very similar to the inverted blood absorption spectrum. In other words, the depth is minimal at blood absorption maxima. The calculated absorption spectra enable the power and irradiation wavelength providing the required light effect to be selected. Relationships between the penetration depth and the diffuse reflectance coefficient of skin (unambiguously expressed through the absorption coefficient) are analyzed at different wavelengths. This makes it possible to find relationships between the light fields inside and outside the tissue.

A class of semiparametric cure models with current status data.

PubMed

Diao, Guoqing; Yuan, Ao

2018-02-08

Current status data occur in many biomedical studies where we only know whether the event of interest occurs before or after a particular time point. In practice, some subjects may never experience the event of interest, i.e., a certain fraction of the population is cured or is not susceptible to the event of interest. We consider a class of semiparametric transformation cure models for current status data with a survival fraction. This class includes both the proportional hazards and the proportional odds cure models as two special cases. We develop efficient likelihood-based estimation and inference procedures. We show that the maximum likelihood estimators for the regression coefficients are consistent, asymptotically normal, and asymptotically efficient. Simulation studies demonstrate that the proposed methods perform well in finite samples. For illustration, we provide an application of the models to a study on the calcification of the hydrogel intraocular lenses.

Polynomial asymptotes of the second kind

NASA Astrophysics Data System (ADS)

Dobbs, David E.

2011-03-01

This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and conics. Prerequisites include the division algorithm for polynomials with coefficients in the field of real numbers and elementary facts about limits from calculus. This note could be used as enrichment material in courses ranging from Calculus to Real Analysis to Abstract Algebra.

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

PubMed Central

Zhang, Zhihua

2014-01-01

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

Asymptotic Normality Through Factorial Cumulants and Partition Identities

PubMed Central

Bobecka, Konstancja; Hitczenko, Paweł; López-Blázquez, Fernando; Rempała, Grzegorz; Wesołowski, Jacek

2013-01-01

In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for ‘moments’ of partitions of numbers. The general limiting result is then used to (re-)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution. PMID:24591773

Asymptotic normalization coefficients of resonant and bound states from the phase shifts for α α and α 12C scattering

NASA Astrophysics Data System (ADS)

Orlov, Yu. V.; Irgaziev, B. F.; Nikitina, L. I.

2016-01-01

Recently we have published a paper [Irgaziev, Phys. Rev. C 91, 024002 (2015), 10.1103/PhysRevC.91.024002] where the S -matrix pole method (SMP), which is only valid for resonances, has been developed to derive an explicit expression for the asymptotic normalization coefficient (ANC) and is applied to the low-energy resonant states of nucleon +α and α +12C systems. The SMP results are compared with the effective-range expansion method (EFE) results. In the present paper the SMP and EFE plus the Padé approximation are applied to study the excited 2+ resonant states of 9Be. A contradiction is found between descriptions of the experimental phase shift data for α α scattering and of the 9Be resonant energy for 2+ state. Using the EFE method, we also calculate the ANC for the 9Be ground 0+ state with a very small width. This ANC agrees well with the value calculated using the known analytical expression for narrow resonances. In addition, for the α +12C states 1- and 3- the SMP results are compared with the Padé approximation results. We find that the Padé approximation improves a resonance width description compared with the EFE results. The EFE method is also used to calculate the ANCs for the bound 0mml:mprescripts>O ground 0+ state and for the excited 1- and 2+ levels, which are situated near the threshold of α +12C channel.

Caustics, counting maps and semi-classical asymptotics

NASA Astrophysics Data System (ADS)

Ercolani, N. M.

2011-02-01

This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z0(t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain tied random walks on a 1D lattice, and the large time asymptotics of random matrix partition functions.

Asymptotically Exact Solution of the Problem of Harmonic Vibrations of an Elastic Parallelepiped

NASA Astrophysics Data System (ADS)

Papkov, S. O.

2017-11-01

An asymptotically exact solution of the classical problem of elasticity about the steadystate forced vibrations of an elastic rectangular parallelepiped is constructed. The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients, and an infinite system of linear algebraic equations is obtained for determining these coefficients. An analysis of the infinite system permits determining the asymptotics of the unknowns which are used to convolve the double series in both equations of the infinite systems and the displacement and stress components. The efficiency of this approach is illustrated by numerical examples and comparison with known solutions. The spectrum of the parallelepiped symmetric vibrations is studied for various ratios of its sides.

Superdiffusive Dispersals Impart the Geometry of Underlying Random Walks

NASA Astrophysics Data System (ADS)

Zaburdaev, V.; Fouxon, I.; Denisov, S.; Barkai, E.

2016-12-01

It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

Renormalized asymptotic enumeration of Feynman diagrams

NASA Astrophysics Data System (ADS)

Borinsky, Michael

2017-10-01

A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT and its asymptotics. The procedure heavily applies techniques from singularity analysis. To utilize singularity analysis, a representation of the zero-dimensional path integral as a generalized hyperelliptic curve is deduced. As applications the full asymptotic expansions of the number of disconnected, connected, 1PI and skeleton Feynman diagrams in various theories are given.

Additive hazards regression and partial likelihood estimation for ecological monitoring data across space.

PubMed

Lin, Feng-Chang; Zhu, Jun

2012-01-01

We develop continuous-time models for the analysis of environmental or ecological monitoring data such that subjects are observed at multiple monitoring time points across space. Of particular interest are additive hazards regression models where the baseline hazard function can take on flexible forms. We consider time-varying covariates and take into account spatial dependence via autoregression in space and time. We develop statistical inference for the regression coefficients via partial likelihood. Asymptotic properties, including consistency and asymptotic normality, are established for parameter estimates under suitable regularity conditions. Feasible algorithms utilizing existing statistical software packages are developed for computation. We also consider a simpler additive hazards model with homogeneous baseline hazard and develop hypothesis testing for homogeneity. A simulation study demonstrates that the statistical inference using partial likelihood has sound finite-sample properties and offers a viable alternative to maximum likelihood estimation. For illustration, we analyze data from an ecological study that monitors bark beetle colonization of red pines in a plantation of Wisconsin.

Strength of Wet and Dry Montmorillonite

NASA Astrophysics Data System (ADS)

Morrow, C. A.; Lockner, D. A.; Moore, D. E.

2015-12-01

Montmorillonite, an expandable smectite clay, is a common mineral in fault zones to a depth of around 3 km. Its low strength relative to other common fault gouge minerals is important in many models of fault rheology. However, the coefficient of friction is not well constrained in the literature due to the difficulty of establishing fully drained or fully dried states in the laboratory. For instance, in some reported studies, samples were either partially saturated or possibly over pressured, leading to wide variability in reported shear strength. In this study, the coefficient of friction, μ, of both saturated and oven-dried (at 150°C) Na-montmorillonite was measured at normal stresses up to 680 MPa at room temperature and shortening rates from 1.0 to 0.01 μm/s. Care was taken to shear saturated samples slowly enough to avoid pore fluid overpressure in the clay layers. Coefficients of friction are reported after 8 mm of axial displacement in a triaxial apparatus on saw-cut samples containing a layer of montmorillonite gouge, with either granite or sandstone driving blocks. For saturated samples, μ increased from around 0.1 at low pressure to 0.25 at the highest test pressures. In contrast, values for oven-dried samples decreased asymptotically from approximately 0.78 at 10 MPa normal stress to around 0.45 at 400-680 MPa. While wet and dry strengths approached each other with increasing effective normal stress, wet strength remained only about half of the dry strength at 600 MPa effective normal stress. The increased coefficient of friction can be correlated with a reduction in the number of loosely bound lubricating surface water layers on the clay platelets due to applied normal stress under saturated conditions. The steady-state rate dependence of friction, a-b, was positive and dependent on normal stress. For saturated samples, a-b increased linearly with applied normal stress from ~0 to 0.004, while for dry samples a-b decreased with increasing normal stress from 0.008 to 0.002. All values were either neutral or rate strengthening, indicating a tendency for stable sliding.

Oscillation and asymptotic properties of a class of second-order Emden-Fowler neutral differential equations.

PubMed

Wang, Rui; Li, Qiqiang

2016-01-01

We consider a class of second-order Emden-Fowler equations with positive and nonpositve neutral coefficients. By using the Riccati transformation and inequalities, several oscillation and asymptotic results are established. Some examples are given to illustrate the main results.

Effective conductivity of a periodic dilute composite with perfect contact and its series expansion

NASA Astrophysics Data System (ADS)

Pukhtaievych, Roman

2018-06-01

We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter ɛ . We assume a perfect thermal contact at constituent interfaces, i.e., a continuity of the normal component of the heat flux and of the temperature. For ɛ small, we prove that the effective conductivity can be represented as a convergent power series in ɛ and we determine the coefficients in terms of the solutions of explicit systems of integral equations.

Asymptotic expansions of the kernel functions for line formation with continuous absorption

NASA Technical Reports Server (NTRS)

Hummer, D. G.

1991-01-01

Asymptotic expressions are obtained for the kernel functions M2(tau, alpha, beta) and K2(tau, alpha, beta) appearing in the theory of line formation with complete redistribution over a Voigt profile with damping parameter a, in the presence of a source of continuous opacity parameterized by beta. For a greater than 0, each coefficient in the asymptotic series is expressed as the product of analytic functions of a and eta. For Doppler broadening, only the leading term can be evaluated analytically.

Regression analysis of sparse asynchronous longitudinal data.

PubMed

Cao, Hongyuan; Zeng, Donglin; Fine, Jason P

2015-09-01

We consider estimation of regression models for sparse asynchronous longitudinal observations, where time-dependent responses and covariates are observed intermittently within subjects. Unlike with synchronous data, where the response and covariates are observed at the same time point, with asynchronous data, the observation times are mismatched. Simple kernel-weighted estimating equations are proposed for generalized linear models with either time invariant or time-dependent coefficients under smoothness assumptions for the covariate processes which are similar to those for synchronous data. For models with either time invariant or time-dependent coefficients, the estimators are consistent and asymptotically normal but converge at slower rates than those achieved with synchronous data. Simulation studies evidence that the methods perform well with realistic sample sizes and may be superior to a naive application of methods for synchronous data based on an ad hoc last value carried forward approach. The practical utility of the methods is illustrated on data from a study on human immunodeficiency virus.

Hájek-Rényi inequality for m-asymptotically almost negatively associated random vectors in Hilbert space and applications.

PubMed

Ko, Mi-Hwa

2018-01-01

In this paper, we obtain the Hájek-Rényi inequality and, as an application, we study the strong law of large numbers for H -valued m -asymptotically almost negatively associated random vectors with mixing coefficients [Formula: see text] such that [Formula: see text].

Transport and fluctuation-dissipation relations in asymptotic and preasymptotic diffusion across channels with variable section.

PubMed

Forte, Giuseppe; Cecconi, Fabio; Vulpiani, Angelo

2014-12-01

We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient D(eff) is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.

Experimental investigation of turbulent diffusion of slightly buoyant droplets in locally isotropic turbulence

NASA Astrophysics Data System (ADS)

Gopalan, Balaji; Malkiel, Edwin; Katz, Joseph

2008-09-01

High-speed inline digital holographic cinematography is used for studying turbulent diffusion of slightly buoyant 0.5-1.2 mm diameter diesel droplets and 50 μm diameter neutral density particles. Experiments are performed in a 50×50×70 mm3 sample volume in a controlled, nearly isotropic turbulence facility, which is characterized by two dimensional particle image velocimetry. An automated tracking program has been used for measuring velocity time history of more than 17 000 droplets and 15 000 particles. For most of the present conditions, rms values of horizontal droplet velocity exceed those of the fluid. The rms values of droplet vertical velocity are higher than those of the fluid only for the highest turbulence level. The turbulent diffusion coefficient is calculated by integration of the ensemble-averaged Lagrangian velocity autocovariance. Trends of the asymptotic droplet diffusion coefficient are examined by noting that it can be viewed as a product of a mean square velocity and a diffusion time scale. To compare the effects of turbulence and buoyancy, the turbulence intensity (ui') is scaled by the droplet quiescent rise velocity (Uq). The droplet diffusion coefficients in horizontal and vertical directions are lower than those of the fluid at low normalized turbulence intensity, but exceed it with increasing normalized turbulence intensity. For most of the present conditions the droplet horizontal diffusion coefficient is higher than the vertical diffusion coefficient, consistent with trends of the droplet velocity fluctuations and in contrast to the trends of the diffusion timescales. The droplet diffusion coefficients scaled by the product of turbulence intensity and an integral length scale are a monotonically increasing function of ui'/Uq.

A Functional Varying-Coefficient Single-Index Model for Functional Response Data

PubMed Central

Li, Jialiang; Huang, Chao; Zhu, Hongtu

2016-01-01

Motivated by the analysis of imaging data, we propose a novel functional varying-coefficient single index model (FVCSIM) to carry out the regression analysis of functional response data on a set of covariates of interest. FVCSIM represents a new extension of varying-coefficient single index models for scalar responses collected from cross-sectional and longitudinal studies. An efficient estimation procedure is developed to iteratively estimate varying coefficient functions, link functions, index parameter vectors, and the covariance function of individual functions. We systematically examine the asymptotic properties of all estimators including the weak convergence of the estimated varying coefficient functions, the asymptotic distribution of the estimated index parameter vectors, and the uniform convergence rate of the estimated covariance function and their spectrum. Simulation studies are carried out to assess the finite-sample performance of the proposed procedure. We apply FVCSIM to investigating the development of white matter diffusivities along the corpus callosum skeleton obtained from Alzheimer’s Disease Neuroimaging Initiative (ADNI) study. PMID:29200540

A Functional Varying-Coefficient Single-Index Model for Functional Response Data.

PubMed

Li, Jialiang; Huang, Chao; Zhu, Hongtu

2017-01-01

Motivated by the analysis of imaging data, we propose a novel functional varying-coefficient single index model (FVCSIM) to carry out the regression analysis of functional response data on a set of covariates of interest. FVCSIM represents a new extension of varying-coefficient single index models for scalar responses collected from cross-sectional and longitudinal studies. An efficient estimation procedure is developed to iteratively estimate varying coefficient functions, link functions, index parameter vectors, and the covariance function of individual functions. We systematically examine the asymptotic properties of all estimators including the weak convergence of the estimated varying coefficient functions, the asymptotic distribution of the estimated index parameter vectors, and the uniform convergence rate of the estimated covariance function and their spectrum. Simulation studies are carried out to assess the finite-sample performance of the proposed procedure. We apply FVCSIM to investigating the development of white matter diffusivities along the corpus callosum skeleton obtained from Alzheimer's Disease Neuroimaging Initiative (ADNI) study.

Cookbook asymptotics for spiral and scroll waves in excitable media.

PubMed

Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion. (c) 2002 American Institute of Physics.

Cookbook asymptotics for spiral and scroll waves in excitable media

NASA Astrophysics Data System (ADS)

Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion.

Asymptotic Solutions for Optical Properties of Large Particles with Strong Absorption

NASA Technical Reports Server (NTRS)

Yang, Ping; Gao, Bo-Cai; Baum, Bryan A.; Hu, Yong X.; Wiscombe, Warren J.; Mishchenko, Michael I.; Winker, Dave M.; Nasiri, Shaima L.; Einaudi, Franco (Technical Monitor)

2000-01-01

For scattering calculations involving nonspherical particles such as ice crystals, we show that the transverse wave condition is not applicable to the refracted electromagnetic wave in the context of geometric optics when absorption is involved. Either the TM wave condition (i.e., where the magnetic field of the refracted wave is transverse with respect to the wave direction) or the TE wave condition (i.e., where the electric field is transverse with respect to the propagating direction of the wave) may be assumed for the refracted wave in an absorbing medium to locally satisfy the electromagnetic boundary condition in the ray tracing calculation. The wave mode assumed for the refracted wave affects both the reflection and refraction coefficients. As a result, a nonunique solution for these coefficients is derived from the electromagnetic boundary condition. In this study we have identified the appropriate solution for the Fresnel reflection/refraction coefficients in light scattering calculation based on the ray tracing technique. We present the 3 x 2 refraction or transmission matrix that completely accounts for the inhomogeneity of the refracted wave in an absorbing medium. Using the Fresnel coefficients for an absorbing medium, we derive an asymptotic solution in an analytical format for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations. The asymptotic theory can produce reasonable accuracy in the phase function calculations in the infrared window region (wavelengths near 10 micron) if the particle size (in diameter) is on the order of 40 micron or larger. However, since strong absorption is assumed in the computation of the single-scattering albedo in the asymptotic theory, the single scattering albedo does not change with variation of the particle size. As a result, the asymptotic theory can lead to substantial errors in the computation of single-scattering albedo for small and moderate particle sizes. However, from comparison of the asymptotic results with the FDTD solution, it is expected that a convergence between the FDTD results and the asymptotic theory results can be reached when the particle size approaches 200 micron. We show that the phase function at side-scattering and backscattering angles is insensitive to particle shape if the random orientation condition is assumed. However, if preferred orientations are assumed for particles, the phase function has a strong dependence on scattering azimuthal angle. The single-scattering albedo also shows very strong dependence on the inclination angle of incident radiation with respect to the rotating axis for the preferred particle orientations.

Asymptotic analysis of numerical wave propagation in finite difference equations

NASA Technical Reports Server (NTRS)

Giles, M.; Thompkins, W. T., Jr.

1983-01-01

An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.

1993-01-01

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

ON ASYMPTOTIC DISTRIBUTION AND ASYMPTOTIC EFFICIENCY OF LEAST SQUARES ESTIMATORS OF SPATIAL VARIOGRAM PARAMETERS. (R827257)

EPA Science Inventory

Abstract

In this article, we consider the least-squares approach for estimating parameters of a spatial variogram and establish consistency and asymptotic normality of these estimators under general conditions. Large-sample distributions are also established under a sp...

Asymptotic Effect of Misspecification in the Random Part of the Multilevel Model

ERIC Educational Resources Information Center

Berkhof, Johannes; Kampen, Jarl Kennard

2004-01-01

The authors examine the asymptotic effect of omitting a random coefficient in the multilevel model and derive expressions for the change in (a) the variance components estimator and (b) the estimated variance of the fixed effects estimator. They apply the method of moments, which yields a closed form expression for the omission effect. In…

Simultaneous multiple non-crossing quantile regression estimation using kernel constraints

PubMed Central

Liu, Yufeng; Wu, Yichao

2011-01-01

Quantile regression (QR) is a very useful statistical tool for learning the relationship between the response variable and covariates. For many applications, one often needs to estimate multiple conditional quantile functions of the response variable given covariates. Although one can estimate multiple quantiles separately, it is of great interest to estimate them simultaneously. One advantage of simultaneous estimation is that multiple quantiles can share strength among them to gain better estimation accuracy than individually estimated quantile functions. Another important advantage of joint estimation is the feasibility of incorporating simultaneous non-crossing constraints of QR functions. In this paper, we propose a new kernel-based multiple QR estimation technique, namely simultaneous non-crossing quantile regression (SNQR). We use kernel representations for QR functions and apply constraints on the kernel coefficients to avoid crossing. Both unregularised and regularised SNQR techniques are considered. Asymptotic properties such as asymptotic normality of linear SNQR and oracle properties of the sparse linear SNQR are developed. Our numerical results demonstrate the competitive performance of our SNQR over the original individual QR estimation. PMID:22190842

Alpha-capture reaction rates for 22 Ne (α , n) via sub-Coulomb alpha-transfer and its effect on final abundances of s-process isotopes

NASA Astrophysics Data System (ADS)

Jayatissa, Heshani; Rogachev, Grigory; Koshchiy, Yevgeny; Goldberg, Vladilen; Hooker, Joshua; Hunt, Curtis; Magana, Cordero; Roeder, Brian; Saastamoinen, Antti; Spiridon, Alexandria; Upadhyayula, Sriteja; Trippella, Oscar

2017-09-01

The 22 Ne (α , n) reaction is a very important neutron source reaction for the slow neutron capture process (s-process) in asymptotic giant branch stars. These direct measurements are very difficult to carry out at the energy regimes of interest for astrophysics (Gamow energies) due to the extremely small reaction cross section. The large uncertainties introduced when extrapolating direct measurements at high energies down to the Gamow energies can be overcome by measuring the Asymptotic Normalization Coefficients (ANC) of the relevant states using α-transfer reactions at sub-Coulomb energies to reduce the optical model dependence. The study of the 22Ne(6Li,d) and 22Ne(7Li,t) reaction was carried out at the Cyclotron Institute at Texas A&M University. The α-ANC measurements for the near α-threshold resonances of 26Mg provide constraints for the 22Ne(α,n) reaction rate. The effect of this reaction rate on the final abundances of the s-process isotopes will be discussed.

Testing a single regression coefficient in high dimensional linear models

PubMed Central

Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2017-01-01

In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z-test to assess the significance of each covariate. Based on the p-value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively. PMID:28663668

Testing a single regression coefficient in high dimensional linear models.

PubMed

Lan, Wei; Zhong, Ping-Shou; Li, Runze; Wang, Hansheng; Tsai, Chih-Ling

2016-11-01

In linear regression models with high dimensional data, the classical z -test (or t -test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z -test to assess the significance of each covariate. Based on the p -value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively.

Global asymptotic stabilisation of rational dynamical systems based on solving BMI

NASA Astrophysics Data System (ADS)

Esmaili, Farhad; Kamyad, A. V.; Jahed-Motlagh, Mohammad Reza; Pariz, Naser

2017-08-01

In this paper, the global asymptotic stabiliser design of rational systems is studied in detail. To develop the idea, the state equations of the system are transformed to a new coordinate via polynomial transformation and the state feedback control law. This in turn is followed by the satisfaction of the linear growth condition (i.e. Lipschitz at zero). Based on a linear matrix inequality solution, the system in the new coordinate is globally asymptotically stabilised and then, leading to the global asymptotic stabilisation of the primary system. The polynomial transformation coefficients are derived by solving the bilinear matrix inequality problem. To confirm the capability of this method, three examples are highlighted.

Generalized energy detector for weak random signals via vibrational resonance

NASA Astrophysics Data System (ADS)

Ren, Yuhao; Pan, Yan; Duan, Fabing

2018-03-01

In this paper, the generalized energy (GE) detector is investigated for detecting weak random signals via vibrational resonance (VR). By artificially injecting the high-frequency sinusoidal interferences into an array of GE statistics formed for the detector, we show that the normalized asymptotic efficacy can be maximized when the interference intensity takes an appropriate non-zero value. It is demonstrated that the normalized asymptotic efficacy of the dead-zone-limiter detector, aided by the VR mechanism, outperforms that of the GE detector without the help of high-frequency interferences. Moreover, the maximum normalized asymptotic efficacy of dead-zone-limiter detectors can approach a quarter of the second-order Fisher information for a wide range of non-Gaussian noise types.

Normal versus anomalous self-diffusion in two-dimensional fluids: memory function approach and generalized asymptotic Einstein relation.

PubMed

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-07

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

NASA Astrophysics Data System (ADS)

Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun

2014-12-01

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

NASA Technical Reports Server (NTRS)

Hwang, Y. M.

1974-01-01

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Mixed boundary-value problem for an orthotropic rectangular strip with variable coefficients of elasticity

NASA Astrophysics Data System (ADS)

Sargsyan, M. Z.; Poghosyan, H. M.

2018-04-01

A dynamical problem for a rectangular strip with variable coefficients of elasticity is solved by an asymptotic method. It is assumed that the strip is orthotropic, the elasticity coefficients are exponential functions of y, and mixed boundary conditions are posed. The solution of the inner problem is obtained using Bessel functions.

On the asymptotic improvement of supervised learning by utilizing additional unlabeled samples - Normal mixture density case

NASA Technical Reports Server (NTRS)

Shahshahani, Behzad M.; Landgrebe, David A.

1992-01-01

The effect of additional unlabeled samples in improving the supervised learning process is studied in this paper. Three learning processes. supervised, unsupervised, and combined supervised-unsupervised, are compared by studying the asymptotic behavior of the estimates obtained under each process. Upper and lower bounds on the asymptotic covariance matrices are derived. It is shown that under a normal mixture density assumption for the probability density function of the feature space, the combined supervised-unsupervised learning is always superior to the supervised learning in achieving better estimates. Experimental results are provided to verify the theoretical concepts.

Earthquake Nucleation on Faults With Heterogeneous Frictional Properties, Normal Stress

NASA Astrophysics Data System (ADS)

Ray, Sohom; Viesca, Robert C.

2017-10-01

We examine the development of an instability of fault slip rate. We consider a slip rate and state dependence of fault frictional strength, in which frictional properties and normal stress are functions of position. We pose the problem for a slip rate distribution that diverges quasi-statically within finite time in a self-similar fashion. Scenarios of property variations are considered and the corresponding self-similar solutions found. We focus on variations of coefficients, a and b, respectively, controlling the magnitude of a direct effect on strength due to instantaneous changes in slip rate and of strength evolution due to changes in a state variable. These results readily extend to variations in fault-normal stress, σ, or the characteristic slip distance for state evolution, Dc. We find that heterogeneous properties lead to a finite number of self-similar solutions, located about critical points of the distributions: maxima, minima, and between them. We examine the stability of these solutions and find that only a subset is asymptotically stable, occurring at just one of the critical point types. Such stability implies that during instability development, slip rate and state evolution can be attracted to develop in the manner of the self-similar solution, which is also confirmed by solutions to initial value problems for slip rate and state. A quasi-static slip rate divergence is ultimately limited by inertia, leading to the nucleation of an outward expanding dynamic rupture: asymptotic stability of self-similar solutions then implies preferential sites for earthquake nucleation, which are determined by distribution of frictional properties.

Investigating resonances above and below the threshold in nuclear reactions of astrophysical interest and beyond

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

La Cognata, M., E-mail: lacognata@lns.infn.it; Kiss, G. G.; Mukhamedzhanov, A. M.

2015-10-15

Resonances in nuclear cross sections dramatically change their trends. Therefore, the presence of unexpected resonances might lead to unpredicted consequences on astrophysics and nuclear physics. In nuclear physics, resonances allow one to study states in the intermediate compound systems, to evaluate their cluster structure, for instance, especially in the energy regions approaching particle decay thresholds. In astrophysics, resonances might lead to changes in the nucleosynthesis flow, determining different isotopic compositions of the nuclear burning ashes. For these reasons, the Trojan Horse method has been modified to investigate resonant reactions. Thanks to this novel approach, for the first time normalization tomore » direct data might be avoided. Moreover, in the case of sub threshold resonances, the Trojan Horse method modified to investigate resonances allows one to deduce the asymptotic normalization coefficient, showing the close connection between the two indirect approaches.« less

Internal and external radiative widths in the combined R -matrix and potential-model formalism

NASA Astrophysics Data System (ADS)

Mukhamedzhanov, A. M.; Shubhchintak, Bertulani, C. A.; Hao, T. V. Nhan

2017-02-01

By using the R -matrix approach we calculate the radiative width for a resonance decaying to a bound state through electric-dipole E 1 transitions. The total radiative width is determined by the interference of the nuclear internal and external radiative width amplitudes. For a given channel radius the external radiative width amplitude is model independent and is determined by the asymptotic normalization coefficient (ANC) of the bound state to which the resonance decays. It also depends on the partial resonance width. To calculate the internal radiative width amplitude we show that a single-particle-potential model is appropriate. We compare our results with a few experimental data.

Edge Diffraction Coefficients around Critical Rays

NASA Astrophysics Data System (ADS)

Fradkin, L.; Harmer, M.; Darmon, M.

2014-04-01

The classical GTD (Geometrical Theory of Diffraction) gives a recipe, based on high-frequency asymptotics, for calculating edge diffraction coefficients in the geometrical regions where only diffracted waves propagate. The Uniform GTD extends this recipe to transition zones between irradiated and silent regions, known as penumbra. For many industrial materials, e.g. steels, and frequencies utlized in industrial ultrasonic transducers, that is, around 5 MHz, asymptotics suggested for description of geometrical regions supporting the head waves or transition regions surrounding their boundaries, known as critical rays, prove unsatisfactory. We present a numerical extension of GTD, which is based on a regularized, variable step Simpson's method for evaluating the edge diffraction coefficients in the regions of interference between head waves, diffracted waves and/or reflected waves. In mathematical terms, these are the regions of coalescence of three critical points - a branch point, stationary point and/or pole, respectively. We show that away from the shadow boundaries, near the critical rays the GTD still produces correct values of the edge diffraction coefficients.

Periodic oscillation of higher-order bidirectional associative memory neural networks with periodic coefficients and delays

NASA Astrophysics Data System (ADS)

Ren, Fengli; Cao, Jinde

2007-03-01

In this paper, several sufficient conditions are obtained ensuring existence, global attractivity and global asymptotic stability of the periodic solution for the higher-order bidirectional associative memory neural networks with periodic coefficients and delays by using the continuation theorem of Mawhin's coincidence degree theory, the Lyapunov functional and the non-singular M-matrix. Two examples are exploited to illustrate the effectiveness of the proposed criteria. These results are more effective than the ones in the literature for some neural networks, and can be applied to the design of globally attractive or globally asymptotically stable networks and thus have important significance in both theory and applications.

Asymptotic properties of Pearson's rank-variate correlation coefficient under contaminated Gaussian model.

PubMed

Ma, Rubao; Xu, Weichao; Zhang, Yun; Ye, Zhongfu

2014-01-01

This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means of the well known Delta method. To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE). Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

Regression analysis of sparse asynchronous longitudinal data

PubMed Central

Cao, Hongyuan; Zeng, Donglin; Fine, Jason P.

2015-01-01

Summary We consider estimation of regression models for sparse asynchronous longitudinal observations, where time-dependent responses and covariates are observed intermittently within subjects. Unlike with synchronous data, where the response and covariates are observed at the same time point, with asynchronous data, the observation times are mismatched. Simple kernel-weighted estimating equations are proposed for generalized linear models with either time invariant or time-dependent coefficients under smoothness assumptions for the covariate processes which are similar to those for synchronous data. For models with either time invariant or time-dependent coefficients, the estimators are consistent and asymptotically normal but converge at slower rates than those achieved with synchronous data. Simulation studies evidence that the methods perform well with realistic sample sizes and may be superior to a naive application of methods for synchronous data based on an ad hoc last value carried forward approach. The practical utility of the methods is illustrated on data from a study on human immunodeficiency virus. PMID:26568699

Thomas-Fermi model electron density with correct boundary conditions: Application to atoms and ions

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

Patil, S.H.

1999-01-01

The author proposes an electron density in atoms and ions, which has the Thomas-Fermi-Dirac form in the intermediate region of r, satisfies the Kato condition for small r, and has the correct asymptotic behavior at large values of r, where r is the distance from the nucleus. He also analyzes the perturbation in the density produced by multipolar fields. He uses these densities in the Poisson equation to deduce average values of r{sup m}, multipolar polarizabilities, and dispersion coefficients of atoms and ions. The predictions are in good agreement with experimental and other theoretical values, generally within about 20%. Hemore » tabulates here the coefficient A in the asymptotic density; radial expectation values (r{sup m}) for m = 2, 4, 6; multipolar polarizabilities {alpha}{sub 1}, {alpha}{sub 2}, {alpha}{sub 3}; expectation values {l_angle}r{sup 0}{r_angle} and {l_angle}r{sup 2}{r_angle} of the asymptotic electron density; and the van der Waals coefficient C{sub 6} for atoms and ions with 2 {le} Z {le} 92. Many of the results, particularly the multipolar polarizabilities and the higher order dispersion coefficients, are the only ones available in the literature. The variation of these properties also provides interesting insight into the shell structure of atoms and ions. Overall, the Thomas-Fermi-Dirac model with the correct boundary conditions provides a good global description of atoms and ions.« less

Estimates of the Sampling Distribution of Scalability Coefficient H

ERIC Educational Resources Information Center

Van Onna, Marieke J. H.

2004-01-01

Coefficient "H" is used as an index of scalability in nonparametric item response theory (NIRT). It indicates the degree to which a set of items rank orders examinees. Theoretical sampling distributions, however, have only been derived asymptotically and only under restrictive conditions. Bootstrap methods offer an alternative possibility to…

Solution of the relativistic asymptotic equations in electron-ion scattering

NASA Astrophysics Data System (ADS)

Young, I. G.; Norrington, P. H.

1994-12-01

Two asymptotic expansions are suggested for the solution of the coupled equations for the radial channel wavefunctions arising from the treament of electron-ion scattering using the Dirac Hamiltonian. The recurrence relations obtained for the expansions coefficients are given. A method is suggested for calculation of the one-electron Dirac-Coulomb functions used in the second expansion using solutions of the non-relativistic Coulomb equation with complex arguments.

Asymptotic approximations to posterior distributions via conditional moment equations

USGS Publications Warehouse

Yee, J.L.; Johnson, W.O.; Samaniego, F.J.

2002-01-01

We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations that arise naturally in the development. Asymptotic covariance matrices flow naturally from the work of Arnold & Press (1989) and involve the conditional asymptotic covariance matrices and first derivative matrices for conditional mean functions. When the fixed point equations admit an analytical solution, explicit formulae are subsequently obtained for the covariance structure of the joint limiting distribution, which may shed light on the use of the given statistical model. Two illustrations are given. ?? 2002 Biometrika Trust.

Alpha-capture reaction rates for 22Ne(alpha,n) via sub-Coulomb alpha-transfer

NASA Astrophysics Data System (ADS)

Jayatissa, Heshani; Rogachev, Grigory; Koshchiy, Yevgen; Goldberg, Vladilen; Bedoor, Shadi; Hooker, Joshua; Hunt, Curtis; Magana, Cordero; Roeder, Brian; Saastamoinen, Antti; Spiridon, Alexandria; Upadhyayula, Sriteja

2016-09-01

Direct measurements of α-capture reactions at energies relevant to astrophysics is extremely difficult to carry out due to the very small reaction cross section. The large uncertainties introduced when extrapolating direct measurements at high energies down to the Gamow energies can be overcome by measuring the Asymptotic Normalization Coefficients (ANC) of the relevant states using (6Li,d) α-transfer reactions at sub-Coulomb energies to reduce the model dependence. The study of the 22Ne(6Li,d) reaction was carried out at the Cyclotron Institute at Texas A&M University. The α-ANC measurements for the near α-threshold resonances of 26Mg will provide constraints for the reaction rate of the 22Ne(α,n) reaction.

Entanglement entropy in the long-range Kitaev chain

NASA Astrophysics Data System (ADS)

Ares, Filiberto; Esteve, José G.; Falceto, Fernando; de Queiroz, Amilcar R.

2018-06-01

In this paper we complete the study on the asymptotic behavior of the entanglement entropy for Kitaev chains with long-range pairing. We discover that when the couplings decay with the distance with a critical exponent new properties for the asymptotic growth of the entropy appear. The coefficient of the leading term is not universal any more and the connection with conformal field theories is lost. We perform a numerical and analytical approach to the problem showing a perfect agreement. In order to carry out the analytical study, a technique for computing the asymptotic behavior of block Toeplitz determinants with discontinuous symbols has been developed.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Confidence Intervals for Squared Semipartial Correlation Coefficients: The Effect of Nonnormality

ERIC Educational Resources Information Center

Algina, James; Keselman, H. J.; Penfield, Randall D.

2010-01-01

The increase in the squared multiple correlation coefficient ([delta]R[superscript 2]) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. Algina, Keselman, and Penfield found that intervals based on asymptotic principles were typically very inaccurate, even though the sample size…

An asymptotic theory for cross-correlation between auto-correlated sequences and its application on neuroimaging data.

PubMed

Zhou, Yunyi; Tao, Chenyang; Lu, Wenlian; Feng, Jianfeng

2018-04-20

Functional connectivity is among the most important tools to study brain. The correlation coefficient, between time series of different brain areas, is the most popular method to quantify functional connectivity. Correlation coefficient in practical use assumes the data to be temporally independent. However, the time series data of brain can manifest significant temporal auto-correlation. A widely applicable method is proposed for correcting temporal auto-correlation. We considered two types of time series models: (1) auto-regressive-moving-average model, (2) nonlinear dynamical system model with noisy fluctuations, and derived their respective asymptotic distributions of correlation coefficient. These two types of models are most commonly used in neuroscience studies. We show the respective asymptotic distributions share a unified expression. We have verified the validity of our method, and shown our method exhibited sufficient statistical power for detecting true correlation on numerical experiments. Employing our method on real dataset yields more robust functional network and higher classification accuracy than conventional methods. Our method robustly controls the type I error while maintaining sufficient statistical power for detecting true correlation in numerical experiments, where existing methods measuring association (linear and nonlinear) fail. In this work, we proposed a widely applicable approach for correcting the effect of temporal auto-correlation on functional connectivity. Empirical results favor the use of our method in functional network analysis. Copyright © 2018. Published by Elsevier B.V.

Generalized local emission tomography

DOEpatents

Katsevich, Alexander J.

1998-01-01

Emission tomography enables locations and values of internal isotope density distributions to be determined from radiation emitted from the whole object. In the method for locating the values of discontinuities, the intensities of radiation emitted from either the whole object or a region of the object containing the discontinuities are inputted to a local tomography function .function..sub..LAMBDA..sup.(.PHI.) to define the location S of the isotope density discontinuity. The asymptotic behavior of .function..sub..LAMBDA..sup.(.PHI.) is determined in a neighborhood of S, and the value for the discontinuity is estimated from the asymptotic behavior of .function..sub..LAMBDA..sup.(.PHI.) knowing pointwise values of the attenuation coefficient within the object. In the method for determining the location of the discontinuity, the intensities of radiation emitted from an object are inputted to a local tomography function .function..sub..LAMBDA..sup.(.PHI.) to define the location S of the density discontinuity and the location .GAMMA. of the attenuation coefficient discontinuity. Pointwise values of the attenuation coefficient within the object need not be known in this case.

Poisson denoising on the sphere

NASA Astrophysics Data System (ADS)

Schmitt, J.; Starck, J. L.; Fadili, J.; Grenier, I.; Casandjian, J. M.

2009-08-01

In the scope of the Fermi mission, Poisson noise removal should improve data quality and make source detection easier. This paper presents a method for Poisson data denoising on sphere, called Multi-Scale Variance Stabilizing Transform on Sphere (MS-VSTS). This method is based on a Variance Stabilizing Transform (VST), a transform which aims to stabilize a Poisson data set such that each stabilized sample has an (asymptotically) constant variance. In addition, for the VST used in the method, the transformed data are asymptotically Gaussian. Thus, MS-VSTS consists in decomposing the data into a sparse multi-scale dictionary (wavelets, curvelets, ridgelets...), and then applying a VST on the coefficients in order to get quasi-Gaussian stabilized coefficients. In this present article, the used multi-scale transform is the Isotropic Undecimated Wavelet Transform. Then, hypothesis tests are made to detect significant coefficients, and the denoised image is reconstructed with an iterative method based on Hybrid Steepest Descent (HST). The method is tested on simulated Fermi data.

Nature of self-diffusion in two-dimensional fluids

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

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

An "ASYMPTOTIC FRACTAL" Approach to the Morphology of Malignant Cell Nuclei

NASA Astrophysics Data System (ADS)

Landini, Gabriel; Rippin, John W.

To investigate quantitatively nuclear membrane irregularity, 672 nuclei from 10 cases of oral cancer (squamous cell carcinoma) and normal cells from oral mucosa were studied in transmission electron micrographs. The nuclei were photographed at ×1400 magnification and transferred to computer memory (1 pixel = 35 nm). The perimeter of the profiles was analysed using the "yardstick method" of fractal dimension estimation, and the log-log plot of ruler size vs. boundary length demonstrated that there exists a significant effect of resolution on length measurement. However, this effect seems to disappear at higher resolutions. As this observation is compatible with the concept of asymptotic fractal, we estimated the parameters c, L and Bm from the asymptotic fractal formula Br = Bm {1 + (r / L)c}-1 , where Br is the boundary length measured with a ruler of size r, Bm is the maximum boundary for r → 0, L is a constant, and c = asymptotic fractal dimension minus topological dimension (D - Dt) for r → ∞. Analyses of variance showed c to be significantly higher in the normal than malignant cases (P < 0.001), but log(L) and Bm to be significantly higher in the malignant cases (P < 0.001). A multivariate linear discrimination analysis on c, log(L) and Bm re-classified 76.6% of the cells correctly (84.8% of the normal and 67.5% of the tumor). Furthermore, this shows that asymptotic fractal analysis applied to nuclear profiles has great potential for shape quantification in diagnosis of oral cancer.

Fisher information and asymptotic normality in system identification for quantum Markov chains

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

Guta, Madalin

2011-06-15

This paper deals with the problem of estimating the coupling constant {theta} of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of {theta} whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolutemore » bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of {theta}=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.« less

Understanding the power reflection and transmission coefficients of a plane wave at a planar interface

NASA Astrophysics Data System (ADS)

Ye, Qian; Jiang, Yikun; Lin, Haoze

2017-03-01

In most textbooks, after discussing the partial transmission and reflection of a plane wave at a planar interface, the power (energy) reflection and transmission coefficients are introduced by calculating the normal-to-interface components of the Poynting vectors for the incident, reflected and transmitted waves, separately. Ambiguity arises among students since, for the Poynting vector to be interpreted as the energy flux density, on the incident (reflected) side, the electric and magnetic fields involved must be the total fields, namely, the sum of incident and reflected fields, instead of the partial fields which are just the incident (reflected) fields. The interpretation of the cross product of partial fields as energy flux has not been obviously justified in most textbooks. Besides, the plane wave is actually an idealisation that is only ever found in textbooks, then what do the reflection and transmission coefficients evaluated for a plane wave really mean for a real beam of limited extent? To provide a clearer physical picture, we exemplify a light beam of finite transverse extent by a fundamental Gaussian beam and simulate its reflection and transmission at a planar interface. Due to its finite transverse extent, we can then insert the incident fields or reflected fields as total fields into the expression of the Poynting vector to evaluate the energy flux and then power reflection and transmission coefficients. We demonstrate that the power reflection and transmission coefficients of a beam of finite extent turn out to be the weighted sum of the corresponding coefficients for all constituent plane wave components that form the beam. The power reflection and transmission coefficients of a single plane wave serve, in turn, as the asymptotes for the corresponding coefficients of a light beam as its width expands infinitely.

FAST TRACK COMMUNICATION: The unusual asymptotics of three-sided prudent polygons

NASA Astrophysics Data System (ADS)

Beaton, Nicholas R.; Flajolet, Philippe; Guttmann, Anthony J.

2010-08-01

We have studied the area-generating function of prudent polygons on the square lattice. Exact solutions are obtained for the generating function of two-sided and three-sided prudent polygons, and a functional equation is found for four-sided prudent polygons. This is used to generate series coefficients in polynomial time, and these are analysed to determine the asymptotics numerically. A careful asymptotic analysis of the three-sided polygons produces a most surprising result. A transcendental critical exponent is found, and the leading amplitude is not quite a constant, but is a constant plus a small oscillatory component with an amplitude approximately 10-8 times that of the leading amplitude. This effect cannot be seen by any standard numerical analysis, but it may be present in other models. If so, it changes our whole view of the asymptotic behaviour of lattice models.

Fractal analysis of lateral movement in biomembranes.

PubMed

Gmachowski, Lech

2018-04-01

Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.

Theory of concentration dependence in drag reduction by polymers and of the maximum drag reduction asymptote.

PubMed

Benzi, Roberto; Ching, Emily S C; Horesh, Nizan; Procaccia, Itamar

2004-02-20

A simple model of the effect of polymer concentration on the amount of drag reduction in turbulence is presented, simulated, and analyzed. The qualitative phase diagram of drag coefficient versus Reynolds number (Re) is recaptured in this model, including the theoretically elusive onset of drag reduction and the maximum drag reduction (MDR) asymptote. The Re-dependent drag and the MDR are analytically explained, and the dependence of the amount of drag on material parameters is rationalized.

A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

NASA Astrophysics Data System (ADS)

Deift, P.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Venakides, S.; Zhou, X.

2001-08-01

A few years ago the authors introduced a new approach to study asymptotic questions for orthogonal polynomials. In this paper we give an overview of our method and review the results which have been obtained in Deift et al. (Internat. Math. Res. Notices (1997) 759, Comm. Pure Appl. Math. 52 (1999) 1491, 1335), Deift (Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes, Vol. 3, New York University, 1999), Kriecherbauer and McLaughlin (Internat. Math. Res. Notices (1999) 299) and Baik et al. (J. Amer. Math. Soc. 12 (1999) 1119). We mainly consider orthogonal polynomials with respect to weights on the real line which are either (1) Freud-type weights d[alpha](x)=e-Q(x) dx (Q polynomial or Q(x)=x[beta], [beta]>0), or (2) varying weights d[alpha]n(x)=e-nV(x) dx (V analytic, limx-->[infinity] V(x)/logx=[infinity]). We obtain Plancherel-Rotach-type asymptotics in the entire complex plane as well as asymptotic formulae with error estimates for the leading coefficients, for the recurrence coefficients, and for the zeros of the orthogonal polynomials. Our proof starts from an observation of Fokas et al. (Comm. Math. Phys. 142 (1991) 313) that the orthogonal polynomials can be determined as solutions of certain matrix valued Riemann-Hilbert problems. We analyze the Riemann-Hilbert problems by a steepest descent type method introduced by Deift and Zhou (Ann. Math. 137 (1993) 295) and further developed in Deift and Zhou (Comm. Pure Appl. Math. 48 (1995) 277) and Deift et al. (Proc. Nat. Acad. Sci. USA 95 (1998) 450). A crucial step in our analysis is the use of the well-known equilibrium measure which describes the asymptotic distribution of the zeros of the orthogonal polynomials.

Measured pressure distributions, aerodynamic coefficients and shock shapes on blunt bodies at incidence in hypersonic air and CF4

NASA Technical Reports Server (NTRS)

Miller, C. G., III

1982-01-01

Pressure distributions, aerodynamic coefficients, and shock shapes were measured on blunt bodies of revolution in Mach 6 CF4 and in Mach 6 and Mach 10 air. The angle of attack was varied from 0 deg to 20 deg in 4 deg increments. Configurations tested were a hyperboloid with an asymptotic angle of 45 deg, a sonic-corner paraboloid, a paraboloid with an angle of 27.6 deg at the base, a Viking aeroshell generated in a generalized orthogonal coordinate system, and a family of cones having a 45 deg half-angle with spherical, flattened, concave, and cusp nose shapes. Real-gas effects were simulated for the hperboloid and paraboloid models at Mach 6 by testing at a normal-shock density ratio of 5.3 in air and 12 CF4. Predictions from simple theories and numerical flow field programs are compared with measurement. It is anticipated that the data presented in this report will be useful for verification of analytical methods for predicting hypersonic flow fields about blunt bodies at incidence.

On Complicated Expansions of Solutions to ODES

NASA Astrophysics Data System (ADS)

Bruno, A. D.

2018-03-01

Polynomial ordinary differential equations are studied by asymptotic methods. The truncated equation associated with a vertex or a nonhorizontal edge of their polygon of the initial equation is assumed to have a solution containing the logarithm of the independent variable. It is shown that, under very weak constraints, this nonpower asymptotic form of solutions to the original equation can be extended to an asymptotic expansion of these solutions. This is an expansion in powers of the independent variable with coefficients being Laurent series in decreasing powers of the logarithm. Such expansions are sometimes called psi-series. Algorithms for such computations are described. Six examples are given. Four of them are concern with Painlevé equations. An unexpected property of these expansions is revealed.

A method of bias correction for maximal reliability with dichotomous measures.

PubMed

Penev, Spiridon; Raykov, Tenko

2010-02-01

This paper is concerned with the reliability of weighted combinations of a given set of dichotomous measures. Maximal reliability for such measures has been discussed in the past, but the pertinent estimator exhibits a considerable bias and mean squared error for moderate sample sizes. We examine this bias, propose a procedure for bias correction, and develop a more accurate asymptotic confidence interval for the resulting estimator. In most empirically relevant cases, the bias correction and mean squared error correction can be performed simultaneously. We propose an approximate (asymptotic) confidence interval for the maximal reliability coefficient, discuss the implementation of this estimator, and investigate the mean squared error of the associated asymptotic approximation. We illustrate the proposed methods using a numerical example.

Concurrent Application of ANC and THM to assess the 13C(α, n)16O Absolute Cross Section at Astrophysical Energies and Possible Consequences for Neutron Production in Low-mass AGB Stars

NASA Astrophysics Data System (ADS)

Trippella, O.; La Cognata, M.

2017-03-01

The {}13{{C}}{(α ,n)}16{{O}} reaction is considered to be the main neutron source responsible for the production of heavy nuclides (from {Sr} to {Bi}) through slow n-capture nucleosynthesis (s-process) at low temperatures during the asymptotic giant branch phase of low-mass stars (≲ 3{--}4 {M}⊙ , or LMSs). In recent years, several direct and indirect measurements have been carried out to determine the cross section at the energies of astrophysical interest (around 190+/- 40 {keV}). However, they yield inconsistent results that cause a highly uncertain reaction rate and affect the neutron release in LMSs. In this work we have combined two indirect approaches, the asymptotic normalization coefficient and the Trojan horse method, to unambiguously determine the absolute value of the {}13{{C}}{(α ,n)}16{{O}} astrophysical factor. With these, we have determined a very accurate reaction rate to be introduced into astrophysical models of s-process nucleosynthesis in LMSs. Calculations using this recommended rate have shown limited variations in the production of those neutron-rich nuclei (with 86≤slant A≤slant 209) that receive contribution only by slow neutron captures.

A Near-Wall Reynolds-Stress Closure without Wall Normals

NASA Technical Reports Server (NTRS)

Yuan, S. P.; So, R. M. C.

1997-01-01

With the aid of near-wall asymptotic analysis and results of direct numerical simulation, a new near-wall Reynolds stress model (NNWRS) is formulated based on the SSG high-Reynolds-stress model with wall-independent near-wall corrections. Only one damping function is used for flows with a wide range of Reynolds numbers to ensure that the near-wall modifications diminish away from the walls. The model is able to reproduce complicated flow phenomena induced by complex geometry, such as flow recirculation, reattachment and boundary-layer redevelopment in backward-facing step flow and secondary flow in three-dimensional square duct flow. In simple flows, including fully developed channel/pipe flow, Couette flow and boundary-layer flow, the wall effects are dominant, and the NNWRS model predicts less degree of turbulent anisotropy in the near-wall region compared with a wall-dependent near-wall Reynolds Stress model (NWRS) developed by So and colleagues. The comparison of the predictions given by the two models rectifies the misconception that the overshooting of skin friction coefficient in backward-facing step flow prevalent in those near-wall, models with wall normal is caused by he use of wall normal.

Dynamics analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks.

PubMed

Zhang, Juping; Yang, Chan; Jin, Zhen; Li, Jia

2018-07-14

In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations. Copyright © 2018 Elsevier Ltd. All rights reserved.

The Asymptotic Distribution of Ability Estimates: Beyond Dichotomous Items and Unidimensional IRT Models

ERIC Educational Resources Information Center

Sinharay, Sandip

2015-01-01

The maximum likelihood estimate (MLE) of the ability parameter of an item response theory model with known item parameters was proved to be asymptotically normally distributed under a set of regularity conditions for tests involving dichotomous items and a unidimensional ability parameter (Klauer, 1990; Lord, 1983). This article first considers…

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

NASA Technical Reports Server (NTRS)

Peters, C. (Principal Investigator)

1980-01-01

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

Clustering of change patterns using Fourier coefficients.

