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.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

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.

Asymptotic analysis of dissipative waves with applications to their numerical simulation

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1990-01-01

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

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.

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.

Asymptotic modal analysis and statistical energy analysis

NASA Technical Reports Server (NTRS)

Dowell, Earl H.

1992-01-01

Asymptotic Modal Analysis (AMA) is a method which is used to model linear dynamical systems with many participating modes. The AMA method was originally developed to show the relationship between statistical energy analysis (SEA) and classical modal analysis (CMA). In the limit of a large number of modes of a vibrating system, the classical modal analysis result can be shown to be equivalent to the statistical energy analysis result. As the CMA result evolves into the SEA result, a number of systematic assumptions are made. Most of these assumptions are based upon the supposition that the number of modes approaches infinity. It is for this reason that the term 'asymptotic' is used. AMA is the asymptotic result of taking the limit of CMA as the number of modes approaches infinity. AMA refers to any of the intermediate results between CMA and SEA, as well as the SEA result which is derived from CMA. The main advantage of the AMA method is that individual modal characteristics are not required in the model or computations. By contrast, CMA requires that each modal parameter be evaluated at each frequency. In the latter, contributions from each mode are computed and the final answer is obtained by summing over all the modes in the particular band of interest. AMA evaluates modal parameters only at their center frequency and does not sum the individual contributions from each mode in order to obtain a final result. The method is similar to SEA in this respect. However, SEA is only capable of obtaining spatial averages or means, as it is a statistical method. Since AMA is systematically derived from CMA, it can obtain local spatial information as well.

Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States

NASA Astrophysics Data System (ADS)

Blokhintsev, L. D.; Savin, D. A.

2018-03-01

It is shown that values obtained for asymptotic normalization coefficients by means of a potential fitted to experimental data on elastic scattering depend substantially on the presence and the number n of possible forbidden states in the fitted potential. The present analysis was performed within exactly solvable potential models for various nuclear systems and various potentials without and with allowance for Coulomb interaction. Various methods for changing the number n that are based on the use of various versions of the change in the parameters of the potential model were studied. A compact analytic expression for the asymptotic normalization coefficients was derived for the case of the Hulthén potential. Specifically, the d + α and α + 12C systems, which are of importance for astrophysics, were examined. It was concluded that an incorrect choice of n could lead to a substantial errors in determining the asymptotic normalization coefficients. From the results of our calculations, it also follows that, for systems with a low binding energy and, as a consequence, with a large value of the Coulomb parameter, the inclusion of the Coulomb interaction may radically change the asymptotic normalization coefficients, increasing them sharply.

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.

Bubble motion in a rotating liquid body. [ground based tests for space shuttle experiments

NASA Technical Reports Server (NTRS)

Annamalai, P.; Subramanian, R. S.; Cole, R.

1982-01-01

The behavior of a single gas bubble inside a rotating liquid-filled sphere has been investigated analytically and experimentally as part of ground-based investigations aimed at aiding in the design and interpretation of Shuttle experiments. In the analysis, a quasi-static description of the motion of a bubble was developed in the limit of small values of the Taylor number. A series of rotation experiments using air bubbles and silicone oils were designed to match the conditions specified in the analysis, i.e., the bubble size, sphere rotation rate, and liquid kinematic viscosity were chosen such that the Taylor number was much less than unity. The analytical description predicts the bubble velocity and its asymptotic location. It is shown that the asymptotic position is removed from the axis of rotation.

Higher-order harmonics of general limited diffraction Bessel beams

NASA Astrophysics Data System (ADS)

Ding, De-Sheng; Huang, Jin-Huang

2016-12-01

In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).

Efficient Approaches for Evaluating the Planar Microstrip Green's Function and its Applications to the Analysis of Microstrip Antennas.

NASA Astrophysics Data System (ADS)

Barkeshli, Sina

A relatively simple and efficient closed form asymptotic representation of the microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the planar microstrip configuration. Surprisingly, this asymptotic solution remains accurate even for very small (almost two tenths of a wavelength) lateral separation of the source and field points. The present asymptotic Green's function will thus allow a very efficient calculation of the currents excited on microstrip antenna patches/feed lines and monolithic millimeter and microwave integrated circuit (MIMIC) elements based on a moment method (MM) solution of an integral equation for these currents. The kernal of the latter integral equation is the present asymptotic form of the microstrip Green's function. It is noted that the conventional Sommerfeld integral representation of the microstrip surface Green's function is very poorly convergent when used in this MM formulation. In addition, an efficient exact steepest descent path integral form employing a radially propagating representation of the microstrip dyadic Green's function is also derived which exhibits a relatively faster convergence when compared to the conventional Sommerfeld integral representation. The same steepest descent form could also be obtained by deforming the integration contour of the conventional Sommerfeld representation; however, the radially propagating integral representation exhibits better convergence properties for laterally separated source and field points even before the steepest descent path of integration is used. Numerical results based on the efficient closed form asymptotic solution for the microstrip surface Green's function developed in this work are presented for the mutual coupling between a pair of dipoles on a single layer grounded dielectric slab. The accuracy of the latter calculations is confirmed by comparison with results based on an exact integral representation for that Green's function.

Higher-Order Asymptotics and Its Application to Testing the Equality of the Examinee Ability Over Two Sets of Items.

PubMed

Sinharay, Sandip; Jensen, Jens Ledet

2018-06-27

In educational and psychological measurement, researchers and/or practitioners are often interested in examining whether the ability of an examinee is the same over two sets of items. Such problems can arise in measurement of change, detection of cheating on unproctored tests, erasure analysis, detection of item preknowledge, etc. Traditional frequentist approaches that are used in such problems include the Wald test, the likelihood ratio test, and the score test (e.g., Fischer, Appl Psychol Meas 27:3-26, 2003; Finkelman, Weiss, & Kim-Kang, Appl Psychol Meas 34:238-254, 2010; Glas & Dagohoy, Psychometrika 72:159-180, 2007; Guo & Drasgow, Int J Sel Assess 18:351-364, 2010; Klauer & Rettig, Br J Math Stat Psychol 43:193-206, 1990; Sinharay, J Educ Behav Stat 42:46-68, 2017). This paper shows that approaches based on higher-order asymptotics (e.g., Barndorff-Nielsen & Cox, Inference and asymptotics. Springer, London, 1994; Ghosh, Higher order asymptotics. Institute of Mathematical Statistics, Hayward, 1994) can also be used to test for the equality of the examinee ability over two sets of items. The modified signed likelihood ratio test (e.g., Barndorff-Nielsen, Biometrika 73:307-322, 1986) and the Lugannani-Rice approximation (Lugannani & Rice, Adv Appl Prob 12:475-490, 1980), both of which are based on higher-order asymptotics, are shown to provide some improvement over the traditional frequentist approaches in three simulations. Two real data examples are also provided.

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.

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.

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

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

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

Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

On equivalent parameter learning in simplified feature space based on Bayesian asymptotic analysis.

PubMed

Yamazaki, Keisuke

2012-07-01

Parametric models for sequential data, such as hidden Markov models, stochastic context-free grammars, and linear dynamical systems, are widely used in time-series analysis and structural data analysis. Computation of the likelihood function is one of primary considerations in many learning methods. Iterative calculation of the likelihood such as the model selection is still time-consuming though there are effective algorithms based on dynamic programming. The present paper studies parameter learning in a simplified feature space to reduce the computational cost. Simplifying data is a common technique seen in feature selection and dimension reduction though an oversimplified space causes adverse learning results. Therefore, we mathematically investigate a condition of the feature map to have an asymptotically equivalent convergence point of estimated parameters, referred to as the vicarious map. As a demonstration to find vicarious maps, we consider the feature space, which limits the length of data, and derive a necessary length for parameter learning in hidden Markov models. Copyright © 2012 Elsevier Ltd. All rights reserved.

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.

Dynamic Analysis of the Melanoma Model: From Cancer Persistence to Its Eradication

NASA Astrophysics Data System (ADS)

Starkov, Konstantin E.; Jimenez Beristain, Laura

In this paper, we study the global dynamics of the five-dimensional melanoma model developed by Kronik et al. This model describes interactions of tumor cells with cytotoxic T cells and respective cytokines under cellular immunotherapy. We get the ultimate upper and lower bounds for variables of this model, provide formulas for equilibrium points and present local asymptotic stability/hyperbolic instability conditions. Next, we prove the existence of the attracting set. Based on these results we come to global asymptotic melanoma eradication conditions via global stability analysis. Finally, we provide bounds for a locus of the melanoma persistence equilibrium point, study the case of melanoma persistence and describe conditions under which we observe global attractivity to the unique melanoma persistence equilibrium point.

LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays

NASA Astrophysics Data System (ADS)

Zhang, Hai; Ye, Renyu; Liu, Song; Cao, Jinde; Alsaedi, Ahmad; Li, Xiaodi

2018-02-01

This paper is concerned with the asymptotic stability of the Riemann-Liouville fractional-order neural networks with discrete and distributed delays. By constructing a suitable Lyapunov functional, two sufficient conditions are derived to ensure that the addressed neural network is asymptotically stable. The presented stability criteria are described in terms of the linear matrix inequalities. The advantage of the proposed method is that one may avoid calculating the fractional-order derivative of the Lyapunov functional. Finally, a numerical example is given to show the validity and feasibility of the theoretical results.

Asymptotic modal analysis of a rectangular acoustic cavity excited by wall vibration

NASA Technical Reports Server (NTRS)

Peretti, Linda F.; Dowell, Earl H.

1992-01-01

Asymptotic modal analysis, a method that has recently been developed for structural dynamical systems, has been applied to a rectangular acoustic cavity. The cavity had a flexible vibrating portion on one wall, and the other five walls were rigid. Banded white noise was transmitted through the flexible portion (plate) only. Both the location along the wall and the size of the plate were varied. The mean square pressure levels of the cavity interior were computed as a ratio of the result obtained from classical modal analysis to that obtained from asymptotic modal analysis for the various plate configurations. In general, this ratio converged to 1.0 as the number of responding modes increased. Intensification effects were found due to both the excitation location and the response location. The asymptotic modal analysis method was both efficient and accurate in solving the given problem. The method has advantages over the traditional methods that are used for solving dynamics problems with a large number of responding modes.

Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

NASA Astrophysics Data System (ADS)

Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.

2017-11-01

Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Brody, Dorje C.

2018-04-01

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

Structure and propagation of supersonic singularities from helicoidal sources

NASA Technical Reports Server (NTRS)

Myers, M. K.; Farassat, F.

1987-01-01

An asymptotic analysis of the acoustic field radiated by a supersonic helicoidal line source distribution is given. The asymptotic results are valid in the vicinity of the Mach surfaces associated with the moving sources. Particular attention is paid to the singular nature of the field on the Mach surfaces, which the analysis describes exactly. In addition, it is found that the asymptotic approximation predicts numerical values of the pressure with considerable accuracy. Some details on the field of a single source are derived as a special case.

Plane Poiseuille Flow of a Rarefied Gas in the Presence of a Strong Gravitation

NASA Astrophysics Data System (ADS)

Doi, Toshiyuki

2010-11-01

Poiseuille flow of a rarefied gas between two horizontal planes in the presence of a strong gravitation is considered, where the gravity is so strong that the path of a molecule is curved considerably as it ascends or descends the distance of the planes. The gas behavior is studied based on the Boltzmann equation. An asymptotic analysis for a slow variation in the longitudinal direction is carried out and the problem is reduced to a spatially one dimensional problem, as was in the Poiseuille flow problem in the absence of the gravitation. The mass flow rate as well as the macroscopic variables is obtained for a wide range of the mean free path of the gas and the gravity. A numerical analysis of a two dimensional problem is also carried out and the result of the asymptotic analysis is verified.

Identifiability and Performance Analysis of Output Over-sampling Approach to Direct Closed-loop Identification

NASA Astrophysics Data System (ADS)

Sun, Lianming; Sano, Akira

Output over-sampling based closed-loop identification algorithm is investigated in this paper. Some instinct properties of the continuous stochastic noise and the plant input, output in the over-sampling approach are analyzed, and they are used to demonstrate the identifiability in the over-sampling approach and to evaluate its identification performance. Furthermore, the selection of plant model order, the asymptotic variance of estimated parameters and the asymptotic variance of frequency response of the estimated model are also explored. It shows that the over-sampling approach can guarantee the identifiability and improve the performance of closed-loop identification greatly.

Analysis of polarization in hydrogen bonded complexes: An asymptotic projection approach

NASA Astrophysics Data System (ADS)

Drici, Nedjoua

2018-03-01

The asymptotic projection technique is used to investigate the polarization effect that arises from the interaction between the relaxed, and frozen monomeric charge densities of a set of neutral and charged hydrogen bonded complexes. The AP technique based on the resolution of the original Kohn-Sham equations can give an acceptable qualitative description of the polarization effect in neutral complexes. The significant overlap of the electron densities, in charged and π-conjugated complexes, impose further development of a new functional, describing the coupling between constrained and non-constrained electron densities within the AP technique to provide an accurate representation of the polarization effect.

Breaking Megrelishvili protocol using matrix diagonalization

NASA Astrophysics Data System (ADS)

Arzaki, Muhammad; Triantoro Murdiansyah, Danang; Adi Prabowo, Satrio

2018-03-01

In this article we conduct a theoretical security analysis of Megrelishvili protocol—a linear algebra-based key agreement between two participants. We study the computational complexity of Megrelishvili vector-matrix problem (MVMP) as a mathematical problem that strongly relates to the security of Megrelishvili protocol. In particular, we investigate the asymptotic upper bounds for the running time and memory requirement of the MVMP that involves diagonalizable public matrix. Specifically, we devise a diagonalization method for solving the MVMP that is asymptotically faster than all of the previously existing algorithms. We also found an important counterintuitive result: the utilization of primitive matrix in Megrelishvili protocol makes the protocol more vulnerable to attacks.

On the ground state energy of the delta-function Fermi gas

NASA Astrophysics Data System (ADS)

Tracy, Craig A.; Widom, Harold

2016-10-01

The weak coupling asymptotics to order γ of the ground state energy of the delta-function Fermi gas, derived heuristically in the literature, is here made rigorous. Further asymptotics are in principle computable. The analysis applies to the Gaudin integral equation, a method previously used by one of the authors for the asymptotics of large Toeplitz matrices.

Estimating the change in asymptotic direction due to secular changes in the geomagnetic field

NASA Technical Reports Server (NTRS)

Flueckiger, E. O.; Smart, D. F.; Shea, M. A.; Gentile, L. C.; Bathurat, A. A.

1985-01-01

The concept of geomagnetic optics, as described by the asymptotic directions of approach, is extremely useful in the analysis of cosmic radiation data. However, when changes in cutoff occur as a result of evolution in the geomagnetic field, there are corresponding changes in the asymptotic cones of acceptance. A method is introduced of estimating the change in the asymptotic direction of approach for vertically incident cosmic ray particles from a reference set of directions at a specific epoch by considering the change in the geomagnetic cutoff.

On recent developments in marginal separation theory.

PubMed

Braun, S; Scheichl, S

2014-07-28

Thin aerofoils are prone to localized flow separation at their leading edge if subjected to moderate angles of attack α. Although 'laminar separation bubbles' at first do not significantly alter the aerofoil performance, they tend to 'burst' if α is increased further or if perturbations acting upon the flow reach a certain intensity. This then either leads to global flow separation (stall) or triggers the laminar-turbulent transition process within the boundary layer flow. This paper addresses the asymptotic analysis of the early stages of the latter phenomenon in the limit as the characteristic Reynolds number [Formula: see text], commonly referred to as marginal separation theory. A new approach based on the adjoint operator method is presented that enables the fundamental similarity laws of marginal separation theory to be derived and the analysis to be extended to higher order. Special emphasis is placed on the breakdown of the flow description, i.e. the formation of finite-time singularities (a manifestation of the bursting process), and on its resolution being based on asymptotic arguments. The passage to the subsequent triple-deck stage is described in detail, which is a prerequisite for carrying out a future numerical treatment of this stage in a proper way. Moreover, a composite asymptotic model is developed in order for the inherent ill-posedness of the Cauchy problems associated with the current flow description to be resolved.

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

Fisher waves and front roughening in a two-species invasion model with preemptive competition.

PubMed

O'Malley, L; Kozma, B; Korniss, G; Rácz, Z; Caraco, T

2006-10-01

We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits an effective power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law's exponent slightly differs from the individual-based model's result. We also study roughening of the front, using the framework of nonequilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of O(t(-2/3)).

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.

The analysis and modelling of dilatational terms in compressible turbulence

NASA Technical Reports Server (NTRS)

Sarkar, S.; Erlebacher, G.; Hussaini, M. Y.; Kreiss, H. O.

1991-01-01

It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

The analysis and modeling of dilatational terms in compressible turbulence

NASA Technical Reports Server (NTRS)

Sarkar, S.; Erlebacher, G.; Hussaini, M. Y.; Kreiss, H. O.

1989-01-01

It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

Receiver Operating Characteristic Analysis for Classification Based on Various Prior Probabilities of Groups with an Application to Breath Analysis

NASA Astrophysics Data System (ADS)

Cimermanová, K.

2009-01-01

In this paper we illustrate the influence of prior probabilities of diseases on diagnostic reasoning. For various prior probabilities of classified groups characterized by volatile organic compounds of breath profile, smokers and non-smokers, we constructed the ROC curve and the Youden index with related asymptotic pointwise confidence intervals.

Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks

NASA Astrophysics Data System (ADS)

Huo, Jingjing; Zhao, Hongyong

2016-04-01

In this paper, a fractional SIR model with birth and death rates on heterogeneous complex networks is proposed. Firstly, we obtain a threshold value R0 based on the existence of endemic equilibrium point E∗, which completely determines the dynamics of the model. Secondly, by using Lyapunov function and Kirchhoff's matrix tree theorem, the globally asymptotical stability of the disease-free equilibrium point E0 and the endemic equilibrium point E∗ of the model are investigated. That is, when R0 < 1, the disease-free equilibrium point E0 is globally asymptotically stable and the disease always dies out; when R0 > 1, the disease-free equilibrium point E0 becomes unstable and in the meantime there exists a unique endemic equilibrium point E∗, which is globally asymptotically stable and the disease is uniformly persistent. Finally, the effects of various immunization schemes are studied and compared. Numerical simulations are given to demonstrate the main results.

Plane Poiseuille flow of a rarefied gas in the presence of strong gravitation.

PubMed

Doi, Toshiyuki

2011-02-01

Plane Poiseuille flow of a rarefied gas, which flows horizontally in the presence of strong gravitation, is studied based on the Boltzmann equation. Applying the asymptotic analysis for a small variation in the flow direction [Y. Sone, Molecular Gas Dynamics (Birkhäuser, 2007)], the two-dimensional problem is reduced to a one-dimensional problem, as in the case of a Poiseuille flow in the absence of gravitation, and the solution is obtained in a semianalytical form. The reduced one-dimensional problem is solved numerically for a hard sphere molecular gas over a wide range of the gas-rarefaction degree and the gravitational strength. The presence of gravitation reduces the mass flow rate, and the effect of gravitation is significant for large Knudsen numbers. To verify the validity of the asymptotic solution, a two-dimensional problem of a flow through a long channel is directly solved numerically, and the validity of the asymptotic solution is confirmed. ©2011 American Physical Society

Asymptotic modal analysis and statistical energy analysis

NASA Technical Reports Server (NTRS)

Dowell, Earl H.

1988-01-01

Statistical Energy Analysis (SEA) is defined by considering the asymptotic limit of Classical Modal Analysis, an approach called Asymptotic Modal Analysis (AMA). The general approach is described for both structural and acoustical systems. The theoretical foundation is presented for structural systems, and experimental verification is presented for a structural plate responding to a random force. Work accomplished subsequent to the grant initiation focusses on the acoustic response of an interior cavity (i.e., an aircraft or spacecraft fuselage) with a portion of the wall vibrating in a large number of structural modes. First results were presented at the ASME Winter Annual Meeting in December, 1987, and accepted for publication in the Journal of Vibration, Acoustics, Stress and Reliability in Design. It is shown that asymptotically as the number of acoustic modes excited becomes large, the pressure level in the cavity becomes uniform except at the cavity boundaries. However, the mean square pressure at the cavity corner, edge and wall is, respectively, 8, 4, and 2 times the value in the cavity interior. Also it is shown that when the portion of the wall which is vibrating is near a cavity corner or edge, the response is significantly higher.

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.

Asymptotic analysis of noisy fitness maximization, applied to metabolism & growth

NASA Astrophysics Data System (ADS)

De Martino, Daniele; Masoero, Davide

2016-12-01

We consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modeling. In the asymptotic regime of slow diffusion, that coincides with the relevant experimental range, the resulting non-linear Fokker-Planck equation is solved for the steady state in the WKB approximation that maps it into the ground state of a quantum particle in an Airy potential plus a centrifugal term. We retrieve scaling laws for growth rate fluctuations and time response with respect to the distance from the maximum growth rate suggesting that suboptimal populations can have a faster response to perturbations.

Asymptotically stable phase synchronization revealed by autoregressive circle maps

NASA Astrophysics Data System (ADS)

Drepper, F. R.

2000-11-01

A specially designed of nonlinear time series analysis is introduced based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit estimation scheme for the potentially underlying autoregressive circle map (next phase map) guarantee the invertibility of reconstructed phase space trajectories to the original coordinates. The resulting Fourier approximated, invertibility enforcing phase space map allows us to detect conditional asymptotic stability of coupled phases. This comparatively general synchronization criterion unites two existing generalizations of the old concept and can successfully be applied, e.g., to phases obtained from electrocardiogram and airflow recordings characterizing cardiorespiratory interaction.

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.

Spreading of a surfactant-laden droplet down an inclined and pre-wetted plane - Numerics, Asymptotics and Linear Stability Analysis

NASA Astrophysics Data System (ADS)

Goddard, Joseph

2012-11-01

Non-uniformities in surfactant concentration result in a surface shear stress, known as the Marangoni stress. This stress, if sufficiently large, can influence the flow at the interface. Naturally occurring surfactants in the mammalian lung reduce the surface tension within the liquid lining the airways and help to prevent collapse of smaller airways. Premature infants produce insufficient surfactant because the lungs are under developed. Resulting Respiratory Distress Syndrome is treated by Surfactant Replacement Therapy. Motivated by this medical application we theoretically investigate a model problem involving the spreading of a drop laden with an insoluble surfactant down an inclined and pre-wetted plane. Our focus is on understanding the mechanisms behind a ``fingering'' instability observed experimentally by high-resolution numerics revealing a multi-region asymptotic structure of the spreading droplet. Approximate solutions for each region are then derived using asymptotic analysis. In particular, a quasi-steady similarity solution is obtained for the leading edge of the droplet and a linear stability analysis shows that the base state is linearly unstable to long-wavelength perturbations for all inclination angles. The Marangoni effect is shown to be behind this instability at small inclination angles. A stability criterion is derived at small wave number and it's implication in the onset of the instability will be discussed.

Asymptotic research of transonic gas flows

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Tamarova, Yuliya A.

2017-12-01

The article is dedicated to the development asymptotic theory of gas flowing at speed next to sound velocity, particularly of gas transonic flows, i.e. the flows, containing both, subsonic and supersonic areas. The main issue, when styding such flows, are nonlinearity and combined type of equations, describing the transonic flow. Based on asymptotic nonlinear equation obtained in the article, the gas transonic flows is studied, considering transverse disturbance with respect to the main flow. The asymptotic conditions at shock-wave front and conditions on the streamlined surface are found. Moreover, the equation of sound surface and asymptotic formula defining the pressure are recorded. Several exact particular solutions of such equation are given, and their application to solve several tasks of transonic aerodynamics is indicated. Specifically, the polynomial form solution describing gas axisymmetric flows in Laval nozzles with constant acceleration in direction of the nozzle's axis and flow swirling is obtained. The solutions describing the unsteady flow along the channels between spinning surfaces are presented. The asymptotic equation is obtained, describing the flow, appearing during non-separated and separated flow past, closely approximated to cylindrical one. Specific solutions are given, based on which the examples of steady flow are formed.

Numerical analysis of the asymptotic two-point boundary value solution for N-body trajectories.

NASA Technical Reports Server (NTRS)

Lancaster, J. E.; Allemann, R. A.

1972-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.

Revisiting r > g-The asymptotic dynamics of wealth inequality

NASA Astrophysics Data System (ADS)

Berman, Yonatan; Shapira, Yoash

2017-02-01

Studying the underlying mechanisms of wealth inequality dynamics is essential for its understanding and for policy aiming to regulate its level. We apply a heterogeneous non-interacting agent-based modeling approach, solved using iterated maps to model the dynamics of wealth inequality based on 3 parameters-the economic output growth rate g, the capital value change rate a and the personal savings rate s and show that for a < g the wealth distribution reaches an asymptotic shape and becomes close to the income distribution. If a > g, the wealth distribution constantly becomes more and more inegalitarian. We also show that when a < g, wealth is asymptotically accumulated at the same rate as the economic output, which also implies that the wealth-disposable income ratio asymptotically converges to s /(g - a) .

Energy in higher-dimensional spacetimes

NASA Astrophysics Data System (ADS)

Barzegar, Hamed; Chruściel, Piotr T.; Hörzinger, Michael

2017-12-01

We derive expressions for the total Hamiltonian energy of gravitating systems in higher-dimensional theories in terms of the Riemann tensor, allowing a cosmological constant Λ ∈R . Our analysis covers asymptotically anti-de Sitter spacetimes, asymptotically flat spacetimes, as well as Kaluza-Klein asymptotically flat spacetimes. We show that the Komar mass equals the Arnowitt-Deser-Misner (ADM) mass in stationary asymptotically flat spacetimes in all dimensions, generalizing the four-dimensional result of Beig, and that this is no longer true with Kaluza-Klein asymptotics. We show that the Hamiltonian mass does not necessarily coincide with the ADM mass in Kaluza-Klein asymptotically flat spacetimes, and that the Witten positivity argument provides a lower bound for the Hamiltonian mass—and not for the ADM mass—in terms of the electric charge. We illustrate our results on the five-dimensional Rasheed metrics, which we study in some detail, pointing out restrictions that arise from the requirement of regularity, which have gone seemingly unnoticed so far in the literature.

Lyapunov function-based control laws for revolute robot arms - Tracking control, robustness, and adaptive control

NASA Technical Reports Server (NTRS)

Wen, John T.; Kreutz-Delgado, Kenneth; Bayard, David S.

1992-01-01

A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to a recently proposed energy-like Liapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates (i.e., certainty equivalence adaptation).

A new class of energy based control laws for revolute robot arms - Tracking control, robustness enhancement and adaptive control

NASA Technical Reports Server (NTRS)

Wen, John T.; Kreutz, Kenneth; Bayard, David S.

1988-01-01

A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.

Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay.

PubMed

Velmurugan, G; Rakkiyappan, R; Vembarasan, V; Cao, Jinde; Alsaedi, Ahmed

2017-02-01

As we know, the notion of dissipativity is an important dynamical property of neural networks. Thus, the analysis of dissipativity of neural networks with time delay is becoming more and more important in the research field. In this paper, the authors establish a class of fractional-order complex-valued neural networks (FCVNNs) with time delay, and intensively study the problem of dissipativity, as well as global asymptotic stability of the considered FCVNNs with time delay. Based on the fractional Halanay inequality and suitable Lyapunov functions, some new sufficient conditions are obtained that guarantee the dissipativity of FCVNNs with time delay. Moreover, some sufficient conditions are derived in order to ensure the global asymptotic stability of the addressed FCVNNs with time delay. Finally, two numerical simulations are posed to ensure that the attention of our main results are valuable. Copyright © 2016 Elsevier Ltd. All rights reserved.

Asymptotic modal analysis of a rectangular acoustic cavity and characterization of its intensification zones

NASA Technical Reports Server (NTRS)

Peretti, Linda F.; Dowell, Earl H.

1989-01-01

Asymptotic modal analysis (AMA) is used to study a rectangular cavity with a flexible vibrating portion on one wall and five rigid walls. The agreement between mean square pressure levels of the cavity interior calculated from classical modal analysis and from the AMA method improved as the number of responding modes increased. It is shown that intensification effects were due to both the excitation location and the response location.

Asymptotic symmetries and geometry on the boundary in the first order formalism

NASA Astrophysics Data System (ADS)

Korovin, Yegor

2018-03-01

Proper understanding of the geometry on the boundary of a spacetime is a critical step on the way to extending holography to spaces with non-AdS asymptotics. In general the boundary cannot be described in terms of the Riemannian geometry and the first order formalism is more appropriate as we show. We analyze the asymptotic symmetries in the first order formalism for large classes of theories on AdS, Lifshitz or flat space. In all cases the asymptotic symmetry algebra is realized on the first order variables as a gauged symmetry algebra. First order formalism geometrizes and simplifies the analysis. We apply our framework to the issue of scale versus conformal invariance in AdS/CFT and obtain new perspective on the structure of asymptotic expansions for AdS and flat spaces.

Analysis of Point Based Image Registration Errors With Applications in Single Molecule Microscopy

PubMed Central

Cohen, E. A. K.; Ober, R. J.

2014-01-01

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data. PMID:24634573

Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay

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

Brantley, P S

2006-09-27

We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinarymore » differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.« less

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.

Cloud Properties Derived from Surface-Based Near-Infrared Spectral Transmission

NASA Technical Reports Server (NTRS)

Pilewskie, Peter; Twomey, S.; Gore, Warren J. Y. (Technical Monitor)

1996-01-01

Surface based near-infrared cloud spectral transmission measurements from a recent precipitation/cloud physics field study are used to determine cloud physical properties and relate them to other remote sensing and in situ measurements. Asymptotic formulae provide an effective means of closely approximating the qualitative and quantitative behavior of transmission computed by more laborious detailed methods. Relationships derived from asymptotic formulae are applied to measured transmission spectra to test objectively the internal consistency of data sets acquired during the field program and they confirmed the quality of the measurements. These relationships appear to be very useful in themselves, not merely as a quality control measure, but also a potentially valuable remote-sensing technique in its own right. Additional benefits from this analysis have been the separation of condensed water (cloud) transmission and water vapor transmission and the development of a method to derive cloud liquid water content.

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 exact computational method for performance analysis of sequential test algorithms for detecting network intrusions

NASA Astrophysics Data System (ADS)

Chen, Xinjia; Lacy, Fred; Carriere, Patrick

2015-05-01

Sequential test algorithms are playing increasingly important roles for quick detecting network intrusions such as portscanners. In view of the fact that such algorithms are usually analyzed based on intuitive approximation or asymptotic analysis, we develop an exact computational method for the performance analysis of such algorithms. Our method can be used to calculate the probability of false alarm and average detection time up to arbitrarily pre-specified accuracy.

Asymptotic analysis of the density of states in random matrix models associated with a slowly decaying weight

NASA Astrophysics Data System (ADS)

Kuijlaars, A. B. J.

2001-08-01

The asymptotic behavior of polynomials that are orthogonal with respect to a slowly decaying weight is very different from the asymptotic behavior of polynomials that are orthogonal with respect to a Freud-type weight. While the latter has been extensively studied, much less is known about the former. Following an earlier investigation into the zero behavior, we study here the asymptotics of the density of states in a unitary ensemble of random matrices with a slowly decaying weight. This measure is also naturally connected with the orthogonal polynomials. It is shown that, after suitable rescaling, the weak limit is the same as the weak limit of the rescaled zeros.

Asymptotic stability and instability of large-scale systems. [using vector Liapunov functions

NASA Technical Reports Server (NTRS)

Grujic, L. T.; Siljak, D. D.

1973-01-01

The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations.

Improved Filon-type asymptotic methods for highly oscillatory differential equations with multiple time scales

NASA Astrophysics Data System (ADS)

Wang, Bin; Wu, Xinyuan

2014-11-01

In this paper we consider multi-frequency highly oscillatory second-order differential equations x″ (t) + Mx (t) = f (t , x (t) ,x‧ (t)) where high-frequency oscillations are generated by the linear part Mx (t), and M is positive semi-definite (not necessarily nonsingular). It is known that Filon-type methods are effective approach to numerically solving highly oscillatory problems. Unfortunately, however, existing Filon-type asymptotic methods fail to apply to the highly oscillatory second-order differential equations when M is singular. We study and propose an efficient improvement on the existing Filon-type asymptotic methods, so that the improved Filon-type asymptotic methods can be able to numerically solving this class of multi-frequency highly oscillatory systems with a singular matrix M. The improved Filon-type asymptotic methods are designed by combining Filon-type methods with the asymptotic methods based on the variation-of-constants formula. We also present one efficient and practical improved Filon-type asymptotic method which can be performed at lower cost. Accompanying numerical results show the remarkable efficiency.

Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method

NASA Astrophysics Data System (ADS)

Bekhoucha, F.; Rechak, S.; Cadou, J. M.

2016-12-01

In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.

Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations

PubMed Central

Ceyhan, Elvan

2014-01-01

We consider two types of spatial symmetry, namely, symmetry in the mixed or shared nearest neighbor (NN) structures. We use Pielou's and Dixon's symmetry tests which are defined using contingency tables based on the NN relationships between the data points. We generalize these tests to multiple classes and demonstrate that both the asymptotic and exact versions of Pielou's first type of symmetry test are extremely conservative in rejecting symmetry in the mixed NN structure and hence should be avoided or only the Monte Carlo randomized version should be used. Under RL, we derive the asymptotic distribution for Dixon's symmetry test and also observe that the usual independence test seems to be appropriate for Pielou's second type of test. Moreover, we apply variants of Fisher's exact test on the shared NN contingency table for Pielou's second test and determine the most appropriate version for our setting. We also consider pairwise and one-versus-rest type tests in post hoc analysis after a significant overall symmetry test. We investigate the asymptotic properties of the tests, prove their consistency under appropriate null hypotheses, and investigate finite sample performance of them by extensive Monte Carlo simulations. The methods are illustrated on a real-life ecological data set. PMID:24605061

An Asymptotically-Optimal Sampling-Based Algorithm for Bi-directional Motion Planning

PubMed Central

Starek, Joseph A.; Gomez, Javier V.; Schmerling, Edward; Janson, Lucas; Moreno, Luis; Pavone, Marco

2015-01-01

Bi-directional search is a widely used strategy to increase the success and convergence rates of sampling-based motion planning algorithms. Yet, few results are available that merge both bi-directional search and asymptotic optimality into existing optimal planners, such as PRM*, RRT*, and FMT*. The objective of this paper is to fill this gap. Specifically, this paper presents a bi-directional, sampling-based, asymptotically-optimal algorithm named Bi-directional FMT* (BFMT*) that extends the Fast Marching Tree (FMT*) algorithm to bidirectional search while preserving its key properties, chiefly lazy search and asymptotic optimality through convergence in probability. BFMT* performs a two-source, lazy dynamic programming recursion over a set of randomly-drawn samples, correspondingly generating two search trees: one in cost-to-come space from the initial configuration and another in cost-to-go space from the goal configuration. Numerical experiments illustrate the advantages of BFMT* over its unidirectional counterpart, as well as a number of other state-of-the-art planners. PMID:27004130

Nonminimal hints for asymptotic safety

NASA Astrophysics Data System (ADS)

Eichhorn, Astrid; Lippoldt, Stefan; Skrinjar, Vedran

2018-01-01

In the asymptotic-safety scenario for gravity, nonzero interactions are present in the ultraviolet. This property should also percolate into the matter sector. Symmetry-based arguments suggest that nonminimal derivative interactions of scalars with curvature tensors should therefore be present in the ultraviolet regime. We perform a nonminimal test of the viability of the asymptotic-safety scenario by working in a truncation of the renormalization group flow, where we discover the existence of an interacting fixed point for a corresponding nonminimal coupling. The back-coupling of such nonminimal interactions could in turn destroy the asymptotically safe fixed point in the gravity sector. As a key finding, we observe nontrivial indications of stability of the fixed-point properties under the impact of nonminimal derivative interactions, further strengthening the case for asymptotic safety in gravity-matter systems.

Counterflow diffusion flames: effects of thermal expansion and non-unity Lewis numbers

NASA Astrophysics Data System (ADS)

Koundinyan, Sushilkumar P.; Matalon, Moshe; Stewart, D. Scott

2018-05-01

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame-flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier-Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the 'exact' numerical integration of the governing equations, comparing predictions of the various flame properties.

On the multiple imputation variance estimator for control-based and delta-adjusted pattern mixture models.

PubMed

Tang, Yongqiang

2017-12-01

Control-based pattern mixture models (PMM) and delta-adjusted PMMs are commonly used as sensitivity analyses in clinical trials with non-ignorable dropout. These PMMs assume that the statistical behavior of outcomes varies by pattern in the experimental arm in the imputation procedure, but the imputed data are typically analyzed by a standard method such as the primary analysis model. In the multiple imputation (MI) inference, Rubin's variance estimator is generally biased when the imputation and analysis models are uncongenial. One objective of the article is to quantify the bias of Rubin's variance estimator in the control-based and delta-adjusted PMMs for longitudinal continuous outcomes. These PMMs assume the same observed data distribution as the mixed effects model for repeated measures (MMRM). We derive analytic expressions for the MI treatment effect estimator and the associated Rubin's variance in these PMMs and MMRM as functions of the maximum likelihood estimator from the MMRM analysis and the observed proportion of subjects in each dropout pattern when the number of imputations is infinite. The asymptotic bias is generally small or negligible in the delta-adjusted PMM, but can be sizable in the control-based PMM. This indicates that the inference based on Rubin's rule is approximately valid in the delta-adjusted PMM. A simple variance estimator is proposed to ensure asymptotically valid MI inferences in these PMMs, and compared with the bootstrap variance. The proposed method is illustrated by the analysis of an antidepressant trial, and its performance is further evaluated via a simulation study. © 2017, The International Biometric Society.

Sustainability, collapse and oscillations in a simple World-Earth model

NASA Astrophysics Data System (ADS)

Nitzbon, Jan; Heitzig, Jobst; Parlitz, Ulrich

2017-07-01

The Anthropocene is characterized by close interdependencies between the natural Earth system and the global human society, posing novel challenges to model development. Here we present a conceptual model describing the long-term co-evolution of natural and socio-economic subsystems of Earth. While the climate is represented via a global carbon cycle, we use economic concepts to model socio-metabolic flows of biomass and fossil fuels between nature and society. A well-being-dependent parametrization of fertility and mortality governs human population dynamics. Our analysis focuses on assessing possible asymptotic states of the Earth system for a qualitative understanding of its complex dynamics rather than quantitative predictions. Low dimension and simple equations enable a parameter-space analysis allowing us to identify preconditions of several asymptotic states and hence fates of humanity and planet. These include a sustainable co-evolution of nature and society, a global collapse and everlasting oscillations. We consider different scenarios corresponding to different socio-cultural stages of human history. The necessity of accounting for the ‘human factor’ in Earth system models is highlighted by the finding that carbon stocks during the past centuries evolved opposing to what would ‘naturally’ be expected on a planet without humans. The intensity of biomass use and the contribution of ecosystem services to human well-being are found to be crucial determinants of the asymptotic state in a (pre-industrial) biomass-only scenario without capital accumulation. The capitalistic, fossil-based scenario reveals that trajectories with fundamentally different asymptotic states might still be almost indistinguishable during even a centuries-long transient phase. Given current human population levels, our study also supports the claim that besides reducing the global demand for energy, only the extensive use of renewable energies may pave the way into a sustainable future.

