exponential-power series solutions: Topics by Science.gov

Sample records for exponential-power series solutions

Power Series Solution to the Pendulum Equation

ERIC Educational Resources Information Center

Benacka, Jan

2009-01-01

This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…
On the Prony series representation of stretched exponential relaxation

NASA Astrophysics Data System (ADS)

Mauro, John C.; Mauro, Yihong Z.

2018-09-01

Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β. The fitting quality of the Prony series is analyzed as a function of the number of terms in the series. With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its "fat tail" at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.
Power series solutions of ordinary differential equations in MACSYMA

NASA Technical Reports Server (NTRS)

Lafferty, E. L.

1977-01-01

A program is described which extends the differential equation solving capability of MACSYMA to power series solutions and is available via the SHARE library. The program is directed toward those classes of equations with variable coefficients (in particular, those with singularities) and uses the method of Frobenius. Probably the most important distinction between this package and others currently available or being developed is that, wherever possible, this program will attempt to provide a complete solution to the equation rather than an approximation, i.e., a finite number of terms. This solution will take the form of a sum of infinite series.
The matrix exponential in transient structural analysis

NASA Technical Reports Server (NTRS)

Minnetyan, Levon

1987-01-01

The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.
Exponentiated power Lindley distribution.

PubMed

Ashour, Samir K; Eltehiwy, Mahmoud A

2015-11-01

A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data.
Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our
On power series representing solutions of the one-dimensional time-independent Schrödinger equation

NASA Astrophysics Data System (ADS)

Trotsenko, N. P.

2017-06-01

For the equation χ″( x) = u( x)χ( x) with infinitely smooth u( x), the general solution χ( x) is found in the form of a power series. The coefficients of the series are expressed via all derivatives u ( m)( y) of the function u( x) at a fixed point y. Examples of solutions for particular functions u( x) are considered.
Optical solitons, complexitons, Gaussian soliton and power series solutions of a generalized Hirota equation

NASA Astrophysics Data System (ADS)

Mao, Jin-Jin; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

2018-05-01

In this paper, we consider a generalized Hirota equation with a bounded potential, which can be used to describe the propagation properties of optical soliton solutions. By employing the hypothetical method and the sub-equation method, we construct the bright soliton, dark soliton, complexitons and Gaussian soliton solutions of the Hirota equation. Moreover, we explicitly derive the power series solutions with their convergence analysis. Finally, we provide the graphical analysis of such soliton solutions in order to better understand their dynamical behavior.
Power Laws, Scale Invariance and the Generalized Frobenius Series:

NASA Astrophysics Data System (ADS)

Visser, Matt; Yunes, Nicolas

We present a self-contained formalism for calculating the background solution, the linearized solutions and a class of generalized Frobenius-like solutions to a system of scale-invariant differential equations. We first cast the scale-invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. While discussions of the linearized system are common, and one can often find a discussion of power-series with integer exponents, power series with irrational (indeed complex) exponents are much rarer in the extant literature. The Frobenius-like series we encounter can be viewed as a variant of the rarely-discussed Liapunov expansion theorem (not to be confused with the more commonly encountered Liapunov functions and Liapunov exponents). As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and construct two separate power series with the overlapping radius of convergence. The second of these power series solutions represents an expansion around "spatial infinity," and in realistic models it is this second power series that gives information about the stellar core, and the damped oscillations in core mass and core radius as the central pressure goes to infinity. The power-series solutions we obtain extend classical results; as exemplified for instance by the work of Lane, Emden, and Chandrasekhar in the Newtonian case, and that of Harrison, Thorne, Wakano, and Wheeler in the relativistic case. We also indicate how to
A Power Series Expansion and Its Applications

ERIC Educational Resources Information Center

Chen, Hongwei

2006-01-01

Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.
Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution

NASA Astrophysics Data System (ADS)

Beléndez, Augusto; Francés, Jorge; Beléndez, Tarsicio; Bleda, Sergio; Pascual, Carolina; Arribas, Enrique

2015-05-01

A family of conservative, truly nonlinear, oscillators with integer or non-integer order nonlinearity is considered. These oscillators have only one odd power-form elastic-term and exact expressions for their period and solution were found in terms of Gamma functions and a cosine-Ateb function, respectively. Only for a few values of the order of nonlinearity, is it possible to obtain the periodic solution in terms of more common functions. However, for this family of conservative truly nonlinear oscillators we show in this paper that it is possible to obtain the Fourier series expansion of the exact solution, even though this exact solution is unknown. The coefficients of the Fourier series expansion of the exact solution are obtained as an integral expression in which a regularized incomplete Beta function appears. These coefficients are a function of the order of nonlinearity only and are computed numerically. One application of this technique is to compare the amplitudes for the different harmonics of the solution obtained using approximate methods with the exact ones computed numerically as shown in this paper. As an example, the approximate amplitudes obtained via a modified Ritz method are compared with the exact ones computed numerically.
Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Power law versus exponential state transition dynamics: application to sleep-wake architecture.