PubMed

Kim, Jaehee; Kim, Haseong

2008-01-15

To understand the behavior of genes, it is important to explore how the patterns of gene expression change over a time period because biologically related gene groups can share the same change patterns. Many clustering algorithms have been proposed to group observation data. However, because of the complexity of the underlying functions there have not been many studies on grouping data based on change patterns. In this study, the problem of finding similar change patterns is induced to clustering with the derivative Fourier coefficients. The sample Fourier coefficients not only provide information about the underlying functions, but also reduce the dimension. In addition, as their limiting distribution is a multivariate normal, a model-based clustering method incorporating statistical properties would be appropriate. This work is aimed at discovering gene groups with similar change patterns that share similar biological properties. We developed a statistical model using derivative Fourier coefficients to identify similar change patterns of gene expression. We used a model-based method to cluster the Fourier series estimation of derivatives. The model-based method is advantageous over other methods in our proposed model because the sample Fourier coefficients asymptotically follow the multivariate normal distribution. Change patterns are automatically estimated with the Fourier representation in our model. Our model was tested in simulations and on real gene data sets. The simulation results showed that the model-based clustering method with the sample Fourier coefficients has a lower clustering error rate than K-means clustering. Even when the number of repeated time points was small, the same results were obtained. We also applied our model to cluster change patterns of yeast cell cycle microarray expression data with alpha-factor synchronization. It showed that, as the method clusters with the probability-neighboring data, the model-based clustering with our proposed model yielded biologically interpretable results. We expect that our proposed Fourier analysis with suitably chosen smoothing parameters could serve as a useful tool in classifying genes and interpreting possible biological change patterns. The R program is available upon the request.

The intermediates take it all: asymptotics of higher criticism statistics and a powerful alternative based on equal local levels.

PubMed

Gontscharuk, Veronika; Landwehr, Sandra; Finner, Helmut

2015-01-01

The higher criticism (HC) statistic, which can be seen as a normalized version of the famous Kolmogorov-Smirnov statistic, has a long history, dating back to the mid seventies. Originally, HC statistics were used in connection with goodness of fit (GOF) tests but they recently gained some attention in the context of testing the global null hypothesis in high dimensional data. The continuing interest for HC seems to be inspired by a series of nice asymptotic properties related to this statistic. For example, unlike Kolmogorov-Smirnov tests, GOF tests based on the HC statistic are known to be asymptotically sensitive in the moderate tails, hence it is favorably applied for detecting the presence of signals in sparse mixture models. However, some questions around the asymptotic behavior of the HC statistic are still open. We focus on two of them, namely, why a specific intermediate range is crucial for GOF tests based on the HC statistic and why the convergence of the HC distribution to the limiting one is extremely slow. Moreover, the inconsistency in the asymptotic and finite behavior of the HC statistic prompts us to provide a new HC test that has better finite properties than the original HC test while showing the same asymptotics. This test is motivated by the asymptotic behavior of the so-called local levels related to the original HC test. By means of numerical calculations and simulations we show that the new HC test is typically more powerful than the original HC test in normal mixture models. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Data on inelastic processes in low-energy potassium-hydrogen and rubidium-hydrogen collisions

NASA Astrophysics Data System (ADS)

Yakovleva, S. A.; Barklem, P. S.; Belyaev, A. K.

2018-01-01

Two sets of rate coefficients for low-energy inelastic potassium-hydrogen and rubidium-hydrogen collisions were computed for each collisional system based on two model electronic structure calculations, performed by the quantum asymptotic semi-empirical and the quantum asymptotic linear combinations of atomic orbitals (LCAO) approaches, followed by quantum multichannel calculations for the non-adiabatic nuclear dynamics. The rate coefficients for the charge transfer (mutual neutralization, ion-pair formation), excitation and de-excitation processes are calculated for all transitions between the five lowest lying covalent states and the ionic states for each collisional system for the temperature range 1000-10 000 K. The processes involving higher lying states have extremely low rate coefficients and, hence, are neglected. The two model calculations both single out the same partial processes as having large and moderate rate coefficients. The largest rate coefficients correspond to the mutual neutralization processes into the K(5s 2S) and Rb(4d 2D) final states and at temperature 6000 K have values exceeding 3 × 10-8 cm3 s-1 and 4 × 10-8 cm3 s-1, respectively. It is shown that both the semi-empirical and the LCAO approaches perform equally well on average and that both sets of atomic data have roughly the same accuracy. The processes with large and moderate rate coefficients are likely to be important for non-LTE modelling in atmospheres of F, G and K-stars, especially metal-poor stars.

Marginal regression analysis of recurrent events with coarsened censoring times.

PubMed

Hu, X Joan; Rosychuk, Rhonda J

2016-12-01

Motivated by an ongoing pediatric mental health care (PMHC) study, this article presents weakly structured methods for analyzing doubly censored recurrent event data where only coarsened information on censoring is available. The study extracted administrative records of emergency department visits from provincial health administrative databases. The available information of each individual subject is limited to a subject-specific time window determined up to concealed data. To evaluate time-dependent effect of exposures, we adapt the local linear estimation with right censored survival times under the Cox regression model with time-varying coefficients (cf. Cai and Sun, Scandinavian Journal of Statistics 2003, 30, 93-111). We establish the pointwise consistency and asymptotic normality of the regression parameter estimator, and examine its performance by simulation. The PMHC study illustrates the proposed approach throughout the article. © 2016, The International Biometric Society.

Convergence of Asymptotic Systems of Non-autonomous Neural Network Models with Infinite Distributed Delays

NASA Astrophysics Data System (ADS)

Oliveira, José J.

2017-10-01

In this paper, we investigate the global convergence of solutions of non-autonomous Hopfield neural network models with discrete time-varying delays, infinite distributed delays, and possible unbounded coefficient functions. Instead of using Lyapunov functionals, we explore intrinsic features between the non-autonomous systems and their asymptotic systems to ensure the boundedness and global convergence of the solutions of the studied models. Our results are new and complement known results in the literature. The theoretical analysis is illustrated with some examples and numerical simulations.

Photoassociation studies of ultracold NaCs from the Cs 6(2)P(3/2) asymptote.

PubMed

Wakim, A; Zabawa, P; Bigelow, N P

2011-11-14

A combination of pulsed depletion spectroscopy and photoassociation spectroscopy is utilized to assign photoassociation spectra of NaCs. These methods investigate the ab initio Ω = 2 potential energy curve and indicate a previously unknown avoided crossing between the (3)Ω = 1 and (4)Ω = 1 electronic states. We present rotational assignments of deeply bound singlet ground state molecules, an improved C(6) coefficient for the (4)Ω = 1 and assignments for all twenty-three photoassociation resonances detuned from the Cs 6(2)P(3/2) asymptote.

On Nonequivalence of Several Procedures of Structural Equation Modeling

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Chan, Wai

2005-01-01

The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure…

A differential equation for the asymptotic fitness distribution in the Bak-Sneppen model with five species.

PubMed

Schlemm, Eckhard

2015-09-01

The Bak-Sneppen model is an abstract representation of a biological system that evolves according to the Darwinian principles of random mutation and selection. The species in the system are characterized by a numerical fitness value between zero and one. We show that in the case of five species the steady-state fitness distribution can be obtained as a solution to a linear differential equation of order five with hypergeometric coefficients. Similar representations for the asymptotic fitness distribution in larger systems may help pave the way towards a resolution of the question of whether or not, in the limit of infinitely many species, the fitness is asymptotically uniformly distributed on the interval [fc, 1] with fc ≳ 2/3. Copyright © 2015 Elsevier Inc. All rights reserved.

Interval estimation and optimal design for the within-subject coefficient of variation for continuous and binary variables

PubMed Central

Shoukri, Mohamed M; Elkum, Nasser; Walter, Stephen D

2006-01-01

Background In this paper we propose the use of the within-subject coefficient of variation as an index of a measurement's reliability. For continuous variables and based on its maximum likelihood estimation we derive a variance-stabilizing transformation and discuss confidence interval construction within the framework of a one-way random effects model. We investigate sample size requirements for the within-subject coefficient of variation for continuous and binary variables. Methods We investigate the validity of the approximate normal confidence interval by Monte Carlo simulations. In designing a reliability study, a crucial issue is the balance between the number of subjects to be recruited and the number of repeated measurements per subject. We discuss efficiency of estimation and cost considerations for the optimal allocation of the sample resources. The approach is illustrated by an example on Magnetic Resonance Imaging (MRI). We also discuss the issue of sample size estimation for dichotomous responses with two examples. Results For the continuous variable we found that the variance stabilizing transformation improves the asymptotic coverage probabilities on the within-subject coefficient of variation for the continuous variable. The maximum like estimation and sample size estimation based on pre-specified width of confidence interval are novel contribution to the literature for the binary variable. Conclusion Using the sample size formulas, we hope to help clinical epidemiologists and practicing statisticians to efficiently design reliability studies using the within-subject coefficient of variation, whether the variable of interest is continuous or binary. PMID:16686943

QCD Condensates and Holographic Wilson Loops for Asymptotically AdS Spaces

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

Quevedo, R. Carcasses; Goity, Jose L.; Trinchero, Roberto C.

2014-02-01

The minimization of the Nambu-Goto (NG) action for a surface whose contour defines a circular Wilson loop of radius a placed at a finite value of the coordinate orthogonal to the border is considered. This is done for asymptotically AdS spaces. The condensates of dimension n = 2, 4, 6, 8, and 10 are calculated in terms of the coefficients in the expansion in powers of the radius a of the on-shell subtracted NG action for small a->0. The subtraction employed is such that it presents no conflict with conformal invariance in the AdS case and need not introduce anmore » additional infrared scale for the case of confining geometries. It is shown that the UV value of the gluon condensates is universal in the sense that it only depends on the first coefficients of the difference with the AdS case.« less

Collisional excitation of the highly excited hydrogen atoms in the dipole form of the semiclassical impact parameter and Born approximations

NASA Technical Reports Server (NTRS)

Omidvar, K.

1971-01-01

Expressions for the excitation cross section of the highly excited states of the hydrogenlike atoms by fast charged particles have been derived in the dipole approximation of the semiclassical impact parameter and the Born approximations, making use of a formula for the asymptotic expansion of the oscillator strength of the hydrogenlike atoms given by Menzel. When only the leading term in the asymptotic expansion is retained, the expression for the cross section becomes identical to the expression obtained by the method of the classical collision and correspondence principle given by Percival and Richards. Comparisons are made between the Bethe coefficients obtained here and the Bethe coefficients of the Born approximation for transitions where the Born calculation is available. Satisfactory agreement is obtained only for n yields n + 1 transitions, with n the principal quantum number of the excited state.

ASYMPTOTIC DISTRIBUTION OF ΔAUC, NRIs, AND IDI BASED ON THEORY OF U-STATISTICS

PubMed Central

Demler, Olga V.; Pencina, Michael J.; Cook, Nancy R.; D’Agostino, Ralph B.

2017-01-01

The change in AUC (ΔAUC), the IDI, and NRI are commonly used measures of risk prediction model performance. Some authors have reported good validity of associated methods of estimating their standard errors (SE) and construction of confidence intervals, whereas others have questioned their performance. To address these issues we unite the ΔAUC, IDI, and three versions of the NRI under the umbrella of the U-statistics family. We rigorously show that the asymptotic behavior of ΔAUC, NRIs, and IDI fits the asymptotic distribution theory developed for U-statistics. We prove that the ΔAUC, NRIs, and IDI are asymptotically normal, unless they compare nested models under the null hypothesis. In the latter case, asymptotic normality and existing SE estimates cannot be applied to ΔAUC, NRIs, or IDI. In the former case SE formulas proposed in the literature are equivalent to SE formulas obtained from U-statistics theory if we ignore adjustment for estimated parameters. We use Sukhatme-Randles-deWet condition to determine when adjustment for estimated parameters is necessary. We show that adjustment is not necessary for SEs of the ΔAUC and two versions of the NRI when added predictor variables are significant and normally distributed. The SEs of the IDI and three-category NRI should always be adjusted for estimated parameters. These results allow us to define when existing formulas for SE estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models. We also use the U-statistic theory to develop a new SE estimate of ΔAUC. PMID:28627112

Asymptotic distribution of ∆AUC, NRIs, and IDI based on theory of U-statistics.

PubMed

Demler, Olga V; Pencina, Michael J; Cook, Nancy R; D'Agostino, Ralph B

2017-09-20

The change in area under the curve (∆AUC), the integrated discrimination improvement (IDI), and net reclassification index (NRI) are commonly used measures of risk prediction model performance. Some authors have reported good validity of associated methods of estimating their standard errors (SE) and construction of confidence intervals, whereas others have questioned their performance. To address these issues, we unite the ∆AUC, IDI, and three versions of the NRI under the umbrella of the U-statistics family. We rigorously show that the asymptotic behavior of ∆AUC, NRIs, and IDI fits the asymptotic distribution theory developed for U-statistics. We prove that the ∆AUC, NRIs, and IDI are asymptotically normal, unless they compare nested models under the null hypothesis. In the latter case, asymptotic normality and existing SE estimates cannot be applied to ∆AUC, NRIs, or IDI. In the former case, SE formulas proposed in the literature are equivalent to SE formulas obtained from U-statistics theory if we ignore adjustment for estimated parameters. We use Sukhatme-Randles-deWet condition to determine when adjustment for estimated parameters is necessary. We show that adjustment is not necessary for SEs of the ∆AUC and two versions of the NRI when added predictor variables are significant and normally distributed. The SEs of the IDI and three-category NRI should always be adjusted for estimated parameters. These results allow us to define when existing formulas for SE estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models. We also use the U-statistic theory to develop a new SE estimate of ∆AUC. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Functional Linear Model with Zero-value Coefficient Function at Sub-regions.

PubMed

Zhou, Jianhui; Wang, Nae-Yuh; Wang, Naisyin

2013-01-01

We propose a shrinkage method to estimate the coefficient function in a functional linear regression model when the value of the coefficient function is zero within certain sub-regions. Besides identifying the null region in which the coefficient function is zero, we also aim to perform estimation and inferences for the nonparametrically estimated coefficient function without over-shrinking the values. Our proposal consists of two stages. In stage one, the Dantzig selector is employed to provide initial location of the null region. In stage two, we propose a group SCAD approach to refine the estimated location of the null region and to provide the estimation and inference procedures for the coefficient function. Our considerations have certain advantages in this functional setup. One goal is to reduce the number of parameters employed in the model. With a one-stage procedure, it is needed to use a large number of knots in order to precisely identify the zero-coefficient region; however, the variation and estimation difficulties increase with the number of parameters. Owing to the additional refinement stage, we avoid this necessity and our estimator achieves superior numerical performance in practice. We show that our estimator enjoys the Oracle property; it identifies the null region with probability tending to 1, and it achieves the same asymptotic normality for the estimated coefficient function on the non-null region as the functional linear model estimator when the non-null region is known. Numerically, our refined estimator overcomes the shortcomings of the initial Dantzig estimator which tends to under-estimate the absolute scale of non-zero coefficients. The performance of the proposed method is illustrated in simulation studies. We apply the method in an analysis of data collected by the Johns Hopkins Precursors Study, where the primary interests are in estimating the strength of association between body mass index in midlife and the quality of life in physical functioning at old age, and in identifying the effective age ranges where such associations exist.

Unifying Pore Network Modeling, Continuous Time Random Walk Theory and Experiment - Accomplishments and Future Directions

NASA Astrophysics Data System (ADS)

Bijeljic, B.

2008-05-01

This talk will describe and highlight the advantages offered by a methodology that unifies pore network modeling, CTRW theory and experiment in description of solute dispersion in porous media. Solute transport in a porous medium is characterized by the interplay of advection and diffusion (described by Peclet number, Pe) that cause spreading of solute particles. This spreading is traditionally described by dispersion coefficients, D, defined by σ 2 = 2Dt, where σ 2 is the variance of the solute position and t is the time. Using a pore-scale network model based on particle tracking, the rich Peclet- number dependence of dispersion coefficient is predicted from first principles and is shown to compare well with experimental data for restricted diffusion, transition, power-law and mechanical dispersion regimes in the asymptotic limit. In the asymptotic limit D is constant and can be used in an averaged advection-dispersion equation. However, it is highly important to recognize that, until the velocity field is fully sampled, the particle transport is non-Gaussian and D possesses temporal or spatial variation. Furthermore, temporal probability density functions (PDF) of tracer particles are studied in pore networks and an excellent agreement for the spectrum of transition times for particles from pore to pore is obtained between network model results and CTRW theory. Based on the truncated power-law interpretation of PDF-s, the physical origin of the power-law scaling of dispersion coefficient vs. Peclet number has been explained for unconsolidated porous media, sands and a number of sandstones, arriving at the same conclusion from numerical network modelling, analytic CTRW theory and experiment. Future directions for further applications of the methodology presented are discussed in relation to the scale- dependent solute dispersion and reactive transport. Significance of pre-asymptotic dispersion in porous media is addressed from pore-scale upwards and the impact of heterogeneity is discussed. The length traveled by solute plumes before Gaussian behaviour is reached increases with an increase in heterogeneity and/or Pe. This opens up the question on the nature of dispersion in natural systems where the heterogeneities at the larger scales will profoundly increase the range of velocities in the aquifer, thus considerably delaying the asymptotic approach to Gaussian behaviour. As a consequence, the asymptotic behaviour might not be reached at the field scale.

Gravity-oriented satellite dynamics subject to gravitational and active damping torques

NASA Astrophysics Data System (ADS)

Sarychev, V. A.; Gutnik, S. A.

2018-01-01

The dynamics of the rotational motion of a satellite moving in the central Newtonian field of force over a circular orbit under the effect of gravitational and active damping torques, which depend on the satellite angular velocity projections, has been investigated. The paper proposes a method of determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of damping coefficients and principal central moments of inertia. The conditions of their existence have been obtained. For a zero equilibrium position where the axes of the satellite-centered coordinate system coincide with the axes of the orbital coordinate system, the necessary and sufficient conditions for asymptotic stability are obtained using the Routh-Hurwitz criterion. A detailed analysis of the regions where the conditions of the asymptotic stability of a zero equilibrium position are fulfilled have been obtained depending on three dimensionless parameters of the problem, and the numerical study of the process of attenuation of satellite's spatial oscillations for various damping coefficients has been carried out. It has been shown that there is a wide range of damping parameters from which, by choosing the necessary values, one can provide the asymptotic stability of satellite's zero equilibrium position in the orbital coordinate system.

Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Glushikhina, M. V.

2018-04-01

The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman-Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron-electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron-electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8.

Deformation of a plate with periodically changing parameters

NASA Astrophysics Data System (ADS)

Naumova, Natalia V.; Ivanov, Denis; Voloshinova, Tatiana

2018-05-01

Deformation of reinforced square plate under external pressure is considered. The averaged fourth-order partial differential equation for the plate deflection w is obtained. The new mathematical model of the plate is offered. Asymptotic averaging and Finite Elements Method (ANSYS) are used to get the values of normal deflections of the plate surface. The comparison of numerical and asymptotic results is performed.

Finite element analysis of the biaxial cyclic tensile loading of the elastoplastic plate with the central hole: asymptotic regimes

NASA Astrophysics Data System (ADS)

Turkova, Vera; Stepanova, Larisa

2018-03-01

For elastistoplastic structure elements under cyclic loading three types of asymptotic behavior are well known: shakedown, cyclic plasticity or ratcheting. In structure elements operating in real conditions ratcheting must always be excluded since it caused the incremental fracture of structure by means of the accumulation of plastic strains. In the present study results of finite-element (FEM) calculations of the asymptotical behavior of an elastoplastic plate with the central circular and elliptic holes under the biaxial cyclic loading for three different materials are presented. Incremental cyclic loading of the sample with stress concentrator (the central hole) is performed in the multifunctional finite-element package SIMULIA Abaqus. The ranges of loads found for shakedown, cyclic plasticity and ratcheting are presented. The results obtained are generalized and analyzed. Convenient normalization is suggested. The chosen normalization allows us to present all computed results, corresponding to separate materials, within one common curve with minimum scattering of the points. Convenience of the generalized diagram consists in a possibility to find an asymptotical behavior of an inelastic structure for materials for which computer calculations were not made.

Asymptotic modeling of transport phenomena at the interface between a fluid and a porous layer: Jump conditions

NASA Astrophysics Data System (ADS)

Angot, Philippe; Goyeau, Benoît; Ochoa-Tapia, J. Alberto

2017-06-01

We develop asymptotic modeling for two- or three-dimensional viscous fluid flow and convective transfer at the interface between a fluid and a porous layer. The asymptotic model is based on the fact that the thickness d of the interfacial transition region Ωfp of the one-domain representation is very small compared to the macroscopic length scale L . The analysis leads to an equivalent two-domain representation where transport phenomena in the transition layer of the one-domain approach are represented by algebraic jump boundary conditions at a fictive dividing interface Σ between the homogeneous fluid and porous regions. These jump conditions are thus stated up to first-order in O (d /L ) with d /L ≪1 . The originality and relevance of this asymptotic model lies in its general and multidimensional character. Indeed, it is shown that all the jump interface conditions derived for the commonly used 1D-shear flow are recovered by taking the tangential component of the asymptotic model. In that case, the comparison between the present model and the different models available in the literature gives explicit expressions of the effective jump coefficients and their associated scaling. In addition for multi-dimensional flows, the general asymptotic model yields the different components of the jump conditions including a new specific equation for the cross-flow pressure jump on Σ .

Asymptotic modeling of transport phenomena at the interface between a fluid and a porous layer: Jump conditions.

PubMed

Angot, Philippe; Goyeau, Benoît; Ochoa-Tapia, J Alberto

2017-06-01

We develop asymptotic modeling for two- or three-dimensional viscous fluid flow and convective transfer at the interface between a fluid and a porous layer. The asymptotic model is based on the fact that the thickness d of the interfacial transition region Ω_{fp} of the one-domain representation is very small compared to the macroscopic length scale L. The analysis leads to an equivalent two-domain representation where transport phenomena in the transition layer of the one-domain approach are represented by algebraic jump boundary conditions at a fictive dividing interface Σ between the homogeneous fluid and porous regions. These jump conditions are thus stated up to first-order in O(d/L) with d/L≪1. The originality and relevance of this asymptotic model lies in its general and multidimensional character. Indeed, it is shown that all the jump interface conditions derived for the commonly used 1D-shear flow are recovered by taking the tangential component of the asymptotic model. In that case, the comparison between the present model and the different models available in the literature gives explicit expressions of the effective jump coefficients and their associated scaling. In addition for multi-dimensional flows, the general asymptotic model yields the different components of the jump conditions including a new specific equation for the cross-flow pressure jump on Σ.

Homogeneity Pursuit

PubMed Central

Ke, Tracy; Fan, Jianqing; Wu, Yichao

2014-01-01

This paper explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when regression coefficients corresponding to neighboring geographical regions or a similar cluster of covariates are expected to be approximately the same. Sparsity corresponds to a special case of homogeneity with a large cluster of known atom zero. In this article, we propose a new method called clustering algorithm in regression via data-driven segmentation (CARDS) to explore homogeneity. New mathematics are provided on the gain that can be achieved by exploring homogeneity. Statistical properties of two versions of CARDS are analyzed. In particular, the asymptotic normality of our proposed CARDS estimator is established, which reveals better estimation accuracy for homogeneous parameters than that without homogeneity exploration. When our methods are combined with sparsity exploration, further efficiency can be achieved beyond the exploration of sparsity alone. This provides additional insights into the power of exploring low-dimensional structures in high-dimensional regression: homogeneity and sparsity. Our results also shed lights on the properties of the fussed Lasso. The newly developed method is further illustrated by simulation studies and applications to real data. Supplementary materials for this article are available online. PMID:26085701

Volume dependence of N-body bound states

NASA Astrophysics Data System (ADS)

König, Sebastian; Lee, Dean

2018-04-01

We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any number of spatial dimensions. The only assumptions are that the interactions have finite range. The finite-volume correction is a sum of contributions from all possible breakup channels. In the case where the separation is into two bound clusters, our result gives the leading volume dependence up to exponentially small corrections. If the separation is into three or more clusters, there is a power-law factor that is beyond the scope of this work, however our result again determines the leading exponential dependence. We also present two independent methods that use finite-volume data to determine asymptotic normalization coefficients. The coefficients are useful to determine low-energy capture reactions into weakly bound states relevant for nuclear astrophysics. Using the techniques introduced here, one can even extract the infinite-volume energy limit using data from a single-volume calculation. The derived relations are tested using several exactly solvable systems and numerical examples. We anticipate immediate applications to lattice calculations of hadronic, nuclear, and cold atomic systems.

Traversable wormholes satisfying the weak energy condition in third-order Lovelock gravity

NASA Astrophysics Data System (ADS)

Zangeneh, Mahdi Kord; Lobo, Francisco S. N.; Dehghani, Mohammad Hossein

2015-12-01

In this paper, we consider third-order Lovelock gravity with a cosmological constant term in an n -dimensional spacetime M4×Kn -4, where Kn -4 is a constant curvature space. We decompose the equations of motion to four and higher dimensional ones and find wormhole solutions by considering a vacuum Kn -4 space. Applying the latter constraint, we determine the second- and third-order Lovelock coefficients and the cosmological constant in terms of specific parameters of the model, such as the size of the extra dimensions. Using the obtained Lovelock coefficients and Λ , we obtain the four-dimensional matter distribution threading the wormhole. Furthermore, by considering the zero tidal force case and a specific equation of state, given by ρ =(γ p -τ )/[ω (1 +γ )], we find the exact solution for the shape function which represents both asymptotically flat and nonflat wormhole solutions. We show explicitly that these wormhole solutions in addition to traversibility satisfy the energy conditions for suitable choices of parameters and that the existence of a limited spherically symmetric traversable wormhole with normal matter in a four-dimensional spacetime implies a negative effective cosmological constant.

Helicopter rotor loads using matched asymptotic expansions: User's manual

NASA Technical Reports Server (NTRS)

Pierce, G. A.; Vaidyanathan, A. R.

1983-01-01

Computer programs were developed to implement the computational scheme arising from Van Holten's asymptotic method for calculating airloads on a helicopter rotor blade in forward flight, and a similar technique which is based on a discretized version of the method. The basic outlines of the two programs are presented, followed by separate descriptions of the input requirements and output format. Two examples illustrating job entry with appropriate input data and corresponding output are included. Appendices contain a sample table of lift coefficient data for the NACA 0012 air foil and listings of the two programs.

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

PubMed

Kanna, T; Sakkaravarthi, K; Tamilselvan, K

2013-12-01

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.

Reaction rate of the 13C(α,n)16O neutron source using the ANC of the -3 keV resonance measured with the THM

NASA Astrophysics Data System (ADS)

La Cognata, M.; Spitaleri, C.; Trippella, O.; Kiss, G. G.; Rogachev, G. V.; Mukhamedzhanov, A. M.; Avila, M.; Guardo, G. L.; Koshchiy, E.; Kuchera, A.; Lamia, L.; Puglia, S. M. R.; Romano, S.; Santiago, D.; Spartà, R.

2016-01-01

The s-process is responsible of the synthesis of most of the nuclei in the mass range 90 ≤ A ≤ 208. It consists in a series of neutron capture reactions on seed nuclei followed by β-decays, since the neutron accretion rate is slower than the β-decay rate. Such small neutron flux is supplied by the 13C(α,n)16O reaction. It is active inside the helium-burning shell of asymptotic giant branch stars, at temperatures < 108 K, corresponding to an energy interval of 140-230 keV. In this region, the astrophysical S (E)-factor is dominated by the -3 keV sub-threshold resonance due to the 6.356 MeV level in 17O. In this work, we have applied the Trojan Horse Method (THM) to the 13C(6Li,n16O)d quasi-free reaction to extract the 6.356 MeV level resonance parameters, in particular the asymptotic normalization coefficient . A preliminary analysis of a partial data set has lead to , slightly larger than the values in the literature. However, the deduced 13C(α, n)16O reaction rate is in agreement with most results in the literature at ˜ 108 K, with enhanced accuracy thanks to our innovative approach merging together ANC and THM.

Third Bose fugacity coefficient in one dimension, as a function of asymptotic quantities

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

Amaya-Tapia, A., E-mail: jano@fis.unam.mx; Larsen, S.Y.; Lassaut, M.

2011-02-15

In one of the very few exact quantum mechanical calculations of fugacity coefficients, [L.R. Dodd, A.M. Gibbs. J. Math. Phys. 15 (1974) 41] obtained b{sub 2} and b{sub 3} for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For b{sub 2}, we have shown [A. Amaya-Tapia, S.Y. Larsen, M. Lassaut. Mol. Phys. 103 (2005) 1301-1306. < (arXiv:physics/0405150)>] that Dodd and Gibbs' result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in one dimension. Now, we develop an exact expressionmore » for b{sub 3}-b{sub 3}{sup 0} (where b{sub 3}{sup 0} is the free particle fugacity coefficient) in terms of sums and differences of three-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a Distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the twofold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel. The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.« less

On the gravitational potential and field anomalies due to thin mass layers

NASA Technical Reports Server (NTRS)

Ockendon, J. R.; Turcotte, D. L.

1977-01-01

The gravitational potential and field anomalies for thin mass layers are derived using the technique of matched asymptotic expansions. An inner solution is obtained using an expansion in powers of the thickness and it is shown that the outer solution is given by a surface distribution of mass sources and dipoles. Coefficients are evaluated by matching the inner expansion of the outer solution with the outer expansion of the inner solution. The leading term in the inner expansion for the normal gravitational field gives the Bouguer formula. The leading term in the expansion for the gravitational potential gives an expression for the perturbation to the geoid. The predictions given by this term are compared with measurements by satellite altimetry. The second-order terms in the expansion for the gravitational field are required to predict the gravity anomaly at a continental margin. The results are compared with observations.

Multiple normalized solutions for a planar gauged nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Luo, Xiao

2018-06-01

We study the existence, multiplicity, quantitative property and asymptotic behavior of normalized solutions for a gauged nonlinear Schrödinger equation arising from the Chern-Simons theory Δ u + ω u +|x|^2u+ λ ( {{h^2}(| x | )}/{{{| x | ^2}}} + \\int \\limits _{| x | }^{ + ∞} {{h(s)}/s} {u^2}(s)ds) u = {| u | ^{p - 2}}u,\\quad x\\in R^2, where ω \\in R, λ >0, p>4 and h(s) = 1/2\\int \\limits _0^s {r{u^2}(r)dr} . Combining constraint minimization method and minimax principle, we prove that the problem possesses at least two normalized solutions: One is a ground state and the other is an excited state. Furthermore, the asymptotic behavior and quantitative property of the ground state are analyzed.

Two parametric voice source models and their asymptotic analysis

NASA Astrophysics Data System (ADS)

Leonov, A. S.; Sorokin, V. N.

2014-05-01

The paper studies the asymptotic behavior of the function for the area of the glottis near moments of its opening and closing for two mathematical voice source models. It is shown that in the first model, the asymptotics of the area function obeys a power law with an exponent of no less that 1. Detailed analysis makes it possible to refine these limits depending on the relative sizes of the intervals of a closed and open glottis. This work also studies another parametric model of the area of the glottis, which is based on a simplified physical-geometrical representation of vocal-fold vibration processes. This is a special variant of the well-known two-mass model and contains five parameters: the period of the main tone, equivalent masses on the lower and upper edge of vocal folds, the coefficient of elastic resistance of the lower vocal fold, and the delay time between openings of the upper and lower folds. It is established that the asymptotics of the obtained function for the area of the glottis obey a power law with an exponent of 1 both for opening and closing.

An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher-KPP equation

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.; Trifonov, A. Yu.

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher-KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.

Khokhlov Zabolotskaya Kuznetsov type equation: nonlinear acoustics in heterogeneous media

NASA Astrophysics Data System (ADS)

Kostin, Ilya; Panasenko, Grigory

2006-04-01

The KZK type equation introduced in this Note differs from the traditional form of the KZK model known in acoustics by the assumptions on the nonlinear term. For this modified form, a global existence and uniqueness result is established for the case of non-constant coefficients. Afterwards the asymptotic behaviour of the solution of the KZK type equation with rapidly oscillating coefficients is studied. To cite this article: I. Kostin, G. Panasenko, C. R. Mecanique 334 (2006).

Long-time asymptotics of the Navier-Stokes and vorticity equations on R(3).

PubMed

Gallay, Thierry; Wayne, C Eugene

2002-10-15

We use the vorticity formulation to study the long-time behaviour of solutions to the Navier-Stokes equation on R(3). We assume that the initial vorticity is small and decays algebraically at infinity. After introducing self-similar variables, we compute the long-time asymptotics of the rescaled vorticity equation up to second order. Each term in the asymptotics is a self-similar divergence-free vector field with Gaussian decay at infinity, and the coefficients in the expansion can be determined by solving a finite system of ordinary differential equations. As a consequence of our results, we are able to characterize the set of solutions for which the velocity field satisfies ||u(.,t)||(L(2)) = o(t(-5/4)) as t-->+ infinity. In particular, we show that these solutions lie on a smooth invariant submanifold of codimension 11 in our function space.

Holography for a De Sitter-Esque geometry

NASA Astrophysics Data System (ADS)

Anninos, Dionysios; de Buyl, Sophie; Detournay, Stéphane

2011-05-01

Warped dS3 arises as a solution to topologically massive gravity (TMG) with positive cosmological constant +1/ ℓ 2 and Chern-Simons coefficient 1/ μ in the region μ 2 ℓ 2 < 27. It is given by a real line fibration over two-dimensional de Sitter space and is equivalent to the rotating Nariai geometry at fixed polar angle. We study the thermodynamic and asymptotic structure of a family of geometries with warped dS3 asymptotics. Interestingly, these solutions have both a cosmological horizon and an internal one, and their entropy is unbounded from above unlike black holes in regular de Sitter space. The asymptotic symmetry group resides at future infinity and is given by a semi-direct product of a Virasoro algebra and a current algebra. The right moving central charge vanishes when μ 2 ℓ 2 = 27/5. We discuss the possible holographic interpretation of these de Sitter-esque spacetimes.

Estimation and model selection of semiparametric multivariate survival functions under general censorship.

PubMed

Chen, Xiaohong; Fan, Yanqin; Pouzo, Demian; Ying, Zhiliang

2010-07-01

We study estimation and model selection of semiparametric models of multivariate survival functions for censored data, which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals. We obtain the consistency and root- n asymptotic normality of a two-step copula estimator to the pseudo-true copula parameter value according to KLIC, and provide a simple consistent estimator of its asymptotic variance, allowing for a first-step nonparametric estimation of the marginal survivals. We establish the asymptotic distribution of the penalized pseudo-likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship. An empirical application is provided.

Estimation and model selection of semiparametric multivariate survival functions under general censorship

PubMed Central

Chen, Xiaohong; Fan, Yanqin; Pouzo, Demian; Ying, Zhiliang

2013-01-01

We study estimation and model selection of semiparametric models of multivariate survival functions for censored data, which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals. We obtain the consistency and root-n asymptotic normality of a two-step copula estimator to the pseudo-true copula parameter value according to KLIC, and provide a simple consistent estimator of its asymptotic variance, allowing for a first-step nonparametric estimation of the marginal survivals. We establish the asymptotic distribution of the penalized pseudo-likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship. An empirical application is provided. PMID:24790286

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

Starchenko, S. V., E-mail: sstarchenko@mail.ru

The optimum (to my mind) scaling of the combined thermal and compositional convection in a rapidly rotating plane layer is proposed.This scaling follows from self-consistent estimates of typical physical quantities. Similarity coefficients are introduced for the ratio convection dissipation/convection generation (s) and the ratio thermal convection/compositional convection (r). The third new and most important coefficient δ is the ratio of the characteristic size normal to the axis of rotation to the layer thickness. The faster the rotation, the lower δ. In the case of the liquid Earth core, δ ~ 10{sup –3} substitutes for the generally accepted Ekman number (Emore » ~ 10{sup –15}) and s ~ 10{sup –6} substitutes for the inverse Rayleigh number 1/Ra ~ 10{sup –30}. It is found that, at turbulent transport coefficients, number s and the Prandtl number are on the order of unity for any objects and δ is independent of transport coefficients. As a result of expansion in powers of δ, an initially 3D system of six variables is simplified to an almost 2D system of four variables without δ. The problem of convection excitation in the main volume is algebraically solved and this problem for critical values is analytically solved. Dispersion relations and general expressions for critical wavenumbers, numbers s (which determine Rayleigh numbers), other critical parameters, and asymptotic solutions are derived. Numerical estimates are made for the liquid cores in the planets that resemble the Earth. Further possible applications of the results obtained are proposed for the interior of planets, moons, their oceans, stars, and experimental objects.« less

Stellar reaction rate for {sup 22}Mg+p->{sup 23}Al from the asymptotic normalization coefficient in the mirror nuclear system {sup 22}Ne+n->{sup 23}Ne

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

Al-Abdullah, T.; Physics Department, Hashemite University, Zarqa 13115; Carstoiu, F.

2010-03-15

The production of {sup 22}Na in ONe novae can be influenced by the {sup 22}Mg(p,gamma){sup 23}Al reaction. To investigate this reaction rate at stellar energies, we have determined the asymptotic normalization coefficient (ANC) for {sup 22}Mg+p->{sup 23}Al through measurements of the ANCs in the mirror nuclear system {sup 22}Ne+n->{sup 23}Ne. The peripheral neutron-transfer reactions {sup 13}C({sup 12}C,{sup 13}C){sup 12}C and {sup 13}C({sup 22}Ne,{sup 23}Ne){sup 12}C were studied. The identical entrance and exit channels of the first reaction make it possible to extract independently the ground-state ANC in {sup 13}C. Our experiment gives C{sub p{sub 1/2}}{sup 2}({sup 13}C)=2.24+-0.11 fm{sup -1}, whichmore » agrees with the value obtained from several previous measurements. The weighted average for all the obtained C{sub p{sub 1/2}}{sup 2} is 2.31+-0.08 fm{sup -1}. This value is adopted to be used in obtaining the ANCs in {sup 23}Ne. The differential cross sections for the reaction {sup 13}C({sup 22}Ne,{sup 23}Ne){sup 12}C leading to the J{sup {pi}}=5/2{sup +} and 1/2{sup +} states in {sup 23}Ne have been measured at 12 MeV/u. Optical model parameters for use in the DWBA calculations were obtained from measurements of the elastic scatterings {sup 22}Ne+{sup 13}C and {sup 22}Ne+{sup 12}C. The extracted ANC for the ground state in {sup 23}Ne, C{sub d{sub 5/2}}{sup 2}=0.86+-0.08+-0.12 fm{sup -1}, is converted to its corresponding value in {sup 23}Al using mirror symmetry to give C{sub d{sub 5/2}}{sup 2}({sup 23}Al)=(4.63+-0.77)x10{sup 3} fm{sup -1}. The astrophysical S factor S(0) for the {sup 22}Mg(p,gamma) reaction was determined to be 0.96+-0.11 keV b. The consequences for nuclear astrophysics are discussed.« less

Mode-independent attenuation in evanescent-field sensors

NASA Astrophysics Data System (ADS)

Gnewuch, Harald; Renner, Hagen

1995-03-01

Generally, the total power attenuation in multimode evanescent-field sensor waveguides is nonproportional to the bulk absorbance because the modal attenuation constants differ. Hence a direct measurement is difficult and is additionally aggravated because the waveguide absorbance is highly sensitive to the specific launching conditions at the waveguide input. A general asymptotic formula for the modal power attenuation in strongly asymmetric inhomogeneous planar waveguides with arbitrarily distributed weak absorption in the low-index superstrate is derived. Explicit expressions for typical refractive-index profiles are given. Except when very close to the cutoff, the predicted asymptotic attenuation behavior agrees well with exact calculations. The ratio of TM versus TE absorption has been derived to be (2 - n0 2/nf2 ) for arbitrary profiles. Waveguides with a linear refractive-index profile show mode-independent attenuation coefficients within each polarization. Further, the asymptotic sensitivity is independent of the wavelength, so that it should be possible to directly measure the spectral variation of the bulk absorption. The mode independence of the attenuation has been verified experimentally for a second-order polynomial profile, which is close to a linear refractive-index distribution. In contrast, the attenuation in the step-profile waveguide has been found to depend strongly on the mode number, as predicted by theory. A strong spread of the modal attenuation coefficients is also predicted for the parabolic-profile waveguide sensor.

Analytical scalings of the linear Richtmyer-Meshkov instability when a shock is reflected.

PubMed

Campos, F Cobos; Wouchuk, J G

2016-05-01

When a planar shock hits a corrugated contact surface between two fluids, hydrodynamic perturbations are generated in both fluids that result in asymptotic normal and tangential velocity perturbations in the linear stage, the so called Richtmyer-Meshkov instability. In this work, explicit and exact analytical expansions of the asymptotic normal velocity (δv_{i}^{∞}) are presented for the general case in which a shock is reflected back. The expansions are derived from the conservation equations and take into account the whole perturbation history between the transmitted and reflected fronts. The important physical limits of weak and strong shocks and the high/low preshock density ratio at the contact surface are shown. An approximate expression for the normal velocity, valid even for high compression regimes, is given. A comparison with recent experimental data is done. The contact surface ripple growth is studied during the linear phase showing good agreement between theory and experiments done in a wide range of incident shock Mach numbers and preshock density ratios, for the cases in which the initial ripple amplitude is small enough. In particular, it is shown that in the linear asymptotic phase, the contact surface ripple (ψ_{i}) grows as ψ_{∞}+δv_{i}^{∞}t, where ψ_{∞} is an asymptotic ordinate different from the postshock ripple amplitude at t=0+. This work is a continuation of the calculations of F. Cobos Campos and J. G. Wouchuk, [Phys. Rev. E 90, 053007 (2014)PLEEE81539-375510.1103/PhysRevE.90.053007] for a single shock moving into one fluid.

Propagation and stability of wavelike solutions of finite difference equations with variable coefficients

NASA Technical Reports Server (NTRS)

Giles, M. B.; Thompkins, W. T., Jr.

1985-01-01

The propagation and dissipation of wavelike solutions to finite difference equations is analyzed on the basis of an asymptotic approach in which a wave solution is expressed as a product of a complex amplitude and an oscillatory phase function whose frequency and wavenumber may also be complex. An asymptotic expansion leads to a local dispersion relation for wavenumber and frequency; the first-order terms produce an equation for the amplitude in which the local group velocity appears as the convection velocity of the amplitude. Equations for the motion of wavepackets and their interaction at boundaries are derived, and a global stability analysis is carried out.

Unsteady transonic flow analysis for low aspect ratio, pointed wings.

NASA Technical Reports Server (NTRS)

Kimble, K. R.; Ruo, S. Y.; Wu, J. M.; Liu, D. Y.

1973-01-01

Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flow field. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms.

Estimation of Renyi exponents in random cascades

USGS Publications Warehouse

Troutman, Brent M.; Vecchia, Aldo V.

1999-01-01

We consider statistical estimation of the Re??nyi exponent ??(h), which characterizes the scaling behaviour of a singular measure ?? defined on a subset of Rd. The Re??nyi exponent is defined to be lim?????0 [{log M??(h)}/(-log ??)], assuming that this limit exists, where M??(h) = ??i??h(??i) and, for ??>0, {??i} are the cubes of a ??-coordinate mesh that intersect the support of ??. In particular, we demonstrate asymptotic normality of the least-squares estimator of ??(h) when the measure ?? is generated by a particular class of multiplicative random cascades, a result which allows construction of interval estimates and application of hypothesis tests for this scaling exponent. Simulation results illustrating this asymptotic normality are presented. ?? 1999 ISI/BS.

Semiclassical geometry of integrable systems

NASA Astrophysics Data System (ADS)

Reshetikhin, Nicolai

2018-04-01

The main result of this paper is a formula for the scalar product of semiclassical eigenvectors of two integrable systems on the same symplectic manifold. An important application of this formula is the Ponzano–Regge type of asymptotic of Racah–Wigner coefficients. Dedicated to the memory of P P Kulish.

Aspects of Cool-Flame Supported Droplet Combustion in Microgravity

NASA Technical Reports Server (NTRS)

Nayagam, Vedha; Dietrich, Daniel L.; Williams, Forman A.

2015-01-01

Droplet combustion experiments performed on board the International Space Station have shown that normal-alkane fuels with negative temperature coefficient (NTC) chemistry can support quasi-steady, low-temperature combustion without any visible flame. Here we review the results for n-decane, n-heptane, and n-octane droplets burning in carbon dioxidehelium diluted environments at different pressures and initial droplet sizes. Experimental results for cool-flame burning rates, flame standoff ratios, and extinction diameters are compared against simplified theoretical models of the phenomenon. A simplified quasi-steady model based on the partial-burning regime of Lin predicts the burning rate, and flame standoff ratio reasonably well for all three normal alkanes. The second-stage cool-flame burning and extinction following the first-stage hot-flame combustion, however, shows a small dependence on the initial droplet size, thus deviating from the quasi-steady results. An asymptotic model that estimates the oxygen depletion by the hot flame and its influence on cool-flame burning rates is shown to correct the quasi-steady results and provide a better comparison with the measured burning-rate results.This work was supported by the NASA Space Life and Physical Sciences Research and Applications Program and the International Space Station Program.

A Third Moment Adjusted Test Statistic for Small Sample Factor Analysis.

PubMed

Lin, Johnny; Bentler, Peter M

2012-01-01

Goodness of fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square; but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne's asymptotically distribution-free method and Satorra Bentler's mean scaling statistic were developed under the presumption of non-normality in the factors and errors. This paper finds new application to the case where factors and errors are normally distributed in the population but the skewness of the obtained test statistic is still high due to sampling error in the observed indicators. An extension of Satorra Bentler's statistic is proposed that not only scales the mean but also adjusts the degrees of freedom based on the skewness of the obtained test statistic in order to improve its robustness under small samples. A simple simulation study shows that this third moment adjusted statistic asymptotically performs on par with previously proposed methods, and at a very small sample size offers superior Type I error rates under a properly specified model. Data from Mardia, Kent and Bibby's study of students tested for their ability in five content areas that were either open or closed book were used to illustrate the real-world performance of this statistic.

The effect of normalization of Partial Directed Coherence on the statistical assessment of connectivity patterns: a simulation study.

PubMed

Toppi, J; Petti, M; Vecchiato, G; Cincotti, F; Salinari, S; Mattia, D; Babiloni, F; Astolfi, L

2013-01-01

Partial Directed Coherence (PDC) is a spectral multivariate estimator for effective connectivity, relying on the concept of Granger causality. Even if its original definition derived directly from information theory, two modifies were introduced in order to provide better physiological interpretations of the estimated networks: i) normalization of the estimator according to rows, ii) squared transformation. In the present paper we investigated the effect of PDC normalization on the performances achieved by applying the statistical validation process on investigated connectivity patterns under different conditions of Signal to Noise ratio (SNR) and amount of data available for the analysis. Results of the statistical analysis revealed an effect of PDC normalization only on the percentages of type I and type II errors occurred by using Shuffling procedure for the assessment of connectivity patterns. No effects of the PDC formulation resulted on the performances achieved during the validation process executed instead by means of Asymptotic Statistic approach. Moreover, the percentages of both false positives and false negatives committed by Asymptotic Statistic are always lower than those achieved by Shuffling procedure for each type of normalization.

Simulating Pre-Asymptotic, Non-Fickian Transport Although Doing Simple Random Walks - Supported By Empirical Pore-Scale Velocity Distributions and Memory Effects

NASA Astrophysics Data System (ADS)

Most, S.; Jia, N.; Bijeljic, B.; Nowak, W.

2016-12-01

Pre-asymptotic characteristics are almost ubiquitous when analyzing solute transport processes in porous media. These pre-asymptotic aspects are caused by spatial coherence in the velocity field and by its heterogeneity. For the Lagrangian perspective of particle displacements, the causes of pre-asymptotic, non-Fickian transport are skewed velocity distribution, statistical dependencies between subsequent increments of particle positions (memory) and dependence between the x, y and z-components of particle increments. Valid simulation frameworks should account for these factors. We propose a particle tracking random walk (PTRW) simulation technique that can use empirical pore-space velocity distributions as input, enforces memory between subsequent random walk steps, and considers cross dependence. Thus, it is able to simulate pre-asymptotic non-Fickian transport phenomena. Our PTRW framework contains an advection/dispersion term plus a diffusion term. The advection/dispersion term produces time-series of particle increments from the velocity CDFs. These time series are equipped with memory by enforcing that the CDF values of subsequent velocities change only slightly. The latter is achieved through a random walk on the axis of CDF values between 0 and 1. The virtual diffusion coefficient for that random walk is our only fitting parameter. Cross-dependence can be enforced by constraining the random walk to certain combinations of CDF values between the three velocity components in x, y and z. We will show that this modelling framework is capable of simulating non-Fickian transport by comparison with a pore-scale transport simulation and we analyze the approach to asymptotic behavior.

Statistical aspects of genetic association testing in small samples, based on selective DNA pooling data in the arctic fox.

PubMed

Szyda, Joanna; Liu, Zengting; Zatoń-Dobrowolska, Magdalena; Wierzbicki, Heliodor; Rzasa, Anna

2008-01-01

We analysed data from a selective DNA pooling experiment with 130 individuals of the arctic fox (Alopex lagopus), which originated from 2 different types regarding body size. The association between alleles of 6 selected unlinked molecular markers and body size was tested by using univariate and multinomial logistic regression models, applying odds ratio and test statistics from the power divergence family. Due to the small sample size and the resulting sparseness of the data table, in hypothesis testing we could not rely on the asymptotic distributions of the tests. Instead, we tried to account for data sparseness by (i) modifying confidence intervals of odds ratio; (ii) using a normal approximation of the asymptotic distribution of the power divergence tests with different approaches for calculating moments of the statistics; and (iii) assessing P values empirically, based on bootstrap samples. As a result, a significant association was observed for 3 markers. Furthermore, we used simulations to assess the validity of the normal approximation of the asymptotic distribution of the test statistics under the conditions of small and sparse samples.

Normality of different orders for Cantor series expansions

NASA Astrophysics Data System (ADS)

Airey, Dylan; Mance, Bill

2017-10-01

Let S \\subseteq {N} have the property that for each k \\in S the set (S - k) \\cap {N} \\setminus S has asymptotic density 0. We prove that there exists a basic sequence Q where the set of numbers Q-normal of all orders in S but not Q-normal of all orders not in S has full Hausdorff dimension. If the function \

Measuring agreement of multivariate discrete survival times using a modified weighted kappa coefficient.

PubMed

Guo, Ying; Manatunga, Amita K

2009-03-01

Assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects. We present a modified weighted kappa coefficient to measure agreement between bivariate discrete survival times. The proposed kappa coefficient accommodates censoring by redistributing the mass of censored observations within the grid where the unobserved events may potentially happen. A generalized modified weighted kappa is proposed for multivariate discrete survival times. We estimate the modified kappa coefficients nonparametrically through a multivariate survival function estimator. The asymptotic properties of the kappa estimators are established and the performance of the estimators are examined through simulation studies of bivariate and trivariate survival times. We illustrate the application of the modified kappa coefficient in the presence of censored observations with data from a prostate cancer study.

Cylindrical Couette flow of a rarefied gas: Effect of a boundary condition on the inverted velocity profile.

PubMed

Kosuge, Shingo

2015-07-01

The cylindrical Couette flow of a rarefied gas between a rotating inner cylinder and a stationary outer cylinder is investigated under the following two kinds of kinetic boundary conditions. One is the modified Maxwell-type boundary condition proposed by Dadzie and Méolans [J. Math. Phys. 45, 1804 (2004)] and the other is the Cercignani-Lampis condition, both of which have separate accommodation coefficients associated with the molecular velocity component normal to the boundary and with the tangential component. An asymptotic analysis of the Boltzmann equation for small Knudsen numbers and a numerical analysis of the Bhatnagar-Gross-Krook model equation for a wide range of the Knudsen number are performed to clarify the effect of each accommodation coefficient as well as of the boundary condition itself on the behavior of the gas, especially on the flow-velocity profile. As a result, the velocity-slip and temperature-jump conditions corresponding to the above kinetic boundary conditions are derived, which are necessary for the fluid-dynamic description of the problem for small Knudsen numbers. The parameter range for the onset of the velocity inversion phenomenon, which is related mainly to the decrease in the tangential momentum accommodation, is also obtained.