Large-Signal Lyapunov-Based Stability Analysis of DC/AC Inverters and Inverter-Based Microgrids

NASA Astrophysics Data System (ADS)

Kabalan, Mahmoud

Microgrid stability studies have been largely based on small-signal linearization techniques. However, the validity and magnitude of the linearization domain is limited to small perturbations. Thus, there is a need to examine microgrids with large-signal nonlinear techniques to fully understand and examine their stability. Large-signal stability analysis can be accomplished by Lyapunov-based mathematical methods. These Lyapunov methods estimate the domain of asymptotic stability of the studied system. A survey of Lyapunov-based large-signal stability studies showed that few large-signal studies have been completed on either individual systems (dc/ac inverters, dc/dc rectifiers, etc.) or microgrids. The research presented in this thesis addresses the large-signal stability of droop-controlled dc/ac inverters and inverter-based microgrids. Dc/ac power electronic inverters allow microgrids to be technically feasible. Thus, as a prelude to examining the stability of microgrids, the research presented in Chapter 3 analyzes the stability of inverters. First, the 13 th order large-signal nonlinear model of a droop-controlled dc/ac inverter connected to an infinite bus is presented. The singular perturbation method is used to decompose the nonlinear model into 11th, 9th, 7th, 5th, 3rd and 1st order models. Each model ignores certain control or structural components of the full order model. The aim of the study is to understand the accuracy and validity of the reduced order models in replicating the performance of the full order nonlinear model. The performance of each model is studied in three different areas: time domain simulations, Lyapunov's indirect method and domain of attraction estimation. The work aims to present the best model to use in each of the three domains of study. Results show that certain reduced order models are capable of accurately reproducing the performance of the full order model while others can be used to gain insights into those three areas of study. This will enable future studies to save computational effort and produce the most accurate results according to the needs of the study being performed. Moreover, the effect of grid (line) impedance on the accuracy of droop control is explored using the 5th order model. Simulation results show that traditional droop control is valid up to R/X line impedance value of 2. Furthermore, the 3rd order nonlinear model improves the currently available inverter-infinite bus models by accounting for grid impedance, active power-frequency droop and reactive power-voltage droop. Results show the 3rd order model's ability to account for voltage and reactive power changes during a transient event. Finally, the large-signal Lyapunov-based stability analysis is completed for a 3 bus microgrid system (made up of 2 inverters and 1 linear load). The thesis provides a systematic state space large-signal nonlinear mathematical modeling method of inverter-based microgrids. The inverters include the dc-side dynamics associated with dc sources. The mathematical model is then used to estimate the domain of asymptotic stability of the 3 bus microgrid. The three bus microgrid system was used as a case study to highlight the design and optimization capability of a large-signal-based approach. The study explores the effect of system component sizing, load transient and generation variations on the asymptotic stability of the microgrid. Essentially, this advancement gives microgrid designers and engineers the ability to manipulate the domain of asymptotic stability depending on performance requirements. Especially important, this research was able to couple the domain of asymptotic stability of the ac microgrid with that of the dc side voltage source. Time domain simulations were used to demonstrate the mathematical nonlinear analysis results.

Use of asymptotic analysis of the large activation-energy limit to compare graphical methods of treating thermogravimetry data

Treesearch

A. Broido; F.A. Williams

1973-01-01

An earIier numerical analysis showed that the second approximate method of Horotitz and Metzger can be rendered exceedingly accurate for reduction of thermo-gravimetry data. It is demonstrated here that this result can be justified on the basis of an asymptotic expansion with a nondimensional activation energy as the large parameter. The order of magnitude of the error...

On the transition towards slow manifold in shallow-water and 3D Euler equations in a rotating frame

NASA Technical Reports Server (NTRS)

Mahalov, A.

1994-01-01

The long-time, asymptotic state of rotating homogeneous shallow-water equations is investigated. Our analysis is based on long-time averaged rotating shallow-water equations describing interactions of large-scale, horizontal, two-dimensional motions with surface inertial-gravity waves field for a shallow, uniformly rotating fluid layer. These equations are obtained in two steps: first by introducing a Poincare/Kelvin linear propagator directly into classical shallow-water equations, then by averaging. The averaged equations describe interaction of wave fields with large-scale motions on time scales long compared to the time scale 1/f(sub o) introduced by rotation (f(sub o)/2-angular velocity of background rotation). The present analysis is similar to the one presented by Waleffe (1991) for 3D Euler equations in a rotating frame. However, since three-wave interactions in rotating shallow-water equations are forbidden, the final equations describing the asymptotic state are simplified considerably. Special emphasis is given to a new conservation law found in the asymptotic state and decoupling of the dynamics of the divergence free part of the velocity field. The possible rising of a decoupled dynamics in the asymptotic state is also investigated for homogeneous turbulence subjected to a background rotation. In our analysis we use long-time expansion, where the velocity field is decomposed into the 'slow manifold' part (the manifold which is unaffected by the linear 'rapid' effects of rotation or the inertial waves) and a formal 3D disturbance. We derive the physical space version of the long-time averaged equations and consider an invariant, basis-free derivation. This formulation can be used to generalize Waleffe's (1991) helical decomposition to viscous inhomogeneous flows (e.g. problems in cylindrical geometry with no-slip boundary conditions on the cylinder surface and homogeneous in the vertical direction).

Phase structure of completely asymptotically free SU(Nc) models with quarks and scalar quarks

NASA Astrophysics Data System (ADS)

Hansen, F. F.; Janowski, T.; Langæble, K.; Mann, R. B.; Sannino, F.; Steele, T. G.; Wang, Z. W.

2018-03-01

We determine the phase diagram of completely asymptotically free SU (Nc) gauge theories featuring Ns complex scalars and Nf Dirac quarks transforming according to the fundamental representation of the gauge group. The analysis is performed at the maximum known order in perturbation theory. We unveil a very rich dynamics and associated phase structure. Intriguingly, we discover that the completely asymptotically free conditions guarantee that the infrared dynamics displays long-distance conformality, and in a regime when perturbation theory is applicable. We conclude our analysis by determining the quantum corrected potential of the model and summarizing the possible patterns of radiative symmetry breaking. These models are of potential phenomenological interest as either elementary or composite ultraviolet finite extensions of the standard model.

Stokes phenomena in discrete Painlevé I.

PubMed

Joshi, N; Lustri, C J

2015-05-08

In this study, we consider the asymptotic behaviour of the first discrete Painlevé equation in the limit as the independent variable becomes large. Using an asymptotic series expansion, we identify two types of solutions which are pole-free within some sector of the complex plane containing the positive real axis. Using exponential asymptotic techniques, we determine Stokes phenomena effects present within these solutions, and hence the regions in which the asymptotic series expression is valid. From a careful analysis of the switching behaviour across Stokes lines, we find that the first type of solution is uniquely defined, while the second type contains two free parameters, and that the region of validity may be extended for appropriate choice of these parameters.

Expansion of a Rarefied Gas Cloud in a Vacuum: Asymptotic Treatment

NASA Astrophysics Data System (ADS)

Zhuk, V. I.

2018-02-01

The unsteady expansion of a rarefied gas of finite mass in an unlimited space is studied. The long-time asymptotic behavior of the solution is examined at Knudsen numbers tending to zero. An asymptotic analysis shows that, in the limit of small Knudsen numbers, the behavior of the macroscopic parameters of the expanding gas cloud at long times (i.e., for small density values) has nothing to do with the free-molecular or continuum flow regimes. This conclusion is unexpected and not obvious, but follows from a uniformly suitable solution constructed by applying the method of outer and inner asymptotic expansions. In particular, the unusual temperature behavior is of interest as applied to remote sensing of rocket exhaust plumes.

Some applications of categorical data analysis to epidemiological studies.

PubMed Central

Grizzle, J E; Koch, G G

1979-01-01

Several examples of categorized data from epidemiological studies are analyzed to illustrate that more informative analysis than tests of independence can be performed by fitting models. All of the analyses fit into a unified conceptual framework that can be performed by weighted least squares. The methods presented show how to calculate point estimate of parameters, asymptotic variances, and asymptotically valid chi 2 tests. The examples presented are analysis of relative risks estimated from several 2 x 2 tables, analysis of selected features of life tables, construction of synthetic life tables from cross-sectional studies, and analysis of dose-response curves. PMID:540590

Asymptotic approximation method of force reconstruction: Application and analysis of stationary random forces

NASA Astrophysics Data System (ADS)

Sanchez, J.

2018-06-01

In this paper, the application and analysis of the asymptotic approximation method to a single degree-of-freedom has recently been produced. The original concepts are summarized, and the necessary probabilistic concepts are developed and applied to single degree-of-freedom systems. Then, these concepts are united, and the theoretical and computational models are developed. To determine the viability of the proposed method in a probabilistic context, numerical experiments are conducted, and consist of a frequency analysis, analysis of the effects of measurement noise, and a statistical analysis. In addition, two examples are presented and discussed.

An asymptotic preserving multidimensional ALE method for a system of two compressible flows coupled with friction

NASA Astrophysics Data System (ADS)

Del Pino, S.; Labourasse, E.; Morel, G.

2018-06-01

We present a multidimensional asymptotic preserving scheme for the approximation of a mixture of compressible flows. Fluids are modelled by two Euler systems of equations coupled with a friction term. The asymptotic preserving property is mandatory for this kind of model, to derive a scheme that behaves well in all regimes (i.e. whatever the friction parameter value is). The method we propose is defined in ALE coordinates, using a Lagrange plus remap approach. This imposes a multidimensional definition and analysis of the scheme.

On the asymptotic equivalence between differential Hebbian and temporal difference learning.

PubMed

Kolodziejski, Christoph; Porr, Bernd; Wörgötter, Florentin

2009-04-01

In this theoretical contribution, we provide mathematical proof that two of the most important classes of network learning-correlation-based differential Hebbian learning and reward-based temporal difference learning-are asymptotically equivalent when timing the learning with a modulatory signal. This opens the opportunity to consistently reformulate most of the abstract reinforcement learning framework from a correlation-based perspective more closely related to the biophysics of neurons.

[Formula: see text]-convergence, complete convergence, and weak laws of large numbers for asymptotically negatively associated random vectors with values in [Formula: see text].

PubMed

Ko, Mi-Hwa

2018-01-01

In this paper, based on the Rosenthal-type inequality for asymptotically negatively associated random vectors with values in [Formula: see text], we establish results on [Formula: see text]-convergence and complete convergence of the maximums of partial sums are established. We also obtain weak laws of large numbers for coordinatewise asymptotically negatively associated random vectors with values in [Formula: see text].

Transactions of the Army Conference on Applied Mathematics and Computing (1st) Held at Washington, DC on 9-11 May 1983

DTIC Science & Technology

1984-02-01

I . . . . . . An Introduction to Geometric Programming Patrick D. Allen and David W. Baker . . . . . . , . . . . . . . Space and Time...Zarwyn, US-Army Electronics R & D Comhiand GEOMETRIC PROGRAMING SPACE AND TIFFE ANALYSIS IN DYNAMIC PROGRAMING ALGORITHMS Renne..tf Stizti, AkeanXa...physical and parameter space can be connected by asymptotic matching. The purpose of the asymptotic analysis is to define the simplest problems

Asymptotic analysis of online algorithms and improved scheme for the flow shop scheduling problem with release dates

NASA Astrophysics Data System (ADS)

Bai, Danyu

2015-08-01

This paper discusses the flow shop scheduling problem to minimise the total quadratic completion time (TQCT) with release dates in offline and online environments. For this NP-hard problem, the investigation is focused on the performance of two online algorithms based on the Shortest Processing Time among Available jobs rule. Theoretical results indicate the asymptotic optimality of the algorithms as the problem scale is sufficiently large. To further enhance the quality of the original solutions, the improvement scheme is provided for these algorithms. A new lower bound with performance guarantee is provided, and computational experiments show the effectiveness of these heuristics. Moreover, several results of the single-machine TQCT problem with release dates are also obtained for the deduction of the main theorem.

A CLT on the SNR of Diagonally Loaded MVDR Filters

NASA Astrophysics Data System (ADS)

Rubio, Francisco; Mestre, Xavier; Hachem, Walid

2012-08-01

This paper studies the fluctuations of the signal-to-noise ratio (SNR) of minimum variance distorsionless response (MVDR) filters implementing diagonal loading in the estimation of the covariance matrix. Previous results in the signal processing literature are generalized and extended by considering both spatially as well as temporarily correlated samples. Specifically, a central limit theorem (CLT) is established for the fluctuations of the SNR of the diagonally loaded MVDR filter, under both supervised and unsupervised training settings in adaptive filtering applications. Our second-order analysis is based on the Nash-Poincar\\'e inequality and the integration by parts formula for Gaussian functionals, as well as classical tools from statistical asymptotic theory. Numerical evaluations validating the accuracy of the CLT confirm the asymptotic Gaussianity of the fluctuations of the SNR of the MVDR filter.

Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.

PubMed

Chen, Boshan; Chen, Jiejie

2015-08-01

We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved.

A numerical study of attraction/repulsion collective behavior models: 3D particle analyses and 1D kinetic simulations

NASA Astrophysics Data System (ADS)

Vecil, Francesco; Lafitte, Pauline; Rosado Linares, Jesús

2013-10-01

We study at particle and kinetic level a collective behavior model based on three phenomena: self-propulsion, friction (Rayleigh effect) and an attractive/repulsive (Morse) potential rescaled so that the total mass of the system remains constant independently of the number of particles N. In the first part of the paper, we introduce the particle model: the agents are numbered and described by their position and velocity. We identify five parameters that govern the possible asymptotic states for this system (clumps, spheres, dispersion, mills, rigid-body rotation, flocks) and perform a numerical analysis on the 3D setting. Then, in the second part of the paper, we describe the kinetic system derived as the limit from the particle model as N tends to infinity; we propose, in 1D, a numerical scheme for the simulations, and perform a numerical analysis devoted to trying to recover asymptotically patterns similar to those emerging for the equivalent particle systems, when particles originally evolved on a circle.

Directions for model building from asymptotic safety

NASA Astrophysics Data System (ADS)

Bond, Andrew D.; Hiller, Gudrun; Kowalska, Kamila; Litim, Daniel F.

2017-08-01

Building on recent advances in the understanding of gauge-Yukawa theories we explore possibilities to UV-complete the Standard Model in an asymptotically safe manner. Minimal extensions are based on a large flavor sector of additional fermions coupled to a scalar singlet matrix field. We find that asymptotic safety requires fermions in higher representations of SU(3) C × SU(2) L . Possible signatures at colliders are worked out and include R-hadron searches, diboson signatures and the evolution of the strong and weak coupling constants.

Quantum walks with an anisotropic coin II: scattering theory

NASA Astrophysics Data System (ADS)

Richard, S.; Suzuki, A.; de Aldecoa, R. Tiedra

2018-05-01

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of unitary operators in a two-Hilbert spaces setting, which is of independent interest.

A Class of Factor Analysis Estimation Procedures with Common Asymptotic Sampling Properties

ERIC Educational Resources Information Center

Swain, A. J.

1975-01-01

Considers a class of estimation procedures for the factor model. The procedures are shown to yield estimates possessing the same asymptotic sampling properties as those from estimation by maximum likelihood or generalized last squares, both special members of the class. General expressions for the derivatives needed for Newton-Raphson…

Universal properties from a local geometric structure of a Killing horizon

NASA Astrophysics Data System (ADS)

Koga, Jun-ichirou

2007-06-01

We consider universal properties that arise from a local geometric structure of a Killing horizon, and analyse whether such universal properties give rise to degeneracy of classical configurations. We first introduce a non-perturbative definition of such a local geometric structure, which we call an asymptotic Killing horizon. It is then shown that infinitely many asymptotic Killing horizons reside on a common null hypersurface, once there exists one asymptotic Killing horizon, which is thus considered as degeneracy. In order to see how this degeneracy is physically meaningful, we analyse also the acceleration of the orbits of the vector that generates an asymptotic Killing horizon. It is shown that there exists the diff(S1) or diff(R1) sub-algebra on an asymptotic Killing horizon universally, which is picked out naturally, based on the behaviour of the acceleration. We argue that the discrepancy between string theory and the Euclidean approach in the entropy of an extreme black hole may be resolved, if the microscopic states responsible for black hole thermodynamics are connected with asymptotic Killing horizons.

Exact and Monte carlo resampling procedures for the Wilcoxon-Mann-Whitney and Kruskal-Wallis tests.

PubMed

Berry, K J; Mielke, P W

2000-12-01

Exact and Monte Carlo resampling FORTRAN programs are described for the Wilcoxon-Mann-Whitney rank sum test and the Kruskal-Wallis one-way analysis of variance for ranks test. The program algorithms compensate for tied values and do not depend on asymptotic approximations for probability values, unlike most algorithms contained in PC-based statistical software packages.

Accuracy of latent-variable estimation in Bayesian semi-supervised learning.

PubMed

Yamazaki, Keisuke

2015-09-01

Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying data-generation process, respectively. Unsupervised learning tasks, such as cluster analysis, are regarded as estimations of latent variables based on the observable ones. The estimation of latent variables in semi-supervised learning, where some labels are observed, will be more precise than that in unsupervised, and one of the concerns is to clarify the effect of the labeled data. However, there has not been sufficient theoretical analysis of the accuracy of the estimation of latent variables. In a previous study, a distribution-based error function was formulated, and its asymptotic form was calculated for unsupervised learning with generative models. It has been shown that, for the estimation of latent variables, the Bayes method is more accurate than the maximum-likelihood method. The present paper reveals the asymptotic forms of the error function in Bayesian semi-supervised learning for both discriminative and generative models. The results show that the generative model, which uses all of the given data, performs better when the model is well specified. Copyright © 2015 Elsevier Ltd. All rights reserved.

Comparing methods for modelling spreading cell fronts.

PubMed

Markham, Deborah C; Simpson, Matthew J; Maini, Philip K; Gaffney, Eamonn A; Baker, Ruth E

2014-07-21

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and the asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods: (i) mean-field, (ii) pair-wise, and (iii) one-hole approximations. We discuss the performance of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made. Copyright © 2014 Elsevier Ltd. All rights reserved.

Properties of one-dimensional anharmonic lattice solitons

NASA Astrophysics Data System (ADS)

Szeftel, Jacob; Laurent-Gengoux, Pascal; Ilisca, Ernest; Hebbache, Mohamed

2000-12-01

The existence of bell- and kink-shaped solitons moving at constant velocity while keeping a permanent profile is studied in infinite periodic monoatomic chains of arbitrary anharmonicity by taking advantage of the equation of motion being integrable with respect to solitons. A second-order, non-linear differential equation involving advanced and retarded terms must be solved, which is done by implementing a scheme based on the finite element and Newton's methods. If the potential has a harmonic limit, the asymptotic time-decay behaves exponentially and there is a dispersion relation between propagation velocity and decay time. Inversely if the potential has no harmonic limit, the asymptotic regime shows up either as a power-law or faster than exponential. Excellent agreement is achieved with Toda's model. Illustrative examples are also given for the Fermi-Pasta-Ulam and sine-Gordon potentials. Owing to integrability an effective one-body potential is worked out in each case. Lattice and continuum solitons differ markedly from one another as regards the amplitude versus propagation velocity relationship and the asymptotic time behavior. The relevance of the linear stability analysis when applied to solitons propagating in an infinite crystal is questioned. The reasons preventing solitons from arising in a diatomic lattice are discussed.

A Global Existence and Uniqueness Theorem for a Riccati Equation.

DTIC Science & Technology

1981-01-01

made to an asymptotic stochastic analysis of a noisy duel problem. / DTICELECTE[I JUN 2 3 19820 !--i *This w paper was partially supported by AFOSR Grant...of these results is made to an asymptotic stochastic analysis of I ntssy duel problem. DD ,OR 1473 EDITION O, 1.OV 1SIS OSOLTE UNCLASTFIED SCUJRITY...motivated by the approach used in [3] and [6] to analyze the equal-accuracy noisy duel problem for two players having finite unequal units of ammunition

Dynamical analysis for a scalar-tensor model with kinetic and nonminimal couplings

NASA Astrophysics Data System (ADS)

Granda, L. N.; Jimenez, D. F.

We study the autonomous system for a scalar-tensor model of dark energy with nonminimal coupling to curvature and nonminimal kinetic coupling to the Einstein tensor. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential were considered: power-law and exponential functions of the scalar field. For power-law couplings, the restrictions on stable quintessence and phantom solutions lead to asymptotic freedom regime for the gravitational interaction. For the exponential functions, the stable quintessence, phantom or de Sitter solutions allow asymptotic behaviors where the effective Newtonian coupling can reach either the asymptotic freedom regime or constant value. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation dominated phases can also be described.

Idiopathic Pulmonary Fibrosis: Data-driven Textural Analysis of Extent of Fibrosis at Baseline and 15-Month Follow-up.

PubMed

Humphries, Stephen M; Yagihashi, Kunihiro; Huckleberry, Jason; Rho, Byung-Hak; Schroeder, Joyce D; Strand, Matthew; Schwarz, Marvin I; Flaherty, Kevin R; Kazerooni, Ella A; van Beek, Edwin J R; Lynch, David A

2017-10-01

Purpose To evaluate associations between pulmonary function and both quantitative analysis and visual assessment of thin-section computed tomography (CT) images at baseline and at 15-month follow-up in subjects with idiopathic pulmonary fibrosis (IPF). Materials and Methods This retrospective analysis of preexisting anonymized data, collected prospectively between 2007 and 2013 in a HIPAA-compliant study, was exempt from additional institutional review board approval. The extent of lung fibrosis at baseline inspiratory chest CT in 280 subjects enrolled in the IPF Network was evaluated. Visual analysis was performed by using a semiquantitative scoring system. Computer-based quantitative analysis included CT histogram-based measurements and a data-driven textural analysis (DTA). Follow-up CT images in 72 of these subjects were also analyzed. Univariate comparisons were performed by using Spearman rank correlation. Multivariate and longitudinal analyses were performed by using a linear mixed model approach, in which models were compared by using asymptotic χ 2 tests. Results At baseline, all CT-derived measures showed moderate significant correlation (P < .001) with pulmonary function. At follow-up CT, changes in DTA scores showed significant correlation with changes in both forced vital capacity percentage predicted (ρ = -0.41, P < .001) and diffusing capacity for carbon monoxide percentage predicted (ρ = -0.40, P < .001). Asymptotic χ 2 tests showed that inclusion of DTA score significantly improved fit of both baseline and longitudinal linear mixed models in the prediction of pulmonary function (P < .001 for both). Conclusion When compared with semiquantitative visual assessment and CT histogram-based measurements, DTA score provides additional information that can be used to predict diminished function. Automatic quantification of lung fibrosis at CT yields an index of severity that correlates with visual assessment and functional change in subjects with IPF. © RSNA, 2017.

Revisiting tests for neglected nonlinearity using artificial neural networks.

PubMed

Cho, Jin Seo; Ishida, Isao; White, Halbert

2011-05-01

Tests for regression neglected nonlinearity based on artificial neural networks (ANNs) have so far been studied by separately analyzing the two ways in which the null of regression linearity can hold. This implies that the asymptotic behavior of general ANN-based tests for neglected nonlinearity is still an open question. Here we analyze a convenient ANN-based quasi-likelihood ratio statistic for testing neglected nonlinearity, paying careful attention to both components of the null. We derive the asymptotic null distribution under each component separately and analyze their interaction. Somewhat remarkably, it turns out that the previously known asymptotic null distribution for the type 1 case still applies, but under somewhat stronger conditions than previously recognized. We present Monte Carlo experiments corroborating our theoretical results and showing that standard methods can yield misleading inference when our new, stronger regularity conditions are violated.

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.

Asymptotic self-restabilization of a continuous elastic structure

NASA Astrophysics Data System (ADS)

Bosi, F.; Misseroni, D.; Dal Corso, F.; Neukirch, S.; Bigoni, D.

2016-12-01

A challenge in soft robotics and soft actuation is the determination of an elastic system that spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behavior is that a displacement component spontaneously cycles around a null value, thus producing a cyclic soft mechanism. An example of such a system is theoretically proven through the solution of the elastica and a stability analysis based on dynamic perturbations. It is shown that the asymptotic self-restabilization is driven by the development of a configurational force, of similar nature to the Peach-Koehler interaction between dislocations in crystals, which is derived from the principle of least action. A proof-of-concept prototype of the discovered elastic system is designed, realized, and tested, showing that this innovative behavior can be obtained in a real mechanical apparatus.

The Laplace method for probability measures in Banach spaces

NASA Astrophysics Data System (ADS)

Piterbarg, V. I.; Fatalov, V. R.

1995-12-01

Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Hölder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces L_k^p and l^2. Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the l_k^p-norm of a Gaussian finite-dimensional vector with dependent coordinates, p > 1 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type \\chi^2 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of l^2-valued Gaussian processes 8.5. Exact asymptotics of large deviations for the l^2-valued Ornstein-Uhlenbeck process Bibliography

An Extended Trajectory Mechanics Approach for Calculating the Path of a Pressure Transient: Derivation and Illustration

NASA Astrophysics Data System (ADS)

Vasco, D. W.

2018-04-01

Following an approach used in quantum dynamics, an exponential representation of the hydraulic head transforms the diffusion equation governing pressure propagation into an equivalent set of ordinary differential equations. Using a reservoir simulator to determine one set of dependent variables leaves a reduced set of equations for the path of a pressure transient. Unlike the current approach for computing the path of a transient, based on a high-frequency asymptotic solution, the trajectories resulting from this new formulation are valid for arbitrary spatial variations in aquifer properties. For a medium containing interfaces and layers with sharp boundaries, the trajectory mechanics approach produces paths that are compatible with travel time fields produced by a numerical simulator, while the asymptotic solution produces paths that bend too strongly into high permeability regions. The breakdown of the conventional asymptotic solution, due to the presence of sharp boundaries, has implications for model parameter sensitivity calculations and the solution of the inverse problem. For example, near an abrupt boundary, trajectories based on the asymptotic approach deviate significantly from regions of high sensitivity observed in numerical computations. In contrast, paths based on the new trajectory mechanics approach coincide with regions of maximum sensitivity to permeability changes.

Consensus-Based Formation Control of a Class of Multi-Agent Systems

NASA Technical Reports Server (NTRS)

Joshi, Suresh; Gonzalez, Oscar R.

2014-01-01

This paper presents a consensus-based formation control scheme for autonomous multi-agent systems represented by double integrator dynamics. Assuming that the information graph topology consists of an undirected connected graph, a leader-based consensus-type control law is presented and shown to provide asymptotic formation stability when subjected to piecewise constant formation velocity commands. It is also shown that global asymptotic stability is preserved in the presence of (0, infinity)- sector monotonic non-decreasing actuator nonlinearities.

Risk analysis in cohort studies with heterogeneous strata. A global chi2-test for dose-response relationship, generalizing the Mantel-Haenszel procedure.

PubMed

Ahlborn, W; Tuz, H J; Uberla, K

1990-03-01

In cohort studies the Mantel-Haenszel estimator ORMH is computed from sample data and is used as a point estimator of relative risk. Test-based confidence intervals are estimated with the help of the asymptotic chi-squared distributed MH-statistic chi 2MHS. The Mantel-extension-chi-squared is used as a test statistic for a dose-response relationship. Both test statistics--the Mantel-Haenszel-chi as well as the Mantel-extension-chi--assume homogeneity of risk across strata, which is rarely present. Also an extended nonparametric statistic, proposed by Terpstra, which is based on the Mann-Whitney-statistics assumes homogeneity of risk across strata. We have earlier defined four risk measures RRkj (k = 1,2,...,4) in the population and considered their estimates and the corresponding asymptotic distributions. In order to overcome the homogeneity assumption we use the delta-method to get "test-based" confidence intervals. Because the four risk measures RRkj are presented as functions of four weights gik we give, consequently, the asymptotic variances of these risk estimators also as functions of the weights gik in a closed form. Approximations to these variances are given. For testing a dose-response relationship we propose a new class of chi 2(1)-distributed global measures Gk and the corresponding global chi 2-test. In contrast to the Mantel-extension-chi homogeneity of risk across strata must not be assumed. These global test statistics are of the Wald type for composite hypotheses.(ABSTRACT TRUNCATED AT 250 WORDS)

Penrose inequality in anti-de Sitter space

NASA Astrophysics Data System (ADS)

Husain, Viqar; Singh, Suprit

2017-11-01

For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-de Sitter (AAdS) spacetimes, and show that the inequality holds for time asymmetric data in spherical symmetry. Our analysis is motivated by the constant-negative-spatial-curvature form of the AdS black hole metric.

Optimal designs based on the maximum quasi-likelihood estimator

PubMed Central

Shen, Gang; Hyun, Seung Won; Wong, Weng Kee

2016-01-01

We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just as well or better than optimal designs based on any other asymptotically linear unbiased estimators such as the least square estimator (LSE). In addition, we show current algorithms for finding optimal designs can be directly used to find optimal designs based on the MqLE. As an illustrative application, we construct a variety of locally optimal designs based on the MqLE for the 4-parameter logistic (4PL) model and study their robustness properties to misspecifications in the model using asymptotic relative efficiency. The results suggest that optimal designs based on the MqLE can be easily generated and they are quite robust to mis-specification in the probability distribution of the responses. PMID:28163359

Asymptotic analysis of stability for prismatic solids under axial loads

NASA Astrophysics Data System (ADS)

Scherzinger, W.; Triantafyllidis, N.

1998-06-01

This work addresses the stability of axially loaded prismatic beams with any simply connected crosssection. The solids obey a general class of rate-independent constitutive laws, and can sustain finite strains in either compression or tension. The proposed method is based on multiple scale asymptotic analysis, and starts with the full Lagrangian formulation for the three-dimensional stability problem, where the boundary conditions are chosen to avoid the formation of boundary layers. The calculations proceed by taking the limit of the beam's slenderness parameter, ɛ (ɛ 2 ≡ area/length 2), going to zero, thus resulting in asymptotic expressions for the critical loads and modes. The analysis presents a consistent and unified treatment for both compressive (buckling) and tensile (necking) instabilities, and is carried out explicitly up to o( ɛ4) in each case. The present method circumvents the standard structural mechanics approach for the stability problem of beams which requires the choice of displacement and stress field approximations in order to construct a nonlinear beam theory. Moreover, this work provides a consistent way to calculate the effect of the beam's slenderness on the critical load and mode to any order of accuracy required. In contrast, engineering theories give accurately the lowest order terms ( O( ɛ2)—Euler load—in compression or O(1)—maximum load—in tension) but give only approximately the next higher order terms, with the exception of simple section geometries where exact stability results are available. The proposed method is used to calculate the critical loads and eigenmodes for bars of several different cross-sections (circular, square, cruciform and L-shaped). Elastic beams are considered in compression and elastoplastic beams are considered in tension. The O( ɛ2) and O( ɛ4) asymptotic results are compared to the exact finite element calculations for the corresponding three-dimensional prismatic solids. The O( ɛ4) results give significant improvement over the O( ɛ2) results, even for extremely stubby beams, and in particular for the case of cross-sections with commensurate dimensions.

The difference between two random mixed quantum states: exact and asymptotic spectral analysis

NASA Astrophysics Data System (ADS)

Mejía, José; Zapata, Camilo; Botero, Alonso

2017-01-01

We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson’s theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance.

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.

Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions

NASA Astrophysics Data System (ADS)

Kamiński, Wojciech; Steinhaus, Sebastian

2013-12-01

We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.

Asymptotics of empirical eigenstructure for high dimensional spiked covariance.

PubMed

Wang, Weichen; Fan, Jianqing

2017-06-01

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those in Paul (2007) to a more general setting and solve the rates of convergence problems in Shen et al. (2013). They also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called shrinkage principal orthogonal complement thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks of large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies.

Asymptotics of empirical eigenstructure for high dimensional spiked covariance

PubMed Central

Wang, Weichen

2017-01-01

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those in Paul (2007) to a more general setting and solve the rates of convergence problems in Shen et al. (2013). They also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called shrinkage principal orthogonal complement thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks of large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies. PMID:28835726

A problem with inverse time for a singularly perturbed integro-differential equation with diagonal degeneration of the kernel of high order

NASA Astrophysics Data System (ADS)

Bobodzhanov, A. A.; Safonov, V. F.

2016-04-01

We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).

Analysis of Eigenvalue and Eigenfunction of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Lilis Elviyanti, Isnaini

2018-04-01

Analysis of relativistic energy and wave function for zero spin particles using Klein Gordon equation was influenced by separable noncentral cylindrical potential was solved by asymptotic iteration method (AIM). By using cylindrical coordinates, the Klein Gordon equation for the case of symmetry spin was reduced to three one-dimensional Schrodinger like equations that were solvable using variable separation method. The relativistic energy was calculated numerically with Matlab software, and the general unnormalized wave function was expressed in hypergeometric terms.

Asymptotically suboptimal control of weakly interconnected dynamical systems

NASA Astrophysics Data System (ADS)

Dmitruk, N. M.; Kalinin, A. I.

2016-10-01

Optimal control problems for a group of systems with weak dynamical interconnections between its constituent subsystems are considered. A method for decentralized control is proposed which distributes the control actions between several controllers calculating in real time control inputs only for theirs subsystems based on the solution of the local optimal control problem. The local problem is solved by asymptotic methods that employ the representation of the weak interconnection by a small parameter. Combination of decentralized control and asymptotic methods allows to significantly reduce the dimension of the problems that have to be solved in the course of the control process.

Stability of stationary solutions for inflow problem on the micropolar fluid model

NASA Astrophysics Data System (ADS)

Yin, Haiyan

2017-04-01

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half-line R+:=(0,∞). We prove that the corresponding stationary solutions of the small amplitude to the inflow problem for the micropolar fluid model are time asymptotically stable under small H1 perturbations in both the subsonic and degenerate cases. The microrotation velocity brings us some additional troubles compared with Navier-Stokes equations in the absence of the microrotation velocity. The proof of asymptotic stability is based on the basic energy method.

Asymptotics of nonparametric L-1 regression models with dependent data

PubMed Central

ZHAO, ZHIBIAO; WEI, YING; LIN, DENNIS K.J.

2013-01-01

We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration. PMID:24955016

Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters

NASA Astrophysics Data System (ADS)

Kruglov, Vladimir I.; Harvey, John D.

2006-12-01

We present exact asymptotic similariton solutions of the generalized nonlinear Schrödinger equation (NLSE) with gain or loss terms for a normal-dispersion fiber amplifier with dispersion, nonlinearity, and gain profiles that depend on the propagation distance. Our treatment is based on the mapping of the NLSE with varying parameters to the NLSE with constant dispersion and nonlinearity coefficients and an arbitrary varying gain function. We formulate an effective procedure that leads directly, under appropriate conditions, to a wide range of exact asymptotic similariton solutions of NLSE demonstrating self-similar propagating regimes with linear chirp.

Chiral fermions in asymptotically safe quantum gravity

NASA Astrophysics Data System (ADS)

Meibohm, J.; Pawlowski, J. M.

2016-05-01

We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.

Realization of non-holonomic constraints and singular perturbation theory for plane dumbbells

NASA Astrophysics Data System (ADS)

Koshkin, Sergiy; Jovanovic, Vojin

2017-10-01

We study the dynamics of pairs of connected masses in the plane, when nonholonomic (knife-edge) constraints are realized by forces of viscous friction, in particular its relation to constrained dynamics, and its approximation by the method of matching asymptotics of singular perturbation theory when the mass to friction ratio is taken as the small parameter. It turns out that long term behaviors of the frictional and constrained systems may differ dramatically no matter how small the perturbation is, and when this happens is not determined by any transparent feature of the equations of motion. The choice of effective time scales for matching asymptotics is also subtle and non-obvious, and secular terms appearing in them can not be dealt with by the classical methods. Our analysis is based on comparison to analytic solutions, and we present a reduction procedure for plane dumbbells that leads to them in some cases.

Chiral fermions in asymptotically safe quantum gravity.

PubMed

Meibohm, J; Pawlowski, J M

2016-01-01

We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.

Survival analysis for the missing censoring indicator model using kernel density estimation techniques

PubMed Central

Subramanian, Sundarraman

2008-01-01

This article concerns asymptotic theory for a new estimator of a survival function in the missing censoring indicator model of random censorship. Specifically, the large sample results for an inverse probability-of-non-missingness weighted estimator of the cumulative hazard function, so far not available, are derived, including an almost sure representation with rate for a remainder term, and uniform strong consistency with rate of convergence. The estimator is based on a kernel estimate for the conditional probability of non-missingness of the censoring indicator. Expressions for its bias and variance, in turn leading to an expression for the mean squared error as a function of the bandwidth, are also obtained. The corresponding estimator of the survival function, whose weak convergence is derived, is asymptotically efficient. A numerical study, comparing the performances of the proposed and two other currently existing efficient estimators, is presented. PMID:18953423

Survival analysis for the missing censoring indicator model using kernel density estimation techniques.

PubMed

Subramanian, Sundarraman

2006-01-01

This article concerns asymptotic theory for a new estimator of a survival function in the missing censoring indicator model of random censorship. Specifically, the large sample results for an inverse probability-of-non-missingness weighted estimator of the cumulative hazard function, so far not available, are derived, including an almost sure representation with rate for a remainder term, and uniform strong consistency with rate of convergence. The estimator is based on a kernel estimate for the conditional probability of non-missingness of the censoring indicator. Expressions for its bias and variance, in turn leading to an expression for the mean squared error as a function of the bandwidth, are also obtained. The corresponding estimator of the survival function, whose weak convergence is derived, is asymptotically efficient. A numerical study, comparing the performances of the proposed and two other currently existing efficient estimators, is presented.

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.

On stability of fixed points and chaos in fractional systems.

PubMed

Edelman, Mark

2018-02-01

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0<α<2. The method is tested on various forms of fractional generalizations of the standard and logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

Nonlinear adaptive control system design with asymptotically stable parameter estimation error

NASA Astrophysics Data System (ADS)

Mishkov, Rumen; Darmonski, Stanislav

2018-01-01

The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. The advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time. The method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach. The modification is based on the generalised prediction error, a priori constraints with a hierarchical parameter projection algorithm, and the stable data accumulation concepts. The data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation. It relies on the parametric identifiability system property introduced. Necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived. The approach is applied in a nonlinear adaptive speed tracking vector control of a three-phase induction motor.

Modeling spanwise nonuniformity in the cross-sectional analysis of composite beams

NASA Astrophysics Data System (ADS)

Ho, Jimmy Cheng-Chung

Spanwise nonuniformity effects are modeled in the cross-sectional analysis of beam theory. This modeling adheres to an established numerical framework on cross-sectional analysis of uniform beams with arbitrary cross-sections. This framework is based on two concepts: decomposition of the rotation tensor and the variational-asymptotic method. Allowance of arbitrary materials and geometries in the cross-section is from discretization of the warping field by finite elements. By this approach, dimensional reduction from three-dimensional elasticity is performed rigorously and the sectional strain energy is derived to be asymptotically-correct. Elastic stiffness matrices are derived for inputs into the global beam analysis. Recovery relations for the displacement, stress, and strain fields are also derived with care to be consistent with the energy. Spanwise nonuniformity effects appear in the form of pointwise and sectionwise derivatives, which are approximated by finite differences. The formulation also accounts for the effects of spanwise variations in initial twist and/or curvature. A linearly tapered isotropic strip is analyzed to demonstrate spanwise nonuniformity effects on the cross-sectional analysis. The analysis is performed analytically by the variational-asymptotic method. Results from beam theory are validated against solutions from plane stress elasticity. These results demonstrate that spanwise nonuniformity effects become significant as the rate at which the cross-sections vary increases. The modeling of transverse shear modes of deformation is accomplished by transforming the strain energy into generalized Timoshenko form. Approximations in this transformation procedure from previous works, when applied to uniform beams, are identified. The approximations are not used in the present work so as to retain more accuracy. Comparison of present results with those previously published shows that these approximations sometimes change the results measurably and thus are inappropriate. Static and dynamic results, from the global beam analysis, are calculated to show the differences between using stiffness constants from previous works and the present work. As a form of validation of the transformation procedure, calculations from the global beam analysis of initially twisted isotropic beams from using curvilinear coordinate axes featuring twist are shown to be equivalent to calculations using Cartesian coordinates.