PubMed

Chu-Shore, Jesse; Westover, M Brandon; Bianchi, Matt T

2010-12-02

Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot. To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the "incorrect" model over a range of parameters. The "zone of mimicry" of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions. Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.
Exponential Approximations Using Fourier Series Partial Sums

NASA Technical Reports Server (NTRS)

Banerjee, Nana S.; Geer, James F.

1997-01-01

The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Power series solution of the inhomogeneous exclusion process

NASA Astrophysics Data System (ADS)

Szavits-Nossan, Juraj; Romano, M. Carmen; Ciandrini, Luca

2018-05-01

We develop a power series method for the nonequilibrium steady state of the inhomogeneous one-dimensional totally asymmetric simple exclusion process (TASEP) in contact with two particle reservoirs and with site-dependent hopping rates in the bulk. The power series is performed in the entrance or exit rates governing particle exchange with the reservoirs, and the corresponding particle current is computed analytically up to the cubic term in the entry or exit rate, respectively. We also show how to compute higher-order terms using combinatorial objects known as Young tableaux. Our results address the long outstanding problem of finding the exact nonequilibrium steady state of the inhomogeneous TASEP. The findings are particularly relevant to the modeling of mRNA translation in which the rate of translation initiation, corresponding to the entrance rate in the TASEP, is typically small.
Using Exponential Smoothing to Specify Intervention Models for Interrupted Time Series.

ERIC Educational Resources Information Center

Mandell, Marvin B.; Bretschneider, Stuart I.

1984-01-01

The authors demonstrate how exponential smoothing can play a role in the identification of the intervention component of an interrupted time-series design model that is analogous to the role that the sample autocorrelation and partial autocorrelation functions serve in the identification of the noise portion of such a model. (Author/BW)
High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

NASA Astrophysics Data System (ADS)

Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

2018-06-01

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.
A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.
Efficient Generation and Use of Power Series for Broad Application.

NASA Astrophysics Data System (ADS)

Rudmin, Joseph; Sochacki, James

2017-01-01

A brief history and overview of the Parker-Sockacki Method of Power Series generation is presented. This method generates power series to order n in time n2 for any system of differential equations that has a power series solution. The method is simple enough that novices to differential equations can easily learn it and immediately apply it. Maximal absolute error estimates allow one to determine the number of terms needed to reach desired accuracy. Ratios of coefficients in a solution with global convergence differ signficantly from that for a solution with only local convergence. Divergence of the series prevents one from overlooking poles. The method can always be cast in polynomial form, which allows separation of variables in almost all physical systems, facilitating exploration of hidden symmetries, and is implicitly symplectic.
A series solution for horizontal infiltration in an initially dry aquifer

NASA Astrophysics Data System (ADS)

Furtak-Cole, Eden; Telyakovskiy, Aleksey S.; Cooper, Clay A.

2018-06-01

The porous medium equation (PME) is a generalization of the traditional Boussinesq equation for hydraulic conductivity as a power law function of height. We analyze the horizontal recharge of an initially dry unconfined aquifer of semi-infinite extent, as would be found in an aquifer adjacent a rising river. If the water level can be modeled as a power law function of time, similarity variables can be introduced and the original problem can be reduced to a boundary value problem for a nonlinear ordinary differential equation. The position of the advancing front is not known ahead of time and must be found in the process of solution. We present an analytical solution in the form of a power series, with the coefficients of the series given by a recurrence relation. The analytical solution compares favorably with a highly accurate numerical solution, and only a small number of terms of the series are needed to achieve high accuracy in the scenarios considered here. We also conduct a series of physical experiments in an initially dry wedged Hele-Shaw cell, where flow is modeled by a special form of the PME. Our analytical solution closely matches the hydraulic head profiles in the Hele-Shaw cell experiment.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
Stretched exponentials and power laws in granular avalanching

NASA Astrophysics Data System (ADS)

Head, D. A.; Rodgers, G. J.