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. II - Wall shear stress

NASA Technical Reports Server (NTRS)

Liou, M. S.; Adamson, T. C., Jr.

1980-01-01

Asymptotic methods are used to calculate the shear stress at the wall for the interaction between a normal shock wave and a turbulent boundary layer on a flat plate. A mixing length model is used for the eddy viscosity. The shock wave is taken to be strong enough that the sonic line is deep in the boundary layer and the upstream influence is thus very small. It is shown that unlike the result found for laminar flow an asymptotic criterion for separation is not found; however, conditions for incipient separation are computed numerically using the derived solution for the shear stress at the wall. Results are compared with available experimental measurements.

Finite field equation of Yang--Mills theory

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

Brandt, R.A.; Wing-Chiu, N.; Yeung, W.

1980-03-01

We consider the finite local field equation -)(1+1/..cap alpha.. (1+f/sub 4/))g/sup munu/D'Alembertian-partial/sup ..mu../partial/sup ..nu../)A/sup nua/ =-(1+f/sub 3/) g/sup 2/N(A/sup c/..nu..A/sup a/..mu..A/sub ..nu..//sup c/) +xxx+(1-s)/sup 2/M/sup 2/A/sup a/..mu.., introduced by Lowenstein to rigorously describe SU(2) Yang--Mills theory, which is written in terms of normal products. We also consider the operator product expansion A/sup c/..nu..(x+xi) A/sup a/..mu..(x) A/sup b/lambda(x-xi) approx...sigma..M/sup c/ab..nu mu..lambda/sub c/'a'b'..nu..'..mu..'lambda' (xi) N(A/sup nuprimec/'A/sup muprimea/'A/sup lambdaprimeb/')(x), and using asymptotic freedom, we compute the leading behavior of the Wilson coefficients M/sup ...//sub .../(xi) with the help of a computer, and express the normal products in the field equation in terms ofmore » products of the c-number Wilson coefficients and of operator products like A/sup c/..nu..(x+xi) A/sup a/..mu..(x) A/sup b/lambda(x-xi) at separated points. Our result is -)(1+(1/..cap alpha..)(1+f/sub 4/))g/sup munu/D'Alembertian-partial/sup ..mu../partial/sup ..nu../)A/sup nua/ =-(1+f/sub 3/) g/sup 2/lim/sub xiarrow-right0/) (lnxi)/sup -0.28/2b/(A/sup c/..nu.. (x+xi) A/sup a/..mu..(x) A/sub ..nu..//sup c/(x-xi) +epsilon/sup a/bcA/sup muc/(x+xi) partial/sup ..nu../A/sup b//sub ..nu../(x)+xxx) +xxx)+(1-s)/sup 2/M/sup 2/A/sup a/..mu.., where ..beta.. (g) =-bg/sup 3/, and so (lnxi)/sup -0.28/2b/ is the leading behavior of the c-number coefficient multiplying the operator products in the field equation.« less

A stochastic asymptotic-preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty

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

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, School of Mathematical Science, MOELSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Shu, Ruiwen, E-mail: rshu2@math.wisc.edu

In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker–Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operatormore » that arises in the inversion of the Fokker–Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes.« less

M-Estimation for Discrete Data: Asymptotic Distribution Theory and Implications.

DTIC Science & Technology

1985-11-01

the influence function of an M-estimator is proportional to its score function; see Hampel (1974) or Huber (1981) for details. Surprisingly, M...consistently estimates 0 when the model is correct. Suppose now that OcR The influence function at F of an M-estimator for e has the form a(x,e...variance and the bound on the influence function at F This is assuming, of course, that the estimator is asymptotically normal at Fe. 6’ The truncation

A Third Moment Adjusted Test Statistic for Small Sample Factor Analysis

PubMed Central

Lin, Johnny; Bentler, Peter M.

2012-01-01

Goodness of fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square; but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne’s asymptotically distribution-free method and Satorra Bentler’s mean scaling statistic were developed under the presumption of non-normality in the factors and errors. This paper finds new application to the case where factors and errors are normally distributed in the population but the skewness of the obtained test statistic is still high due to sampling error in the observed indicators. An extension of Satorra Bentler’s statistic is proposed that not only scales the mean but also adjusts the degrees of freedom based on the skewness of the obtained test statistic in order to improve its robustness under small samples. A simple simulation study shows that this third moment adjusted statistic asymptotically performs on par with previously proposed methods, and at a very small sample size offers superior Type I error rates under a properly specified model. Data from Mardia, Kent and Bibby’s study of students tested for their ability in five content areas that were either open or closed book were used to illustrate the real-world performance of this statistic. PMID:23144511

Extrapolation of astrophysical S factors for the reaction {sup 14}N((p, {gamma}) {sup 15}O to near-zero energies

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

Artemov, S. V.; Igamov, S. B., E-mail: igamov@inp.uz; Tursunmakhatov, Q. I.

2012-03-15

The astrophysical S factors for the radiative-capture reaction {sup 14}N(p, {gamma}){sup 15}O in the region of ultralow energies were calculated on the basis of the R-matrix approach. The values of the radiative and protonic widths were fitted to new experimental data. The contribution of direct radiative capture to bound states of the {sup 15}O nucleus was determined with the aid of asymptotic normalization coefficients, whose values were refined in the present study on the basis of the results obtained from an analysis of the reaction {sup 14}N({sup 3}He, d){sup 15}O at three different energies of incident helium ions. A valuemore » of S(0) = 1.79 {+-} 0.31 keV b was obtained for the total astrophysical S factor, and the reaction rate was determined for the process {sup 14}N(p, {gamma}){sup 15}O.« less

A novel approach to interpretation of the time-dependent self-diffusion coefficient as a probe of porous media geometry.

PubMed

Loskutov, V V; Sevriugin, V A

2013-05-01

This article presents a new approximation describing fluid diffusion in porous media. Time dependence of the self-diffusion coefficient D(t) in the permeable porous medium is studied based on the assumption that diffusant molecules move randomly. An analytical expression for time dependence of the self-diffusion coefficient was obtained in the following form: D(t)=(D0-D∞)exp(-D0t/λ)+D∞, where D0 is the self-diffusion coefficient of bulk fluid, D∞ is the asymptotic value of the self-diffusion coefficient in the limit of long time values (t→∞), λ is the characteristic parameter of this porous medium with dimensionality of length. Applicability of the solution obtained to the analysis of experimental data is shown. The possibility of passing to short-time and long-time regimes is discussed. Copyright © 2013 Elsevier Inc. All rights reserved.

Normal versus Noncentral Chi-Square Asymptotics of Misspecified Models

ERIC Educational Resources Information Center

Chun, So Yeon; Shapiro, Alexander

2009-01-01

The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…

Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood versus Robust Methods

ERIC Educational Resources Information Center

Zhong, Xiaoling; Yuan, Ke-Hai

2011-01-01

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

Approximations to the distribution of a test statistic in covariance structure analysis: A comprehensive study.

PubMed

Wu, Hao

2018-05-01

In structural equation modelling (SEM), a robust adjustment to the test statistic or to its reference distribution is needed when its null distribution deviates from a χ 2 distribution, which usually arises when data do not follow a multivariate normal distribution. Unfortunately, existing studies on this issue typically focus on only a few methods and neglect the majority of alternative methods in statistics. Existing simulation studies typically consider only non-normal distributions of data that either satisfy asymptotic robustness or lead to an asymptotic scaled χ 2 distribution. In this work we conduct a comprehensive study that involves both typical methods in SEM and less well-known methods from the statistics literature. We also propose the use of several novel non-normal data distributions that are qualitatively different from the non-normal distributions widely used in existing studies. We found that several under-studied methods give the best performance under specific conditions, but the Satorra-Bentler method remains the most viable method for most situations. © 2017 The British Psychological Society.

Asymptotic dynamics of the exceptional Bianchi cosmologies

NASA Astrophysics Data System (ADS)

Hewitt, C. G.; Horwood, J. T.; Wainwright, J.

2003-05-01

In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies, being of the same generality as the models of Bianchi types VIII and IX. Secondly, it is the SH limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies. Using the orthonormal frame formalism and Hubble-normalized variables, we show that the exceptional Bianchi cosmologies differ from the non-exceptional Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the models exhibit an oscillatory approach to the initial singularity and hence are not asymptotically self-similar. Secondly, at late times, although the models are asymptotically self-similar, the future attractor for the vacuum-dominated models is the so-called Robinson-Trautman SH model instead of the vacuum SH plane wave models.

Asymptotic Normality of the Maximum Pseudolikelihood Estimator for Fully Visible Boltzmann Machines.

PubMed

Nguyen, Hien D; Wood, Ian A

2016-04-01

Boltzmann machines (BMs) are a class of binary neural networks for which there have been numerous proposed methods of estimation. Recently, it has been shown that in the fully visible case of the BM, the method of maximum pseudolikelihood estimation (MPLE) results in parameter estimates, which are consistent in the probabilistic sense. In this brief, we investigate the properties of MPLE for the fully visible BMs further, and prove that MPLE also yields an asymptotically normal parameter estimator. These results can be used to construct confidence intervals and to test statistical hypotheses. These constructions provide a closed-form alternative to the current methods that require Monte Carlo simulation or resampling. We support our theoretical results by showing that the estimator behaves as expected in simulation studies.

Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse

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

Kawakami, Hayato; Mitsuda, Eiji; Nambu, Yasusada

In considering the gravitational collapse of matter, it is an important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla et al. to the spherically symmetric gravitational collapse of a perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecturemore » that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.« less

Transport properties of gases and binary liquids near the critical point

NASA Technical Reports Server (NTRS)

Sengers, J. V.

1972-01-01

A status report is presented on the anomalies observed in the behavior of transport properties near the critical point of gases and binary liquids. The shear viscosity exhibits a weak singularity near the critical point. An analysis is made of the experimental data for those transport properties, thermal conductivity and thermal diffusivity near the gas-liquid critical point and binary diffusion coefficient near the critical mixing point, that determine the critical slowing down of the thermodynamic fluctuations in the order parameter. The asymptotic behavior of the thermal conductivity appears to be closely related to the asymptotic behavior of the correlation length. The experimental data for the thermal conductivity and diffusivity are shown to be in substantial agreement with current theoretical predictions.

Asymptotic 3-loop heavy flavor corrections to the charged current structure functions FLW+-W-(x ,Q2) and F2W+-W-(x ,Q2)

NASA Astrophysics Data System (ADS)

Behring, A.; Blümlein, J.; Falcioni, G.; De Freitas, A.; von Manteuffel, A.; Schneider, C.

2016-12-01

We derive the massive Wilson coefficients for the heavy flavor contributions to the nonsinglet charged current deep-inelastic scattering structure functions FLW+(x ,Q2)-FLW-(x ,Q2) and F2W+(x ,Q2)-F2W-(x ,Q2) in the asymptotic region Q2≫m2 to 3-loop order in quantum chromodynamics at general values of the Mellin variable N and the momentum fraction x . Besides the heavy quark pair production, also the single heavy flavor excitation s →c contributes. Numerical results are presented for the charm quark contributions, and consequences on the unpolarized Bjorken sum rule and Adler sum rule are discussed.

A New Test of Linear Hypotheses in OLS Regression under Heteroscedasticity of Unknown Form

ERIC Educational Resources Information Center

Cai, Li; Hayes, Andrew F.

2008-01-01

When the errors in an ordinary least squares (OLS) regression model are heteroscedastic, hypothesis tests involving the regression coefficients can have Type I error rates that are far from the nominal significance level. Asymptotically, this problem can be rectified with the use of a heteroscedasticity-consistent covariance matrix (HCCM)…

Diastolic function of the nonfilling human left ventricle.

PubMed

Paulus, W J; Vantrimpont, P J; Rousseau, M F

1992-12-01

To investigate an early-diastolic left ventricular suction effect in humans, tip-micromanometer left ventricular pressure recordings were obtained in patients with mitral stenosis at the time of balloon inflations during percutaneous mitral valvuloplasty performed with a self-positioning Inoue balloon, which fits tightly in the mitral orifice. When mitral inflow was impeded in anesthetized dogs, left ventricular pressure decayed to a negative asymptote value. This negative asymptote value was consistent with an early diastolic suction effect. Tip-micromanometer left ventricular pressure recordings were obtained in 23 patients with symptomatic mitral stenosis at the time of balloon inflations during percutaneous mitral valvuloplasty performed with a self-positioning Inoue balloon. The left ventricular diastolic asymptote pressure (P(asy)) was determined in 47 nonfilling beats with a sufficiently long (greater than 200 ms) diastolic time interval (that is, the interval from minimal first derivative of left ventricular pressure to left ventricular end-diastolic pressure) and equaled 2 +/- 3 mm Hg for beats with normal intraventricular conduction and 3 +/- 2 mm Hg for beats with aberrant intraventricular conduction. Left ventricular angiography was performed in five patients during the first inflation of the Inoue balloon at the time of complete balloon expansion. Left ventricular end-diastolic volume of the nonfilling beats averaged 38 +/- 14 ml and was comparable to the left ventricular end-systolic volume (39 +/- 19 ml) measured during baseline angiography before mitral valvuloplasty. Time constants of left ventricular pressure decay were calculated on 21 nonfilling beats with a diastolic time interval greater than 200 ms, normal intraventricular conduction and peak left ventricular pressure greater than 50 mm Hg. Time constants (T0 and TBF) derived from an exponential curve fit with zero asymptote pressure and with a best-fit asymptote pressure were compared with a time constant (T(asy)) derived from an exponential curve fit with the measured diastolic left ventricular asymptote pressure. The value for T(asy) (37 +/- 9 ms) was significantly smaller than that for TBF (68 +/- 28 ms, p less than 0.001) and the value for the measured diastolic left ventricular asymptote pressure (2 +/- 4 mm Hg) was significantly larger than that for the best-fit asymptote pressure (-9 +/- 11 mm Hg, p less than 0.001). T0 (44 +/- 20 ms) was significantly (p less than 0.01) different from TBF but not from T(asy). During balloon inflation of a self-positioning Inoue balloon, left ventricular pressure decayed continuously toward a positive asymptote value and left ventricular cavity volume was comparable to the left ventricular end-systolic volume of filling beats. In these nonfilling beats, the best-fit asymptote pressure was unrelated to the measured asymptote pressure and T0 was a better measure of T(asy) than was TBF. Reduced internal myocardial restoring forces, caused by different extracellular matrix of the human heart, reduced external myocardial restoring forces caused by low coronary perfusion pressure during the balloon inflation and inward motion of the balloon-occluded mitral valve into the left ventricular cavity could explain the failure to observe significant diastolic left ventricular suction in the human heart.

Transonic aerodynamic characteristics of the 10-percent-thick NASA supercritical airfoil 31

NASA Technical Reports Server (NTRS)

Harris, C. D.

1975-01-01

Refinements in a 10 percent thick supercritical airfoil (airfoil 31) have produced significant improvements in the drag characteristics compared with those for an earlier supercritical airfoil (airfoil 12) designed for the same normal force coefficient of 0.7. Drag creep was practically eliminated at normal force coefficients between about 0.4 and 0.7 and was greatly reduced at other normal force coefficients. Substantial reductions in the drag levels preceding drag divergence were also achieved at all normal force coefficients. The Mach numbers at which drag diverges were delayed for airfoil 31 at normal force coefficients up to about 0.6 (by approximately 0.01 and 0.02 at normal force coefficients of 0.4 and 0.6, respectively) but drag divergence occurred at slightly lower Mach numbers at higher normal force coefficients.

Seismological properties of intermediate-mass stars

NASA Astrophysics Data System (ADS)

Audard, N.; Provost, J.

1994-02-01

Stars more massive than about 1.2 solar mass are characterized by a convective core, which induces at its frontier a rapid variation of the density, sound speed and Brunt-Vaisala frequency, close to a discontinuity. For three stars of 1, 1.5 and 2 solar mass we have studied the properties of p-mode frequencies of high radial order and low degree, and we present results on the effects on p-mode oscillations of some rapid variations of the internal structure. We first point out the difficulties of the classical asymptotic theory to represent with accuracy the p-mode spectrum of the stars considered. We compare the numerical frequencies with asymptotic and polynomial approximations obtained from fits. The variation of the derived global coefficients characterizing the p-mode spectrum along the evolutionary tracks has been estimated; it would help to separate the effects of age and mass of intermediate-mass stars. The sensitivity of these coefficients to stellar parameters substantially depends on the stellar mass and must be considered for asteroseismic calibration. The effects of rapid variations in the stellar internal structure are finally considered. An asymptotic formula taking into account the rapid variation of the sound speed at the convective core boundary of the 1.5 and 2 solar mass stars predicts an oscillatory behavior of the frequencies with a very large period. We also show that the second frequency difference delta2nu = nun, l - 2nun-1, l + nun-2, l exhibits a substantial oscillation which corresponds to the region of the He II ionization of the 1, 1.5 and 2 solar mass stars.

Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)

NASA Technical Reports Server (NTRS)

Syed, H. H.; Volakis, John L.

1991-01-01

Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

An asymptotic analysis of the logrank test.

PubMed

Strawderman, R L

1997-01-01

Asymptotic expansions for the null distribution of the logrank statistic and its distribution under local proportional hazards alternatives are developed in the case of iid observations. The results, which are derived from the work of Gu (1992) and Taniguchi (1992), are easy to interpret, and provide some theoretical justification for many behavioral characteristics of the logrank test that have been previously observed in simulation studies. We focus primarily upon (i) the inadequacy of the usual normal approximation under treatment group imbalance; and, (ii) the effects of treatment group imbalance on power and sample size calculations. A simple transformation of the logrank statistic is also derived based on results in Konishi (1991) and is found to substantially improve the standard normal approximation to its distribution under the null hypothesis of no survival difference when there is treatment group imbalance.

Tensor products of process matrices with indefinite causal structure

NASA Astrophysics Data System (ADS)

Jia, Ding; Sakharwade, Nitica

2018-03-01

Theories with indefinite causal structure have been studied from both the fundamental perspective of quantum gravity and the practical perspective of information processing. In this paper we point out a restriction in forming tensor products of objects with indefinite causal structure in certain models: there exist both classical and quantum objects the tensor products of which violate the normalization condition of probabilities, if all local operations are allowed. We obtain a necessary and sufficient condition for when such unrestricted tensor products of multipartite objects are (in)valid. This poses a challenge to extending communication theory to indefinite causal structures, as the tensor product is the fundamental ingredient in the asymptotic setting of communication theory. We discuss a few options to evade this issue. In particular, we show that the sequential asymptotic setting does not suffer the violation of normalization.

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

NASA Technical Reports Server (NTRS)

Beam, Richard M.; Warming, Robert F.

1991-01-01

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations.

Electromagnetic sensing for the monitoring of structures and infrastructures: a model for the diffraction by penetrable wedges

NASA Astrophysics Data System (ADS)

Riccio, G.; Gennarelli, G.

2012-04-01

As well-known, the observation of structures and infrastructures by radar remote sensing involves the investigation of the high-frequency electromagnetic scattering by canonical shapes, such as cylinders and wedges. For instance, the ruptures caused by natural disasters can be represented in the form of a wedge-shaped fracture [1]. They modify the electromagnetic response of the scene under investigation and the Geometrical Theory of Diffraction (GTD) can be used as efficient tool for describing this occurrence. Diffraction by a wedge is a well-covered topic in the scientific literature, but the available results mainly concern impenetrable structures. The aim of this work is to provide Uniform Asymptotic Physical Optics (UAPO) diffraction coefficients in the case of lossless penetrable wedges illuminated by plane waves having normal incidence with respect to the edge. To this end, the original problem is subdivided into two parts relevant to the internal region of the wedge and the surrounding space. For what concerns the evaluation of the field diffracted in the outer region, equivalent electric and magnetic PO surface currents are used as sources in the radiation integral. They lie on the external faces of the wedge and their expressions change in accordance with the incidence direction. As a matter of fact, they involve the reflection and transmission Fresnel's coefficients when one external face is directly illuminated, and only the reflection Fresnel's coefficients if both the external faces are considered. A useful approximation and a uniform asymptotic evaluation of the resulting radiation integrals allow one to obtain the diffraction coefficients in terms of the Geometrical Optics (GO) response and the standard transition function of the Uniform Theory of Diffraction (UTD) [2]. The evaluation of the field diffracted in the inner region is tackled and solved by using equivalent PO surface currents on the internal faces of the wedge. Once such currents are determined, the diffracted field is evaluated by using a method like that employed for the exterior problem. The UAPO solutions for the diffracted field allow one to compensate the GO field discontinuities in the interior and exterior regions. Furthermore, they are simple to handle and implement in numerical simulators for radar remote sensing. Their accuracy is well assessed by comparisons with Finite-Difference Time-Domain (FDTD) results. [1] A.I. Kozlov, L. Lighart, A.I. Logvin, "Radar reflection from surfaces with ruptures," Proc. of MIKON 2000, vol. 1, pp. 347-350. [2] R.G. Kouyoumjian, P.H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. of IEEE, vol. 62, pp. 1448-1461, 1974.

Asymptotic expansions for 2D symmetrical laminar wakes

NASA Astrophysics Data System (ADS)

Belan, Marco; Tordella, Daniela

1999-11-01

An extension of the well known asymptotic representation of the 2D laminar incompressible wake past a symmetrical body is presented. Using the thin free shear layer approximation we determined solutions in terms of infinite asymptotic expansions. These are power series of the streamwise space variable with fractional negative coefficients. The general n-th order term has been analytically established. Through analysis of the behaviour of the same expansions inserted into the Navier-Stokes equations, we verified the self-consistency of the approximation showing that at the third order the correction due to pressure variations identically vanishes while the contribution of the longitudinal diffusion is still two-three order of magnitude smaller than that of the transversal diffusion, depending on Re. When the procedure is applied to the Navier-Stokes equations, we showed that further mathematical difficulties do not arise. Where opportune one may thus easily shift to the complete model. Through a spatial multiscaling approach, a brief account on the stability properties of these expansions as representing the non parallel basic flow of 2D wakes will be given.

Optical properties of non-spherical desert dust particles in the terrestrial infrared - An asymptotic approximation approach

NASA Astrophysics Data System (ADS)

Klüser, Lars; Di Biagio, Claudia; Kleiber, Paul D.; Formenti, Paola; Grassian, Vicki H.

2016-07-01

Optical properties (extinction efficiency, single scattering albedo, asymmetry parameter and scattering phase function) of five different desert dust minerals have been calculated with an asymptotic approximation approach (AAA) for non-spherical particles. The AAA method combines Rayleigh-limit approximations with an asymptotic geometric optics solution in a simple and straightforward formulation. The simulated extinction spectra have been compared with classical Lorenz-Mie calculations as well as with laboratory measurements of dust extinction. This comparison has been done for single minerals and with bulk dust samples collected from desert environments. It is shown that the non-spherical asymptotic approximation improves the spectral extinction pattern, including position of the extinction peaks, compared to the Lorenz-Mie calculations for spherical particles. Squared correlation coefficients from the asymptotic approach range from 0.84 to 0.96 for the mineral components whereas the corresponding numbers for Lorenz-Mie simulations range from 0.54 to 0.85. Moreover the blue shift typically found in Lorenz-Mie results is not present in the AAA simulations. The comparison of spectra simulated with the AAA for different shape assumptions suggests that the differences mainly stem from the assumption of the particle shape and not from the formulation of the method itself. It has been shown that the choice of particle shape strongly impacts the quality of the simulations. Additionally, the comparison of simulated extinction spectra with bulk dust measurements indicates that within airborne dust the composition may be inhomogeneous over the range of dust particle sizes, making the calculation of reliable radiative properties of desert dust even more complex.

Invariant target detection by a correlation radiometer

NASA Astrophysics Data System (ADS)

Murza, L. P.

1986-12-01

The paper is concerned with the problem of the optimal detection of a heat-emitting target by a two-channel radiometer with an unstable amplification circuit. An expression is obtained for an asymptotically sufficient detection statistic which is invariant to changes in the amplification coefficients of the channels. The algorithm proposed here can be implemented numerically using a relatively simple program.

Nonlinear stability of oscillatory core-annular flow: A generalized Kuramoto-Sivashinsky equation with time periodic coefficients

NASA Technical Reports Server (NTRS)

Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.

1994-01-01

In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.

Spectral methods in edge-diffraction theories

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

Arnold, J.M.

Spectral methods for the construction of uniform asymptotic representations of the field diffracted by an aperture in a plane screen are reviewed. These are separated into contrasting approaches, roughly described as physical and geometrical. It is concluded that the geometrical methods provide a direct route to the construction of uniform representations that are formally identical to the equivalent-edge-current concept. Some interpretive and analytical difficulties that complicate the physical methods of obtaining uniform representations are analyzed. Spectral synthesis proceeds directly from the ray geometry and diffraction coefficients, without any intervening current representation, and the representation is uniform at shadow boundaries andmore » caustics of the diffracted field. The physical theory of diffraction postulates currents on the diffracting screen that give rise to the diffracted field. The difficulties encountered in evaluating the current integrals are throughly examined, and it is concluded that the additional data provided by the physical theory of diffraction (diffraction coefficients off the Keller diffraction cone) are not actually required for obtaining uniform asymptotics at the leading order. A new diffraction representation that generalizes to arbitrary plane-convex apertures a formula given by Knott and Senior [Proc. IEEE 62, 1468 (1974)] for circular apertures is deduced. 34 refs., 1 fig.« less

Unifying Pore Network Modeling, Continuous Time Random Walk (CTRW) Theory and Experiment to Describe Impact of Spatial Heterogeneities on Solute Dispersion at Multiple Length-scales

NASA Astrophysics Data System (ADS)

Bijeljic, B.; Blunt, M. J.; Rhodes, M. E.

2009-04-01

This talk will describe and highlight the advantages offered by a novel methodology that unifies pore network modeling, CTRW theory and experiment in description of solute dispersion in porous media. Solute transport in a porous medium is characterized by the interplay of advection and diffusion (described by Peclet number, Pe) that cause dispersion of solute particles. Dispersion is traditionally described by dispersion coefficients, D, that are commonly calculated from the spatial moments of the plume. Using a pore-scale network model based on particle tracking, the rich Peclet-number dependence of dispersion coefficient is predicted from first principles and is shown to compare well with experimental data for restricted diffusion, transition, power-law and mechanical dispersion regimes in the asymptotic limit. In the asymptotic limit D is constant and can be used in an averaged advection-dispersion equation. However, it is highly important to recognize that, until the velocity field is fully sampled, the particle transport is non-Gaussian and D possesses temporal or spatial variation. Furthermore, temporal probability density functions (PDF) of tracer particles are studied in pore networks and an excellent agreement for the spectrum of transition times for particles from pore to pore is obtained between network model results and CTRW theory. Based on the truncated power-law interpretation of PDF-s, the physical origin of the power-law scaling of dispersion coefficient vs. Peclet number has been explained for unconsolidated porous media, sands and a number of sandstones, arriving at the same conclusion from numerical network modelling, analytic CTRW theory and experiment. The length traveled by solute plumes before Gaussian behaviour is reached increases with an increase in heterogeneity and/or Pe. This opens up the question on the nature of dispersion in natural systems where the heterogeneities at the larger scales will significantly increase the range of velocities in the reservoir, thus significantly delaying the asymptotic approach to Gaussian behaviour. As a consequence, the asymptotic behaviour might not be reached at the field scale. This is illustrated by the multi-scale approach in which transport at core, gridblock and field scale is viewed as a series of particle transitions between discrete nodes governed by probability distributions. At each scale of interest a distribution that represents transport physics (and the heterogeneity) is used as an input to model a subsequent reservoir scale. The extensions to reactive transport are discussed.

Change in the frequency and intensity of the spectral lines of a hydrogen-like atom in the field of a point charge

NASA Astrophysics Data System (ADS)

Ovsyannikov, V. D.; Kamenskii, A. A.

2002-03-01

The changes in the wave functions and the energies of a hydrogen-like atom in the static field of a structureless charged particle are calculated in the asymptotic approximation. The corrections to the energy of states, as well as to the dipole matrix elements of radiative transitions caused by the interaction of the atom with the point charge at long range are calculated using the perturbation theory and the Sturm series for a reduced Coulomb Green’s function in parabolic coordinates. The analytical expressions are derived and tables of numerical values of the coefficients of asymptotic series that determine the corrections to the matrix elements and the intensities of transitions of the Lyman and Balmer series are presented.

Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori

NASA Astrophysics Data System (ADS)

Iochum, B.; Masson, T.

2018-07-01

Let P be a Laplace type operator acting on a smooth hermitean vector bundle V of fiber CN over a compact Riemannian manifold given locally by P = - [gμν u(x) ∂μ∂ν +vν(x) ∂ν + w(x) ] where u ,vν , w are MN(C) -valued functions with u(x) positive and invertible. For any a ∈ Γ(End(V)) , we consider the asymptotics Tr(ae-tP) ∼ t↓0+ ∑r=0∞ ar(a , P) t (r - d) / 2 where the coefficients ar(a , P) can be written as an integral of the functions ar(a , P) (x) = tr [ a(x) Rr(x) ] . The computation of R2 is performed opening the opportunity to calculate the modular scalar curvature for noncommutative tori.

Asymptotic co- and post-seismic displacements in a homogeneous Maxwell sphere

NASA Astrophysics Data System (ADS)

Tang, He; Sun, Wenke

2018-07-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, that is, via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

Asymptotic Co- and Post-seismic displacements in a homogeneous Maxwell sphere

NASA Astrophysics Data System (ADS)

Tang, He; Sun, Wenke

2018-05-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, i.e. via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity, and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

Soliton interactions, Bäcklund transformations, Lax pair for a variable-coefficient generalized dispersive water-wave system

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Zhen, Hui-Ling; Liu, De-Yin; Xie, Xi-Yang

2018-04-01

Under investigation in this paper is a variable-coefficient generalized dispersive water-wave system, which can simulate the propagation of the long weakly non-linear and weakly dispersive surface waves of variable depth in the shallow water. Under certain variable-coefficient constraints, by virtue of the Bell polynomials, Hirota method and symbolic computation, the bilinear forms, one- and two-soliton solutions are obtained. Bäcklund transformations and new Lax pair are also obtained. Our Lax pair is different from that previously reported. Based on the asymptotic and graphic analysis, with different forms of the variable coefficients, we find that there exist the elastic interactions for u, while either the elastic or inelastic interactions for v, with u and v as the horizontal velocity field and deviation height from the equilibrium position of the water, respectively. When the interactions are inelastic, we see the fission and fusion phenomena.

Modeling individualized coefficient alpha to measure quality of test score data.

PubMed

Liu, Molei; Hu, Ming; Zhou, Xiao-Hua

2018-05-23

Individualized coefficient alpha is defined. It is item and subject specific and is used to measure the quality of test score data with heterogenicity among the subjects and items. A regression model is developed based on 3 sets of generalized estimating equations. The first set of generalized estimating equation models the expectation of the responses, the second set models the response's variance, and the third set is proposed to estimate the individualized coefficient alpha, defined and used to measure individualized internal consistency of the responses. We also use different techniques to extend our method to handle missing data. Asymptotic property of the estimators is discussed, based on which inference on the coefficient alpha is derived. Performance of our method is evaluated through simulation study and real data analysis. The real data application is from a health literacy study in Hunan province of China. Copyright © 2018 John Wiley & Sons, Ltd.

EVOLUTION OF THE MAGNETIC FIELD LINE DIFFUSION COEFFICIENT AND NON-GAUSSIAN STATISTICS

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

Snodin, A. P.; Ruffolo, D.; Matthaeus, W. H.

The magnetic field line random walk (FLRW) plays an important role in the transport of energy and particles in turbulent plasmas. For magnetic fluctuations that are transverse or almost transverse to a large-scale mean magnetic field, theories describing the FLRW usually predict asymptotic diffusion of magnetic field lines perpendicular to the mean field. Such theories often depend on the assumption that one can relate the Lagrangian and Eulerian statistics of the magnetic field via Corrsin’s hypothesis, and additionally take the distribution of magnetic field line displacements to be Gaussian. Here we take an ordinary differential equation (ODE) model with thesemore » underlying assumptions and test how well it describes the evolution of the magnetic field line diffusion coefficient in 2D+slab magnetic turbulence, by comparisons to computer simulations that do not involve such assumptions. In addition, we directly test the accuracy of the Corrsin approximation to the Lagrangian correlation. Over much of the studied parameter space we find that the ODE model is in fairly good agreement with computer simulations, in terms of both the evolution and asymptotic values of the diffusion coefficient. When there is poor agreement, we show that this can be largely attributed to the failure of Corrsin’s hypothesis rather than the assumption of Gaussian statistics of field line displacements. The degree of non-Gaussianity, which we measure in terms of the kurtosis, appears to be an indicator of how well Corrsin’s approximation works.« less

Fluid self-diffusion in Scots pine sapwood tracheid cells.

PubMed

Johannessen, Espen H; Hansen, Eddy W; Rosenholm, Jarl B

2006-02-09

The self-diffusion coefficients of water and toluene in Scots pine sapwood was measured using low field pulsed field gradient nuclear magnetic resonance (PFG-NMR). Wood chips of 8 mm diameter were saturated with the respective liquids, and liquid self-diffusion was then traced in one dimension orthogonal to the tracheid cell walls in the wood's radial direction. The experimental echo attenuation curves were exponential, and characteristic self-diffusion coefficients were produced for diffusion times spanning from very short times to times on the order of magnitude of seconds. Observed self-diffusion coefficients were decaying asymptotically as a function of diffusion time, an effect which was ascribed to the cell walls' restriction on confined liquid diffusion. The observed self-diffusion behavior in Scots pine sapwood was compared to self-diffusion coefficients obtained from simulations of diffusion in a square. Principles of molecular displacements in confined geometries were used for elucidating the wood's cellular structure from the observed diffusion coefficients. The results were compared with a mathematical model for diffusion between parallel planes.

SURE Estimates for a Heteroscedastic Hierarchical Model

PubMed Central

Xie, Xianchao; Kou, S. C.; Brown, Lawrence D.

2014-01-01

Hierarchical models are extensively studied and widely used in statistics and many other scientific areas. They provide an effective tool for combining information from similar resources and achieving partial pooling of inference. Since the seminal work by James and Stein (1961) and Stein (1962), shrinkage estimation has become one major focus for hierarchical models. For the homoscedastic normal model, it is well known that shrinkage estimators, especially the James-Stein estimator, have good risk properties. The heteroscedastic model, though more appropriate for practical applications, is less well studied, and it is unclear what types of shrinkage estimators are superior in terms of the risk. We propose in this paper a class of shrinkage estimators based on Stein’s unbiased estimate of risk (SURE). We study asymptotic properties of various common estimators as the number of means to be estimated grows (p → ∞). We establish the asymptotic optimality property for the SURE estimators. We then extend our construction to create a class of semi-parametric shrinkage estimators and establish corresponding asymptotic optimality results. We emphasize that though the form of our SURE estimators is partially obtained through a normal model at the sampling level, their optimality properties do not heavily depend on such distributional assumptions. We apply the methods to two real data sets and obtain encouraging results. PMID:25301976

Final Report: Studies in Structural, Stochastic and Statistical Reliability for Communication Networks and Engineered Systems

DTIC Science & Technology

to do so, and (5) three distinct versions of the problem of estimating component reliability from system failure-time data are treated, each resulting inconsistent estimators with asymptotically normal distributions.

Efficient Estimation of the Standardized Value

ERIC Educational Resources Information Center

Longford, Nicholas T.

2009-01-01

We derive an estimator of the standardized value which, under the standard assumptions of normality and homoscedasticity, is more efficient than the established (asymptotically efficient) estimator and discuss its gains for small samples. (Contains 1 table and 3 figures.)

Beyond Principal Component Analysis: A Trilinear Decomposition Model and Least Squares Estimation.

ERIC Educational Resources Information Center

Pham, Tuan Dinh; Mocks, Joachim

1992-01-01

Sufficient conditions are derived for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis. The limiting covariance matrix is computed. (Author/SLD)

Discretization and control of an SEIR epidemic model under equilibrium Wiener noise disturbances

NASA Astrophysics Data System (ADS)

Alonso, Santiago; De la Sen, Manuel; Nistal, Raul; Ibeas, Asier

2017-11-01

A discretized SEIR epidemic model, subject to Wiener noise disturbances of the equilibrium points, is studied. The discrete-time model is got from a general discretization technique applied to its continuous-time counterpart so that its behaviour be close to its continuous-time counterpart irrespective of the size of the discretization period. The positivity and stability of a normalized version of such a discrete-time model are emphasized. The paper also proposes the design of a periodic impulsive vaccination which is periodically injected to the susceptible subpopulation in order to eradicate the propagation of the disease or, at least, to reduce its unsuitable infective effects within the potentially susceptible subpopulation. The existence and asymptotic stability of a disease-free periodic solution are proved. In particular, both the exposed and infectious subpopulations converge asymptotically to zero as time tends to infinity while the normalized subpopulations of susceptible and recovered by immunization oscillate.

Approximation of epidemic models by diffusion processes and their statistical inference.

PubMed

Guy, Romain; Larédo, Catherine; Vergu, Elisabeta

2015-02-01

Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.

High frequency scattering by a smooth coated cylinder simulated with generalized impedance boundary conditions

NASA Technical Reports Server (NTRS)

Syed, Hasnain H.; Volakis, John L.

1991-01-01

Rigorous uniform geometrical theory of diffraction (UGTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristic to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. As usual, the diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Asymptotic inference in system identification for the atom maser.

PubMed

Catana, Catalin; van Horssen, Merlijn; Guta, Madalin

2012-11-28

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

Extrema of mass, first law of black hole mechanics, and a staticity theorem in Einstein-Maxwell-axion-dilaton gravity

NASA Astrophysics Data System (ADS)

Rogatko, Marek

1998-08-01

Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we derive the formulas for the variation of mass and other asymptotic conserved quantities in the theory under consideration. Generalizing this kind of reasoning to the initial data for the manifold with an interior boundary we get the generalized first law of black hole mechanics. We consider an asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity describing a black hole with a Killing vector field timelike at infinity, the horizon of which comprises a bifurcate Killing horizon with a bifurcate surface. Supposing that the Killing vector field is asymptotically orthogonal to the static hypersurface with boundary S and a compact interior, we find that the solution is static in the exterior world, when the timelike vector field is normal to the horizon and has vanishing electric and axion-electric fields on static slices.

A Semiparametric Change-Point Regression Model for Longitudinal Observations.

PubMed

Xing, Haipeng; Ying, Zhiliang

2012-12-01

Many longitudinal studies involve relating an outcome process to a set of possibly time-varying covariates, giving rise to the usual regression models for longitudinal data. When the purpose of the study is to investigate the covariate effects when experimental environment undergoes abrupt changes or to locate the periods with different levels of covariate effects, a simple and easy-to-interpret approach is to introduce change-points in regression coefficients. In this connection, we propose a semiparametric change-point regression model, in which the error process (stochastic component) is nonparametric and the baseline mean function (functional part) is completely unspecified, the observation times are allowed to be subject-specific, and the number, locations and magnitudes of change-points are unknown and need to be estimated. We further develop an estimation procedure which combines the recent advance in semiparametric analysis based on counting process argument and multiple change-points inference, and discuss its large sample properties, including consistency and asymptotic normality, under suitable regularity conditions. Simulation results show that the proposed methods work well under a variety of scenarios. An application to a real data set is also given.

Global asymptotic stability and hopf bifurcation for a blood cell production model.

PubMed

Crauste, Fabien

2006-04-01

We analyze the asymptotic stability of a nonlinear system of two differential equations with delay, describing the dynamics of blood cell produc- tion. This process takes place in the bone marrow, where stem cells differen- tiate throughout division in blood cells. Taking into account an explicit role of the total population of hematopoietic stem cells in the introduction of cells in cycle, we are led to study a characteristic equation with delay-dependent coefficients. We determine a necessary and sufficient condition for the global stability of the first steady state of our model, which describes the popula- tion's dying out, and we obtain the existence of a Hopf bifurcation for the only nontrivial positive steady state, leading to the existence of periodic solutions. These latter are related to dynamical diseases affecting blood cells known for their cyclic nature.

Comparison of RNFL thickness and RPE-normalized RNFL attenuation coefficient for glaucoma diagnosis

NASA Astrophysics Data System (ADS)

Vermeer, K. A.; van der Schoot, J.; Lemij, H. G.; de Boer, J. F.

2013-03-01

Recently, a method to determine the retinal nerve fiber layer (RNFL) attenuation coefficient, based on normalization on the retinal pigment epithelium, was introduced. In contrast to conventional RNFL thickness measures, this novel measure represents a scattering property of the RNFL tissue. In this paper, we compare the RNFL thickness and the RNFL attenuation coefficient on 10 normal and 8 glaucomatous eyes by analyzing the correlation coefficient and the receiver operator curves (ROCs). The thickness and attenuation coefficient showed moderate correlation (r=0.82). Smaller correlation coefficients were found within normal (r=0.55) and glaucomatous (r=0.48) eyes. The full separation between normal and glaucomatous eyes based on the RNFL attenuation coefficient yielded an area under the ROC (AROC) of 1.0. The AROC for the RNFL thickness was 0.9875. No statistically significant difference between the two measures was found by comparing the AROC. RNFL attenuation coefficients may thus replace current RNFL thickness measurements or be combined with it to improve glaucoma diagnosis.

Proportional hazards model with varying coefficients for length-biased data.

PubMed

Zhang, Feipeng; Chen, Xuerong; Zhou, Yong

2014-01-01

Length-biased data arise in many important applications including epidemiological cohort studies, cancer prevention trials and studies of labor economics. Such data are also often subject to right censoring due to loss of follow-up or the end of study. In this paper, we consider a proportional hazards model with varying coefficients for right-censored and length-biased data, which is used to study the interact effect nonlinearly of covariates with an exposure variable. A local estimating equation method is proposed for the unknown coefficients and the intercept function in the model. The asymptotic properties of the proposed estimators are established by using the martingale theory and kernel smoothing techniques. Our simulation studies demonstrate that the proposed estimators have an excellent finite-sample performance. The Channing House data is analyzed to demonstrate the applications of the proposed method.

Subset Selection Procedures: A Review and an Assessment

DTIC Science & Technology

1984-02-01

distance function (Alam and Rizvi, 1966; Gupta, 1966; Gupta and Studden, 1970), generalized variance ( Gnanadesikan and Gupta, 1970), and multiple... Gnanadesikan (1966) considered a location type procedure based on sample component means. Except in the case of bivariate normal, only a lower bound of the...Frischtak, 1973; Gnanadesikan , 1966) for ranking multivariate normal populations but the results in these cases are very limited in scope or are asymptotic

Surprising structures hiding in Penrose’s future null infinity

NASA Astrophysics Data System (ADS)

Newman, Ezra T.

2017-07-01

Since the late1950s, almost all discussions of asymptotically flat (Einstein-Maxwell) space-times have taken place in the context of Penrose’s null infinity, I+. In addition, almost all calculations have used the Bondi coordinate and tetrad systems. Beginning with a known asymptotically flat solution to the Einstein-Maxwell equations, we show first, that there are other natural coordinate systems, near I+, (analogous to light-cones in flat-space) that are based on (asymptotically) shear-free null geodesic congruences (analogous to the flat-space case). Using these new coordinates and their associated tetrad, we define the complex dipole moment, (the mass dipole plus i times angular momentum), from the l  =  1 harmonic coefficient of a component of the asymptotic Weyl tensor. Second, from this definition, from the Bianchi identities and from the Bondi-Sachs mass and linear momentum, we show that there exists a large number of results—identifications and dynamics—identical to those of classical mechanics and electrodynamics. They include, among many others, {P}=M{v}+..., {L}= {r} × {P} , spin, Newton’s second law with the rocket force term (\\dotM v) and radiation reaction, angular momentum conservation and others. All these relations take place in the rather mysterious H-space rather than in space-time. This leads to the enigma: ‘why do these well known relations of classical mechanics take place in H-space?’ and ‘What is the physical meaning of H-space?’

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

Silin, D.; Goloshubin, G.

Analysis of compression wave propagation in a poroelastic medium predicts a peak of reflection from a high-permeability layer in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of Biot's model of poroelasticity. A review of the derivation of the main equations from the Hooke's law, momentum and mass balance equations, and Darcy's law suggests an alternative new physical interpretation of some coefficients ofmore » the classical poroelasticity. The velocity of wave propagation, the attenuation factor, and the wave number, are expressed in the form of power series with respect to a small dimensionless parameter. The absolute value of this parameter is equal to the product of the kinematic reservoir fluid mobility and the wave frequency. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly-permeable layer (a lens). Practical applications of the obtained asymptotic formulae are seismic modeling, inversion, and at-tribute analysis.« less

Theoretical foundations for finite-time transient stability and sensitivity analysis of power systems

NASA Astrophysics Data System (ADS)

Dasgupta, Sambarta

Transient stability and sensitivity analysis of power systems are problems of enormous academic and practical interest. These classical problems have received renewed interest, because of the advancement in sensor technology in the form of phasor measurement units (PMUs). The advancement in sensor technology has provided unique opportunity for the development of real-time stability monitoring and sensitivity analysis tools. Transient stability problem in power system is inherently a problem of stability analysis of the non-equilibrium dynamics, because for a short time period following a fault or disturbance the system trajectory moves away from the equilibrium point. The real-time stability decision has to be made over this short time period. However, the existing stability definitions and hence analysis tools for transient stability are asymptotic in nature. In this thesis, we discover theoretical foundations for the short-term transient stability analysis of power systems, based on the theory of normally hyperbolic invariant manifolds and finite time Lyapunov exponents, adopted from geometric theory of dynamical systems. The theory of normally hyperbolic surfaces allows us to characterize the rate of expansion and contraction of co-dimension one material surfaces in the phase space. The expansion and contraction rates of these material surfaces can be computed in finite time. We prove that the expansion and contraction rates can be used as finite time transient stability certificates. Furthermore, material surfaces with maximum expansion and contraction rate are identified with the stability boundaries. These stability boundaries are used for computation of stability margin. We have used the theoretical framework for the development of model-based and model-free real-time stability monitoring methods. Both the model-based and model-free approaches rely on the availability of high resolution time series data from the PMUs for stability prediction. The problem of sensitivity analysis of power system, subjected to changes or uncertainty in load parameters and network topology, is also studied using the theory of normally hyperbolic manifolds. The sensitivity analysis is used for the identification and rank ordering of the critical interactions and parameters in the power network. The sensitivity analysis is carried out both in finite time and in asymptotic. One of the distinguishing features of the asymptotic sensitivity analysis is that the asymptotic dynamics of the system is assumed to be a periodic orbit. For asymptotic sensitivity analysis we employ combination of tools from ergodic theory and geometric theory of dynamical systems.

Aerodynamic characteristics of the 10-percent-thick NASA supercritical airfoil 33 designed for a normal-force coefficient of 0.7

NASA Technical Reports Server (NTRS)

Harris, C. D.

1975-01-01

A 10-percent-thick supercritical airfoil based on an off-design sonic-pressure plateau criterion was developed and experimental aerodynamic characteristics measured. The airfoil had a design normal-force coefficient of 0.7 and was identified as supercritical airfoil 33. Results show the airfoil to have good drag rise characteristics over a wide range of normal-force coefficients with no measurable shock losses up to the Mach numbers at which drag divergence occurred for normal-force coefficients up to 0.7. Comparisons of experimental and theoretical characteristics were made and composite drag rise characteristics were derived for normal-force coefficients of 0.5 and 0.7 and a Reynolds number of 40 million.

The Aerodynamic and Dynamic Loading of a Slender Structure by an Impacting Tornado-Like Vortex: The Influence of Relative Vortex-to-Structure Size on Structural Loading

NASA Astrophysics Data System (ADS)

Strasser, Matthew N.

Structural loading produced by an impacting vortex is a hazardous phenomenon that is encountered in numerous applications ranging from the destruction of residences by tornados to the chopping of tip vortices by rotors. Adequate design of structures to resist vortex-induced structural loading necessitates study of the phenomenon that control the structural loading produced by an impacting vortex. This body of work extends the current knowledge base of vortex-structure interaction by evaluating the influence of the relative vortex-to-structure size on the structural loading that the vortex produces. A computer model is utilized to directly simulate the two-dimensional impact of an impinging vortex with a slender, cylindrical structure. The vortex's tangential velocity profile (TVP) is defined by a normalization of the Vatistas analytical (TVP) which realistically replicates the documented spectrum of measured vortex TVPs. The impinging vortex's maximum tangential velocity is fixed, and the vortex's critical radius is incremented from one to one-hundred times the structure's diameter. When the impinging vortex is small, it interacts with vortices produced on the structure by the free stream, and maximum force coefficient amplitudes vary by more than 400% when the impinging vortex impacts the structure at different times. Maximum drag and lift force coefficient amplitudes reach asymptotic values as the impinging vortex's size increases that are respectively 94.77% and 10.66% less than maximum force coefficients produced by an equivalent maximum velocity free stream. The vortex produces maximum structural loading when its path is shifted above the structure's centerline, and maximum drag and lift force coefficients are respectively up to 4.80% and 34.07% greater than maximum force coefficients produced by an equivalent-velocity free stream. Finally, the dynamic load factor (DLF) concept is used to develop a generalized methodology to assess the dynamic amplification of a structure's response to vortex loading and to assess the dynamic loading threat that tornados pose. Typical civil and residential structures will not experience significant response amplification, but responses of very flexible structures may be amplified by up to 2.88 times.

Extinction models for cancer stem cell therapy

PubMed Central

Sehl, Mary; Zhou, Hua; Sinsheimer, Janet S.; Lange, Kenneth L.

2012-01-01

Cells with stem cell-like properties are now viewed as initiating and sustaining many cancers. This suggests that cancer can be cured by driving these cancer stem cells to extinction. The problem with this strategy is that ordinary stem cells are apt to be killed in the process. This paper sets bounds on the killing differential (difference between death rates of cancer stem cells and normal stem cells) that must exist for the survival of an adequate number of normal stem cells. Our main tools are birth–death Markov chains in continuous time. In this framework, we investigate the extinction times of cancer stem cells and normal stem cells. Application of extreme value theory from mathematical statistics yields an accurate asymptotic distribution and corresponding moments for both extinction times. We compare these distributions for the two cell populations as a function of the killing rates. Perhaps a more telling comparison involves the number of normal stem cells NH at the extinction time of the cancer stem cells. Conditioning on the asymptotic time to extinction of the cancer stem cells allows us to calculate the asymptotic mean and variance of NH. The full distribution of NH can be retrieved by the finite Fourier transform and, in some parameter regimes, by an eigenfunction expansion. Finally, we discuss the impact of quiescence (the resting state) on stem cell dynamics. Quiescence can act as a sanctuary for cancer stem cells and imperils the proposed therapy. We approach the complication of quiescence via multitype branching process models and stochastic simulation. Improvements to the τ-leaping method of stochastic simulation make it a versatile tool in this context. We conclude that the proposed therapy must target quiescent cancer stem cells as well as actively dividing cancer stem cells. The current cancer models demonstrate the virtue of attacking the same quantitative questions from a variety of modeling, mathematical, and computational perspectives. PMID:22001354

Extinction models for cancer stem cell therapy.