Estimating and comparing microbial diversity in the presence of sequencing errors

PubMed Central

Chiu, Chun-Huo

2016-01-01

Estimating and comparing microbial diversity are statistically challenging due to limited sampling and possible sequencing errors for low-frequency counts, producing spurious singletons. The inflated singleton count seriously affects statistical analysis and inferences about microbial diversity. Previous statistical approaches to tackle the sequencing errors generally require different parametric assumptions about the sampling model or about the functional form of frequency counts. Different parametric assumptions may lead to drastically different diversity estimates. We focus on nonparametric methods which are universally valid for all parametric assumptions and can be used to compare diversity across communities. We develop here a nonparametric estimator of the true singleton count to replace the spurious singleton count in all methods/approaches. Our estimator of the true singleton count is in terms of the frequency counts of doubletons, tripletons and quadrupletons, provided these three frequency counts are reliable. To quantify microbial alpha diversity for an individual community, we adopt the measure of Hill numbers (effective number of taxa) under a nonparametric framework. Hill numbers, parameterized by an order q that determines the measures’ emphasis on rare or common species, include taxa richness (q = 0), Shannon diversity (q = 1, the exponential of Shannon entropy), and Simpson diversity (q = 2, the inverse of Simpson index). A diversity profile which depicts the Hill number as a function of order q conveys all information contained in a taxa abundance distribution. Based on the estimated singleton count and the original non-singleton frequency counts, two statistical approaches (non-asymptotic and asymptotic) are developed to compare microbial diversity for multiple communities. (1) A non-asymptotic approach refers to the comparison of estimated diversities of standardized samples with a common finite sample size or sample completeness. This approach aims to compare diversity estimates for equally-large or equally-complete samples; it is based on the seamless rarefaction and extrapolation sampling curves of Hill numbers, specifically for q = 0, 1 and 2. (2) An asymptotic approach refers to the comparison of the estimated asymptotic diversity profiles. That is, this approach compares the estimated profiles for complete samples or samples whose size tends to be sufficiently large. It is based on statistical estimation of the true Hill number of any order q ≥ 0. In the two approaches, replacing the spurious singleton count by our estimated count, we can greatly remove the positive biases associated with diversity estimates due to spurious singletons and also make fair comparisons across microbial communities, as illustrated in our simulation results and in applying our method to analyze sequencing data from viral metagenomes. PMID:26855872

Asymptotic forms for the energy of force-free magnetic field ion figurations of translational symmetry

NASA Technical Reports Server (NTRS)

Sturrock, P. A.; Antiochos, S. K.; Klinchuk, J. A.; Roumeliotis, G.

1994-01-01

It is known from computer calculations that if a force-free magnetic field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution and the energy of the field increases progressively. For configurations of translationalsymmetry, it has been found empirically that the energy tends asymptotically to a certain functional form. It is here shown that analysis of a simple model of the asymptotic form of force-free fields of translational symmetry leads to and therefore justifies this functional form. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.

The asymptotic structure of nonpremixed methane-air flames with oxidizer leakage of order unity

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

Seshadri, K.; Ilincic, N.

1995-04-01

The asymptotic structure of nonpremixed methane-air flames is analyzed using a reduced three-step mechanism. The three global steps of this reduced mechanism are similar to those used in a previous analysis. The rates of the three steps are related to the rates of the elementary reactions appearing in the C{sub 1}-mechanism for oxidation of methane. The present asymptotic analysis differs from the previous analysis in that oxygen is presumed to leak from the reaction zone to the leading order. Chemical reactions are presumed to occur in three asymptotically thin layers: the fuel-consumption layer, the nonequilibrium layer for the water-gas shiftmore » reaction and the oxidation layer. The structure of the fuel-consumption layer is presumed to be identical to that analyzed previously and in this layer the fuel reacts with the radicals to form primarily CO and H{sub 2} and some CO{sub 2} and H{sub 2}O In the oxidation layer the CO and H{sub 2} formed in the fuel-consumption layer are oxidized to CO{sub 2} and H{sub 2}O. The present analysis of the oxidation layer is simpler than the previous analysis because the variation in the values of the concentration of oxygen can be neglected to the leading order and this is a better representation of the flame structure in the vicinity of the critical conditions of extinction. The predictions of the critical conditions of extinction of the present model are compared with the predictions of previous models. It is anticipated that the present simple model can be easily extended to more complex problems such as pollutant formation in flames or chemical inhibition of flames.« less

Solving Upwind-Biased Discretizations: Defect-Correction Iterations

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

1999-01-01

This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.

A framework for comparing different image segmentation methods and its use in studying equivalences between level set and fuzzy connectedness frameworks

PubMed Central

Ciesielski, Krzysztof Chris; Udupa, Jayaram K.

2011-01-01

In the current vast image segmentation literature, there seems to be considerable redundancy among algorithms, while there is a serious lack of methods that would allow their theoretical comparison to establish their similarity, equivalence, or distinctness. In this paper, we make an attempt to fill this gap. To accomplish this goal, we argue that: (1) every digital segmentation algorithm A should have a well defined continuous counterpart MA, referred to as its model, which constitutes an asymptotic of A when image resolution goes to infinity; (2) the equality of two such models MA and MA′ establishes a theoretical (asymptotic) equivalence of their digital counterparts A and A′. Such a comparison is of full theoretical value only when, for each involved algorithm A, its model MA is proved to be an asymptotic of A. So far, such proofs do not appear anywhere in the literature, even in the case of algorithms introduced as digitizations of continuous models, like level set segmentation algorithms. The main goal of this article is to explore a line of investigation for formally pairing the digital segmentation algorithms with their asymptotic models, justifying such relations with mathematical proofs, and using the results to compare the segmentation algorithms in this general theoretical framework. As a first step towards this general goal, we prove here that the gradient based thresholding model M∇ is the asymptotic for the fuzzy connectedness Udupa and Samarasekera segmentation algorithm used with gradient based affinity A∇. We also argue that, in a sense, M∇ is the asymptotic for the original front propagation level set algorithm of Malladi, Sethian, and Vemuri, thus establishing a theoretical equivalence between these two specific algorithms. Experimental evidence of this last equivalence is also provided. PMID:21442014

Asymptotics of bivariate generating functions with algebraic singularities

NASA Astrophysics Data System (ADS)

Greenwood, Torin

Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.

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.

Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics

PubMed Central

Dziarmaga, Jacek; Zurek, Wojciech H.

2014-01-01

Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon. PMID:25091996

Lax Integrability and the Peakon Problem for the Modified Camassa-Holm Equation

NASA Astrophysics Data System (ADS)

Chang, Xiangke; Szmigielski, Jacek

2018-02-01

Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak solutions in the case of the modified Camassa-Holm equation studied in this paper is dictated by the distributional compatibility of its Lax pair and, as a result, it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the Burgers type. Subsequently, we give a complete construction of peakon solutions satisfying the modified Camassa-Holm equation in the sense of distributions; our approach is based on solving certain inverse boundary value problem, the solution of which hinges on a combination of classical techniques of analysis involving Stieltjes' continued fractions and multi-point Padé approximations. We propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons that share asymptotic speeds, as well as Toda-like sorting property.

A High-Order, Adaptive, Discontinuous Galerkin Finite Element Method for the Reynolds-Averaged Navier-Stokes Equations

DTIC Science & Technology

2008-09-01

Element Method. Wellesley- Cambridge Press, Wellesly, MA, 1988. [97] E. F. Toro . Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical...introducing additional state variables, are generally asymptotically dual consistent. Numerical results are presented to confirm the results of the analysis...dependence on the state gradient is handled by introducing additional state variables, are generally asymptotically dual consistent. Numerical results are

A Comparison of Pseudo-Maximum Likelihood and Asymptotically Distribution-Free Dynamic Factor Analysis Parameter Estimation in Fitting Covariance Structure Models to Block-Toeplitz Matrices Representing Single-Subject Multivariate Time-Series.

ERIC Educational Resources Information Center

Molenaar, Peter C. M.; Nesselroade, John R.

1998-01-01

Pseudo-Maximum Likelihood (p-ML) and Asymptotically Distribution Free (ADF) estimation methods for estimating dynamic factor model parameters within a covariance structure framework were compared through a Monte Carlo simulation. Both methods appear to give consistent model parameter estimates, but only ADF gives standard errors and chi-square…

Ignition of a combustible half space

NASA Technical Reports Server (NTRS)

Olmstead, W. E.

1983-01-01

A half space of combustible material is subjected to an arbitrary energy flux at the boundary where convection heat loss is also allowed. An asymptotic analysis of the temperature growth reveals two conditions necessary for ignition to occur. Cases of both large and order unity Lewis number are shown to lead to a nonlinear integral equation governing the thermal runaway. Some global and asymptotic properties of the integral equation are obtained.

Asymptotic analysis of the contact-line microregion for a perfectly wetting volatile liquid in a pure-vapor atmosphere

NASA Astrophysics Data System (ADS)

Rednikov, A. Ye.; Colinet, P.

2017-12-01

We revisit the Wayner problem of the microregion of a contact line at rest formed by a perfectly wetting single-component liquid on an isothermal superheated flat substrate in an atmosphere of its own pure vapor. The focus is on the evaporation-induced apparent contact angles. The microregion is shaped by the effects of viscosity, Laplace and disjoining pressures (the latter in the form of an inverse-cubic law), and evaporation. The evaporation is in turn determined by heat conduction across the liquid film, kinetic resistance, and the Kelvin effect (i.e., saturation-condition dependence on the liquid-vapor pressure difference). While an asymptotic limit of large kinetic resistances was considered by Morris nearly two decades ago [J. Fluid Mech. 432, 1 (2001)], here we are concerned rather with matched asymptotic expansions in the limits of weak and strong Kelvin effects. Certain extensions are also touched upon within the asymptotic analysis. These are a more general form of the disjoining pressure and account for the Navier slip. Most notably, these also include the possibility of Wayner's extended microfilms (covering macroscopically dry parts of the substrate) actually getting truncated. A number of isolated cases encountered in the literature are thereby systematically recovered.

On the use and misuse of scalar scores of confounders in design and analysis of observational studies.

PubMed

Pfeiffer, R M; Riedl, R

2015-08-15

We assess the asymptotic bias of estimates of exposure effects conditional on covariates when summary scores of confounders, instead of the confounders themselves, are used to analyze observational data. First, we study regression models for cohort data that are adjusted for summary scores. Second, we derive the asymptotic bias for case-control studies when cases and controls are matched on a summary score, and then analyzed either using conditional logistic regression or by unconditional logistic regression adjusted for the summary score. Two scores, the propensity score (PS) and the disease risk score (DRS) are studied in detail. For cohort analysis, when regression models are adjusted for the PS, the estimated conditional treatment effect is unbiased only for linear models, or at the null for non-linear models. Adjustment of cohort data for DRS yields unbiased estimates only for linear regression; all other estimates of exposure effects are biased. Matching cases and controls on DRS and analyzing them using conditional logistic regression yields unbiased estimates of exposure effect, whereas adjusting for the DRS in unconditional logistic regression yields biased estimates, even under the null hypothesis of no association. Matching cases and controls on the PS yield unbiased estimates only under the null for both conditional and unconditional logistic regression, adjusted for the PS. We study the bias for various confounding scenarios and compare our asymptotic results with those from simulations with limited sample sizes. To create realistic correlations among multiple confounders, we also based simulations on a real dataset. Copyright © 2015 John Wiley & Sons, Ltd.

Sampling-Based Motion Planning Algorithms for Replanning and Spatial Load Balancing

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

Boardman, Beth Leigh

The common theme of this dissertation is sampling-based motion planning with the two key contributions being in the area of replanning and spatial load balancing for robotic systems. Here, we begin by recalling two sampling-based motion planners: the asymptotically optimal rapidly-exploring random tree (RRT*), and the asymptotically optimal probabilistic roadmap (PRM*). We also provide a brief background on collision cones and the Distributed Reactive Collision Avoidance (DRCA) algorithm. The next four chapters detail novel contributions for motion replanning in environments with unexpected static obstacles, for multi-agent collision avoidance, and spatial load balancing. First, we show improved performance of the RRT*more » when using the proposed Grandparent-Connection (GP) or Focused-Refinement (FR) algorithms. Next, the Goal Tree algorithm for replanning with unexpected static obstacles is detailed and proven to be asymptotically optimal. A multi-agent collision avoidance problem in obstacle environments is approached via the RRT*, leading to the novel Sampling-Based Collision Avoidance (SBCA) algorithm. The SBCA algorithm is proven to guarantee collision free trajectories for all of the agents, even when subject to uncertainties in the knowledge of the other agents’ positions and velocities. Given that a solution exists, we prove that livelocks and deadlock will lead to the cost to the goal being decreased. We introduce a new deconfliction maneuver that decreases the cost-to-come at each step. This new maneuver removes the possibility of livelocks and allows a result to be formed that proves convergence to the goal configurations. Finally, we present a limited range Graph-based Spatial Load Balancing (GSLB) algorithm which fairly divides a non-convex space among multiple agents that are subject to differential constraints and have a limited travel distance. The GSLB is proven to converge to a solution when maximizing the area covered by the agents. The analysis for each of the above mentioned algorithms is confirmed in simulations.« less

Simultaneous Inference For The Mean Function Based on Dense Functional Data

PubMed Central

Cao, Guanqun; Yang, Lijian; Todem, David

2012-01-01

A polynomial spline estimator is proposed for the mean function of dense functional data together with a simultaneous confidence band which is asymptotically correct. In addition, the spline estimator and its accompanying confidence band enjoy oracle efficiency in the sense that they are asymptotically the same as if all random trajectories are observed entirely and without errors. The confidence band is also extended to the difference of mean functions of two populations of functional data. Simulation experiments provide strong evidence that corroborates the asymptotic theory while computing is efficient. The confidence band procedure is illustrated by analyzing the near infrared spectroscopy data. PMID:22665964

One Step Quantum Key Distribution Based on EPR Entanglement.

PubMed

Li, Jian; Li, Na; Li, Lei-Lei; Wang, Tao

2016-06-30

A novel quantum key distribution protocol is presented, based on entanglement and dense coding and allowing asymptotically secure key distribution. Considering the storage time limit of quantum bits, a grouping quantum key distribution protocol is proposed, which overcomes the vulnerability of first protocol and improves the maneuverability. Moreover, a security analysis is given and a simple type of eavesdropper's attack would introduce at least an error rate of 46.875%. Compared with the "Ping-pong" protocol involving two steps, the proposed protocol does not need to store the qubit and only involves one step.

A quantum kinematics for asymptotically flat gravity

NASA Astrophysics Data System (ADS)

Campiglia, Miguel; Varadarajan, Madhavan

2015-07-01

We construct a quantum kinematics for asymptotically flat gravity based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying loop quantum gravity (LQG) which supports, in addition to the usual LQG operators, the action of ‘background exponential operators’, which are connection dependent operators labelled by ‘background’ su(2) electric fields. KS states have, in addition to the LQG state label corresponding to one dimensional excitations of the triad, a label corresponding to a ‘background’ electric field that describes three dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields that label the states and the background electric fields that label the operators. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We show that KS states can be realised as wave functions on a quantum configuration space of generalized connections and that the asymptotic behaviour of each such generalized connection is determined by that of the background electric fields which label the background exponential operators. Similar to the spatially compact case, the Gauss law and diffeomorphism constraints are then imposed through group averaging techniques to obtain a large sector of gauge invariant states. It is shown that this sector supports a unitary action of the group of asymptotic rotations and translations and that, as anticipated by Friedman and Sorkin, for appropriate spatial topology, this sector contains states that display fermionic behaviour under 2π rotations.

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.

Asymptotic analysis to the effect of temperature gradient on the propagation of triple flames

NASA Astrophysics Data System (ADS)

Al-Malki, Faisal

2018-05-01

We study asymptotically in this paper the influence of the temperature gradient across the mixing layer on the propagation triple flames formed inside a porous wall channel. The study begins by formulating the problem mathematically using the thermo-diffusive model and then presents a thorough asymptotic analysis of the problem in the limit of large activation energy and thin flames. Analytical formulae for the local burning speed, the flame shape and the propagation speed in terms of the temperature gradient parameter have been derived. It was shown that varying the feed temperatures can significantly enhance the burning of the reactants up to a critical threshold, beyond which no solutions can be obtained. In addition, the study showed that increasing the temperature at the boundaries will modify the usual triple structure of the flame by inverting the upper premixed branch and extending it to the boundary, which may have great implications on the safety of the adopted combustion chambers.

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.

Mathematical justification of a viscoelastic elliptic membrane problem

NASA Astrophysics Data System (ADS)

Castiñeira, Gonzalo; Rodríguez-Arós, Ángel

2017-12-01

We consider a family of linearly viscoelastic elliptic shells, and we use asymptotic analysis to justify that what we have identified as the two-dimensional viscoelastic elliptic membrane problem is an accurate approximation when the thickness of the shell tends to zero. Most noticeable is that the limit problem includes a long-term memory that takes into account the previous history of deformations. We provide convergence results which justify our asymptotic approach.

On the Asymptotic Regimes and the Strongly Stratified Limit of Rotating Boussinesq Equations

NASA Technical Reports Server (NTRS)

Babin, A.; Mahalov, A.; Nicolaenko, B.; Zhou, Y.

1997-01-01

Asymptotic regimes of geophysical dynamics are described for different Burger number limits. Rotating Boussinesq equations are analyzed in the asymptotic limit, of strong stratification in the Burger number of order one situation as well as in the asymptotic regime of strong stratification and weak rotation. It is shown that in both regimes horizontally averaged buoyancy variable is an adiabatic invariant for the full Boussinesq system. Spectral phase shift corrections to the buoyancy time scale associated with vertical shearing of this invariant are deduced. Statistical dephasing effects induced by turbulent processes on inertial-gravity waves are evidenced. The 'split' of the energy transfer of the vortical and the wave components is established in the Craya-Herring cyclic basis. As the Burger number increases from zero to infinity, we demonstrate gradual unfreezing of energy cascades for ageostrophic dynamics. The energy spectrum and the anisotropic spectral eddy viscosity are deduced with an explicit dependence on the anisotropic rotation/stratification time scale which depends on the vertical aspect ratio parameter. Intermediate asymptotic regime corresponding to strong stratification and weak rotation is analyzed where the effects of weak rotation are accounted for by an asymptotic expansion with full control (saturation) of vertical shearing. The regularizing effect of weak rotation differs from regularizations based on vertical viscosity. Two scalar prognostic equations for ageostrophic components (divergent velocity potential and geostrophic departure ) are obtained.

High-Dimensional Multivariate Repeated Measures Analysis with Unequal Covariance Matrices.

PubMed

Harrar, Solomon W; Kong, Xiaoli

2015-03-01

In this paper, test statistics for repeated measures design are introduced when the dimension is large. By large dimension is meant the number of repeated measures and the total sample size grow together but either one could be larger than the other. Asymptotic distribution of the statistics are derived for the equal as well as unequal covariance cases in the balanced as well as unbalanced cases. The asymptotic framework considered requires proportional growth of the sample sizes and the dimension of the repeated measures in the unequal covariance case. In the equal covariance case, one can grow at much faster rate than the other. The derivations of the asymptotic distributions mimic that of Central Limit Theorem with some important peculiarities addressed with sufficient rigor. Consistent and unbiased estimators of the asymptotic variances, which make efficient use of all the observations, are also derived. Simulation study provides favorable evidence for the accuracy of the asymptotic approximation under the null hypothesis. Power simulations have shown that the new methods have comparable power with a popular method known to work well in low-dimensional situation but the new methods have shown enormous advantage when the dimension is large. Data from Electroencephalograph (EEG) experiment is analyzed to illustrate the application of the results.

High-Dimensional Multivariate Repeated Measures Analysis with Unequal Covariance Matrices

PubMed Central

Harrar, Solomon W.; Kong, Xiaoli

2015-01-01

In this paper, test statistics for repeated measures design are introduced when the dimension is large. By large dimension is meant the number of repeated measures and the total sample size grow together but either one could be larger than the other. Asymptotic distribution of the statistics are derived for the equal as well as unequal covariance cases in the balanced as well as unbalanced cases. The asymptotic framework considered requires proportional growth of the sample sizes and the dimension of the repeated measures in the unequal covariance case. In the equal covariance case, one can grow at much faster rate than the other. The derivations of the asymptotic distributions mimic that of Central Limit Theorem with some important peculiarities addressed with sufficient rigor. Consistent and unbiased estimators of the asymptotic variances, which make efficient use of all the observations, are also derived. Simulation study provides favorable evidence for the accuracy of the asymptotic approximation under the null hypothesis. Power simulations have shown that the new methods have comparable power with a popular method known to work well in low-dimensional situation but the new methods have shown enormous advantage when the dimension is large. Data from Electroencephalograph (EEG) experiment is analyzed to illustrate the application of the results. PMID:26778861

Cosmic Censorship for Gowdy Spacetimes.

PubMed

Ringström, Hans

2010-01-01

Due to the complexity of Einstein's equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behavior of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof and in the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.

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.

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.

Information Theoretic Studies and Assessment of Space Object Identification

DTIC Science & Technology

2014-03-24

localization are contained in Ref. [5]. 1.7.1 A Bayesian MPE Based Analysis of 2D Point-Source-Pair Superresolution In a second recently submitted paper [6], a...related problem of the optical superresolution (OSR) of a pair of equal-brightness point sources separated spatially by a distance (or angle) smaller...1403.4897 [physics.optics] (19 March 2014). 6. S. Prasad, “Asymptotics of Bayesian error probability and 2D pair superresolution ,” submitted to Opt. Express

Assessment of the Need to Perform Life-Saving Interventions Using Comprehensive Analysis of the Electrocardiogram and Artificial Neural Networks

DTIC Science & Technology

2010-04-01

the lower and higher asymptotic 95 % confidence intervals were 0.812 and 0.924, respectively. Based on these results, we consider automated ...commercial success of the cardioverter- defibrillator industry clearly demonstrates that the obstacles at hand can be successfully overcome. 4.1...Does HRC Work in Real-Life Noisy Data? One of the methods reportedly designed to deal with nonstationary RRI data sets is the point correlation

Asymptotic Analysis of Melt Growth for Antimonide-Based Compound Semiconductor Crystals in Magnetic and Electric Fields

DTIC Science & Technology

2006-10-01

F. Bliss, Gerald W. Iseler and Piotr Becla, "Combining static and rotating magnetic fields during modified vertical Bridgman crystal growth ," AIAA...Wang and Nancy Ma, "Semiconductor crystal growth by the vertical Bridgman process with rotating magnetic fields," ASME Journal of Heat Transfer...2005. 15. Stephen J. LaPointe, Nancy Ma and Donald W. Mueller, Jr., " Growth of binary alloyed semiconductor crystals by the vertical Bridgman

Stability Analysis of Distributed Order Fractional Chen System

PubMed Central

Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

Asymptotics of quasi-classical localized states in 2D system of charged hard-core bosons

NASA Astrophysics Data System (ADS)

Panov, Yu. D.; Moskvin, A. S.

2018-05-01

The continuous quasi-classical two-sublattice approximation is constructed for the 2D system of charged hard-core bosons to explore metastable inhomogeneous states analogous to inhomogeneous localized excitations in magnetic systems. The types of localized excitations are determined by asymptotic analysis and compared with numerical results. Depending on the homogeneous ground state, the excitations are the ferro and antiferro type vortices, the skyrmion-like topological excitations or linear domain walls.

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Raasakka, Matti

2014-06-01

We apply the non-commutative Fourier transform for Lie groups to formulate the non-commutative metric representation of the Ponzano-Regge spin foam model for 3d quantum gravity. The non-commutative representation allows to express the amplitudes of the model as a first order phase space path integral, whose properties we consider. In particular, we study the asymptotic behavior of the path integral in the semi-classical limit. First, we compare the stationary phase equations in the classical limit for three different non-commutative structures corresponding to the symmetric, Duflo and Freidel-Livine-Majid quantization maps. We find that in order to unambiguously recover discrete geometric constraints for non-commutative metric boundary data through the stationary phase method, the deformation structure of the phase space must be accounted for in the variational calculus. When this is understood, our results demonstrate that the non-commutative metric representation facilitates a convenient semi-classical analysis of the Ponzano-Regge model, which yields as the dominant contribution to the amplitude the cosine of the Regge action in agreement with previous studies. We also consider the asymptotics of the SU(2) 6j-symbol using the non-commutative phase space path integral for the Ponzano-Regge model, and explain the connection of our results to the previous asymptotic results in terms of coherent states.

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.

An asymptotic analysis of the laminar-turbulent transition of yield stress fluids in pipes

NASA Astrophysics Data System (ADS)

Myers, Tim G.; Mitchell, Sarah L.; Slatter, Paul

2017-02-01

The work in this paper concerns the axisymmetric pipe flow of a Herschel-Bulkley fluid, with the aim of determining a relation between the critical velocity (defining the transition between laminar and turbulent flow) and the pipe diameter in terms of the Reynolds number Re 3. The asymptotic behaviour for large and small pipes is examined and simple expressions for the leading order terms are presented. Results are then compared with experimental data. A nonlinear regression analysis shows that for the tested fluids the transition occurs at similar values to the Newtonian case, namely in the range 2100 < Re 3 < 2500.

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"

Pseudo and conditional score approach to joint analysis of current count and current status data.

PubMed

Wen, Chi-Chung; Chen, Yi-Hau

2018-04-17

We develop a joint analysis approach for recurrent and nonrecurrent event processes subject to case I interval censorship, which are also known in literature as current count and current status data, respectively. We use a shared frailty to link the recurrent and nonrecurrent event processes, while leaving the distribution of the frailty fully unspecified. Conditional on the frailty, the recurrent event is assumed to follow a nonhomogeneous Poisson process, and the mean function of the recurrent event and the survival function of the nonrecurrent event are assumed to follow some general form of semiparametric transformation models. Estimation of the models is based on the pseudo-likelihood and the conditional score techniques. The resulting estimators for the regression parameters and the unspecified baseline functions are shown to be consistent with rates of square and cubic roots of the sample size, respectively. Asymptotic normality with closed-form asymptotic variance is derived for the estimator of the regression parameters. We apply the proposed method to a fracture-osteoporosis survey data to identify risk factors jointly for fracture and osteoporosis in elders, while accounting for association between the two events within a subject. © 2018, The International Biometric Society.

Transonic flow of steam with non-equilibrium and homogenous condensation

NASA Astrophysics Data System (ADS)

Virk, Akashdeep Singh; Rusak, Zvi

2017-11-01

A small-disturbance model for studying the physical behavior of a steady transonic flow of steam with non-equilibrium and homogeneous condensation around a thin airfoil is derived. The steam thermodynamic behavior is described by van der Waals equation of state. The water condensation rate is calculated according to classical nucleation and droplet growth models. The current study is based on an asymptotic analysis of the fluid flow and condensation equations and boundary conditions in terms of the small thickness of the airfoil, small angle of attack, closeness of upstream flow Mach number to unity and small amount of condensate. The asymptotic analysis gives the similarity parameters that govern the problem. The flow field may be described by a non-homogeneous transonic small-disturbance equation coupled with a set of four ordinary differential equations for the calculation of the condensate mass fraction. An iterative numerical scheme which combines Murman & Cole's (1971) method with Simpson's integration rule is applied to solve the coupled system of equations. The model is used to study the effects of energy release from condensation on the aerodynamic performance of airfoils operating at high pressures and temperatures and near the vapor-liquid saturation conditions.

Asymptotic behavior of modulated Taylor-Couette flows with a crystalline inner cylinder

NASA Technical Reports Server (NTRS)

Braun, R. J.; Mcfadden, G. B.; Murray, B. T.; Coriell, S. R.; Glicksman, M. E.; Selleck, M. E.

1993-01-01

The linear stability of a modulated Taylor-Couette system when the inner cylindrical boundary consists of a crystalline solid-liquid interface is considered. Both experimentally and in numerical calculations it is found that the two-phase system is significantly less stable than the analogous rigid-walled system for materials with moderately large Prandtl numbers. A numerical treatment based on Floquet theory is described, which gives results that are in good agreement with preliminary experimental findings. In addition, this instability is further examined by carrying out a formal asymptotic expansion of the solution in the limit of large Prandtl number. In this limit the Floquet analysis is considerably simplified, and the linear stability of the modulated system can be determined to leading order through a conventional stability analysis, without recourse to Floquet theory. The resulting simplified problem is then studied for both the narrow gap geometry and for the case of a finite gap. It is surprising that the determination of the linear stability of the two-phase system is considerably simpler than that of the rigid-walled system, despite the complications introduced by the presence of the crystal-melt interface.

A non-asymptotic model of dynamics of honeycomb lattice-type plates

NASA Astrophysics Data System (ADS)

Cielecka, Iwona; Jędrysiak, Jarosław

2006-09-01

Lightweight structures, consisted of special composite material systems like sandwich plates, are often used in aerospace or naval engineering. In composite sandwich plates, the intermediate core is usually made of cellular structures, e.g. honeycomb micro-frames, reinforcing static and dynamic properties of these plates. Here, a new non-asymptotic continuum model of honeycomb lattice-type plates is shown and applied to the analysis of dynamic problems. The general formulation of the model for periodic lattice-type plates of an arbitrary lay-out was presented by Cielecka and Jędrysiak [Journal of Theoretical and Applied Mechanics 40 (2002) 23-46]. This model, partly based on the tolerance averaging method developed for periodic composite solids by Woźniak and Wierzbicki [Averaging techniques in thermomechanics of composite solids, Wydawnictwo Politechniki Częstochowskiej, Częstochowa, 2000], takes into account the effect of the length microstructure size on the dynamic plate behaviour. The shown method leads to the model equations describing the above effect for honeycomb lattice-type plates. These equations have the form similar to equations for isotropic cases. The dynamic analysis of such plates exemplifies this effect, which is significant and cannot be neglected. The physical correctness of the obtained results is also discussed.

Directions of arrival estimation with planar antenna arrays in the presence of mutual coupling

NASA Astrophysics Data System (ADS)

Akkar, Salem; Harabi, Ferid; Gharsallah, Ali

2013-06-01

Directions of arrival (DoAs) estimation of multiple sources using an antenna array is a challenging topic in wireless communication. The DoAs estimation accuracy depends not only on the selected technique and algorithm, but also on the geometrical configuration of the antenna array used during the estimation. In this article the robustness of common planar antenna arrays against unaccounted mutual coupling is examined and their DoAs estimation capabilities are compared and analysed through computer simulations using the well-known MUltiple SIgnal Classification (MUSIC) algorithm. Our analysis is based on an electromagnetic concept to calculate an approximation of the impedance matrices that define the mutual coupling matrix (MCM). Furthermore, a CRB analysis is presented and used as an asymptotic performance benchmark of the studied antenna arrays. The impact of the studied antenna arrays geometry on the MCM structure is also investigated. Simulation results show that the UCCA has more robustness against unaccounted mutual coupling and performs better results than both UCA and URA geometries. The performed simulations confirm also that, although the UCCA achieves better performance under complicated scenarios, the URA shows better asymptotic (CRB) behaviour which promises more accuracy on DoAs estimation.

Model reference tracking control of an aircraft: a robust adaptive approach

NASA Astrophysics Data System (ADS)

Tanyer, Ilker; Tatlicioglu, Enver; Zergeroglu, Erkan

2017-05-01

This work presents the design and the corresponding analysis of a nonlinear robust adaptive controller for model reference tracking of an aircraft that has parametric uncertainties in its system matrices and additive state- and/or time-dependent nonlinear disturbance-like terms in its dynamics. Specifically, robust integral of the sign of the error feedback term and an adaptive term is fused with a proportional integral controller. Lyapunov-based stability analysis techniques are utilised to prove global asymptotic convergence of the output tracking error. Extensive numerical simulations are presented to illustrate the performance of the proposed robust adaptive controller.

An asymptotic induced numerical method for the convection-diffusion-reaction equation

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

Hadronic Form Factors in Asymptotically Free Field Theories

DOE R&D Accomplishments Database

Gross, D. J.; Treiman, S. B.

1974-01-01

The breakdown of Bjorken scaling in asymptotically free gauge theories of the strong interactions is explored for its implications on the large q{sup 2} behavior of nucleon form factors. Duality arguments of Bloom and Gilman suggest a connection between the form factors and the threshold properties of the deep inelastic structure functions. The latter are addressed directly in an analysis of asymptotically free theories; and through the duality connection we are then led to statements about the form factors. For very large q{sup 2} the form factors are predicted to fall faster than any inverse power of q{sup 2}. For the more modest range of q{sup 2} reached in existing experiments the agreement with data is fairly good, though this may well be fortuitous. Extrapolations beyond this range are presented.

Boundary asymptotics for a non-neutral electrochemistry model with small Debye length

NASA Astrophysics Data System (ADS)

Lee, Chiun-Chang; Ryham, Rolf J.

2018-04-01

This article addresses the boundary asymptotics of the electrostatic potential in non-neutral electrochemistry models with small Debye length in bounded domains. Under standard physical assumptions motivated by non-electroneutral phenomena in oxidation-reduction reactions, we show that the electrostatic potential asymptotically blows up at boundary points with respect to the bulk reference potential as the scaled Debye length tends to zero. The analysis gives a lower bound for the blow-up rate with respect to the model parameters. Moreover, the maximum potential difference over any compact subset of the physical domain vanishes exponentially in the zero-Debye-length limit. The results mathematically confirm the physical description that electrolyte solutions are electrically neutral in the bulk and are strongly electrically non-neutral near charged surfaces.

Local Stability of AIDS Epidemic Model Through Treatment and Vertical Transmission with Time Delay

NASA Astrophysics Data System (ADS)

Novi W, Cascarilla; Lestari, Dwi

2016-02-01

This study aims to explain stability of the spread of AIDS through treatment and vertical transmission model. Human with HIV need a time to positively suffer AIDS. The existence of a time, human with HIV until positively suffer AIDS can be delayed for a time so that the model acquired is the model with time delay. The model form is a nonlinear differential equation with time delay, SIPTA (susceptible-infected-pre AIDS-treatment-AIDS). Based on SIPTA model analysis results the disease free equilibrium point and the endemic equilibrium point. The disease free equilibrium point with and without time delay are local asymptotically stable if the basic reproduction number is less than one. The endemic equilibrium point will be local asymptotically stable if the time delay is less than the critical value of delay, unstable if the time delay is more than the critical value of delay, and bifurcation occurs if the time delay is equal to the critical value of delay.

Dynamics of an experimental unconfined aquifer

NASA Astrophysics Data System (ADS)

Lajeunesse, E.; Guérin, A.; Devauchelle, O.

2015-12-01

During a rain event, water infiltrates into the ground where it flows slowly towards rivers. We use a tank filled with glass beads to simulate this process in a simplified laboratory experiment. A sprinkler pipe generates rain, which infiltrates into the porous material. Groundwater exits this laboratory aquifer through one side of the tank. The resulting water discharge increases rapidly during rainfall, and decays slowly after the rain has stopped.A theoretical analysis based on Darcy's law and the shallow-water approximation reveals two asymptotic regimes. At the beginning of a rain event, the water discharge increases linearly with time, with a slope proportional to the rainfall rate at the power of 3/2. Long after the rain has stopped, it decreases as the inverse time squared, as predicted by Polubarinova-Kochina (1962). These predictions compare well against our experimental data.Field measurements from two distinct catchments exhibit the same asymptotic behaviours as our experiment. This observation suggests that, despite the simplicity of the setup, our experimental results could be extended to natural groundwater flows.

Statistical methods for incomplete data: Some results on model misspecification.

PubMed

McIsaac, Michael; Cook, R J

2017-02-01

Inverse probability weighted estimating equations and multiple imputation are two of the most studied frameworks for dealing with incomplete data in clinical and epidemiological research. We examine the limiting behaviour of estimators arising from inverse probability weighted estimating equations, augmented inverse probability weighted estimating equations and multiple imputation when the requisite auxiliary models are misspecified. We compute limiting values for settings involving binary responses and covariates and illustrate the effects of model misspecification using simulations based on data from a breast cancer clinical trial. We demonstrate that, even when both auxiliary models are misspecified, the asymptotic biases of double-robust augmented inverse probability weighted estimators are often smaller than the asymptotic biases of estimators arising from complete-case analyses, inverse probability weighting or multiple imputation. We further demonstrate that use of inverse probability weighting or multiple imputation with slightly misspecified auxiliary models can actually result in greater asymptotic bias than the use of naïve, complete case analyses. These asymptotic results are shown to be consistent with empirical results from simulation studies.

Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method.

PubMed

Li, Xuanying; Li, Xiaotong; Hu, Cheng

2017-12-01

In this paper, without transforming the second order inertial neural networks into the first order differential systems by some variable substitutions, asymptotic stability and synchronization for a class of delayed inertial neural networks are investigated. Firstly, a new Lyapunov functional is constructed to directly propose the asymptotic stability of the inertial neural networks, and some new stability criteria are derived by means of Barbalat Lemma. Additionally, by designing a new feedback control strategy, the asymptotic synchronization of the addressed inertial networks is studied and some effective conditions are obtained. To reduce the control cost, an adaptive control scheme is designed to realize the asymptotic synchronization. It is noted that the dynamical behaviors of inertial neural networks are directly analyzed in this paper by constructing some new Lyapunov functionals, this is totally different from the traditional reduced-order variable substitution method. Finally, some numerical simulations are given to demonstrate the effectiveness of the derived theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Can we define an asymptotic value for the ice active surface site density for heterogeneous ice nucleation?

NASA Astrophysics Data System (ADS)

Niedermeier, Dennis; Augustin-Bauditz, Stefanie; Hartmann, Susan; Wex, Heike; Ignatius, Karoliina; Stratmann, Frank

2015-05-01

The immersion freezing behavior of droplets containing size-segregated, monodisperse feldspar particles was investigated. For all particle sizes investigated, a leveling off of the frozen droplet fraction was observed reaching a plateau within the heterogeneous freezing temperature regime (T >- 38°C). The frozen fraction in the plateau region was proportional to the particle surface area. Based on these findings, an asymptotic value for ice active surface site density ns, which we named ns⋆, could be determined for the investigated feldspar sample. The comparison of these results with those of other studies not only elucidates the general feasibility of determining such an asymptotic value but also shows that the value of ns⋆ strongly depends on the method of the particle surface area determination. However, such an asymptotic value might be an important input parameter for atmospheric modeling applications. At least it shows that care should be taken when ns is extrapolated to lower or higher temperature.

Turbomachinery computational fluid dynamics: asymptotes and paradigm shifts.

PubMed

Dawes, W N

2007-10-15

This paper reviews the development of computational fluid dynamics (CFD) specifically for turbomachinery simulations and with a particular focus on application to problems with complex geometry. The review is structured by considering this development as a series of paradigm shifts, followed by asymptotes. The original S1-S2 blade-blade-throughflow model is briefly described, followed by the development of two-dimensional then three-dimensional blade-blade analysis. This in turn evolved from inviscid to viscous analysis and then from steady to unsteady flow simulations. This development trajectory led over a surprisingly small number of years to an accepted approach-a 'CFD orthodoxy'. A very important current area of intense interest and activity in turbomachinery simulation is in accounting for real geometry effects, not just in the secondary air and turbine cooling systems but also associated with the primary path. The requirements here are threefold: capturing and representing these geometries in a computer model; making rapid design changes to these complex geometries; and managing the very large associated computational models on PC clusters. Accordingly, the challenges in the application of the current CFD orthodoxy to complex geometries are described in some detail. The main aim of this paper is to argue that the current CFD orthodoxy is on a new asymptote and is not in fact suited for application to complex geometries and that a paradigm shift must be sought. In particular, the new paradigm must be geometry centric and inherently parallel without serial bottlenecks. The main contribution of this paper is to describe such a potential paradigm shift, inspired by the animation industry, based on a fundamental shift in perspective from explicit to implicit geometry and then illustrate this with a number of applications to turbomachinery.