1999-02-01

We introduce a model for granular surface flow which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the overdamped, sliding motion of particle clusters. The crossover in behaviour observed in experiments on piles of rice is attributed to a change in the dominant mode of transport. We predict that power law avalanching will be observed whenever surface flow is dominated by clustered motion.
Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

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

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; López-López, M. G.; Alvarado-Martínez, V. M.

2018-03-01

In this paper, the two-dimensional projectile motion was studied; for this study two cases were considered, for the first one, we considered that there is no air resistance and, for the second case, we considered a resisting medium k . The study was carried out by using fractional calculus. The solution to this study was obtained by using fractional operators with power law, exponential decay and Mittag-Leffler kernel in the range of γ \\in (0,1] . These operators were considered in the Liouville-Caputo sense to use physical initial conditions with a known physical interpretation. The range and the maximum height of the projectile were obtained using these derivatives. With the aim of exploring the validity of the obtained results, we compared our results with experimental data given in the literature. A multi-objective particle swarm optimization approach was used for generating Pareto-optimal solutions for the parameters k and γ for different fixed values of velocity v0 and angle θ . The results showed some relevant qualitative differences between the use of power law, exponential decay and Mittag-Leffler law.
Design of a 9-loop quasi-exponential waveform generator

NASA Astrophysics Data System (ADS)

Banerjee, Partha; Shukla, Rohit; Shyam, Anurag

2015-12-01

We know in an under-damped L-C-R series circuit, current follows a damped sinusoidal waveform. But if a number of sinusoidal waveforms of decreasing time period, generated in an L-C-R circuit, be combined in first quarter cycle of time period, then a quasi-exponential nature of output current waveform can be achieved. In an L-C-R series circuit, quasi-exponential current waveform shows a rising current derivative and thereby finds many applications in pulsed power. Here, we have described design and experiment details of a 9-loop quasi-exponential waveform generator. In that, design details of magnetic switches have also been described. In the experiment, output current of 26 kA has been achieved. It has been shown that how well the experimentally obtained output current profile matches with the numerically computed output.
Design of a 9-loop quasi-exponential waveform generator.

PubMed

Banerjee, Partha; Shukla, Rohit; Shyam, Anurag

2015-12-01

We know in an under-damped L-C-R series circuit, current follows a damped sinusoidal waveform. But if a number of sinusoidal waveforms of decreasing time period, generated in an L-C-R circuit, be combined in first quarter cycle of time period, then a quasi-exponential nature of output current waveform can be achieved. In an L-C-R series circuit, quasi-exponential current waveform shows a rising current derivative and thereby finds many applications in pulsed power. Here, we have described design and experiment details of a 9-loop quasi-exponential waveform generator. In that, design details of magnetic switches have also been described. In the experiment, output current of 26 kA has been achieved. It has been shown that how well the experimentally obtained output current profile matches with the numerically computed output.
On stable exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

NASA Astrophysics Data System (ADS)

Ivashchuk, V. D.; Ernazarov, K. K.

2017-01-01

A (n + 1)-dimensional gravitational model with cosmological constant and Gauss-Bonnet term is studied. The ansatz with diagonal cosmological metrics is adopted and solutions with exponential dependence of scale factors: ai ˜ exp (vit), i = 1, …, n, are considered. The stability analysis of the solutions with non-static volume factor is presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and small enough variation of the effective gravitational constant G are stable if certain restriction on (vi ) is obeyed. New examples of stable exponential solutions with zero variation of G in dimensions D = 1 + m + 2 with m > 2 are presented.
Real-Time Exponential Curve Fits Using Discrete Calculus

NASA Technical Reports Server (NTRS)

Rowe, Geoffrey

2010-01-01

An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Lie Symmetry Analysis, Conservation Laws and Exact Power Series Solutions for Time-Fractional Fordy-Gibbons Equation

NASA Astrophysics Data System (ADS)

Feng, Lian-Li; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian

2016-09-01

In this paper, the time fractional Fordy-Gibbons equation is investigated with Riemann-Liouville derivative. The equation can be reduced to the Caudrey-Dodd-Gibbon equation, Savada-Kotera equation and the Kaup-Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method. Supported by the Fundamental Research Funds for Key Discipline Construction under Grant No. XZD201602, the Fundamental Research Funds for the Central Universities under Grant Nos. 2015QNA53 and 2015XKQY14, the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Mines, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2015M570498, and Natural Sciences Foundation of China under Grant No. 11301527
Poissonian renormalizations, exponentials, and power laws.