PubMed

Sehl, Mary; Zhou, Hua; Sinsheimer, Janet S; Lange, Kenneth L

2011-12-01

Cells with stem cell-like properties are now viewed as initiating and sustaining many cancers. This suggests that cancer can be cured by driving these cancer stem cells to extinction. The problem with this strategy is that ordinary stem cells are apt to be killed in the process. This paper sets bounds on the killing differential (difference between death rates of cancer stem cells and normal stem cells) that must exist for the survival of an adequate number of normal stem cells. Our main tools are birth-death Markov chains in continuous time. In this framework, we investigate the extinction times of cancer stem cells and normal stem cells. Application of extreme value theory from mathematical statistics yields an accurate asymptotic distribution and corresponding moments for both extinction times. We compare these distributions for the two cell populations as a function of the killing rates. Perhaps a more telling comparison involves the number of normal stem cells NH at the extinction time of the cancer stem cells. Conditioning on the asymptotic time to extinction of the cancer stem cells allows us to calculate the asymptotic mean and variance of NH. The full distribution of NH can be retrieved by the finite Fourier transform and, in some parameter regimes, by an eigenfunction expansion. Finally, we discuss the impact of quiescence (the resting state) on stem cell dynamics. Quiescence can act as a sanctuary for cancer stem cells and imperils the proposed therapy. We approach the complication of quiescence via multitype branching process models and stochastic simulation. Improvements to the τ-leaping method of stochastic simulation make it a versatile tool in this context. We conclude that the proposed therapy must target quiescent cancer stem cells as well as actively dividing cancer stem cells. The current cancer models demonstrate the virtue of attacking the same quantitative questions from a variety of modeling, mathematical, and computational perspectives. Copyright © 2011 Elsevier Inc. All rights reserved.

High powered rocketry: design, construction, and launching experience and analysis

NASA Astrophysics Data System (ADS)

Paulson, Pryce; Curtis, Jarret; Bartel, Evan; Owens Cyr, Waycen; Lamsal, Chiranjivi

2018-01-01

In this study, the nuts and bolts of designing and building a high powered rocket have been presented. A computer simulation program called RockSim was used to design the rocket. Simulation results are consistent with time variations of altitude, velocity, and acceleration obtained in the actual flight. The actual drag coefficient was determined by using altitude back-tracking method and found to be 0.825. Speed of the exhaust determined to be 2.5 km s-1 by analyzing the thrust curve of the rocket. Acceleration in the coasting phase of the flight, represented by the second-degree polynomial of a small leading coefficient, have been found to approach ‘-g’ asymptotically.

Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis.

PubMed

Bishara, Anthony J; Li, Jiexiang; Nash, Thomas

2018-02-01

When bivariate normality is violated, the default confidence interval of the Pearson correlation can be inaccurate. Two new methods were developed based on the asymptotic sampling distribution of Fisher's z' under the general case where bivariate normality need not be assumed. In Monte Carlo simulations, the most successful of these methods relied on the (Vale & Maurelli, 1983, Psychometrika, 48, 465) family to approximate a distribution via the marginal skewness and kurtosis of the sample data. In Simulation 1, this method provided more accurate confidence intervals of the correlation in non-normal data, at least as compared to no adjustment of the Fisher z' interval, or to adjustment via the sample joint moments. In Simulation 2, this approximate distribution method performed favourably relative to common non-parametric bootstrap methods, but its performance was mixed relative to an observed imposed bootstrap and two other robust methods (PM1 and HC4). No method was completely satisfactory. An advantage of the approximate distribution method, though, is that it can be implemented even without access to raw data if sample skewness and kurtosis are reported, making the method particularly useful for meta-analysis. Supporting information includes R code. © 2017 The British Psychological Society.

Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays

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

Bi, Ping; Center for Partial Differential Equations, East China Normal University, 500 Dongchuan Rd., Shanghai 200241; Ruan, Shigui, E-mail: ruan@math.miami.edu

2014-06-15

In this paper, a tumor and immune system interaction model consisted of two differential equations with three time delays is considered in which the delays describe the proliferation of tumor cells, the process of effector cells growth stimulated by tumor cells, and the differentiation of immune effector cells, respectively. Conditions for the asymptotic stability of equilibria and existence of Hopf bifurcations are obtained by analyzing the roots of a second degree exponential polynomial characteristic equation with delay dependent coefficients. It is shown that the positive equilibrium is asymptotically stable if all three delays are less than their corresponding critical valuesmore » and Hopf bifurcations occur if any one of these delays passes through its critical value. Numerical simulations are carried out to illustrate the rich dynamical behavior of the model with different delay values including the existence of regular and irregular long periodic oscillations.« less

Inflation in Flatland

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

Hinterbichler, Kurt; Joyce, Austin; Khoury, Justin, E-mail: kurt.hinterbichler@case.edu, E-mail: austin.joyce@columbia.edu, E-mail: jkhoury@sas.upenn.edu

We investigate the symmetry structure of inflation in 2+1 dimensions. In particular, we show that the asymptotic symmetries of three-dimensional de Sitter space are in one-to-one correspondence with cosmological adiabatic modes for the curvature perturbation. In 2+1 dimensions, the asymptotic symmetry algebra is infinite-dimensional, given by two copies of the Virasoro algebra, and can be traced to the conformal symmetries of the two-dimensional spatial slices of de Sitter. We study the consequences of this infinite-dimensional symmetry for inflationary correlation functions, finding new soft theorems that hold only in 2+1 dimensions. Expanding the correlation functions as a power series in themore » soft momentum q , these relations constrain the traceless part of the tensorial coefficient at each order in q in terms of a lower-point function. As a check, we verify that the O( q {sup 2}) identity is satisfied by inflationary correlation functions in the limit of small sound speed.« less

Asymptotics for metamaterials and photonic crystals

PubMed Central

Antonakakis, T.; Craster, R. V.; Guenneau, S.

2013-01-01

Metamaterial and photonic crystal structures are central to modern optics and are typically created from multiple elementary repeating cells. We demonstrate how one replaces such structures asymptotically by a continuum, and therefore by a set of equations, that captures the behaviour of potentially high-frequency waves propagating through a periodic medium. The high-frequency homogenization that we use recovers the classical homogenization coefficients in the low-frequency long-wavelength limit. The theory is specifically developed in electromagnetics for two-dimensional square lattices where every cell contains an arbitrary hole with Neumann boundary conditions at its surface and implemented numerically for cylinders and split-ring resonators. Illustrative numerical examples include lensing via all-angle negative refraction, as well as omni-directive antenna, endoscope and cloaking effects. We also highlight the importance of choosing the correct Brillouin zone and the potential of missing interesting physical effects depending upon the path chosen. PMID:23633908

Homogenization models for thin rigid structured surfaces and films.

PubMed

Marigo, Jean-Jacques; Maurel, Agnès

2016-07-01

A homogenization method for thin microstructured surfaces and films is presented. In both cases, sound hard materials are considered, associated with Neumann boundary conditions and the wave equation in the time domain is examined. For a structured surface, a boundary condition is obtained on an equivalent flat wall, which links the acoustic velocity to its normal and tangential derivatives (of the Myers type). For a structured film, jump conditions are obtained for the acoustic pressure and the normal velocity across an equivalent interface (of the Ventcels type). This interface homogenization is based on a matched asymptotic expansion technique, and differs slightly from the classical homogenization, which is known to fail for small structuration thicknesses. In order to get insight into what causes this failure, a two-step homogenization is proposed, mixing classical homogenization and matched asymptotic expansion. Results of the two homogenizations are analyzed in light of the associated elementary problems, which correspond to problems of fluid mechanics, namely, potential flows around rigid obstacles.

Confidence bounds and hypothesis tests for normal distribution coefficients of variation

Treesearch

Steve Verrill; Richard A. Johnson

2007-01-01

For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.

Solute boundary layer on a rotating crystal

NASA Astrophysics Data System (ADS)

Povinelli, Michelle L.; Korpela, Seppo A.; Chait, Arnon

1994-11-01

A perturbation analysis has been carried out for the solutal boundary layer next to a rotating crystal. Our aim is to extend the classical results of Burton, Prim and Slicher [1] in order to obtain higher order terms in asymptotic expansions for the concentration field and boundary-layer thickness. Expressions for the effective segregation coefficient are directly obtained from the concentration solution in the two limits that correspond to weak and strong rotation.

Observability of discretized partial differential equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

Acoustic waves in polydispersed bubbly liquids

NASA Astrophysics Data System (ADS)

Gubaidullin, D. A.; Gubaidullina, D. D.; Fedorov, Yu V.

2014-11-01

The propagation of acoustic waves in polydispersed mixtures of liquid with two sorts of gas bubbles each of which has its own bubble size distribution function is studied. The system of the differential equations of the perturbed motion of a mixture is presented, the dispersion relation is obtained. Equilibrium speed of sound, low-frequency and high-frequency asymptotes of the attenuation coefficient are found. Comparison of the developed theory with known experimental data is presented.

Graphene-clad tapered fiber: effective nonlinearity and propagation losses.

PubMed

Gorbach, A V; Marini, A; Skryabin, D V

2013-12-15

We derive a pulse propagation equation for a graphene-clad optical fiber, treating the optical response of the graphene and nonlinearity of the dielectric fiber core as perturbations in asymptotic expansion of Maxwell equations. We analyze the effective nonlinear and attenuation coefficients due to the graphene layer. Based on the recent experimental measurements of the nonlinear graphene conductivity, we predict considerable enhancement of the effective nonlinearity for subwavelength fiber core diameters.

Horizontal pre-asymptotic solute transport in a plane fracture with significant density contrasts.

PubMed

Bouquain, J; Meheust, Y; Davy, P

2011-03-01

We investigate the dispersion of a finite amount of solute after it has been injected into the laminar flow occurring in a horizontal smooth fracture of constant aperture. When solute buoyancy is negligible, the dispersion process eventually leads to the well-known asymptotic Taylor-Aris dispersion regime, in which the solute progresses along the fracture at the average fluid velocity, according to a one-dimensional longitudinal advection-dispersion process. This paper addresses more realistic configurations for which the solute-induced density contrasts within the fluid play an important role on solute transport, in particular at small and moderate times. Flow and transport are coupled, since the solute distribution impacts the variations in time of the advecting velocity field. Transport is simulated using (i) a mathematical description based on the Boussinesq approximation and (ii) a numerical scheme based on a finite element analysis. This enables complete characterization of the process, in particular at moderate times for which existing analytical models are not valid. At very short times as well as very long times, the overall downward advective solute mass flow is observed to scale as the square of the injected concentration. The asymptotic Taylor-Aris effective dispersion coefficient is reached eventually, but vertical density currents, which are significant at short and moderate times, are responsible for a systematic retardation of the asymptotic mean solute position with respect to the frame moving at the mean fluid velocity, as well as for a time shift in the establishment of the asymptotic dispersion regime. These delays are characterized as functions of the Péclet number and another non-dimensional number which we call advective Archimedes number, and which quantifies the ratio of buoyancy to viscous forces. Depending on the Péclet number, the asymptotic dispersion is measured to be either larger or smaller than what it would be in the absence of buoyancy effects. Breakthrough curves measured at distances larger than the typical distance needed to reach the asymptotic dispersion regime are impacted accordingly. These findings suggest that, under certain conditions, density/buoyancy effects may have to be taken into consideration when interpreting field measurement of solute transport in fractured media. They also allow an estimate of the conditions under which density effects related to fracture wall roughness are likely to be significant. Copyright © 2010 Elsevier B.V. All rights reserved.

Impedance of strip-traveling waves on an elastic half space - Asymptotic solution

NASA Technical Reports Server (NTRS)

Crandall, S. H.; Nigam, A. K.

1973-01-01

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

From shunting inhibition to dynamic normalization: Attentional selection and decision-making in brief visual displays.

PubMed

Smith, Philip L; Sewell, David K; Lilburn, Simon D

2015-11-01

Normalization models of visual sensitivity assume that the response of a visual mechanism is scaled divisively by the sum of the activity in the excitatory and inhibitory mechanisms in its neighborhood. Normalization models of attention assume that the weighting of excitatory and inhibitory mechanisms is modulated by attention. Such models have provided explanations of the effects of attention in both behavioral and single-cell recording studies. We show how normalization models can be obtained as the asymptotic solutions of shunting differential equations, in which stimulus inputs and the activity in the mechanism control growth rates multiplicatively rather than additively. The value of the shunting equation approach is that it characterizes the entire time course of the response, not just its asymptotic strength. We describe two models of attention based on shunting dynamics, the integrated system model of Smith and Ratcliff (2009) and the competitive interaction theory of Smith and Sewell (2013). These models assume that attention, stimulus salience, and the observer's strategy for the task jointly determine the selection of stimuli into visual short-term memory (VSTM) and the way in which stimulus representations are weighted. The quality of the VSTM representation determines the speed and accuracy of the decision. The models provide a unified account of a variety of attentional phenomena found in psychophysical tasks using single-element and multi-element displays. Our results show the generality and utility of the normalization approach to modeling attention. Copyright © 2014 Elsevier B.V. All rights reserved.

Absence of Asymptotic Freedom in Doped Mott Insulators: Breakdown of Strong Coupling Expansions

NASA Astrophysics Data System (ADS)

Phillips, Philip; Galanakis, Dimitrios; Stanescu, Tudor D.

2004-12-01

We show that doped Mott insulators such as the copper-oxide superconductors are asymptotically slaved in that the quasiparticle weight Z near half-filling depends critically on the existence of the high-energy scale set by the upper Hubbard band. In particular, near half-filling, the following dichotomy arises: Z≠0 when the high-energy scale is integrated out but Z=0 in the thermodynamic limit when it is retained. Slavery to the high-energy scale arises from quantum interference between electronic excitations across the Mott gap. Broad spectral features seen in photoemission in the normal state of the cuprates are argued to arise from high-energy slavery.

Asymptotic Distribution of the Likelihood Ratio Test Statistic for Sphericity of Complex Multivariate Normal Distribution.

DTIC Science & Technology

1981-08-01

RATIO TEST STATISTIC FOR SPHERICITY OF COMPLEX MULTIVARIATE NORMAL DISTRIBUTION* C. Fang P. R. Krishnaiah B. N. Nagarsenker** August 1981 Technical...and their applications in time sEries, the reader is referred to Krishnaiah (1976). Motivated by the applications in the area of inference on multiple...for practical purposes. Here, we note that Krishnaiah , Lee and Chang (1976) approxi- mated the null distribution of certain power of the likeli

Transmittance of semitransparent windows with absorbing cap-shaped droplets condensed on their backside

NASA Astrophysics Data System (ADS)

Zhu, Keyong; Pilon, Laurent

2017-11-01

This study aims to investigate systematically light transfer through semitransparent windows with absorbing cap-shaped droplets condensed on their backside as encountered in greenhouses, solar desalination plants, photobioreactors and covered raceway ponds. The Monte Carlo ray-tracing method was used to predict the normal-hemispherical transmittance, reflectance, and normal absorptance accounting for reflection and refraction at the air/droplet, droplet/window, and window/air interfaces and absorption in both the droplets and the window. The droplets were monodisperse or polydisperse and arranged either in an ordered hexagonal pattern or randomly distributed on the backside with droplet contact angle θc ranging between 0 and 180° The normal-hemispherical transmittance was found to be independent of the spatial distribution of droplets. However, it decreased with increasing droplet diameter and polydispersity. The normal-hemispherical transmittance featured four distinct optical regimes for semitransparent window supporting nonabsorbing droplets. These optical regimes were defined based on contact angle and critical angle for internal reflection at the droplet/air interface. However, for strongly absorbing droplets, the normal-hemispherical transmittance (i) decreased monotonously with increasing contact angle for θc <90° and (ii) remained constant and independent of droplet absorption index kd, droplet mean diameter dm, and contact angle θc for θc ≥ 90° Analytical expressions for the normal-hemispherical transmittance were provided in the asymptotic cases when (1) the window was absorbing but the droplets were nonabsorbing with any contact angles θc, and (2) the droplets were strongly absorbing with contact angle θc >90° Finally, the spectral normal-hemispherical transmittance of a 3 mm-thick glass window supporting condensed water droplets for wavelength between 0.4 and 5 μm was predicted and discussed in light of the earlier parametric study and asymptotic behavior.

The asymptotic homogenization elasticity tensor properties for composites with material discontinuities

NASA Astrophysics Data System (ADS)

Penta, Raimondo; Gerisch, Alf

2017-01-01

The classical asymptotic homogenization approach for linear elastic composites with discontinuous material properties is considered as a starting point. The sharp length scale separation between the fine periodic structure and the whole material formally leads to anisotropic elastic-type balance equations on the coarse scale, where the arising fourth rank operator is to be computed solving single periodic cell problems on the fine scale. After revisiting the derivation of the problem, which here explicitly points out how the discontinuity in the individual constituents' elastic coefficients translates into stress jump interface conditions for the cell problems, we prove that the gradient of the cell problem solution is minor symmetric and that its cell average is zero. This property holds for perfect interfaces only (i.e., when the elastic displacement is continuous across the composite's interface) and can be used to assess the accuracy of the computed numerical solutions. These facts are further exploited, together with the individual constituents' elastic coefficients and the specific form of the cell problems, to prove a theorem that characterizes the fourth rank operator appearing in the coarse-scale elastic-type balance equations as a composite material effective elasticity tensor. We both recover known facts, such as minor and major symmetries and positive definiteness, and establish new facts concerning the Voigt and Reuss bounds. The latter are shown for the first time without assuming any equivalence between coarse and fine-scale energies ( Hill's condition), which, in contrast to the case of representative volume elements, does not identically hold in the context of asymptotic homogenization. We conclude with instructive three-dimensional numerical simulations of a soft elastic matrix with an embedded cubic stiffer inclusion to show the profile of the physically relevant elastic moduli (Young's and shear moduli) and Poisson's ratio at increasing (up to 100 %) inclusion's volume fraction, thus providing a proxy for the design of artificial elastic composites.

Non-equilibrium reaction rates in chemical kinetic equations

NASA Astrophysics Data System (ADS)

Gorbachev, Yuriy

2018-05-01

Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established.

Buoyancy-driven instabilities around miscible A+B→C reaction fronts: a general classification.

PubMed

Trevelyan, P M J; Almarcha, C; De Wit, A

2015-02-01

Upon contact between miscible solutions of reactants A and B along a horizontal interface in the gravity field, various buoyancy-driven instabilities can develop when an A+B→C reaction takes place and the density varies with the concentrations of the various chemicals. To classify the possible convective instability scenarios, we analyze the spatial dependence of the large time asymptotic density profiles as a function of the key parameters of the problem, which are the ratios of diffusion coefficients and of solutal expansion coefficients of species A, B, and C. We find that 62 different density profiles can develop in the reactive problem, whereas only 6 of them can be obtained in the nonreactive one.

Cartesian-Grid Simulations of a Canard-Controlled Missile with a Free-Spinning Tail

NASA Technical Reports Server (NTRS)

Murman, Scott M.; Aftosmis, Michael J.; Kwak, Dochan (Technical Monitor)

2002-01-01

The proposed paper presents a series of simulations of a geometrically complex, canard-controlled, supersonic missile with free-spinning tail fins. Time-dependent simulations were performed using an inviscid Cartesian-grid-based method with results compared to both experimental data and high-resolution Navier-Stokes computations. At fixed free stream conditions and canard deflections, the tail spin rate was iteratively determined such that the net rolling moment on the empennage is zero. This rate corresponds to the time-asymptotic rate of the free-to-spin fin system. After obtaining spin-averaged aerodynamic coefficients for the missile, the investigation seeks a fixed-tail approximation to the spin-averaged aerodynamic coefficients, and examines the validity of this approximation over a variety of freestream conditions.

Keesom coefficients in gases

NASA Astrophysics Data System (ADS)

Magnasco, Valerio; Battezzati, Michele; Rapallo, Arnaldo; Costa, Camilla

2006-09-01

T-dependent long-range Keesom coefficients are evaluated up to the R-10 term for small values of the dimensionless parameter |a|. For large values of |a| corrections must be introduced mostly for the dipole-dipole term, the correct values of C6 being best obtained from a recently derived asymptotic formula. The corresponding attractive energies are the isotropic electrostatic contributions to the interaction energy and are temperature-dependent. Comparison with long-range induction and dispersion energy results for some simple polar axially symmetric molecules in the gas phase shows that at R = 10 a0 and T = 293 K the electrostatic dipole-dipole component is dominant for ∣ a11∣ > 0.5. For centrosymmetric molecules the corresponding electrostatic contribution is usually negligible with respect to dispersion.

Lossy radial diffusion of relativistic Jovian electrons. [calculation of synchrotron radiation and electron radiation for Jupiter

NASA Technical Reports Server (NTRS)

Barbosa, D. D.; Coroniti, F. V.

1976-01-01

The radial diffusion equation with synchrotron losses was solved by the Laplace transform method for near-equatorially mirroring relativistic electrons. The evolution of a power law distribution function was found and the characteristics of synchrotron burn-off are stated in terms of explicit parameters for an arbitrary diffusion coefficient. Emissivity from the radiation belts of Jupiter was studied. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.

On the Berry-Esséen bound of frequency polygons for ϕ-mixing samples.

PubMed

Huang, Gan-Ji; Xing, Guodong

2017-01-01

Under some mild assumptions, the Berry-Esséen bound of frequency polygons for ϕ -mixing samples is presented. By the bound derived, we obtain the corresponding convergence rate of uniformly asymptotic normality, which is nearly [Formula: see text] under the given conditions.

Propensity Score Weighting with Error-Prone Covariates

ERIC Educational Resources Information Center

McCaffrey, Daniel F.; Lockwood, J. R.; Setodji, Claude M.

2011-01-01

Inverse probability weighting (IPW) estimates are widely used in applications where data are missing due to nonresponse or censoring or in observational studies of causal effects where the counterfactuals cannot be observed. This extensive literature has shown the estimators to be consistent and asymptotically normal under very general conditions,…

Aerodynamic characteristics of an improved 10-percent-thick NASA supercritical airfoil. [Langley 8 foot transonic tunnel tests

NASA Technical Reports Server (NTRS)

Harris, C. D.

1974-01-01

Refinements in a 10 percent thick supercritical airfoil produced improvements in the overall drag characteristics at normal force coefficients from about 0.30 to 0.65 compared with earlier supercritical airfoils which were developed for a normal force coefficient of 0.7. The drag divergence Mach number of the improved supercritical airfoil (airfoil 26a) varied from approximately 0.82 at a normal force coefficient to of 0.30, to 0.78 at a normal force coefficient of 0.80 with no drag creep evident. Integrated section force and moment data, surface pressure distributions, and typical wake survey profiles are presented.

Crossover from anomalous to normal diffusion in porous media

NASA Astrophysics Data System (ADS)

Aarão Reis, F. D. A.; di Caprio, Dung

2014-06-01

Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover to long-time normal diffusion is observed in most samples. The anomalous concentration profile remains at long times in very porous solids if the walker steps are restricted to nearest neighbors and is accompanied with subdiffusion features. These findings are correlated with a decay of the explored area with z. The study of RW of tracer particles left at the internal part of the solid rules out an interpretation by diffusion equations with position-dependent coefficients. A model of RW in a tube of decreasing cross section explains those results by showing long crossovers from an effective subdiffusion regime to an asymptotic normal diffusion. The crossover position and density are analytically calculated for a tube with area decreasing exponentially with z and show good agreement with numerical data. The anomalous decay of the concentration profile is interpreted as a templating effect of the tube shape on the total number of diffusing particles at each depth, while the volumetric concentration in the actually explored porous region may not have significant decay. These results may explain the anomalous diffusion of metal atoms in porous deposits observed in recent works. They also confirm the difficulty in interpreting experimental or computational data on anomalous transport reported in recent works, particularly if only the concentration profiles are measured.

Peripheral elastic and inelastic scattering of O17,18 on light targets at 12 MeV/nucleon

NASA Astrophysics Data System (ADS)

Al-Abdullah, T.; Carstoiu, F.; Gagliardi, C. A.; Tabacaru, G.; Trache, L.; Tribble, R. E.

2014-06-01

A study of interaction of neutron-rich oxygen isotopes O17,18 with light targets has been undertaken in order to determine the optical potentials needed for the transfer reaction C13(O17,O18)C12. Optical potentials in both incoming and outgoing channels have been determined in a single experiment. This transfer reaction was used to infer the direct capture rate to the F17(p,γ)Ne18 which is essential to estimate the production of F18 at stellar energies in ONe novae. The success of the asymptotic normalization coefficient (ANC) as indirect method for astrophysics is guaranteed if the reaction mechanism is peripheral and the distorted wave Born approximation cross-section calculations are warranted and stable against the optical model potential (OMP) used. We demonstrate the stability of the ANC method and the OMP results by using good-quality elastic and inelastic-scattering data with stable beams before extending the procedures to rare-ion beams. The peripherality of our reaction is inferred from a semiclassical decomposition of the total-scattering amplitude into barrier and internal barrier components. Comparison between elastic scattering of O17, O18, and O16 projectiles is made.

The astrophysical S-factor of the direct 18O(p, γ)19F capture by the ANC method

NASA Astrophysics Data System (ADS)

Burjan, V.; Hons, Z.; Kroha, V.; Mrázek, J.; Piskoř, Š.; Mukhamedzhanov, A. M.; Trache, L.; Tribble, R. E.; La Cognata, M.; Lamia, L.; Pizzone, G. R.; Romano, S.; Spitaleri, C.; Tumino, A.

2018-01-01

We attempted to determine the astrophysical S-factor of the direct part of the 18O(p, γ)19F capture by the indirect method of asymptotic normalization coefficients (ANC). We measured the differential cross section of the transfer reaction 18O(3He, d)19F at a 3He energy of 24.6 MeV. The measurement was realized on the cyclotron of the NPI in Řež, Czech Republic, with the gas target consisting of the high purity 18O (99.9 %). The reaction products were measured by eight ΔE-E telescopes composed from thin and thick silicon surface-barrier detectors. The parameters of the optical model for the input channel were deduced by means of the code ECIS and the analysis of transfer reactions to 12 levels of the 19F nucleus up to 8.014 MeV was made by the code FRESCO. The deduced ANCs were then used to specify the direct contribution to the 18O(p, γ)19F capture process and were compared with the mutually different results of two works.

Maximum Likelihood Estimations and EM Algorithms with Length-biased Data

PubMed Central

Qin, Jing; Ning, Jing; Liu, Hao; Shen, Yu

2012-01-01

SUMMARY Length-biased sampling has been well recognized in economics, industrial reliability, etiology applications, epidemiological, genetic and cancer screening studies. Length-biased right-censored data have a unique data structure different from traditional survival data. The nonparametric and semiparametric estimations and inference methods for traditional survival data are not directly applicable for length-biased right-censored data. We propose new expectation-maximization algorithms for estimations based on full likelihoods involving infinite dimensional parameters under three settings for length-biased data: estimating nonparametric distribution function, estimating nonparametric hazard function under an increasing failure rate constraint, and jointly estimating baseline hazards function and the covariate coefficients under the Cox proportional hazards model. Extensive empirical simulation studies show that the maximum likelihood estimators perform well with moderate sample sizes and lead to more efficient estimators compared to the estimating equation approaches. The proposed estimates are also more robust to various right-censoring mechanisms. We prove the strong consistency properties of the estimators, and establish the asymptotic normality of the semi-parametric maximum likelihood estimators under the Cox model using modern empirical processes theory. We apply the proposed methods to a prevalent cohort medical study. Supplemental materials are available online. PMID:22323840

Statistics of Weighted Brain Networks Reveal Hierarchical Organization and Gaussian Degree Distribution

PubMed Central

Ivković, Miloš; Kuceyeski, Amy; Raj, Ashish

2012-01-01

Whole brain weighted connectivity networks were extracted from high resolution diffusion MRI data of 14 healthy volunteers. A statistically robust technique was proposed for the removal of questionable connections. Unlike most previous studies our methods are completely adapted for networks with arbitrary weights. Conventional statistics of these weighted networks were computed and found to be comparable to existing reports. After a robust fitting procedure using multiple parametric distributions it was found that the weighted node degree of our networks is best described by the normal distribution, in contrast to previous reports which have proposed heavy tailed distributions. We show that post-processing of the connectivity weights, such as thresholding, can influence the weighted degree asymptotics. The clustering coefficients were found to be distributed either as gamma or power-law distribution, depending on the formula used. We proposed a new hierarchical graph clustering approach, which revealed that the brain network is divided into a regular base-2 hierarchical tree. Connections within and across this hierarchy were found to be uncommonly ordered. The combined weight of our results supports a hierarchically ordered view of the brain, whose connections have heavy tails, but whose weighted node degrees are comparable. PMID:22761649

Statistics of weighted brain networks reveal hierarchical organization and Gaussian degree distribution.

PubMed

Ivković, Miloš; Kuceyeski, Amy; Raj, Ashish

2012-01-01

Whole brain weighted connectivity networks were extracted from high resolution diffusion MRI data of 14 healthy volunteers. A statistically robust technique was proposed for the removal of questionable connections. Unlike most previous studies our methods are completely adapted for networks with arbitrary weights. Conventional statistics of these weighted networks were computed and found to be comparable to existing reports. After a robust fitting procedure using multiple parametric distributions it was found that the weighted node degree of our networks is best described by the normal distribution, in contrast to previous reports which have proposed heavy tailed distributions. We show that post-processing of the connectivity weights, such as thresholding, can influence the weighted degree asymptotics. The clustering coefficients were found to be distributed either as gamma or power-law distribution, depending on the formula used. We proposed a new hierarchical graph clustering approach, which revealed that the brain network is divided into a regular base-2 hierarchical tree. Connections within and across this hierarchy were found to be uncommonly ordered. The combined weight of our results supports a hierarchically ordered view of the brain, whose connections have heavy tails, but whose weighted node degrees are comparable.

Comparison of observed rheological properties of hard wheat flour dough with predictions of the Giesekus-Leonov, White-Metzner and Phan-Thien Tanner models

NASA Technical Reports Server (NTRS)

Dhanasekharan, M.; Huang, H.; Kokini, J. L.; Janes, H. W. (Principal Investigator)

1999-01-01

The measured rheological behavior of hard wheat flour dough was predicted using three nonlinear differential viscoelastic models. The Phan-Thien Tanner model gave good zero shear viscosity prediction, but overpredicted the shear viscosity at higher shear rates and the transient and extensional properties. The Giesekus-Leonov model gave similar predictions to the Phan-Thien Tanner model, but the extensional viscosity prediction showed extension thickening. Using high values of the mobility factor, extension thinning behavior was observed but the predictions were not satisfactory. The White-Metzner model gave good predictions of the steady shear viscosity and the first normal stress coefficient but it was unable to predict the uniaxial extensional viscosity as it exhibited asymptotic behavior in the tested extensional rates. It also predicted the transient shear properties with moderate accuracy in the transient phase, but very well at higher times, compared to the Phan-Thien Tanner model and the Giesekus-Leonov model. None of the models predicted all observed data consistently well. Overall the White-Metzner model appeared to make the best predictions of all the observed data.

Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models.

PubMed

Haem, Elham; Harling, Kajsa; Ayatollahi, Seyyed Mohammad Taghi; Zare, Najaf; Karlsson, Mats O

2017-02-01

One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.

On new non-modal hydrodynamic stability modes and resulting non-exponential growth rates - a Lie symmetry approach

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan

2016-11-01

Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.

An approach to the quantization of black hole quasi-normal modes

NASA Astrophysics Data System (ADS)

Pal, Soham; Rajeev, Karthik; Shankaranarayanan, S.

2015-07-01

In this work, we derive the asymptotic quasi-normal modes of a Banados-Teitelboim-Zanelli (BTZ) black hole using a quantum field theoretic Lagrangian. The BTZ black hole is a very popular system in the context of 2 + 1-dimensional quantum gravity. However, to our knowledge the quasi-normal modes of the BTZ black hole have been studied only in the classical domain. Here we show a way to quantize the quasi-normal modes of the BTZ black hole by mapping it to the Bateman-Feschbach-Tikochinsky oscillator and the Caldirola-Kanai oscillator. We have also discussed a couple of other black hole potentials to which this method can be applied.

ON THE APPROACH TO NON-EQUILIBRIUM STATIONARY STATES AND THE THEORY OF TRANSPORT COEFFICIENTS

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

Balescu, R.

1961-07-01

A general formula for the time dependent electric current arising from a constant electric field is derived similarly to Kubo's theory. This formula connects the time dependence of the current to the singularities of the resolvent of Liouville's operator of a classical system. Direct contact is made with the general theory of approach to equilibrium developed by Prigogine and his coworkers. It constitutes a framework for a diagram expansion of transport coefficients. A proof of the existence of a stationary state and of its stability (to first order in the field) are given. It is rigorously shown that, whereas themore » approach to the stationary state is in general governed by complicated non-markoffian equations, the stationary state itself (and thus the calculation of transport coefficients) is always determined by an asymptotic cross section. This implies that transport coefficients can always be calculated from a markoffian Boltzmann-like equation even in situations in which that equation does not describe properly the approach to the stationary state. (auth)« less

Penalized spline estimation for functional coefficient regression models.

PubMed

Cao, Yanrong; Lin, Haiqun; Wu, Tracy Z; Yu, Yan

2010-04-01

The functional coefficient regression models assume that the regression coefficients vary with some "threshold" variable, providing appreciable flexibility in capturing the underlying dynamics in data and avoiding the so-called "curse of dimensionality" in multivariate nonparametric estimation. We first investigate the estimation, inference, and forecasting for the functional coefficient regression models with dependent observations via penalized splines. The P-spline approach, as a direct ridge regression shrinkage type global smoothing method, is computationally efficient and stable. With established fixed-knot asymptotics, inference is readily available. Exact inference can be obtained for fixed smoothing parameter λ, which is most appealing for finite samples. Our penalized spline approach gives an explicit model expression, which also enables multi-step-ahead forecasting via simulations. Furthermore, we examine different methods of choosing the important smoothing parameter λ: modified multi-fold cross-validation (MCV), generalized cross-validation (GCV), and an extension of empirical bias bandwidth selection (EBBS) to P-splines. In addition, we implement smoothing parameter selection using mixed model framework through restricted maximum likelihood (REML) for P-spline functional coefficient regression models with independent observations. The P-spline approach also easily allows different smoothness for different functional coefficients, which is enabled by assigning different penalty λ accordingly. We demonstrate the proposed approach by both simulation examples and a real data application.

Quantitative RNFL attenuation coefficient measurements by RPE-normalized OCT data

NASA Astrophysics Data System (ADS)

Vermeer, K. A.; van der Schoot, J.; Lemij, H. G.; de Boer, J. F.

2012-03-01

We demonstrate significantly different scattering coefficients of the retinal nerve fiber layer (RNFL) between normal and glaucoma subjects. In clinical care, SD-OCT is routinely used to assess the RNFL thickness for glaucoma management. In this way, the full OCT data set is conveniently reduced to an easy to interpret output, matching results from older (non- OCT) instruments. However, OCT provides more data, such as the signal strength itself, which is due to backscattering in the retinal layers. For quantitative analysis, this signal should be normalized to adjust for local differences in the intensity of the beam that reaches the retina. In this paper, we introduce a model that relates the OCT signal to the attenuation coefficient of the tissue. The average RNFL signal (within an A-line) was then normalized based on the observed RPE signal, resulting in normalized RNFL attenuation coefficient maps. These maps showed local defects matching those found in thickness data. The average (normalized) RNFL attenuation coefficient of a fixed band around the optic nerve head was significantly lower in glaucomatous eyes than in normal eyes (3.0mm-1 vs. 4.9mm-1, P<0.01, Mann-Whitney test).

Edgeworth expansions of stochastic trading time

NASA Astrophysics Data System (ADS)

Decamps, Marc; De Schepper, Ann

2010-08-01

Under most local and stochastic volatility models the underlying forward is assumed to be a positive function of a time-changed Brownian motion. It relates nicely the implied volatility smile to the so-called activity rate in the market. Following Young and DeWitt-Morette (1986) [8], we propose to apply the Duru-Kleinert process-cum-time transformation in path integral to formulate the transition density of the forward. The method leads to asymptotic expansions of the transition density around a Gaussian kernel corresponding to the average activity in the market conditional on the forward value. The approximation is numerically illustrated for pricing vanilla options under the CEV model and the popular normal SABR model. The asymptotics can also be used for Monte Carlo simulations or backward integration schemes.

On the measure of conformal difference between Euclidean and Lobachevsky spaces

NASA Astrophysics Data System (ADS)

Zorich, Vladimir A.

2011-12-01

Euclidean space R^n and Lobachevsky space H^n are known to be not equivalent either conformally or quasiconformally. In this work we give exact asymptotics of the critical order of growth at infinity for the quasiconformality coefficient of a diffeomorphism f\\colon R^n\\to H^n for which such a mapping f is possible. We also consider the general case of immersions f\\colon M^n\\to N^n of conformally parabolic Riemannian manifolds. Bibliography: 17 titles.

Portfolio theory of optimal isometric force production: Variability predictions and nonequilibrium fluctuation dissipation theorem

NASA Astrophysics Data System (ADS)

Frank, T. D.; Patanarapeelert, K.; Beek, P. J.

2008-05-01

We derive a fundamental relationship between the mean and the variability of isometric force. The relationship arises from an optimal collection of active motor units such that the force variability assumes a minimum (optimal isometric force). The relationship is shown to be independent of the explicit motor unit properties and of the dynamical features of isometric force production. A constant coefficient of variation in the asymptotic regime and a nonequilibrium fluctuation-dissipation theorem for optimal isometric force are predicted.

Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20

DOE PAGES

Michael, J. Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily forl ≤ 4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7.more » In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens method in the Wolfram Mathematicasoftware to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.« less

On the null distribution of Bayes factors in linear regression

USDA-ARS?s Scientific Manuscript database

We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...

Ultrasonic modeling of an embedded elliptic crack

NASA Astrophysics Data System (ADS)

Fradkin, Larissa Ju.; Zalipaev, Victor

2000-05-01

Experiments indicate that the radiating near zone of a compressional circular transducer directly coupled to a homogeneous and isotropic solid has the following structure: there are geometrical zones where one can distinguish a plane compressional wave and toroidal waves, both compressional and shear, radiated by the transducer rim. As has been shown previously the modern diffraction theory allows to describe these explicitly. It also gives explicit asymptotic description of waves present in the transition zones. In case of a normal incidence of a plane compressional wave the explicit expressions have been obtained by Achenbach and co-authors for the fields diffracted by a penny-shaped crack. We build on the above work by applying the uniform GTD to model an oblique incidence of a plane compressional wave on an elliptical crack. We compare our asymptotic results with numerical results based on the boundary integral code as developed by Glushkovs, Krasnodar University, Russia. The asymptotic formulas form a basis of a code for high-frequency simulation of ultrasonic scattering by elliptical cracks situated in the vicinity of a compressional circular transducer, currently under development at our Center.

Measuring the critical band for speech.

PubMed

Healy, Eric W; Bacon, Sid P

2006-02-01

The current experiments were designed to measure the frequency resolution employed by listeners during the perception of everyday sentences. Speech bands having nearly vertical filter slopes and narrow bandwidths were sharply partitioned into various numbers of equal log- or ERBN-width subbands. The temporal envelope from each partition was used to amplitude modulate a corresponding band of low-noise noise, and the modulated carriers were combined and presented to normal-hearing listeners. Intelligibility increased and reached asymptote as the number of partitions increased. In the mid- and high-frequency regions of the speech spectrum, the partition bandwidth corresponding to asymptotic performance matched current estimates of psychophysical tuning across a number of conditions. These results indicate that, in these regions, the critical band for speech matches the critical band measured using traditional psychoacoustic methods and nonspeech stimuli. However, in the low-frequency region, partition bandwidths at asymptote were somewhat narrower than would be predicted based upon psychophysical tuning. It is concluded that, overall, current estimates of psychophysical tuning represent reasonably well the ability of listeners to extract spectral detail from running speech.

Asymptotic Distributions of Coalescence Times and Ancestral Lineage Numbers for Populations with Temporally Varying Size

PubMed Central

Chen, Hua; Chen, Kun

2013-01-01

The distributions of coalescence times and ancestral lineage numbers play an essential role in coalescent modeling and ancestral inference. Both exact distributions of coalescence times and ancestral lineage numbers are expressed as the sum of alternating series, and the terms in the series become numerically intractable for large samples. More computationally attractive are their asymptotic distributions, which were derived in Griffiths (1984) for populations with constant size. In this article, we derive the asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size. For a sample of size n, denote by Tm the mth coalescent time, when m + 1 lineages coalesce into m lineages, and An(t) the number of ancestral lineages at time t back from the current generation. Similar to the results in Griffiths (1984), the number of ancestral lineages, An(t), and the coalescence times, Tm, are asymptotically normal, with the mean and variance of these distributions depending on the population size function, N(t). At the very early stage of the coalescent, when t → 0, the number of coalesced lineages n − An(t) follows a Poisson distribution, and as m → n, n(n−1)Tm/2N(0) follows a gamma distribution. We demonstrate the accuracy of the asymptotic approximations by comparing to both exact distributions and coalescent simulations. Several applications of the theoretical results are also shown: deriving statistics related to the properties of gene genealogies, such as the time to the most recent common ancestor (TMRCA) and the total branch length (TBL) of the genealogy, and deriving the allele frequency spectrum for large genealogies. With the advent of genomic-level sequencing data for large samples, the asymptotic distributions are expected to have wide applications in theoretical and methodological development for population genetic inference. PMID:23666939

Asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size.

PubMed

Chen, Hua; Chen, Kun

2013-07-01

The distributions of coalescence times and ancestral lineage numbers play an essential role in coalescent modeling and ancestral inference. Both exact distributions of coalescence times and ancestral lineage numbers are expressed as the sum of alternating series, and the terms in the series become numerically intractable for large samples. More computationally attractive are their asymptotic distributions, which were derived in Griffiths (1984) for populations with constant size. In this article, we derive the asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size. For a sample of size n, denote by Tm the mth coalescent time, when m + 1 lineages coalesce into m lineages, and An(t) the number of ancestral lineages at time t back from the current generation. Similar to the results in Griffiths (1984), the number of ancestral lineages, An(t), and the coalescence times, Tm, are asymptotically normal, with the mean and variance of these distributions depending on the population size function, N(t). At the very early stage of the coalescent, when t → 0, the number of coalesced lineages n - An(t) follows a Poisson distribution, and as m → n, $$n\\left(n-1\\right){T}_{m}/2N\\left(0\\right)$$ follows a gamma distribution. We demonstrate the accuracy of the asymptotic approximations by comparing to both exact distributions and coalescent simulations. Several applications of the theoretical results are also shown: deriving statistics related to the properties of gene genealogies, such as the time to the most recent common ancestor (TMRCA) and the total branch length (TBL) of the genealogy, and deriving the allele frequency spectrum for large genealogies. With the advent of genomic-level sequencing data for large samples, the asymptotic distributions are expected to have wide applications in theoretical and methodological development for population genetic inference.

Confidence bounds and hypothesis tests for normal distribution coefficients of variation

Treesearch

Steve P. Verrill; Richard A. Johnson

2007-01-01

For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations. To develop these confidence bounds and test, we first establish that estimators based on Newton steps from n-...

Coherent-Anomaly Method in Self-Avoiding Walk Problems

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

Self-avoiding walk (SAW), being a nonequilibrium cooperative phenomenon, is investigated with a finite-order-restricted-walk (finite-ORW or FORW) coherent-anomaly method (CAM). The coefficient β1r in the asymptotic form Cnr ≃ βlrλn1r for the total number Cnr of r-ORW's with respect to the step number n is investigated for the first time. An asymptotic form for SAW's is thus obtained from the series of FORW approximants, Cnr ≃ brgμ(1 + a/r)n, as the envelope curve Cn ≃ b(ae/g)gμnng. Numerical results are given by Cn ≃ 1.424n0.27884.1507n and Cn ≃ 1.179n0.158710.005n for the plane triangular lattice and f.c.c. lattice, respectively. A good coincidence of the total numbers estimated from the above simple formulae with exact enumerations for finite-step SAW's implies that the essential nature of SAW (non-Markov process) can be understood from FORW (Markov process) in the CAM framework.

Tidal Love Numbers of Neutron Stars

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

Hinderer, Tanja

For a variety of fully relativistic polytropic neutron star models we calculate the star's tidal Love number k{sub 2}. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n {approx} 0.5-1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l = 2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second-order differential equation for the perturbation to the metric coefficient g{sub tt} and matching the exterior solution to themore » asymptotic expansion of the metric in the star's local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to {approx}24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.« less

Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas

NASA Astrophysics Data System (ADS)

Chacon, Luis; Del-Castillo-Negrete, Diego

2012-03-01

Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (the transport-coefficient ratio χ/χ˜10^10 in fusion plasmas). Recently, a novel Lagrangian Green's function method has been proposedfootnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011); D. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, submitted (2011) to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids numerical pollution, is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the Lagrangian Green's function approach to include perpendicular transport terms and sources. We present an asymptotic-preserving numerical formulation, which ensures a consistent numerical discretization temporally and spatially for arbitrary χ/χ ratios. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.

Light-cone reduction vs. TsT transformations: a fluid dynamics perspective

NASA Astrophysics Data System (ADS)

Dutta, Suvankar; Krishna, Hare

2018-05-01

We compute constitutive relations for a charged (2+1) dimensional Schrödinger fluid up to first order in derivative expansion, using holographic techniques. Starting with a locally boosted, asymptotically AdS, 4 + 1 dimensional charged black brane geometry, we uplift that to ten dimensions and perform TsT transformations to obtain an effective five dimensional local black brane solution with asymptotically Schrödinger isometries. By suitably implementing the holographic techniques, we compute the constitutive relations for the effective fluid living on the boundary of this space-time and extract first order transport coefficients from these relations. Schrödinger fluid can also be obtained by reducing a charged relativistic conformal fluid over light-cone. It turns out that both the approaches result the same system at the end. Fluid obtained by light-cone reduction satisfies a restricted class of thermodynamics. Here, we see that the charged fluid obtained holographically also belongs to the same restricted class.

Evaluation of Hamaker coefficients using Diffusion Monte Carlo method

NASA Astrophysics Data System (ADS)

Maezono, Ryo; Hongo, Kenta

We evaluated the Hamaker's constant for Cyclohexasilane to investigate its wettability, which is used as an ink of 'liquid silicon' in 'printed electronics'. Taking three representative geometries of the dimer coalescence (parallel, lined, and T-shaped), we evaluated these binding curves using diffusion Monte Carlo method. The parallel geometry gave the most long-ranged exponent, ~ 1 /r6 , in its asymptotic behavior. Evaluated binding lengths are fairly consistent with the experimental density of the molecule. The fitting of the asymptotic curve gave an estimation of Hamaker's constant being around 100 [zJ]. We also performed a CCSD(T) evaluation and got almost similar result. To check its justification, we applied the same scheme to Benzene and compared the estimation with those by other established methods, Lifshitz theory and SAPT (Symmetry-adopted perturbation theory). The result by the fitting scheme turned to be twice larger than those by Lifshitz and SAPT, both of which coincide with each other. It is hence implied that the present evaluation for Cyclohexasilane would be overestimated.

Simple, Efficient Estimators of Treatment Effects in Randomized Trials Using Generalized Linear Models to Leverage Baseline Variables

PubMed Central

Rosenblum, Michael; van der Laan, Mark J.

2010-01-01

Models, such as logistic regression and Poisson regression models, are often used to estimate treatment effects in randomized trials. These models leverage information in variables collected before randomization, in order to obtain more precise estimates of treatment effects. However, there is the danger that model misspecification will lead to bias. We show that certain easy to compute, model-based estimators are asymptotically unbiased even when the working model used is arbitrarily misspecified. Furthermore, these estimators are locally efficient. As a special case of our main result, we consider a simple Poisson working model containing only main terms; in this case, we prove the maximum likelihood estimate of the coefficient corresponding to the treatment variable is an asymptotically unbiased estimator of the marginal log rate ratio, even when the working model is arbitrarily misspecified. This is the log-linear analog of ANCOVA for linear models. Our results demonstrate one application of targeted maximum likelihood estimation. PMID:20628636

Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential

NASA Astrophysics Data System (ADS)

Guérin, T.; Dean, D. S.

2017-01-01

We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F . The system is studied in the region where the force is close to the critical value Fc at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F >Fc , whereas for F

An Investigation into the Effect of Hydrodynamic Cavitation on Diesel using Optical Extinction

NASA Astrophysics Data System (ADS)

Lockett, R. D.; Fatmi, Z.; Kuti, O.; Price, R.

2015-12-01

A conventional diesel and paraffinic-rich model diesel fuel were subjected to sustained cavitation in a custom-built high-pressure recirculation flow rig. Changes to the spectral extinction coefficient at 405 nm were measured using a simple optical arrangement. The spectral extinction coefficient at 405 nm for the conventional diesel sample was observed to increase to a maximum value and then asymptotically decrease to a steady-state value, while that for the paraffinic-rich model diesel was observed to progressively decrease. It is suggested that this is caused by the sonochemical pyrolysis of mono-aromatics to form primary soot-like carbonaceous particles, which then coagulate to form larger particles, which are then trapped by the filter, leading to a steady-state spectral absorbance.

Accurate determination of complex materials coefficients of piezoelectric resonators.

PubMed

Du, Xiao-Hong; Wang, Qing-Ming; Uchino, Kenji

2003-03-01

This paper presents a method of accurately determining the complex piezoelectric and elastic coefficients of piezoelectric ceramic resonators from the measurement of the normalized electric admittance, Y, which is electric admittance Y of piezoelectric resonator normalized by the angular frequency omega. The coefficients are derived from the measurements near three special frequency points that correspond to the maximum and the minimum normalized susceptance (B) and the maximum normalized conductance (G). The complex elastic coefficient is determined from the frequencies at these points, and the real and imaginary parts of the piezoelectric coefficient are related to the derivative of the susceptance with respect to the frequency and the asymmetry of the conductance, respectively, near the maximum conductance point. The measurements for some lead zirconate titanate (PZT) based ceramics are used as examples to demonstrate the calculation and experimental procedures and the comparisons with the standard methods.

Determination of rolling resistance coefficient based on normal tyre stiffness

NASA Astrophysics Data System (ADS)

Rykov, S. P.; Tarasuyk, V. N.; Koval, V. S.; Ovchinnikova, N. I.; Fedotov, A. I.; Fedotov, K. V.

2018-03-01

The purpose of the article is to develop analytical dependence of wheel rolling resistance coefficient based on the mathematical description of normal tyre stiffness. The article uses the methods of non-holonomic mechanics and plane section methods. The article shows that the abscissa of gravity center of tyre stiffness expansion by the length of the contact area is the shift of normal road response. It can be used for determining rolling resistance coefficient. When determining rolling resistance coefficient using ellipsis and power function equations, one can reduce labor costs for testing and increase assessment accuracy.

Effective screening length and quasiuniversality for the restricted primitive model of an electrolyte solution.

PubMed

Janecek, Jirí; Netz, Roland R

2009-02-21

Monte Carlo simulations for the restricted primitive model of an electrolyte solution above the critical temperature are performed at a wide range of concentrations and temperatures. Thermodynamic properties such as internal energy, osmotic coefficient, activity coefficient, as well as spatial correlation functions are determined. These observables are used to investigate whether quasiuniversality in terms of an effective screening length exists, similar to the role played by the effective electron mass in solid-state physics. To that end, an effective screening length is extracted from the asymptotic behavior of the Fourier-transformed charge-correlation function and plugged into the Debye-Huckel limiting expressions for various thermodynamic properties. Comparison with numerical results is favorable, suggesting that correlation and other effects not captured on the Debye-Huckel limiting level can be successfully incorporated by a single effective parameter while keeping the functional form of Debye-Huckel expressions. We also compare different methods to determine mean ionic activity coefficient in molecular simulations and check the internal consistency of the numerical data.