Ultrahigh-resolution spectroscopy with atomic or molecular dark resonances: Exact steady-state line shapes and asymptotic profiles in the adiabatic pulsed regime

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

Zanon-Willette, Thomas; Clercq, Emeric de; Arimondo, Ennio

2011-12-15

Exact and asymptotic line shape expressions are derived from the semiclassical density matrix representation describing a set of closed three-level {Lambda} atomic or molecular states including decoherences, relaxation rates, and light shifts. An accurate analysis of the exact steady-state dark-resonance profile describing the Autler-Townes doublet, the electromagnetically induced transparency or coherent population trapping resonance, and the Fano-Feshbach line shape leads to the linewidth expression of the two-photon Raman transition and frequency shifts associated to the clock transition. From an adiabatic analysis of the dynamical optical Bloch equations in the weak field limit, a pumping time required to efficiently trap amore » large number of atoms into a coherent superposition of long-lived states is established. For a highly asymmetrical configuration with different decay channels, a strong two-photon resonance based on a lower states population inversion is established when the driving continuous-wave laser fields are greatly unbalanced. When time separated resonant two-photon pulses are applied in the adiabatic pulsed regime for atomic or molecular clock engineering, where the first pulse is long enough to reach a coherent steady-state preparation and the second pulse is very short to avoid repumping into a new dark state, dark-resonance fringes mixing continuous-wave line shape properties and coherent Ramsey oscillations are created. Those fringes allow interrogation schemes bypassing the power broadening effect. Frequency shifts affecting the central clock fringe computed from asymptotic profiles and related to the Raman decoherence process exhibit nonlinear shapes with the three-level observable used for quantum measurement. We point out that different observables experience different shifts on the lower-state clock transition.« less

Design and analysis of SEIQR worm propagation model in mobile internet

NASA Astrophysics Data System (ADS)

Xiao, Xi; Fu, Peng; Dou, Changsheng; Li, Qing; Hu, Guangwu; Xia, Shutao

2017-02-01

The mobile Internet has considerably facilitated daily life in recent years. However, it has become the breeding ground for lots of new worms, including the Bluetooth-based worm, the SMS/MMS-based worm and the Wi-Fi-based worm. At present, Wi-Fi is widely used for mobile devices to connect to the Internet. But it exposes these devices to the dangerous environment. Most current worm propagation models aim to solve the problems of computer worms. They cannot be used directly in the mobile environment, particularly in the Wi-Fi scenario, because of the differences between computers and mobile devices. In this paper, we propose a worm propagation model in the Wi-Fi environment, called SEIQR (Susceptible-Exposed-Infectious- Quarantined-Recovered). In the model, infected nodes can be quarantined by the Wi-Fi base station, and a new state named the Quarantined state (Q) is established to represent these infected nodes. Based on this model, we present an effective method to inhibit the spread of the Wi-Fi-based worms. Furthermore, related stabilities of the worm-free and endemic equilibriums are studied based on the basic reproduction number R0. The worm-free equilibrium is locally and globally asymptotically stable if R0 < 1, whereas the endemic equilibrium is locally asymptotically stable if R0 < 1. Finally, we evaluate the performance of our model by comprehensive experiments with different infection rates and quarantine rates. The results indicate that our mechanism can combat the worms propagated via Wi-Fi.

Discrete-time switching periodic adaptive control for time-varying parameters with unknown periodicity

NASA Astrophysics Data System (ADS)

Yu, Miao; Huang, Deqing; Yang, Wanqiu

2018-06-01

In this paper, we address the problem of unknown periodicity for a class of discrete-time nonlinear parametric systems without assuming any growth conditions on the nonlinearities. The unknown periodicity hides in the parametric uncertainties, which is difficult to estimate with existing techniques. By incorporating a logic-based switching mechanism, we identify the period and bound of unknown parameter simultaneously. Lyapunov-based analysis is given to demonstrate that a finite number of switchings can guarantee the asymptotic tracking for the nonlinear parametric systems. The simulation result also shows the efficacy of the proposed switching periodic adaptive control approach.

One Step Quantum Key Distribution Based on EPR Entanglement

PubMed Central

Li, Jian; Li, Na; Li, Lei-Lei; Wang, Tao

2016-01-01

A novel quantum key distribution protocol is presented, based on entanglement and dense coding and allowing asymptotically secure key distribution. Considering the storage time limit of quantum bits, a grouping quantum key distribution protocol is proposed, which overcomes the vulnerability of first protocol and improves the maneuverability. Moreover, a security analysis is given and a simple type of eavesdropper’s attack would introduce at least an error rate of 46.875%. Compared with the “Ping-pong” protocol involving two steps, the proposed protocol does not need to store the qubit and only involves one step. PMID:27357865

Asymptotic Analysis of the parton branching equation at LHC Energies

NASA Astrophysics Data System (ADS)

Wang, W. Y.; Lau, H. P.; Leong, Q.; Chan, A. H.; Oh, C. H.

2018-01-01

An asymptotic solution to the QCD parton branching equation is derived using the method of Laplace transformation and saddle point approximation. The distribution is applied to charged particle multiplicity distributions in proton-proton collisions at √s = 0.9, 2.36, and 7 TeV for |ƞ| < 0.5, 1.0, 1.5, 2.0, 2.4, and 8 TeV for |ƞ| < 0.5, 1.0, 1.5, as well as 13 TeV data for |ƞ| < 0.8 and 2.5.

Pinning synchronization of memristor-based neural networks with time-varying delays.

PubMed

Yang, Zhanyu; Luo, Biao; Liu, Derong; Li, Yueheng

2017-09-01

In this paper, the synchronization of memristor-based neural networks with time-varying delays via pinning control is investigated. A novel pinning method is introduced to synchronize two memristor-based neural networks which denote drive system and response system, respectively. The dynamics are studied by theories of differential inclusions and nonsmooth analysis. In addition, some sufficient conditions are derived to guarantee asymptotic synchronization and exponential synchronization of memristor-based neural networks via the presented pinning control. Furthermore, some improvements about the proposed control method are also discussed in this paper. Finally, the effectiveness of the obtained results is demonstrated by numerical simulations. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Continuous-Variable Measurement-Device-Independent Multipartite Quantum Communication Using Coherent States

NASA Astrophysics Data System (ADS)

Zhou, Jian; Guo, Ying

2017-02-01

A continuous-variable measurement-device-independent (CV-MDI) multipartite quantum communication protocol is designed to realize multipartite communication based on the GHZ state analysis using Gaussian coherent states. It can remove detector side attack as the multi-mode measurement is blindly done in a suitable Black Box. The entanglement-based CV-MDI multipartite communication scheme and the equivalent prepare-and-measurement scheme are proposed to analyze the security and guide experiment, respectively. The general eavesdropping and coherent attack are considered for the security analysis. Subsequently, all the attacks are ascribed to coherent attack against imperfect links. The asymptotic key rate of the asymmetric configuration is also derived with the numeric simulations illustrating the performance of the proposed protocol.

ADAPTIVE MATCHING IN RANDOMIZED TRIALS AND OBSERVATIONAL STUDIES

PubMed Central

van der Laan, Mark J.; Balzer, Laura B.; Petersen, Maya L.

2014-01-01

SUMMARY In many randomized and observational studies the allocation of treatment among a sample of n independent and identically distributed units is a function of the covariates of all sampled units. As a result, the treatment labels among the units are possibly dependent, complicating estimation and posing challenges for statistical inference. For example, cluster randomized trials frequently sample communities from some target population, construct matched pairs of communities from those included in the sample based on some metric of similarity in baseline community characteristics, and then randomly allocate a treatment and a control intervention within each matched pair. In this case, the observed data can neither be represented as the realization of n independent random variables, nor, contrary to current practice, as the realization of n/2 independent random variables (treating the matched pair as the independent sampling unit). In this paper we study estimation of the average causal effect of a treatment under experimental designs in which treatment allocation potentially depends on the pre-intervention covariates of all units included in the sample. We define efficient targeted minimum loss based estimators for this general design, present a theorem that establishes the desired asymptotic normality of these estimators and allows for asymptotically valid statistical inference, and discuss implementation of these estimators. We further investigate the relative asymptotic efficiency of this design compared with a design in which unit-specific treatment assignment depends only on the units’ covariates. Our findings have practical implications for the optimal design and analysis of pair matched cluster randomized trials, as well as for observational studies in which treatment decisions may depend on characteristics of the entire sample. PMID:25097298

Ponderomotive effects in multiphoton pair production

NASA Astrophysics Data System (ADS)

Kohlfürst, Christian; Alkofer, Reinhard

2018-02-01

The Dirac-Heisenberg-Wigner formalism is employed to investigate electron-positron pair production in cylindrically symmetric but otherwise spatially inhomogeneous, oscillating electric fields. The oscillation frequencies are hereby tuned to obtain multiphoton pair production in the nonperturbative threshold regime. An effective mass, as well as a trajectory-based semiclassical analysis, is introduced in order to interpret the numerical results for the distribution functions as well as for the particle yields and spectra. The results, including the asymptotic particle spectra, display clear signatures of ponderomotive forces.

On the dispersion relations for an inhomogeneous waveguide with attenuation

NASA Astrophysics Data System (ADS)

Vatul'yan, A. O.; Yurlov, V. O.

2016-09-01

Some general laws concerning the structure of dispersion relations for solid inhomogeneous waveguides with attenuation are studied. An approach based on the analysis of a first-order matrix differential equation is presented in the framework of the concept of complex moduli. Some laws concerning the structure of components of the dispersion set for a viscoelastic inhomogeneous cylindrical waveguide are studied analytically and numerically, and the asymptotics of components of the dispersion set are constructed for arbitrary inhomogeneity laws in the low-frequency region.

A comparison of locally adaptive multigrid methods: LDC, FAC and FIC

NASA Technical Reports Server (NTRS)

Khadra, Khodor; Angot, Philippe; Caltagirone, Jean-Paul

1993-01-01

This study is devoted to a comparative analysis of three 'Adaptive ZOOM' (ZOom Overlapping Multi-level) methods based on similar concepts of hierarchical multigrid local refinement: LDC (Local Defect Correction), FAC (Fast Adaptive Composite), and FIC (Flux Interface Correction)--which we proposed recently. These methods are tested on two examples of a bidimensional elliptic problem. We compare, for V-cycle procedures, the asymptotic evolution of the global error evaluated by discrete norms, the corresponding local errors, and the convergence rates of these algorithms.

Revisiting the Estimation of Dinosaur Growth Rates

PubMed Central

Myhrvold, Nathan P.

2013-01-01

Previous growth-rate studies covering 14 dinosaur taxa, as represented by 31 data sets, are critically examined and reanalyzed by using improved statistical techniques. The examination reveals that some previously reported results cannot be replicated by using the methods originally reported; results from new methods are in many cases different, in both the quantitative rates and the qualitative nature of the growth, from results in the prior literature. Asymptotic growth curves, which have been hypothesized to be ubiquitous, are shown to provide best fits for only four of the 14 taxa. Possible reasons for non-asymptotic growth patterns are discussed; they include systematic errors in the age-estimation process and, more likely, a bias toward younger ages among the specimens analyzed. Analysis of the data sets finds that only three taxa include specimens that could be considered skeletally mature (i.e., having attained 90% of maximum body size predicted by asymptotic curve fits), and eleven taxa are quite immature, with the largest specimen having attained less than 62% of predicted asymptotic size. The three taxa that include skeletally mature specimens are included in the four taxa that are best fit by asymptotic curves. The totality of results presented here suggests that previous estimates of both maximum dinosaur growth rates and maximum dinosaur sizes have little statistical support. Suggestions for future research are presented. PMID:24358133

An Analysis of the Optimal Control Modification Method Applied to Flutter Suppression

NASA Technical Reports Server (NTRS)

Drew, Michael; Nguyen, Nhan T.; Hashemi, Kelley E.; Ting, Eric; Chaparro, Daniel

2017-01-01

Unlike basic Model Reference Adaptive Control (MRAC)l, Optimal Control Modification (OCM) has been shown to be a promising MRAC modification with robustness and analytical properties not present in other adaptive control methods. This paper presents an analysis of the OCM method, and how the asymptotic property of OCM is useful for analyzing and tuning the controller. We begin with a Lyapunov stability proof of an OCM controller having two adaptive gain terms, then the less conservative and easily analyzed OCM asymptotic property is presented. Two numerical examples are used to show how this property can accurately predict steady state stability and quantitative robustness in the presence of time delay, and relative to linear plant perturbations, and nominal Loop Transfer Recovery (LTR) tuning. The asymptotic property of the OCM controller is then used as an aid in tuning the controller applied to a large scale aeroservoelastic longitudinal aircraft model for flutter suppression. Control with OCM adaptive augmentation is shown to improve performance over that of the nominal non-adaptive controller when significant disparities exist between the controller/observer model and the true plant model.

Asymptotic formulae for likelihood-based tests of new physics

NASA Astrophysics Data System (ADS)

Cowan, Glen; Cranmer, Kyle; Gross, Eilam; Vitells, Ofer

2011-02-01

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the "Asimov data set", which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.

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

Error of semiclassical eigenvalues in the semiclassical limit - an asymptotic analysis of the Sinai billiard

NASA Astrophysics Data System (ADS)

Dahlqvist, Per

1999-10-01

We estimate the error in the semiclassical trace formula for the Sinai billiard under the assumption that the largest source of error is due to penumbra diffraction: namely, diffraction effects for trajectories passing within a distance Ricons/Journals/Common/cdot" ALT="cdot" ALIGN="TOP"/>O((kR)-2/3) to the disc and trajectories being scattered in very forward directions. Here k is the momentum and R the radius of the scatterer. The semiclassical error is estimated by perturbing the Berry-Keating formula. The analysis necessitates an asymptotic analysis of very long periodic orbits. This is obtained within an approximation originally due to Baladi, Eckmann and Ruelle. We find that the average error, for sufficiently large values of kR, will exceed the mean level spacing.

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

Sevast'yanov, E A; Sadekova, E Kh

The Bulgarian mathematicians Sendov, Popov, and Boyanov have well-known results on the asymptotic behaviour of the least deviations of 2{pi}-periodic functions in the classes H{sup {omega}} from trigonometric polynomials in the Hausdorff metric. However, the asymptotics they give are not adequate to detect a difference in, for example, the rate of approximation of functions f whose moduli of continuity {omega}(f;{delta}) differ by factors of the form (log(1/{delta})){sup {beta}}. Furthermore, a more detailed determination of the asymptotic behaviour by traditional methods becomes very difficult. This paper develops an approach based on using trigonometric snakes as approximating polynomials. The snakes of ordermore » n inscribed in the Minkowski {delta}-neighbourhood of the graph of the approximated function f provide, in a number of cases, the best approximation for f (for the appropriate choice of {delta}). The choice of {delta} depends on n and f and is based on constructing polynomial kernels adjusted to the Hausdorff metric and polynomials with special oscillatory properties. Bibliography: 19 titles.« less

Rank-based permutation approaches for non-parametric factorial designs.

PubMed

Umlauft, Maria; Konietschke, Frank; Pauly, Markus

2017-11-01

Inference methods for null hypotheses formulated in terms of distribution functions in general non-parametric factorial designs are studied. The methods can be applied to continuous, ordinal or even ordered categorical data in a unified way, and are based only on ranks. In this set-up Wald-type statistics and ANOVA-type statistics are the current state of the art. The first method is asymptotically exact but a rather liberal statistical testing procedure for small to moderate sample size, while the latter is only an approximation which does not possess the correct asymptotic α level under the null. To bridge these gaps, a novel permutation approach is proposed which can be seen as a flexible generalization of the Kruskal-Wallis test to all kinds of factorial designs with independent observations. It is proven that the permutation principle is asymptotically correct while keeping its finite exactness property when data are exchangeable. The results of extensive simulation studies foster these theoretical findings. A real data set exemplifies its applicability. © 2017 The British Psychological Society.

Black p-branes versus black holes in non-asymptotically flat Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Habib Mazharimousavi, S.; Halilsoy, M.

2016-09-01

We present a class of non-asymptotically flat (NAF) charged black p-branes (BpB) with p-compact dimensions in higher-dimensional Einstein-Yang-Mills theory. Asymptotically the NAF structure manifests itself as an anti-de sitter spacetime. We determine the total mass/energy enclosed in a thin shell located outside the event horizon. By comparing the entropies of BpB with those of black holes in the same dimensions we derive transition criteria between the two types of black objects. Given certain conditions satisfied, our analysis shows that BpB can be considered excited states of black holes. An event horizon r+ versus charge square Q2 plot for the BpB reveals such a transition where r+ is related to the horizon radius rh of the black hole (BH) both with the common charge Q.

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

NASA Technical Reports Server (NTRS)

Shaw, Stephen J.; Duck, Peter W.

1992-01-01

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

NASA Technical Reports Server (NTRS)

Shaw, Stephen J.; Duck, Peter W.

1990-01-01

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions, are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

Transcriptome Analysis of Liangshan Pig Muscle Development at the Growth Curve Inflection Point and Asymptotic Stages Using Digital Gene Expression Profiling

PubMed Central

Du, Jingjing; Liu, Chendong; Wu, Xiaoqian; Pu, Qiang; Fu, Yuhua; Tang, Qianzi; Liu, Yuanrui; Li, Qiang; Yang, Runlin; Li, Xuewei; Tang, Guoqing; Jiang, Yanzhi; Li, Mingzhou; Zhang, Shunhua; Zhu, Li

2015-01-01

Animal growth curves can provide essential information for animal breeders to optimize feeding and management strategies. However, the genetic mechanism underlying the phenotypic differentiation between the inflection point and asymptotic stages of the growth curve is not well characterized. Here, we employed Liangshan pigs in stages of growth at the inflection point (under inflection point: UIP) and the two asymptotic stages (before the inflection point: BIP, after the inflection point: AIP) as models to survey global gene expression in the longissimus dorsi muscle using digital gene expression (DGE) tag profiling. We found Liangshan pigs reached maximum growth rate (UIP) at 163.6 days of age and a weight of 134.6 kg. The DGE libraries generated 117 million reads of 5.89 gigabases in length. 21,331, 20,996 and 20,139 expressed transcripts were identified BIP, UIP and AIP, respectively. Among them, we identified 757 differentially expressed genes (DEGs) between BIP and UIP, and 271 DEGs between AIP and UIP. An enrichment analysis of DEGs proved the immune system was strengthened in the AIP stage. Energy metabolism rate, global transcriptional activity and bone development intensity were highest UIP. Meat from Liangshan pigs had the highest intramuscular fat content and most favorable fatty acid composition in the AIP. Three hundred eighty (27.70%) specific expression genes were highly enriched in QTL regions for growth and meat quality traits. This study completed a comprehensive analysis of diverse genetic mechanisms underlying the inflection point and asymptotic stages of growth. Our findings will serve as an important resource in the understanding of animal growth and development in indigenous pig breeds. PMID:26292092

Transcriptome Analysis of Liangshan Pig Muscle Development at the Growth Curve Inflection Point and Asymptotic Stages Using Digital Gene Expression Profiling.

PubMed

Shen, Linyuan; Luo, Jia; Du, Jingjing; Liu, Chendong; Wu, Xiaoqian; Pu, Qiang; Fu, Yuhua; Tang, Qianzi; Liu, Yuanrui; Li, Qiang; Yang, Runlin; Li, Xuewei; Tang, Guoqing; Jiang, Yanzhi; Li, Mingzhou; Zhang, Shunhua; Zhu, Li

2015-01-01

Animal growth curves can provide essential information for animal breeders to optimize feeding and management strategies. However, the genetic mechanism underlying the phenotypic differentiation between the inflection point and asymptotic stages of the growth curve is not well characterized. Here, we employed Liangshan pigs in stages of growth at the inflection point (under inflection point: UIP) and the two asymptotic stages (before the inflection point: BIP, after the inflection point: AIP) as models to survey global gene expression in the longissimus dorsi muscle using digital gene expression (DGE) tag profiling. We found Liangshan pigs reached maximum growth rate (UIP) at 163.6 days of age and a weight of 134.6 kg. The DGE libraries generated 117 million reads of 5.89 gigabases in length. 21,331, 20,996 and 20,139 expressed transcripts were identified BIP, UIP and AIP, respectively. Among them, we identified 757 differentially expressed genes (DEGs) between BIP and UIP, and 271 DEGs between AIP and UIP. An enrichment analysis of DEGs proved the immune system was strengthened in the AIP stage. Energy metabolism rate, global transcriptional activity and bone development intensity were highest UIP. Meat from Liangshan pigs had the highest intramuscular fat content and most favorable fatty acid composition in the AIP. Three hundred eighty (27.70%) specific expression genes were highly enriched in QTL regions for growth and meat quality traits. This study completed a comprehensive analysis of diverse genetic mechanisms underlying the inflection point and asymptotic stages of growth. Our findings will serve as an important resource in the understanding of animal growth and development in indigenous pig breeds.

Unsteady Aerodynamic Models for Turbomachinery Aeroelastic and Aeroacoustic Applications

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Barnett, Mark; Ayer, Timothy C.

1995-01-01

Theoretical analyses and computer codes are being developed for predicting compressible unsteady inviscid and viscous flows through blade rows of axial-flow turbomachines. Such analyses are needed to determine the impact of unsteady flow phenomena on the structural durability and noise generation characteristics of the blading. The emphasis has been placed on developing analyses based on asymptotic representations of unsteady flow phenomena. Thus, high Reynolds number flows driven by small amplitude unsteady excitations have been considered. The resulting analyses should apply in many practical situations and lead to a better understanding of the relevant flow physics. In addition, they will be efficient computationally, and therefore, appropriate for use in aeroelastic and aeroacoustic design studies. Under the present effort, inviscid interaction and linearized inviscid unsteady flow models have been formulated, and inviscid and viscid prediction capabilities for subsonic steady and unsteady cascade flows have been developed. In this report, we describe the linearized inviscid unsteady analysis, LINFLO, the steady inviscid/viscid interaction analysis, SFLOW-IVI, and the unsteady viscous layer analysis, UNSVIS. These analyses are demonstrated via application to unsteady flows through compressor and turbine cascades that are excited by prescribed vortical and acoustic excitations and by prescribed blade vibrations. Recommendations are also given for the future research needed for extending and improving the foregoing asymptotic analyses, and to meet the goal of providing efficient inviscid/viscid interaction capabilities for subsonic and transonic unsteady cascade flows.

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…

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)

A family of asymptotically stable control laws for flexible robots based on a passivity approach

NASA Technical Reports Server (NTRS)

Lanari, Leonardo; Wen, John T.

1991-01-01

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility.

On the strain energy of laminated composite plates

NASA Technical Reports Server (NTRS)

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.

Linear regression analysis of survival data with missing censoring indicators.

PubMed

Wang, Qihua; Dinse, Gregg E

2011-04-01

Linear regression analysis has been studied extensively in a random censorship setting, but typically all of the censoring indicators are assumed to be observed. In this paper, we develop synthetic data methods for estimating regression parameters in a linear model when some censoring indicators are missing. We define estimators based on regression calibration, imputation, and inverse probability weighting techniques, and we prove all three estimators are asymptotically normal. The finite-sample performance of each estimator is evaluated via simulation. We illustrate our methods by assessing the effects of sex and age on the time to non-ambulatory progression for patients in a brain cancer clinical trial.

Orientational analysis of planar fibre systems observed as a Poisson shot-noise process.

PubMed

Kärkkäinen, Salme; Lantuéjoul, Christian

2007-10-01

We consider two-dimensional fibrous materials observed as a digital greyscale image. The problem addressed is to estimate the orientation distribution of unobservable thin fibres from a greyscale image modelled by a planar Poisson shot-noise process. The classical stereological approach is not straightforward, because the point intensities of thin fibres along sampling lines may not be observable. For such cases, Kärkkäinen et al. (2001) suggested the use of scaled variograms determined from grey values along sampling lines in several directions. Their method is based on the assumption that the proportion between the scaled variograms and point intensities in all directions of sampling lines is constant. This assumption is proved to be valid asymptotically for Boolean models and dead leaves models, under some regularity conditions. In this work, we derive the scaled variogram and its approximations for a planar Poisson shot-noise process using the modified Bessel function. In the case of reasonable high resolution of the observed image, the scaled variogram has an approximate functional relation to the point intensity, and in the case of high resolution the relation is proportional. As the obtained relations are approximative, they are tested on simulations. The existing orientation analysis method based on the proportional relation is further experimented on images with different resolutions. The new result, the asymptotic proportionality between the scaled variograms and the point intensities for a Poisson shot-noise process, completes the earlier results for the Boolean models and for the dead leaves models.

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.

Better band gaps with asymptotically corrected local exchange potentials

NASA Astrophysics Data System (ADS)

Singh, Prashant; Harbola, Manoj K.; Hemanadhan, M.; Mookerjee, Abhijit; Johnson, D. D.

2016-02-01

We formulate a spin-polarized van Leeuwen and Baerends (vLB) correction to the local density approximation (LDA) exchange potential [R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994), 10.1103/PhysRevA.49.2421] that enforces the ionization potential (IP) theorem following T. Stein et al. [Phys. Rev. Lett. 105, 266802 (2010), 10.1103/PhysRevLett.105.266802]. For electronic-structure problems, the vLB correction replicates the behavior of exact-exchange potentials, with improved scaling and well-behaved asymptotics, but with the computational cost of semilocal functionals. The vLB + IP correction produces a large improvement in the eigenvalues over those from the LDA due to correct asymptotic behavior and atomic shell structures, as shown in rare-gas, alkaline-earth, zinc-based oxides, alkali halides, sulfides, and nitrides. In half-Heusler alloys, this asymptotically corrected LDA reproduces the spin-polarized properties correctly, including magnetism and half-metallicity. We also consider finite-sized systems [e.g., ringed boron nitride (B12N12 ) and graphene (C24)] to emphasize the wide applicability of the method.

Better band gaps with asymptotically corrected local exchange potentials

DOE PAGES

Singh, Prashant; Harbola, Manoj K.; Hemanadhan, M.; ...

2016-02-22

In this study, we formulate a spin-polarized van Leeuwen and Baerends (vLB) correction to the local density approximation (LDA) exchange potential [R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994)] that enforces the ionization potential (IP) theorem following T. Stein et al. [Phys. Rev. Lett. 105, 266802 (2010)]. For electronic-structure problems, the vLB correction replicates the behavior of exact-exchange potentials, with improved scaling and well-behaved asymptotics, but with the computational cost of semilocal functionals. The vLB + IP correction produces a large improvement in the eigenvalues over those from the LDA due to correct asymptotic behaviormore » and atomic shell structures, as shown in rare-gas, alkaline-earth, zinc-based oxides, alkali halides, sulfides, and nitrides. In half-Heusler alloys, this asymptotically corrected LDA reproduces the spin-polarized properties correctly, including magnetism and half-metallicity. We also consider finite-sized systems [e.g., ringed boron nitride (B 12N 12) and graphene (C 24)] to emphasize the wide applicability of the method.« less

Time-frequency signal analysis and synthesis - The choice of a method and its application

NASA Astrophysics Data System (ADS)

Boashash, Boualem

In this paper, the problem of choosing a method for time-frequency signal analysis is discussed. It is shown that a natural approach leads to the introduction of the concepts of the analytic signal and instantaneous frequency. The Wigner-Ville Distribution (WVD) is a method of analysis based upon these concepts and it is shown that an accurate Time-Frequency representation of a signal can be obtained by using the WVD for the analysis of a class of signals referred to as 'asymptotic'. For this class of signals, the instantaneous frequency describes an important physical parameter characteristic of the process under investigation. The WVD procedure for signal analysis and synthesis is outlined and its properties are reviewed for deterministic and random signals.

Time-Frequency Signal Analysis And Synthesis The Choice Of A Method And Its Application

NASA Astrophysics Data System (ADS)

Boashash, Boualem

1988-02-01

In this paper, the problem of choosing a method for time-frequency signal analysis is discussed. It is shown that a natural approach leads to the introduction of the concepts of the analytic signal and in-stantaneous frequency. The Wigner-Ville Distribution (WVD) is a method of analysis based upon these concepts and it is shown that an accurate Time-Frequency representation of a signal can be obtained by using the WVD for the analysis of a class of signals referred to as "asymptotic". For this class of signals, the instantaneous frequency describes an important physical parameter characteristic of the process under investigation. The WVD procedure for signal analysis and synthesis is outlined and its properties are reviewed for deterministic and random signals.

Fast penetration of megagauss fields into metallic conductors

NASA Astrophysics Data System (ADS)

Schnitzer, Ory

2014-08-01

Megagauss magnetic-field penetration into a conducting material is studied via a simplified but representative model, wherein the magnetic-diffusion equation is coupled with a thermal-energy balance. The specific scenario considered is that of a prescribed magnetic field rising (in proportion to an arbitrary power r of time) at the surface of a conducting half-space whose electric conductivity is assumed proportional to an arbitrary inverse power γ of temperature. We employ a systematic asymptotic scheme in which the case of a strong surface field corresponds to a singular asymptotic limit. In this limit, the highly magnetized and hot "skin" terminates at a distinct propagating wave-front. Employing the method of matched asymptotic expansions, we find self-similar solutions of the magnetized region which match a narrow boundary-layer region about the advancing wave front. The rapidly decaying magnetic-field profile in the latter region is also self similar; when scaled by the instantaneous propagation speed, its shape is time-invariant, depending only on the parameter γ. The analysis furnishes a simple asymptotic formula for the skin-depth (i.e., the wave-front position), which substantially generalizes existing approximations. It scales with the power γr + 1/2 of time and the power γ of field strength, and is much larger than the field-independent skin depth predicted by an athermal model. The formula further involves a dimensionless O(1) pre-factor which depends on r and γ. It is determined by solving a nonlinear eigenvalue problem governing the magnetized region. Another main result of the analysis, apparently unprecedented, is an asymptotic formula for the magnitude of the current-density peak characterizing the wave-front region. Complementary to these systematic results, we provide a closed-form but ad hoc generalization of the theory approximately applicable to arbitrary monotonically rising surface fields. Our results are in excellent agreement with numerical simulations of the model, and compare favourably with detailed magnetohydrodynamic simulations reported in the literature.

Asymptotics with a positive cosmological constant: I. Basic framework

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2015-01-01

The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant Λ is zero. The resulting framework lies at the foundation of research in diverse areas in gravitational science. Examples include: (i) positive energy theorems in geometric analysis; (ii) the coordinate invariant characterization of gravitational waves in full, nonlinear general relativity; (iii) computations of the energy-momentum emission in gravitational collapse and binary mergers in numerical relativity and relativistic astrophysics; and (iv) constructions of asymptotic Hilbert spaces to calculate S-matrices and analyze the issue of information loss in the quantum evaporation of black holes. However, by now observations have led to a strong consensus that Λ is positive in our universe. In this paper we show that, unfortunately, the standard framework does not extend from the Λ =0 case to the Λ \\gt 0 case in a physically useful manner. In particular, we do not have positive energy theorems, nor an invariant notion of gravitational waves in the nonlinear regime, nor asymptotic Hilbert spaces in dynamical situations of semi-classical gravity. A suitable framework to address these conceptual issues of direct physical importance is developed in subsequent papers.

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.

Stability analysis of gyroscopic systems with delay via decomposition

NASA Astrophysics Data System (ADS)

Aleksandrov, A. Yu.; Zhabko, A. P.; Chen, Y.

2018-05-01

A mechanical system describing by the second order linear differential equations with a positive parameter at the velocity forces and with time delay in the positional forces is studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are obtained under which from the asymptotic stability of two auxiliary first order subsystems it follows that, for sufficiently large values of the parameter, the original system is also asymptotically stable. Moreover, it is shown that the proposed approach can be applied to the stability investigation of linear gyroscopic systems with switched positional forces.

Asymptotic behaviors of a cell-to-cell HIV-1 infection model perturbed by white noise

NASA Astrophysics Data System (ADS)

Liu, Qun

2017-02-01

In this paper, we analyze a mathematical model of cell-to-cell HIV-1 infection to CD4+ T cells perturbed by stochastic perturbations. First of all, we investigate that there exists a unique global positive solution of the system for any positive initial value. Then by using Lyapunov analysis methods, we study the asymptotic property of this solution. Moreover, we discuss whether there is a stationary distribution for this system and if it owns the ergodic property. Numerical simulations are presented to illustrate the theoretical results.

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.

Use of asymptotic methods in vibration analysis

NASA Technical Reports Server (NTRS)

Ashley, H.

1978-01-01

The derivation of dynamic differential equations, suitable for studying the vibrations of rotating, curved, slender structures was examined, and the Hamiltonian procedure was advocated for this purpose. Various reductions of the full system are displayed, which govern the vibrating troposkien when various order of magnitude restrictions are placed on important parameters. Possible advantages of the WKB asymptotic method for solving these classes of problems are discussed. A special case of this method is used illustratively to calculate eigenvalues and eigenfunctions for a flat turbine blade with small flexural stiffness.

Global stability of a multiple infected compartments model for waterborne diseases

NASA Astrophysics Data System (ADS)

Wang, Yi; Cao, Jinde

2014-10-01

In this paper, mathematical analysis is carried out for a multiple infected compartments model for waterborne diseases, such as cholera, giardia, and rotavirus. The model accounts for both person-to-person and water-to-person transmission routes. Global stability of the equilibria is studied. In terms of the basic reproduction number R0, we prove that, if R0⩽1, then the disease-free equilibrium is globally asymptotically stable and the infection always disappears; whereas if R0>1, there exists a unique endemic equilibrium which is globally asymptotically stable for the corresponding fast-slow system. Numerical simulations verify our theoretical results and present that the decay rate of waterborne pathogens has a significant impact on the epidemic growth rate. Also, we observe numerically that the unique endemic equilibrium is globally asymptotically stable for the whole system. This statement indicates that the present method need to be improved by other techniques.

Global solutions to physical vacuum problem of non-isentropic viscous gaseous stars and nonlinear asymptotic stability of stationary solutions

NASA Astrophysics Data System (ADS)

Hong, Guangyi; Luo, Tao; Zhu, Changjiang

2018-07-01

This paper is concerned with spherically symmetric motions of non-isentropic viscous gaseous stars with self-gravitation. When the stationary entropy S ‾ (x) is spherically symmetric and satisfies a suitable smallness condition, the existence and properties of the stationary solutions are obtained for 6/5 < γ < 2 with weaker constraints upon S ‾ (x) compared with the one in [26], where γ is the adiabatic exponent. The global existence of strong solutions capturing the physical vacuum singularity that the sound speed is C 1/2 -Hölder continuous across the vacuum boundary to a simplified system for non-isentropic viscous flow with self-gravitation and the nonlinear asymptotic stability of the stationary solution are proved when 4/3 < γ < 2 with the detailed convergence rates, motivated by the results and analysis of the nonlinear asymptotic stability of Lane-Emden solutions for isentropic flows in [29,30].

Strings from massive higher spins: the asymptotic uniqueness of the Veneziano amplitude

NASA Astrophysics Data System (ADS)

Caron-Huot, Simon; Komargodski, Zohar; Sever, Amit; Zhiboedov, Alexander

2017-10-01

We consider weakly coupled theories of massive higher-spin particles. This class of models includes, for instance, tree-level String Theory and Large-N Yang-Mills theory. The S-matrix in such theories is a meromorphic function obeying unitarity and crossing symmetry. We discuss the (unphysical) regime s, t ≫ 1, in which we expect the amplitude to be universal and exponentially large. We develop methods to study this regime and show that the amplitude necessarily coincides with the Veneziano amplitude there. In particular, this implies that the leading Regge trajectory, j( t), is asymptotically linear in Yang-Mills theory. Further, our analysis shows that any such theory of higherspin particles has stringy excitations and infinitely many asymptotically parallel subleading trajectories. More generally, we argue that, under some assumptions, any theory with at least one higher-spin particle must have strings.

Asymptotic analysis of the Boltzmann equation for dark matter relics in the presence of a running dilaton and space-time defects

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Mavromatos, Nick E.; Sarkar, Sarben

2013-03-01

The interplay of dilatonic effects in dilaton cosmology and stochastic quantum space-time defects within the framework of string/brane cosmologies is examined. The Boltzmann equation describes the physics of thermal dark-matter-relic abundances in the presence of rolling dilatons. These dilatons affect the coupling of stringy matter to D-particle defects, which are generic in string theory. This coupling leads to an additional source term in the Boltzmann equation. The techniques of asymptotic matching and boundary-layer theory, which were recently applied by two of the authors (Bender and Sarkar) to a Boltzmann equation, are used here to find the detailed asymptotic relic abundances for all ranges of the expectation value of the dilaton field. The phenomenological implications for the search for supersymmetric dark matter in current colliders, such as the LHC, are discussed.

Plasma-Sheath Model

NASA Astrophysics Data System (ADS)

Riemann, Karl-Ulrich

2012-10-01

In typical gas discharges a quasineutral plasma is shielded from a negativ absorbing wall by a thin positive sheath that is nearly planar and collision-free. The subdivision of ``plasma'' and ``sheath'' was introduced by Langmuir and is based on a small ratio of the electron Debye lenghth λD to the dominant competing characteristic plasma length l. Depending on the special conditions, l may represent, e.g., the plasma extension, the ionization length, the ion mean free path, the ion gyro radius, or a geometric length. Strictly speaking, this subdivion is possible only in the asymptotic limit λD/l->0. The asymptotic analysis results in singularities at the ``sheath edge'' closely related to the ``Bohm criterion.'' Due to these singularities a direct smooth matching of the separate plasma and sheath soltions is not possible. To obtain a consistent smooth transition, the singular sheath edge must be bridged by an additinal narrow ``intermediate'' model zone accounting both for plasma processes (e.g., collisions) and for the first build up of space charge. Due to this complexity and to different interpretations of the ``classical'' papers by Langmuir and Bohm, the asymptotic plasma-sheath concept and the definition of the sheath edge were questioned and resulted in controversies during the last two decades. We discuss attempts to re-define the sheath edge, to account for finite values of λD/l in the Bohm criterion, and demonstrate the consistent matching of plasma and sheath. The investigations of the plasma-sheath transition discussed so far are based on a simplified fluid analysis that cannot account for the essential inhomogeneity of the boundary layer and for the dominant role of slow ions in space charge formation. Therefore we give special emphasis to the kinetic theory of the plasma-sheath transition. Unfortunately this approach results in an additional mathematical difficulty caused by ions with zero velocity. We discuss attempts to avoid this singularity by a modification of the kinetic Bohm criterion and investigate the influence of slow ions on the structure of the plasma-sheath transition. The most important conclusions are illustrated with selected examples.