PubMed

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Poissonian renormalizations, exponentials, and power laws

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2013-05-01

This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Double power series method for approximating cosmological perturbations

NASA Astrophysics Data System (ADS)

Wren, Andrew J.; Malik, Karim A.

2017-04-01

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.
Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation. Part 1; Analysis

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Nemeth, Noel N.; Gyekenyesi, John P.

2002-01-01

Extensive slow-crack-growth (SCG) analysis was made using a primary exponential crack-velocity formulation under three widely used load configurations: constant stress rate, constant stress, and cyclic stress. Although the use of the exponential formulation in determining SCG parameters of a material requires somewhat inconvenient numerical procedures, the resulting solutions presented gave almost the same degree of simplicity in both data analysis and experiments as did the power-law formulation. However, the fact that the inert strength of a material should be known in advance to determine the corresponding SCG parameters was a major drawback of the exponential formulation as compared with the power-law formulation.
An Unusual Exponential Graph

ERIC Educational Resources Information Center

Syed, M. Qasim; Lovatt, Ian

2014-01-01

This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

NASA Astrophysics Data System (ADS)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.
The many faces of the quantum Liouville exponentials

NASA Astrophysics Data System (ADS)

Gervais, Jean-Loup; Schnittger, Jens

1994-01-01

First, it is proven that the three main operator approaches to the quantum Liouville exponentials—that is the one of Gervais-Neveu (more recently developed further by Gervais), Braaten-Curtright-Ghandour-Thorn, and Otto-Weigt—are equivalent since they are related by simple basis transformations in the Fock space of the free field depending upon the zero-mode only. Second, the GN-G expressions for quantum Liouville exponentials, where the U q( sl(2)) quantum-group structure is manifest, are shown to be given by q-binomial sums over powers of the chiral fields in the J = {1}/{2} representation. Third, the Liouville exponentials are expressed as operator tau functions, whose chiral expansion exhibits a q Gauss decomposition, which is the direct quantum analogue of the classical solution of Leznov and Saveliev. It involves q exponentials of quantum-group generators with group "parameters" equal to chiral components of the quantum metric. Fourth, we point out that the OPE of the J = {1}/{2} Liouville exponential provides the quantum version of the Hirota bilinear equation.
Method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1972-01-01

Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.
Exponential Stability of Almost Periodic Solutions for Memristor-Based Neural Networks with Distributed Leakage Delays.

PubMed

Xu, Changjin; Li, Peiluan; Pang, Yicheng

2016-12-01

In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).
An explicit asymptotic model for the surface wave in a viscoelastic half-space based on applying Rabotnov's fractional exponential integral operators

NASA Astrophysics Data System (ADS)

Wilde, M. V.; Sergeeva, N. V.

2018-05-01

An explicit asymptotic model extracting the contribution of a surface wave to the dynamic response of a viscoelastic half-space is derived. Fractional exponential Rabotnov's integral operators are used for describing of material properties. The model is derived by extracting the principal part of the poles corresponding to the surface waves after applying Laplace and Fourier transforms. The simplified equations for the originals are written by using power series expansions. Padè approximation is constructed to unite short-time and long-time models. The form of this approximation allows to formulate the explicit model using a fractional exponential Rabotnov's integral operator with parameters depending on the properties of surface wave. The applicability of derived models is studied by comparing with the exact solutions of a model problem. It is revealed that the model based on Padè approximation is highly effective for all the possible time domains.
On non-exponential cosmological solutions with two factor spaces of dimensions m and 1 in the Einstein-Gauss-Bonnet model with a Λ-term

NASA Astrophysics Data System (ADS)

Ernazarov, K. K.

2017-12-01

We consider a (m + 2)-dimensional Einstein-Gauss-Bonnet (EGB) model with the cosmological Λ-term. We restrict the metrics to be diagonal ones and find for certain Λ = Λ(m) class of cosmological solutions with non-exponential time dependence of two scale factors of dimensions m > 2 and 1. Any solution from this class describes an accelerated expansion of m-dimensional subspace and tends asymptotically to isotropic solution with exponential dependence of scale factors.

Expression Templates for Truncated Power Series

NASA Astrophysics Data System (ADS)

Cary, John R.; Shasharina, Svetlana G.