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

Exact determination of asymptotic CMB temperature-redshift relation

NASA Astrophysics Data System (ADS)

Hahn, Steffen; Hofmann, Ralf

2018-02-01

Based on energy conservation in a Friedmann-Lemaître-Robertson-Walker (FLRW) Universe, on the Legendre transformation between energy density and pressure, and on nonperturbative asymptotic freedom at high temperatures, we derive the coefficient νCMB in the high-temperature (T) — redshift (z) relation, T/T0 = νCMB(z + 1), of the Cosmic Microwave Background (CMB). Theoretically, our calculation relies on a deconfining SU(2) rather than a U(1) photon gas. We prove that νCMB = (1/4)1/3 = 0.629960(5), representing a topological invariant. Interestingly, the relative deviation of νCMB from the critical exponent associated with the correlation length l of the 3D Ising model, νIsing = 0.629971(4), is less than 2 × 10-5. We are not in a position to establish a direct theoretical link between νCMB and νIsing as suggested by the topological nature of νCMB and the fact that both theories are members of the same universality class. We do, however, spell out a somewhat speculative, strictly monotonic map from the physical Ising temperature 𝜃 to a fictitious SU(2) Yang-Mills temperature T, the latter continuing the asymptotic dependence of the scale factor a on T/T0 for T/T0 ≫ 1 down to T = 0, and we identify an exponential map from a to l to reproduce critical Ising behavior.

Estimating inelastic heavy-particle - hydrogen collision data. II. Simplified model for ionic collisions and application to barium-hydrogen ionic collisions

NASA Astrophysics Data System (ADS)

Belyaev, Andrey K.; Yakovleva, Svetlana A.

2017-12-01

Aims: A simplified model is derived for estimating rate coefficients for inelastic processes in low-energy collisions of heavy particles with hydrogen, in particular, the rate coefficients with high and moderate values. Such processes are important for non-local thermodynamic equilibrium modeling of cool stellar atmospheres. Methods: The derived method is based on the asymptotic approach for electronic structure calculations and the Landau-Zener model for nonadiabatic transition probability determination. Results: It is found that the rate coefficients are expressed via statistical probabilities and reduced rate coefficients. It is shown that the reduced rate coefficients for neutralization and ion-pair formation processes depend on single electronic bound energies of an atomic particle, while the reduced rate coefficients for excitation and de-excitation processes depend on two electronic bound energies. The reduced rate coefficients are calculated and tabulated as functions of electronic bound energies. The derived model is applied to barium-hydrogen ionic collisions. For the first time, rate coefficients are evaluated for inelastic processes in Ba+ + H and Ba2+ + H- collisions for all transitions between the states from the ground and up to and including the ionic state. Tables with calculated data are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/608/A33

Estimating inelastic heavy-particle-hydrogen collision data. I. Simplified model and application to potassium-hydrogen collisions

NASA Astrophysics Data System (ADS)

Belyaev, Andrey K.; Yakovleva, Svetlana A.

2017-10-01

Aims: We derive a simplified model for estimating atomic data on inelastic processes in low-energy collisions of heavy-particles with hydrogen, in particular for the inelastic processes with high and moderate rate coefficients. It is known that these processes are important for non-LTE modeling of cool stellar atmospheres. Methods: Rate coefficients are evaluated using a derived method, which is a simplified version of a recently proposed approach based on the asymptotic method for electronic structure calculations and the Landau-Zener model for nonadiabatic transition probability determination. Results: The rate coefficients are found to be expressed via statistical probabilities and reduced rate coefficients. It turns out that the reduced rate coefficients for mutual neutralization and ion-pair formation processes depend on single electronic bound energies of an atom, while the reduced rate coefficients for excitation and de-excitation processes depend on two electronic bound energies. The reduced rate coefficients are calculated and tabulated as functions of electronic bound energies. The derived model is applied to potassium-hydrogen collisions. For the first time, rate coefficients are evaluated for inelastic processes in K+H and K++H- collisions for all transitions from ground states up to and including ionic states. Tables with calculated data are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/606/A147

Self-similarity in the inertial region of wall turbulence.

PubMed

Klewicki, J; Philip, J; Marusic, I; Chauhan, K; Morrill-Winter, C

2014-12-01

The inverse of the von Kármán constant κ is the leading coefficient in the equation describing the logarithmic mean velocity profile in wall bounded turbulent flows. Klewicki [J. Fluid Mech. 718, 596 (2013)] connects the asymptotic value of κ with an emerging condition of dynamic self-similarity on an interior inertial domain that contains a geometrically self-similar hierarchy of scaling layers. A number of properties associated with the asymptotic value of κ are revealed. This is accomplished using a framework that retains connection to invariance properties admitted by the mean statement of dynamics. The development leads toward, but terminates short of, analytically determining a value for κ. It is shown that if adjacent layers on the hierarchy (or their adjacent positions) adhere to the same self-similarity that is analytically shown to exist between any given layer and its position, then κ≡Φ(-2)=0.381966..., where Φ=(1+√5)/2 is the golden ratio. A number of measures, derived specifically from an analysis of the mean momentum equation, are subsequently used to empirically explore the veracity and implications of κ=Φ(-2). Consistent with the differential transformations underlying an invariant form admitted by the governing mean equation, it is demonstrated that the value of κ arises from two geometric features associated with the inertial turbulent motions responsible for momentum transport. One nominally pertains to the shape of the relevant motions as quantified by their area coverage in any given wall-parallel plane, and the other pertains to the changing size of these motions in the wall-normal direction. In accord with self-similar mean dynamics, these two features remain invariant across the inertial domain. Data from direct numerical simulations and higher Reynolds number experiments are presented and discussed relative to the self-similar geometric structure indicated by the analysis, and in particular the special form of self-similarity shown to correspond to κ=Φ(-2).

On the Asymptotic Relative Efficiency of Planned Missingness Designs.

PubMed

Rhemtulla, Mijke; Savalei, Victoria; Little, Todd D

2016-03-01

In planned missingness (PM) designs, certain data are set a priori to be missing. PM designs can increase validity and reduce cost; however, little is known about the loss of efficiency that accompanies these designs. The present paper compares PM designs to reduced sample (RN) designs that have the same total number of data points concentrated in fewer participants. In 4 studies, we consider models for both observed and latent variables, designs that do or do not include an "X set" of variables with complete data, and a full range of between- and within-set correlation values. All results are obtained using asymptotic relative efficiency formulas, and thus no data are generated; this novel approach allows us to examine whether PM designs have theoretical advantages over RN designs removing the impact of sampling error. Our primary findings are that (a) in manifest variable regression models, estimates of regression coefficients have much lower relative efficiency in PM designs as compared to RN designs, (b) relative efficiency of factor correlation or latent regression coefficient estimates is maximized when the indicators of each latent variable come from different sets, and (c) the addition of an X set improves efficiency in manifest variable regression models only for the parameters that directly involve the X-set variables, but it substantially improves efficiency of most parameters in latent variable models. We conclude that PM designs can be beneficial when the model of interest is a latent variable model; recommendations are made for how to optimize such a design.

Application of Vorob'ev's asymptotic solution to retrieval of the structural characteristics Cn2 from BSA-lidar data

NASA Astrophysics Data System (ADS)

Razenkov, I. A.

2017-11-01

Micro pulse lasers have allowed solution of some technical problems and design of a specialized aerosol lidar capable of recording backscattering amplification (BSA) in a turbulent atmosphere (2014) by now. The BSA-lidar has two receiving channels, one of which is affected by a turbulence. The measurement result is the ratio of echo signals, i.e., the coefficient of backscattering amplification. The problem of lidar data inversion and retrieval of "optical" turbulence parameters was recently solved by V.V. Vorob'ev theoretically (2016). A lidar experiment was organized for testing the solution, and the asymptotic solution was applied to echo signals, which allowed estimating the daily behavior of the structural characteristics Cn 2 along a horizontal 2-km path. The experiment was accompanied by parallel independent measurements of Cn 2 by an image jitter sensor along the same path. It was shown experimentally that the Vorob'ev solution is applicable to Cn 2 retrieval from BSA-lidar data if β0 2<=3 for β0 2>3, the saturation of the amplification effect and a decrease in the experimental data with respect to calculation results are observed. The coefficient of correlation between the retrieved structural characteristics Cn 2 of the lidar and jitter sensor is 0.8-0.9. The Cn 2 values retrieved from lidar signals turned out to be 20-40% lower than the Cn 2 values of the image jitter sensor.

Performance of Modified Test Statistics in Covariance and Correlation Structure Analysis under Conditions of Multivariate Nonnormality.

ERIC Educational Resources Information Center

Fouladi, Rachel T.

2000-01-01

Provides an overview of standard and modified normal theory and asymptotically distribution-free covariance and correlation structure analysis techniques and details Monte Carlo simulation results on Type I and Type II error control. Demonstrates through the simulation that robustness and nonrobustness of structure analysis techniques vary as a…

The Central Limit Theorem for Supercritical Oriented Percolation in Two Dimensions

NASA Astrophysics Data System (ADS)

Tzioufas, Achillefs

2018-04-01

We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the standard normal law. This resolves a longstanding open problem pointed out to in several instances in the literature. The result applies also to the continuous-time analog of the process, viz. the basic one-dimensional contact process. We also derive general random-indices central limit theorems for associated random variables as byproducts of our proof.

The Central Limit Theorem for Supercritical Oriented Percolation in Two Dimensions

NASA Astrophysics Data System (ADS)

Tzioufas, Achillefs

2018-06-01

We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the standard normal law. This resolves a longstanding open problem pointed out to in several instances in the literature. The result applies also to the continuous-time analog of the process, viz. the basic one-dimensional contact process. We also derive general random-indices central limit theorems for associated random variables as byproducts of our proof.

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1989-01-01

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

Confidence bounds for normal and lognormal distribution coefficients of variation

Treesearch

Steve Verrill

2003-01-01

This paper compares the so-called exact approach for obtaining confidence intervals on normal distribution coefficients of variation to approximate methods. Approximate approaches were found to perform less well than the exact approach for large coefficients of variation and small sample sizes. Web-based computer programs are described for calculating confidence...

Normalized lift: an energy interpretation of the lift coefficient simplifies comparisons of the lifting ability of rotating and flapping surfaces.

PubMed

Burgers, Phillip; Alexander, David E

2012-01-01

For a century, researchers have used the standard lift coefficient C(L) to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv(2), where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S), compared against the total kinetic energy required for generating said lift, ½v(2). This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.

Normalized Lift: An Energy Interpretation of the Lift Coefficient Simplifies Comparisons of the Lifting Ability of Rotating and Flapping Surfaces

PubMed Central

Burgers, Phillip; Alexander, David E.

2012-01-01

For a century, researchers have used the standard lift coefficient CL to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv 2, where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders. This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S), compared against the total kinetic energy required for generating said lift, ½v2. This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran. The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings. PMID:22629326

A Method for Approximating the Bivariate Normal Correlation Coefficient.

ERIC Educational Resources Information Center

Kirk, David B.

Improvements of the Gaussian quadrature in conjunction with the Newton-Raphson iteration technique (TM 000 789) are discussed as effective methods of calculating the bivariate normal correlation coefficient. (CK)

Transport in sheared stochastic magnetic fields

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

Vanden Eijnden, E.; Balescu, R.

1997-02-01

The transport of test particles in a stochastic magnetic field with a sheared component is studied. Two stages in the particle dynamics are distinguished depending on whether the collisional effects perpendicular to the main field are negligible or not. Whenever the perpendicular collisions are unimportant, the particles show a subdiffusive behavior which is slower in the presence of shear. The particle dynamics is then inhomogeneous and non-Markovian and no diffusion coefficient may be properly defined. When the perpendicular collision frequency is small, this subdiffusive stage may be very long. In the truly asymptotic stage, however, the perpendicular collisions must bemore » accounted for and the particle motion eventually becomes diffusive. Here again, however, the shear is shown to reduce the anomalous diffusion coefficient of the system. {copyright} {ital 1997 American Institute of Physics.}« less

Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential.

PubMed

Guérin, T; Dean, D S

2017-01-01

We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F. The system is studied in the region where the force is close to the critical value F_{c} at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F>F_{c}, whereas for F

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

Vibrations of a thin cylindrical shell stiffened by rings with various stiffness

NASA Astrophysics Data System (ADS)

Nesterchuk, G. A.

2018-05-01

The problem of vibrations of a thin-walled elastic cylindrical shell reinforced by frames of different rigidity is investigated. The solution for the case of the clamped shell edges was obtained by asymptotic methods and refined by the finite element method. Rings with zero eccentricity and stiffness varying along the generatrix of the shell cylinder are considered. Varying the optimal coefficients of the distribution functions of the rigidity of the frames and finding more precise parameters makes it possible to find correction factors for analytical formulas of approximate calculation.

Study of clustering structures through breakup reactions

NASA Astrophysics Data System (ADS)

Capel, Pierre

2014-12-01

Models for the description of breakup reactions used to study the structure of exotic cluster structures like halos are reviewed. The sensitivity of these models to the projectile description is presented. Calculations are sensitive to the projectile ground state mostly through its asymptotic normalisation coefficient (ANC). They also probe the continuum of the projectile. This enables studying not only resonant states of the projectile but also its non-resonant continuum both resonant and non-resonant. This opens the possibility to study correlations between both halo neutrons in two-neutron halo nuclei.

Optimizing snake locomotion on an inclined plane

NASA Astrophysics Data System (ADS)

Wang, Xiaolin; Osborne, Matthew T.; Alben, Silas

2014-01-01

We develop a model to study the locomotion of snakes on inclined planes. We determine numerically which snake motions are optimal for two retrograde traveling-wave body shapes, triangular and sinusoidal waves, across a wide range of frictional parameters and incline angles. In the regime of large transverse friction coefficients, we find power-law scalings for the optimal wave amplitudes and corresponding costs of locomotion. We give an asymptotic analysis to show that the optimal snake motions are traveling waves with amplitudes given by the same scaling laws found in the numerics.

Rotating non-Boussinesq Rayleigh-Benard convection

NASA Astrophysics Data System (ADS)

Moroz, Vadim Vladimir

This thesis makes quantitative predictions about the formation and stability of hexagonal and roll patterns in convecting system unbounded in horizontal direction. Starting from the Navier-Stokes, heat and continuity equations, the convection problem is then reduced to normal form equations using equivariant bifurcation theory. The relative stabilities of patterns lying on a hexagonal lattice in Fourier space are then determined using appropriate amplitude equations, with coefficients obtained via asymptotic expansion of the governing partial differential equations, with the conducting state being the base state, and the control parameter and the non-Boussinesq effects being small. The software package Mathematica was used to calculate amplitude coefficients of the appropriate coupled Ginzburg-Landau equations for the rigid-rigid and free-free case. A Galerkin code (initial version of which was written by W. Pesch et al.) is used to determine pattern stability further from onset and for strongly non-Boussinesq fluids. Specific predictions about the stability of hexagon and roll patterns for realistic experimental conditions are made. The dependence of the stability of the convective patterns on the Rayleigh number, planform wavenumber and the rotation rate is studied. Long- and shortwave instabilities, both steady and oscillatory, are identified. For small Prandtl numbers oscillatory sideband instabilities are found already very close to onset. A resonant mode interaction in hexagonal patterns arising in non-Boussinesq Rayleigh-Benard convection is studied using symmetry group methods. The lowest-order coupling terms for interacting patterns are identified. A bifurcation analysis of the resulting system of equations shows that the bifurcation is transcritical. Stability properties of resulting patterns are discussed. It is found that for some fluid properties the traditional hexagon convection solution does not exist. Analytical results are supported by numerical solutions of the convection equations using the Galerkin procedure and a Floquet analysis.

Psychometric functions for informational masking

NASA Astrophysics Data System (ADS)

Lutfi, Robert A.; Kistler, Doris J.; Callahan, Michael R.; Wightman, Frederic L.

2003-04-01

The method of constant stimuli was used to obtain complete psychometric functions (PFs) from 44 normal-hearing listeners in conditions known to produce varying amounts of informational masking. The task was to detect a pure-tone signal in the presence of a broadband noise and in the presence of multitone maskers with frequencies and amplitudes that varied at random from one presentation to the next. Relative to the broadband noise condition, significant reductions were observed in both the slope and the upper asymptote of the PF for multitone maskers producing large amounts of informational masking. Slope was affected more for some listeners while asymptote was affected more for others. Mean slopes and asymptotes varied nonmonotonically with the number of masker components in much the same manner as mean thresholds. The results are consistent with a model that assumes trial-by-trial judgments are based on a weighted sum of dB levels at the output of independent auditory filters. For many listeners, however, the weights appear to reflect how often a nonsignal auditory filter is mistaken for the signal filter. For these listeners adaptive procedures may produce a significant bias in the estimates of threshold for conditions of informational masking. [Work supported by NIDCD.

Epidemiological modeling in a branching population. Particular case of a general SIS model with two age classes.

PubMed

Jacob, C; Viet, A F

2003-03-01

This paper covers the elaboration of a general class of multitype branching processes for modeling in a branching population, the evolution of a disease with horizontal and vertical transmissions. When the size of the population may tend to infinity, normalization must be carried out. As the initial size tends to infinity, the normalized model converges a.s. to a dynamical system the solution of which is the probability law of the state of health for an individual ancestors line. The focal point of this study concerns the transient and asymptotical behaviors of a SIS model with two age classes in a branching population. We will compare the asymptotical probability of extinction on the scale of a finite population and on the scale of an individual in an infinite population: when the rates of transmission are small compared to the rate of renewing the population of susceptibles, the two models lead to a.s. extinction, giving consistent results, which no longer applies to the opposite situation of important transmissions. In that case the size of the population plays a crucial role in the spreading of the disease.

The effect of sensor spacing on wind measurements at the Shuttle Landing Facility

NASA Technical Reports Server (NTRS)

Merceret, Francis J.

1995-01-01

This document presents results of a field study of the effect of sensor spacing on the validity of wind measurements at the Space Shuttle landing Facility (SLF). Standard measurements are made at one second intervals from 30 foot (9.1m) towers located 500 feet (152m) from the SLF centerline. The centerline winds are not exactly the same as those measured by the towers. This study quantifies the differences as a function of statistics of the observed winds and distance between the measurements and points of interest. The field program used logarithmically spaced portable wind towers to measure wind speed and direction over a range of conditions. Correlations, spectra, moments, and structure functions were computed. A universal normalization for structure functions was devised. The normalized structure functions increase as the 2/3 power of separation distance until an asymptotic value is approached. This occurs at spacings of several hundred feet (about 100m). At larger spacings, the structure functions are bounded by the asymptote. This enables quantitative estimates of the expected differences between the winds at the measurement point and the points of interest to be made from the measured wind statistics. A procedure is provided for making these estimates.

Sequential parallel comparison design with binary and time-to-event outcomes.

PubMed

Silverman, Rachel Kloss; Ivanova, Anastasia; Fine, Jason

2018-04-30

Sequential parallel comparison design (SPCD) has been proposed to increase the likelihood of success of clinical trials especially trials with possibly high placebo effect. Sequential parallel comparison design is conducted with 2 stages. Participants are randomized between active therapy and placebo in stage 1. Then, stage 1 placebo nonresponders are rerandomized between active therapy and placebo. Data from the 2 stages are pooled to yield a single P value. We consider SPCD with binary and with time-to-event outcomes. For time-to-event outcomes, response is defined as a favorable event prior to the end of follow-up for a given stage of SPCD. We show that for these cases, the usual test statistics from stages 1 and 2 are asymptotically normal and uncorrelated under the null hypothesis, leading to a straightforward combined testing procedure. In addition, we show that the estimators of the treatment effects from the 2 stages are asymptotically normal and uncorrelated under the null and alternative hypothesis, yielding confidence interval procedures with correct coverage. Simulations and real data analysis demonstrate the utility of the binary and time-to-event SPCD. Copyright © 2018 John Wiley & Sons, Ltd.

Is Coefficient Alpha Robust to Non-Normal Data?

PubMed Central

Sheng, Yanyan; Sheng, Zhaohui

2011-01-01

Coefficient alpha has been a widely used measure by which internal consistency reliability is assessed. In addition to essential tau-equivalence and uncorrelated errors, normality has been noted as another important assumption for alpha. Earlier work on evaluating this assumption considered either exclusively non-normal error score distributions, or limited conditions. In view of this and the availability of advanced methods for generating univariate non-normal data, Monte Carlo simulations were conducted to show that non-normal distributions for true or error scores do create problems for using alpha to estimate the internal consistency reliability. The sample coefficient alpha is affected by leptokurtic true score distributions, or skewed and/or kurtotic error score distributions. Increased sample sizes, not test lengths, help improve the accuracy, bias, or precision of using it with non-normal data. PMID:22363306

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

Howell, L. W., Jr.

2003-01-01

A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.

Studies of X-ray burst reactions with radioactive ion beams from RESOLUT

NASA Astrophysics Data System (ADS)

Blackmon, J. C.; Wiedenhöver, I.; Belarge, J.; Kuvin, S. A.; Anastasiou, M.; Baby, L. T.; Baker, J.; Colbert, K.; Deibel, C. M.; de Lucio, O.; Gardiner, H. E.; Gay, D. L.; Good, E.; Höflich, P.; Hood, A. A. D.; Keely, N.; Lai, J.; Laminack, A.; Linhardt, L. E.; Lighthall, J.; Macon, K. T.; Need, E.; Quails, N.; Rasco, B. C.; Rijal, N.; Volya, A.

2018-01-01

Reactions on certain proton-rich, radioactive nuclei have been shown to have a significant influence on X-ray bursts. We provide an overview of two recent measurements of important X-ray burst reactions using in-flight radioactive ion beams from the RESOLUT facility at the J. D. Fox Superconducting Accelerator Laboratory at Florida State University. The 17F(d,n)18Ne reaction was measured, and Asymptotic Normalization Coefficients were extracted for bound states in 18Ne that determine the direct-capture cross section dominating the 17F(p,γ)18Ne reaction rate for T≲ 0.45 GK. Unbound resonant states were also studied, and the single-particle strength for the 4.523-MeV (3+) state was found to be consistent with previous results. The 19Ne(d,n)20Na proton transfer reaction was used to study resonances in the 19Ne(p,γ)20Na reaction. The most important 2.65-MeV state in 20Na was observed to decay by proton emission to both the ground and first-excited states in 19Ne, providing strong evidence for a 3+ spin assignment and indicating that proton capture on the thermally-populated first-excited state in 19Ne is an important contributor to the 19Ne(p,γ)20Na reaction rate.

Spectroscopic factors near the r-process path using (d , p) measurements at two energies

NASA Astrophysics Data System (ADS)

Walter, D.; Cizewski, J. A.; Baugher, T.; Ratkiewicz, A.; Manning, B.; Pain, S. D.; Nunes, F. M.; Ahn, S.; Cerizza, G.; Thornsberry, C.; Jones, K. L.

2016-09-01

To determine spectroscopic factors, it is necessary to use a nuclear reaction model that is dependent on the bound-state potential. A poorly constrained potential can drastically increase uncertainties in extracted spectroscopic factors. Mukhamedzhanov and Nunes have proposed a technique to mitigate this uncertainty by combining transfer reaction measurements at two energies. At peripheral reaction energies ( 5 MeV/u), the external contribution of the wave function can be reliably extracted, and then combined with the higher energy reaction ( 40 MeV/u) with a larger contribution from the interior. The two measurements will constrain the single-particle asymptotic normalization coefficient, ANC, and enable spectroscopic factors to be determined with uncertainties dominated by the cross section measurements rather than in the bound-state potential. Published measurements of 86Kr(d , p) at 5.5 MeV/u have been combined with recent results at 35 MeV/u at the NSCL using the ORRUBA and SIDAR arrays of silicon-strip detectors. Preliminary analysis shows that the single-particle ANC can be constrained. The details of the analysis and prospects for measurements with rare isotope beams will be presented. This research by the ORRUBA Collaboration is supported in part by the NSF and the U.S. DOE.

Experimental Studies of Light-Ion Nuclear Reactions Using Low-Energy RI Beams

NASA Astrophysics Data System (ADS)

Yamaguchi, H.; Kahl, D.; Hayakawa, S.; Sakaguchi, Y.; Abe, K.; Shimuzu, H.; Wakabayashi, Y.; Hashimoto, T.; Cherubini, S.; Gulino, M.; Spitaleri, C.; Rapisarda, G. G.; La Cognata, M.; Lamia, L.; Romano, S.; Kubono, S.; Iwasa, N.; Teranishi, T.; Kawabata, T.; Kwon, Y. K.; Binh, D. N.; Khiem, L. H.; Duy, N. N.; Kato, S.; Komatsubara, T.; Coc, A.; de Sereville, N.; Hammache, F.; Kiss, G.; Bishop, S.

CRIB (CNS Radio-Isotope Beam separator) is a low-energy RI beam separator of Center for Nuclear Study (CNS), the University of Tokyo. Studies on nuclear astrophysics, nuclear structure, and other interests have been performed using the RI beams at CRIB, forming international collaborations. A striking method to study astrophyiscal reactions involving radioactive nuclei is the thick-target method in inverse kinematics. Several astrophysical alpha-induced reactions have been be studied with that method at CRIB. A recent example is on the α resonant scattering with a radioactive 7Be beam. This study is related to the astrophysical 7Be(α , γ ) reactions, important at hot p-p chain and ν p-process in supernovae. There have been measurements based on several indirect methods, such as the asymptotic normalization coefficient (ANC) and Trojan horse method (THM). The first THM measurement using an RI beam has been performed at CRIB, to study the 18F(p, α )15O reaction at astrophysical energies via the three body reaction 2H(18F, α 15O)n. The 18F(p, α )15O reaction rate is crucial to understand the 511-keV γ -ray production in nova explosion phenomena, and we successfully evaluated the reaction cross section at novae temperature and below experimentally for the first time.

Resonance-state properties from a phase shift analysis with the S -matrix pole method and the effective-range method

NASA Astrophysics Data System (ADS)

Irgaziev, B. F.; Orlov, Yu. V.

2015-02-01

Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing an important role in nuclear physics and astrophysics. We derive a new useful relationship between ANCs of the Gamow radial wave function and the renormalized (due to the Coulomb interaction) Coulomb-nuclear partial scattering amplitude. We use an analytical approximation in the form of a series for the nonresonant part of the phase shift which can be analytically continued to the point of an isolated resonance pole in the complex plane of the momentum. Earlier, this method which we call the S -matrix pole method was used by us to find the resonance pole energy. We find the corresponding fitting parameters for the 5He,5Li , and 16O concrete resonance states. Additionally, based on the theory of the effective range, we calculate the parameters of the p3 /2 and p1 /2 resonance states of the nuclei 5He and 5Li and compare them with the results obtained by the S -matrix pole method. ANC values are found which can be used to calculate the reaction rate through the 16O resonances which lie slightly above the threshold for the α 12C channel.

Halo effective field theory constrains the solar 7Be + p → 8B + γ rate

DOE PAGES

Zhang, Xilin; Nollett, Kenneth M.; Phillips, D. R.

2015-11-06

In this study, we report an improved low-energy extrapolation of the cross section for the process 7Be(p,γ) 8B, which determines the 8B neutrino flux from the Sun. Our extrapolant is derived from Halo Effective Field Theory (EFT) at next-to-leading order. We apply Bayesian methods to determine the EFT parameters and the low-energy S-factor, using measured cross sections and scattering lengths as inputs. Asymptotic normalization coefficients of 8B are tightly constrained by existing radiative capture data, and contributions to the cross section beyond external direct capture are detected in the data at E < 0.5 MeV. Most importantly, the S-factor atmore » zero energy is constrained to be S(0) = 21.3 ± 0.7 eV b, which is an uncertainty smaller by a factor of two than previously recommended. That recommendation was based on the full range for S(0) obtained among a discrete set of models judged to be reasonable. In contrast, Halo EFT subsumes all models into a controlled low-energy approximant, where they are characterized by nine parameters at next-to-leading order. These are fit to data, and marginalized over via Monte Carlo integration to produce the improved prediction for S(E).« less

Measurement of the {sup 13}C(α,n){sup 16}O reaction with the Trojan horse method: Focus on the sub threshold resonance at −3 keV

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

La Cognata, M.; Spitaleri, C.; Guardo, G. L.

2014-05-02

The {sup 13}C(α,n){sup 16}O reaction is the neutron source of the main component of the s-process. The astrophysical S(E)-factor is dominated by the −3 keV sub-threshold resonance due to the 6.356 MeV level in {sup 17}O. Its contribution is still controversial as extrapolations, e.g., through R-matrix calculations, and indirect techniques, such as the asymptotic normalization coefficient (ANC), yield inconsistent results. Therefore, we have applied the Trojan Horse Method (THM) to the {sup 13}C({sup 6}Li,n{sup 16}O)d reaction to measure its contribution. For the first time, the ANC for the 6.356 MeV level has been deduced through the THM, allowing to attainmore » an unprecedented accuracy. Though a larger ANC for the 6.356 MeV level is measured, our experimental S(E) factor agrees with the most recent extrapolation in the literature in the 140-230 keV energy interval, the accuracy being greatly enhanced thanks to this innovative approach, merging together two well establish indirect techniques, namely, the THM and the ANC.« less

Assessment of dual-point drag reduction for an executive-jet modified airfoil section

NASA Technical Reports Server (NTRS)

Allison, Dennis O.; Mineck, Raymond E.

1996-01-01

This paper presents aerodynamic characteristics and pressure distributions for an executive-jet modified airfoil and discusses drag reduction relative to a baseline airfoil for two cruise design points. A modified airfoil was tested in the adaptive-wall test section of the NASA Langley 0.3-Meter Transonic Cryogenic Tunnel (0.3-m TCT) for Mach numbers ranging from 0.250 to 0.780 and chord Reynolds numbers ranging from 3.0 x 10(exp 6) to 18.0 x 10(exp 6). The angle of attack was varied from minus 2 degrees to almost 10 degrees. Boundary-layer transition was fixed at 5 percent of chord on both the upper and lower surfaces of the model for most of the test. The two design Mach numbers were 0.654 and 0.735, chord Reynolds numbers were 4.5 x 10(exp 6) and 8.9 x 10(exp 6), and normal-force coefficients were 0.98 and 0.51. Test data are presented graphically as integrated force and moment coefficients and chordwise pressure distributions. The maximum normal-force coefficient decreases with increasing Mach number. At a constant normal-force coefficient in the linear region, as Mach number increases an increase occurs in the slope of normal-force coefficient versus angle of attack, negative pitching-moment coefficient, and drag coefficient. With increasing Reynolds number at a constant normal-force coefficient, the pitching-moment coefficient becomes more negative and the drag coefficient decreases. The pressure distributions reveal that when present, separation begins at the trailing edge as angle of attack is increased. The modified airfoil, which is designed with pitching moment and geometric constraints relative to the baseline airfoil, achieved drag reductions for both design points (12 and 22 counts). The drag reductions are associated with stronger suction pressures in the first 10 percent of the upper surface and weakened shock waves.

On the asymptotically Poincaré-Einstein 4-manifolds with harmonic curvature

NASA Astrophysics Data System (ADS)

Hu, Xue

2018-06-01

In this paper, we discuss the mass aspect tensor and the rigidity of an asymptotically Poincaré-Einstein (APE) 4-manifold with harmonic curvature. We prove that the trace-free part of the mass aspect tensor of an APE 4-manifold with harmonic curvature and normalized Einstein conformal infinity is zero. As to the rigidity, we first show that a complete noncompact Riemannian 4-manifold with harmonic curvature and positive Yamabe constant as well as a L2-pinching condition is Einstein. As an application, we then obtain that an APE 4-manifold with harmonic curvature and positive Yamabe constant is isometric to the hyperbolic space provided that the L2-norm of the traceless Ricci tensor or the Weyl tensor is small enough and the conformal infinity is a standard round 3-sphere.

Estimating residual fault hitting rates by recapture sampling

NASA Technical Reports Server (NTRS)

Lee, Larry; Gupta, Rajan

1988-01-01

For the recapture debugging design introduced by Nayak (1988) the problem of estimating the hitting rates of the faults remaining in the system is considered. In the context of a conditional likelihood, moment estimators are derived and are shown to be asymptotically normal and fully efficient. Fixed sample properties of the moment estimators are compared, through simulation, with those of the conditional maximum likelihood estimators. Properties of the conditional model are investigated such as the asymptotic distribution of linear functions of the fault hitting frequencies and a representation of the full data vector in terms of a sequence of independent random vectors. It is assumed that the residual hitting rates follow a log linear rate model and that the testing process is truncated when the gaps between the detection of new errors exceed a fixed amount of time.

Hazard Function Estimation with Cause-of-Death Data Missing at Random.

PubMed

Wang, Qihua; Dinse, Gregg E; Liu, Chunling

2012-04-01

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data.

On the Helicity in 3D-Periodic Navier-Stokes Equations II: The Statistical Case

NASA Astrophysics Data System (ADS)

Foias, Ciprian; Hoang, Luan; Nicolaenko, Basil

2009-09-01

We study the asymptotic behavior of the statistical solutions to the Navier-Stokes equations using the normalization map [9]. It is then applied to the study of mean energy, mean dissipation rate of energy, and mean helicity of the spatial periodic flows driven by potential body forces. The statistical distribution of the asymptotic Beltrami flows are also investigated. We connect our mathematical analysis with the empirical theory of decaying turbulence. With appropriate mathematically defined ensemble averages, the Kolmogorov universal features are shown to be transient in time. We provide an estimate for the time interval in which those features may still be present. Our collaborator and friend Basil Nicolaenko passed away in September of 2007, after this work was completed. Honoring his contribution and friendship, we dedicate this article to him.

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. I - Pressure distribution

NASA Technical Reports Server (NTRS)

Messiter, A. F.

1980-01-01

Asymptotic solutions are derived for the pressure distribution in the interaction of a weak normal shock wave with a turbulent boundary layer. The undisturbed boundary layer is characterized by the law of the wall and the law of the wake for compressible flow. In the limiting case considered, for 'high' transonic speeds, the sonic line is very close to the wall. Comparisons with experiment are shown, with corrections included for the effect of longitudinal wall curvature and for the boundary-layer displacement effect in a circular pipe.

Contact problem on indentation of an elastic half-plane with an inhomogeneous coating by a flat punch in the presence of tangential stresses on a surface

NASA Astrophysics Data System (ADS)

Volkov, Sergei S.; Vasiliev, Andrey S.; Aizikovich, Sergei M.; Sadyrin, Evgeniy V.

2018-05-01

Indentation of an elastic half-space with functionally graded coating by a rigid flat punch is studied. The half-plane is additionally subjected to distributed tangential stresses. Tangential stresses are represented in a form of Fourier series. The problem is reduced to the solution of two dual integral equations over even and odd functions describing distribution of unknown normal contact stresses. The solutions of these dual integral equations are constructed by the bilateral asymptotic method. Approximated analytical expressions for contact normal stresses are provided.

A hybrid asymptotic-modal analysis of the EM scattering by an open-ended S-shaped rectangular waveguide cavity

NASA Technical Reports Server (NTRS)

Law, P. H.; Burkholder, R. J.; Pathak, P. H.

1988-01-01

The electromagnetic fields (EM) backscatter from a 3-dimensional perfectly conducting S-shaped open-ended cavity with a planar interior termination is analyzed when it is illuminated by an external plane wave. The analysis is based on a self-consistent multiple scattering method which accounts for the multiple wave interactions between the open end and the interior termination. The scattering matrices which described the reflection and transmission coefficients of the waveguide modes reflected and transmitted at each junction between the different waveguide sections, as well at the scattering from the edges at the open end are found via asymptotic high frequency methods such as the geometrical and physical theories of diffraction used in conjunction with the equivalent current method. The numerical results for an S-shaped inlet cavity are compared with the backscatter from a straight inlet cavity; the backscattered patterns are different because the curvature of an S-shaped inlet cavity redistributes the energy reflected from the interior termination in a way that is different from a straight inlet cavity.

Coherent-anomaly method in self-avoiding walk problems

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

1988-06-01

Self-avoiding walk (SAW), being a nonequilibrium cooperative phenomenon, is investigated with a finite-order-restricted-walk (finite-ORW or FORW) coherent-anomaly method (CAM). The coefficient β 1 r in the asymptotic form C nr≅ β 1 r λ n1 r for the total number C nr of r- ORW's with respect to the step number n is investigated for the first time. An asymptotic form for SAW's is thus obtained form the series of FORW approximants, C nr≅ brgμ n(1 + a/r) n, as the envelope curve C n≅b(ae/g) gμ nn g. Numerical results are given by C n≅1.424 n0.27884.1507 n and C n≅1.179 n0.158710.005 n for the plane triangular lattice and f.c.c. lattice, respectively. A good coincidence of the total numbers estimated from the above simple formulae with exact enumerations for finite-step SAW's implies that the essential nature of SAW (non-Markov process) can be understood from FORW (Markov process) in the CAM framework.

Improvements to the George/Castillo Boundary Layer Theory

NASA Astrophysics Data System (ADS)

Wosnik, Martin; George, William K.; Castillo, Luciano

2000-11-01

George and Castillo (1997)(George WK and Castillo L (1997) Appl.Mech.Rev.), 50, 12/1, 689-729. presented a new theory for Zero Pressure Gradient Turbulent Boundary Layers based on an application of Near-Asymptotics to scaling laws derived from equilibrium similarity to the Reynolds-averaged equations. The resulting overlap velocity profiles retained a dependence on local Reynolds number, the parameters for which had to satisfy the following constraint equation: ln \\varepsilon fracdγd ln δ^+ = fracdln [C_o/C_i] d ln δ^+ where γ is the power exponent, Co and Ci are the coefficients in inner and outer variables respectively. GC considered only the first term in an asymptotic expansion of the exact solution, but higher order terms can be considered with no increase in the number of unknowns. The improved theory is tested against new experimental Zero Pressure Gradient Turbulent Boundary Layer data of Smith (1994), Oesterlund (1999) and Johansson and Castillo (2000). For the friction law, the first order term is sufficient, but for Co and γ the higher order terms improve the fit to the velocity profiles significantly.

Exact representation of the asymptotic drift speed and diffusion matrix for a class of velocity-jump processes

NASA Astrophysics Data System (ADS)

Mascia, Corrado

2016-01-01

This paper examines a class of linear hyperbolic systems which generalizes the Goldstein-Kac model to an arbitrary finite number of speeds vi with transition rates μij. Under the basic assumptions that the transition matrix is symmetric and irreducible, and the differences vi -vj generate all the space, the system exhibits a large-time behavior described by a parabolic advection-diffusion equation. The main contribution is to determine explicit formulas for the asymptotic drift speed and diffusion matrix in term of the kinetic parameters vi and μij, establishing a complete connection between microscopic and macroscopic coefficients. It is shown that the drift speed is the arithmetic mean of the velocities vi. The diffusion matrix has a more complicate representation, based on the graph with vertices the velocities vi and arcs weighted by the transition rates μij. The approach is based on an exhaustive analysis of the dispersion relation and on the application of a variant of the Kirchoff's matrix tree Theorem from graph theory.

GENERAL: The Analytic Solution of Schrödinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

NASA Astrophysics Data System (ADS)

Hu, Xian-Quan; Luo, Guang; Cui, Li-Peng; Li, Fang-Yu; Niu, Lian-Bin

2009-03-01

The analytic solution of the radial Schrödinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrödinger equation is V(r) = α1r8 + α2r3 + α3r2 + β3r-1 + β2r-3 + β1r-4. Generally speaking, there is only an approximate solution, but not analytic solution for Schrödinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrödinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schrödinger equation; and lastly, they discuss the solutions and make conclusions.

Super-delta: a new differential gene expression analysis procedure with robust data normalization.

PubMed

Liu, Yuhang; Zhang, Jinfeng; Qiu, Xing

2017-12-21

Normalization is an important data preparation step in gene expression analyses, designed to remove various systematic noise. Sample variance is greatly reduced after normalization, hence the power of subsequent statistical analyses is likely to increase. On the other hand, variance reduction is made possible by borrowing information across all genes, including differentially expressed genes (DEGs) and outliers, which will inevitably introduce some bias. This bias typically inflates type I error; and can reduce statistical power in certain situations. In this study we propose a new differential expression analysis pipeline, dubbed as super-delta, that consists of a multivariate extension of the global normalization and a modified t-test. A robust procedure is designed to minimize the bias introduced by DEGs in the normalization step. The modified t-test is derived based on asymptotic theory for hypothesis testing that suitably pairs with the proposed robust normalization. We first compared super-delta with four commonly used normalization methods: global, median-IQR, quantile, and cyclic loess normalization in simulation studies. Super-delta was shown to have better statistical power with tighter control of type I error rate than its competitors. In many cases, the performance of super-delta is close to that of an oracle test in which datasets without technical noise were used. We then applied all methods to a collection of gene expression datasets on breast cancer patients who received neoadjuvant chemotherapy. While there is a substantial overlap of the DEGs identified by all of them, super-delta were able to identify comparatively more DEGs than its competitors. Downstream gene set enrichment analysis confirmed that all these methods selected largely consistent pathways. Detailed investigations on the relatively small differences showed that pathways identified by super-delta have better connections to breast cancer than other methods. As a new pipeline, super-delta provides new insights to the area of differential gene expression analysis. Solid theoretical foundation supports its asymptotic unbiasedness and technical noise-free properties. Implementation on real and simulated datasets demonstrates its decent performance compared with state-of-art procedures. It also has the potential of expansion to be incorporated with other data type and/or more general between-group comparison problems.

Thermodynamic properties of α-uranium

NASA Astrophysics Data System (ADS)

Ren, Zhiyong; Wu, Jun; Ma, Rong; Hu, Guichao; Luo, Chao

2016-11-01

The lattice constants and equilibrium atomic volume of α-uranium were calculated by Density Functional Theory (DFT). The first principles calculation results of the lattice for α-uranium are in agreement with the experimental results well. The thermodynamic properties of α-uranium from 0 to 900 K and 0-100 GPa were calculated with the quasi-harmonic Debye model. Volume, bulk modulus, entropy, Debye temperature, thermal expansion coefficient and the heat capacity of α-uranium were calculated. The calculated results show that the bulk modulus and Debye temperature increase with the increasing pressure at a given temperature while decreasing with the increasing temperature at a given pressure. Volume, entropy, thermal expansion coefficient and the heat capacity decrease with the increasing pressure while increasing with the increasing temperature. The theoretical results of entropy, Debye temperature, thermal expansion coefficient and the heat capacity show good agreement with the general trends of the experimental values. The constant-volume heat capacity shows typical Debye T3 power-law behavior at low temperature limit and approaches to the classical asymptotic Dulong-Petit limit at high temperature limit.

Viscous, radiating hypersonic flow about a blunt body

NASA Technical Reports Server (NTRS)

Passamaneck, R. S.

1974-01-01

The viscous, radiating hypersonic flow past an axisymmetric blunt body is analyzed based on the Navier-Stokes equations, plus a radiative equation of transfer derived from the Milne-Eddington differential approximation. The fluid is assumed to be a perfect gas with constant specific heats, a constant Prandtl number of order unity, a viscosity coefficient varying as a power of the temperature, and an absorption coefficient varying as the first power of the density and as a power of the temperature. The gray gas assumption is invoked, thereby making the absorption coefficient independent of the spectral frequency. Limiting forms of the solutions are studied as the freestream Mach number freestream Reynolds number and the temperature ratio across the shock wave, go to infinity, and as the Bouguer number and the density ratio across the shock wave go to zero. The method of matched asymptotic expansions is used in the analysis, and it is shown that there is a far-field precursor, composed of two regions, in which the fluid mechanics can be neglected for all practical purposes but included for completeness.

On the heat trace of Schroedinger operators

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

Banuelos, R.; Sa Barreto, A.

1995-12-31

Trace formulae for heat kernels of Schroedinger operators have been widely studied in connection with spectral and scattering theory. They have been used to obtain information about a potential from its spectrum, or from its scattering data, and vice-versa. Using elementary Fourier transform methods we obtain a formula for the general coefficient in the asymptotic expansion of the trace of the heat kernel of the Schroedinger operator {minus}{Delta} + V, as t {down_arrow} 0, with V {element_of} S(R{sup n}), the class of functions with rapid decay at infinity. In dimension n = 1 a recurrent formula for the general coefficientmore » in the expansion is obtained in [6]. However the KdV methods used there do not seem to generalize to higher dimension. Using the formula of [6] and the symmetry of some integrals, Y. Colin de Verdiere has computed the first four coefficients for potentials in three space dimensions. Also in [1] a different method is used to compute heat coefficients for differential operators on manifolds. 14 refs.« less

Characterization of the Distribution of the Lz Index of Person Fit According to the Estimated Proficiency Level

ERIC Educational Resources Information Center

Raiche, Gilles; Blais, Jean-Guy

2005-01-01

The distribution of person fit indices is not easy to describe in tests where the item sample is too small to conform to a theoretical asymptotic statistical distribution, particularly the normal N(0,1). In practice, it is always the fact and, consequently, it is difficult to get the critical percentile value indicating person misfit. First, we…

A Didactic Presentation of Snijders's "l[subscript z]*" Index of Person Fit with Emphasis on Response Model Selection and Ability Estimation

ERIC Educational Resources Information Center

Magis, David; Raiche, Gilles; Beland, Sebastien

2012-01-01

This paper focuses on two likelihood-based indices of person fit, the index "l[subscript z]" and the Snijders's modified index "l[subscript z]*". The first one is commonly used in practical assessment of person fit, although its asymptotic standard normal distribution is not valid when true abilities are replaced by sample…

Development of a "First Principles" Water Potential with Flexible Monomers: Dimer Potential Energy Surface, VRT Spectrum, and Second Virial Coefficient.

PubMed

Babin, Volodymyr; Leforestier, Claude; Paesani, Francesco

2013-12-10

The development of a "first principles" water potential with flexible monomers (MB-pol) for molecular simulations of water systems from gas to condensed phases is described. MB-pol is built upon the many-body expansion of the intermolecular interactions, and the specific focus of this study is on the two-body term (V2B) representing the full-dimensional intermolecular part of the water dimer potential energy surface. V2B is constructed by fitting 40,000 dimer energies calculated at the CCSD(T)/CBS level of theory and imposing the correct asymptotic behavior at long-range as predicted from "first principles". The comparison of the calculated vibration-rotation tunneling (VRT) spectrum and second virial coefficient with the corresponding experimental results demonstrates the accuracy of the MB-pol dimer potential energy surface.

Similarity solutions in the theory of curvature driven diffusion along planar curves: II. Curves that travel at constant speed

NASA Astrophysics Data System (ADS)

Asvadurov, Sergey; Coleman, Bernard D.

1999-07-01

In the theory of curvature driven diffusion along curves, the rate υ at which a planar curve C= C( t) advances along its normal vector is proportional to the second derivative of the curvature κ with respect to the curve’s arc-length parameter, s, i.e., υ( s, t)= Aκss( s, t). The curve is called invariant if it evolves without deformation or rotation; its motion is then a steady translation, and the angle θ= θ( s) from the direction of propagation of C to the tangent vector at s obeys the equation Aθ″‧(s)=V sin θ(s) in which V is the speed of propagation. When C is an infinite curve, this equation with V>0 implies that as s→+∞ or -∞, C either is asymptotic to a straight line parallel to the direction of propagation or spirals to a limit point with κ‧( s) approaching a non-zero constant. If C spirals to a point x+∞ as s increases to +∞, C may either spiral to a point x-∞ or be asymptotic to a line l- as s decreases to -∞. The curves that are asymptotic to lines both as s→+∞ and as s→-∞ differ by only similarity transformations and are such that l+= l- and have that line as an axis of symmetry. A discussion is given of properties that data of the form ( θ(0), θ‧(0), θ″(0)) must have to determine a curve asymptotic to a line for either large or small s.

Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20.

PubMed

Michael, J Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7 (Paturle & Coppens, 1988). In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle-Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.

Quantifying glucose permeability and enhanced light penetration in ex vivo human normal and cancerous esophagus tissues with optical coherence tomography

NASA Astrophysics Data System (ADS)

Zhao, Q. L.; Si, J. L.; Guo, Z. Y.; Wei, H. J.; Yang, H. Q.; Wu, G. Y.; Xie, S. S.; Li, X. Y.; Guo, X.; Zhong, H. Q.; Li, L. Q.

2011-01-01

We report our pilot results on quantification of glucose (G) diffusion permeability in human normal esophagus and ESCC tissues in vitro by using OCT technique. The permeability coefficient of 40% aqueous solution of G was found to be (1.74±0.04)×10-5 cm/s in normal esophagus and (2.45±0.06)×10-5 cm/s in ESCC tissues. The results from this study indicate that ESCC tissues had a higher permeability coefficient compared to normal esophageal tissues, and the light penetration depths gradually increase with the increase of applied topically with G time for the normal esophageal and ESCC tissues. The results indicate that the permeability coefficient of G in cancer tissues was 1.41-fold than that in normal tissues, and the light penetration depth for the ESCC tissues is significantly smaller than that of normal esophagus tissues in the same time range. These results demonstrate that the optical clearing of normal and cancer esophagus tissues are improved after application of G.

An Experimental Study on Normal Stress and Shear Rate Dependency of Basic Friction Coefficient in Dry and Wet Limestone Joints

NASA Astrophysics Data System (ADS)

Mehrishal, Seyedahmad; Sharifzadeh, Mostafa; Shahriar, Korosh; Song, Jae-Jon

2016-12-01

Among all parameters that affect the friction of rocks, variable normal stress and slip rate are the most important second-order parameters. The shear-rate- and normal-stress-dependent friction behavior of rock discontinuities may significantly influence the dynamic responses of rock mass. In this research, two limestone rock types, which were travertine and onyx marble with slickenside and grinded #80 surfaces, were prepared and CNL direct shear tests were performed on the joints under various shear conditions. The shearing rate varied from 0.1 to 50 mm/min under different normal stresses (from 2 to 30 % of UCS) in both dry and wet conditions. Experiments showed that the friction coefficient of slickensided and ground #80 surfaces of limestone increased with the increasing shear velocity and decreased with the increasing normal stress. Micro-asperity interlocking between ground #80 surfaces showed higher wear and an increase in friction coefficient ( µ) compared to slickensided surfaces. Slickensided samples with moist surfaces showed an increase in the coefficient of friction compared to dry surfaces; however, on ground #80 surfaces, the moisture decreased the coefficient of friction to a smaller value. Slickenside of limestone typically slides stably in a dry condition and by stick-slip on moist surfaces. The observed shear-rate- and normal-stress-dependent friction behavior can be explained by a similar framework to that of the adhesion theory of friction and a friction mechanism that involves the competition between microscopic dilatant slip and surface asperity deformation. The results have important implications for understanding the behavior of basic and residual friction coefficients of limestone rock surfaces.

Holographic Lifshitz superconductors: Analytic solution

NASA Astrophysics Data System (ADS)

Natsuume, Makoto; Okamura, Takashi

2018-03-01

We construct an analytic solution for a one-parameter family of holographic superconductors in asymptotically Lifshitz spacetimes. We utilize this solution to explore various properties of the systems such as (1) the superfluid phase background and the grand canonical potential, (2) the order parameter response function or the susceptibility, (3) the London equation, and (4) the background with a superfluid flow or a magnetic field. From these results, we identify the dual Ginzburg-Landau theory including numerical coefficients. Also, the dynamic critical exponent zD associated with the critical point is given by zD=2 irrespective of the value of the Lifshitz exponent z .

Robust Portfolio Optimization Using Pseudodistances.