Asymptotically optimal data analysis for rejecting local realism

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

Zhang, Yanbao; Applied and Computational Mathematics Division, National Institute of Standards and Technology, Boulder, Colorado 80305; Glancy, Scott

2011-12-15

Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small p value. We propose a prediction-based-ratio (PBR) analysis protocol whose p values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurement settings and outcomes. It is therefore not subjectmore » to the memory loophole [J. Barrett et al., Phys. Rev. A 66, 042111 (2002)]. If the prepared state does not vary in time, the p values are asymptotically optimal. For comparison, we consider protocols derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, e-print arXiv:quant-ph/0110137]. We find that the p values of the former can be too small and are therefore not statistically valid, while those derived from the latter are suboptimal. PBR p values do not require a predetermined Bell inequality and can be used to compare results from different tests of local realism independent of experimental details.« less

Phase noise analysis of voltage controlled oscillator used in cesium atomic clock

NASA Astrophysics Data System (ADS)

Zhi, Menghui; Tang, Liang; Qiao, Donghai

2017-03-01

Coherent population trapping (CPT) cesium frequency standard plays a significant role in precision guidance of missile and global positioning system (GPS). Low noise 4.596 GHz voltage controlled oscillator (VCO) is an indispensable part of microwave signal source in cesium frequency standard. Low-phase noise is also the most important and difficult performance indicator of VCO. Starting from phase noise analysis method proposed by Leeson, the formulas about the relationship between phase noise of output signal of oscillator feedback model and phase fluctuation spectrum of amplifier, phase noise of oscillator are derived in this paper. Finally, the asymptote model of microwave oscillator is proposed based on the formula derivation. The experiment shows that when the reverse bias voltage of variode is 1.8 V, the designed oscillation frequency of VCO is 4.596 GHz, the power is -1 dBm and the DC power consumption is 19.6 mW. The tendency of phase noise simulation curve and actual test curve conform to asymptote model. The phase noise in 1 and 10 kHz is, respectively, -60.86 and -86.58 dBc/Hz. The significance of the paper lies in determining the main factors influencing oscillator phase noise and providing guiding direction for the design of low-phase noise VCO.

Ignition and structure of a laminar diffusion flame in the field of a vortex

NASA Technical Reports Server (NTRS)

Macaraeg, Michele G.; Jackson, T. L.; Hussaini, M. Y.

1991-01-01

The distortion of flames in flows with vortical motion is examined via asymptotic analysis and numerical simulation. The model consists of a constant density, one step, irreversible Arrhenius reaction between initially unmixed species occupying adjacent half-planes which are then allowed to mix and react in the presence of a vortex. The evolution in time of the temperature and mass fraction fields is followed. Emphasis is placed on the ignition time and location as a function of vortex Reynolds number and initial temperature differences of the reacting species. The study brings out the influence of the vortex on the chemical reaction. In all phases, good agreement is observed between asymptotic analysis and the full numerical solution of the model equations.

Discrete time modeling and stability analysis of TCP Vegas

NASA Astrophysics Data System (ADS)

You, Byungyong; Koo, Kyungmo; Lee, Jin S.

2007-12-01

This paper presents an analysis method for TCP Vegas network model with single link and single source. Some papers showed global stability of several network models, but those models are not a dual problem where dynamics both exist in sources and links such as TCP Vegas. Other papers studied TCP Vegas as a dual problem, but it did not fully derive an asymptotic stability region. Therefore we analyze TCP Vegas with Jury's criterion which is necessary and sufficient condition. So we use state space model in discrete time and by using Jury's criterion, we could find an asymptotic stability region of TCP Vegas network model. This result is verified by ns-2 simulation. And by comparing with other results, we could know our method performed well.

Tracking problem for electromechanical system under influence of external perturbations

NASA Astrophysics Data System (ADS)

Kochetkov, Sergey A.; Krasnova, Svetlana A.; Utkin, Victor A.

2017-01-01

For electromechanical objects the new control algorithms (vortex algprithms) are developed on the base of discontinuous functions. The distinctive feature of these algorithms is providing of asymptotical convergence of the output variables to zero under influence of unknown bounded disturbances of prescribed class. The advantages of proposed approach is demonstrated for direct current motor with permanent excitation. It is shown that inner variables of the system converge to unknown bounded disturbances and guarantee asymptotical convergence of output variables to zero.

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.

On the Rate of Relaxation for the Landau Kinetic Equation and Related Models

NASA Astrophysics Data System (ADS)

Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong

2017-08-01

We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

NASA Astrophysics Data System (ADS)

Wang, Zhi-Gang; Gao, Rui-Mei; Fan, Xiao-Ming; Han, Qi-Xing

2014-09-01

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ0, when the stochastic system obeys some conditions and ℛ0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.

The crack problem in a specially orthotropic shell with double curvature

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1983-01-01

The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip. Previously announced in STAR as N83-16782

The self-organization of grid cells in 3D

PubMed Central

Stella, Federico; Treves, Alessandro

2015-01-01

Do we expect periodic grid cells to emerge in bats, or perhaps dolphins, exploring a three-dimensional environment? How long will it take? Our self-organizing model, based on ring-rate adaptation, points at a complex answer. The mathematical analysis leads to asymptotic states resembling face centered cubic (FCC) and hexagonal close packed (HCP) crystal structures, which are calculated to be very close to each other in terms of cost function. The simulation of the full model, however, shows that the approach to such asymptotic states involves several sub-processes over distinct time scales. The smoothing of the initially irregular multiple fields of individual units and their arrangement into hexagonal grids over certain best planes are observed to occur relatively quickly, even in large 3D volumes. The correct mutual orientation of the planes, though, and the coordinated arrangement of different units, take a longer time, with the network showing no sign of convergence towards either a pure FCC or HCP ordering. DOI: http://dx.doi.org/10.7554/eLife.05913.001 PMID:25821989

The crack problem in a specially orthotropic shell with double curvature

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip.

Simple robust control laws for robot manipulators. Part 2: Adaptive case

NASA Technical Reports Server (NTRS)

Bayard, D. S.; Wen, J. T.

1987-01-01

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations.

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

NL(q) Theory: A Neural Control Framework with Global Asymptotic Stability Criteria.

PubMed

Vandewalle, Joos; De Moor, Bart L.R.; Suykens, Johan A.K.

1997-06-01

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NL(q) system form. NL(q) systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NL(q)s sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L(2)-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NL(q) stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H( infinity ) control theory and &mgr; theory. Copyright 1997 Elsevier Science Ltd.

Honest Importance Sampling with Multiple Markov Chains

PubMed Central

Tan, Aixin; Doss, Hani; Hobert, James P.

2017-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π1 is replaced by a Harris ergodic Markov chain with invariant density π1, then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π1, …, πk, are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection. PMID:28701855

Honest Importance Sampling with Multiple Markov Chains.

PubMed

Tan, Aixin; Doss, Hani; Hobert, James P

2015-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection.

A two-scale model for dynamic damage evolution

NASA Astrophysics Data System (ADS)

Keita, Oumar; Dascalu, Cristian; François, Bertrand

2014-03-01

This paper presents a new micro-mechanical damage model accounting for inertial effect. The two-scale damage model is fully deduced from small-scale descriptions of dynamic micro-crack propagation under tensile loading (mode I). An appropriate micro-mechanical energy analysis is combined with homogenization based on asymptotic developments in order to obtain the macroscopic evolution law for damage. Numerical simulations are presented in order to illustrate the ability of the model to describe known behaviors like size effects for the structural response, strain-rate sensitivity, brittle-ductile transition and wave dispersion.

Large-Scale Multiantenna Multisine Wireless Power Transfer

NASA Astrophysics Data System (ADS)

Huang, Yang; Clerckx, Bruno

2017-11-01

Wireless Power Transfer (WPT) is expected to be a technology reshaping the landscape of low-power applications such as the Internet of Things, Radio Frequency identification (RFID) networks, etc. Although there has been some progress towards multi-antenna multi-sine WPT design, the large-scale design of WPT, reminiscent of massive MIMO in communications, remains an open challenge. In this paper, we derive efficient multiuser algorithms based on a generalizable optimization framework, in order to design transmit sinewaves that maximize the weighted-sum/minimum rectenna output DC voltage. The study highlights the significant effect of the nonlinearity introduced by the rectification process on the design of waveforms in multiuser systems. Interestingly, in the single-user case, the optimal spatial domain beamforming, obtained prior to the frequency domain power allocation optimization, turns out to be Maximum Ratio Transmission (MRT). In contrast, in the general weighted sum criterion maximization problem, the spatial domain beamforming optimization and the frequency domain power allocation optimization are coupled. Assuming channel hardening, low-complexity algorithms are proposed based on asymptotic analysis, to maximize the two criteria. The structure of the asymptotically optimal spatial domain precoder can be found prior to the optimization. The performance of the proposed algorithms is evaluated. Numerical results confirm the inefficiency of the linear model-based design for the single and multi-user scenarios. It is also shown that as nonlinear model-based designs, the proposed algorithms can benefit from an increasing number of sinewaves.

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.

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.

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.

On the distribution of saliency.

PubMed

Berengolts, Alexander; Lindenbaum, Michael

2006-12-01

Detecting salient structures is a basic task in perceptual organization. Saliency algorithms typically mark edge-points with some saliency measure, which grows with the length and smoothness of the curve on which these edge-points lie. Here, we propose a modified saliency estimation mechanism that is based on probabilistically specified grouping cues and on curve length distributions. In this framework, the Shashua and Ullman saliency mechanism may be interpreted as a process for detecting the curve with maximal expected length. Generalized types of saliency naturally follow. We propose several specific generalizations (e.g., gray-level-based saliency) and rigorously derive the limitations on generalized saliency types. We then carry out a probabilistic analysis of expected length saliencies. Using ergodicity and asymptotic analysis, we derive the saliency distributions associated with the main curves and with the rest of the image. We then extend this analysis to finite-length curves. Using the derived distributions, we derive the optimal threshold on the saliency for discriminating between figure and background and bound the saliency-based figure-from-ground performance.

Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays.

PubMed

Arik, Sabri

2005-05-01

This paper presents a sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with distributed time delays. The results impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all continuous nonmonotonic neuron activation functions. It is shown that in some special cases of the results, the stability criteria can be easily checked. Some examples are also given to compare the results with the previous results derived in the literature.

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. I - Velocity selection. II - Stability

NASA Technical Reports Server (NTRS)

Tanveer, S.

1989-01-01

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. First the bubble velocity relative to the fluid velocity at infinity is determined for small surface tension by means of a transcendentally small correction to the asymptotic series solution. In addition, a linear stability analysis shows that only the solution branch corresponding to the largest possible bubble velocity for given surface tension is stable, while all the others are unstable.

Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment

NASA Astrophysics Data System (ADS)

Khan, Muhammad Altaf; Khan, Yasir; Islam, Saeed

2018-03-01

In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R0 < 1. The model is locally as well as globally asymptotically stable at endemic equilibrium when R0 > 1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results.

Wealth distribution under Yard-Sale exchange with proportional taxes

NASA Astrophysics Data System (ADS)

Bustos-Guajardo, R.; Moukarzel, Cristian F.

2016-03-01

Recent analysis of a Yard-Sale (YS) exchange model supplemented with redistributive proportional taxation suggested an asymptotic behavior P(w)˜1/wμ for the wealth distribution, with a parameter-dependent exponent μ. Revisiting this problem, it is here shown analytically, and confirmed by extensive numerical simulation, that the asymptotic behavior of P(w) is not power-law but rather a Gaussian. When taxation is weak, we furthermore show that a restricted-range power-law behavior appears for wealths around the mean value. The corresponding power-law exponent equals 3/2 when the return distribution has zero mean.

A note on two-dimensional asymptotic magnetotail equilibria

NASA Technical Reports Server (NTRS)

Voigt, Gerd-Hannes; Moore, Brian D.

1994-01-01

In order to understand, on the fluid level, the structure, the time evolution, and the stability of current sheets, such as the magnetotail plasma sheet in Earth's magnetosphere, one has to consider magnetic field configurations that are in magnetohydrodynamic (MHD) force equilibrium. Any reasonable MHD current sheet model has to be two-dimensional, at least in an asymptotic sense (B(sub z)/B (sub x)) = epsilon much less than 1. The necessary two-dimensionality is described by a rather arbitrary function f(x). We utilize the free function f(x) to construct two-dimensional magnetotail equilibria are 'equivalent' to current sheets in empirical three-dimensional models. We obtain a class of asymptotic magnetotail equilibria ordered with respect to the magnetic disturbance index Kp. For low Kp values the two-dimensional MHD equilibria reflect some of the realistic, observation-based, aspects of three-dimensional models. For high Kp values the three-dimensional models do not fit the asymptotic MHD equlibria, which is indicative of their inconsistency with the assumed pressure function. This, in turn, implies that high magnetic activity levels of the real magnetosphere might be ruled by thermodynamic conditions different from local thermodynamic equilibrium.

Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams

NASA Astrophysics Data System (ADS)

Lim, C. W.; Wang, C. M.

2007-03-01

This article presents a complete and asymptotic representation of the one-dimensional nanobeam model with nonlocal stress via an exact variational principle approach. An asymptotic governing differential equation of infinite-order strain gradient model and the corresponding infinite number of boundary conditions are derived and discussed. For practical applications, it explores and presents a reduced higher-order solution to the asymptotic nonlocal model. It is also identified here and explained at length that most publications on this subject have inaccurately employed an excessively simplified lower-order model which furnishes intriguing solutions under certain loading and boundary conditions where the results become identical to the classical solution, i.e., without the small-scale effect at all. Various nanobeam examples are solved to demonstrate the difference between using the simplified lower-order nonlocal model and the asymptotic higher-order strain gradient nonlocal stress model. An important conclusion is the discovery of significant over- or underestimation of stress levels using the lower-order model, particularly at the vicinity of the clamped end of a cantilevered nanobeam under a tip point load. The consequence is that the design of a nanobeam based on the lower-order strain gradient model could be flawed in predicting the nonlocal stress at the clamped end where it could, depending on the magnitude of the small-scale parameter, significantly over- or underestimate the failure criteria of a nanobeam which are governed by the level of stress.

Behavior of asymptotically electro-Λ spacetimes

NASA Astrophysics Data System (ADS)

Saw, Vee-Liem

2017-04-01

We present the asymptotic solutions for spacetimes with nonzero cosmological constant Λ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with Λ ≠0 . The results are given in two different null tetrads: the Newman-Unti and Szabados-Tod null tetrads, where the peeling property is exhibited in the former but not the latter. Using these asymptotic solutions, we discuss the mass loss of an isolated electrogravitating system with cosmological constant. In a universe with Λ >0 , the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: (1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. (2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike I and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with Λ in the Bondi mass-loss formula in an unusual manner, unlike the gravitational counterpart where outgoing gravitational radiation induces nonconformal flatness of I . These asymptotic solutions to the Einstein-Maxwell-de Sitter equations presented here may be used to extend a raft of existing results based on Newman-Unti's asymptotic solutions to the Einstein-Maxwell equations where Λ =0 , to now incorporate the cosmological constant Λ .

Linear discriminant analysis with misallocation in training samples

NASA Technical Reports Server (NTRS)

Chhikara, R. (Principal Investigator); Mckeon, J.

1982-01-01

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general appraoch to modeling of mislocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained and the asymptotic first two moments of the two types of error rate given. Certain numerical results for the error rates are presented by considering the random and two non-random misallocation models. It is shown that when the allocation procedure for training samples is objectively formulated, the effect of misallocation on the error rates of the Bayes linear discriminant rule can almost be eliminated. If, however, this is not possible, the use of Fisher rule may be preferred over the Bayes rule.

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.

Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions

NASA Astrophysics Data System (ADS)

Li, Chang-Feng; Sureshkumar, Radhakrishna; Khomami, Bamin

2015-10-01

Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains O (1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.

Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions.

PubMed

Li, Chang-Feng; Sureshkumar, Radhakrishna; Khomami, Bamin

2015-10-01

Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains O(1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

Challenges for semilocal density functionals with asymptotically nonvanishing potentials

NASA Astrophysics Data System (ADS)

Aschebrock, Thilo; Armiento, Rickard; Kümmel, Stephan

2017-08-01

The Becke-Johnson model potential [A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 (2006), 10.1063/1.2213970] and the potential of the AK13 functional [R. Armiento and S. Kümmel, Phys. Rev. Lett. 111, 036402 (2013), 10.1103/PhysRevLett.111.036402] have been shown to mimic features of the exact Kohn-Sham exchange potential, such as step structures that are associated with shell closings and particle-number changes. A key element in the construction of these functionals is that the potential has a limiting value far outside a finite system that is a system-dependent constant rather than zero. We discuss a set of anomalous features in these functionals that are closely connected to the nonvanishing asymptotic potential. The findings constitute a formidable challenge for the future development of semilocal functionals based on the concept of a nonvanishing asymptotic constant.

Robust model predictive control for constrained continuous-time nonlinear systems

NASA Astrophysics Data System (ADS)

Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong

2018-02-01

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.

Large gyres as a shallow-water asymptotic solution of Euler's equation in spherical coordinates

NASA Astrophysics Data System (ADS)

Constantin, A.; Johnson, R. S.

2017-04-01

Starting from the Euler equation expressed in a rotating frame in spherical coordinates, coupled with the equation of mass conservation and the appropriate boundary conditions, a thin-layer (i.e. shallow water) asymptotic approximation is developed. The analysis is driven by a single, overarching assumption based on the smallness of one parameter: the ratio of the average depth of the oceans to the radius of the Earth. Consistent with this, the magnitude of the vertical velocity component through the layer is necessarily much smaller than the horizontal components along the layer. A choice of the size of this speed ratio is made, which corresponds, roughly, to the observational data for gyres; thus the problem is characterized by, and reduced to an analysis based on, a single small parameter. The nonlinear leading-order problem retains all the rotational contributions of the moving frame, describing motion in a thin spherical shell. There are many solutions of this system, corresponding to different vorticities, all described by a novel vorticity equation: this couples the vorticity generated by the spin of the Earth with the underlying vorticity due to the movement of the oceans. Some explicit solutions are obtained, which exhibit gyre-like flows of any size; indeed, the technique developed here allows for many different choices of the flow field and of any suitable free-surface profile. We comment briefly on the next order problem, which provides the structure through the layer. Some observations about the new vorticity equation are given, and a brief indication of how these results can be extended is offered.

Analysis of the width-w non-adjacent form in conjunction with hyperelliptic curve cryptography and with lattices☆

PubMed Central

Krenn, Daniel

2013-01-01

In this work the number of occurrences of a fixed non-zero digit in the width-w non-adjacent forms of all elements of a lattice in some region (e.g. a ball) is analysed. As bases, expanding endomorphisms with eigenvalues of the same absolute value are allowed. Applications of the main result are on numeral systems with an algebraic integer as base. Those come from efficient scalar multiplication methods (Frobenius-and-add methods) in hyperelliptic curves cryptography, and the result is needed for analysing the running time of such algorithms. The counting result itself is an asymptotic formula, where its main term coincides with the full block length analysis. In its second order term a periodic fluctuation is exhibited. The proof follows Delange’s method. PMID:23805020

Analysis of the width-[Formula: see text] non-adjacent form in conjunction with hyperelliptic curve cryptography and with lattices.

PubMed

Krenn, Daniel

2013-06-17

In this work the number of occurrences of a fixed non-zero digit in the width-[Formula: see text] non-adjacent forms of all elements of a lattice in some region (e.g. a ball) is analysed. As bases, expanding endomorphisms with eigenvalues of the same absolute value are allowed. Applications of the main result are on numeral systems with an algebraic integer as base. Those come from efficient scalar multiplication methods (Frobenius-and-add methods) in hyperelliptic curves cryptography, and the result is needed for analysing the running time of such algorithms. The counting result itself is an asymptotic formula, where its main term coincides with the full block length analysis. In its second order term a periodic fluctuation is exhibited. The proof follows Delange's method.

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.

Asymptotic coefficients for one-interacting-level Voigt profiles

NASA Astrophysics Data System (ADS)

Cope, D.; Lovett, R. J.

1988-02-01

The asymptotic behavior of general Voigt profiles with general width and shift functions has been determined by Cope and Lovett (1987). The resulting asymptotic coefficients are functions of the perturber/radiator mass ratio; also, the coefficients for the one-interacting-level (OIL) profiles proposed by Ward et al. (1974) were studied. In this paper, the behavior of the OIL asymptotic coefficients for large mass ratio values is determined, thereby providing a complete picture of OIL asymptotics for all mass ratios.

Robust Estimation Based on Walsh Averages for the General Linear Model.

DTIC Science & Technology

1983-11-01

estimate of I minimizing Ip(Z ) has an influence function proportional to p(y) and its asymptotic 2 2-1 variance-covariance matrix is E(* )/(E...in particular, on the influence function h(y) and quantities appearing in the asymptotic vari- ance. Some cno-ents are made on the one- and two...for signed rank estimates. The function P2 (t) of (1.4) has derivative 2(t) = - if t < -c 0 if It < c + I if t > c. *Then the influence function is h(t

Quasilocal conserved charges in a covariant theory of gravity.

PubMed

Kim, Wontae; Kulkarni, Shailesh; Yi, Sang-Heon

2013-08-23

In any generally covariant theory of gravity, we show the relationship between the linearized asymptotically conserved current and its nonlinear completion through the identically conserved current. Our formulation for conserved charges is based on the Lagrangian description, and so completely covariant. By using this result, we give a prescription to define quasilocal conserved charges in any higher derivative gravity. As applications of our approach, we demonstrate the angular momentum invariance along the radial direction of black holes and reproduce more efficiently the linearized potential on the asymptotic anti-de Sitter space.

Anticontrol of chaos in continuous-time systems via time-delay feedback.

PubMed

Wang, Xiao Fan; Chen, Guanrong; Yu, Xinghuo

2000-12-01

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.

pp interaction at very high energies in cosmic ray experiments

NASA Astrophysics Data System (ADS)

Kendi Kohara, A.; Ferreira, Erasmo; Kodama, Takeshi

2014-11-01

An analysis of p-air cross section data from extensive air shower measurements is presented, based on an analytical representation of the pp scattering amplitudes that describes with high precision all available accelerator data at ISR, SPS and LHC energies. The theoretical basis of the representation, together with the very smooth energy dependence of parameters controlled by unitarity and dispersion relations, permits reliable extrapolation to high energy cosmic ray (CR) and asymptotic energy ranges. Calculations of σ p-airprod based on Glauber formalism are made using the input values of the quantities σ , ρ , BI and BR at high energies, with attention given to the independence of the slope parameters, with {{B}R}\

Finding differentially expressed genes in high dimensional data: Rank based test statistic via a distance measure.

PubMed

Mathur, Sunil; Sadana, Ajit

2015-12-01

We present a rank-based test statistic for the identification of differentially expressed genes using a distance measure. The proposed test statistic is highly robust against extreme values and does not assume the distribution of parent population. Simulation studies show that the proposed test is more powerful than some of the commonly used methods, such as paired t-test, Wilcoxon signed rank test, and significance analysis of microarray (SAM) under certain non-normal distributions. The asymptotic distribution of the test statistic, and the p-value function are discussed. The application of proposed method is shown using a real-life data set. © The Author(s) 2011.

Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population.

PubMed

Ducrot, Arnaud; Giletti, Thomas

2014-09-01

In this work we study the asymptotic behaviour of the Kermack-McKendrick reaction-diffusion system in a periodic environment with non-diffusive susceptible population. This problem was proposed by Kallen et al. as a model for the spatial spread for epidemics, where it can be reasonable to assume that the susceptible population is motionless. For arbitrary dimensional space we prove that large classes of solutions of such a system have an asymptotic spreading speed in large time, and that the infected population has some pulse-like asymptotic shape. The analysis of the one-dimensional problem is more developed, as we are able to uncover a much more accurate description of the profile of solutions. Indeed, we will see that, for some initially compactly supported infected population, the profile of the solution converges to some pulsating travelling wave with minimal speed, that is to some entire solution moving at a constant positive speed and whose profile's shape is periodic in time.

Asymptotic Analysis Of The Total Least Squares ESPRIT Algorithm'

NASA Astrophysics Data System (ADS)

Ottersten, B. E.; Viberg, M.; Kailath, T.

1989-11-01

This paper considers the problem of estimating the parameters of multiple narrowband signals arriving at an array of sensors. Modern approaches to this problem often involve costly procedures for calculating the estimates. The ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm was recently proposed as a means for obtaining accurate estimates without requiring a costly search of the parameter space. This method utilizes an array invariance to arrive at a computationally efficient multidimensional estimation procedure. Herein, the asymptotic distribution of the estimation error is derived for the Total Least Squares (TLS) version of ESPRIT. The Cramer-Rao Bound (CRB) for the ESPRIT problem formulation is also derived and found to coincide with the variance of the asymptotic distribution through numerical examples. The method is also compared to least squares ESPRIT and MUSIC as well as to the CRB for a calibrated array. Simulations indicate that the theoretic expressions can be used to accurately predict the performance of the algorithm.

Stability of large-scale systems with stable and unstable subsystems.

NASA Technical Reports Server (NTRS)

Grujic, Lj. T.; Siljak, D. D.

1972-01-01

The purpose of this paper is to develop new methods for constructing vector Liapunov functions and broaden the application of Liapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. With minor technical adjustments, the same criterion can be used to determine connective asymptotic stability of large-scale systems subject to structural perturbations. By redefining the constraints imposed on the interconnections among the subsystems, the considered class of systems is broadened in an essential way to include composite systems with unstable subsystems. In this way, the theory is brought substantially closer to reality since stability of all subsystems is no longer a necessary assumption in establishing stability of the overall composite system.

An improved Four-Russians method and sparsified Four-Russians algorithm for RNA folding.

PubMed

Frid, Yelena; Gusfield, Dan

2016-01-01

The basic RNA secondary structure prediction problem or single sequence folding problem (SSF) was solved 35 years ago by a now well-known [Formula: see text]-time dynamic programming method. Recently three methodologies-Valiant, Four-Russians, and Sparsification-have been applied to speedup RNA secondary structure prediction. The sparsification method exploits two properties of the input: the number of subsequence Z with the endpoints belonging to the optimal folding set and the maximum number base-pairs L. These sparsity properties satisfy [Formula: see text] and [Formula: see text], and the method reduces the algorithmic running time to O(LZ). While the Four-Russians method utilizes tabling partial results. In this paper, we explore three different algorithmic speedups. We first expand the reformulate the single sequence folding Four-Russians [Formula: see text]-time algorithm, to utilize an on-demand lookup table. Second, we create a framework that combines the fastest Sparsification and new fastest on-demand Four-Russians methods. This combined method has worst-case running time of [Formula: see text], where [Formula: see text] and [Formula: see text]. Third we update the Four-Russians formulation to achieve an on-demand [Formula: see text]-time parallel algorithm. This then leads to an asymptotic speedup of [Formula: see text] where [Formula: see text] and [Formula: see text] the number of subsequence with the endpoint j belonging to the optimal folding set. The on-demand formulation not only removes all extraneous computation and allows us to incorporate more realistic scoring schemes, but leads us to take advantage of the sparsity properties. Through asymptotic analysis and empirical testing on the base-pair maximization variant and a more biologically informative scoring scheme, we show that this Sparse Four-Russians framework is able to achieve a speedup on every problem instance, that is asymptotically never worse, and empirically better than achieved by the minimum of the two methods alone.

The null distribution of the heterogeneity lod score does depend on the assumed genetic model for the trait.

PubMed

Huang, J; Vieland, V J

2001-01-01

It is well known that the asymptotic null distribution of the homogeneity lod score (LOD) does not depend on the genetic model specified in the analysis. When appropriately rescaled, the LOD is asymptotically distributed as 0.5 chi(2)(0) + 0.5 chi(2)(1), regardless of the assumed trait model. However, because locus heterogeneity is a common phenomenon, the heterogeneity lod score (HLOD), rather than the LOD itself, is often used in gene mapping studies. We show here that, in contrast with the LOD, the asymptotic null distribution of the HLOD does depend upon the genetic model assumed in the analysis. In affected sib pair (ASP) data, this distribution can be worked out explicitly as (0.5 - c)chi(2)(0) + 0.5chi(2)(1) + cchi(2)(2), where c depends on the assumed trait model. E.g., for a simple dominant model (HLOD/D), c is a function of the disease allele frequency p: for p = 0.01, c = 0.0006; while for p = 0.1, c = 0.059. For a simple recessive model (HLOD/R), c = 0.098 independently of p. This latter (recessive) distribution turns out to be the same as the asymptotic distribution of the MLS statistic under the possible triangle constraint, which is asymptotically equivalent to the HLOD/R. The null distribution of the HLOD/D is close to that of the LOD, because the weight c on the chi(2)(2) component is small. These results mean that the cutoff value for a test of size alpha will tend to be smaller for the HLOD/D than the HLOD/R. For example, the alpha = 0.0001 cutoff (on the lod scale) for the HLOD/D with p = 0.05 is 3.01, while for the LOD it is 3.00, and for the HLOD/R it is 3.27. For general pedigrees, explicit analytical expression of the null HLOD distribution does not appear possible, but it will still depend on the assumed genetic model. Copyright 2001 S. Karger AG, Basel

Asympotics with positive cosmological constant

NASA Astrophysics Data System (ADS)

Bonga, Beatrice; Ashtekar, Abhay; Kesavan, Aruna

2014-03-01

Since observations to date imply that our universe has a positive cosmological constant, one needs an extension of the theory of isolated systems and gravitational radiation in full general relativity from the asymptotically flat to asymptotically de Sitter space-times. In current definitions, one mimics the boundary conditions used in asymptotically AdS context to conclude that the asymptotic symmetry group is the de Sitter group. However, these conditions severely restricts radiation and in fact rules out non-zero flux of energy, momentum and angular momentum carried by gravitational waves. Therefore, these formulations of asymptotically de Sitter space-times are uninteresting beyond non-radiative spacetimes. The situation is compared and contrasted with conserved charges and fluxes at null infinity in asymptotically flat space-times.

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.

The capital-asset-pricing model and arbitrage pricing theory: A unification

PubMed Central

Khan, M. Ali; Sun, Yeneng

1997-01-01

We present a model of a financial market in which naive diversification, based simply on portfolio size and obtained as a consequence of the law of large numbers, is distinguished from efficient diversification, based on mean-variance analysis. This distinction yields a valuation formula involving only the essential risk embodied in an asset’s return, where the overall risk can be decomposed into a systematic and an unsystematic part, as in the arbitrage pricing theory; and the systematic component further decomposed into an essential and an inessential part, as in the capital-asset-pricing model. The two theories are thus unified, and their individual asset-pricing formulas shown to be equivalent to the pervasive economic principle of no arbitrage. The factors in the model are endogenously chosen by a procedure analogous to the Karhunen–Loéve expansion of continuous time stochastic processes; it has an optimality property justifying the use of a relatively small number of them to describe the underlying correlational structures. Our idealized limit model is based on a continuum of assets indexed by a hyperfinite Loeb measure space, and it is asymptotically implementable in a setting with a large but finite number of assets. Because the difficulties in the formulation of the law of large numbers with a standard continuum of random variables are well known, the model uncovers some basic phenomena not amenable to classical methods, and whose approximate counterparts are not already, or even readily, apparent in the asymptotic setting. PMID:11038614

The capital-asset-pricing model and arbitrage pricing theory: a unification.

PubMed

Ali Khan, M; Sun, Y

1997-04-15

We present a model of a financial market in which naive diversification, based simply on portfolio size and obtained as a consequence of the law of large numbers, is distinguished from efficient diversification, based on mean-variance analysis. This distinction yields a valuation formula involving only the essential risk embodied in an asset's return, where the overall risk can be decomposed into a systematic and an unsystematic part, as in the arbitrage pricing theory; and the systematic component further decomposed into an essential and an inessential part, as in the capital-asset-pricing model. The two theories are thus unified, and their individual asset-pricing formulas shown to be equivalent to the pervasive economic principle of no arbitrage. The factors in the model are endogenously chosen by a procedure analogous to the Karhunen-Loéve expansion of continuous time stochastic processes; it has an optimality property justifying the use of a relatively small number of them to describe the underlying correlational structures. Our idealized limit model is based on a continuum of assets indexed by a hyperfinite Loeb measure space, and it is asymptotically implementable in a setting with a large but finite number of assets. Because the difficulties in the formulation of the law of large numbers with a standard continuum of random variables are well known, the model uncovers some basic phenomena not amenable to classical methods, and whose approximate counterparts are not already, or even readily, apparent in the asymptotic setting.

Motion of a Drop on a Solid Surface Due to a Wettability Gradient

NASA Technical Reports Server (NTRS)

Subramanian, R.; Moumen, Nadjoua; McLaughlin, John B.

2005-01-01

The hydrodynamic force experienced by a spherical-cap drop moving on a solid surface is obtained from two approximate analytical solutions and used to predict the quasi-steady speed of the drop in a wettability gradient. One solution is based on approximation of the shape of the drop as a collection of wedges, and the other is based on lubrication theory. Also, asymptotic results from both approximations for small contact angles, as well as an asymptotic result from lubrication theory that is good when the length scale of the drop is large compared with the slip length, are given. The results for the hydrodynamic force also can be used to predict the quasi-steady speed of a drop sliding down an incline.

Rigorous derivation of the effective model describing a non-isothermal fluid flow in a vertical pipe filled with porous medium

NASA Astrophysics Data System (ADS)

Beneš, Michal; Pažanin, Igor

2018-03-01

This paper reports an analytical investigation of non-isothermal fluid flow in a thin (or long) vertical pipe filled with porous medium via asymptotic analysis. We assume that the fluid inside the pipe is cooled (or heated) by the surrounding medium and that the flow is governed by the prescribed pressure drop between pipe's ends. Starting from the dimensionless Darcy-Brinkman-Boussinesq system, we formally derive a macroscopic model describing the effective flow at small Brinkman-Darcy number. The asymptotic approximation is given by the explicit formulae for the velocity, pressure and temperature clearly acknowledging the effects of the cooling (heating) and porous structure. The theoretical error analysis is carried out to indicate the order of accuracy and to provide a rigorous justification of the effective model.

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.

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.

The Existence and Stability Analysis of the Equilibria in Dengue Disease Infection Model

NASA Astrophysics Data System (ADS)

Anggriani, N.; Supriatna, A. K.; Soewono, E.

2015-06-01

In this paper we formulate an SIR (Susceptible - Infective - Recovered) model of Dengue fever transmission with constant recruitment. We found a threshold parameter K0, known as the Basic Reproduction Number (BRN). This model has two equilibria, disease-free equilibrium and endemic equilibrium. By constructing suitable Lyapunov function, we show that the disease- free equilibrium is globally asymptotic stable whenever BRN is less than one and when it is greater than one, the endemic equilibrium is globally asymptotic stable. Numerical result shows the dynamic of each compartment together with effect of multiple bio-agent intervention as a control to the dengue transmission.

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.

Tunnel ionization of atoms and molecules: How accurate are the weak-field asymptotic formulas?

NASA Astrophysics Data System (ADS)

Labeye, Marie; Risoud, François; Maquet, Alfred; Caillat, Jérémie; Taïeb, Richard

2018-05-01

Weak-field asymptotic formulas for the tunnel ionization rate of atoms and molecules in strong laser fields are often used for the analysis of strong field recollision experiments. We investigate their accuracy and domain of validity for different model systems by confronting them to exact numerical results, obtained by solving the time dependent Schrödinger equation. We find that corrections that take the dc-Stark shift into account are a simple and efficient way to improve the formula. Furthermore, analyzing the different approximations used, we show that error compensation plays a crucial role in the fair agreement between exact and analytical results.

A study of delamination buckling of laminates

NASA Technical Reports Server (NTRS)

Mukherjee, Yu-Xie; Xie, Zhi-Cheng; Ingraffea, Anthony

1990-01-01

The subject of this paper is the buckling of laminated plates, with a preexisting delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results are presented for several examples. The effects of the shape, size, and position of the delamination on the buckling load are studied through these examples.

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…

Effect of fluid inertia on the motion of a collinear swimmer.

PubMed

Felderhof, B U

2016-12-01

The swimming of a two-sphere system and of a three-sphere chain in an incompressible viscous fluid is studied on the basis of simplified equations of motion which take account of both Stokes friction and added mass effects. The analysis is based on an explicit expression for the asymptotic periodic swimming velocity and a corresponding evaluation of the mean rate of dissipation. The mean swimming velocity of the two-sphere system is found to be nonvanishing provided that the two spheres are not identical. The swimming of a comparable chain of three identical spheres is much more efficient.

The Pasinetti-Solow Growth Model with Optimal Saving Behaviour: A Local Bifurcation Analysis

NASA Astrophysics Data System (ADS)

Commendatore, P.; Palmisani, C.

We present a discrete time version of the Pasinetti-Solow economic growth model. Workers and capitalists are assumed to save on the basis of rational choices. Workers face a finite time horizon and base their consumption choices on a life-cycle motive, whereas capitalists behave like an infinitely-lived dynasty. The accumulation of both capitalists' and workers' wealth through time is reduced to a two-dimensional map whose local asymptotic stability properties are studied. Various types of bifurcation emerge (flip, Neimark-Sacker, saddle-node and transcritical): a precondition for chaotic dynamics.

Analysis techniques for multivariate root loci. [a tool in linear control systems

NASA Technical Reports Server (NTRS)

Thompson, P. M.; Stein, G.; Laub, A. J.

1980-01-01

Analysis and techniques are developed for the multivariable root locus and the multivariable optimal root locus. The generalized eigenvalue problem is used to compute angles and sensitivities for both types of loci, and an algorithm is presented that determines the asymptotic properties of the optimal root locus.

Factor Analysis by Generalized Least Squares.

ERIC Educational Resources Information Center

Joreskog, Karl G.; Goldberger, Arthur S.

Aitkin's generalized least squares (GLS) principle, with the inverse of the observed variance-covariance matrix as a weight matrix, is applied to estimate the factor analysis model in the exploratory (unrestricted) case. It is shown that the GLS estimates are scale free and asymptotically efficient. The estimates are computed by a rapidly…

Asymptotic Safety Guaranteed in Supersymmetry

NASA Astrophysics Data System (ADS)

Bond, Andrew D.; Litim, Daniel F.

2017-11-01

We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories.

Exceeding the Asymptotic Limit of Polymer Drag Reduction.

PubMed

Choueiri, George H; Lopez, Jose M; Hof, Björn

2018-03-23

The drag of turbulent flows can be drastically decreased by adding small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view, we show that, for an appropriate choice of parameters, polymers can reduce the drag beyond the suggested asymptotic limit, eliminating turbulence and giving way to laminar flow. At higher polymer concentrations, however, the laminar state becomes unstable, resulting in a fluctuating flow with the characteristic drag of the MDR asymptote. Our findings indicate that the asymptotic state is hence dynamically disconnected from ordinary turbulence.

Exceeding the Asymptotic Limit of Polymer Drag Reduction

NASA Astrophysics Data System (ADS)

Choueiri, George H.; Lopez, Jose M.; Hof, Björn

2018-03-01

The drag of turbulent flows can be drastically decreased by adding small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view, we show that, for an appropriate choice of parameters, polymers can reduce the drag beyond the suggested asymptotic limit, eliminating turbulence and giving way to laminar flow. At higher polymer concentrations, however, the laminar state becomes unstable, resulting in a fluctuating flow with the characteristic drag of the MDR asymptote. Our findings indicate that the asymptotic state is hence dynamically disconnected from ordinary turbulence.

Development of a near-wall Reynolds-stress closure based on the SSG model for the pressure strain

NASA Technical Reports Server (NTRS)

So, R. M. C.; Aksoy, H.; Sommer, T. P.; Yuan, S. P.