1997-05-01

Truncated power series are used extensively in accelerator transport modeling for rapid tracking and analysis of nonlinearity. Such mathematical objects are naturally represented computationally as objects in C++. This is more intuitive and produces more transparent code through operator overloading. However, C++ object use often comes with a computational speed loss due, e.g., to the creation of temporaries. We have developed a subset of truncated power series expression templates(http://monet.uwaterloo.ca/blitz/). Such expression templates use the powerful template processing facility of C++ to combine complicated expressions into series operations that exectute more rapidly. We compare computational speeds with existing truncated power series libraries.
Efficient algorithm for locating and sizing series compensation devices in large power transmission grids: II. Solutions and applications

DOE PAGES

Frolov, Vladimir; Backhaus, Scott; Chertkov, Misha

2014-10-01

In a companion manuscript, we developed a novel optimization method for placement, sizing, and operation of Flexible Alternating Current Transmission System (FACTS) devices to relieve transmission network congestion. Specifically, we addressed FACTS that provide Series Compensation (SC) via modification of line inductance. In this manuscript, this heuristic algorithm and its solutions are explored on a number of test cases: a 30-bus test network and a realistically-sized model of the Polish grid (~ 2700 nodes and ~ 3300 lines). The results on the 30-bus network are used to study the general properties of the solutions including non-locality and sparsity. The Polishmore » grid is used as a demonstration of the computational efficiency of the heuristics that leverages sequential linearization of power flow constraints and cutting plane methods that take advantage of the sparse nature of the SC placement solutions. Using these approaches, the algorithm is able to solve an instance of Polish grid in tens of seconds. We explore the utility of the algorithm by analyzing transmission networks congested by (a) uniform load growth, (b) multiple overloaded configurations, and (c) sequential generator retirements.« less
GENERAL: The Analytic Solution of Schrödinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

NASA Astrophysics Data System (ADS)

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

2009-03-01

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

NASA Technical Reports Server (NTRS)

Raj, S. V.; Pharr, G. M.

1989-01-01

Creep tests conducted on NaCl single crystals in the temperature range from 373 to 1023 K show that true steady state creep is obtained only above 873 K when the ratio of the applied stress to the shear modulus is less than or equal to 0.0001. Under other stress and temperature conditions, corresponding to both power law and exponential creep, the creep rate decreases monotonically with increasing strain. The transition from power law to exponential creep is shown to be associated with increases in the dislocation density, the cell boundary width, and the aspect ratio of the subgrains along the primary slip planes. The relation between dislocation structure and creep behavior is also assessed.
Remarks on the general solution for the flat Friedmann universe with exponential scalar-field potential and dust

NASA Astrophysics Data System (ADS)

Andrianov, A. A.; Cannata, F.; Kamenshchik, A. Yu.

2012-11-01

We show that the simple extension of the method of obtaining the general exact solution for the cosmological model with the exponential scalar-field potential to the case when the dust is present fails, and we discuss the reasons of this puzzling phenomenon.
Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth.

PubMed

Yan, Wanfeng; van Tuyll van Serooskerken, Edgar

2015-01-01

Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator.
Similarity solutions for unsteady flow behind an exponential shock in a self-gravitating non-ideal gas with azimuthal magnetic field

NASA Astrophysics Data System (ADS)

Nath, G.; Pathak, R. P.; Dutta, Mrityunjoy

2018-01-01

Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical or spherical) moving with time according to an exponential law is obtained. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The effects of variation of ambient magnetic field, non-idealness of the gas, adiabatic exponent and gravitational parameter are worked out in detail. It is shown that the increase in the non-idealness of the gas or the adiabatic exponent of the gas or presence of magnetic field have decaying effect on the shock wave. Consideration of the isothermal flow and the self-gravitational field increase the shock strength. Also, the consideration of isothermal flow or the presence of magnetic field removes the singularity in the density distribution, which arises in the case of adiabatic flow. The result of our study may be used to interpret measurements carried out by space craft in the solar wind and in neighborhood of the Earth's magnetosphere.
Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution.