PubMed

Toma, Aida; Leoni-Aubin, Samuela

2015-01-01

The presence of outliers in financial asset returns is a frequently occurring phenomenon which may lead to unreliable mean-variance optimized portfolios. This fact is due to the unbounded influence that outliers can have on the mean returns and covariance estimators that are inputs in the optimization procedure. In this paper we present robust estimators of mean and covariance matrix obtained by minimizing an empirical version of a pseudodistance between the assumed model and the true model underlying the data. We prove and discuss theoretical properties of these estimators, such as affine equivariance, B-robustness, asymptotic normality and asymptotic relative efficiency. These estimators can be easily used in place of the classical estimators, thereby providing robust optimized portfolios. A Monte Carlo simulation study and applications to real data show the advantages of the proposed approach. We study both in-sample and out-of-sample performance of the proposed robust portfolios comparing them with some other portfolios known in literature.

Robust Portfolio Optimization Using Pseudodistances

PubMed Central

2015-01-01

The presence of outliers in financial asset returns is a frequently occurring phenomenon which may lead to unreliable mean-variance optimized portfolios. This fact is due to the unbounded influence that outliers can have on the mean returns and covariance estimators that are inputs in the optimization procedure. In this paper we present robust estimators of mean and covariance matrix obtained by minimizing an empirical version of a pseudodistance between the assumed model and the true model underlying the data. We prove and discuss theoretical properties of these estimators, such as affine equivariance, B-robustness, asymptotic normality and asymptotic relative efficiency. These estimators can be easily used in place of the classical estimators, thereby providing robust optimized portfolios. A Monte Carlo simulation study and applications to real data show the advantages of the proposed approach. We study both in-sample and out-of-sample performance of the proposed robust portfolios comparing them with some other portfolios known in literature. PMID:26468948

A composite likelihood approach for spatially correlated survival data

PubMed Central

Paik, Jane; Ying, Zhiliang

2013-01-01

The aim of this paper is to provide a composite likelihood approach to handle spatially correlated survival data using pairwise joint distributions. With e-commerce data, a recent question of interest in marketing research has been to describe spatially clustered purchasing behavior and to assess whether geographic distance is the appropriate metric to describe purchasing dependence. We present a model for the dependence structure of time-to-event data subject to spatial dependence to characterize purchasing behavior from the motivating example from e-commerce data. We assume the Farlie-Gumbel-Morgenstern (FGM) distribution and then model the dependence parameter as a function of geographic and demographic pairwise distances. For estimation of the dependence parameters, we present pairwise composite likelihood equations. We prove that the resulting estimators exhibit key properties of consistency and asymptotic normality under certain regularity conditions in the increasing-domain framework of spatial asymptotic theory. PMID:24223450

Maximum likelihood estimation for semiparametric transformation models with interval-censored data

PubMed Central

Mao, Lu; Lin, D. Y.

2016-01-01

Abstract Interval censoring arises frequently in clinical, epidemiological, financial and sociological studies, where the event or failure of interest is known only to occur within an interval induced by periodic monitoring. We formulate the effects of potentially time-dependent covariates on the interval-censored failure time through a broad class of semiparametric transformation models that encompasses proportional hazards and proportional odds models. We consider nonparametric maximum likelihood estimation for this class of models with an arbitrary number of monitoring times for each subject. We devise an EM-type algorithm that converges stably, even in the presence of time-dependent covariates, and show that the estimators for the regression parameters are consistent, asymptotically normal, and asymptotically efficient with an easily estimated covariance matrix. Finally, we demonstrate the performance of our procedures through simulation studies and application to an HIV/AIDS study conducted in Thailand. PMID:27279656

Hawking radiation, entanglement, and teleportation in the background of an asymptotically flat static black hole

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

Pan Qiyuan; Jing Jiliang

2008-09-15

The effect of the Hawking temperature on the entanglement and teleportation for the scalar field in a most general, static, and asymptotically flat black hole with spherical symmetry has been investigated. It has been shown that the same 'initial entanglement' for the state parameter {alpha} and its 'normalized partners'{radical}(1-{alpha}{sup 2}) will be degraded by the Hawking effect with increasing Hawking temperature along two different trajectories except for the maximally entangled state. In the infinite Hawking temperature limit, corresponding to the case of the black hole evaporating completely, the state no longer has distillable entanglement for any {alpha}. It is interestingmore » to note that the mutual information in this limit is equal to just half of the 'initially mutual information'. It has also been demonstrated that the fidelity of teleportation decreases as the Hawking temperature increases, which indicates the degradation of entanglement.« less

Fourier Spot Volatility Estimator: Asymptotic Normality and Efficiency with Liquid and Illiquid High-Frequency Data

PubMed Central

2015-01-01

The recent availability of high frequency data has permitted more efficient ways of computing volatility. However, estimation of volatility from asset price observations is challenging because observed high frequency data are generally affected by noise-microstructure effects. We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002. We prove a central limit theorem for this estimator with optimal rate and asymptotic variance. An extensive simulation study shows the accuracy of the spot volatility estimates obtained using the Fourier estimator and its robustness even in the presence of different microstructure noise specifications. An empirical analysis on high frequency data (U.S. S&P500 and FIB 30 indices) illustrates how the Fourier spot volatility estimates can be successfully used to study intraday variations of volatility and to predict intraday Value at Risk. PMID:26421617

Analytical scalings of the linear Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Cobos, Francisco; Wouchuk, Juan Gustavo

2017-11-01

In the linear Richtmyer-Meshkov instability (RMI), hydrodynamic perturbations are generated behind the transmitted and reflected rippled fronts. The contact surface reaches an asymptotic normal velocity and two different tangential velocities at each side, which are always different for moderate to strong levels of compression, depending on the amount of vorticity generated by the corrugated shocks. We show analytical scaling laws for the ripple velocity (δvi∞)in different physical limits and approximate formulas are provided, valid for arbitrary initial pre-shock parameters. An asymptotic growth for the contact surface ripple of the form ψi(t) ψ∞ + δ vi∞t is obtained. The quantity ψ∞ is in general different from the initial post-shock ripple amplitude, in agreement with the early finding of. Comparison to simulations and experimental work is shown. F.C. acknowledges support from UCLM for a predoctoral fellowship. This work has received support from MINECO, JCCM, and UCLM (Spain).

Hazard Function Estimation with Cause-of-Death Data Missing at Random

PubMed Central

Wang, Qihua; Dinse, Gregg E.; Liu, Chunling

2010-01-01

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Specifically, we present a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators are uniformly strongly consistent and asymptotically normal. We derive asymptotic representations of the mean squared error and the mean integrated squared error for these estimators and we discuss a data-driven bandwidth selection method. A simulation study, conducted to assess finite sample behavior, demonstrates that the proposed hazard estimators perform relatively well. We illustrate our methods with an analysis of some vascular disease data. PMID:22267874

A composite likelihood approach for spatially correlated survival data.

PubMed

Paik, Jane; Ying, Zhiliang

2013-01-01

The aim of this paper is to provide a composite likelihood approach to handle spatially correlated survival data using pairwise joint distributions. With e-commerce data, a recent question of interest in marketing research has been to describe spatially clustered purchasing behavior and to assess whether geographic distance is the appropriate metric to describe purchasing dependence. We present a model for the dependence structure of time-to-event data subject to spatial dependence to characterize purchasing behavior from the motivating example from e-commerce data. We assume the Farlie-Gumbel-Morgenstern (FGM) distribution and then model the dependence parameter as a function of geographic and demographic pairwise distances. For estimation of the dependence parameters, we present pairwise composite likelihood equations. We prove that the resulting estimators exhibit key properties of consistency and asymptotic normality under certain regularity conditions in the increasing-domain framework of spatial asymptotic theory.

Effect of double-layer polarization on the forces that act on a nanosized cylindrical particle in an ac electrical field.

PubMed

Zhao, Hui; Bau, Haim H

2008-06-17

The polarization of, the forces acting on, and the electroosmotic flow field around a cylindrical particle of radius a* and uniform zeta potential zeta* submerged in an electrolyte solution and subjected to alternating electric fields are computed by solving the Poisson-Nernst-Planck (PNP) equations (the standard model). The dipole coefficient and the electrostatic and hydrodynamic forces are calculated as functions of the electric field's frequency, the solute concentration, and the particle's surface charge. The calculations are not restricted to small Debye screening lengths (lambdaD*). At relatively low frequencies, the polarization coefficient is nearly frequency-independent. As the frequency increases above D*/a*(2), where D* is the effective diffusion coefficient, the polarization coefficient initially increases, attains a maximum, and then decreases to an asymptotic value (when the frequency exceeds (1+Du)D*/lambdaD(*2), where Du is the Dukhin number). At low frequencies, when (lambdaD*/a*)(2)e(|zeta*F*/(2R*T*)|) < 1, the PNP calculations are in excellent agreement with the predictions of the Dukhin-Shilov (DS) low-frequency theory. At high frequencies, when lambda D*/a* < 1, the PNP calculations are in excellent agreement with the Maxwell-Wagner-O'Konski (MWO) theory.

Developmental hearing loss impedes auditory task learning and performance in gerbils

PubMed Central

von Trapp, Gardiner; Aloni, Ishita; Young, Stephen; Semple, Malcolm N.; Sanes, Dan H.

2016-01-01

The consequences of developmental hearing loss have been reported to include both sensory and cognitive deficits. To investigate these issues in a non-human model, auditory learning and asymptotic psychometric performance were compared between normal hearing (NH) adult gerbils and those reared with conductive hearing loss (CHL). At postnatal day 10, before ear canal opening, gerbil pups underwent bilateral malleus removal to induce a permanent CHL. Both CHL and control animals were trained to approach a water spout upon presentation of a target (Go stimuli), and withhold for foils (Nogo stimuli). To assess the rate of task acquisition and asymptotic performance, animals were tested on an amplitude modulation (AM) rate discrimination task. Behavioral performance was calculated using a signal detection theory framework. Animals reared with developmental CHL displayed a slower rate of task acquisition for AM discrimination task. Slower acquisition was explained by an impaired ability to generalize to newly introduced stimuli, as compared to controls. Measurement of discrimination thresholds across consecutive testing blocks revealed that CHL animals required a greater number of testing sessions to reach asymptotic threshold values, as compared to controls. However, with sufficient training, CHL animals approached control performance. These results indicate that a sensory impediment can delay auditory learning, and increase the risk of poor performance on a temporal task. PMID:27746215

Early-time solution of the horizontal unconfined aquifer in the build-up phase

NASA Astrophysics Data System (ADS)

Gravanis, Elias; Akylas, Evangelos

2017-04-01

The Boussinesq equation is a dynamical equation for the free surface of saturated subsurface flows over an impervious bed. Boussinesq equation is non-linear. The non-linearity comes from the reduction of the dimensionality of the problem: The flow is assumed to be vertically homogeneous, therefore the flow rate through a cross section of the flow is proportional to the free surface height times the hydraulic gradient, which is assumed to be equal to the slope of the free surface (Dupuit approximation). In general, 'vertically' means normally on the bed; combining the Dupuit approximation with the continuity equation leads to the Boussinesq equation. There are very few transient exact solutions. Self- similar solutions have been constructed in the past by various authors. A power series type of solution was derived for a self-similar Boussinesq equation by Barenblatt in 1990. That type of solution has generated a certain amount of literature. For the unconfined flow case for zero recharge rate Boussinesq derived for the horizontal aquifer an exact solution assuming separation of variables. This is actually an exact asymptotic solution of the horizontal aquifer recession phase for late times. The kinematic wave is an interesting solution obtained by dropping the non-linear term in the Boussinesq equation. Although it is an approximate solution, and holds well only for small values of the Henderson and Wooding λ parameter (that is, for steep slopes, high conductivity or small recharge rate), it becomes less and less approximate for smaller values of the parameter, that is, it is asymptotically exact with respect to that parameter. In the present work we consider the case of the unconfined subsurface flow over horizontal bed in the build-up phase under constant recharge rate. This is a case with an infinite Henderson and Wooding parameter, that is, it is the limiting case where the non-linear term is present in the Boussinesq while the linear spatial derivative term goes away. Nonetheless, no analogue of the kinematic wave or the Boussinesq separable solution exists in this case. The late time state of the build-up phase under constant recharge rate is very simply the steady state solution. Our aim is to construct the early time asymptotic solution of this problem. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turn out to be asymptotic and it is regularized by re-summation techniques which are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.

Causality Analysis: Identifying the Leading Element in a Coupled Dynamical System

PubMed Central

BozorgMagham, Amir E.; Motesharrei, Safa; Penny, Stephen G.; Kalnay, Eugenia

2015-01-01

Physical systems with time-varying internal couplings are abundant in nature. While the full governing equations of these systems are typically unknown due to insufficient understanding of their internal mechanisms, there is often interest in determining the leading element. Here, the leading element is defined as the sub-system with the largest coupling coefficient averaged over a selected time span. Previously, the Convergent Cross Mapping (CCM) method has been employed to determine causality and dominant component in weakly coupled systems with constant coupling coefficients. In this study, CCM is applied to a pair of coupled Lorenz systems with time-varying coupling coefficients, exhibiting switching between dominant sub-systems in different periods. Four sets of numerical experiments are carried out. The first three cases consist of different coupling coefficient schemes: I) Periodic–constant, II) Normal, and III) Mixed Normal/Non-normal. In case IV, numerical experiment of cases II and III are repeated with imposed temporal uncertainties as well as additive normal noise. Our results show that, through detecting directional interactions, CCM identifies the leading sub-system in all cases except when the average coupling coefficients are approximately equal, i.e., when the dominant sub-system is not well defined. PMID:26125157

Effect of friction on vibrotactile sensation of normal and dehydrated skin.

PubMed

Chen, S; Ge, S; Tang, W; Zhang, J

2016-02-01

Vibrotactile sensation mediated is highly dependent on surface mechanical and frictional properties. Dehydration of skin could change these properties. To investigate the relationship between friction and vibrotactile sensation of normal and dehydrated skin. Vibrations were firstly measured during surface exploration using a biomimetic sensor. Piglet skin was used as human skin model to study frictional properties for both normal and dehydrated skin using an atomic force microscope on nanoscale and a pin-on-disk tribometer on macroscale. Effect of vibrational frequency on friction and vibrotactile perception was also observed on nano and macro scale for normal and dehydrated skin. The result indicated that dehydrated skin was less sensitive than normal skin. The coefficient of friction of dehydrated skin is smaller than that of normal skin on both nano and macro scale. The coefficient of friction increases as increasing scanning frequencies. There is a positive correlation between coefficient of friction and vibrotactile sensation on nanoscale and macroscale. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Asymptotic Normality of Poly-T Densities with Bayesian Applications.

DTIC Science & Technology

1987-10-01

be extended to the case of many t-like factors in a straightforward manner. Obviously, the computational complexity will increase rapidly as the number...York: Marcel-Dekker. Broemeling, L.D. and Abdullah, M.Y. (1984). An approximation to the poly-t distribution. Communciations in Statistics A,11, 1407...Street Center Champaign, IL 61820 Austin, TX 78703 Dr. Steven Hunks Dr. James Krantz Department of Education Computer -based Education University of

Densification and structural transitions in networks that grow by node copying

NASA Astrophysics Data System (ADS)

Bhat, U.; Krapivsky, P. L.; Lambiotte, R.; Redner, S.

2016-12-01

We introduce a growing network model, the copying model, in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability p . When p <1/2 , this algorithm generates sparse networks, in which the average node degree is finite. A power-law degree distribution also arises, with a nonuniversal exponent whose value is determined by a transcendental equation in p . In the sparse regime, the network is "normal," e.g., the relative fluctuations in the number of links are asymptotically negligible. For p ≥1/2 , the emergent networks are dense (the average degree increases with the number of nodes N ), and they exhibit intriguing structural behaviors. In particular, the N dependence of the number of m cliques (complete subgraphs of m nodes) undergoes m -1 transitions from normal to progressively more anomalous behavior at an m -dependent critical values of p . Different realizations of the network, which start from the same initial state, exhibit macroscopic fluctuations in the thermodynamic limit: absence of self-averaging. When linking to second neighbors of the target node can occur, the number of links asymptotically grows as N2 as N →∞ , so that the network is effectively complete as N →∞ .

Coefficient of restitution of sports balls: A normal drop test

NASA Astrophysics Data System (ADS)

Haron, Adli; Ismail, K. A.

2012-09-01

Dynamic behaviour of bodies during impact is investigated through impact experiment, the simplest being a normal drop test. Normally, a drop test impact experiment involves measurement of kinematic data; this includes measurement of incident and rebound velocity in order to calculate a coefficient of restitution (COR). A high speed video camera is employed for measuring the kinematic data where speed is calculated from displacement of the bodies. Alternatively, sensors can be employed to measure speeds, especially for a normal impact where there is no spin of the bodies. This paper compares experimental coefficients of restitution (COR) for various sports balls, namely golf, table tennis, hockey and cricket. The energy loss in term of measured COR and effects of target plate are discussed in relation to the material and construction of these sports balls.

Precision Composite Space Structures

DTIC Science & Technology

2007-10-15

large structures. 15. SUBJECT TERMS Composite materials, dimensional stability, microcracking, thermal expansion , space structures, degradation...Figure 32. Variation of normalized coefficients of thermal expansion α11(n), α22(n), and α33(n) with normalized crack density of an AS4/3501-6...coefficients of thermal expansion α11(n), α22(n), and α33(n) with normalized crack density of an AS4/3501-6 composite lamina with a fiber volume

Numerical modeling of solar irradiance on earth's surface

NASA Astrophysics Data System (ADS)

Mera, E.; Gutierez, L.; Da Silva, L.; Miranda, E.

2016-05-01

Modeling studies and estimation of solar radiation in base area, touch from the problems of estimating equation of time, distance equation solar space, solar declination, calculation of surface irradiance, considering that there are a lot of studies you reported the inability of these theoretical equations to be accurate estimates of radiation, many authors have proceeded to make corrections through calibrations with Pyranometers field (solarimeters) or the use of satellites, this being very poor technique last because there a differentiation between radiation and radiant kinetic effects. Because of the above and considering that there is a weather station properly calibrated ground in the Susques Salar in the Jujuy Province, Republic of Argentina, proceeded to make the following modeling of the variable in question, it proceeded to perform the following process: 1. Theoretical Modeling, 2. graphic study of the theoretical and actual data, 3. Adjust primary calibration data through data segmentation on an hourly basis, through horizontal and adding asymptotic constant, 4. Analysis of scatter plot and contrast series. Based on the above steps, the modeling data obtained: Step One: Theoretical data were generated, Step Two: The theoretical data moved 5 hours, Step Three: an asymptote of all negative emissivity values applied, Solve Excel algorithm was applied to least squares minimization between actual and modeled values, obtaining new values of asymptotes with the corresponding theoretical reformulation of data. Add a constant value by month, over time range set (4:00 pm to 6:00 pm). Step Four: The modeling equation coefficients had monthly correlation between actual and theoretical data ranging from 0.7 to 0.9.

Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

DOE PAGES

Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.; ...

2015-10-30

We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less

Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

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

Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.

We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less

Torsional Tribological Behavior and Torsional Friction Model of Polytetrafluoroethylene against 1045 Steel

PubMed Central

Wang, Shibo; Niu, Chengchao

2016-01-01

In this work, the plane-on-plane torsional fretting tribological behavior of polytetrafluoroethylene (PTFE) was studied. A model of a rigid, flat-ended punch acting on an elastic half-space was built according to the experimental conditions. The results indicate that the shape of T–θ curves was influenced by both the torsional angle and the normal load. The torsion friction torque and wear rate of PTFE exponentially decreased when the torsion angle rose. The torsional torque increased from 0.025 N·m under a normal load of 43 N to 0.082 N·m under a normal load of 123 N. With sequentially increasing normal load, the value of torque was maintained. With rising normal load, the wear mass loss of PTFE disks was increased and the wear rate was decreased. Good agreement was found with the calculated torque according to the model and the experimental torque except for that under a normal load of 163 N. The difference under a normal load of 163 N was caused by the coefficient of friction. Usually the coefficient of friction of a polymer decreases with increasing normal load, whereas a constant coefficient of friction was applied in the model. PMID:26799324

Temporal behavior of the effective diffusion coefficients for transport in heterogeneous saturated aquifers

NASA Astrophysics Data System (ADS)

Suciu, N.; Vamos, C.; Vereecken, H.; Vanderborght, J.; Hardelauf, H.

2003-04-01

When the small scale transport is modeled by a Wiener process and the large scale heterogeneity by a random velocity field, the effective coefficients, Deff, can be decomposed as sums between the local coefficient, D, a contribution of the random advection, Dadv, and a contribution of the randomness of the trajectory of plume center of mass, Dcm: Deff=D+Dadv-Dcm. The coefficient Dadv is similar to that introduced by Taylor in 1921, and more recent works associate it with the thermodynamic equilibrium. The ``ergodic hypothesis'' says that over large time intervals Dcm vanishes and the effect of the heterogeneity is described by Dadv=Deff-D. In this work we investigate numerically the long time behavior of the effective coefficients as well as the validity of the ergodic hypothesis. The transport in every realization of the velocity field is modeled with the Global Random Walk Algorithm, which is able to track as many particles as necessary to achieve a statistically reliable simulation of the process. Averages over realizations are further used to estimate mean coefficients and standard deviations. In order to remain in the frame of most of the theoretical approaches, the velocity field was generated in a linear approximation and the logarithm of the hydraulic conductivity was taken to be exponential decaying correlated with variance equal to 0.1. Our results show that even in these idealized conditions, the effective coefficients tend to asymptotic constant values only when the plume travels thousands of correlations lengths (while the first order theories usually predict Fickian behavior after tens of correlations lengths) and that the ergodicity conditions are still far from being met.

Craig's XY distribution and the statistics of Lagrangian power in two-dimensional turbulence

NASA Astrophysics Data System (ADS)

Bandi, Mahesh M.; Connaughton, Colm

2008-03-01

We examine the probability distribution function (PDF) of the energy injection rate (power) in numerical simulations of stationary two-dimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an electromagnetically driven fluid layer, a well-documented system for generating 2D turbulence in the laboratory. In our simulations, the forcing and velocity fields are close to Gaussian. On the other hand, the measured PDF of injected power is very sharply peaked at zero, suggestive of a singularity there, with tails which are exponential but asymmetric. Large positive fluctuations are more probable than large negative fluctuations. It is this asymmetry of the tails which leads to a net positive mean value for the energy input despite the most probable value being zero. The main features of the power distribution are well described by Craig’s XY distribution for the PDF of the product of two correlated normal variables. We show that the power distribution should exhibit a logarithmic singularity at zero and decay exponentially for large absolute values of the power. We calculate the asymptotic behavior and express the asymmetry of the tails in terms of the correlation coefficient of the force and velocity. We compare the measured PDFs with the theoretical calculations and briefly discuss how the power PDF might change with other forcing mechanisms.

Sediment erosion by Görtler vortices: the scour-hole problem

NASA Astrophysics Data System (ADS)

Hopfinger, E. J.; Kurniawan, A.; Graf, W. H.; Lemmin, U.

2004-12-01

Experimental results on sediment erosion (scour) by a plane turbulent wall jet, issuing from a sluice gate, are presented which show clearly it seems for the first time that the turbulent wall layer is destabilized by the concave curvature of the water/sediment interface. The streamwise Görtler vortices which emerge create sediment streaks or longitudinal sediment ridges. The analysis of the results in terms of Görtler instability of the wall layer indicates that the strength of these curvature-excited streamwise vortices is such that the sediment transport is primarily due to turbulence created by these vortices. Their contribution to the wall shear stress is taken to be of the same form as the normal turbulent wall shear stress. For this reason, the model developed by Hogg et al. (J. Fluid Mech. Vol. 338, 1997, p. 317) remains valid; only the numerical coefficients are affected. The logarithmic dependency of the time evolution of the scour-hole depth predicted by this model is shown to be in good agreement with experiments. New scaling laws for the quasi-steady state depth and the associated time, inspired by the Hogg et al. (1997) model are proposed. Furthermore, it is emphasized that at least two scouring regimes must be distinguished: a short-time regime after which a quasi-steady state is reached, followed by a long-time regime, leading to an asymptotic state of virtually no sediment transport.

Determination of astrophysical 7Be(p, γ)8B reaction rates from the 7Li(d, p)8Li reaction

NASA Astrophysics Data System (ADS)

Du, XianChao; Guo, Bing; Li, ZhiHong; Pang, DanYang; Li, ErTao; Liu, WeiPing

2015-06-01

The 7Be(p, γ)8B reaction plays a central role not only in the evaluation of solar neutrino fluxes but also in the evolution of the first stars. Study of this reaction requires the asymptotic normalization coefficient (ANC) for the virtual decay 8B g.s. → 7Be + p. By using the charge symmetry relation, we obtain this proton ANC with the single neutron ANC of 8Li g.s. →7Li + n, which is determined with the distorted wave Born approximation (DWBA) and adiabatic distorted wave approximation (ADWA) analysis of the 7Li(d, p)8Li angular distribution. The astrophysical S-factors and reaction rates of the direct capture process in the 7Be(p, γ)8B reaction are further deduced at energies of astrophysical relevance. The astrophysical S-factor at zero energy for direct capture, S 17(0), is derived to be (19.9 ± 3.5) eV b in good agreement with the most recent recommended value. The contributions of the 1+ and 3+ resonances to the S-factor and reaction rate are also evaluated. The present result demonstrates that the direct capture dominates the 7Be(p, γ)8B reaction in the whole temperature range. This work provides an independent examination to the current results of the 7Be(p, γ)8B reaction.

Craig's XY distribution and the statistics of Lagrangian power in two-dimensional turbulence.

PubMed

Bandi, Mahesh M; Connaughton, Colm

2008-03-01

We examine the probability distribution function (PDF) of the energy injection rate (power) in numerical simulations of stationary two-dimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an electromagnetically driven fluid layer, a well-documented system for generating 2D turbulence in the laboratory. In our simulations, the forcing and velocity fields are close to Gaussian. On the other hand, the measured PDF of injected power is very sharply peaked at zero, suggestive of a singularity there, with tails which are exponential but asymmetric. Large positive fluctuations are more probable than large negative fluctuations. It is this asymmetry of the tails which leads to a net positive mean value for the energy input despite the most probable value being zero. The main features of the power distribution are well described by Craig's XY distribution for the PDF of the product of two correlated normal variables. We show that the power distribution should exhibit a logarithmic singularity at zero and decay exponentially for large absolute values of the power. We calculate the asymptotic behavior and express the asymmetry of the tails in terms of the correlation coefficient of the force and velocity. We compare the measured PDFs with the theoretical calculations and briefly discuss how the power PDF might change with other forcing mechanisms.

Extraction of the ANC from the 10Be(d, p)11Be transfer reaction using the ADWA method

NASA Astrophysics Data System (ADS)

Yang, J.; Capel, P.

2018-05-01

A halo nucleus is built from a core and at least one weakly bound neutron or proton. To understand this unique cluster structure, lots of efforts have been undertaken. During the past decades, the (d, p) reaction has been widely used in experiments and has become an important tool for extracting single-particle properties of nuclei. In this work, our goal is to obtain the Asymptotic Normalization Coefficient (ANC) of the halo nuclei 11Be using the ADWA method. We perform the analysis for the 10Be(d, p)11Be stripping reaction at Ed =21.4, 18, 15, and 12MeV for the ground state and first excited state of the composite nucleus 11Be. The experimental measurement was carried out at Oak Ridge National Laboratory by Schmitt et al. [1] The sensitivity of the calculations to the optical potential choice is also checked. Overall, the transfer process becomes more peripheral at lower energies and forward angles. Investigation in this area is the best way to extract a reliable ANC from the experimental data. For the ground state of 11Be, the ANC obtained using our method (C={0.785}-0.030+0.026{\\text{fm}}-1/2) shows perfect agreement with the one obtained by Ab initio calculations (C Ab=0.786 fm‑1/2) [2].

Measurement of 17F(d ,n )18Ne and the impact on the 17F(p ,γ )18Ne reaction rate for astrophysics

NASA Astrophysics Data System (ADS)

Kuvin, S. A.; Belarge, J.; Baby, L. T.; Baker, J.; Wiedenhöver, I.; Höflich, P.; Volya, A.; Blackmon, J. C.; Deibel, C. M.; Gardiner, H. E.; Lai, J.; Linhardt, L. E.; Macon, K. T.; Rasco, B. C.; Quails, N.; Colbert, K.; Gay, D. L.; Keeley, N.

2017-10-01

Background: The 17F(p ,γ )18Ne reaction is part of the astrophysical "hot CNO" cycles that are important in astrophysical environments like novas. Its thermal reaction rate is low owing to the relatively high energy of the resonances and therefore is dominated by direct, nonresonant capture in stellar environments at temperatures below 0.4 GK. Purpose: An experimental method is established to extract the proton strength to bound and unbound states in experiments with radioactive ion beams and to determine the parameters of direct and resonant capture in the 17F(p ,γ )18Ne reaction. Method: The 17F(d ,n )18Ne reaction is measured in inverse kinematics using a beam of the short-lived isotope 17F and a compact setup of neutron, proton, γ -ray, and heavy-ion detectors called resoneut. Results: The spectroscopic factors for the lowest l =0 proton resonances at Ec .m .=0.60 and 1.17 MeV are determined, yielding results consistent within 1.4 σ of previous proton elastic-scattering measurements. The asymptotic normalization coefficients of the bound 21+ and 22+ states in 18Ne are determined and the resulting direct-capture reaction rates are extracted. Conclusions: The direct-capture component of the 17F(p ,γ )18Ne reaction is determined for the first time from experimental data on 18Ne.

Self-Critical, and Robust, Procedures for the Analysis of Multivariate Normal Data.

DTIC Science & Technology

1982-06-01

Influence Functions The influence function is the most important tt of qual- itative zobustness since many other robustness characteristics of an estimator...may be derived from it. The influence function characterizes the (asymptotic) response of an estimator to an additional observation as a function of...the influence function be bounded. It is also advantageous, in our opinion, if the influence functions are re-descending to zero. The influence function for

A Note on Asymptotic Joint Distribution of the Eigenvalues of a Noncentral Multivariate F Matrix.

DTIC Science & Technology

1984-11-01

Krishnaiah (1982). Now, let us consider the samples drawn from the k multivariate normal popuiejons. Let (Xlt....Xpt) denote the mean vector of the t...to maltivariate problems. Sankh-ya, 4, 381-39(s. (71 KRISHNAIAH , P. R. (1982). Selection of variables in discrimlnant analysis. In Handbook of...Statistics, Volume 2 (P. R. Krishnaiah , editor), 805-820. North-Holland Publishing Company. 6. Unclassifie INSTRUCTIONS REPORT DOCUMENTATION PAGE

Chemical Reactions in Turbulent Mixing Flows

DTIC Science & Technology

1992-07-01

Chemically-Reacting, Gas-Phase Turbulent Jets (Gilbrech 1991), that explored Reynolds number effects on turbulent flame length and the influence of...and asymptotes to a constant value beyond the flame tip. The main result of the work is that the flame length , as estimated from the temperature...8217. Specifically, the normalized flame length Lf/d* displays a linear dependence on the stoichiometric mixture ratio 0, with a slope that decreases from Re "• 1.0

Electron bulk speed lags the protons in the collisionless solar wind

NASA Astrophysics Data System (ADS)

Tong, Y.; Bale, S. D.; Salem, C. S.; Pulupa, M.

2017-12-01

We use a large, statistical set of in situ measurements of the solar wind electron distribution from the Wind/3DP instrument to show that the magnetic field-aligned core electron-proton drift speed tend to small values at high collisionality and asymptotes towards a large limiting value in the collisionless limit. This collisionless drift-limit, when normalized to the local Alfven speed is large and may drive instabilities.

Wave propagation in a strongly heterogeneous elastic porous medium: Homogenization of Biot medium with double porosities

NASA Astrophysics Data System (ADS)

Rohan, Eduard; Naili, Salah; Nguyen, Vu-Hieu

2016-08-01

We study wave propagation in an elastic porous medium saturated with a compressible Newtonian fluid. The porous network is interconnected whereby the pores are characterized by two very different characteristic sizes. At the mesoscopic scale, the medium is described using the Biot model, characterized by a high contrast in the hydraulic permeability and anisotropic elasticity, whereas the contrast in the Biot coupling coefficient is only moderate. Fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. The homogenization method based on the asymptotic analysis is used to obtain a macroscopic model. To respect the high contrast in the material properties, they are scaled by the small parameter, which is involved in the asymptotic analysis and characterized by the size of the heterogeneities. Using the estimates of wavelengths in the double-porosity networks, it is shown that the macroscopic descriptions depend on the contrast in the static permeability associated with pores and micropores and on the frequency. Moreover, the microflow in the double porosity is responsible for fading memory effects via the macroscopic poroviscoelastic constitutive law. xml:lang="fr"

Gini estimation under infinite variance

NASA Astrophysics Data System (ADS)

Fontanari, Andrea; Taleb, Nassim Nicholas; Cirillo, Pasquale

2018-07-01

We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index α ∈(1 , 2)). We show that, in such a case, the Gini coefficient cannot be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges under fat tails. This has important implications for the ongoing discussion about economic inequality. We start by discussing how the nonparametric estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution, as the data distribution shifts from the domain of attraction of a light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We also show how the nonparametric Gini bias increases with lower values of α. We then prove that maximum likelihood estimation outperforms nonparametric methods, requiring a much smaller sample size to reach efficiency. Finally, for fat-tailed data, we provide a simple correction mechanism to the small sample bias of the nonparametric estimator based on the distance between the mode and the mean of its asymptotic distribution.

Patterns of Stochastic Behavior in Dynamically Unstable High-Dimensional Biochemical Networks

PubMed Central

Rosenfeld, Simon

2009-01-01

The question of dynamical stability and stochastic behavior of large biochemical networks is discussed. It is argued that stringent conditions of asymptotic stability have very little chance to materialize in a multidimensional system described by the differential equations of chemical kinetics. The reason is that the criteria of asymptotic stability (Routh-Hurwitz, Lyapunov criteria, Feinberg’s Deficiency Zero theorem) would impose the limitations of very high algebraic order on the kinetic rates and stoichiometric coefficients, and there are no natural laws that would guarantee their unconditional validity. Highly nonlinear, dynamically unstable systems, however, are not necessarily doomed to collapse, as a simple Jacobian analysis would suggest. It is possible that their dynamics may assume the form of pseudo-random fluctuations quite similar to a shot noise, and, therefore, their behavior may be described in terms of Langevin and Fokker-Plank equations. We have shown by simulation that the resulting pseudo-stochastic processes obey the heavy-tailed Generalized Pareto Distribution with temporal sequence of pulses forming the set of constituent-specific Poisson processes. Being applied to intracellular dynamics, these properties are naturally associated with burstiness, a well documented phenomenon in the biology of gene expression. PMID:19838330

A Continuous Threshold Expectile Model.

PubMed

Zhang, Feipeng; Li, Qunhua

2017-12-01

Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. A continuous threshold expectile regression is developed for modeling data in which the effect of a covariate on the response variable is linear but varies below and above an unknown threshold in a continuous way. The estimators for the threshold and the regression coefficients are obtained using a grid search approach. The asymptotic properties for all the estimators are derived, and the estimator for the threshold is shown to achieve root-n consistency. A weighted CUSUM type test statistic is proposed for the existence of a threshold at a given expectile, and its asymptotic properties are derived under both the null and the local alternative models. This test only requires fitting the model under the null hypothesis in the absence of a threshold, thus it is computationally more efficient than the likelihood-ratio type tests. Simulation studies show that the proposed estimators and test have desirable finite sample performance in both homoscedastic and heteroscedastic cases. The application of the proposed method on a Dutch growth data and a baseball pitcher salary data reveals interesting insights. The proposed method is implemented in the R package cthreshER .

Optical scattering coefficient estimated by optical coherence tomography correlates with collagen content in ovarian tissue

NASA Astrophysics Data System (ADS)

Yang, Yi; Wang, Tianheng; Biswal, Nrusingh C.; Wang, Xiaohong; Sanders, Melinda; Brewer, Molly; Zhu, Quing

2011-09-01

Optical scattering coefficient from ex vivo unfixed normal and malignant ovarian tissue was quantitatively extracted by fitting optical coherence tomography (OCT) A-line signals to a single scattering model. 1097 average A-line measurements at a wavelength of 1310 nm were performed at 108 sites obtained from 18 ovaries. The average scattering coefficient obtained from the normal tissue group consisted of 833 measurements from 88 sites was 2.41 mm-1 (+/-0.59), while the average coefficient obtained from the malignant tissue group consisted of 264 measurements from 20 sites was 1.55 mm-1 (+/-0.46). The malignant ovarian tissue showed significant lower scattering than the normal group (p < 0.001). The amount of collagen within OCT imaging depth was analyzed from the tissue histological section stained with Sirius Red. The average collagen area fraction (CAF) obtained from the normal tissue group was 48.4% (+/-12.3%), while the average CAF obtained from the malignant tissue group was 11.4% (+/-4.7%). A statistical significance of the collagen content was found between the two groups (p < 0.001). These results demonstrated that quantitative measurements of optical scattering coefficient from OCT images could be a potential powerful method for ovarian cancer detection.

Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

NASA Astrophysics Data System (ADS)

Shevchenko, I. I.

2008-05-01

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.

Testing for gene-environment interaction under exposure misspecification.

PubMed

Sun, Ryan; Carroll, Raymond J; Christiani, David C; Lin, Xihong

2017-11-09

Complex interplay between genetic and environmental factors characterizes the etiology of many diseases. Modeling gene-environment (GxE) interactions is often challenged by the unknown functional form of the environment term in the true data-generating mechanism. We study the impact of misspecification of the environmental exposure effect on inference for the GxE interaction term in linear and logistic regression models. We first examine the asymptotic bias of the GxE interaction regression coefficient, allowing for confounders as well as arbitrary misspecification of the exposure and confounder effects. For linear regression, we show that under gene-environment independence and some confounder-dependent conditions, when the environment effect is misspecified, the regression coefficient of the GxE interaction can be unbiased. However, inference on the GxE interaction is still often incorrect. In logistic regression, we show that the regression coefficient is generally biased if the genetic factor is associated with the outcome directly or indirectly. Further, we show that the standard robust sandwich variance estimator for the GxE interaction does not perform well in practical GxE studies, and we provide an alternative testing procedure that has better finite sample properties. © 2017, The International Biometric Society.

Diffusion with Varying Drag; the Runaway Problem.

NASA Astrophysics Data System (ADS)

Rollins, David Kenneth

We study the motion of electrons in an ionized plasma of electrons and ions in an external electric field. A probability distribution function describes the electron motion and is a solution of a Fokker-Planck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron runaway phenomenon. We treat the electric field as a small perturbation. We consider various diffusion coefficients for the one dimensional problem and determine the runaway current as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coefficient decays with velocity are then considered. To determine the runaway current, the equivalent Schrodinger eigenvalue problem is analysed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the three dimensional problem.

Mesoscopic structure of neuronal tracts from time-dependent diffusion.

PubMed

Burcaw, Lauren M; Fieremans, Els; Novikov, Dmitry S

2015-07-01

Interpreting brain diffusion MRI measurements in terms of neuronal structure at a micrometer level is an exciting unresolved problem. Here we consider diffusion transverse to a bundle of fibers, and show theoretically, as well as using Monte Carlo simulations and measurements in a phantom made of parallel fibers mimicking axons, that the time dependent diffusion coefficient approaches its macroscopic limit slowly, in a (ln t)/t fashion. The logarithmic singularity arises due to short range disorder in the fiber packing. We identify short range disorder in axonal fibers based on histological data from the splenium, and argue that the time dependent contribution to the overall diffusion coefficient from the extra-axonal water dominates that of the intra-axonal water. This dominance may explain the bias in measuring axon diameters in clinical settings. The short range disorder is also reflected in the asymptotically linear frequency dependence of the diffusion coefficient measured with oscillating gradients, in agreement with recent experiments. Our results relate the measured diffusion to the mesoscopic structure of neuronal tissue, uncovering the sensitivity of diffusion metrics to axonal arrangement within a fiber tract, and providing an alternative interpretation of axonal diameter mapping techniques. Copyright © 2015 Elsevier Inc. All rights reserved.

Reproducibility of retinal nerve fiber layer thickness measures using eye tracking in children with nonglaucomatous optic neuropathy.

PubMed

Rajjoub, Raneem D; Trimboli-Heidler, Carmelina; Packer, Roger J; Avery, Robert A

2015-01-01

To determine the intra- and intervisit reproducibility of circumpapillary retinal nerve fiber layer (RNFL) thickness measures using eye tracking-assisted spectral-domain optical coherence tomography (SD OCT) in children with nonglaucomatous optic neuropathy. Prospective longitudinal study. Circumpapillary RNFL thickness measures were acquired with SD OCT using the eye-tracking feature at 2 separate study visits. Children with normal and abnormal vision (visual acuity ≥ 0.2 logMAR above normal and/or visual field loss) who demonstrated clinical and radiographic stability were enrolled. Intra- and intervisit reproducibility was calculated for the global average and 9 anatomic sectors by calculating the coefficient of variation and intraclass correlation coefficient. Forty-two subjects (median age 8.6 years, range 3.9-18.2 years) met inclusion criteria and contributed 62 study eyes. Both the abnormal and normal vision cohort demonstrated the lowest intravisit coefficient of variation for the global RNFL thickness. Intervisit reproducibility remained good for those with normal and abnormal vision, although small but statistically significant increases in the coefficient of variation were observed for multiple anatomic sectors in both cohorts. The magnitude of visual acuity loss was significantly associated with the global (ß = 0.026, P < .01) and temporal sector coefficient of variation (ß = 0.099, P < .01). SD OCT with eye tracking demonstrates highly reproducible RNFL thickness measures. Subjects with vision loss demonstrate greater intra- and intervisit variability than those with normal vision. Copyright © 2015 Elsevier Inc. All rights reserved.

Unique Normal Form and the Associated Coefficients for a Class of Three-Dimensional Nilpotent Vector Fields

NASA Astrophysics Data System (ADS)

Li, Jing; Kou, Liying; Wang, Duo; Zhang, Wei

2017-12-01

In this paper, we mainly focus on the unique normal form for a class of three-dimensional vector fields via the method of transformation with parameters. A general explicit recursive formula is derived to compute the higher order normal form and the associated coefficients, which can be achieved easily by symbolic calculations. To illustrate the efficiency of the approach, a comparison of our result with others is also presented.

Optical characterization of pancreatic normal and tumor tissues with double integrating sphere system

NASA Astrophysics Data System (ADS)

Kiris, Tugba; Akbulut, Saadet; Kiris, Aysenur; Gucin, Zuhal; Karatepe, Oguzhan; Bölükbasi Ates, Gamze; Tabakoǧlu, Haşim Özgür

2015-03-01

In order to develop minimally invasive, fast and precise diagnostic and therapeutic methods in medicine by using optical methods, first step is to examine how the light propagates, scatters and transmitted through medium. So as to find out appropriate wavelengths, it is required to correctly determine the optical properties of tissues. The aim of this study is to measure the optical properties of both cancerous and normal ex-vivo pancreatic tissues. Results will be compared to detect how cancerous and normal tissues respond to different wavelengths. Double-integrating-sphere system and computational technique inverse adding doubling method (IAD) were used in the study. Absorption and reduced scattering coefficients of normal and cancerous pancreatic tissues have been measured within the range of 500-650 nm. Statistical significant differences between cancerous and normal tissues have been obtained at 550 nm and 630 nm for absorption coefficients. On the other hand; there were no statistical difference found for scattering coefficients at any wavelength.

Yield surfaces for frictional sphere assemblages

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

Goddard, J.D.; Didwania, A.K.

1995-12-31

By means of a recently developed computer algorithm for simulation of the quasi-static I mechanics of sphere assemblages, we have performed extensive computations of the dilatancy and plasticity of such systems for various proportional loading histories. We have investigated the effect of initial packing density or void ratio, size polydispersity, friction coefficient and plastic strain on the evolution of the yield surface. We find that all the yield surfaces tend to an asymptotic form which is well represented by the Lade-Duncan yield surface, developed originally for sand, suggesting that the Lade-Duncan form may reflect some universality in the behavior ofmore » assemblages of rigid frictional particles.« less

Analysis of delamination related fracture processes in composites

NASA Technical Reports Server (NTRS)

Armanios, Erian A.

1992-01-01

An anisotropic thin walled closed section beam theory was developed based on an asymptotical analysis of the shell energy functional. The displacement field is not assumed a priori and emerges as a result of the analysis. In addition to the classical out-of-plane torsional warping, two new contributions are identified namely, axial strain and bending warping. A comparison of the derived governing equations confirms the theory developed by Reissner and Tsai. Also, explicit closed form expressions for the beam stiffness coefficients, the stress and displacement fields are provided. The predictions of the present theory were validated by comparison with finite element simulation, other closed form analyses and test data.

Analytical solution for the normal emission portion of the averaged Yarkovsky-O'Keefe-Radzvieskii-Paddack coefficient for a single facet

NASA Astrophysics Data System (ADS)

Albuja, Antonella A.; Scheeres, Daniel J.

2015-02-01

The Yarkovsky-O'Keefe-Radzvieskii-Paddack (YORP) effect has been well studied for asteroids. This paper develops an analytic solution to find the normal emission YORP component for a single facet. The solution presented here does not account for self-shadowing or self-heating. The YORP coefficient for all facets can be summed together to find the total coefficient of the asteroid. The normal emission component of YORP has been shown to be the most important for asteroids and it directly affects the rate of change of the asteroid's spin period. The analytical solution found is a sole function of the facet's geometry and the obliquity of the asteroid. This solution is universal for any facet and its orientation. The behaviour of the coefficient is analysed with this analytical solution. The closed-form solution is used to find the total YORP coefficient for the asteroids Apollo and 1998 ML14 whose shape models are composed of different numbers of facets. The results are then compared to published results and those obtained through numerical quadrature for validation.

Cardiopulmonary fitness is strongly associated with body cell mass and fat-free mass: The Study of Health in Pomerania (SHIP).

PubMed

Köhler, A; King, R; Bahls, M; Groß, S; Steveling, A; Gärtner, S; Schipf, S; Gläser, S; Völzke, H; Felix, S B; Markus, M R P; Dörr, M

2018-01-18

Peak oxygen uptake (VO2peak) is commonly indexed by total body weight (TBW) to determine cardiopulmonary fitness (CPF). This approach may lead to misinterpretation, particularly in obese subjects. We investigated the normalization of VO2peak by different body composition markers. We analyzed combined data of 3848 subjects (1914 women; 49.7%), aged 20-90, from two independent cohorts of the population-based Study of Health in Pomerania (SHIP-2 and SHIP-TREND). VO2peak was assessed by cardiopulmonary exercise testing. Body cell mass (BCM), fat-free mass (FFM), and fat mass (FM) were determined by bioelectrical impedance analysis. The suitability of the different markers as a normalization variable was evaluated by taking into account correlation coefficients (r) and intercept (α-coefficient) values from linear regression models. A combination of high r and low α values was considered as preferable for normalization purposes. BCM was the best normalization variable for VO2peak (r = .72; P ≤ .001; α-coefficient = 63.3 mL/min; 95% confidence interval [CI]: 3.48-123) followed by FFM (r = .63; P ≤ .001; α-coefficient = 19.6 mL/min; 95% CI: -57.9-97.0). On the other hand, a much weaker correlation and a markedly higher intercept were found for TBW (r = .42; P ≤ .001; α-coefficient = 579 mL/min; 95% CI: 483 to 675). Likewise, FM was also identified as a poor normalization variable (r = .10; P ≤ .001; α-coefficient = 2133; 95% CI: 2074-2191). Sex-stratified analyses confirmed the above order for the different normalization variables. Our results suggest that BCM, followed by FFM, might be the most appropriate marker for the normalization of VO2peak when comparing CPF between subjects with different body shape. © 2018 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Developmental hearing loss impedes auditory task learning and performance in gerbils.

PubMed

von Trapp, Gardiner; Aloni, Ishita; Young, Stephen; Semple, Malcolm N; Sanes, Dan H

2017-04-01

The consequences of developmental hearing loss have been reported to include both sensory and cognitive deficits. To investigate these issues in a non-human model, auditory learning and asymptotic psychometric performance were compared between normal hearing (NH) adult gerbils and those reared with conductive hearing loss (CHL). At postnatal day 10, before ear canal opening, gerbil pups underwent bilateral malleus removal to induce a permanent CHL. Both CHL and control animals were trained to approach a water spout upon presentation of a target (Go stimuli), and withhold for foils (Nogo stimuli). To assess the rate of task acquisition and asymptotic performance, animals were tested on an amplitude modulation (AM) rate discrimination task. Behavioral performance was calculated using a signal detection theory framework. Animals reared with developmental CHL displayed a slower rate of task acquisition for AM discrimination task. Slower acquisition was explained by an impaired ability to generalize to newly introduced stimuli, as compared to controls. Measurement of discrimination thresholds across consecutive testing blocks revealed that CHL animals required a greater number of testing sessions to reach asymptotic threshold values, as compared to controls. However, with sufficient training, CHL animals approached control performance. These results indicate that a sensory impediment can delay auditory learning, and increase the risk of poor performance on a temporal task. Copyright © 2016 Elsevier B.V. All rights reserved.

Viscoelastic subdiffusion: from anomalous to normal.

PubMed

Goychuk, Igor

2009-10-01

We study viscoelastic subdiffusion in bistable and periodic potentials within the generalized Langevin equation approach. Our results justify the (ultra)slow fluctuating rate view of the corresponding bistable non-Markovian dynamics which displays bursting and anticorrelation of the residence times in two potential wells. The transition kinetics is asymptotically stretched exponential when the potential barrier V0 several times exceeds thermal energy k(B)T [V(0) approximately (2-10)k(B)T] and it cannot be described by the non-Markovian rate theory (NMRT). The well-known NMRT result approximates, however, ever better with the increasing barrier height, the most probable logarithm of the residence times. Moreover, the rate description is gradually restored when the barrier height exceeds a fuzzy borderline which depends on the power-law exponent of free subdiffusion alpha . Such a potential-free subdiffusion is ergodic. Surprisingly, in periodic potentials it is not sensitive to the barrier height in the long time asymptotic limit. However, the transient to this asymptotic regime is extremally slow and it does profoundly depend on the barrier height. The time scale of such subdiffusion can exceed the mean residence time in a potential well or in a finite spatial domain by many orders of magnitude. All these features are in sharp contrast with an alternative subdiffusion mechanism involving jumps among traps with the divergent mean residence time in these traps.

Reducing Bias and Error in the Correlation Coefficient Due to Nonnormality

ERIC Educational Resources Information Center

Bishara, Anthony J.; Hittner, James B.

2015-01-01

It is more common for educational and psychological data to be nonnormal than to be approximately normal. This tendency may lead to bias and error in point estimates of the Pearson correlation coefficient. In a series of Monte Carlo simulations, the Pearson correlation was examined under conditions of normal and nonnormal data, and it was compared…

A rapid-pressure correlation representation consistent with the Taylor-Proudman theorem materially-frame-indifferent in the 2D limit

NASA Technical Reports Server (NTRS)

Ristorcelli, J. R.; Lumley, J. L.; Abid, R.

1994-01-01

A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.

Dispersion controlled by permeable surfaces: surface properties and scaling

DOE PAGES

Ling, Bowen; Tartakovsky, Alexandre M.; Battiato, Ilenia

2016-08-25

Permeable and porous surfaces are common in natural and engineered systems. Flow and transport above such surfaces are significantly affected by the surface properties, e.g. matrix porosity and permeability. However, the relationship between such properties and macroscopic solute transport is largely unknown. In this work, we focus on mass transport in a two-dimensional channel with permeable porous walls under fully developed laminar flow conditions. By means of perturbation theory and asymptotic analysis, we derive the set of upscaled equations describing mass transport in the coupled channel–porous-matrix system and an analytical expression relating the dispersion coefficient with the properties of themore » surface, namely porosity and permeability. Our analysis shows that their impact on the dispersion coefficient strongly depends on the magnitude of the Péclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviours of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transverse mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Péclet number. By elucidating the impact of matrix porosity and permeability on solute transport, our upscaled model lays the foundation for the improved understanding, control and design of microporous coatings with targeted macroscopic transport features.« less

On the possibility of spectroscopic cancer diagnostics

NASA Astrophysics Data System (ADS)

Khairullina, Alphiya Y.; Oleinik, Tatiana V.; Korolevich, Alexander N.; Sevkovsky, Yacob I.