1994-01-01

In this research, a near-wall second-order closure based on the Speziable et al.(1991) or SSG model for the pressure-strain term is proposed. Unlike the LRR model, the SSG model is quasi-nonlinear and yields better results when applied to calculate rotating homogeneous turbulent flows. An asymptotic analysis near the wall is applied to both the exact and modeled, equations so that appropriate near-wall corrections to the SSG model and the modeled dissipation-rate equation can be derived to satisfy the physical wall boundary conditions as well as the asymptotic near-wall behavior of the exact equations. Two additional model constants are introduced and they are determined by calibrating against one set of near-wall channel flow data. Once determined, their values are found to remain constant irrespective of the type of flow examined. The resultant model is used to calculate simple turbulent flows, near separating turbulent flows, complex turbulent flows and compressible turbulent flows with a freestream Mach number as high as 10. In all the flow cases investigated, the calculated results are in good agreement with data. This new near-wall model is less ad hoc, physically and mathematically more sound and eliminates the empiricism introduced by Zhang. Therefore, it is quite general, as demonstrated by the good agreement achieved with measurements covering a wide range of Reynolds numbers and Mach numbers.

Deep learning ensemble with asymptotic techniques for oscillometric blood pressure estimation.

PubMed

Lee, Soojeong; Chang, Joon-Hyuk

2017-11-01

This paper proposes a deep learning based ensemble regression estimator with asymptotic techniques, and offers a method that can decrease uncertainty for oscillometric blood pressure (BP) measurements using the bootstrap and Monte-Carlo approach. While the former is used to estimate SBP and DBP, the latter attempts to determine confidence intervals (CIs) for SBP and DBP based on oscillometric BP measurements. This work originally employs deep belief networks (DBN)-deep neural networks (DNN) to effectively estimate BPs based on oscillometric measurements. However, there are some inherent problems with these methods. First, it is not easy to determine the best DBN-DNN estimator, and worthy information might be omitted when selecting one DBN-DNN estimator and discarding the others. Additionally, our input feature vectors, obtained from only five measurements per subject, represent a very small sample size; this is a critical weakness when using the DBN-DNN technique and can cause overfitting or underfitting, depending on the structure of the algorithm. To address these problems, an ensemble with an asymptotic approach (based on combining the bootstrap with the DBN-DNN technique) is utilized to generate the pseudo features needed to estimate the SBP and DBP. In the first stage, the bootstrap-aggregation technique is used to create ensemble parameters. Afterward, the AdaBoost approach is employed for the second-stage SBP and DBP estimation. We then use the bootstrap and Monte-Carlo techniques in order to determine the CIs based on the target BP estimated using the DBN-DNN ensemble regression estimator with the asymptotic technique in the third stage. The proposed method can mitigate the estimation uncertainty such as large the standard deviation of error (SDE) on comparing the proposed DBN-DNN ensemble regression estimator with the DBN-DNN single regression estimator, we identify that the SDEs of the SBP and DBP are reduced by 0.58 and 0.57  mmHg, respectively. These indicate that the proposed method actually enhances the performance by 9.18% and 10.88% compared with the DBN-DNN single estimator. The proposed methodology improves the accuracy of BP estimation and reduces the uncertainty for BP estimation. Copyright © 2017 Elsevier B.V. All rights reserved.

Discrete breathers in a two-dimensional hexagonal Fermi Pasta Ulam lattice

NASA Astrophysics Data System (ADS)

Butt, Imran A.; Wattis, Jonathan A. D.

2007-02-01

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a reduction to a cubic nonlinear Schrödinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher order analysis yielding a generalized NLS, which includes known stabilizing terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, asymptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximized for stationary breathers and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt and Wattis 2006 J. Phys. A: Math. Gen. 39 4955), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalized NLS equation.

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.

Fluctuation correlation models for receptor immobilization

NASA Astrophysics Data System (ADS)

Fourcade, B.

2017-12-01

Nanoscale dynamics with cycles of receptor diffusion and immobilization by cell-external-or-internal factors is a key process in living cell adhesion phenomena at the origin of a plethora of signal transduction pathways. Motivated by modern correlation microscopy approaches, the receptor correlation functions in physical models based on diffusion-influenced reaction is studied. Using analytical and stochastic modeling, this paper focuses on the hybrid regime where diffusion and reaction are not truly separable. The time receptor autocorrelation functions are shown to be indexed by different time scales and their asymptotic expansions are given. Stochastic simulations show that this analysis can be extended to situations with a small number of molecules. It is also demonstrated that this analysis applies when receptor immobilization is coupled to environmental noise.

POST ASYMPTOTIC GIANT BRANCH BIPOLAR REFLECTION NEBULAE: RESULT OF DYNAMICAL EJECTION OR SELECTIVE ILLUMINATION?

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

Koning, N.; Kwok, Sun; Steffen, W., E-mail: nico.koning@ucalgary.ca, E-mail: sunkwok@hku.hk, E-mail: wsteffen@astrosen.unam.mx

2013-03-10

A model for post asymptotic giant branch bipolar reflection nebulae has been constructed based on a pair of evacuated cavities in a spherical dust envelope. Many of the observed features of bipolar nebulae, including filled bipolar lobes, an equatorial torus, searchlight beams, and a bright central light source, can be reproduced. The effects on orientation and dust densities are studied and comparisons with some observed examples are offered. We suggest that many observed properties of bipolar nebulae are the result of optical effects and any physical modeling of these nebulae has to take these factors into consideration.

Asymptotic Representations of Quantum Affine Superalgebras

NASA Astrophysics Data System (ADS)

Zhang, Huafeng

2017-08-01

We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called q-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.

Adaptive tracking control for a class of stochastic switched systems

NASA Astrophysics Data System (ADS)

Zhang, Hui; Xia, Yuanqing

2018-02-01

The problem of adaptive tracking is considered for a class of stochastic switched systems, in this paper. As preliminaries, the criterion of global asymptotical practical stability in probability is first presented by the aid of common Lyapunov function method. Based on the Lyapunov stability criterion, adaptive backstepping controllers are designed to guarantee that the closed-loop system has a unique global solution, which is globally asymptotically practically stable in probability, and the tracking error in the fourth moment converges to an arbitrarily small neighbourhood of zero. Simulation examples are given to demonstrate the efficiency of the proposed schemes.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim; Shaw, Leah

2012-02-01

Adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a moment-closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and epidemic spread model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim

2013-03-01

Dynamics of adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a systematic approach to moment closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the mean-field prediction and simulations of the full network system.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim S.; Shaw, Leah B.

2013-11-01

Adaptive social networks, in which nodes and network structure coevolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher-order topological structures. We propose a new approach to moment closure based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

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.

Analysis and Synthesis of Memory-Based Fuzzy Sliding Mode Controllers.

PubMed

Zhang, Jinhui; Lin, Yujuan; Feng, Gang

2015-12-01

This paper addresses the sliding mode control problem for a class of Takagi-Sugeno fuzzy systems with matched uncertainties. Different from the conventional memoryless sliding surface, a memory-based sliding surface is proposed which consists of not only the current state but also the delayed state. Both robust and adaptive fuzzy sliding mode controllers are designed based on the proposed memory-based sliding surface. It is shown that the sliding surface can be reached and the closed-loop control system is asymptotically stable. Furthermore, to reduce the chattering, some continuous sliding mode controllers are also presented. Finally, the ball and beam system is used to illustrate the advantages and effectiveness of the proposed approaches. It can be seen that, with the proposed control approaches, not only can the stability be guaranteed, but also its transient performance can be improved significantly.

Observer-based output consensus of a class of heterogeneous multi-agent systems with unmatched disturbances

NASA Astrophysics Data System (ADS)

Zhang, Jiancheng; Zhu, Fanglai

2018-03-01

In this paper, the output consensus of a class of linear heterogeneous multi-agent systems with unmatched disturbances is considered. Firstly, based on the relative output information among neighboring agents, we propose an asymptotic sliding-mode based consensus control scheme, under which, the output consensus error can converge to zero by removing the disturbances from output channels. Secondly, in order to reach the consensus goal, we design a novel high-order unknown input observer for each agent. It can estimate not only each agent's states and disturbances, but also the disturbances' high-order derivatives, which are required in the control scheme aforementioned above. The observer-based consensus control laws and the convergence analysis of the consensus error dynamics are given. Finally, a simulation example is provided to verify the validity of our methods.

Perturbative stability of SFT-based cosmological models

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

Galli, Federico; Koshelev, Alexey S., E-mail: fgalli@tena4.vub.ac.be, E-mail: alexey.koshelev@vub.ac.be

2011-05-01

We review the appearance of multiple scalar fields in linearized SFT based cosmological models with a single non-local scalar field. Some of these local fields are canonical real scalar fields and some are complex fields with unusual coupling. These systems only admit numerical or approximate analysis. We introduce a modified potential for multiple scalar fields that makes the system exactly solvable in the cosmological context of Friedmann equations and at the same time preserves the asymptotic behavior expected from SFT. The main part of the paper consists of the analysis of inhomogeneous cosmological perturbations in this system. We show numericallymore » that perturbations corresponding to the new type of complex fields always vanish. As an example of application of this model we consider an explicit construction of the phantom divide crossing and prove the perturbative stability of this process at the linear order. The issue of ghosts and ways to resolve it are briefly discussed.« less

Geometric saliency to characterize radar exploitation performance

NASA Astrophysics Data System (ADS)

Nolan, Adam; Keserich, Brad; Lingg, Andrew; Goley, Steve

2014-06-01

Based on the fundamental scattering mechanisms of facetized computer-aided design (CAD) models, we are able to define expected contributions (EC) to the radar signature. The net result of this analysis is the prediction of the salient aspects and contributing vehicle morphology based on the aspect. Although this approach does not provide the fidelity of an asymptotic electromagnetic (EM) simulation, it does provide very fast estimates of the unique scattering that can be consumed by a signature exploitation algorithm. The speed of this approach is particularly relevant when considering the high dimensionality of target configuration variability due to articulating parts which are computationally burdensome to predict. The key scattering phenomena considered in this work are the specular response from a single bounce interaction with surfaces and dihedral response formed between the ground plane and vehicle. Results of this analysis are demonstrated for a set of civilian target models.

A Model for Predicting Thermomechanical Response of Large Space Structures.

DTIC Science & Technology

1985-06-01

Field in a Thermomechanically Heated Viscoplastic ....... Space Truss Structure 6.5 Analysis of a Thermoviscoplastic Uniaxial " Bar Under Prescribed...Stress Part I - Theoretical Development . -- 6.6 Analysis of a Thermoviscoplastic Uniaxial codes Bar Under Prescribed Stress Part II - or Boundary Layer...and Asymptotic Analysis 6.7 Analysis of a Thermoviscoplastic Uniaxial Bar Under Prescribed Stress Part III - Numerical Results for a Bar with Radiative

Approximate message passing for nonconvex sparse regularization with stability and asymptotic analysis

NASA Astrophysics Data System (ADS)

Sakata, Ayaka; Xu, Yingying

2018-03-01

We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm considering nonconvex regularization, namely SCAD-AMP, and analytically show that the stability condition corresponds to the de Almeida-Thouless condition in spin glass literature. Through asymptotic analysis, we show the correspondence between the density evolution of SCAD-AMP and the replica symmetric (RS) solution. Numerical experiments confirm that for a sufficiently large system size, SCAD-AMP achieves the optimal performance predicted by the replica method. Through replica analysis, a phase transition between replica symmetric and replica symmetry breaking (RSB) region is found in the parameter space of SCAD. The appearance of the RS region for a nonconvex penalty is a significant advantage that indicates the region of smooth landscape of the optimization problem. Furthermore, we analytically show that the statistical representation performance of the SCAD penalty is better than that of \

Asymptotic Spreading Rate of Initially Compressible Jets-Experiment and Analysis

NASA Technical Reports Server (NTRS)

Zaman, K. B. M. Q.

1998-01-01

Experimental results for the spreading and centerline velocity decay rates for round, compressible jets, from a convergent and a convergent-divergent nozzle, are presented. The spreading rate is determined from the variation of streamwise mass flux obtained from Pitot probe surveys. Results for the far asymptotic region show that both spreading and centerline velocity decay rates, when nondimensionalized by parameters at the nozzle exit, decrease with increasing "jet Mach number" M(sub j). Dimensional analysis with the assumption of momentum conservation, together with compressible flow calculations for the conditions at the nozzle exit, predict this Mach number dependence well. The analysis also demonstrates that an increase in the "potential core length" of the jet occurring with increasing M(sub j), a commonly observed trend, is largely accounted for simply by the variations in the density and static pressure at the nozzle exit. The effect of decreasing mixing efficiency with increasing compressibility is inferred to contribute only partially to the latter trend.

Multivariate longitudinal data analysis with censored and intermittent missing responses.

PubMed

Lin, Tsung-I; Lachos, Victor H; Wang, Wan-Lun

2018-05-08

The multivariate linear mixed model (MLMM) has emerged as an important analytical tool for longitudinal data with multiple outcomes. However, the analysis of multivariate longitudinal data could be complicated by the presence of censored measurements because of a detection limit of the assay in combination with unavoidable missing values arising when subjects miss some of their scheduled visits intermittently. This paper presents a generalization of the MLMM approach, called the MLMM-CM, for a joint analysis of the multivariate longitudinal data with censored and intermittent missing responses. A computationally feasible expectation maximization-based procedure is developed to carry out maximum likelihood estimation within the MLMM-CM framework. Moreover, the asymptotic standard errors of fixed effects are explicitly obtained via the information-based method. We illustrate our methodology by using simulated data and a case study from an AIDS clinical trial. Experimental results reveal that the proposed method is able to provide more satisfactory performance as compared with the traditional MLMM approach. Copyright © 2018 John Wiley & Sons, Ltd.

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…

Gravitational geons in asymptotically anti-de Sitter spacetimes

NASA Astrophysics Data System (ADS)

Martinon, Grégoire; Fodor, Gyula; Grandclément, Philippe; Forgács, Peter

2017-06-01

We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3  +  1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order  ∼1/2 of the AdS length, and with deviations of the order of 50% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities, such as mass and angular momentum, are computed using two independent frameworks that agree with each other at the 0.1% level. We also provide strong evidence for the existence of ‘excited’ (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.

Cosmic equilibration: A holographic no-hair theorem from the generalized second law

NASA Astrophysics Data System (ADS)

Carroll, Sean M.; Chatwin-Davies, Aidan

2018-02-01

In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen ("quantum" holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the generalized second law conjectured by Bousso and Engelhardt, increases up to a finite maximum value along the screen, then the spacetime is asymptotically de Sitter in the future. Moreover, the limiting value of generalized entropy coincides with the de Sitter horizon entropy. We do not use the Einstein field equations in our proof, nor do we assume the existence of a positive cosmological constant. As such, asymptotic relaxation to a de Sitter phase can, in a precise sense, be thought of as cosmological equilibration.

Asymptotic Equivalence of Probability Measures and Stochastic Processes

NASA Astrophysics Data System (ADS)

Touchette, Hugo

2018-03-01

Let P_n and Q_n be two probability measures representing two different probabilistic models of some system (e.g., an n-particle equilibrium system, a set of random graphs with n vertices, or a stochastic process evolving over a time n) and let M_n be a random variable representing a "macrostate" or "global observable" of that system. We provide sufficient conditions, based on the Radon-Nikodym derivative of P_n and Q_n, for the set of typical values of M_n obtained relative to P_n to be the same as the set of typical values obtained relative to Q_n in the limit n→ ∞. This extends to general probability measures and stochastic processes the well-known thermodynamic-limit equivalence of the microcanonical and canonical ensembles, related mathematically to the asymptotic equivalence of conditional and exponentially-tilted measures. In this more general sense, two probability measures that are asymptotically equivalent predict the same typical or macroscopic properties of the system they are meant to model.

Robust ADP Design for Continuous-Time Nonlinear Systems With Output Constraints.

PubMed

Fan, Bo; Yang, Qinmin; Tang, Xiaoyu; Sun, Youxian

2018-06-01

In this paper, a novel robust adaptive dynamic programming (RADP)-based control strategy is presented for the optimal control of a class of output-constrained continuous-time unknown nonlinear systems. Our contribution includes a step forward beyond the usual optimal control result to show that the output of the plant is always within user-defined bounds. To achieve the new results, an error transformation technique is first established to generate an equivalent nonlinear system, whose asymptotic stability guarantees both the asymptotic stability and the satisfaction of the output restriction of the original system. Furthermore, RADP algorithms are developed to solve the transformed nonlinear optimal control problem with completely unknown dynamics as well as a robust design to guarantee the stability of the closed-loop systems in the presence of unavailable internal dynamic state. Via small-gain theorem, asymptotic stability of the original and transformed nonlinear system is theoretically guaranteed. Finally, comparison results demonstrate the merits of the proposed control policy.

Transient Mobility on Submonolayer Island Growth: An Exploration of Asymptotic Effects in Modeling

NASA Astrophysics Data System (ADS)

Morales-Cifuentes, Josue; Einstein, Theodore L.; Pimpinelli, Alberto

In studies of epitaxial growth, modeling of the smallest stable cluster (i+1 monomers, with i the critical nucleus size), is paramount in understanding growth dynamics. Our previous work has tackled submonolayer growth by modeling the effect of ballistic monomers, hot-precursors, on diffusive dynamics. Different scaling regimes and energies were predicted, with initial confirmation by applying to para-hexaphenyl submonolayer studies. Lingering questions about the applicability and behavior of the model are addressed. First, we show how an asymptotic approximation based on the growth exponent, α (N Fα) allows for robustness of modeling to experimental data; second, we answer questions about non-monotonicity by exploring the behavior of the growth exponent across realizable parameter spaces; third, we revisit our previous para-hexaphenyl work and examine relevant physical parameters, namely the speed of the hot-monomers. We conclude with an exploration of how the new asymptotic approximation can be used to strengthen the application of our model to other physical systems.

Homogenous polynomially parameter-dependent H∞ filter designs of discrete-time fuzzy systems.

PubMed

Zhang, Huaguang; Xie, Xiangpeng; Tong, Shaocheng

2011-10-01

This paper proposes a novel H(∞) filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H(∞) filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H(∞) performance of the filtering error system. Second, relaxed conditions for H(∞) performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H(∞) filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

Finite element implementation of state variable-based viscoplasticity models

NASA Technical Reports Server (NTRS)

Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

1991-01-01

The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

Experiments on the applicability of MAE techniques for predicting sound diffraction by irregular terrains. [Matched Asymptotic Expansion

NASA Technical Reports Server (NTRS)

Berthelot, Yves H.; Pierce, Allan D.; Kearns, James A.

1987-01-01

The sound field diffracted by a single smooth hill of finite impedance is studied both analytically, within the context of the theory of Matched Asymptotic Expansions (MAE), and experimentally, under laboratory scale modeling conditions. Special attention is given to the sound field on the diffracting surface and throughout the transition region between the illuminated and the shadow zones. The MAE theory yields integral equations that are amenable to numerical computations. Experimental results are obtained with a spark source producing a pulse of 42 microsec duration and about 130 Pa at 1 m. The insertion loss of the hill is inferred from measurements of the acoustic signals at two locations in the field, with subsequent Fourier analysis on an IBM PC/AT. In general, experimental results support the predictions of the MAE theory, and provide a basis for the analysis of more complicated geometries.

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

Asymptotic proportionality (weak ergodicity) and conditional asymptotic equality of solutions to time-heterogeneous sublinear difference and differential equations

NASA Astrophysics Data System (ADS)

Thieme, Horst R.

The concept of asymptotic proportionality and conditional asymptotic equality which is presented here aims at making global asymptotic stability statements for time-heterogeneous difference and differential equations. For such non-autonomous problems (apart from special cases) no prominent special solutions (equilibra, periodic solutions) exist which are natural candidates for the asymptotic behaviour of arbitrary solutions. One way out of this dilemma consists in looking for conditions under which any two solutions to the problem (with different initial conditions) behave in a similar or even the same way as time tends to infinity. We study a general sublinear difference equation in an ordered Banach space and, for illustration, time-heterogeneous versions of several well-known differential equations modelling the spread of gonorrhea in a heterogeneous population, the spread of a vector-borne infectious disease, and the dynamics of a logistically growing spatially diffusing population.

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.

The stochastic runoff-runon process: Extending its analysis to a finite hillslope

NASA Astrophysics Data System (ADS)

Jones, O. D.; Lane, P. N. J.; Sheridan, G. J.

2016-10-01

The stochastic runoff-runon process models the volume of infiltration excess runoff from a hillslope via the overland flow path. Spatial variability is represented in the model by the spatial distribution of rainfall and infiltration, and their ;correlation scale;, that is, the scale at which the spatial correlation of rainfall and infiltration become negligible. Notably, the process can produce runoff even when the mean rainfall rate is less than the mean infiltration rate, and it displays a gradual increase in net runoff as the rainfall rate increases. In this paper we present a number of contributions to the analysis of the stochastic runoff-runon process. Firstly we illustrate the suitability of the process by fitting it to experimental data. Next we extend previous asymptotic analyses to include the cases where the mean rainfall rate equals or exceeds the mean infiltration rate, and then use Monte Carlo simulation to explore the range of parameters for which the asymptotic limit gives a good approximation on finite hillslopes. Finally we use this to obtain an equation for the mean net runoff, consistent with our asymptotic results but providing an excellent approximation for finite hillslopes. Our function uses a single parameter to capture spatial variability, and varying this parameter gives us a family of curves which interpolate between known upper and lower bounds for the mean net runoff.

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.

Scaling for Dynamical Systems in Biology.

PubMed

Ledder, Glenn

2017-11-01

Asymptotic methods can greatly simplify the analysis of all but the simplest mathematical models and should therefore be commonplace in such biological areas as ecology and epidemiology. One essential difficulty that limits their use is that they can only be applied to a suitably scaled dimensionless version of the original dimensional model. Many books discuss nondimensionalization, but with little attention given to the problem of choosing the right scales and dimensionless parameters. In this paper, we illustrate the value of using asymptotics on a properly scaled dimensionless model, develop a set of guidelines that can be used to make good scaling choices, and offer advice for teaching these topics in differential equations or mathematical biology courses.

Scalar charges and the first law of black hole thermodynamics

NASA Astrophysics Data System (ADS)

Astefanesei, Dumitru; Ballesteros, Romina; Choque, David; Rojas, Raúl

2018-07-01

We present a variational formulation of Einstein-Maxwell-dilaton theory in flat spacetime, when the asymptotic value of the scalar field is not fixed. We obtain the boundary terms that make the variational principle well posed and then compute the finite gravitational action and corresponding Brown-York stress tensor. We show that the total energy has a new contribution that depends on the asymptotic value of the scalar field and discuss the role of scalar charges for the first law of thermodynamics. We also extend our analysis to hairy black holes in Anti-de Sitter spacetime and investigate the thermodynamics of an exact solution that breaks the conformal symmetry of the boundary.

On estimation of linear transformation models with nested case–control sampling

PubMed Central

Liu, Mengling

2011-01-01

Nested case–control (NCC) sampling is widely used in large epidemiological cohort studies for its cost effectiveness, but its data analysis primarily relies on the Cox proportional hazards model. In this paper, we consider a family of linear transformation models for analyzing NCC data and propose an inverse selection probability weighted estimating equation method for inference. Consistency and asymptotic normality of our estimators for regression coefficients are established. We show that the asymptotic variance has a closed analytic form and can be easily estimated. Numerical studies are conducted to support the theory and an application to the Wilms’ Tumor Study is also given to illustrate the methodology. PMID:21912975

On the accuracy of Whitham's method. [for steady ideal gas flow past cones

NASA Technical Reports Server (NTRS)

Zahalak, G. I.; Myers, M. K.

1974-01-01

The steady flow of an ideal gas past a conical body is studied by the method of matched asymptotic expansions and by Whitham's method in order to assess the accuracy of the latter. It is found that while Whitham's method does not yield a correct asymptotic representation of the perturbation field to second order in regions where the flow ahead of the Mach cone of the apex is disturbed, it does correctly predict the changes of the second-order perturbation quantities across a shock (the first-order shock strength). The results of the analysis are illustrated by a special case of a flat, rectangular plate at incidence.

Asymptotic behavior of curvature of surface elements in isotropic turbulence

NASA Technical Reports Server (NTRS)

Girimaji, S. S.

1991-01-01

The asymptotic behavior of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. Several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times, the (first five) moments of the logarithm of characteristic curvature and shape factor asymptote to values that are independent of the initial curvature or shape. This evidence strongly suggests that the asymptotic pdf's of the curvature and shape of material elements are stationary and independent of initial conditions. Irrespective of initial curvature or shape, the asymptotic shape of a material surface is cylindrical with a high probability.

Asymptotic derivation of nonlocal plate models from three-dimensional stress gradient elasticity

NASA Astrophysics Data System (ADS)

Hache, F.; Challamel, N.; Elishakoff, I.

2018-01-01

This paper deals with the asymptotic derivation of thin and thick nonlocal plate models at different orders from three-dimensional stress gradient elasticity, through the power series expansions of the displacements in the thickness ratio of the plate. Three nonlocal asymptotic approaches are considered: a partial nonlocality following the thickness of the plate, a partial nonlocality following the two directions of the plates and a full nonlocality (following all the directions). The three asymptotic approaches lead at the zeroth order to a nonlocal Kirchhoff-Love plate model, but differ in the expression of the length scale. The nonlocal asymptotic models coincide at this order with the stress gradient Kirchhoff-Love plate model, only when the nonlocality is following the two directions of the plate and expressed through a nabla operator. This asymptotic model also yields the nonlocal truncated Uflyand-Mindlin plate model at the second order. However, the two other asymptotic models lead to equations that differ from the current existing nonlocal engineering models (stress gradient engineering plate models). The natural frequencies for an all-edges simply supported plate are obtained for each model. It shows that the models provide similar results for low orders of frequencies or small thickness ratio or nonlocal lengths. Moreover, only the asymptotic model with a partial nonlocality following the two directions of the plates is consistent with a stress gradient plate model, whatever the geometry of the plate.

Discriminant analysis in wildlife research: Theory and applications

USGS Publications Warehouse

Williams, B.K.; Capen, D.E.

1981-01-01

Discriminant analysis, a method of analyzing grouped multivariate data, is often used in ecological investigations. It has both a predictive and an explanatory function, the former aiming at classification of individuals of unknown group membership. The goal of the latter function is to exhibit group separation by means of linear transforms, and the corresponding method is called canonical analysis. This discussion focuses on the application of canonical analysis in ecology. In order to clarify its meaning, a parametric approach is taken instead of the usual data-based formulation. For certain assumptions the data-based canonical variates are shown to result from maximum likelihood estimation, thus insuring consistency and asymptotic efficiency. The distorting effects of covariance heterogeneity are examined, as are certain difficulties which arise in interpreting the canonical functions. A 'distortion metric' is defined, by means of which distortions resulting from the canonical transformation can be assessed. Several sampling problems which arise in ecological applications are considered. It is concluded that the method may prove valuable for data exploration, but is of limited value as an inferential procedure.

Pseudo-incompressible, finite-amplitude gravity waves: wave trains and stability

NASA Astrophysics Data System (ADS)

Schlutow, Mark; Klein, Rupert

2017-04-01

Based on weak asymptotic WKB-like solutions for two-dimensional atmospheric gravity waves (GWs) traveling wave solutions (wave trains) are derived and analyzed with respect to stability. A systematic multiple-scale analysis using the ratio of the dominant wavelength and the scale height as a scale separation parameter is applied on the fully compressible Euler equations. A distinguished limit favorable for GWs close to static instability, reveals that pseudo-incompressible rather than Boussinesq theory applies. A spectral expansion including a mean flow, combined with the additional WKB assumption of slowly varying phases and amplitudes, is used to find general weak asymptotic solutions. This ansatz allows for arbitrarily strong, non-uniform stratification and holds even for finite-amplitude waves. It is deduced that wave trains as leading order solutions can only exist if either some non-uniform background stratification is given but the wave train propagates only horizontally or if the wave train velocity vector is given but the background is isothermal. For the first case, general analytical solutions are obtained that may be used to model mountain lee waves. For the second case with the additional assumption of horizontal periodicity, upward propagating wave train fronts were found. These wave train fronts modify the mean flow beyond the non-acceleration theorem. Stability analysis reveal that they are intrinsically modulationally unstable. The range of validity for the scale separation parameter was tested with fully nonlinear simulations. Even for large values an excellent agreement with the theory was found.

On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation

NASA Astrophysics Data System (ADS)

Rottschäfer, Vivi; Doelman, Arjen

1998-07-01

The Ginzburg-Landau (GL) equation ‘generically’ describes the behaviour of small perturbations of a marginally unstable basic state in systems on unbounded domains. In this paper we consider the transition from this generic situation to a degenerate (co-dimension 2) case in which the GL approach is no longer valid. Instead of studying a general underlying model problem, we consider a two-dimensional system of coupled reaction-diffusion equations in one spatial dimension. We show that near the degeneration the behaviour of small perturbations is governed by the extended Fisher-Kolmogorov (eFK) equation (at leading order). The relation between the GL-equation and the eFK-equation is quite subtle, but can be analysed in detail. The main goal of this paper is to study this relation, which we do asymptotically. The asymptotic analysis is compared to numerical simulations of the full reaction-diffusion system. As one approaches the co-dimension 2 point, we observe that the stable stationary periodic patterns predicted by the GL-equation evolve towards various different families of stable, stationary (but not necessarily periodic) so-called ‘multi-bump’ solutions. In the literature, these multi-bump patterns are shown to exist as solutions of the eFK-equation, but there is no proof of the asymptotic stability of these solutions. Our results suggest that these multi-bump patterns can also be asymptotically stable in large classes of model problems.

Asymptotics for moist deep convection I: refined scalings and self-sustaining updrafts

NASA Astrophysics Data System (ADS)

Hittmeir, Sabine; Klein, Rupert

2018-04-01

Moist processes are among the most important drivers of atmospheric dynamics, and scale analysis and asymptotics are cornerstones of theoretical meteorology. Accounting for moist processes in systematic scale analyses therefore seems of considerable importance for the field. Klein and Majda (Theor Comput Fluid Dyn 20:525-551, 2006) proposed a scaling regime for the incorporation of moist bulk microphysics closures in multiscale asymptotic analyses of tropical deep convection. This regime is refined here to allow for mixtures of ideal gases and to establish consistency with a more general multiple scales modeling framework for atmospheric flows. Deep narrow updrafts, the so-called hot towers, constitute principal building blocks of larger scale storm systems. They are analyzed here in a sample application of the new scaling regime. A single quasi-one-dimensional upright columnar cloud is considered on the vertical advective (or tower life cycle) time scale. The refined asymptotic scaling regime is essential for this example as it reveals a new mechanism for the self-sustainance of such updrafts. Even for strongly positive convectively available potential energy, a vertical balance of buoyancy forces is found in the presence of precipitation. This balance induces a diagnostic equation for the vertical velocity, and it is responsible for the generation of self-sustained balanced updrafts. The time-dependent updraft structure is encoded in a Hamilton-Jacobi equation for the precipitation mixing ratio. Numerical solutions of this equation suggest that the self-sustained updrafts may strongly enhance hot tower life cycles.

On critical behaviour in generalized Kadomtsev-Petviashvili equations

NASA Astrophysics Data System (ADS)

Dubrovin, B.; Grava, T.; Klein, C.

2016-10-01

An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev-Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a special solution to an ordinary differential equation of the Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the dispersive shock waves.

Relation between proton and neutron asymptotic normalization coefficients for light mirror nuclei and its relevance to nuclear astrophysics.

PubMed

Timofeyuk, N K; Johnson, R C; Mukhamedzhanov, A M

2003-12-05

We show how the charge symmetry of strong interactions can be used to relate the proton and neutron asymptotic normalization coefficients (ANCs) of the one-nucleon overlap integrals for light mirror nuclei. This relation extends to the case of real proton decay where the mirror analog is a virtual neutron decay of a loosely bound state. In this case, a link is obtained between the proton width and the squared ANC of the mirror neutron state. The relation between mirror overlaps can be used to study astrophysically relevant proton capture reactions based on information obtained from transfer reactions with stable beams.

Asymptotic convertibility of entanglement: An information-spectrum approach to entanglement concentration and dilution

NASA Astrophysics Data System (ADS)

Jiao, Yong; Wakakuwa, Eyuri; Ogawa, Tomohiro

2018-02-01

We consider asymptotic convertibility of an arbitrary sequence of bipartite pure states into another by local operations and classical communication (LOCC). We adopt an information-spectrum approach to address cases where each element of the sequences is not necessarily a tensor power of a bipartite pure state. We derive necessary and sufficient conditions for the LOCC convertibility of one sequence to another in terms of spectral entropy rates of entanglement of the sequences. Based on these results, we also provide simple proofs for previously known results on the optimal rates of entanglement concentration and dilution of general sequences of bipartite pure states.

Enhanced asymptotic BMS3 algebra of the flat spacetime solutions of generalized minimal massive gravity

NASA Astrophysics Data System (ADS)

Setare, M. R.; Adami, H.

2018-01-01

We apply the new fall of conditions presented in the paper [1] on asymptotically flat spacetime solutions of Chern-Simons-like theories of gravity. We show that the considered fall of conditions asymptotically solve equations of motion of generalized minimal massive gravity. We demonstrate that there exist two type of solutions, one of those is trivial and the others are non-trivial. By looking at non-trivial solutions, for asymptotically flat spacetimes in the generalized minimal massive gravity, in contrast to Einstein gravity, cosmological parameter can be non-zero. We obtain the conserved charges of the asymptotically flat spacetimes in generalized minimal massive gravity, and by introducing Fourier modes we show that the asymptotic symmetry algebra is a semidirect product of a BMS3 algebra and two U (1) current algebras. Also we verify that the BMS3 algebra can be obtained by a contraction of the AdS3 asymptotic symmetry algebra when the AdS3 radius tends to infinity in the flat-space limit. Finally we find energy, angular momentum and entropy for a particular case and deduce that these quantities satisfy the first law of flat space cosmologies.

Global asymptotic stability of density dependent integral population projection models.

PubMed

Rebarber, Richard; Tenhumberg, Brigitte; Townley, Stuart

2012-02-01

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium. Copyright © 2011 Elsevier Inc. All rights reserved.

Simple radiative transfer model for relationships between canopy biomass and reflectance

NASA Technical Reports Server (NTRS)

Park, J. K.; Deering, D. W.

1982-01-01

A modified Kubelka-Munk model has been utilized to derive useful equations for the analysis of apparent canopy reflectance. Based on the solution to the model simple working equations were formulated by employing reflectance characteristic parameters. The relationships derived show the asymptotic nature of reflectance data that is typically observed in remote sensing studies of plant biomass. They also establish the range of expected apparent canopy reflectance values for specific plant canopy types. The usefulness of the simplified equations was demonstrated by the exceptionally close fit of the theoretical curves to two separately acquired data sets for alfalfa and shortgrass prairie canopies.

Feynman graphs and the large dimensional limit of multipartite entanglement

NASA Astrophysics Data System (ADS)

Di Martino, Sara; Facchi, Paolo; Florio, Giuseppe

2018-01-01

In this paper, we extend the analysis of multipartite entanglement, based on techniques from classical statistical mechanics, to a system composed of n d-level parties (qudits). We introduce a suitable partition function at a fictitious temperature with the average local purity of the system as Hamiltonian. In particular, we analyze the high-temperature expansion of this partition function, prove the convergence of the series, and study its asymptotic behavior as d → ∞. We make use of a diagrammatic technique, classify the graphs, and study their degeneracy. We are thus able to evaluate their contributions and estimate the moments of the distribution of the local purity.

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

NASA Astrophysics Data System (ADS)

Umezu, Kenichiro

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.

Les résonances d'un trou noir de Schwarzschild.

NASA Astrophysics Data System (ADS)

Bachelot, A.; Motet-Bachelot, A.

1993-09-01

This paper is devoted to the theoretical and computational investigations of the scattering frequencies of scalar, electromagnetic, gravitational waves around a spherical black hole. The authors adopt a time dependent approach: construction of wave operators for the hyperbolic Regge-Wheeler equation; asymptotic completeness; outgoing and incoming spectral representations; meromorphic continuation of the Heisenberg matrix; approximation by dumping and cut-off of the potentials and interpretation of the semi group Z(t) in the framework of the membrane paradigma. They develop a new procedure for the computation of the resonances by the spectral analysis of the transient scattered wave, based on Prony's algorithm.

New class of control laws for robotic manipulators. I - Nonadaptive case. II - Adaptive case

NASA Technical Reports Server (NTRS)

Wen, John T.; Bayard, David S.

1988-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is discussed. Closed-loop exponential stability has been demonstrated for both the set point and tracking control problems by a slight modification of the energy Lyapunov function and the use of a lemma which handles third-order terms in the Lyapunov function derivatives. In the second part, these control laws are adapted in a simple fashion to achieve asymptotically stable adaptive control. The analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and uses a parameterization based on physical (time-invariant) quantities.

Discriminative components of data.

PubMed

Peltonen, Jaakko; Kaski, Samuel

2005-01-01

A simple probabilistic model is introduced to generalize classical linear discriminant analysis (LDA) in finding components that are informative of or relevant for data classes. The components maximize the predictability of the class distribution which is asymptotically equivalent to 1) maximizing mutual information with the classes, and 2) finding principal components in the so-called learning or Fisher metrics. The Fisher metric measures only distances that are relevant to the classes, that is, distances that cause changes in the class distribution. The components have applications in data exploration, visualization, and dimensionality reduction. In empirical experiments, the method outperformed, in addition to more classical methods, a Renyi entropy-based alternative while having essentially equivalent computational cost.

Privacy-Preserving Distributed Information Sharing

DTIC Science & Technology

2006-07-01

80 B.2.4 Analysis for Bloom Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 B.3 Details of One...be chosen by slightly adjusting the analysis given in the proof of Theorem 26. 59 Using Bloom Filters. Bloom filters provide a compact probabilistic...representation of set membership [6]. Instead of using T filters, we can use a combined Bloom filter. This achieves the same asymptotic communication

Human Mars Mission: Launch Window from Earth Orbit. Pt. 1

NASA Technical Reports Server (NTRS)

Young, Archie

1999-01-01

The determination of orbital window characteristics is of major importance in the analysis of human interplanetary missions and systems. The orbital launch window characteristics are directly involved in the selection of mission trajectories, the development of orbit operational concepts, and the design of orbital launch systems. The orbital launch window problem arises because of the dynamic nature of the relative geometry between outgoing (departure) asymptote of the hyperbolic escape trajectory and the earth parking orbit. The orientation of the escape hyperbola asymptotic relative to the earth is a function of time. The required hyperbola energy level also varies with time. In addition, the inertial orientation of the parking orbit is a function of time because of the perturbations caused by the Earth's oblateness. Thus, a coplanar injection onto the escape hyperbola can be made only at a point in time when the outgoing escape asymptote is contained by the plane of parking orbit. Even though this condition may be planned as a nominal situation, it will not generally represent the more probable injection geometry. The general case of an escape injection maneuver performed at a time other than the coplanar time will involve both a path angle and plane change and, therefore, a delta V penalty. Usually, because of the delta V penalty the actual departure injection window is smaller in duration than that determined by energy requirement alone. This report contains the formulation, characteristics, and test cases for five different launch window modes for Earth orbit. These modes are: 1) One impulsive maneuver from a Highly Elliptical Orbit (HEO); 2) Two impulsive maneuvers from a Highly Elliptical Orbit (HEO); 3) One impulsive maneuver from a Low Earth Orbit (LEO); 4) Two impulsive maneuvers form LEO; and 5) Three impulsive maneuvers form LEO. The formulation of these five different launch window modes provides a rapid means of generating realistic parametric data for space exploration studies. Also the formulation provides vector and geometrical data sufficient for use as a good starting point in detail trajectory analysis based on calculus of variations, steepest descent, or parameter optimization program techniques.