PubMed

Rigby, Robert A; Stasinopoulos, D Mikis

2004-10-15

The Box-Cox power exponential (BCPE) distribution, developed in this paper, provides a model for a dependent variable Y exhibiting both skewness and kurtosis (leptokurtosis or platykurtosis). The distribution is defined by a power transformation Y(nu) having a shifted and scaled (truncated) standard power exponential distribution with parameter tau. The distribution has four parameters and is denoted BCPE (mu,sigma,nu,tau). The parameters, mu, sigma, nu and tau, may be interpreted as relating to location (median), scale (approximate coefficient of variation), skewness (transformation to symmetry) and kurtosis (power exponential parameter), respectively. Smooth centile curves are obtained by modelling each of the four parameters of the distribution as a smooth non-parametric function of an explanatory variable. A Fisher scoring algorithm is used to fit the non-parametric model by maximizing a penalized likelihood. The first and expected second and cross derivatives of the likelihood, with respect to mu, sigma, nu and tau, required for the algorithm, are provided. The centiles of the BCPE distribution are easy to calculate, so it is highly suited to centile estimation. This application of the BCPE distribution to smooth centile estimation provides a generalization of the LMS method of the centile estimation to data exhibiting kurtosis (as well as skewness) different from that of a normal distribution and is named here the LMSP method of centile estimation. The LMSP method of centile estimation is applied to modelling the body mass index of Dutch males against age. 2004 John Wiley & Sons, Ltd.
Exponential bound in the quest for absolute zero

NASA Astrophysics Data System (ADS)

Stefanatos, Dionisis

2017-10-01

In most studies for the quantification of the third law of thermodynamics, the minimum temperature which can be achieved with a long but finite-time process scales as a negative power of the process duration. In this article, we use our recent complete solution for the optimal control problem of the quantum parametric oscillator to show that the minimum temperature which can be obtained in this system scales exponentially with the available time. The present work is expected to motivate further research in the active quest for absolute zero.
Exponential bound in the quest for absolute zero.

PubMed

Stefanatos, Dionisis

2017-10-01

In most studies for the quantification of the third law of thermodynamics, the minimum temperature which can be achieved with a long but finite-time process scales as a negative power of the process duration. In this article, we use our recent complete solution for the optimal control problem of the quantum parametric oscillator to show that the minimum temperature which can be obtained in this system scales exponentially with the available time. The present work is expected to motivate further research in the active quest for absolute zero.
The Exponential Function--Part VIII

ERIC Educational Resources Information Center

Bartlett, Albert A.

1978-01-01

Presents part eight of a continuing series on the exponential function in which, given the current population of the Earth and assuming a constant growth rate of 1.9 percent backward looks at world population are made. (SL)
Numerical integration of the N-body ring problem by recurrent power series

NASA Astrophysics Data System (ADS)

Navarro, Juan F.

2018-02-01

The aim of this article is to present a method for the integration of the equations of motion of the N-body ring problem by means of recurrent power series. We prove that the solution is convergent for any set of initial conditions, excluding those corresponding to binary collisions.
Floquet states of a kicked particle in a singular potential: Exponential and power-law profiles

NASA Astrophysics Data System (ADS)

Paul, Sanku; Santhanam, M. S.

2018-03-01

It is well known that, in the chaotic regime, all the Floquet states of kicked rotor system display an exponential profile resulting from dynamical localization. If the kicked rotor is placed in an additional stationary infinite potential well, its Floquet states display power-law profile. It has also been suggested in general that the Floquet states of periodically kicked systems with singularities in the potential would have power-law profile. In this work, we study the Floquet states of a kicked particle in finite potential barrier. By varying the height of finite potential barrier, the nature of transition in the Floquet state from exponential to power-law decay profile is studied. We map this system to a tight-binding model and show that the nature of decay profile depends on energy band spanned by the Floquet states (in unperturbed basis) relative to the potential height. This property can also be inferred from the statistics of Floquet eigenvalues and eigenvectors. This leads to an unusual scenario in which the level spacing distribution, as a window in to the spectral correlations, is not a unique characteristic for the entire system.
Computerized series solution of relativistic equations of motion.

NASA Technical Reports Server (NTRS)

Broucke, R.

1971-01-01

A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.
de la Vallée-Poussin means of Fourier series for the quadratic spectrum and for spectra with power-like density

NASA Astrophysics Data System (ADS)

Bochkarev, S. V.

2014-02-01

A new method is proposed and elaborated for investigating complex or real trigonometric series with various spectra. It is based on new multiplicative inequalities which give a lower bound for the integral norm of the de la Vallée-Poussin means and are themselves based on results establishing corresponding analogues of the Littlewood-Paley theorem in the BMO, Hardy, and Lorentz spaces. For spectra with power-like density a description of the class of absolute values of coefficients such that the corresponding complex or real trigonometric series are Fourier series is found which depends on the arithmetic characteristics of the spectrum and is sharp in limiting cases. Furthermore, for the quadratic spectrum some results of Hardy and Littlewood on elliptic theta functions are generalized and refined. For the quadratic spectrum and power-like spectra with non-integer exponents new lower bounds are found for the integral norms of exponential sums. Bibliography: 41 titles.
Modeling the Role of Dislocation Substructure During Class M and Exponential Creep. Revised

NASA Technical Reports Server (NTRS)

Raj, S. V.; Iskovitz, Ilana Seiden; Freed, A. D.