1993-07-01

The diffuse reflection and transmission coefficients, other optical parameters of normal and cancer tissues have been investigated in visible and infrared spectra. The optimal spectral range for distinguishing the cancer is found. The spectral absorption coefficients and size of cells parameter determined using our approach are analyzed to be different for normal and pathological tissues. The method is proposed for calculating the diffuse reflectance and transmittance of multiple tissue layers. The investigations have shown that cancer may be distinguished under the layers of skin and normal tissue.

A Whole Word and Number Reading Machine Based on Two Dimensional Low Frequency Fourier Transforms

DTIC Science & Technology

1990-12-01

they are energy normalized. The normalization process accounts for brightness variations and is equivalent to graphing each 2DFT onto the surface of an n...determined empirically (trial and error). Each set is energy normalized based on the number of coefficients within the set. Therefore, the actual...using the 6 font group case with the top 1000 words, where the energy has been renormalized based on the particular number of coefficients being used

Friction coefficient and effective interference at the implant-bone interface.

PubMed

Damm, Niklas B; Morlock, Michael M; Bishop, Nicholas E

2015-09-18

Although the contact pressure increases during implantation of a wedge-shaped implant, friction coefficients tend to be measured under constant contact pressure, as endorsed in standard procedures. Abrasion and plastic deformation of the bone during implantation are rarely reported, although they define the effective interference, by reducing the nominal interference between implant and bone cavity. In this study radial forces were analysed during simulated implantation and explantation of angled porous and polished implant surfaces against trabecular bone specimens, to determine the corresponding friction coefficients. Permanent deformation was also analysed to determine the effective interference after implantation. For the most porous surface tested, the friction coefficient initially increased with increasing normal contact stress during implantation and then decreased at higher contact stresses. For a less porous surface, the friction coefficient increased continually with normal contact stress during implantation but did not reach the peak magnitude measured for the rougher surface. Friction coefficients for the polished surface were independent of normal contact stress and much lower than for the porous surfaces. Friction coefficients were slightly lower for pull-out than for push-in for the porous surfaces but not for the polished surface. The effective interference was as little as 30% of the nominal interference for the porous surfaces. The determined variation in friction coefficient with radial contact force, as well as the loss of interference during implantation will enable a more accurate representation of implant press-fitting for simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Divisibility patterns of natural numbers on a complex network.

PubMed

Shekatkar, Snehal M; Bhagwat, Chandrasheel; Ambika, G

2015-09-16

Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of natural numbers in the context of divisibility. In the present paper, we study the divisibility of natural numbers using the framework of a growing complex network. In particular, using tools from the field of statistical inference, we show that the network is scale-free but has a non-stationary degree distribution. Along with this, we report a new kind of similarity pattern for the local clustering, which we call "stretching similarity", in this network. We also show that the various characteristics like average degree, global clustering coefficient and assortativity coefficient of the network vary smoothly with the size of the network. Using analytical arguments we estimate the asymptotic behavior of global clustering and average degree which is validated using numerical analysis.

Turbulence closure for mixing length theories

NASA Astrophysics Data System (ADS)

Jermyn, Adam S.; Lesaffre, Pierre; Tout, Christopher A.; Chitre, Shashikumar M.

2018-05-01

We present an approach to turbulence closure based on mixing length theory with three-dimensional fluctuations against a two-dimensional background. This model is intended to be rapidly computable for implementation in stellar evolution software and to capture a wide range of relevant phenomena with just a single free parameter, namely the mixing length. We incorporate magnetic, rotational, baroclinic, and buoyancy effects exactly within the formalism of linear growth theories with non-linear decay. We treat differential rotation effects perturbatively in the corotating frame using a novel controlled approximation, which matches the time evolution of the reference frame to arbitrary order. We then implement this model in an efficient open source code and discuss the resulting turbulent stresses and transport coefficients. We demonstrate that this model exhibits convective, baroclinic, and shear instabilities as well as the magnetorotational instability. It also exhibits non-linear saturation behaviour, and we use this to extract the asymptotic scaling of various transport coefficients in physically interesting limits.

A Two-Stage Estimation Method for Random Coefficient Differential Equation Models with Application to Longitudinal HIV Dynamic Data.

PubMed

Fang, Yun; Wu, Hulin; Zhu, Li-Xing

2011-07-01

We propose a two-stage estimation method for random coefficient ordinary differential equation (ODE) models. A maximum pseudo-likelihood estimator (MPLE) is derived based on a mixed-effects modeling approach and its asymptotic properties for population parameters are established. The proposed method does not require repeatedly solving ODEs, and is computationally efficient although it does pay a price with the loss of some estimation efficiency. However, the method does offer an alternative approach when the exact likelihood approach fails due to model complexity and high-dimensional parameter space, and it can also serve as a method to obtain the starting estimates for more accurate estimation methods. In addition, the proposed method does not need to specify the initial values of state variables and preserves all the advantages of the mixed-effects modeling approach. The finite sample properties of the proposed estimator are studied via Monte Carlo simulations and the methodology is also illustrated with application to an AIDS clinical data set.

Large-aspect-ratio limit of neoclassical transport theory.

PubMed

Wong, S K; Chan, V S

2003-06-01

This paper presents a comprehensive description of neoclassical transport theory in the banana regime for large-aspect-ratio flux surfaces of arbitrary shapes. The method of matched-asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates the discussion of the treatment of dynamical constraints. It is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard.

Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

PubMed

Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

2017-02-01

We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

On the Link Between Kolmogorov Microscales and Friction in Wall-Bounded Flow of Viscoplastic Fluids

NASA Astrophysics Data System (ADS)

Ramos, Fabio; Anbarlooei, Hamid; Cruz, Daniel; Silva Freire, Atila; Santos, Cecilia M.

2017-11-01

Most discussions in literature on the friction coefficient of turbulent flows of fluids with complex rheology are empirical. As a rule, theoretical frameworks are not available even for some relatively simple constitutive models. In this work, we present a new family of formulas for the evaluation of the friction coefficient of turbulent flows of a large family of viscoplastic fluids. The developments combine an unified analysis for the description of the Kolmogorov's micro-scales and the phenomenological turbulence model of Gioia and Chakraborty. The resulting Blasius-type friction equation has only Blasius' constant as a parameter, and tests against experimental data show excellent agreement over a significant range of Hedstrom and Reynolds numbers. The limits of the proposed model are also discussed. We also comment on the role of the new formula as a possible benchmark test for the convergence of DNS simulations of viscoplastic flows. The friction formula also provides limits for the Maximum Drag Reduction (MDR) for viscoplastic flows, which resembles MDR asymptote for viscoelastic flows.

Varying coefficient subdistribution regression for left-truncated semi-competing risks data.

PubMed

Li, Ruosha; Peng, Limin

2014-10-01

Semi-competing risks data frequently arise in biomedical studies when time to a disease landmark event is subject to dependent censoring by death, the observation of which however is not precluded by the occurrence of the landmark event. In observational studies, the analysis of such data can be further complicated by left truncation. In this work, we study a varying co-efficient subdistribution regression model for left-truncated semi-competing risks data. Our method appropriately accounts for the specifical truncation and censoring features of the data, and moreover has the flexibility to accommodate potentially varying covariate effects. The proposed method can be easily implemented and the resulting estimators are shown to have nice asymptotic properties. We also present inference, such as Kolmogorov-Smirnov type and Cramér Von-Mises type hypothesis testing procedures for the covariate effects. Simulation studies and an application to the Denmark diabetes registry demonstrate good finite-sample performance and practical utility of the proposed method.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Quasibound states in short SNS junctions with point defects

NASA Astrophysics Data System (ADS)

Bespalov, A. A.

2018-04-01

Using the Green functions technique, we study the subgap spectrum of short three-dimensional superconductor-normal metal-superconductor junctions containing one or two point impurities in the normal layer. We find that a single nonmagnetic or magnetic defect induces two quasibound Shiba-like states. If the defect is located close to the junction edge, the energies of these states oscillate as functions of the distance between the impurity and the edge. In the case of two nonmagnetic impurities, there are generally four quasibound states (two per spin projection). Their energies oscillate as functions of the distance between the impurities, and reach their asymptotic values when this distance becomes much larger than the Fermi wavelength. The contributions of the impurities to the Josephson current, local density of states, and to the normal-state conductance of the junction are analyzed.

Aerodynamic characteristics of horizontal tail surfaces

NASA Technical Reports Server (NTRS)

Silverstein, Abe; Katzoff, S

1940-01-01

Collected data are presented on the aerodynamic characteristics of 17 horizontal tail surfaces including several with balanced elevators and two with end plates. Curves are given for coefficients of normal force, drag, and elevator hinge moment. A limited analysis of the results has been made. The normal-force coefficients are in better agreement with the lifting-surface theory of Prandtl and Blenk for airfoils of low aspect ratio than with the usual lifting-line theory. Only partial agreement exists between the elevator hinge-moment coefficients and those predicted by Glauert's thin-airfoil theory.

Analysis of data from NASA B-57B gust gradient program

NASA Technical Reports Server (NTRS)

Frost, W.; Lin, M. C.; Chang, H. P.; Ringnes, E.

1985-01-01

Statistical analysis of the turbulence measured in flight 6 of the NASA B-57B over Denver, Colorado, from July 7 to July 23, 1982 included the calculations of average turbulence parameters, integral length scales, probability density functions, single point autocorrelation coefficients, two point autocorrelation coefficients, normalized autospectra, normalized two point autospectra, and two point cross sectra for gust velocities. The single point autocorrelation coefficients were compared with the theoretical model developed by von Karman. Theoretical analyses were developed which address the effects spanwise gust distributions, using two point spatial turbulence correlations.

Analysis of longitudinal data of beef cattle raised on pasture from northern Brazil using nonlinear models.

PubMed

Lopes, Fernando B; da Silva, Marcelo C; Marques, Ednira G; McManus, Concepta M

2012-12-01

This study was undertaken to aim of estimating the genetic parameters and trends for asymptotic weight (A) and maturity rate (k) of Nellore cattle from northern Brazil. The data set was made available by the Brazilian Association of Zebu Breeders and collected between the years of 1997 and 2007. The Von Bertalanffy, Brody, Gompertz, and logistic nonlinear models were fitted by the Gauss-Newton method to weight-age data of 45,895 animals collected quarterly of the birth to 750 days old. The curve parameters were analyzed using the procedures GLM and CORR. The estimation of (co)variance components and genetic parameters was obtained using the MTDFREML software. The estimated heritability coefficients were 0.21 ± 0.013 and 0.25 ± 0.014 for asymptotic weight and maturity rate, respectively. This indicates that selection for any trait shall results in genetic progress in the herd. The genetic correlation between A and k was negative (-0.57 ± 0.03) and indicated that animals selected for high maturity rate shall result in low asymptotic weight. The Von Bertalanffy function is adequate to establish the mean growth patterns and to predict the adult weight of Nellore cattle. This model is more accurate in predicting the birth weight of these animals and has better overall fit. The prediction of adult weight using nonlinear functions can be accurate when growth curve parameters and their (co)variance components are estimated jointly. The model used in this study can be applied to the prediction of mature weight in herds where a portion of the animals are culled before they reach the adult age.

Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. I. Integer orders

NASA Astrophysics Data System (ADS)

Tica, Christian D.; Galapon, Eric A.

2018-02-01

The paper addresses the exact evaluation of the generalized Stieltjes transform Sn[f ] =∫0∞f (x ) (ω+x ) -nd x of integral order n = 1, 2, 3, … about ω = 0 from which the asymptotic behavior of Sn[f] for small parameters ω is directly extracted. An attempt to evaluate the integral by expanding the integrand (ω + x)-n about ω = 0 and then naively integrating the resulting infinite series term by term leads to an infinite series whose terms are divergent integrals. Assigning values to the divergent integrals, say, by analytic continuation or by Hadamard's finite part is known to reproduce only some of the correct terms of the expansion but completely misses out a group of terms. Here we evaluate explicitly the generalized Stieltjes transform by means of finite-part integration recently introduced in Galapon [Proc. R. Soc. A 473, 20160567 (2017)]. It is shown that, when f(x) does not vanish or has zero of order m at the origin such that (n - m) ≥ 1, the dominant terms of Sn[f] as ω → 0 come from contributions arising from the poles and branch points of the complex valued function f(z)(ω + z)-n. These dominant terms are precisely the terms missed out by naive term by term integration. Furthermore, it is demonstrated how finite-part integration leads to new series representations of special functions by exploiting their known Stieltjes integral representations. Finally, the application of finite part integration in obtaining asymptotic expansions of the effective diffusivity in the limit of high Peclet number, the Green-Kubo formula for the self-diffusion coefficient, and the antisymmetric part of the diffusion tensor in the weak noise limit is discussed.

The Use of Asymptotic Functions for Determining Empirical Values of CN Parameter in Selected Catchments of Variable Land Cover

NASA Astrophysics Data System (ADS)

Wałęga, Andrzej; Młyński, Dariusz; Wachulec, Katarzyna

2017-12-01

The aim of the study was to assess the applicability of asymptotic functions for determining the value of CN parameter as a function of precipitation depth in mountain and upland catchments. The analyses were carried out in two catchments: the Rudawa, left tributary of the Vistula, and the Kamienica, right tributary of the Dunajec. The input material included data on precipitation and flows for a multi-year period 1980-2012, obtained from IMGW PIB in Warsaw. Two models were used to determine empirical values of CNobs parameter as a function of precipitation depth: standard Hawkins model and 2-CN model allowing for a heterogeneous nature of a catchment area. The study analyses confirmed that asymptotic functions properly described P-CNobs relationship for the entire range of precipitation variability. In the case of high rainfalls, CNobs remained above or below the commonly accepted average antecedent moisture conditions AMCII. The study calculations indicated that the runoff amount calculated according to the original SCS-CN method might be underestimated, and this could adversely affect the values of design flows required for the design of hydraulic engineering projects. In catchments with heterogeneous land cover, the results of CNobs were more accurate when 2-CN model was used instead of the standard Hawkins model. 2-CN model is more precise in accounting for differences in runoff formation depending on retention capacity of the substrate. It was also demonstrated that the commonly accepted initial abstraction coefficient λ = 0.20 yielded too big initial loss of precipitation in the analyzed catchments and, therefore, the computed direct runoff was underestimated. The best results were obtained for λ = 0.05.

Stable Lévy motion with inverse Gaussian subordinator

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.

Progressive wave expansions and open boundary problems

NASA Technical Reports Server (NTRS)

Hagstrom, T.; Hariharan, S. I.

1995-01-01

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory.

Log-amplitude statistics for Beck-Cohen superstatistics

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Konno, Hidetoshi

2013-05-01

As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ2, inverse χ2, and log-normal superstatistical distributions. Furthermore, we show that χ2 and inverse χ2 superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ2 superstatistical distribution with degree 2.

Empirical analysis on the connection between power-law distributions and allometries for urban indicators

NASA Astrophysics Data System (ADS)

Alves, L. G. A.; Ribeiro, H. V.; Lenzi, E. K.; Mendes, R. S.

2014-09-01

We report on the existing connection between power-law distributions and allometries. As it was first reported in Gomez-Lievano et al. (2012) for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.

Polynomial Asymptotes of the Second Kind

ERIC Educational Resources Information Center

Dobbs, David E.

2011-01-01

This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…

2D granular flows with the μ(I) rheology and side walls friction: A well-balanced multilayer discretization

NASA Astrophysics Data System (ADS)

Fernández-Nieto, E. D.; Garres-Díaz, J.; Mangeney, A.; Narbona-Reina, G.

2018-03-01

We present here numerical modelling of granular flows with the μ (I) rheology in confined channels. The contribution is twofold: (i) a model to approximate the Navier-Stokes equations with the μ (I) rheology through an asymptotic analysis; under the hypothesis of a one-dimensional flow, this model takes into account side walls friction; (ii) a multilayer discretization following Fernández-Nieto et al. (2016) [20]. In this new numerical scheme, we propose an appropriate treatment of the rheological terms through a hydrostatic reconstruction which allows this scheme to be well-balanced and therefore to deal with dry areas. Based on academic tests, we first evaluate the influence of the width of the channel on the normal profiles of the downslope velocity thanks to the multilayer approach that is intrinsically able to describe changes from Bagnold to S-shaped (and vice versa) velocity profiles. We also check the well-balanced property of the proposed numerical scheme. We show that approximating side walls friction using single-layer models may lead to strong errors. Secondly, we compare the numerical results with experimental data on granular collapses. We show that the proposed scheme allows us to qualitatively reproduce the deposit in the case of a rigid bed (i.e. dry area) and that the error made by replacing the dry area by a small layer of material may be large if this layer is not thin enough. The proposed model is also able to reproduce the time evolution of the free surface and of the flow/no-flow interface. In addition, it reproduces the effect of erosion for granular flows over initially static material lying on the bed. This is possible when using a variable friction coefficient μ (I) but not with a constant friction coefficient.

Simulations of turbulent asymptotic suction boundary layers

NASA Astrophysics Data System (ADS)

Bobke, Alexandra; Örlü, Ramis; Schlatter, Philipp

2016-02-01

A series of large-eddy simulations of a turbulent asymptotic suction boundary layer (TASBL) was performed in a periodic domain, on which uniform suction was applied over a flat plate. Three Reynolds numbers (defined as ratio of free-stream and suction velocity) of Re = 333, 400 and 500 and a variety of domain sizes were considered in temporal simulations in order to investigate the turbulence statistics, the importance of the computational domain size, the arising flow structures as well as temporal development length required to achieve the asymptotic state. The effect of these two important parameters was assessed in terms of their influence on integral quantities, mean velocity, Reynolds stresses, higher order statistics, amplitude modulation and spectral maps. While the near-wall region up to the buffer region appears to scale irrespective of Re and domain size, the parameters of the logarithmic law (i.e. von Kármán and additive coefficient) decrease with increasing Re, while the wake strength decreases with increasing spanwise domain size and vanishes entirely once the spanwise domain size exceeds approximately two boundary-layer thicknesses irrespective of Re. The wake strength also reduces with increasing simulation time. The asymptotic state of the TASBL is characterised by surprisingly large friction Reynolds numbers and inherits features of wall turbulence at numerically high Re. Compared to a turbulent boundary layer (TBL) or a channel flow without suction, the components of the Reynolds-stress tensor are overall reduced, but exhibit a logarithmic increase with decreasing suction rates, i.e. increasing Re. At the same time, the anisotropy is increased compared to canonical wall-bounded flows without suction. The reduced amplitudes in turbulence quantities are discussed in light of the amplitude modulation due to the weakened larger outer structures. The inner peak in the spectral maps is shifted to higher wavelength and the strength of the outer peak is much less than for TBLs. An additional spatial simulation was performed, in order to relate the simulation results to wind tunnel experiments, which - in accordance with the results from the temporal simulation - indicate that a truly TASBL is practically impossible to realise in a wind tunnel. Our unique data set agrees qualitatively with existing literature results for both numerical and experimental studies, and at the same time sheds light on the fact why the asymptotic state could not be established in a wind tunnel experiment, viz. because experimental studies resemble our simulation results from too small simulation boxes or insufficient development times.

Theory and simulation of the time-dependent rate coefficients of diffusion-influenced reactions.

PubMed Central

Zhou, H X; Szabo, A

1996-01-01

A general formalism is developed for calculating the time-dependent rate coefficient k(t) of an irreversible diffusion-influenced reaction. This formalism allows one to treat most factors that affect k(t), including rotational Brownian motion and conformational gating of reactant molecules and orientation constraint for product formation. At long times k(t) is shown to have the asymptotic expansion k(infinity)[1 + k(infinity) (pie Dt)-1/2 /4 pie D + ...], where D is the relative translational diffusion constant. An approximate analytical method for calculating k(t) is presented. This is based on the approximation that the probability density of the reactant pair in the reactive region keeps the equilibrium distribution but with a decreasing amplitude. The rate coefficient then is determined by the Green function in the absence of chemical reaction. Within the framework of this approximation, two general relations are obtained. The first relation allows the rate coefficient for an arbitrary amplitude of the reactivity to be found if the rate coefficient for one amplitude of the reactivity is known. The second relation allows the rate coefficient in the presence of conformational gating to be found from that in the absence of conformational gating. The ratio k(t)/k(0) is shown to be the survival probability of the reactant pair at time t starting from an initial distribution that is localized in the reactive region. This relation forms the basis of the calculation of k(t) through Brownian dynamics simulations. Two simulation procedures involving the propagation of nonreactive trajectories initiated only from the reactive region are described and illustrated on a model system. Both analytical and simulation results demonstrate the accuracy of the equilibrium-distribution approximation method. PMID:8913584

Review of the dynamic behaviour of sports balls during normal and oblique impacts

NASA Astrophysics Data System (ADS)

Haron, Muhammad Adli; Jailani, Azrol; Abdullah, Nik Ahmad Faris Nik; Ismail, Rafis Suizwan; Rahim, Shayfull Zamree Abd; Ghazali, Mohd Fathullah

2017-09-01

In this paper are review of impact experiment to study the dynamic behaviour of sports ball during oblique and normal impacts. In previous studies, the investigation was done on the dynamic behaviour of a sports ball during oblique and normal impacts from experimental, numerical, and theoretical viewpoints. The experimental results are analysed and compared with the theories, in order to understand the dynamics behaviours based on the phenomenological occurrence. Throughout the experimental studies previously, there are results of dynamics behaviours examined by many researchers such as the coefficient of restitution, tangential coefficient, local deformation, dynamic impact force, contact time, angle of impact (inbound and rebound), spin rate of the ball, ball stiffness and damping coefficient which dependable of the initial or impact velocity.

A theory of stationarity and asymptotic approach in dissipative systems

NASA Astrophysics Data System (ADS)

Rubel, Michael Thomas

2007-05-01

The approximate dynamics of many physical phenomena, including turbulence, can be represented by dissipative systems of ordinary differential equations. One often turns to numerical integration to solve them. There is an incompatibility, however, between the answers it can produce (i.e., specific solution trajectories) and the questions one might wish to ask (e.g., what behavior would be typical in the laboratory?) To determine its outcome, numerical integration requires more detailed initial conditions than a laboratory could normally provide. In place of initial conditions, experiments stipulate how tests should be carried out: only under statistically stationary conditions, for example, or only during asymptotic approach to a final state. Stipulations such as these, rather than initial conditions, are what determine outcomes in the laboratory.This theoretical study examines whether the points of view can be reconciled: What is the relationship between one's statistical stipulations for how an experiment should be carried out--stationarity or asymptotic approach--and the expected results? How might those results be determined without invoking initial conditions explicitly?To answer these questions, stationarity and asymptotic approach conditions are analyzed in detail. Each condition is treated as a statistical constraint on the system--a restriction on the probability density of states that might be occupied when measurements take place. For stationarity, this reasoning leads to a singular, invariant probability density which is already familiar from dynamical systems theory. For asymptotic approach, it leads to a new, more regular probability density field. A conjecture regarding what appears to be a limit relationship between the two densities is presented.By making use of the new probability densities, one can derive output statistics directly, avoiding the need to create or manipulate initial data, and thereby avoiding the conceptual incompatibility mentioned above. This approach also provides a clean way to derive reduced-order models, complete with local and global error estimates, as well as a way to compare existing reduced-order models objectively.The new approach is explored in the context of five separate test problems: a trivial one-dimensional linear system, a damped unforced linear oscillator in two dimensions, the isothermal Rayleigh-Plesset equation, Lorenz's equations, and the Stokes limit of Burgers' equation in one space dimension. In each case, various output statistics are deduced without recourse to initial conditions. Further, reduced-order models are constructed for asymptotic approach of the damped unforced linear oscillator, the isothermal Rayleigh-Plesset system, and Lorenz's equations, and for stationarity of Lorenz's equations.

Variance-reduction normalization technique for a compton camera system

NASA Astrophysics Data System (ADS)

Kim, S. M.; Lee, J. S.; Kim, J. H.; Seo, H.; Kim, C. H.; Lee, C. S.; Lee, S. J.; Lee, M. C.; Lee, D. S.

2011-01-01

For an artifact-free dataset, pre-processing (known as normalization) is needed to correct inherent non-uniformity of detection property in the Compton camera which consists of scattering and absorbing detectors. The detection efficiency depends on the non-uniform detection efficiency of the scattering and absorbing detectors, different incidence angles onto the detector surfaces, and the geometry of the two detectors. The correction factor for each detected position pair which is referred to as the normalization coefficient, is expressed as a product of factors representing the various variations. The variance-reduction technique (VRT) for a Compton camera (a normalization method) was studied. For the VRT, the Compton list-mode data of a planar uniform source of 140 keV was generated from a GATE simulation tool. The projection data of a cylindrical software phantom were normalized with normalization coefficients determined from the non-uniformity map, and then reconstructed by an ordered subset expectation maximization algorithm. The coefficient of variations and percent errors of the 3-D reconstructed images showed that the VRT applied to the Compton camera provides an enhanced image quality and the increased recovery rate of uniformity in the reconstructed image.

Comprehensive non-dimensional normalization of gait data.

PubMed

Pinzone, Ornella; Schwartz, Michael H; Baker, Richard

2016-02-01

Normalizing clinical gait analysis data is required to remove variability due to physical characteristics such as leg length and weight. This is particularly important for children where both are associated with age. In most clinical centres conventional normalization (by mass only) is used whereas there is a stronger biomechanical argument for non-dimensional normalization. This study used data from 82 typically developing children to compare how the two schemes performed over a wide range of temporal-spatial and kinetic parameters by calculating the coefficients of determination with leg length, weight and height. 81% of the conventionally normalized parameters had a coefficient of determination above the threshold for a statistical association (p<0.05) compared to 23% of those normalized non-dimensionally. All the conventionally normalized parameters exceeding this threshold showed a reduced association with non-dimensional normalization. In conclusion, non-dimensional normalization is more effective that conventional normalization in reducing the effects of height, weight and age in a comprehensive range of temporal-spatial and kinetic parameters. Copyright © 2015 Elsevier B.V. All rights reserved.

Determination of the optical absorption spectra of thin layers from their photoacoustic spectra

NASA Astrophysics Data System (ADS)

Bychto, Leszek; Maliński, Mirosław; Patryn, Aleksy; Tivanov, Mikhail; Gremenok, Valery

2018-05-01

This paper presents a new method for computations of the optical absorption coefficient spectra from the normalized photoacoustic amplitude spectra of thin semiconductor samples deposited on the optically transparent and thermally thick substrates. This method was tested on CuIn(Te0.7Se0.3)2 thin films. From the normalized photoacoustic amplitude spectra, the optical absorption coefficient spectra were computed with the new formula as also with the numerical iterative method. From these spectra, the value of the energy gap of the thin film material and the type of the optical transitions were determined. From the experimental optical transmission spectra, the optical absorption coefficient spectra were computed too, and compared with the optical absorption coefficient spectra obtained from photoacoustic spectra.

A New Distribution Family for Microarray Data †

PubMed Central

Kelmansky, Diana Mabel; Ricci, Lila

2017-01-01

The traditional approach with microarray data has been to apply transformations that approximately normalize them, with the drawback of losing the original scale. The alternative standpoint taken here is to search for models that fit the data, characterized by the presence of negative values, preserving their scale; one advantage of this strategy is that it facilitates a direct interpretation of the results. A new family of distributions named gpower-normal indexed by p∈R is introduced and it is proven that these variables become normal or truncated normal when a suitable gpower transformation is applied. Expressions are given for moments and quantiles, in terms of the truncated normal density. This new family can be used to model asymmetric data that include non-positive values, as required for microarray analysis. Moreover, it has been proven that the gpower-normal family is a special case of pseudo-dispersion models, inheriting all the good properties of these models, such as asymptotic normality for small variances. A combined maximum likelihood method is proposed to estimate the model parameters, and it is applied to microarray and contamination data. R codes are available from the authors upon request. PMID:28208652

A New Distribution Family for Microarray Data.

PubMed

Kelmansky, Diana Mabel; Ricci, Lila

2017-02-10

The traditional approach with microarray data has been to apply transformations that approximately normalize them, with the drawback of losing the original scale. The alternative stand point taken here is to search for models that fit the data, characterized by the presence of negative values, preserving their scale; one advantage of this strategy is that it facilitates a direct interpretation of the results. A new family of distributions named gpower-normal indexed by p∈R is introduced and it is proven that these variables become normal or truncated normal when a suitable gpower transformation is applied. Expressions are given for moments and quantiles, in terms of the truncated normal density. This new family can be used to model asymmetric data that include non-positive values, as required for microarray analysis. Moreover, it has been proven that the gpower-normal family is a special case of pseudo-dispersion models, inheriting all the good properties of these models, such as asymptotic normality for small variances. A combined maximum likelihood method is proposed to estimate the model parameters, and it is applied to microarray and contamination data. Rcodes are available from the authors upon request.

Estimation in a discrete tail rate family of recapture sampling models

NASA Technical Reports Server (NTRS)

Gupta, Rajan; Lee, Larry D.

1990-01-01

In the context of recapture sampling design for debugging experiments the problem of estimating the error or hitting rate of the faults remaining in a system is considered. Moment estimators are derived for a family of models in which the rate parameters are assumed proportional to the tail probabilities of a discrete distribution on the positive integers. The estimators are shown to be asymptotically normal and fully efficient. Their fixed sample properties are compared, through simulation, with those of the conditional maximum likelihood estimators.

M-Estimation for Discrete Data. Asymptotic Distribution Theory and Implications.

DTIC Science & Technology

1985-10-01

outlying data points, can be specified in a direct way since the influence function of an IM-estimator is proportional to its score function; see HamDel...consistently estimates - when the model is correct. Suppose now that ac RI. The influence function at F of an M-estimator for 3 has the form 2(x,S) = d/ P ("e... influence function at F . This is assuming, of course, that the estimator is asymototically normal at Fe. The truncation point c(f) determines the bounds

Effective-range parameters and vertex constants for Λ-nuclear systems

NASA Astrophysics Data System (ADS)

Rakityansky, S. A.; Gopane, I. M.

For a wide range of the core-nuclei (6 ≤ A ≤ 207), the scattering lengths, effective radii, and the other effective-range parameters (up to the order ˜ k8) for the angular momentum ℓ = 0, 1, 2 are calculated within a two-body ΛA-model. For the same hypernuclear systems, the S-matrix residues as well as the corresponding Nuclear-Vertex and Asymptotic-Normalization constants (NVC’s and ANC’s) for the bound states are also found.

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

Kalugin, A. V., E-mail: Kalugin-AV@nrcki.ru; Tebin, V. V.

The specific features of calculation of the effective multiplication factor using the Monte Carlo method for weakly coupled and non-asymptotic multiplying systems are discussed. Particular examples are considered and practical recommendations on detection and Monte Carlo calculation of systems typical in numerical substantiation of nuclear safety for VVER fuel management problems are given. In particular, the problems of the choice of parameters for the batch mode and the method for normalization of the neutron batch, as well as finding and interpretation of the eigenvalue spectrum for the integral fission matrix, are discussed.

Zonal and tesseral harmonic coefficients for the geopotential function, from zero to 18th order

NASA Technical Reports Server (NTRS)

Kirkpatrick, J. C.

1976-01-01

Zonal and tesseral harmonic coefficients for the geopotential function are usually tabulated in normalized form to provide immediate information as to the relative significance of the coefficients in the gravity model. The normalized form of the geopotential coefficients cannot be used for computational purposes unless the gravity model has been modified to receive them. This modification is usually not done because the absolute or unnormalized form of the coefficients can be obtained from the simple mathematical relationship that relates the two forms. This computation can be quite tedious for hand calculation, especially for the higher order terms, and can be costly in terms of storage and execution time for machine computation. In this report, zonal and tesseral harmonic coefficients for the geopotential function are tabulated in absolute or unnormalized form. The report is designed to be used as a ready reference for both hand and machine calculation to save the user time and effort.

Hawking radiation power equations for black holes

NASA Astrophysics Data System (ADS)

Mistry, Ravi; Upadhyay, Sudhaker; Ali, Ahmed Farag; Faizal, Mir

2017-10-01

We derive the Hawking radiation power equations for black holes in asymptotically flat, asymptotically Anti-de Sitter (AdS) and asymptotically de Sitter (dS) black holes. This is done by using the greybody factor for these black holes. We observe that the radiation power equation for asymptotically flat black holes, corresponding to greybody factor at low frequency, depends on both the Hawking temperature and the horizon radius. However, for the greybody factors at asymptotic frequency, it only depends on the Hawking temperature. We also obtain the power equation for asymptotically AdS black holes both below and above the critical frequency. The radiation power equation for at asymptotic frequency is same for both Schwarzschild AdS and Reissner-Nordström AdS solutions and only depends on the Hawking temperature. We also discuss the power equation for asymptotically dS black holes at low frequency, for both even or odd dimensions.

Reducing Bias and Error in the Correlation Coefficient Due to Nonnormality.

PubMed

Bishara, Anthony J; Hittner, James B

2015-10-01

It is more common for educational and psychological data to be nonnormal than to be approximately normal. This tendency may lead to bias and error in point estimates of the Pearson correlation coefficient. In a series of Monte Carlo simulations, the Pearson correlation was examined under conditions of normal and nonnormal data, and it was compared with its major alternatives, including the Spearman rank-order correlation, the bootstrap estimate, the Box-Cox transformation family, and a general normalizing transformation (i.e., rankit), as well as to various bias adjustments. Nonnormality caused the correlation coefficient to be inflated by up to +.14, particularly when the nonnormality involved heavy-tailed distributions. Traditional bias adjustments worsened this problem, further inflating the estimate. The Spearman and rankit correlations eliminated this inflation and provided conservative estimates. Rankit also minimized random error for most sample sizes, except for the smallest samples ( n = 10), where bootstrapping was more effective. Overall, results justify the use of carefully chosen alternatives to the Pearson correlation when normality is violated.

Reducing Bias and Error in the Correlation Coefficient Due to Nonnormality

PubMed Central

Hittner, James B.

2014-01-01

It is more common for educational and psychological data to be nonnormal than to be approximately normal. This tendency may lead to bias and error in point estimates of the Pearson correlation coefficient. In a series of Monte Carlo simulations, the Pearson correlation was examined under conditions of normal and nonnormal data, and it was compared with its major alternatives, including the Spearman rank-order correlation, the bootstrap estimate, the Box–Cox transformation family, and a general normalizing transformation (i.e., rankit), as well as to various bias adjustments. Nonnormality caused the correlation coefficient to be inflated by up to +.14, particularly when the nonnormality involved heavy-tailed distributions. Traditional bias adjustments worsened this problem, further inflating the estimate. The Spearman and rankit correlations eliminated this inflation and provided conservative estimates. Rankit also minimized random error for most sample sizes, except for the smallest samples (n = 10), where bootstrapping was more effective. Overall, results justify the use of carefully chosen alternatives to the Pearson correlation when normality is violated. PMID:29795841

Apparent diffusion coefficient of breast cancer and normal fibroglandular tissue in diffusion-weighted imaging: the effects of menstrual cycle and menopausal status.

PubMed

Kim, Jin You; Suh, Hie Bum; Kang, Hyun Jung; Shin, Jong Ki; Choo, Ki Seok; Nam, Kyung Jin; Lee, Seok Won; Jung, Young Lae; Bae, Young Tae

2016-05-01

The purpose of this study was to investigate prospectively whether the apparent diffusion coefficients (ADCs) of both breast cancer and normal fibroglandular tissue vary with the menstrual cycle and menopausal status. Institutional review board approval was obtained, and informed consent was obtained from each participant. Fifty-seven women (29 premenopausal, 28 postmenopausal) with newly diagnosed breast cancer underwent diffusion-weighted imaging twice (interval 12-20 days) before surgery. Two radiologists independently measured ADC of breast cancer and normal contralateral breast tissue, and we quantified the differences according to the phases of menstrual cycle and menopausal status. With normal fibroglandular tissue, ADC was significantly lower in postmenopausal than in premenopausal women (P = 0.035). In premenopausal women, ADC did not differ significantly between proliferative and secretory phases in either breast cancer or normal fibroglandular tissue (P = 0.969 and P = 0.519, respectively). In postmenopausal women, no significant differences were found between ADCs measured at different time intervals in either breast cancer or normal fibroglandular tissue (P = 0.948 and P = 0.961, respectively). The within-subject variability of the ADC measurements was quantified using the coefficient of variation (CV) and was small: the mean CVs of tumor ADC were 2.90 % (premenopausal) and 3.43 % (postmenopausal), and those of fibroglandular tissue ADC were 4.37 % (premenopausal) and 2.55 % (postmenopausal). Both intra- and interobserver agreements were excellent for ADC measurements, with intraclass correlation coefficients in the range of 0.834-0.974. In conclusion, the measured ADCs of breast cancer and normal fibroglandular tissue were not affected significantly by menstrual cycle, and the measurements were highly reproducible both within and between observers.

The stochastic distribution of available coefficient of friction for human locomotion of five different floor surfaces.

PubMed

Chang, Wen-Ruey; Matz, Simon; Chang, Chien-Chi

2014-05-01

The maximum coefficient of friction that can be supported at the shoe and floor interface without a slip is usually called the available coefficient of friction (ACOF) for human locomotion. The probability of a slip could be estimated using a statistical model by comparing the ACOF with the required coefficient of friction (RCOF), assuming that both coefficients have stochastic distributions. An investigation of the stochastic distributions of the ACOF of five different floor surfaces under dry, water and glycerol conditions is presented in this paper. One hundred friction measurements were performed on each floor surface under each surface condition. The Kolmogorov-Smirnov goodness-of-fit test was used to determine if the distribution of the ACOF was a good fit with the normal, log-normal and Weibull distributions. The results indicated that the ACOF distributions had a slightly better match with the normal and log-normal distributions than with the Weibull in only three out of 15 cases with a statistical significance. The results are far more complex than what had heretofore been published and different scenarios could emerge. Since the ACOF is compared with the RCOF for the estimate of slip probability, the distribution of the ACOF in seven cases could be considered a constant for this purpose when the ACOF is much lower or higher than the RCOF. A few cases could be represented by a normal distribution for practical reasons based on their skewness and kurtosis values without a statistical significance. No representation could be found in three cases out of 15. Copyright © 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.

A stochastic model for the normal tissue complication probability (NTCP) and applicationss.

PubMed

Stocks, Theresa; Hillen, Thomas; Gong, Jiafen; Burger, Martin

2017-12-11

The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth-death process to define an organ-specific and patient-specific NTCP. We emphasize an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework is based on simple modelling assumptions and it prepares a framework for the use of the NTCP model in clinical practice. As example, we consider side effects of prostate cancer brachytherapy such as increase in urinal frequency, urinal retention and acute rectal dysfunction. © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Monostatic lidar/radar invisibility using coated spheres.

PubMed

Zhai, Peng-Wang; You, Yu; Kattawar, George W; Yang, Ping

2008-02-04

The Lorenz-Mie theory is revisited to explicitly include materials whose permeability is different from unity. The expansion coefficients of the scattered field are given for light scattering by both homogeneous and coated spheres. It is shown that the backscatter is exactly zero if the impedance of the spherical particles is equal to the intrinsic impedance of the surrounding medium. If spherical particles are sufficiently large, the zero backscatter can be explained as impedance matching using the asymptotic expression for the radar backscattering cross section. In the case of a coated sphere, the shell can be regarded as a cloak if the product of the thickness and the imaginary part of the refractive index of the outer shell is large.

Estimation of the Arrival Time and Duration of a Radio Signal with Unknown Amplitude and Initial Phase

NASA Astrophysics Data System (ADS)

Trifonov, A. P.; Korchagin, Yu. E.; Korol'kov, S. V.

2018-05-01

We synthesize the quasi-likelihood, maximum-likelihood, and quasioptimal algorithms for estimating the arrival time and duration of a radio signal with unknown amplitude and initial phase. The discrepancies between the hardware and software realizations of the estimation algorithm are shown. The characteristics of the synthesized-algorithm operation efficiency are obtained. Asymptotic expressions for the biases, variances, and the correlation coefficient of the arrival-time and duration estimates, which hold true for large signal-to-noise ratios, are derived. The accuracy losses of the estimates of the radio-signal arrival time and duration because of the a priori ignorance of the amplitude and initial phase are determined.

Convective stability in the Rayleigh-Benard and directional solidification problems - High-frequency gravity modulation

NASA Technical Reports Server (NTRS)

Wheeler, A. A.; Mcfadden, G. B.; Murray, B. T.; Coriell, S. R.

1991-01-01

The effect of vertical, sinusoidal, time-dependent gravitational acceleration on the onset of solutal convection during directional solidification is analyzed in the limit of large modulation frequency. When the unmodulated state is unstable, the modulation amplitude required to stabilize the system is determined by the method of averaging. When the unmodulated state is stable, resonant modes of instability occur at large modulation amplitude. These are analyzed using matched asymptotic expansions to elucidate the boundary-layer structure for both the Rayleigh-Benard and directional solidification configurations. Based on these analyses, a thorough examination of the dependence of the stability criteria on the unmodulated Rayleigh number, Schmidt number, and distribution coefficient, is carried out.

Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas

NASA Astrophysics Data System (ADS)

Leitmann, Sebastian; Schwab, Thomas; Franosch, Thomas

2018-02-01

We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are evaluated exactly in first order of the obstacle density for arbitrarily strong pulling and all times. The complex time-dependent behavior is analyzed in terms of the diffusion coefficient, local exponent, and the non-Skellam parameter, which quantifies deviations from the dynamics on the lattice in the absence of obstacles. The non-Skellam parameter along the force is analyzed in terms of an asymptotic model and reveals a power-law growth for intermediate times.

Determination of corneal elasticity coefficient using the ORA database.

PubMed

Avetisov, Sergei E; Novikov, Ivan A; Bubnova, Irina A; Antonov, Alexei A; Siplivyi, Vladimir I

2010-07-01

To propose a new approach for the study of corneal biomechanics using the Reichert Ocular Response Analyzer (ORA) database, which is based on changes in velocity retardation in the central cornea at the peak of flattening. The ORA applanation curve was analyzed using a mathematical technique, which allowed calculation of the elasticity coefficient (Ke), which is primarily characteristic of the elastic properties of the cornea. Elasticity coefficient values were obtained in patients with presumably different biomechanical properties of the cornea: "normal" cornea (71 eyes, normal group), keratoconus (34 eyes, keratoconus group), LASIK (36 eyes, LASIK group), and glaucoma with elevated and compensated intraocular pressure (lOP) (38 eyes, glaucoma group). The mean Ke value in the normal group was 11.05 +/- 1.6, and the corneal thickness correlation coefficient r2 was 0.48. In the keratoconus group, the mean Ke value was 4.91 +/- 1.87 and the corneal thickness correlation coefficient r2 was 0.47. In the LASIK group, Ke and r2 were 5.99 +/- 1.18 and 0.39, respectively. In the glaucoma group, the same eyes that experienced a two-fold reduction in lOP developed a statistically significant reduction in the Ke (1.06 times lower), whereas their corneal hysteresis value increased 1.25 times. The elasticity coefficient calculated using the ORA applanation curve can be used in the evaluation of corneal biomechanical properties.

Bose–Einstein condensation temperature of finite systems

NASA Astrophysics Data System (ADS)

Xie, Mi

2018-05-01

In studies of the Bose–Einstein condensation of ideal gases in finite systems, the divergence problem usually arises in the equation of state. In this paper, we present a technique based on the heat kernel expansion and zeta function regularization to solve the divergence problem, and obtain the analytical expression of the Bose–Einstein condensation temperature for general finite systems. The result is represented by the heat kernel coefficients, where the asymptotic energy spectrum of the system is used. Besides the general case, for systems with exact spectra, e.g. ideal gases in an infinite slab or in a three-sphere, the sums of the spectra can be obtained exactly and the calculation of corrections to the critical temperatures is more direct. For a system confined in a bounded potential, the form of the heat kernel is different from the usual heat kernel expansion. We show that as long as the asymptotic form of the global heat kernel can be found, our method works. For Bose gases confined in three- and two-dimensional isotropic harmonic potentials, we obtain the higher-order corrections to the usual results of the critical temperatures. Our method can also be applied to the problem of generalized condensation, and we give the correction of the boundary on the second critical temperature in a highly anisotropic slab.

A random walk description of individual animal movement accounting for periods of rest

NASA Astrophysics Data System (ADS)

Tilles, Paulo F. C.; Petrovskii, Sergei V.; Natti, Paulo L.

2016-11-01

Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or `bouts' (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings.

On the renormalisation of the diffusion asymptotics in the problem of reflection of a narrow optical beam from a biological medium

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

Appanov, A Yu; Barabanenkov, Yu N

2005-12-31

An analytic hybrid method is considered for solving the stationary radiation transfer equation in the problem on reflection of a narrow laser beam from biological media such as the 2% aqueous solution of intralipid and erythrocyte suspension with the volume concentration (hematocrit) H=0.41. The method is based on the reciprocity of the Green function in the radiation transfer theory and on the iteration solution of the integral equation for this function. As a result, the ray intensity is represented as a sum of two terms. The first of them describes the contribution of finite-order scattering to the intensity of amore » beam diffusely reflected from the medium. The second term contains the explicit analytic expression for a spatially distributed effective source of diffuse radiation emerging from the deep layers of the medium to the surface. This approach substantially improves the diffusion approximation for the problem under study and allows one to obtain the uniform asymptotics of the reflection coefficient at the specified interval of distances between the radiation source and detector on the medium surface with the relative error within {+-}6% for the 2% intralipid emulsion and erythrocyte suspension (H=0.41). (radiation scattering)« less

A random walk description of individual animal movement accounting for periods of rest.

PubMed

Tilles, Paulo F C; Petrovskii, Sergei V; Natti, Paulo L

2016-11-01

Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or 'bouts' (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings.

A random walk description of individual animal movement accounting for periods of rest

PubMed Central

Tilles, Paulo F. C.

2016-01-01

Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or ‘bouts’ (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings. PMID:28018645

Algorithm for Stabilizing a POD-Based Dynamical System

NASA Technical Reports Server (NTRS)

Kalb, Virginia L.

2010-01-01

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Bilinearization of the generalized coupled nonlinear Schrödinger equation with variable coefficients and gain and dark-bright pair soliton solutions.

PubMed

Chakraborty, Sushmita; Nandy, Sudipta; Barthakur, Abhijit

2015-02-01

We investigate coupled nonlinear Schrödinger equations (NLSEs) with variable coefficients and gain. The coupled NLSE is a model equation for optical soliton propagation and their interaction in a multimode fiber medium or in a fiber array. By using Hirota's bilinear method, we obtain the bright-bright, dark-bright combinations of a one-soliton solution (1SS) and two-soliton solutions (2SS) for an n-coupled NLSE with variable coefficients and gain. Crucial properties of two-soliton (dark-bright pair) interactions, such as elastic and inelastic interactions and the dynamics of soliton bound states, are studied using asymptotic analysis and graphical analysis. We show that a bright 2-soliton, in addition to elastic interactions, also exhibits multiple inelastic interactions. A dark 2-soliton, on the other hand, exhibits only elastic interactions. We also observe a breatherlike structure of a bright 2-soliton, a feature that become prominent with gain and disappears as the amplitude acquires a minimum value, and after that the solitons remain parallel. The dark 2-soliton, however, remains parallel irrespective of the gain. The results found by us might be useful for applications in soliton control, a fiber amplifier, all optical switching, and optical computing.

Accumulation and dissipation of positive charges induced on a PMMA build-up cap of an ionisation chamber by (60)Co gamma-ray irradiation.

PubMed

Morishita, Y; Takata, N

2013-07-01

The signal current from an ionisation chamber with a PMMA build-up cap decreases with irradiation time due to electric fields produced by positive charges induced on the cap. In the present study, it was confirmed that the signal current decreases faster for irradiation using narrower (60)Co gamma-ray beams. This is because the number of secondary electrons that are emitted from surrounding materials and penetrate the build-up cap is smaller in a narrower gamma-ray beam, so that fewer positive charges are neutralised. The ionisation chamber was first subjected to continuous gamma-ray irradiation for 24 h, following which it was irradiated with shorter periodic gamma-ray bursts while measuring the current signal. This allowed the coefficients of positive charge accumulation and dissipation to be determined. It was found that the dissipation coefficient has a large constant value during gamma-ray irradiation and decreases asymptotically to a small value after irradiation is stopped. From the coefficients, the minimum signal current was calculated, which is the value when accumulation and dissipation balance each other under continuous irradiation. The time required for the signal current to recover following irradiation was also calculated.

Prediction and Validation of Mars Pathfinder Hypersonic Aerodynamic Data Base

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.; Braun, Robert D.; Weilmuenster, K. James; Mitcheltree, Robert A.; Engelund, Walter C.; Powell, Richard W.

1998-01-01

Postflight analysis of the Mars Pathfinder hypersonic, continuum aerodynamic data base is presented. Measured data include accelerations along the body axis and axis normal directions. Comparisons of preflight simulation and measurements show good agreement. The prediction of two static instabilities associated with movement of the sonic line from the shoulder to the nose and back was confirmed by measured normal accelerations. Reconstruction of atmospheric density during entry has an uncertainty directly proportional to the uncertainty in the predicted axial coefficient. The sensitivity of the moment coefficient to freestream density, kinetic models and center-of-gravity location are examined to provide additional consistency checks of the simulation with flight data. The atmospheric density as derived from axial coefficient and measured axial accelerations falls within the range required for sonic line shift and static stability transition as independently determined from normal accelerations.

Fundamental aerodynamic characteristics of delta wings with leading-edge vortex flows

NASA Technical Reports Server (NTRS)

Wood, R. M.; Miller, D. S.

1985-01-01

An investigation of the aerodynamics of sharp leading-edge delta wings at supersonic speeds has been conducted. The supporting experimental data for this investigation were taken from published force, pressure, and flow-visualization data in which the Mach number normal to the wing leading edge is always less than 1.0. The individual upper- and lower-surface nonlinear characteristics for uncambered delta wings are determined and presented in three charts. The upper-surface data show that both the normal-force coefficient and minimum pressure coefficient increase nonlinearly with a decreasing slope with increasing angle of attack. The lower-surface normal-force coefficient was shown to be independent of Mach number and to increase nonlinearly, with an increasing slope, with increasing angle of attack. These charts are then used to define a wing-design space for sharp leading-edge delta wings.

[Carbon monoxide tests in a steady state. Uptake and transfer capacity, normal values and lower limits].

PubMed

Ramonatxo, M; Préfaut, C; Guerrero, H; Moutou, H; Bansard, X; Chardon, G

1982-01-01

The aim of this study was to establish data which would best demonstrate the variations of different tests using Carbon Monoxide as a tracer gas (total and partial functional uptake coefficient and transfer capacity) to establish mean values and lower limits of normal of these tests. Multivariate statistical analysis was used; in the first stage a connection was sought between the fractional uptake coefficient (partial and total) to other parameters, comparing subjects and data. In the second stage the comparison was refined by eliminating the least useful data, trying, despite a small loss of material, to reveal the most important connections, linear or otherwise. The fractional uptake coefficients varied according to sex, also the variation of the partial alveolar-expired fractional uptake equivalent (DuACO) was largely a function of respiratory rate and tidal volume. The alveolar-arterial partial fractional uptake equivalent (DuaCO) depended more on respiratory frequency and age. Finally the total fractional uptake coefficient (DuCO) and the transfer capacity corrected per liter of ventilation (TLCO/V) were functions of these parameters. The last stage of this work, after taking account of the statistical observations consistent with the facts of these physiological hypotheses led to a search for a better way of approaching the laws linking the collected data to the fractional uptake coefficient. The lower limits of normal were arbitrarily defined, separating those 5% of subjects deviating most strongly from the mean. As a result, the relationship between the lower limit of normal and the theoretical mean value was 90% for the partial and total fractional uptake coefficient and 70% for the transfer capacity corrected per liter of ventilation.