Human Exploration Missions Study Launch Window from Earth Orbit

NASA Technical Reports Server (NTRS)

Young, Archie

2001-01-01

The determination of orbital launch window characteristics is of major importance in the analysis of human interplanetary missions and systems. The orbital launch window characteristics are directly involved in the selection of mission trajectories, the development of orbit operational concepts, and the design of orbital launch systems. The orbital launch window problem arises because of the dynamic nature of the relative geometry between outgoing (departure) asymptote of the hyperbolic escape trajectory and the earth parking orbit. The orientation of the escape hyperbola asymptotic relative to earth is a function of time. The required hyperbola energy level also varies with time. In addition, the inertial orientation of the parking orbit is a function of time because of the perturbations caused by the Earth's oblateness. Thus, a coplanar injection onto the escape hyperbola can be made only at a point in time when the outgoing escape asymptote is contained by the plane of parking orbit. Even though this condition may be planned as a nominal situation, it will not generally represent the more probable injection geometry. The general case of an escape injection maneuver performed at a time other than the coplanar time will involve both a path angle and plane change and, therefore, a Delta(V) penalty. Usually, because of the Delta(V) penalty the actual departure injection window is smaller in duration than that determined by energy requirement alone. This report contains the formulation, characteristics, and test cases for five different launch window modes for Earth orbit. These modes are: (1) One impulsive maneuver from a Low Earth Orbit (LEO), (2) Two impulsive maneuvers from LEO, (3) Three impulsive maneuvers from LEO, (4) One impulsive maneuvers from a Highly Elliptical Orbit (HEO), (5) Two impulsive maneuvers from a Highly Elliptical Orbit (HEO) The formulation of these five different launch window modes provides a rapid means of generating realistic parametric data for space exploration studies. Also the formulation provides vector and geometrical data sufficient for use as a good starting point in detail trajectory analysis based on calculus of variations, steepest descent, or parameter optimization program techniques.

Bifurcation Analysis of a Predator-Prey System with Ratio-Dependent Functional Response

NASA Astrophysics Data System (ADS)

Jiang, Xin; She, Zhikun; Feng, Zhaosheng; Zheng, Xiuliang

2017-12-01

In this paper, we are concerned with the structural stability of a density dependent predator-prey system with ratio-dependent functional response. Starting with the geometrical analysis of hyperbolic curves, we obtain that the system has one or two positive equilibria under various conditions. Inspired by the S-procedure and semi-definite programming, we use the sum of squares decomposition based method to ensure the global asymptotic stability of the positive equilibrium through the associated polynomial Lyapunov functions. By exploring the monotonic property of the trace of the Jacobian matrix with respect to r under the given different conditions, we analytically verify that there is a corresponding unique r∗ such that the trace is equal to zero and prove the existence of Hopf bifurcation, respectively.

Monitoring the Durability Performance of Concrete in Nuclear Waste Containment. Technical Progress Report No. 4

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

Ulm, Franz-Josef

2000-06-30

OAK-B135 Monitoring the Durability Performance of Concrete in Nuclear Waste Containment. Technical Progress Report No. 4. The analysis of the effect of cracks on the acceleration of the calcium leaching process of cement-based materials has been pursued. During the last period (Technical Progress Report No 3), we have introduced a modeling accounting for the high diffusivity of fractures in comparison with the weak solid material diffusivity. It has been shown through dimensional and asymptotic analysis that small fractures do not significantly accelerate the material aging process. This important result for the overall structural aging kinetics of containment structure has beenmore » developed in a paper submitted to the international journal ''Transport in Porous Media''.« less

Robust adaptive cruise control of high speed trains.

PubMed

Faieghi, Mohammadreza; Jalali, Aliakbar; Mashhadi, Seyed Kamal-e-ddin Mousavi

2014-03-01

The cruise control problem of high speed trains in the presence of unknown parameters and external disturbances is considered. In particular a Lyapunov-based robust adaptive controller is presented to achieve asymptotic tracking and disturbance rejection. The system under consideration is nonlinear, MIMO and non-minimum phase. To deal with the limitations arising from the unstable zero-dynamics we do an output redefinition such that the zero-dynamics with respect to new outputs becomes stable. Rigorous stability analyses are presented which establish the boundedness of all the internal states and simultaneously asymptotic stability of the tracking error dynamics. The results are presented for two common configurations of high speed trains, i.e. the DD and PPD designs, based on the multi-body model and are verified by several numerical simulations. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Robust stability for stochastic bidirectional associative memory neural networks with time delays

NASA Astrophysics Data System (ADS)

Shu, H. S.; Lv, Z. W.; Wei, G. L.

2008-02-01

In this paper, the asymptotic stability is considered for a class of uncertain stochastic bidirectional associative memory neural networks with time delays and parameter uncertainties. The delays are time-invariant and the uncertainties are norm-bounded that enter into all network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov-Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed criteria.

Steady flow in a rotating sphere with strong precession

NASA Astrophysics Data System (ADS)

Kida, Shigeo

2018-04-01

The steady flow in a rotating sphere is investigated by asymptotic analysis in the limit of strong precession. The whole spherical body is divided into three regions in terms of the flow characteristics: the critical band, which is the close vicinity surrounding the great circle perpendicular to the precession axis, the boundary layer, which is attached to the whole sphere surface and the inviscid region that occupies the majority of the sphere. The analytic expressions, in the leading order of the asymptotic expansion, of the velocity field are obtained in the former two, whereas partial differential equations for the velocity field are derived in the latter, which are solved numerically. This steady flow structure is confirmed by the corresponding direct numerical simulation.

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.

Periodic-disturbance accommodating control of the space station for asymptotic momentum management

NASA Technical Reports Server (NTRS)

Warren, Wayne; Wie, Bong

1989-01-01

Periodic maneuvering control is developed for asymptotic momentum management of control gyros used as primary actuating devices for the Space Station. The proposed controller utilizes the concepts of quaternion feedback control and periodic-disturbance accommodation to achieve oscillations about the constant torque equilibrium attitude, while minimizing the control effort required. Three-axis coupled equations of motion, written in terms of quaternions, are derived for roll/yaw controller design and stability analysis. It is shown that the quaternion feedback controller is very robust for a wide range of pitch angles. It is also shown that the proposed controller tunes the open-loop unstable vehicle to a stable oscillatory motion which minimizes the control effort needed for steady-state operations.

Asymptotic behaviour of two-point functions in multi-species models

NASA Astrophysics Data System (ADS)

Kozlowski, Karol K.; Ragoucy, Eric

2016-05-01

We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance regime re-summation of the form factor expansion of correlation functions. The key feature of our analysis is a technical hypothesis on the large-volume behaviour of the form factors of local operators in such models. We check the validity of this hypothesis on the example of the SU (3)-invariant XXX magnet by means of the determinant representations for the form factors of local operators in this model. Our approach confirms the structure of the critical exponents obtained previously for numerous models solvable by the nested Bethe Ansatz.

Finite key analysis for symmetric attacks in quantum key distribution

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

Meyer, Tim; Kampermann, Hermann; Kleinmann, Matthias

2006-10-15

We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n{approx}10{sup 4}, the finite key rate differs significantly from the asymptotic value for n{yields}{infinity}. However, for larger n, a good approximation of the asymptotic value is found.more » We also study secret key rates for protocols using higher-dimensional quantum systems.« less

Frank Wilczek, Asymptotic Freedom, and Strong Interaction

Science.gov Websites

whereby quarks behave as free particles when they are close together, but become more strongly attracted , Issue 26; 1973 Asymptotically Free Gauge Theories I; DOE Technical Report; 1973 Scaling Deviations for Neutrino Reactions in Asymptotically Free Field Theories; DOE Technical Report; 1974 Weak-interaction

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...

New explicit global asymptotic stability criteria for higher order difference equations

NASA Astrophysics Data System (ADS)

El-Morshedy, Hassan A.

2007-12-01

New explicit sufficient conditions for the asymptotic stability of the zero solution of higher order difference equations are obtained. These criteria can be applied to autonomous and nonautonomous equations. The celebrated Clark asymptotic stability criterion is improved. Also, applications to models from mathematical biology and macroeconomics are given.

An asymptotic method for estimating the vertical ozone distribution in the Earth's atmosphere from satellite measurements of backscattered solar UV-radiation

NASA Technical Reports Server (NTRS)

Ishov, Alexander G.

1994-01-01

An asymptotic approach to solution of the inverse problems of remote sensing is presented. It consists in changing integral operators characteristic of outgoing radiation into their asymptotic analogues. Such approach does not add new principal uncertainties into the problem and significantly reduces computation time that allows to develop the real (or about) time algorithms for interpretation of satellite measurements. The asymptotic approach has been realized for estimating vertical ozone distribution from satellite measurements of backscatter solar UV radiation in the Earth's atmosphere.

Coulomb string tension, asymptotic string tension, and the gluon chain

DOE PAGES

Greensite, Jeff; Szczepaniak, Adam P.

2015-02-01

We compute, via numerical simulations, the non-perturbative Coulomb potential and position-space ghost propagator in pure SU(3) gauge theory in Coulomb gauge. We find that that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.

Asymptotically-Equal-To 10 eV ionization shift in Ir K{alpha}{sub 2} from a near-coincident Lu K-edge

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

Pereira, N. R.; Weber, B. V.; Phipps, D.

Close to an x-ray filter's K-edge the transmission depends strongly on the photon energy. For a few atom pairs, the K-edge of one is only a few tens of eV higher than a K-line energy of another, so that a small change in the line's energy becomes a measurable change in intensity behind such a matching filter. Lutetium's K-edge is Asymptotically-Equal-To 27 eV above iridium's K{alpha}{sub 2} line, Asymptotically-Equal-To 63.287 keV for cold Ir. A Lu filter reduces this line's intensity by Asymptotically-Equal-To 10 % when it is emitted by a plasma, indicating an ionization shift {Delta}E Asymptotically-Equal-To 10{+-}1 eV.

Optimum instantaneous impulsive orbital injection to attain a specified asymptotic velocity vector.

NASA Technical Reports Server (NTRS)

Bean, W. C.

1971-01-01

A nalysis of the necessary conditions of Battin for instantaneous orbital injection, with consideration of the uniqueness of his solution, and of the further problem which arises in the degenerate case when radius vector and asymptotic vector are separated by 180 deg. It is shown that when the angular separation between radius vector and asymptotic velocity vector satisfies theta not equal to 180 deg, there are precisely two insertion-velocity vectors which permit attainment of the target asymptotic velocity vector, one yielding posigrade, the other retrograde motion. When theta equals to 180 deg, there is a family of insertion-velocity vectors which permit attainment of a specified asymptotic velocity vector with a unique insertion-velocity vector for every arbitrary orientation of a target unit angular momentum vector.

Asymptotic Poincare lemma and its applications

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

Ziolkowski, R.W.; Deschamps, G.A.

1984-05-01

An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generatemore » a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures.« less

Seismic low-frequency-based calculation of reservoir fluid mobility and its applications

NASA Astrophysics Data System (ADS)

Chen, Xue-Hua; He, Zhen-Hua; Zhu, Si-Xin; Liu, Wei; Zhong, Wen-Li

2012-06-01

Low frequency content of seismic signals contains information related to the reservoir fluid mobility. Based on the asymptotic analysis theory of frequency-dependent reflectivity from a fluid-saturated poroelastic medium, we derive the computational implementation of reservoir fluid mobility and present the determination of optimal frequency in the implementation. We then calculate the reservoir fluid mobility using the optimal frequency instantaneous spectra at the low-frequency end of the seismic spectrum. The methodology is applied to synthetic seismic data from a permeable gas-bearing reservoir model and real land and marine seismic data. The results demonstrate that the fluid mobility shows excellent quality in imaging the gas reservoirs. It is feasible to detect the location and spatial distribution of gas reservoirs and reduce the non-uniqueness and uncertainty in fluid identification.

Verifiable Adaptive Control with Analytical Stability Margins by Optimal Control Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2010-01-01

This paper presents a verifiable model-reference adaptive control method based on an optimal control formulation for linear uncertain systems. A predictor model is formulated to enable a parameter estimation of the system parametric uncertainty. The adaptation is based on both the tracking error and predictor error. Using a singular perturbation argument, it can be shown that the closed-loop system tends to a linear time invariant model asymptotically under an assumption of fast adaptation. A stability margin analysis is given to estimate a lower bound of the time delay margin using a matrix measure method. Using this analytical method, the free design parameter n of the optimal control modification adaptive law can be determined to meet a specification of stability margin for verification purposes.

A comparative study on book shelf structure based on different domain modal analysis

NASA Astrophysics Data System (ADS)

Sabamehr, Ardalan; Roy, Timir Baran; Bagchi, Ashutosh

2017-04-01

Structural Health Monitoring (SHM) based on the vibration of structures has been very attractive topic for researchers in different fields such as: civil, aeronautical and mechanical engineering. The aim of this paper is to compare three most common modal identification techniques such as Frequency Domain Decomposition (FDD), Stochastic Subspace Identification (SSI) and Continuous Wavelet Transform (CWT) to find modal properties (such as natural frequency, mode shape and damping ratio) of three story book shelf steel structure which was built in Concordia University Lab. The modified Complex Morlet wavelet have been selected for wavelet in order to use asymptotic signal rather than real one with variable bandwidth and wavelet central frequency. So, CWT is able to detect instantaneous modulus and phase by use of local maxima ridge detection.

The Vlasov-Poisson-Boltzmann System for a Disparate Mass Binary Mixture

NASA Astrophysics Data System (ADS)

Duan, Renjun; Liu, Shuangqian

2017-11-01

The Vlasov-Poisson-Boltzmann system is often used to govern the motion of plasmas consisting of electrons and ions with disparate masses when collisions of charged particles are described by the two-component Boltzmann collision operator. The perturbation theory of the system around global Maxwellians recently has been well established in Guo (Commun Pure Appl Math 55:1104-1135, 2002). It should be more interesting to further study the existence and stability of nontrivial large time asymptotic profiles for the system even with slab symmetry in space, particularly understanding the effect of the self-consistent potential on the non-trivial long-term dynamics of the binary system. In this paper, we consider the problem in the setting of rarefaction waves. The analytical tool is based on the macro-micro decomposition introduced in Liu et al. (Physica D 188(3-4):178-192, 2004) that we have been able to develop for the case of the two-component Boltzmann equations around local bi-Maxwellians. Our focus is to explore how the disparate masses and charges of particles play a role in the analysis of the approach of the complex coupling system time-asymptotically toward a non-constant equilibrium state whose macroscopic quantities satisfy the quasineutral nonisentropic Euler system.

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.

Localized overlap algorithm for unexpanded dispersion energies

NASA Astrophysics Data System (ADS)

Rob, Fazle; Misquitta, Alston J.; Podeszwa, Rafał; Szalewicz, Krzysztof

2014-03-01

First-principles-based, linearly scaling algorithm has been developed for calculations of dispersion energies from frequency-dependent density susceptibility (FDDS) functions with account of charge-overlap effects. The transition densities in FDDSs are fitted by a set of auxiliary atom-centered functions. The terms in the dispersion energy expression involving products of such functions are computed using either the unexpanded (exact) formula or from inexpensive asymptotic expansions, depending on the location of these functions relative to the dimer configuration. This approach leads to significant savings of computational resources. In particular, for a dimer consisting of two elongated monomers with 81 atoms each in a head-to-head configuration, the most favorable case for our algorithm, a 43-fold speedup has been achieved while the approximate dispersion energy differs by less than 1% from that computed using the standard unexpanded approach. In contrast, the dispersion energy computed from the distributed asymptotic expansion differs by dozens of percent in the van der Waals minimum region. A further increase of the size of each monomer would result in only small increased costs since all the additional terms would be computed from the asymptotic expansion.

Relaxation processes in a low-order three-dimensional magnetohydrodynamics model

NASA Technical Reports Server (NTRS)

Stribling, Troy; Matthaeus, William H.

1991-01-01

The time asymptotic behavior of a Galerkin model of 3D magnetohydrodynamics (MHD) has been interpreted using the selective decay and dynamic alignment relaxation theories. A large number of simulations has been performed that scan a parameter space defined by the rugged ideal invariants, including energy, cross helicity, and magnetic helicity. It is concluded that time asymptotic state can be interpreted as a relaxation to minimum energy. A simple decay model, based on absolute equilibrium theory, is found to predict a mapping of initial onto time asymptotic states, and to accurately describe the long time behavior of the runs when magnetic helicity is present. Attention is also given to two processes, operating on time scales shorter than selective decay and dynamic alignment, in which the ratio of kinetic to magnetic energy relaxes to values 0(1). The faster of the two processes takes states initially dominant in magnetic energy to a state of near-equipartition between kinetic and magnetic energy through power law growth of kinetic energy. The other process takes states initially dominant in kinetic energy to the near-equipartitioned state through exponential growth of magnetic energy.

Multi-pair two-way massive MIMO AF relaying with ZFR/ZFT beamforming and imperfect CSI over ricean fading channels

NASA Astrophysics Data System (ADS)

Xu, Kui; Sun, Xiaoli; Zhang, Dongmei

2016-10-01

This paper investigates the spectral and energy efficiencies of a multi-pair two-way amplify-and-forward (AF) relay system over Ricean fading channels, where multiple user-pairs exchange information within pair through a relay with very large number of antennas, while each user equipped with a single antenna. Firstly, beamforming matrixe of zero-forcing reception/zero-forcing transmission (ZFR/ZFT) with imperfect channel state information (CSI) at the relay is given. Then, the unified asymptotic signal-to-interference-plus-noise ratio (SINR) expressions with imperfect CSI are obtained analytically. Finally, two power scaling schemes are proposed and the asymptotic spectral and energy efficiencies based on the proposed power scaling schemes are derived and verified by the Monte-Carlo simulations. Theoretical analyses and simulation results show that with imperfect CSI, if the number of relay antennas grows asymptotically large, we need cut down the transmit power of each user and relay to different proportion when the Ricean K-factor is non-zero and zero (Rayleigh fading) in order to maintain a desirable rate.

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 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.

Non-unique turbulent boundary layer flows having a moderately large velocity defect: a rational extension of the classical asymptotic theory

NASA Astrophysics Data System (ADS)

Scheichl, B.; Kluwick, A.

2013-11-01

The classical analysis of turbulent boundary layers in the limit of large Reynolds number Re is characterised by an asymptotically small velocity defect with respect to the external irrotational flow. As an extension of the classical theory, it is shown in the present work that the defect may become moderately large and, in the most general case, independent of Re but still remain small compared to the external streamwise velocity for non-zero pressure gradient boundary layers. That wake-type flow turns out to be characterised by large values of the Rotta-Clauser parameter, serving as an appropriate measure for the defect and hence as a second perturbation parameter besides Re. Most important, it is demonstrated that also this case can be addressed by rigorous asymptotic analysis, which is essentially independent of the choice of a specific Reynolds stress closure. As a salient result of this procedure, transition from the classical small defect to a pronounced wake flow is found to be accompanied by quasi-equilibrium flow, described by a distinguished limit that involves the wall shear stress. This situation is associated with double-valued solutions of the boundary layer equations and an unconventional weak Re-dependence of the external bulk flow—a phenomenon seen to agree well with previous semi-empirical studies and early experimental observations. Numerical computations of the boundary layer flow for various values of Re reproduce these analytical findings with satisfactory agreement.

Confidence Intervals for the Between-Study Variance in Random Effects Meta-Analysis Using Generalised Cochran Heterogeneity Statistics

ERIC Educational Resources Information Center

Jackson, Dan

2013-01-01

Statistical inference is problematic in the common situation in meta-analysis where the random effects model is fitted to just a handful of studies. In particular, the asymptotic theory of maximum likelihood provides a poor approximation, and Bayesian methods are sensitive to the prior specification. Hence, less efficient, but easily computed and…

Comparison of yellow poplar growth models on the basis of derived growth analysis variables

Treesearch

Keith F. Jensen; Daniel A. Yaussy

1986-01-01

Quadratic and cubic polynomials, and Gompertz and Richards asymptotic models were fitted to yellow poplar growth data. These data included height, leaf area, leaf weight and new shoot height for 23 weeks. Seven growth analysis variables were estimated from each function. The Gompertz and Richards models fitted the data best and provided the most accurate derived...

Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

NASA Astrophysics Data System (ADS)

Hadjidoukas, P. E.; Angelikopoulos, P.; Papadimitriou, C.; Koumoutsakos, P.

2015-03-01

We present Π4U, an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.

8. Asymptotically Flat and Regular Cauchy Data

NASA Astrophysics Data System (ADS)

Dain, Sergio

I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.

Parameter estimation of qubit states with unknown phase parameter

NASA Astrophysics Data System (ADS)

Suzuki, Jun

2015-02-01

We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean square errors (MSEs) when estimating relevant parameters with separable measurements based on known precision bounds; the symmetric logarithmic derivative (SLD) Cramér-Rao (CR) bound and Hayashi-Gill-Massar (HGM) bound. We investigate the optimal measurement which attains the HGM bound and discuss its properties. We show that the HGM bound for relevant parameters can be attained asymptotically by using some fraction of given n quantum states to estimate the phase parameter. We also discuss the Holevo bound which can be attained asymptotically by a collective measurement.

Global output feedback control for a class of high-order feedforward nonlinear systems with input delay.

PubMed

Zha, Wenting; Zhai, Junyong; Fei, Shumin

2013-07-01

This paper investigates the problem of output feedback stabilization for a class of high-order feedforward nonlinear systems with time-varying input delay. First, a scaling gain is introduced into the system under a set of coordinate transformations. Then, the authors construct an observer and controller to make the nominal system globally asymptotically stable. Based on homogeneous domination approach and Lyapunov-Krasovskii functional, it is shown that the closed-loop system can be rendered globally asymptotically stable by the scaling gain. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Asymptotic symmetries of Rindler space at the horizon and null infinity

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

Chung, Hyeyoun

2010-08-15

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler spacemore » at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.« less

Asymptotic solutions for flow in microchannels with ridged walls and arbitrary meniscus protrusion

NASA Astrophysics Data System (ADS)

Kirk, Toby

2017-11-01

Flow over structured surfaces exhibiting apparent slip, such as parallel ridges, have received much attention experimentally and numerically, but analytical and asymptotic solutions that account for the microstructure have so far been limited to unbounded geometries such as shear-driven flows. Analysis for channel flows has been limited to (close to) flat interfaces spanning the grooves between ridges, but in applications the interfaces (menisci) can highly protrude and have a significant impact on the apparent slip. In this presentation, we consider pressure-driven flow through a microchannel with longitudinal ridges patterning one or both walls. With no restriction on the meniscus protrusion, we develop explicit formulae for the slip length using a formal matched asymptotic expansion. Assuming the ratio of channel height to ridge period is large, the periodicity is confined to an inner layer close to the ridges, and the expansion is found to all algebraic orders. As a result, the error is exponentially small and, under a further ``diluteness'' assumption, the explicit formulae are compared to finite element solutions. They are found to have a very wide range of validity in channel height (even when the menisci can touch the opposing wall) and so are useful for practitioners.

Universality and tails of long-range interactions in one dimension

NASA Astrophysics Data System (ADS)

Valiente, Manuel; Öhberg, Patrik

2017-07-01

Long-range interactions and, in particular, two-body potentials with power-law long-distance tails are ubiquitous in nature. For two bosons or fermions in one spatial dimension, the latter case being formally equivalent to three-dimensional s -wave scattering, we show how generic asymptotic interaction tails can be accounted for in the long-distance limit of scattering wave functions. This is made possible by introducing a generalization of the collisional phase shifts to include space dependence. We show that this distance dependence is universal, in that it does not depend on short-distance details of the interaction. The energy dependence is also universal, and is fully determined by the asymptotic tails of the two-body potential. As an important application of our findings, we describe how to eliminate finite-size effects with long-range potentials in the calculation of scattering phase shifts from exact diagonalization. We show that even with moderately small system sizes it is possible to accurately extract phase shifts that would otherwise be plagued with finite-size errors. We also consider multichannel scattering, focusing on the estimation of open channel asymptotic interaction strengths via finite-size analysis.

Investigation of the asymptotic state of rotating turbulence using large-eddy simulation

NASA Technical Reports Server (NTRS)

Squires, Kyle D.; Chasnov, Jeffrey R.; Mansour, Nagi N.; Cambon, Claude

1993-01-01

Study of turbulent flows in rotating reference frames has long been an area of considerable scientific and engineering interest. Because of its importance, the subject of turbulence in rotating reference frames has motivated over the years a large number of theoretical, experimental, and computational studies. The bulk of these previous works has served to demonstrate that the effect of system rotation on turbulence is subtle and remains exceedingly difficult to predict. A rotating flow of particular interest in many studies, including the present work, is examination of the effect of solid-body rotation on an initially isotropic turbulent flow. One of the principal reasons for the interest in this flow is that it represents the most basic turbulent flow whose structure is altered by system rotation but without the complicating effects introduced by mean strains or flow inhomogeneities. The assumption of statistical homogeneity considerably simplifies analysis and computation. The principal objective of the present study has been to examine the asymptotic state of solid-body rotation applied to an initially isotropic, high Reynolds number turbulent flow. Of particular interest has been to determine the degree of two-dimensionalization and the existence of asymptotic self-similar states in homogeneous rotating turbulence.

Influence of local demography on asymptotic and transient dynamics of a yellow-bellied marmot metapopulation.

PubMed

Ozgul, Arpat; Oli, Madan K; Armitage, Kenneth B; Blumstein, Daniel T; Van Vuren, Dirk H

2009-04-01

Despite recent advances in biodemography and metapopulation ecology, we still have limited understanding of how local demographic parameters influence short- and long-term metapopulation dynamics. We used long-term data from 17 local populations, along with the recently developed methods of matrix metapopulation modeling and transient sensitivity analysis, to investigate the influence of local demography on long-term (asymptotic) versus short-term (transient) dynamics of a yellow-bellied marmot metapopulation in Colorado. Both long- and short-term dynamics depended primarily on a few colony sites and were highly sensitive to changes in demography at these sites, particularly in survival of reproductive adult females. Interestingly, the relative importance of sites differed between long- and short-term dynamics; the spatial structure and local population sizes, while insignificant for asymptotic dynamics, were influential on transient dynamics. However, considering the spatial structure was uninformative about the relative influence of local demography on metapopulation dynamics. The vital rates that were the most influential on local dynamics were also the most influential on both long- and short-term metapopulation dynamics. Our results show that an explicit consideration of local demography is essential for a complete understanding of the dynamics and persistence of spatially structured populations.

Studies of Evolved Star Mass Loss: GRAMS Modeling of Red Supergiant and Asymptotic Giant Branch Stars in the Magellanic Clouds

NASA Astrophysics Data System (ADS)

Sargent, Benjamin A.; Srinivasan, S.; Riebel, D.; Boyer, M.; Meixner, M.

2012-01-01

As proposed in our NASA Astrophysics Data Analysis Program (ADAP) proposal, my colleagues and I are studying mass loss from evolved stars. Such stars lose their own mass in their dying stages, and in their expelled winds they form stardust. To model mass loss from these evolved stars, my colleagues and I have constructed GRAMS: the Grid of Red supergiant and Asymptotic giant branch star ModelS. These GRAMS radiative transfer models are fit to optical through mid-infrared photometry of red supergiant (RSG) stars and asymptotic giant branch (AGB) stars. I will discuss our current studies of mass loss from AGB and RSG stars in the Small Magellanic Cloud (SMC), fitting GRAMS models to the photometry of SMC evolved star candidates identified from the SAGE-SMC (PI: K. Gordon) Spitzer Space Telescope Legacy survey. This work will be briefly compared to similar work we have done for the LMC. I will also discuss Spitzer Infrared Spectrograph (IRS) studies of the dust produced by AGB and RSG stars in the LMC. BAS is grateful for support from the NASA-ADAP grant NNX11AB06G.

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?’

Structure factors for tunneling ionization rates of molecules: General Hartree-Fock-based integral representation

NASA Astrophysics Data System (ADS)

Madsen, Lars Bojer; Jensen, Frank; Dnestryan, Andrey I.; Tolstikhin, Oleg I.

2017-07-01

In the leading-order approximation of the weak-field asymptotic theory (WFAT), the dependence of the tunneling ionization rate of a molecule in an electric field on its orientation with respect to the field is determined by the structure factor of the ionizing molecular orbital. The WFAT yields an expression for the structure factor in terms of a local property of the orbital in the asymptotic region. However, in general quantum chemistry approaches molecular orbitals are expanded in a Gaussian basis which does not reproduce their asymptotic behavior correctly. This hinders the application of the WFAT to polyatomic molecules, which are attracting increasing interest in strong-field physics. Recently, an integral-equation approach to the WFAT for tunneling ionization of one electron from an arbitrary potential has been developed. The structure factor is expressed in an integral form as a matrix element involving the ionizing orbital. The integral is not sensitive to the asymptotic behavior of the orbital, which resolves the difficulty mentioned above. Here, we extend the integral representation for the structure factor to many-electron systems treated within the Hartree-Fock method and show how it can be implemented on the basis of standard quantum chemistry software packages. We validate the methodology by considering noble-gas atoms and the CO molecule, for which accurate structure factors exist in the literature. We also present benchmark results for CO2 and for NH3 in the pyramidal and planar geometries.

Asymptotically Almost Periodic Solutions of Evolution Equations in Banach Spaces

NASA Astrophysics Data System (ADS)

Ruess, W. M.; Phong, V. Q.

Tile linear abstract evolution equation (∗) u'( t) = Au( t) + ƒ( t), t ∈ R, is considered, where A: D( A) ⊂ E → E is the generator of a strongly continuous semigroup of operators in the Banach space E. Starting from analogs of Kadets' and Loomis' Theorems for vector valued almost periodic Functions, we show that if σ( A) ∩ iR is countable and ƒ: R → E is [asymptotically] almost periodic, then every bounded and uniformly continuous solution u to (∗) is [asymptotically] almost periodic, provided e-λ tu( t) has uniformly convergent means for all λ ∈ σ( A) ∩ iR. Related results on Eberlein-weakly asymptotically almost periodic, periodic, asymptotically periodic and C 0-solutions of (∗), as well as on the discrete case of solutions of difference equations are included.

Handy elementary algebraic properties of the geometry of entanglement

NASA Astrophysics Data System (ADS)

Blair, Howard A.; Alsing, Paul M.

2013-05-01

The space of separable states of a quantum system is a hyperbolic surface in a high dimensional linear space, which we call the separation surface, within the exponentially high dimensional linear space containing the quantum states of an n component multipartite quantum system. A vector in the linear space is representable as an n-dimensional hypermatrix with respect to bases of the component linear spaces. A vector will be on the separation surface iff every determinant of every 2-dimensional, 2-by-2 submatrix of the hypermatrix vanishes. This highly rigid constraint can be tested merely in time asymptotically proportional to d, where d is the dimension of the state space of the system due to the extreme interdependence of the 2-by-2 submatrices. The constraint on 2-by-2 determinants entails an elementary closed formformula for a parametric characterization of the entire separation surface with d-1 parameters in the char- acterization. The state of a factor of a partially separable state can be calculated in time asymptotically proportional to the dimension of the state space of the component. If all components of the system have approximately the same dimension, the time complexity of calculating a component state as a function of the parameters is asymptotically pro- portional to the time required to sort the basis. Metric-based entanglement measures of pure states are characterized in terms of the separation hypersurface.

Eikonal instability of Gauss-Bonnet-(anti-)-de Sitter black holes

NASA Astrophysics Data System (ADS)

Konoplya, R. A.; Zhidenko, A.

2017-05-01

Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of space-time in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in Grozdanov, Kaplis, and Starinets, [J. High Energy Phys. 07 (2016) 151, 10.1007/JHEP07(2016)151] for the higher curvature corrected black hole with the planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of the Gauss-Bonnet term, it was shown [Deppe et al, Phys. Rev. Lett. 114, 071102 (2015), 10.1103/PhysRevLett.114.071102], that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [Frolov, Phys. Rev. Lett. 115, 051102 (2015), 10.1103/PhysRevLett.115.051102]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, dS and asymptotically flat black holes may explain the existing mass gaps in their formation.

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

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

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Cuckoo Search Algorithm Based on Repeat-Cycle Asymptotic Self-Learning and Self-Evolving Disturbance for Function Optimization

PubMed Central

Wang, Jie-sheng; Li, Shu-xia; Song, Jiang-di

2015-01-01

In order to improve convergence velocity and optimization accuracy of the cuckoo search (CS) algorithm for solving the function optimization problems, a new improved cuckoo search algorithm based on the repeat-cycle asymptotic self-learning and self-evolving disturbance (RC-SSCS) is proposed. A disturbance operation is added into the algorithm by constructing a disturbance factor to make a more careful and thorough search near the bird's nests location. In order to select a reasonable repeat-cycled disturbance number, a further study on the choice of disturbance times is made. Finally, six typical test functions are adopted to carry out simulation experiments, meanwhile, compare algorithms of this paper with two typical swarm intelligence algorithms particle swarm optimization (PSO) algorithm and artificial bee colony (ABC) algorithm. The results show that the improved cuckoo search algorithm has better convergence velocity and optimization accuracy. PMID:26366164

Cache-Aware Asymptotically-Optimal Sampling-Based Motion Planning

PubMed Central

Ichnowski, Jeffrey; Prins, Jan F.; Alterovitz, Ron

2014-01-01

We present CARRT* (Cache-Aware Rapidly Exploring Random Tree*), an asymptotically optimal sampling-based motion planner that significantly reduces motion planning computation time by effectively utilizing the cache memory hierarchy of modern central processing units (CPUs). CARRT* can account for the CPU’s cache size in a manner that keeps its working dataset in the cache. The motion planner progressively subdivides the robot’s configuration space into smaller regions as the number of configuration samples rises. By focusing configuration exploration in a region for periods of time, nearest neighbor searching is accelerated since the working dataset is small enough to fit in the cache. CARRT* also rewires the motion planning graph in a manner that complements the cache-aware subdivision strategy to more quickly refine the motion planning graph toward optimality. We demonstrate the performance benefit of our cache-aware motion planning approach for scenarios involving a point robot as well as the Rethink Robotics Baxter robot. PMID:25419474

Cache-Aware Asymptotically-Optimal Sampling-Based Motion Planning.

PubMed

Ichnowski, Jeffrey; Prins, Jan F; Alterovitz, Ron

2014-05-01

We present CARRT* (Cache-Aware Rapidly Exploring Random Tree*), an asymptotically optimal sampling-based motion planner that significantly reduces motion planning computation time by effectively utilizing the cache memory hierarchy of modern central processing units (CPUs). CARRT* can account for the CPU's cache size in a manner that keeps its working dataset in the cache. The motion planner progressively subdivides the robot's configuration space into smaller regions as the number of configuration samples rises. By focusing configuration exploration in a region for periods of time, nearest neighbor searching is accelerated since the working dataset is small enough to fit in the cache. CARRT* also rewires the motion planning graph in a manner that complements the cache-aware subdivision strategy to more quickly refine the motion planning graph toward optimality. We demonstrate the performance benefit of our cache-aware motion planning approach for scenarios involving a point robot as well as the Rethink Robotics Baxter robot.

Asymptotic analysis of corona discharge from thin electrodes

NASA Technical Reports Server (NTRS)

Durbin, P. A.

1986-01-01

The steady discharge of a high-voltage corona is analyzed as a singular perturbation problem. The small parameter is the ratio of the length of the ionization region to the total gap length. By this method, current versus voltage characteristics can be calculated analytically.

Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models

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

Gulisashvili, Archil, E-mail: guli@math.ohiou.ed; Stein, Elias M., E-mail: stein@math.princeton.ed

2010-06-15

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of these densities and give error estimates. As an application of our results, sharp asymptotic formulas for the implied volatility in the Stein-Stein and the Heston model are obtained.

Zipf exponent of trajectory distribution in the hidden Markov model

NASA Astrophysics Data System (ADS)

Bochkarev, V. V.; Lerner, E. Yu

2014-03-01

This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.

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

Gravity tectonics and seismic gaps in the mantle

NASA Technical Reports Server (NTRS)

Liu, H. S.

1974-01-01

The concept of gravity tectonics is applied to reveal the major clue as to the conditions which result in the correspondence of seismic and tectonic gaps in the mantle. An asymptotic theory is developed for the calculation of the thrust and moment when a descending lithospheric plate encounters resistance to its downward motion in the mesosphere. Dynamic analysis falls into two parts: (1) deriving equations for forces in the descending lithosphere, (2) deducing moment distribution which causes the detachment of lithosphere. For the analysis of forces a mathematical theory of shells is given. In order to determine the detachment mechanism, solutions of equations are obtained by asymptotic integration. It is found that a thrust N sub phi coupled with a moment M sub phi due to gravitational forces generated by density contrast may play a key role in the initial detachment of a piece of descending lithosphere. The results are in agreement with the observed seismic gaps beneath South America, Toga-Fiji, New Zealand and New Hebrides regions.

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.

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.

Modulated elliptic wave and asymptotic solitons in a shock problem to the modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Kotlyarov, Vladimir; Minakov, Alexander

2015-07-01

We study the long-time asymptotic behavior of the Cauchy problem for the modified Korteweg—de Vries equation with an initial function of the step type. This function rapidly tends to zero as x\\to +∞ and to some positive constant c as x\\to -∞ . In 1989 Khruslov and Kotlyarov have found (Khruslov and Kotlyarov 1989 Inverse Problems 5 1075-88) that for a large time the solution breaks up into a train of asymptotic solitons located in the domain 4{c}2t-{C}N{ln}t\\lt x≤slant 4{c}2t ({C}N is a constant). The number N of these solitons grows unboundedly as t\\to ∞ . In 2010 Kotlyarov and Minakov have studied temporary asymptotics of the solution of the Cauchy problem on the whole line (Kotlyarov and Minakov 2010 J. Math. Phys. 51 093506) and have found that in the domain -6{c}2t\\lt x\\lt 4{c}2t this solution is described by a modulated elliptic wave. We consider here the modulated elliptic wave in the domain 4{c}2t-{C}N{ln}t\\lt x\\lt 4{c}2t. Our main result shows that the modulated elliptic wave also breaks up into solitons, which are similar to the asymptotic solitons in Khruslov and Kotlyarov (1989 Inverse Problems 5 1075-88), but differ from them in phase. It means that the modulated elliptic wave does not represent the asymptotics of the solution in the domain 4{c}2t-{C}N{ln}t\\lt x\\lt 4{c}2t. The correct asymptotic behavior of the solution is given by the train of asymptotic solitons given in Khruslov and Kotlyarov (1989 Inverse Problems 5 1075-88). However, in the asymptotic regime as t\\to ∞ in the region 4{c}2t-\\displaystyle \\frac{N+1/4}{c}{ln}t\\lt x\\lt 4{c}2t-\\displaystyle \\frac{N-3/4}{c}{ln}t we can watch precisely a pair of solitons with numbers N. One of them is the asymptotic soliton while the other soliton is generated from the elliptic wave. Their phases become closer to each other for a large N, i.e. these solitons are also close to each other. This result gives the answer on a very important question about matching of the asymptotic formulas in the mentioned region where the both formulas are well-defined. Thus we have here a new and previously unknown mechanism (5.35) of matching of the asymptotics of the solution in the adjacent regions.

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.

Interoperating Cloud-based Virtual Farms

NASA Astrophysics Data System (ADS)

Bagnasco, S.; Colamaria, F.; Colella, D.; Casula, E.; Elia, D.; Franco, A.; Lusso, S.; Luparello, G.; Masera, M.; Miniello, G.; Mura, D.; Piano, S.; Vallero, S.; Venaruzzo, M.; Vino, G.