1995-01-01

The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.
BORAX V EXPONENTIAL EXPERIMENT

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

Kirn, F.S.; Hagen, J.I.

1963-04-01

The cadmium ratio was measured in an exponential mockup of Borax V as a function of the void fraction. The extent of voids, simulated by lengths of closed polyethylene tubes, ranged from 0 to 40%. The corresponding cadmium ratios ranged from 6.1 to 4.6. The exponential was also used to determine the radial flux pattern across a Borax-type fuel assembly and the fine flux detail in and around fuel rods. For a normal loading the maximum-to-average power generation across an assembly was 1.24. (auth)
Power Law Versus Exponential Form of Slow Crack Growth of Advanced Structural Ceramics: Dynamic Fatigue

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Gyekenyesi, John P.

2002-01-01

The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.
Dual exponential polynomials and linear differential equations

NASA Astrophysics Data System (ADS)

Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

2018-01-01

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.
The exponential behavior and stabilizability of the stochastic magnetohydrodynamic equations

NASA Astrophysics Data System (ADS)

Wang, Huaqiao

2018-06-01

This paper studies the two-dimensional stochastic magnetohydrodynamic equations which are used to describe the turbulent flows in magnetohydrodynamics. The exponential behavior and the exponential mean square stability of the weak solutions are proved by the application of energy method. Furthermore, we establish the pathwise exponential stability by using the exponential mean square stability. When the stochastic perturbations satisfy certain additional hypotheses, we can also obtain pathwise exponential stability results without using the mean square stability.

Scalar-fluid interacting dark energy: Cosmological dynamics beyond the exponential potential

NASA Astrophysics Data System (ADS)

Dutta, Jibitesh; Khyllep, Wompherdeiki; Tamanini, Nicola

2017-01-01

We extend the dynamical systems analysis of scalar-fluid interacting dark energy models performed in C. G. Boehmer et al., Phys. Rev. D 91, 123002 (2015), 10.1103/PhysRevD.91.123002 by considering scalar field potentials beyond the exponential type. The properties and stability of critical points are examined using a combination of linear analysis, computational methods and advanced mathematical techniques, such as center manifold theory. We show that the interesting results obtained with an exponential potential can generally be recovered also for more complicated scalar field potentials. In particular, employing power law and hyperbolic potentials as examples, we find late time accelerated attractors, transitions from dark matter to dark energy domination with specific distinguishing features, and accelerated scaling solutions capable of solving the cosmic coincidence problem.
Exponential growth and Gaussian—like fluctuations of solutions of stochastic differential equations with maximum functionals

NASA Astrophysics Data System (ADS)

Appleby, J. A. D.; Wu, H.

2008-11-01

In this paper we consider functional differential equations subjected to either instantaneous state-dependent noise, or to a white noise perturbation. The drift of the equations depend linearly on the current value and on the maximum of the solution. The functional term always provides positive feedback, while the instantaneous term can be mean-reverting or can exhibit positive feedback. We show in the white noise case that if the instantaneous term is mean reverting and dominates the history term, then solutions are recurrent, and upper bounds on the a.s. growth rate of the partial maxima of the solution can be found. When the instantaneous term is weaker, or is of positive feedback type, we determine necessary and sufficient conditions on the diffusion coefficient which ensure the exact exponential growth of solutions. An application of these results to an inefficient financial market populated by reference traders and speculators is given, in which the difference between the current instantaneous returns and maximum of the returns over the last few time units is used to determine trading strategies.
Universality in stochastic exponential growth.

PubMed

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Universality in Stochastic Exponential Growth

NASA Astrophysics Data System (ADS)

Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.

2014-07-01

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.
Evaluation of the matrix exponential for use in ground-water-flow and solute-transport simulations; theoretical framework

USGS Publications Warehouse

Umari, A.M.; Gorelick, S.M.