Supersymmetric asymptotic safety is not guaranteed

DOE PAGES

Intriligator, Kenneth; Sannino, Francesco

2015-11-05

It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.

Asymptotic symmetries on Killing horizons

NASA Astrophysics Data System (ADS)

Koga, Jun-Ichirou

2001-12-01

We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in Einstein theory with or without the cosmological constant. These asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of the asymptotic Killing vectors and find that the group of asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved not only under diffeomorphisms but also under nontrivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the Diff(S1) subgroup, which results from supertranslations dependent only on the null coordinate, it is shown that the Poisson brackets algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire nontrivial central charges. Finally, by considering extended symmetries, we discuss the fact that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with nontrivial central charges, which is not justified when we respect the spherical symmetry of Killing horizons.

Global structure of static spherically symmetric solutions surrounded by quintessence

NASA Astrophysics Data System (ADS)

Cruz, Miguel; Ganguly, Apratim; Gannouji, Radouane; Leon, Genly; Saridakis, Emmanuel N.

2017-06-01

We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1  +  1  +  2 formalism and introducing suitable normalized variables involving the Gaussian curvature, we were able to reformulate the field equations as first order differential equations. In the case of a massless canonical scalar field we recovered all known black hole results, such as the Fisher solution, and we found that apart from the Schwarzschild solution all other solutions are naked singularities. Additionally, we identified the symmetric phase space which corresponds to the white hole part of the solution and in the case of a phantom field, we were able to extract the conditions for the existence of wormholes and define all possible classes of solutions such as cold black holes, singular spacetimes and wormholes such as the Ellis wormhole, for example. For an exponential potential, we found that the black hole solution which is asymptotically flat is unique and it is the Schwarzschild spacetime, while all other solutions are naked singularities. Furthermore, we found solutions connecting to a white hole through a maximum radius, and not a minimum radius (throat) such as wormhole solutions, therefore violating the flare-out condition. Finally, we have found a necessary and sufficient condition on the form of the potential to have an asymptotically AdS spacetime along with a necessary condition for the existence of asymptotically flat black holes.

Continuous Diffusion Model for Concentration Dependence of Nitroxide EPR Parameters in Normal and Supercooled Water.

PubMed

Merunka, Dalibor; Peric, Miroslav

2017-05-25

Electron paramagnetic resonance (EPR) spectra of radicals in solution depend on their relative motion, which modulates the Heisenberg spin exchange and dipole-dipole interactions between them. To gain information on radical diffusion from EPR spectra demands both reliable spectral fitting to find the concentration coefficients of EPR parameters and valid expressions between the concentration and diffusion coefficients. Here, we measured EPR spectra of the 14 N- and 15 N-labeled perdeuterated TEMPONE radicals in normal and supercooled water at various concentrations. By fitting the EPR spectra to the functions based on the modified Bloch equations, we obtained the concentration coefficients for the spin dephasing, coherence transfer, and hyperfine splitting parameters. Assuming the continuous diffusion model for radical motion, the diffusion coefficients of radicals were calculated from the concentration coefficients using the standard relations and the relations derived from the kinetic equations for the spin evolution of a radical pair. The latter relations give better agreement between the diffusion coefficients calculated from different concentration coefficients. The diffusion coefficients are similar for both radicals, which supports the presented method. They decrease with lowering temperature slower than is predicted by the Stokes-Einstein relation and slower than the rotational diffusion coefficients, which is similar to the diffusion of water molecules in supercooled water.

Stokes phenomena in discrete Painlevé II.

PubMed

Joshi, N; Lustri, C J; Luu, S

2017-02-01

We consider the asymptotic behaviour of the second discrete Painlevé equation in the limit as the independent variable becomes large. Using asymptotic power series, we find solutions that are asymptotically pole-free within some region of the complex plane. These asymptotic solutions exhibit Stokes phenomena, which is typically invisible to classical power series methods. We subsequently apply exponential asymptotic techniques to investigate such phenomena, and obtain mathematical descriptions of the rapid switching behaviour associated with Stokes curves. Through this analysis, we determine the regions of the complex plane in which the asymptotic behaviour is described by a power series expression, and find that the behaviour of these asymptotic solutions shares a number of features with the tronquée and tri-tronquée solutions of the second continuous Painlevé equation.

Stokes phenomena in discrete Painlevé II

PubMed Central

Joshi, N.

2017-01-01

We consider the asymptotic behaviour of the second discrete Painlevé equation in the limit as the independent variable becomes large. Using asymptotic power series, we find solutions that are asymptotically pole-free within some region of the complex plane. These asymptotic solutions exhibit Stokes phenomena, which is typically invisible to classical power series methods. We subsequently apply exponential asymptotic techniques to investigate such phenomena, and obtain mathematical descriptions of the rapid switching behaviour associated with Stokes curves. Through this analysis, we determine the regions of the complex plane in which the asymptotic behaviour is described by a power series expression, and find that the behaviour of these asymptotic solutions shares a number of features with the tronquée and tri-tronquée solutions of the second continuous Painlevé equation. PMID:28293132

Dispersion in 2D network: Effects of mixing rule at nodes and molecular diffusion

NASA Astrophysics Data System (ADS)

Wang, Y.; Tao, Q.; Li, M.

2017-12-01

We simulate solute transport in 2D network backbone characterized by pore connectivity and pore heterogeneity by particle-tracking method. In order to ensure the dispersion coefficient reaching an asymptotic value, we upscale dispersion from pore-scale to meter-scale by using periodic boundary condition. As comparison, two different flow mechanisms without or with dispersion in a capillary tube, namely mean flow and Taylor-Aris dispersion, are introduced to investigate the evolution of solute spreading. The longitudinal dispersion coefficient DLM without dispersion in a pipe can roughly be regarded as a parameter to quantify the impact of microscopic structure of porous media on solute spreading, which is smaller than that value DL of Taylor-Aris dispersion. The difference between them decreases with the enhancement of the disorder. The mixing rule at nodes has a minor effect on longitudinal spreading, but has a significant effect on transverse spreading, especially for the nearly homogeneous media. An increase of the disorder in network achieved by increasing pore size heterogeneity or/and decreasing pore connectivity diminishes the difference between two mixing rules. Besides, the evolution of longitudinal dispersion coefficient over diffusion presents three different patterns at different velocities for homogenous media, such as monotonically increasing trend, decreasing first and then increasing trend and monotonically decreasing trend. But all are replaced by power law for a high disorder. The simulation results also accurately predict the experimental dependence of the longitudinal coefficient on Peclet number Pe.

Time-dependent breakdown of fiber networks: Uncertainty of lifetime

NASA Astrophysics Data System (ADS)

Mattsson, Amanda; Uesaka, Tetsu

2017-05-01

Materials often fail when subjected to stresses over a prolonged period. The time to failure, also called the lifetime, is known to exhibit large variability of many materials, particularly brittle and quasibrittle materials. For example, a coefficient of variation reaches 100% or even more. Its distribution shape is highly skewed toward zero lifetime, implying a large number of premature failures. This behavior contrasts with that of normal strength, which shows a variation of only 4%-10% and a nearly bell-shaped distribution. The fundamental cause of this large and unique variability of lifetime is not well understood because of the complex interplay between stochastic processes taking place on the molecular level and the hierarchical and disordered structure of the material. We have constructed fiber network models, both regular and random, as a paradigm for general material structures. With such networks, we have performed Monte Carlo simulations of creep failure to establish explicit relationships among fiber characteristics, network structures, system size, and lifetime distribution. We found that fiber characteristics have large, sometimes dominating, influences on the lifetime variability of a network. Among the factors investigated, geometrical disorders of the network were found to be essential to explain the large variability and highly skewed shape of the lifetime distribution. With increasing network size, the distribution asymptotically approaches a double-exponential form. The implication of this result is that, so-called "infant mortality," which is often predicted by the Weibull approximation of the lifetime distribution, may not exist for a large system.

The {sup 18}O(d,p){sup 19}O reaction and the ANC method

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

Burjan, V.; Hons, Z.; Kroha, V.

2014-05-09

The neutron capture rate {sup 18}O(n,γ){sup 19}O is important for analysis of nucleosynthesis in inhomogeneous Big Bang models and also for models of processes in massive red giant stars and AGB stars. Angular distributions of the {sup 18}O(d,p){sup 19}O reaction were measured at a deuteron energy of 16.3 MeV in NPI in Řež, Czech Republic, with the aim to determine Asymptotic Normalization Coefficients which can then be used for indirect determination of the direct contribution to the {sup 18}O(n,γ){sup 19}O process. In the experiment, the gas target with {sup 18}O isotope of high purity 99.9 % was used thus eliminatingmore » any contaminating reactions. Reaction products were measured by the set of 8 ΔE-E telescopes consisting of thin and thick silicon surface-barrier detectors. Angular distributions of proton transfers corresponding to 6 levels of {sup 19}O up to the 4.1093 MeV excitation energy were determined. The analysis of angular distributions in the angular range from 6 to 64 degree including also the angular distribution of elastically scattered deuterons was carried out by means of ECIS and DWUCK codes. From the determined ANCs the direct contribution to the radiative capture {sup 18}O(n,γ){sup 19}O was deduced and compared with existing direct measurements.« less

6 Li and d + α scattering in a three-body momentum space Faddeev model (I)

NASA Astrophysics Data System (ADS)

Jin, Lei; Hlophe, Linda; Elster, Charlotte; Nogga, Andreas; Nunes, Filomena M.

2017-09-01

The (d , p) transfer reaction constitutes an important tool for extracting nuclear structure information such as spectroscopic factors and asymptotic normalization coefficients. In order to treat the dynamics in all reaction channels on the same footing, it is advantageous to view the (d , p) reaction as a three-body problem (n + p + A) within a Faddeev framework. Coulomb poses severe difficulties when studying these reactions on heavy nuclei with momentum space Faddeev equations. One way to address the challenges is to formulate the problem without screening and using separable interactions. An important first step in testing this formulation is to consider the ground state of 6Li, since this system has been studied in detail before within a three-body n + p + α ansatz. For the np interaction, we employ e.g. the CD-Bonn potential, and for n + α and p + α interactions Wood-Saxon type potentials. We introduce a projection method for the Pauli forbidden state which acts only in the relevant subsystem and thus leaves the structure of the Faddeev equations unaltered. Results for the energy and structure of the 6Li ground state will be presented for both the separable and non-separable approaches. Our results demonstrate the accuracy of the separable approach. Supported in part by the U.S. NSF under Contract PHY-1520972 and PHY-1520929, and U.S. DoE under Contract DE-FG02-93ER40756.

Application of hyperosmotic agent to determine gastric cancer with optical coherence tomography ex vivo in mice

NASA Astrophysics Data System (ADS)

Xiong, Honglian; Guo, Zhouyi; Zeng, Changchun; Wang, Like; He, Yonghong; Liu, Songhao

2009-03-01

Noninvasive tumor imaging could lead to the early detection and timely treatment of cancer. Optical coherence tomography (OCT) has been reported as an ideal diagnostic tool for distinguishing tumor tissues from normal tissues based on structural imaging. In this study, the capability of OCT for functional imaging of normal and tumor tissues based on time- and depth-resolved quantification of the permeability of biomolecules through these tissues is investigated. The orthotopic graft model of gastric cancer in nude mice is used, normal and tumor tissues from the gastric wall are imaged, and a diffusion of 20% aqueous solution of glucose in normal stomach tissues and gastric tumor tissues is monitored and quantified as a function of time and tissue depth by an OCT system. Our results show that the permeability coefficient is (0.94+/-0.04)×10-5 cm/s in stomach tissues and (5.32+/-0.17)×10-5 cm/s in tumor tissues, respectively, and that tumor tissues have a higher permeability coefficient compared to normal tissues in optical coherence tomographic images. From the results, it is found that the accurate and sensitive assessment of the permeability coefficients of normal and tumor tissues offers an effective OCT image method for detection of tumor tissues and clinical diagnosis.

Data-driven identification of intensity normalization region based on longitudinal coherency of 18F-FDG metabolism in the healthy brain.

PubMed

Zhang, Huiwei; Wu, Ping; Ziegler, Sibylle I; Guan, Yihui; Wang, Yuetao; Ge, Jingjie; Schwaiger, Markus; Huang, Sung-Cheng; Zuo, Chuantao; Förster, Stefan; Shi, Kuangyu

2017-02-01

In brain 18 F-FDG PET data intensity normalization is usually applied to control for unwanted factors confounding brain metabolism. However, it can be difficult to determine a proper intensity normalization region as a reference for the identification of abnormal metabolism in diseased brains. In neurodegenerative disorders, differentiating disease-related changes in brain metabolism from age-associated natural changes remains challenging. This study proposes a new data-driven method to identify proper intensity normalization regions in order to improve separation of age-associated natural changes from disease related changes in brain metabolism. 127 female and 128 male healthy subjects (age: 20 to 79) with brain 18 F-FDG PET/CT in the course of a whole body cancer screening were included. Brain PET images were processed using SPM8 and were parcellated into 116 anatomical regions according to the AAL template. It is assumed that normal brain 18 F-FDG metabolism has longitudinal coherency and this coherency leads to better model fitting. The coefficient of determination R 2 was proposed as the coherence coefficient, and the total coherence coefficient (overall fitting quality) was employed as an index to assess proper intensity normalization strategies on single subjects and age-cohort averaged data. Age-associated longitudinal changes of normal subjects were derived using the identified intensity normalization method correspondingly. In addition, 15 subjects with clinically diagnosed Parkinson's disease were assessed to evaluate the clinical potential of the proposed new method. Intensity normalizations by paracentral lobule and cerebellar tonsil, both regions derived from the new data-driven coherency method, showed significantly better coherence coefficients than other intensity normalization regions, and especially better than the most widely used global mean normalization. Intensity normalization by paracentral lobule was the most consistent method within both analysis strategies (subject-based and age-cohort averaging). In addition, the proposed new intensity normalization method using the paracentral lobule generates significantly higher differentiation from the age-associated changes than other intensity normalization methods. Proper intensity normalization can enhance the longitudinal coherency of normal brain glucose metabolism. The paracentral lobule followed by the cerebellar tonsil are shown to be the two most stable intensity normalization regions concerning age-dependent brain metabolism. This may provide the potential to better differentiate disease-related changes from age-related changes in brain metabolism, which is of relevance in the diagnosis of neurodegenerative disorders. Copyright © 2016 Elsevier Inc. All rights reserved.

Postural stability of preoperative acoustic neuroma patients assessed by sway magnetometry: are they unsteady?

PubMed

Collins, Melanie M; Johnson, Ian J M; Clifford, Elaine; Birchall, John P; O'Donoghue, Gerald M

2003-04-01

The objective was to evaluate the preoperative postural stability of acoustic neuroma patients using sway magnetometry. Prospective two-center study. Fifty-one patients (mean age, 53 years) diagnosed with unilateral acoustic neuroma on magnetic resonance imaging at two tertiary referral centers were studied. Preoperatively, each patient had sway patterns (with eyes open and with eyes closed, and standing on foam) recorded for 120 seconds by sway magnetometry. Path length for 30 seconds was calculated. The Romberg coefficient (path length with eyes open divided by path length with eyes closed) was calculated. Forty-four percent of patients had abnormal path lengths with eyes open, and 49% with eyes closed. The Romberg coefficients were significantly lower than normal (P <.001; 95% CI, 0.19-0.87). Mean Romberg coefficient was 0.59 (normal value = 0.73), and all patients had a coefficient of less than 1. Half of preoperative acoustic neuroma patients are unsteady, exhibiting abnormal sway patterns based on path length measurements. The increase in sway path length demonstrable in normal subjects with eyes closed was significantly exaggerated in patients with acoustic neuroma.

Aspects of the RVB Luttinger Liquid Theory of the High Temperature Superconductivity

NASA Astrophysics Data System (ADS)

Ren, Yong

1992-01-01

This thesis describes work on a large-U Hubbard model theory for high temperature superconductors. After an introduction to the Hubbard model and the normal state properties of the high T_{rm c} superconductors, we briefly examine the definition of the Fermi liquid and its breakdown. Then we explain why the 1D Hubbard model is the best starting point to approach our problem. In one dimension, the exact Lieb-Wu solution is available. We discuss the Lieb-Wu solution, and calculate various asymptotic correlation functions in the ground state. This clarifies the nature of the ground state which has not been known before. Instead of simply getting the exponents of the correlation functions from the Bethe Ansatz integral equations, we establish the connection between phase shifts at different Fermi points and the asymptotic correlation functions. We believe that this connection contains the most important physics and it can be readily generalized into higher dimensions. We then discuss bosonization in two dimensions and define the 2D RVB-Luttinger liquid theory, proposing that the ground state of the 2D Hubbard model belongs to a different fixed point than the Landau Fermi liquid-Luttinger liquid. Finally we apply the understanding of the 1D result to explain the normal state properties of the high T_ {c} superconductors, putting emphasis on how the non-Fermi liquid correlation functions explain the "anomalous" experimental results. In the Appendix, several issues related to the 1D and 2D Hubbard model are discussed.

On the discretization and control of an SEIR epidemic model with a periodic impulsive vaccination

NASA Astrophysics Data System (ADS)

Alonso-Quesada, S.; De la Sen, M.; Ibeas, A.

2017-01-01

This paper deals with the discretization and control of an SEIR epidemic model. Such a model describes the transmission of an infectious disease among a time-varying host population. The model assumes mortality from causes related to the disease. Our study proposes a discretization method including a free-design parameter to be adjusted for guaranteeing the positivity of the resulting discrete-time model. Such a method provides a discrete-time model close to the continuous-time one without the need for the sampling period to be as small as other commonly used discretization methods require. This fact makes possible the design of impulsive vaccination control strategies with less burden of measurements and related computations if one uses the proposed instead of other discretization methods. The proposed discretization method and the impulsive vaccination strategy designed on the resulting discretized model are the main novelties of the paper. The paper includes (i) the analysis of the positivity of the obtained discrete-time SEIR model, (ii) the study of stability of the disease-free equilibrium point of a normalized version of such a discrete-time model and (iii) the existence and the attractivity of a globally asymptotically stable disease-free periodic solution under a periodic impulsive vaccination. Concretely, the exposed and infectious subpopulations asymptotically converge to zero as time tends to infinity while the normalized subpopulations of susceptible and recovered by immunization individuals oscillate in the context of such a solution. Finally, a numerical example illustrates the theoretic results.

The time course of taste bud regeneration after glossopharyngeal or greater superficial petrosal nerve transection in rats.

PubMed

St John, Steven J; Garcea, Mircea; Spector, Alan C

2003-01-01

We previously have published data detailing the time course of taste bud regeneration in the anterior tongue following transection of the chorda tympani (CT) nerve in the rat. This study extends the prior work by determining the time course of taste bud regeneration in the vallate papilla, soft palate and nasoincisor ducts (NID) following transection of either the glossopharyngeal (GL) or greater superficial petrosal (GSP) nerve. Following GL transection in rats (n = 6 per time point), taste buds reappeared in the vallate papilla between 15 and 28 days after surgery, and returned to 80.3% of control levels (n = 12) of taste buds by 70 days postsurgery. The first appearance and the final percentage of the normal complement of regenerated vallate taste buds after GL transection resembled that seen previously in the anterior tongue after CT transection. However, in the latter case, regenerated taste buds reached asymptotic levels by 42 days after surgery, whereas within the time frame of the present study, a clear asymptotic return of vallate taste buds was not observed. In contrast to the posterior (and anterior) tongue, only 25% of the normal complement of palatal taste buds regenerated by 112 days and 224 days after GSP transection (n = 9). The difference in regenerative capacity might relate to the surgical approach used to transect the GSP. These experiments provide useful parametric data for investigators studying the functional consequences of gustatory nerve transection and regeneration.

Effects of Wall-Normal and Angular Momentum Injections in Airfoil Separation Control

NASA Astrophysics Data System (ADS)

Munday, Phillip M.; Taira, Kunihiko

2018-05-01

The objective of this computational study is to quantify the influence of wall-normal and angular momentum injections in suppressing laminar flow separation over a canonical airfoil. Open-loop control of fully separated, incompressible flow over a NACA 0012 airfoil at $\\alpha = 9^\\circ$ and $Re = 23,000$ is examined with large-eddy simulations. This study independently introduces wall-normal momentum and angular momentum into the separated flow using swirling jets through model boundary conditions. The response of the flow field and the surface vorticity fluxes to various combinations of actuation inputs are examined in detail. It is observed that the addition of angular momentum input to wall-normal momentum injection enhances the suppression of flow separation. Lift enhancement and suppression of separation with the wall-normal and angular momentum inputs are characterized by modifying the standard definition of the coefficient of momentum. The effect of angular momentum is incorporated into the modified coefficient of momentum by introducing a characteristic swirling jet velocity based on the non-dimensional swirl number. With this single modified coefficient of momentum, we are able to categorize each controlled flow into separated, transitional, and attached flows.

Design of a linear projector for use with the normal modes of the GLAS 4th order GCM

NASA Technical Reports Server (NTRS)

Bloom, S. C.

1984-01-01

The design of a linear projector for use with the normal modes of a model of atmospheric circulation is discussed. A central element in any normal mode initialization scheme is the process by which a set of data fields - winds, temperatures or geopotentials, and surface pressures - are expressed ("projected') in terms of the coefficients of a model's normal modes. This process is completely analogous to the Fourier decomposition of a single field (indeed a FFT applied in the zonal direction is a part of the process). Complete separability in all three spatial dimensions is assumed. The basis functions for the modal expansion are given. An important feature of the normal modes is their coupling of the structures of different fields, thus a coefficient in a normal mode expansion would contain both mass and momentum information.

Assessment of collagen changes in ovarian tissue by extracting optical scattering coefficient from OCT images

NASA Astrophysics Data System (ADS)

Yang, Yi; Wang, Tianheng; Biswal, Nrusingh; Wang, Xiaohong; Sanders, Melinda; Brewer, Molly; Zhu, Quing

2012-01-01

Optical scattering coefficient from ex-vivo unfixed normal and malignant ovarian tissue was quantitatively extracted by fitting optical coherence tomography (OCT) A-line signals to a single scattering model. 1097 average A-line measurements at a wavelength of 1310nm were performed at 108 sites obtained from 18 ovaries. The average scattering coefficient obtained from normal group consisted of 833 measurements from 88 sites was 2.41 mm-1 (+/-0.59), while the average coefficient obtained from malignant group consisted of 264 measurements from 20 sites was 1.55 mm-1 (+/-0.46). Using a threshold of 2 mm-1 for each ovary, a sensitivity of 100% and a specificity of 100% were achieved. The amount of collagen within OCT imaging depth was analyzed from the tissue histological section stained with Sirius Red. The average collagen area fraction (CAF) obtained from normal group was 48.4% (+/-12.3%), while the average CAF obtained from malignant group was 11.4% (+/-4.7%). Statistical significance of the collagen content was found between the two groups (p < 0.001). The preliminary data demonstrated that quantitative extraction of optical scattering coefficient from OCT images could be a potential powerful method for ovarian cancer detection and diagnosis.

Invariance of Hypersonic Normal Force Coefficients with Reynolds Number and Determination of Inviscid Wave Drag from Laminar Experimental Results

NASA Technical Reports Server (NTRS)

Hawkins, Richard; Penland, Jim A.

1997-01-01

Observations have been made and reported that the experimental normal force coefficients at a constant angle of attack were constant with a variation of more than 2 orders of magnitude of Reynolds number at a free-stream Mach number M(sub infinity) of 8.00 and more than 1 order of magnitude variation at M(sub infinity) = 6.00 on the same body-wing hypersonic cruise configuration. These data were recorded under laminar, transitional, and turbulent boundary layer conditions with both hot-wall and cold-wall models. This report presents experimental data on 25 configurations of 17 models of both simple and complex geometry taken at M(sub infinity) = 6.00, 6.86, and 8.00 in 4 different hypersonic facilities. Aerodynamic calculations were made by computational fluid dynamics (CID) and engineering methods to analyze these data. The conclusions were that the normal force coefficients at a given altitude are constant with Reynolds numbers at hypersonic speeds and that the axial force coefficients recorded under laminar boundary-layer conditions at several Reynolds numbers may be plotted against the laminar parameter (the reciprocal of the Reynolds number to the one-half power) and extrapolated to the ordinate axis to determine the inviscid-wave-drag coefficient at the intercept.

Radiation effects in silicon and gallium arsenide solar cells using isotropic and normally incident radiation

NASA Technical Reports Server (NTRS)

Anspaugh, B. E.; Downing, R. G.

1984-01-01

Several types of silicon and gallium arsenide solar cells were irradiated with protons with energies between 50 keV and 10 MeV at both normal and isotropic incidence. Damage coefficients for maximum power relative to 10 MeV were derived for these cells for both cases of omni-directional and normal incidence. The damage coefficients for the silicon cells were found to be somewhat lower than those quoted in the Solar Cell Radiation Handbook. These values were used to compute omni-directional damage coefficients suitable for solar cells protected by coverglasses of practical thickness, which in turn were used to compute solar cell degradation in two proton-dominated orbits. In spite of the difference in the low energy proton damage coefficients, the difference between the handbook prediction and the prediction using the newly derived values was negligible. Damage coefficients for GaAs solar cells for short circuit current, open circuit voltage, and maximum power were also computed relative to 10 MeV protons. They were used to predict cell degradation in the same two orbits and in a 5600 nmi orbit. Results show the performance of the GaAs solar cells in these orbits to be superior to that of the Si cells.

I Vivo Quantitative Ultrasound Imaging and Scatter Assessments.

NASA Astrophysics Data System (ADS)

Lu, Zheng Feng

There is evidence that "instrument independent" measurements of ultrasonic scattering properties would provide useful diagnostic information that is not available with conventional ultrasound imaging. This dissertation is a continuing effort to test the above hypothesis and to incorporate quantitative ultrasound methods into clinical examinations for early detection of diffuse liver disease. A well-established reference phantom method was employed to construct quantitative ultrasound images of tissue in vivo. The method was verified by extensive phantom tests. A new method was developed to measure the effective attenuation coefficient of the body wall. The method relates the slope of the difference between the echo signal power spectrum from a uniform region distal to the body wall and the echo signal power spectrum from a reference phantom to the body wall attenuation. The accuracy obtained from phantom tests suggests further studies with animal experiments. Clinically, thirty-five healthy subjects and sixteen patients with diffuse liver disease were studied by these quantitative ultrasound methods. The average attenuation coefficient in normals agreed with previous investigators' results; in vivo backscatter coefficients agreed with the results from normals measured by O'Donnell. Strong discriminating power (p < 0.001) was found for both attenuation and backscatter coefficients between fatty livers and normals; a significant difference (p < 0.01) was observed in the backscatter coefficient but not in the attenuation coefficient between cirrhotic livers and normals. An in vivo animal model of steroid hepatopathy was used to investigate the system sensitivity in detecting early changes in canine liver resulting from corticosteroid administration. The average attenuation coefficient slope increased from 0.7 dB/cm/MHz in controls to 0.82 dB/cm/MHz (at 6 MHz) in treated animals on day 14 into the treatment, and the backscatter coefficient was 26times 10^{ -4}cm^{-1}sr^{-1} in controls compared with 74times 10^{-4}cm^{-1}sr^ {-1} (at 6 MHz) in treated animals. A simplified quantitative approach using video image signals was developed. Results derived both from the r.f. signal analysis and from the video signal analysis are sensitive to the changes in the liver in this animal model.

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

NASA Technical Reports Server (NTRS)

Constantinides, E. D.; Marhefka, R. J.

1994-01-01

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided.

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

Howell, L. W.

2002-01-01

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Surface Collisions Involving Particles and Moisture (SCIP'M)

NASA Technical Reports Server (NTRS)

Davis, Robert H.

2005-01-01

Experiments were performed on the collision of a solid sphere with a nearly horizontal flat surface covered with a thin layer of viscous liquid. High-speed collisions were obtained by dropping the ball onto the surface from various heights, using gravitational acceleration. Low-speed collisions were obtained using pendulums with long strings or by launching the balls at low velocities in the reduced-gravity environment of parabolic flight. The sphere bounces only when the impact velocity exceeds a critical value. The coefficient of restitution (ratio of rebound velocity to impact velocity) increases with increasing impact velocity above the critical value, indicating the increasing relative importance of elastic deformation to viscous dissipation. The critical impact velocity increases, and the coefficient of restitution decreases, with increasing viscosity or thickness of the liquid layer and with decreasing density or size of the sphere. The ratio of the wet and dry coefficients is expressed as a function of the Stokes number (ratio of particle inertia and viscous forces), showing good agreement between theory and experiment. Similar experiments were performed with the flat surface inclined at various angles to the approaching sphere. A modified Stokes number, which is a measure of the ratio of inertia of the sphere in the normal direction to the viscous forces exerted by the fluid layer, was used for the analysis of oblique collisions. Even for these oblique collisions, it was found that no rebound of the ball was observed below a certain critical Stokes number. The coefficient of normal restitution, defined as a ratio of normal rebound velocity to normal approach velocity, was found to increase beyond the critical Stokes number and even out as it approaches the value for dry restitution at high Stokes numbers. It was also found that, for smooth spheres like steel, the normal restitution at the same modified Stokes number is independent of the angle of impact. The tangential coefficient of restitution, defined as the ratio of tangential rebound velocity to tangential approach velocity, is found to be nearly unity, except for very low approach velocities. Thus, as a first approximation, the theories that predict the coefficient of restitution for head-on wet collisions can be extended to predict the coefficient of normal restitution for oblique wet collisions. Additional experiments were performed with soft surfaces in which a porous cloth or sponge layer was placed over the hard, flat surface. In these experiments, the coefficient of restitution was found to decrease with increasing impact velocity, due to inelastic losses in the soft material. A model combining inelastic deformation and flow through porous media was developed to describe these findings.

Required coefficient of friction during turning at self-selected slow, normal, and fast walking speeds.

PubMed

Fino, Peter; Lockhart, Thurmon E

2014-04-11

This study investigated the relationship of required coefficient of friction to gait speed, obstacle height, and turning strategy as participants walked around obstacles of various heights. Ten healthy, young adults performed 90° turns around corner pylons of four different heights at their self selected normal, slow, and fast walking speeds using both step and spin turning strategies. Kinetic data was captured using force plates. Results showed peak required coefficient of friction (RCOF) at push off increased with increased speed (slow μ=0.38, normal μ=0.45, and fast μ=0.54). Obstacle height had no effect on RCOF values. The average peak RCOF for fast turning exceeded the OSHA safety guideline for static COF of μ>0.50, suggesting further research is needed into the minimum static COF to prevent slips and falls, especially around corners. Copyright © 2014 Elsevier Ltd. All rights reserved.

Transformations of asymptotically AdS hyperbolic initial data and associated geometric inequalities

NASA Astrophysics Data System (ADS)

Cha, Ye Sle; Khuri, Marcus

2018-01-01

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

Reliability of Pentacam HR Thickness Maps of the Entire Cornea in Normal, Post-Laser In Situ Keratomileusis, and Keratoconus Eyes.

PubMed

Xu, Zhe; Peng, Mei; Jiang, Jun; Yang, Chun; Zhu, Weigen; Lu, Fan; Shen, Meixiao

2016-02-01

To measure the repeatability and reproducibility of Pentacam HR system thickness maps for the entire cornea in normal, post-laser in situ keratomileusis (post-LASIK), and keratoconus (KC) eyes. Reliability study. Sixty normal subjects (60 eyes), 30 post-LASIK subjects (60 eyes), and 14 KC patients (27 eyes) were imaged with the Pentacam HR system by 2 well-trained operators. For pachymetry the cornea was divided into 4 zones: a central zone (2-mm diameter) and concentric pericentral zone (2-5 mm), transitional zone (5-7 mm), and peripheral zone (7-10 mm). The 3 concentric zones were subdivided into 8 sectors. Intraobserver repeatability and interobserver reproducibility of entire corneal thickness maps were tested by the repeatability and reproducibility coefficients, intraclass correlation coefficients, coefficient of variation, and 95% limits of agreement. From central to peripheral zones, the precision of corneal thickness measurements became gradually smaller. Central zone repeatability and reproducibility were the best in the normal, post-LASIK, and KC groups. The peripheral superior sectors showed poorer repeatability and reproducibility for all subjects. The intraobserver repeatability and interobserver reproducibility for all zones were ≤19.3 μm, ≤22.1 μm, and ≤20.7 μm, in the normal, post-LASIK, and KC groups, respectively. The intraobserver and interobserver coefficients of variation for all zones were ≤1.3%, ≤1.6%, and ≤1.6% for all 3 groups. Pentacam HR system pachymetry of the entire cornea provided good precision in normal, post-LASIK, and KC corneas. Thickness measurements in the peripheral cornea should be interpreted with caution in abnormal corneas after surgery or with diseases. Copyright © 2016 Elsevier Inc. All rights reserved.

RAXBOD- INVISCID TRANSONIC FLOW OVER AXISYMMETRIC BODIES

NASA Technical Reports Server (NTRS)

Keller, J. D.

1994-01-01

The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output can be generated for the Calcomp plotting system. The RAXBOD program was developed in 1976.

The influence of initial conditions on dispersion and reactions

NASA Astrophysics Data System (ADS)

Wood, B. D.

2016-12-01

In various generalizations of the reaction-dispersion problem, researchers have developed frameworks in which the apparent dispersion coefficient can be negative. Such dispersion coefficients raise several difficult questions. Most importantly, the presence of a negative dispersion coefficient at the macroscale leads to a macroscale representation that illustrates an apparent decrease in entropy with increasing time; this, then, appears to be in violation of basic thermodynamic principles. In addition, the proposition of a negative dispersion coefficient leads to an inherently ill-posed mathematical transport equation. The ill-posedness of the problem arises because there is no unique initial condition that corresponds to a later-time concentration distribution (assuming that if discontinuous initial conditions are allowed). In this presentation, we explain how the phenomena of negative dispersion coefficients actually arise because the governing differential equation for early times should, when derived correctly, incorporate a term that depends upon the initial and boundary conditions. The process of reactions introduces a similar phenomena, where the structure of the initial and boundary condition influences the form of the macroscopic balance equations. When upscaling is done properly, new equations are developed that include source terms that are not present in the classical (late-time) reaction-dispersion equation. These source terms depend upon the structure of the initial condition of the reacting species, and they decrease exponentially in time (thus, they converge to the conventional equations at asymptotic times). With this formulation, the resulting dispersion tensor is always positive-semi-definite, and the reaction terms directly incorporate information about the state of mixedness of the system. This formulation avoids many of the problems that would be engendered by defining negative-definite dispersion tensors, and properly represents the effective rate of reaction at early times.

Stagnation point properties for non-continuum gaseous jet impinging at a flat plate surface from a planar exit

NASA Astrophysics Data System (ADS)

Cai, Chunpei

2013-10-01

In this paper, we investigate highly rarefied gaseous jet flows out of a planar exit and impinging at a normally set flat plate. Especially, we concentrate on the plate center stagnation point pressure and heat flux coefficients. For a specular reflective plate, the stagnation point pressure coefficient can be represented using two non-dimensional factors: the characteristic gas exit speed ratio S0 and the geometry ratio of H/L, where H is the planar exit semi-height and L is the center-to-center distance from the exit to the plate. For a diffuse reflective plate, the stagnation point pressure and heat flux coefficients involve an extra factor of T0/Tw, i.e., the ratio of exit gas temperature to the plate wall temperature. These results allow us to develop four diagrams, from which we can conveniently obtain the pressure and heat flux coefficients for the stagnation impingement point, at the collisionless flow limit. After normalization with these maximum coefficients, the pressure and heat flux coefficient distributions along the surface essentially degenerate to almost identical curves. As a result, with known plate surface pressure coefficient distributions and these diagrams, we can conveniently construct the heat flux coefficient distributions along the plate surface, and vice versa.

Quartz tuning-fork oscillations in He II and drag coefficient

NASA Astrophysics Data System (ADS)

Gritsenko, I. A.; Zadorozhko, A. A.; Neoneta, A. S.; Chagovets, V. K.; Sheshin, G. A.

2011-07-01

The temperature dependencies of drag coefficient for quartz tuning forks of various geometric dimensions, immersed in the He II, were determined experimentally in the temperature range 0.1-3 K. It is identified, that these dependencies are similar, but the values of drag coefficient are different for tuning forks with different geometric dimensions. It is shown, that the obtained specific drag coefficient depends only on the temperature and frequency of vibrations, when the value of drag coefficient is normalized to the surface area of moving tuning-fork prong. The temperature dependencies of normalized drag coefficient for the tuning forks of various dimensions, wire, and microsphere, oscillating in the Не II, are compared. It is shown, that in the ballistic regime of scattering of quasiparticles, these dependencies are identical and have a slope proportional to T4, which is determined by the density of thermal excitations. In the hydrodynamic regime at T > 0.5 K, the behavior of the temperature dependence of specific drag coefficient is affected by the size and frequency of vibrating body. The empirical relation, which allows to describe the behavior of specific drag coefficient for vibrating tuning forks, microsphere, and wire everywhere over the temperature region and at various frequencies, is proposed.

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

Ko, Sung Moon; Park, Jeong-Hyuck; Suh, Minwoo, E-mail: sinsmk2003@sogang.ac.kr, E-mail: park@sogang.ac.kr, E-mail: minsuh@usc.edu

Double Field Theory suggests to view the whole massless sector of closed strings as the gravitational unity. The fundamental symmetries therein, including the O( D , D ) covariance, can determine unambiguously how the Standard Model as well as a relativistic point particle should couple to the closed string massless sector. The theory also refines the notion of singularity. We consider the most general, spherically symmetric, asymptotically flat, static vacuum solution to D =4 Double Field Theory, which contains three free parameters and consequently generalizes the Schwarzschild geometry. Analyzing the circular geodesic of a point particle in string frame, wemore » obtain the orbital velocity as a function of R /( M {sub ∞} G ) which is the dimensionless radial variable normalized by mass. The rotation curve generically features a maximum and thus non-Keplerian over a finite range, while becoming asymptotically Keplerian at infinity, R /( M {sub ∞} G )→ ∞. The adoption of the string frame rather than Einstein frame is the consequence of the fundamental symmetry principle. Our result opens up a new scheme to solve the dark matter/energy problems by modifying General Relativity at 'short' range of R /( M {sub ∞} G ).« less

Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.

PubMed

Wang, Zhen; Campbell, Sue Ann

2017-11-01

We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with Z N symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.

An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes

DOE PAGES

Taitano, William; Chacon, Luis; Simakov, Andrei Nikolaevich

2016-04-25

In this paper, we propose an adaptive velocity-space discretization scheme for the multi-species, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass-, momentum-, and energy-conserving. Unlike most earlier studies, our approach normalizes the velocity-space coordinate to the temporally varying individual plasma species' local thermal velocity, v th (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic v th -ratio-based expansion ofmore » the Rosenbluth potentials that only requires the computation of several velocity-space integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocity-grid adaptivity and asymptotic expansions delivers many orders-of-magnitude savings in mesh resolution requirements compared to a single, static uniform mesh.« less

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data.

PubMed

Carmichael, Owen; Sakhanenko, Lyudmila

2015-05-15

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way.

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data

PubMed Central

Carmichael, Owen; Sakhanenko, Lyudmila

2015-01-01

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way. PMID:25937674

Strongly anomalous diffusion in sheared magnetic configurations

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

Vanden Eijnden, E.; Balescu, R.

1996-03-01

The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface {ital x}=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface {ital x}=0. Due to the shear, the diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly non-Gaussian. The reference surface acts likemore » an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of the first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded that the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium. {copyright} {ital 1996 American Institute of Physics.}« less

Experience in using a numerical scheme with artificial viscosity at solving the Riemann problem for a multi-fluid model of multiphase flow

NASA Astrophysics Data System (ADS)

Bulovich, S. V.; Smirnov, E. M.

2018-05-01

The paper covers application of the artificial viscosity technique to numerical simulation of unsteady one-dimensional multiphase compressible flows on the base of the multi-fluid approach. The system of the governing equations is written under assumption of the pressure equilibrium between the "fluids" (phases). No interfacial exchange is taken into account. A model for evaluation of the artificial viscosity coefficient that (i) assumes identity of this coefficient for all interpenetrating phases and (ii) uses the multiphase-mixture Wood equation for evaluation of a scale speed of sound has been suggested. Performance of the artificial viscosity technique has been evaluated via numerical solution of a model problem of pressure discontinuity breakdown in a three-fluid medium. It has been shown that a relatively simple numerical scheme, explicit and first-order, combined with the suggested artificial viscosity model, predicts a physically correct behavior of the moving shock and expansion waves, and a subsequent refinement of the computational grid results in a monotonic approaching to an asymptotic time-dependent solution, without non-physical oscillations.

Chapman-Enskog expansion for the Vicsek model of self-propelled particles

NASA Astrophysics Data System (ADS)

Ihle, Thomas

2016-08-01

Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability distribution and, after making the mean-field assumption of molecular chaos, leads to a multi-particle Enskog-type equation. This equation is treated by a non-standard Chapman-Enskog expansion to extract the macroscopic behavior. The expansion includes terms up to third order in a formal expansion parameter ɛ, and involves a fast time scale. A self-consistent closure of the moment equations is presented that leads to a continuity equation for the particle density and a Navier-Stokes-like equation for the momentum density. Expressions for all transport coefficients in these macroscopic equations are given explicitly in terms of microscopic parameters of the model. The transport coefficients depend on specific angular integrals which are evaluated asymptotically in the limit of infinitely many collision partners, using an analogy to a random walk. The consistency of the Chapman-Enskog approach is checked by an independent calculation of the shear viscosity using a Green-Kubo relation.

Dynamic Nonlinear Elastic Stability of Helicopter Rotor Blades in Hover and in Forward Flight

NASA Technical Reports Server (NTRS)

Friedmann, P.; Tong, P.

1972-01-01

Equations for large coupled flap-lag motion of hingeless elastic helicopter blades are consistently derived. Only torsionally-rigid blades excited by quasi-steady aerodynamic loads are considered. The nonlinear equations of motion in the time and space variables are reduced to a system of coupled nonlinear ordinary differential equations with periodic coefficients, using Galerkin's method for the space variables. The nonlinearities present in the equations are those arising from the inclusion of moderately large deflections in the inertia and aerodynamic loading terms. The resulting system of nonlinear equations has been solved, using an asymptotic expansion procedure in multiple time scales. The stability boundaries, amplitudes of nonlinear response, and conditions for existence of limit cycles are obtained analytically. Thus, the different roles played by the forcing function, parametric excitation, and nonlinear coupling in affecting the solution can be easily identified, and the basic physical mechanism of coupled flap-lag response becomes clear. The effect of forward flight is obtained with the requirement of trimmed flight at fixed values of the thrust coefficient.

Generalized semiparametric varying-coefficient models for longitudinal data

NASA Astrophysics Data System (ADS)

Qi, Li

In this dissertation, we investigate the generalized semiparametric varying-coefficient models for longitudinal data that can flexibly model three types of covariate effects: time-constant effects, time-varying effects, and covariate-varying effects, i.e., the covariate effects that depend on other possibly time-dependent exposure variables. First, we consider the model that assumes the time-varying effects are unspecified functions of time while the covariate-varying effects are parametric functions of an exposure variable specified up to a finite number of unknown parameters. The estimation procedures are developed using multivariate local linear smoothing and generalized weighted least squares estimation techniques. The asymptotic properties of the proposed estimators are established. The simulation studies show that the proposed methods have satisfactory finite sample performance. ACTG 244 clinical trial of HIV infected patients are applied to examine the effects of antiretroviral treatment switching before and after HIV developing the 215-mutation. Our analysis shows benefit of treatment switching before developing the 215-mutation. The proposed methods are also applied to the STEP study with MITT cases showing that they have broad applications in medical research.

Second-order hydrodynamics and universality in non-conformal holographic fluids

NASA Astrophysics Data System (ADS)

Kleinert, Philipp; Probst, Jonas

2016-12-01

We study second-order hydrodynamic transport in strongly coupled non-conformal field theories with holographic gravity duals in asymptotically anti-de Sitter space. We first derive new Kubo formulae for five second-order transport coefficients in non-conformal fluids in (3 + 1) dimensions. We then apply them to holographic RG flows induced by scalar operators of dimension Δ = 3. For general background solutions of the dual bulk geometry, we find explicit expressions for the five transport coefficients at infinite coupling and show that a specific combination, tilde{H}=2η {τ}_{π }-2(κ -{κ}^{ast})-{λ}_2 , always vanishes. We prove analytically that the Haack-Yarom identity H = 2 ητ π - 4λ1 - λ2 = 0, which is known to be true for conformal holographic fluids at infinite coupling, also holds when taking into account leading non-conformal corrections. The numerical results we obtain for two specific families of RG flows suggest that H vanishes regardless of conformal symmetry. Our work provides further evidence that the Haack-Yarom identity H = 0 may be universally satisfied by strongly coupled fluids.

Linearly resummed hydrodynamics in a weakly curved spacetime

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael

2015-04-01

We extend our study of all-order linearly resummed hydrodynamics in a flat space [1, 2] to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically locally AdS5 geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid's energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs. [1, 2], we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref. [3], the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.

A scaling procedure for the response of an isolated system with high modal overlap factor

NASA Astrophysics Data System (ADS)

De Rosa, S.; Franco, F.

2008-10-01

The paper deals with a numerical approach that reduces some physical sizes of the solution domain to compute the dynamic response of an isolated system: it has been named Asymptotical Scaled Modal Analysis (ASMA). The proposed numerical procedure alters the input data needed to obtain the classic modal responses to increase the frequency band of validity of the discrete or continuous coordinates model through the definition of a proper scaling coefficient. It is demonstrated that the computational cost remains acceptable while the frequency range of analysis increases. Moreover, with reference to the flexural vibrations of a rectangular plate, the paper discusses the ASMA vs. the statistical energy analysis and the energy distribution approach. Some insights are also given about the limits of the scaling coefficient. Finally it is shown that the linear dynamic response, predicted with the scaling procedure, has the same quality and characteristics of the statistical energy analysis, but it can be useful when the system cannot be solved appropriately by the standard Statistical Energy Analysis (SEA).

Dipole oscillator strength distributions with improved high-energy behavior: Dipole sum rules and dispersion coefficients for Ne, Ar, Kr, and Xe revisited

NASA Astrophysics Data System (ADS)

Kumar, Ashok; Thakkar, Ajit J.

2010-02-01

The construction of the dipole oscillator strength distribution (DOSD) from theoretical and experimental photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and molar refractivity data is a well-established technique that has been successfully applied to more than 50 species. Such DOSDs are insufficiently accurate at large photon energies. A novel iterative procedure is developed that rectifies this deficiency by using the high-energy asymptotic behavior of the dipole oscillator strength density as an additional constraint. Pilot applications are made for the neon, argon, krypton, and xenon atoms. The resulting DOSDs improve the agreement of the predicted S2 and S1 sum rules with ab initio calculations while preserving the accuracy of the remainder of the moments. Our DOSDs exploit new and more accurate experimental data. Improved estimates of dipole properties for these four atoms and of dipole-dipole C6 and triple-dipole C9 dispersion coefficients for the interactions among them are reported.

Water-vapor foreign-continuum absorption in the 8-12 and 3-5 μm atmospheric windows

NASA Astrophysics Data System (ADS)

Klimeshina, T. E.; Rodimova, O. B.

2015-08-01

The frequency and temperature dependence of the water vapor-nitrogen continuum in the 8-12 and 3-5 μm spectral regions obtained experimentally by CAVIAR and NIST is described with the use of the line contour constructed on the basis of asymptotic line shape theory. The parameters of the theory found from fitting the calculated values of the absorption coefficient to the pertinent experimental data enter into the expression for the classical potential describing the center-of-mass motion of interacting molecules and into the expression for the quantum potential of two interacting molecules. The frequency behavior of the line wing contours appears to depend on the band the lines of which make a major contribution to the absorption in a given spectral interval. The absorption coefficients in the wings of the band in question calculated with the line contours obtained for other bands are outside of experimental errors. The distinction in the line wing behavior may be explained by the difference in the quantum energies of molecules interacting in different vibrational states.

Ultrasonic input-output for transmitting and receiving longitudinal transducers coupled to same face of isotropic elastic plate

NASA Technical Reports Server (NTRS)

Williams, J. H., Jr.; Karagulle, H.; Lee, S. S.

1982-01-01

The quantitative understanding of ultrasonic nondestructive evaluation parameters such as the stress wave factor were studied. Ultrasonic input/output characteristics for an isotropic elastic plate with transmitting and receiving longitudinal transducers coupled to the same face were analyzed. The asymptotic normal stress is calculated for an isotropic elastic half space subjected to a uniform harmonic normal stress applied to a circular region at the surface. The radiated stress waves are traced within the plate by considering wave reflections at the top and bottom faces. The output voltage amplitude of the receiving transducer is estimated by considering only longitudinal waves. Agreement is found between the output voltage wave packet amplitudes and times of arrival due to multiple reflections of the longitudinal waves.

Analysis of the interaction of a weak normal shock wave with a turbulent boundary layer

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Grossman, B.

1974-01-01

The method of matched asymptotic expansions is used to analyze the interaction of a normal shock wave with an unseparated turbulent boundary layer on a flat surface at transonic speeds. The theory leads to a three-layer description of the interaction in the double limit of Reynolds number approaching infinity and Mach number approaching unity. The interaction involves an outer, inviscid rotational layer, a constant shear-stress wall layer, and a blending region between them. The pressure distribution is obtained from a numerical solution of the outer-layer equations by a mixed-flow relaxation procedure. An analytic solution for the skin friction is determined from the inner-layer equations. The significance of the mathematical model is discussed with reference to existing experimental data.

Robust LOD scores for variance component-based linkage analysis.

PubMed

Blangero, J; Williams, J T; Almasy, L

2000-01-01

The variance component method is now widely used for linkage analysis of quantitative traits. Although this approach offers many advantages, the importance of the underlying assumption of multivariate normality of the trait distribution within pedigrees has not been studied extensively. Simulation studies have shown that traits with leptokurtic distributions yield linkage test statistics that exhibit excessive Type I error when analyzed naively. We derive analytical formulae relating the deviation from the expected asymptotic distribution of the lod score to the kurtosis and total heritability of the quantitative trait. A simple correction constant yields a robust lod score for any deviation from normality and for any pedigree structure, and effectively eliminates the problem of inflated Type I error due to misspecification of the underlying probability model in variance component-based linkage analysis.

On dynamic tumor eradication conditions under combined chemical/anti-angiogenic therapies

NASA Astrophysics Data System (ADS)

Starkov, Konstantin E.

2018-02-01

In this paper ultimate dynamics of the five-dimensional cancer tumor growth model at the angiogenesis phase is studied. This model elaborated by Pinho et al. in 2014 describes interactions between normal/cancer/endothelial cells under chemotherapy/anti-angiogenic agents in tumor growth process. The author derives ultimate upper bounds for normal/tumor/endothelial cells concentrations and ultimate upper and lower bounds for chemical/anti-angiogenic concentrations. Global asymptotic tumor clearance conditions are obtained for two versions: the use of only chemotherapy and the combined application of chemotherapy and anti-angiogenic therapy. These conditions are established as the attraction conditions to the maximum invariant set in the tumor free plane, and furthermore, the case is examined when this set consists only of tumor free equilibrium points.