2015-12-01

The present work aims at optimizing the use of computing resources available at the grid Italian Tier-2 sites of the ALICE experiment at CERN LHC by making them accessible to interactive distributed analysis, thanks to modern solutions based on cloud computing. The scalability and elasticity of the computing resources via dynamic (“on-demand”) provisioning is essentially limited by the size of the computing site, reaching the theoretical optimum only in the asymptotic case of infinite resources. The main challenge of the project is to overcome this limitation by federating different sites through a distributed cloud facility. Storage capacities of the participating sites are seen as a single federated storage area, preventing the need of mirroring data across them: high data access efficiency is guaranteed by location-aware analysis software and storage interfaces, in a transparent way from an end-user perspective. Moreover, the interactive analysis on the federated cloud reduces the execution time with respect to grid batch jobs. The tests of the investigated solutions for both cloud computing and distributed storage on wide area network will be presented.

Replica and extreme-value analysis of the Jarzynski free-energy estimator

NASA Astrophysics Data System (ADS)

Palassini, Matteo; Ritort, Felix

2008-03-01

We analyze the Jarzynski estimator of free-energy differences from nonequilibrium work measurements. By a simple mapping onto Derrida's Random Energy Model, we obtain a scaling limit for the expectation of the bias of the estimator. We then derive analytical approximations in three different regimes of the scaling parameter x = log(N)/W, where N is the number of measurements and W the mean dissipated work. Our approach is valid for a generic distribution of the dissipated work, and is based on a replica symmetry breaking scheme for x >> 1, the asymptotic theory of extreme value statistics for x << 1, and a direct approach for x near one. The combination of the three analytic approximations describes well Monte Carlo data for the expectation value of the estimator, for a wide range of values of N, from N=1 to large N, and for different work distributions. Based on these results, we introduce improved free-energy estimators and discuss the application to the analysis of experimental data.

Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids

NASA Astrophysics Data System (ADS)

Efimov, Denis; Schiffer, Johannes; Ortega, Romeo

2016-05-01

Motivated by the problem of phase-locking in droop-controlled inverter-based microgrids with delays, the recently developed theory of input-to-state stability (ISS) for multistable systems is extended to the case of multistable systems with delayed dynamics. Sufficient conditions for ISS of delayed systems are presented using Lyapunov-Razumikhin functions. It is shown that ISS multistable systems are robust with respect to delays in a feedback. The derived theory is applied to two examples. First, the ISS property is established for the model of a nonlinear pendulum and delay-dependent robustness conditions are derived. Second, it is shown that, under certain assumptions, the problem of phase-locking analysis in droop-controlled inverter-based microgrids with delays can be reduced to the stability investigation of the nonlinear pendulum. For this case, corresponding delay-dependent conditions for asymptotic phase-locking are given.

Subpixel based defocused points removal in photon-limited volumetric dataset

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Maraka, Harsha Vardhan R.; Ryle, James P.; Sheridan, John T.

2017-03-01

The asymptotic property of the maximum likelihood estimator (MLE) has been utilized to reconstruct three-dimensional (3D) sectional images in the photon counting imaging (PCI) regime. At first, multiple 2D intensity images, known as Elemental images (EI), are captured. Then the geometric ray-tracing method is employed to reconstruct the 3D sectional images at various depth cues. We note that a 3D sectional image consists of both focused and defocused regions, depending on the reconstructed depth position. The defocused portion is redundant and should be removed in order to facilitate image analysis e.g., 3D object tracking, recognition, classification and navigation. In this paper, we present a subpixel level three-step based technique (i.e. involving adaptive thresholding, boundary detection and entropy based segmentation) to discard the defocused sparse-samples from the reconstructed photon-limited 3D sectional images. Simulation results are presented demonstrating the feasibility and efficiency of the proposed method.

Asymptotic structure of space-time with a positive cosmological constant

NASA Astrophysics Data System (ADS)

Kesavan, Aruna

In general relativity a satisfactory framework for describing isolated systems exists when the cosmological constant Lambda is zero. The detailed analysis of the asymptotic structure of the gravitational field, which constitutes the framework of asymptotic flatness, lays the foundation for research in diverse areas in gravitational science. However, the framework is incomplete in two respects. First, asymptotic flatness provides well-defined expressions for physical observables such as energy and momentum as 'charges' of asymptotic symmetries at null infinity, [special character omitted] +. But the asymptotic symmetry group, called the Bondi-Metzner-Sachs group is infinite-dimensional and a tensorial expression for the 'charge' integral of an arbitrary BMS element is missing. We address this issue by providing a charge formula which is a 2-sphere integral over fields local to the 2-sphere and refers to no extraneous structure. The second, and more significant shortcoming is that observations have established that Lambda is not zero but positive in our universe. Can the framework describing isolated systems and their gravitational radiation be extended to incorporate this fact? In this dissertation we show that, unfortunately, the standard framework does not extend from the Lambda = 0 case to the Lambda > 0 case in a physically useful manner. In particular, we do not have an invariant notion of gravitational waves in the non-linear regime, nor an analog of the Bondi 'news tensor', nor positive energy theorems. In addition, we argue that the stronger boundary condition of conformal flatness of intrinsic metric on [special character omitted]+, which reduces the asymptotic symmetry group from Diff([special character omitted]) to the de Sitter group, is insufficient to characterize gravitational fluxes and is physically unreasonable. To obtain guidance for the full non-linear theory with Lambda > 0, linearized gravitational waves in de Sitter space-time are analyzed in detail. i) We show explicitly that conformal flatness of the boundary removes half the degrees of freedom of the gravitational field by hand and is not justified by physical considerations; ii) We obtain gauge invariant expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at [special character omitted]+; iii) We demonstrate that the flux formulas reduce to the familiar ones in Minkowski spacetime in spite of the fact that the limit Lambda → 0 is discontinuous (since, in particular, [special character omitted]+ changes its space-like character to null in the limit); iv) We obtain a generalization of Einstein's 1918 quadrupole formula for power emission by a linearized source to include a positive Lambda; and, finally v) We show that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy.

College Students' Concept Images of Asymptotes, Limits, and Continuity of Rational Functions

ERIC Educational Resources Information Center

Nair, Girija Sarada

2010-01-01

The purpose of this research was to investigate student conceptions of the topic of asymptotes of rational functions and to understand the connections that students developed between the closely related notions of asymptotes, continuity, and limits. The participants of the study were university students taking Calculus 2 and were mostly freshmen. …

Fast-slow asymptotics for a Markov chain model of fast sodium current

NASA Astrophysics Data System (ADS)

Starý, Tomáš; Biktashev, Vadim N.

2017-09-01

We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.

Asymptotic Behaviour of Solitons with a Double Spectral Parameter for the Bogomolny Equation in (2+1)-Dimensional Anti de Sitter Space

NASA Astrophysics Data System (ADS)

Ji, Xue-Feng; Zhou, Zi-Xiang

2005-07-01

The asymptotic behaviour of the solitons with a double spectral parameter for the Bogomolny equation in (2+1)-dimensional anti de Sitter space is obtained. The asymptotic solution has two ridges close to each other which locates beside the geodesic of the Poincaré half-plane.

Simulation-based sensitivity analysis for non-ignorably missing data.

PubMed

Yin, Peng; Shi, Jian Q

2017-01-01

Sensitivity analysis is popular in dealing with missing data problems particularly for non-ignorable missingness, where full-likelihood method cannot be adopted. It analyses how sensitively the conclusions (output) may depend on assumptions or parameters (input) about missing data, i.e. missing data mechanism. We call models with the problem of uncertainty sensitivity models. To make conventional sensitivity analysis more useful in practice we need to define some simple and interpretable statistical quantities to assess the sensitivity models and make evidence based analysis. We propose a novel approach in this paper on attempting to investigate the possibility of each missing data mechanism model assumption, by comparing the simulated datasets from various MNAR models with the observed data non-parametrically, using the K-nearest-neighbour distances. Some asymptotic theory has also been provided. A key step of this method is to plug in a plausibility evaluation system towards each sensitivity parameter, to select plausible values and reject unlikely values, instead of considering all proposed values of sensitivity parameters as in the conventional sensitivity analysis method. The method is generic and has been applied successfully to several specific models in this paper including meta-analysis model with publication bias, analysis of incomplete longitudinal data and mean estimation with non-ignorable missing data.

Long memory analysis by using maximal overlapping discrete wavelet transform

NASA Astrophysics Data System (ADS)

Shafie, Nur Amalina binti; Ismail, Mohd Tahir; Isa, Zaidi

2015-05-01

Long memory process is the asymptotic decay of the autocorrelation or spectral density around zero. The main objective of this paper is to do a long memory analysis by using the Maximal Overlapping Discrete Wavelet Transform (MODWT) based on wavelet variance. In doing so, stock market of Malaysia, China, Singapore, Japan and United States of America are used. The risk of long term and short term investment are also being looked into. MODWT can be analyzed with time domain and frequency domain simultaneously and decomposing wavelet variance to different scales without loss any information. All countries under studied show that they have long memory. Subprime mortgage crisis in 2007 is occurred in the United States of America are possible affect to the major trading countries. Short term investment is more risky than long term investment.

Ultrasound beam transmission using a discretely orthogonal Gaussian aperture basis

NASA Astrophysics Data System (ADS)

Roberts, R. A.

2018-04-01

Work is reported on development of a computational model for ultrasound beam transmission at an arbitrary geometry transmission interface for generally anisotropic materials. The work addresses problems encountered when the fundamental assumptions of ray theory do not hold, thereby introducing errors into ray-theory-based transmission models. Specifically, problems occur when the asymptotic integral analysis underlying ray theory encounters multiple stationary phase points in close proximity, due to focusing caused by concavity on either the entry surface or a material slowness surface. The approach presented here projects integrands over both the transducer aperture and the entry surface beam footprint onto a Gaussian-derived basis set, thereby distributing the integral over a summation of second-order phase integrals which are amenable to single stationary phase point analysis. Significantly, convergence is assured provided a sufficiently fine distribution of basis functions is used.

The May 17, 2012 Solar Event: Back-Tracing Analysis and Flux Reconstruction with PAMELA

NASA Technical Reports Server (NTRS)

Bruno, A.; Adriani, O.; Barbarino, G. C.; Bazilevskaya, G. A.; Bellotti, R.; Boezio, M.; Bogomolov, E. A.; Bongi, M.; Bonvicini, V.; Bottai, S.;

Nozzle Free Jet Flows Within the Strong Curved Shock Regime

NASA Technical Reports Server (NTRS)

Shih, Tso-Shin

1975-01-01

A study based on inviscid analysis was conducted to examine the flow field produced from a convergent-divergent nozzle when a strong curved shock occurs. It was found that a certain constraint is imposed on the flow solution of the problem which is the unique feature of the flow within this flow regime, and provides the reason why the inverse method of calculation cannot be employed for these problems. An approximate method was developed to calculate the flow field, and results were obtained for two-dimensional flows. Analysis and calculations were performed for flows with axial symmetry. It is shown that under certain conditions, the vorticity generated at the jet boundary may become infinite and the viscous effect becomes important. Under other conditions, the asymptotic free jet height as well as the corresponding shock geometry were determined.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Autobalancing of a rigid rotor in viscoelastic orthotropic supports considering eccentricity of the automatic ball balancer

NASA Astrophysics Data System (ADS)

Bykov, V. G.; Kovachev, A. S.

2018-05-01

A statically unbalanced rotor in viscoelastic orthotropic supports equipped with an automatic ball balancer (ABB), the axis of symmetry of which does not coincide with the symmetry axis of the rotor, is considered. Based on an analysis of the equations describing the stationary modes of motion of the system, the principal impossibility of complete balancing of the rotor is shown. The possibility of the existence of two types of stationary modes is established, one of which has a constant average amplitude of residual vibration equal to the eccentricity of the ABB. The solution corresponding to this almost balanced mode is constructed analytically. A study is made of its asymptotic stability.

Electrostatic Interactions Between Glycosaminoglycan Molecules

NASA Astrophysics Data System (ADS)

Song, Fan; Moyne, Christian; Bai, Yi-Long

2005-02-01

The electrostatic interactions between nearest-neighbouring chondroitin sulfate glycosaminoglycan (CS-GAG) molecular chains are obtained on the bottle brush conformation of proteoglycan aggrecan based on an asymptotic solution of the Poisson-Boltzmann equation the CS-GAGs satisfy under the physiological conditions of articular cartilage. The present results show that the interactions are associated intimately with the minimum separation distance and mutual angle between the molecular chains themselves. Further analysis indicates that the electrostatic interactions are not only expressed to be purely exponential in separation distance and decrease with the increasing mutual angle but also dependent sensitively on the saline concentration in the electrolyte solution within the tissue, which is in agreement with the existed relevant conclusions.

Analysis of Multicomponent Adsorption Close to a Dew Point.

PubMed

Shapiro; Stenby

1998-10-15

We develop the potential theory of multicomponent adsorption close to a dew point. The approach is based on an asymptotic adsorption equation (AAE) which is valid in a vicinity of the dew point. By this equation the thickness of the liquid film is expressed through thermodynamic characteristics of the bulk phase. The AAE makes it possible to study adsorption in the regions of both the normal and the retrograde condensation. A simple correlation of the Kelvin radius for capillary condensation and the thickness of the adsorbed film is established. Numerical testing shows good agreement between the AAE and the direct calculations, even if the mixture is not close to a dew point. Copyright 1998 Academic Press.

Convective and morphological instabilities during crystal growth: Effect of gravity modulation

NASA Technical Reports Server (NTRS)

Coreill, S. R.; Murray, B. T.; Mcfadden, G. B.; Wheeler, A. A.; Saunders, B. V.

1992-01-01

During directional solidification of a binary alloy at constant velocity in the vertical direction, morphological and convective instabilities may occur due to the temperature and solute gradients associated with the solidification process. The effect of time-periodic modulation (vibration) is studied by considering a vertical gravitational acceleration which is sinusoidal in time. The conditions for the onset of solutal convection are calculated numerically, employing two distinct computational procedures based on Floquet theory. In general, a stable state can be destabilized by modulation and an unstable state can be stabilized. In the limit of high frequency modulation, the method of averaging and multiple-scale asymptotic analysis can be used to simplify the calculations.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

NASA Astrophysics Data System (ADS)

Do, K. D.

2018-05-01

Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

Asymptotics of a Class of Solutions to the Cylindrical Toda Equations

NASA Astrophysics Data System (ADS)

Tracy, Craig A.; Widom, Harold

The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, , have the representation where Kk$ are integral operators. This class includes the n-periodic cylindrical Toda equations. For n=2 our results reduce to the previously computed asymptotics of the 2D radial sinh-Gordon equation and for n=3 (and with an additional symmetry constraint) they reduce to earlier results for the radial Bullough-Dodd equation. Both of these special cases are examples of Painlevé III and have arisen in various applications. The asymptotics of are derived by computing the small t asymptotics where explicit formulas are given for the quantities ak and bk. The method consists of showing that the resolvent operator of Kk has an approximation in terms of resolvents of certain Wiener-Hopf operators, for which there are explicit integral formulas.

Asymptotic symmetries in p-form theories

NASA Astrophysics Data System (ADS)

Afshar, Hamid; Esmaeili, Erfan; Sheikh-Jabbari, M. M.

2018-05-01

We consider ( p + 1)-form gauge fields in flat (2 p + 4)-dimensions for which radiation and Coulomb solutions have the same asymptotic fall-off behavior. Imposing appropriate fall-off behavior on fields and adopting a Maxwell-type action, we construct the boundary term which renders the action principle well-defined in the Lorenz gauge. We then compute conserved surface charges and the corresponding asymptotic charge algebra associated with nontrivial gauge transformations. We show that for p ≥ 1, there are three sets of conserved asymptotic charges associated with exact, coexact and zero-mode parts of the corresponding p-form gauge transformations on the asymptotic S 2 p+2. The coexact and zero-mode charges are higher form extensions of the four dimensional electrodynamics ( p = 0), and are commuting. Charges associated with exact gauge transformations have no counterparts in four dimensions and form infinite copies of Heisenberg algebras. We briefly discuss physical implications of these charges and their algebra.

Asymptotically anti-de Sitter spacetimes in topologically massive gravity

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

Henneaux, Marc; Physique theorique et mathematique, Universite Libre de Bruxelles and International Solvay Institutes, ULB Campus Plaine C.P. 231, B-1050 Bruxelles; Martinez, Cristian

2009-04-15

We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter {mu} ({mu}{ne}0). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower falloff than the one relevant for general relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generators are finite. It is found that, at the chiral point |{mu}l|=1 (where l is the anti-demore » Sitter radius), allowing for logarithmic terms (absent for general relativity) in the asymptotic behavior of the metric makes both sets of Virasoro generators nonzero even though one of the central charges vanishes.« less

Analysis of current-driven oscillatory dynamics of single-layer homoepitaxial islands on crystalline conducting substrates

NASA Astrophysics Data System (ADS)

Dasgupta, Dwaipayan; Kumar, Ashish; Maroudas, Dimitrios

2018-03-01

We report results of a systematic study on the complex oscillatory current-driven dynamics of single-layer homoepitaxial islands on crystalline substrate surfaces and the dependence of this driven dynamical behavior on important physical parameters, including island size, substrate surface orientation, and direction of externally applied electric field. The analysis is based on a nonlinear model of driven island edge morphological evolution that accounts for curvature-driven edge diffusion, edge electromigration, and edge diffusional anisotropy. Using a linear theory of island edge morphological stability, we calculate a critical island size at which the island's equilibrium edge shape becomes unstable, which sets a lower bound for the onset of time-periodic oscillatory dynamical response. Using direct dynamical simulations, we study the edge morphological dynamics of current-driven single-layer islands at larger-than-critical size, and determine the actual island size at which the migrating islands undergo a transition from steady to time-periodic asymptotic states through a subcritical Hopf bifurcation. At the highest symmetry of diffusional anisotropy examined, on {111} surfaces of face-centered cubic crystalline substrates, we find that more complex stable oscillatory states can be reached through period-doubling bifurcation at island sizes larger than those at the Hopf points. We characterize in detail the island morphology and dynamical response at the stable time-periodic asymptotic states, determine the range of stability of these oscillatory states terminated by island breakup, and explain the morphological features of the stable oscillating islands on the basis of linear stability theory.

Evolution of Spiral and Scroll Waves of Excitation in a Mathematical Model of Ischaemic Border Zone

PubMed Central

Biktashev, Vadim N.; Biktasheva, Irina V.; Sarvazyan, Narine A.

2011-01-01

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue. PMID:21935402

DHLAS: A web-based information system for statistical genetic analysis of HLA population data.

PubMed

Thriskos, P; Zintzaras, E; Germenis, A

2007-03-01

DHLAS (database HLA system) is a user-friendly, web-based information system for the analysis of human leukocyte antigens (HLA) data from population studies. DHLAS has been developed using JAVA and the R system, it runs on a Java Virtual Machine and its user-interface is web-based powered by the servlet engine TOMCAT. It utilizes STRUTS, a Model-View-Controller framework and uses several GNU packages to perform several of its tasks. The database engine it relies upon for fast access is MySQL, but others can be used a well. The system estimates metrics, performs statistical testing and produces graphs required for HLA population studies: (i) Hardy-Weinberg equilibrium (calculated using both asymptotic and exact tests), (ii) genetics distances (Euclidian or Nei), (iii) phylogenetic trees using the unweighted pair group method with averages and neigbor-joining method, (iv) linkage disequilibrium (pairwise and overall, including variance estimations), (v) haplotype frequencies (estimate using the expectation-maximization algorithm) and (vi) discriminant analysis. The main merit of DHLAS is the incorporation of a database, thus, the data can be stored and manipulated along with integrated genetic data analysis procedures. In addition, it has an open architecture allowing the inclusion of other functions and procedures.

Passivity/Lyapunov based controller design for trajectory tracking of flexible joint manipulators

NASA Technical Reports Server (NTRS)

Sicard, Pierre; Wen, John T.; Lanari, Leonardo

1992-01-01

A passivity and Lyapunov based approach for the control design for the trajectory tracking problem of flexible joint robots is presented. The basic structure of the proposed controller is the sum of a model-based feedforward and a model-independent feedback. Feedforward selection and solution is analyzed for a general model for flexible joints, and for more specific and practical model structures. Passivity theory is used to design a motor state-based controller in order to input-output stabilize the error system formed by the feedforward. Observability conditions for asymptotic stability are stated and verified. In order to accommodate for modeling uncertainties and to allow for the implementation of a simplified feedforward compensation, the stability of the system is analyzed in presence of approximations in the feedforward by using a Lyapunov based robustness analysis. It is shown that under certain conditions, e.g., the desired trajectory is varying slowly enough, stability is maintained for various approximations of a canonical feedforward.

Curve numbers for no-till: field data versus standard tables

USDA-ARS?s Scientific Manuscript database

The Curve Number procedure developed by Soil Conservation Service (Now Natural Resources Conservation Service) in the mid-1950s for estimating direct runoff from rainstorms has not been extensively tested in cropping systems under no-till. Analysis of CNs using the frequency matching and asymptotic ...

A Short Note on the Scaling Function Constant Problem in the Two-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Bothner, Thomas

2018-02-01

We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the 2-point function of the two-dimensional Ising model. This factor was first computed by Tracy (Commun Math Phys 142:297-311, 1991) via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom (Commun Math Phys 190:697-721, 1998) using Fredholm determinant representations of the correlation function and Wiener-Hopf approximation results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058-1092, 1977).

Periodic-disturbance accommodating control of the space station for asymptotic momentum management

NASA Technical Reports Server (NTRS)

Warren, Wayne; Wie, Bong; Geller, David

1989-01-01

Periodic-disturbance accommodating control is investigated for asymptotic momentum management of control moment gyros used as primary actuating devices for the Space Station. The proposed controller utilizes the concepts of quaternion feedback control and periodic-disturbance accommodation to achieve oscillations about the constant torque equilibrium attitude, while minimizing the control effort required. Three-axis coupled equations of motion, written in terms of quaternions, are derived for roll/yaw controller design and stability analysis. The quaternion feedback controller designed using the linear-quadratic regulator synthesis technique is shown to be robust for a wide range of pitch angles. It is also shown that the proposed controller tunes the open-loop unstable vehicle to a stable oscillatory motion which minimizes the control effort needed for steady-state operations.

Exact solution and precise asymptotics of a Fisher-KPP type front

NASA Astrophysics Data System (ADS)

Berestycki, Julien; Brunet, Éric; Derrida, Bernard

2018-01-01

The present work concerns a version of the Fisher-KPP equation where the nonlinear term is replaced by a saturation mechanism, yielding a free boundary problem with mixed conditions. Following an idea proposed in Brunet and Derrida (2015 J. Stat. Phys. 161 801), we show that the Laplace transform of the initial condition is directly related to some functional of the front position μt . We then obtain precise asymptotics of the front position by means of singularity analysis. In particular, we recover the so-called Ebert and van Saarloos correction (Ebert and van Saarloos 2000 Physica D 146 1), we obtain an additional term of order log t /t in this expansion, and we give precise conditions on the initial condition for those terms to be present.

Stability analysis of the Euler discretization for SIR epidemic model

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

Suryanto, Agus

2014-06-19

In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaosmore » phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart.« less

A Survey of Probabilistic Methods for Dynamical Systems with Uncertain Parameters.

DTIC Science & Technology

1986-05-01

J., "An Approach to the Theoretical Background of Statistical Energy Analysis Applied to Structural Vibration," Journ. Acoust. Soc. Amer., Vol. 69...1973, Sect. 8.3. 80. Lyon, R.H., " Statistical Energy Analysis of Dynamical Systems," M.I.T. Press, 1975. e) Late References added in Proofreading !! 81...Dowell, E.H., and Kubota, Y., "Asymptotic Modal Analysis and ’~ y C-" -165- Statistical Energy Analysis of Dynamical Systems," Journ. Appi. - Mech

Hairy black holes in scalar extended massive gravity

NASA Astrophysics Data System (ADS)

Tolley, Andrew J.; Wu, De-Jun; Zhou, Shuang-Yong

2015-12-01

We construct static, spherically symmetric black hole solutions in scalar extended ghost-free massive gravity and show the existence of hairy black holes in this class of extension. While the existence seems to be a generic feature, we focus on the simplest models of this extension and find that asymptotically flat hairy black holes can exist without fine-tuning the theory parameters, unlike the bi-gravity extension, where asymptotical flatness requires fine-tuning in the parameter space. Like the bi-gravity extension, we are unable to obtain asymptotically dS regular black holes in the simplest models considered, but it is possible to obtain asymptotically AdS black holes.

Non-Weyl asymptotics for quantum graphs with general coupling conditions

NASA Astrophysics Data System (ADS)

Davies, E. Brian; Exner, Pavel; Lipovský, Jiří

2010-11-01

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in the case of Kirchhoff or anti-Kirchhoff conditions. While for graphs without permutation symmetry numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight into what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with unequal edge weights.

Generic cosmic-censorship violation in anti-de Sitter space.

PubMed

Hertog, Thomas; Horowitz, Gary T; Maeda, Kengo

2004-04-02

We consider (four-dimensional) gravity coupled to a scalar field with potential V(phi). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonable matter theories in asymptotically anti-de Sitter spacetimes. The asymptotically flat case is more subtle. We suspect that potentials with a local Minkowski minimum may similarly lead to violations of cosmic censorship in asymptotically flat spacetimes, but we do not have definite results.

Asymptotic orderings and approximations of the Master kinetic equation for large hard spheres systems

NASA Astrophysics Data System (ADS)

Tessarotto, Massimo; Asci, Claudio

2017-05-01

In this paper the problem is posed of determining the physically-meaningful asymptotic orderings holding for the statistical description of a large N-body system of hard spheres, i.e., formed by N ≡1/ε ≫ 1 particles, which are allowed to undergo instantaneous and purely elastic unary, binary or multiple collisions. Starting point is the axiomatic treatment recently developed [Tessarotto et al., 2013-2016] and the related discovery of an exact kinetic equation realized by Master equation which advances in time the 1-body probability density function (PDF) for such a system. As shown in the paper the task involves introducing appropriate asymptotic orderings in terms of ε for all the physically-relevant parameters. The goal is that of identifying the relevant physically-meaningful asymptotic approximations applicable for the Master kinetic equation, together with their possible relationships with the Boltzmann and Enskog kinetic equations, and holding in appropriate asymptotic regimes. These correspond either to dilute or dense systems and are formed either by small-size or finite-size identical hard spheres, the distinction between the various cases depending on suitable asymptotic orderings in terms of ε.

Schwarzschild-de Sitter spacetimes, McVittie coordinates, and trumpet geometries

NASA Astrophysics Data System (ADS)

Dennison, Kenneth A.; Baumgarte, Thomas W.

2017-12-01

Trumpet geometries play an important role in numerical simulations of black hole spacetimes, which are usually performed under the assumption of asymptotic flatness. Our Universe is not asymptotically flat, however, which has motivated numerical studies of black holes in asymptotically de Sitter spacetimes. We derive analytical expressions for trumpet geometries in Schwarzschild-de Sitter spacetimes by first generalizing the static maximal trumpet slicing of the Schwarzschild spacetime to static constant mean curvature trumpet slicings of Schwarzschild-de Sitter spacetimes. We then switch to a comoving isotropic radial coordinate which results in a coordinate system analogous to McVittie coordinates. At large distances from the black hole the resulting metric asymptotes to a Friedmann-Lemaître-Robertson-Walker metric with an exponentially-expanding scale factor. While McVittie coordinates have another asymptotically de Sitter end as the radial coordinate goes to zero, so that they generalize the notion of a "wormhole" geometry, our new coordinates approach a horizon-penetrating trumpet geometry in the same limit. Our analytical expressions clarify the role of time-dependence, boundary conditions and coordinate conditions for trumpet slices in a cosmological context, and provide a useful test for black hole simulations in asymptotically de Sitter spacetimes.

A single-index threshold Cox proportional hazard model for identifying a treatment-sensitive subset based on multiple biomarkers.

PubMed

He, Ye; Lin, Huazhen; Tu, Dongsheng

2018-06-04

In this paper, we introduce a single-index threshold Cox proportional hazard model to select and combine biomarkers to identify patients who may be sensitive to a specific treatment. A penalized smoothed partial likelihood is proposed to estimate the parameters in the model. A simple, efficient, and unified algorithm is presented to maximize this likelihood function. The estimators based on this likelihood function are shown to be consistent and asymptotically normal. Under mild conditions, the proposed estimators also achieve the oracle property. The proposed approach is evaluated through simulation analyses and application to the analysis of data from two clinical trials, one involving patients with locally advanced or metastatic pancreatic cancer and one involving patients with resectable lung cancer. Copyright © 2018 John Wiley & Sons, Ltd.

More on asymptotically anti-de Sitter spaces in topologically massive gravity

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

Henneaux, Marc; Physique theorique et mathematique, Universite Libre de Bruxelles and International Solvay Institutes, ULB Campus Plaine C.P. 231, B-1050 Bruxelles; Martinez, Cristian

2010-09-15

Recently, the asymptotic behavior of three-dimensional anti-de Sitter (AdS) gravity with a topological mass term was investigated. Boundary conditions were given that were asymptotically invariant under the two dimensional conformal group and that included a falloff of the metric sufficiently slow to consistently allow pp-wave type of solutions. Now, pp waves can have two different chiralities. Above the chiral point and at the chiral point, however, only one chirality can be considered, namely, the chirality that has the milder behavior at infinity. The other chirality blows up faster than AdS and does not define an asymptotically AdS spacetime. By contrast,more » both chiralities are subdominant with respect to the asymptotic behavior of AdS spacetime below the chiral point. Nevertheless, the boundary conditions given in the earlier treatment only included one of the two chiralities (which could be either one) at a time. We investigate in this paper whether one can generalize these boundary conditions in order to consider simultaneously both chiralities below the chiral point. We show that this is not possible if one wants to keep the two-dimensional conformal group as asymptotic symmetry group. Hence, the boundary conditions given in the earlier treatment appear to be the best possible ones compatible with conformal symmetry. In the course of our investigations, we provide general formulas controlling the asymptotic charges for all values of the topological mass (not just below the chiral point).« less

Surface calculations with asymptotically long-ranged potentials in the full-potential linearized augmented plane-wave method

NASA Astrophysics Data System (ADS)

Ye, Lin-Hui

2015-09-01

Although the supercell method has been widely used for surface calculations, it only works well with short-ranged potentials, but meets difficulty when the potential decays very slowly into the vacuum. Unfortunately, the exact exchange-correlation potential of the density functional theory is asymptotically long ranged, and therefore is not easily handled by use of supercells. This paper illustrates that the authentic slab geometry, another technique for surface calculations, is not affected by this issue: It works equally well with both short- and long-ranged potentials, with the computational cost and the convergence speed being essentially the same. Using the asymptotically long-ranged Becke-Roussel'89 exchange potential as an example, we have calculated six surfaces of various types. We found that accurate potential values can be obtained even in extremely low density regions of more than 100 Å away from the surface. This high performance allows us to explore the asymptotic region, and prove with clean numerical evidence that the Becke-Roussel'89 potential satisfies the correct asymptotic behavior for slab surfaces, as it does for finite systems. Our finding further implies that the Slater component of the exact exchange optimized effective potential is responsible for the asymptotic behavior, not only for jellium slabs, but for slabs of any type. The Becke-Roussel'89 potential may therefore be used to build asymptotically correct model exchange potentials applicable to both finite systems and slab surfaces.

Asymptotic structure of the Einstein-Maxwell theory on AdS3

NASA Astrophysics Data System (ADS)

Pérez, Alfredo; Riquelme, Miguel; Tempo, David; Troncoso, Ricardo

2016-02-01

The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and Henneaux, the variation of the canonical generators associated to the asymptotic Killing vectors can be shown to be finite once required to span the Lie derivative of the fields. The corresponding surface integrals then acquire explicit contributions from the electromagnetic field, and become well-defined provided they fulfill suitable integrability conditions, implying that the leading terms of the asymptotic form of the electromagnetic field are functionally related. Consequently, for a generic choice of boundary conditions, the asymptotic symmetries are broken down to {R}⊗ U(1)⊗ U(1) . Nonetheless, requiring compatibility of the boundary conditions with one of the asymptotic Virasoro symmetries, singles out the set to be characterized by an arbitrary function of a single variable, whose precise form depends on the choice of the chiral copy. Remarkably, requiring the asymptotic symmetries to contain the full conformal group selects a very special set of boundary conditions that is labeled by a unique constant parameter, so that the algebra of the canonical generators is given by the direct sum of two copies of the Virasoro algebra with the standard central extension and U (1). This special set of boundary conditions makes the energy spectrum of electrically charged rotating black holes to be well-behaved.

Output feedback control for a class of nonlinear systems with actuator degradation and sensor noise.

PubMed

Ai, Weiqing; Lu, Zhenli; Li, Bin; Fei, Shumin

2016-11-01

This paper investigates the output feedback control problem of a class of nonlinear systems with sensor noise and actuator degradation. Firstly, by using the descriptor observer approach, the origin system is transformed into a descriptor system. On the basis of the descriptor system, a novel Proportional Derivative (PD) observer is developed to asymptotically estimate sensor noise and system state simultaneously. Then, by designing an adaptive law to estimate the effectiveness of actuator, an adaptive observer-based controller is constructed to ensure that system state can be regulated to the origin asymptotically. Finally, the design scheme is applied to address a flexible joint robot link problem. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Mapping the current–current correlation function near a quantum critical point

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

Prodan, Emil, E-mail: prodan@yu.edu; Bellissard, Jean

2016-05-15

The current–current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson’s localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau–insulator or plateau–plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current–current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current–current correlation function, obtain its asymptotic form near amore » critical point and confirm the theoretical predictions.« less

Analytical Solutions, Moments, and Their Asymptotic Behaviors for the Time-Space Fractional Cable Equation

NASA Astrophysics Data System (ADS)

Li, Can; Deng, Wei-Hua

2014-07-01

Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L. Wearne, Phys. Rev. Lett. 100 (2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law; and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented.

Asymptotic Dynamics of Self-driven Vehicles in a Closed Boundary

NASA Astrophysics Data System (ADS)

Lee, Chi-Lun; Huang, Chia-Ling

2011-08-01

We study the asymptotic dynamics of self-driven vehicles in a loop using a car-following model with the consideration of volume exclusions. In particular, we derive the dynamical steady states for the single-cluster case and obtain the corresponding fundamental diagrams, exhibiting two branches representative of entering and leaving the jam, respectively. By simulations we find that the speed average over all vehicles eventually reaches the same value, regardless of final clustering states. The autocorrelation functions for overall speed average and single-vehicle speed are studied, each revealing a unique time scale. We also discuss the role of noises in vehicular accelerations. Based on our observations we give trial definitions about the degree of chaoticity for general self-driven many-body systems.

Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures

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

Chueshov, Igor, E-mail: chueshov@karazin.ua; Dowell, Earl H., E-mail: dowell@duke.edu; Lasiecka, Irena, E-mail: lasiecka@memphis.edu

2016-06-15

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelasticity, such as flutter and divergence. This leads to a partial differential equation treatment of issues such as well-posedness of finite energy solutions, and long-time (asymptotic) behavior. The latter includes theory of asymptotic stability, convergence to equilibria, and to global attracting sets. We complete the discussion with several well knownmore » observations and conjectures based on experimental/numerical studies.« less

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

DOE PAGES

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory; ...

2015-02-25

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Spectral stability of unitary network models

NASA Astrophysics Data System (ADS)

Asch, Joachim; Bourget, Olivier; Joye, Alain

2015-08-01

We review various unitary network models used in quantum computing, spectral analysis or condensed matter physics and establish relationships between them. We show that symmetric one-dimensional quantum walks are universal, as are CMV matrices. We prove spectral stability and propagation properties for general asymptotically uniform models by means of unitary Mourre theory.

Analysis of First-Term Attrition of Non-Prior Service High-Quality U.S. Army Male Recruits

DTIC Science & Technology

1989-12-13

the estimators. Under broad conditions ( Hanushek , 1977 ), the maximum likelihood estimators are: ( a ) consistent (b) asymptotically efficient, and...Diseases, Vol. 24, 1971, pp. 125 - 158. Hanushek , Eric ., and John E. Jackson, Statistical Methods for Social Scientists, Academic Press, New York, 1977

A nonlinear interface model applied to masonry structures

NASA Astrophysics Data System (ADS)

Lebon, Frédéric; Raffa, Maria Letizia; Rizzoni, Raffaella

2015-12-01

In this paper, a new imperfect interface model is presented. The model includes finite strains, micro-cracks and smooth roughness. The model is consistently derived by coupling a homogenization approach for micro-cracked media and arguments of asymptotic analysis. The model is applied to brick/mortar interfaces. Numerical results are presented.

Factor Rotation and Standard Errors in Exploratory Factor Analysis

ERIC Educational Resources Information Center

Zhang, Guangjian; Preacher, Kristopher J.

2015-01-01

In this article, we report a surprising phenomenon: Oblique CF-varimax and oblique CF-quartimax rotation produced similar point estimates for rotated factor loadings and factor correlations but different standard error estimates in an empirical example. Influences of factor rotation on asymptotic standard errors are investigated using a numerical…

Analysis of backward differentiation formula for nonlinear differential-algebraic equations with 2 delays.

PubMed

Sun, Leping

2016-01-01

This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.

Rigorous joining of advanced reduced-dimensional beam models to three-dimensional finite element models

NASA Astrophysics Data System (ADS)

Song, Huimin

In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and the generalized Timoshenko beam are discussed in this chapter. VABS is also used to obtain the beam constitutive properties and warping functions for stress recovery. Several 3D-beam joint examples are presented to show the convergence and accuracy of the analysis. Accuracy is accessed by comparing the joint results with the full 3D analysis. The fourth chapter provides conclusions from present studies and recommendations for future work.

Asymptotic Eigenstructures

NASA Technical Reports Server (NTRS)

Thompson, P. M.; Stein, G.

1980-01-01

The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.

"Asymptotic Parabola" Fits for Smoothing Generally Asymmetric Light Curves

NASA Astrophysics Data System (ADS)

Andrych, K. D.; Andronov, I. L.; Chinarova, L. L.; Marsakova, V. I.

A computer program is introduced, which allows to determine statistically optimal approximation using the "Asymptotic Parabola" fit, or, in other words, the spline consisting of polynomials of order 1,2,1, or two lines ("asymptotes") connected with a parabola. The function itself and its derivative is continuous. There are 5 parameters: two points, where a line switches to a parabola and vice versa, the slopes of the line and the curvature of the parabola. Extreme cases are either the parabola without lines (i.e.the parabola of width of the whole interval), or lines without a parabola (zero width of the parabola), or "line+parabola" without a second line. Such an approximation is especially effective for pulsating variables, for which the slopes of the ascending and descending branches are generally different, so the maxima and minima have asymmetric shapes. The method was initially introduced by Marsakova and Andronov (1996OAP.....9...127M) and realized as a computer program written in QBasic under DOS. It was used for dozens of variable stars, particularly, for the catalogs of the individual characteristics of pulsations of the Mira (1998OAP....11...79M) and semi-regular (200OAP....13..116C) pulsating variables. For the eclipsing variables with nearly symmetric shapes of the minima, we use a "symmetric" version of the "Asymptotic parabola". Here we introduce a Windows-based program, which does not have DOS limitation for the memory (number of observations) and screen resolution. The program has an user-friendly interface and is illustrated by an application to the test signal and to the pulsating variable AC Her.

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.

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

Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.

The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schroedinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysismore » shows that, for most nonclassicality measures, the Schroedinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ''sudden death''. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.« less