1986-01-01

It is possible to obtain analytic solutions to the groundwater flow and solute transport equations if space variables are discretized but time is left continuous. From these solutions, hydraulic head and concentration fields for any future time can be obtained without ' marching ' through intermediate time steps. This analytical approach involves matrix exponentiation and is referred to as the Matrix Exponential Time Advancement (META) method. Two algorithms are presented for the META method, one for symmetric and the other for non-symmetric exponent matrices. A numerical accuracy indicator, referred to as the matrix condition number, was defined and used to determine the maximum number of significant figures that may be lost in the META method computations. The relative computational and storage requirements of the META method with respect to the time marching method increase with the number of nodes in the discretized problem. The potential greater accuracy of the META method and the associated greater reliability through use of the matrix condition number have to be weighed against this increased relative computational and storage requirements of this approach as the number of nodes becomes large. For a particular number of nodes, the META method may be computationally more efficient than the time-marching method, depending on the size of time steps used in the latter. A numerical example illustrates application of the META method to a sample ground-water-flow problem. (Author 's abstract)
Analysis of Site Position Time Series Derived From Space Geodetic Solutions

NASA Astrophysics Data System (ADS)

Angermann, D.; Meisel, B.; Kruegel, M.; Tesmer, V.; Miller, R.; Drewes, H.

2003-12-01

This presentation deals with the analysis of station coordinate time series obtained from VLBI, SLR, GPS and DORIS solutions. We also present time series for the origin and scale derived from these solutions and discuss their contribution to the realization of the terrestrial reference frame. For these investigations we used SLR and VLBI solutions computed at DGFI with the software systems DOGS (SLR) and OCCAM (VLBI). The GPS and DORIS time series were obtained from weekly station coordinates solutions provided by the IGS, and from the joint DORIS analysis center (IGN-JPL). We analysed the time series with respect to various aspects, such as non-linear motions, periodic signals and systematic differences (biases). A major focus is on a comparison of the results at co-location sites in order to identify technique- and/or solution related problems. This may also help to separate and quantify possible effects, and to understand the origin of still existing discrepancies. Technique-related systematic effects (biases) should be reduced to the highest possible extent, before using the space geodetic solutions for a geophysical interpretation of seasonal signals in site position time series.
Power: Constitutional Update. Bar/School Partnership Programs Series.

ERIC Educational Resources Information Center

American Bar Association, Chicago, IL. Special Committee on Youth Education for Citizenship.

The fourth in a special series of handbooks dealing with constitutional themes, this document looks at power in the context of the U.S. Constitution. "The Constitution's Prescription for Freedom" (L. Peach) examines the separation of powers provided for in the Constitution. "The Concept of Power" (C. Roach) is a series of…
Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

NASA Astrophysics Data System (ADS)

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; Birkholzer, Jens T.

2017-11-01

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1-D, 2-D, and 3-D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, td. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, td0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10-7 relative error) for 1-D isotropic (spheres, cylinders, slabs) and 2-D/3-D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1-D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2-D/3-D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.
Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

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

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less
Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

DOE PAGES

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; ...

2017-10-24

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less
Evaluation of recent GRACE monthly solution series with an ice sheet perspective

NASA Astrophysics Data System (ADS)

Horwath, Martin; Groh, Andreas

2016-04-01

GRACE monthly global gravity field solutions have undergone a remarkable evolution, leading to the latest (Release 5) series by CSR, GFZ, and JPL, to new series by other processing centers, such as ITSG and AIUB, as well as to efforts to derive combined solutions, particularly by the EGSIEM (European Gravity Service for Improved Emergency Management) project. For applications, such as GRACE inferences on ice sheet mass balance, the obvious question is on what GRACE solution series to base the assessment. Here we evaluate different GRACE solution series (including the ones listed above) in a unified framework. We concentrate on solutions expanded up to degree 90 or higher, since this is most appropriate for polar applications. We empirically assess the error levels in the spectral as well as in the spatial domain based on the month-to-month scatter in the high spherical harmonic degrees. We include empirical assessment of error correlations. We then apply all series to infer Antarctic and Greenland mass change time series and compare the results in terms of apparent signal content and noise level. We find that the ITSG solutions show lowest noise level in the high degrees (above 60). A preliminary combined solution from the EGSIEM project shows lowest noise in the degrees below 60. This virtue maps into the derived ice mass time series, where the EGSIEM-based results show the lowest noise in most cases. Meanwhile, there is no indication that any of the considered series systematically dampens actual geophysical signals.
A general formula for Rayleigh-Schroedinger perturbation energy utilizing a power series expansion of the quantum mechanical Hamiltonian

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

Herbert, J.M.

1997-02-01

Perturbation theory has long been utilized by quantum chemists as a method for approximating solutions to the Schroedinger equation. Perturbation treatments represent a system`s energy as a power series in which each additional term further corrects the total energy; it is therefore convenient to have an explicit formula for the nth-order energy correction term. If all perturbations are collected into a single Hamiltonian operator, such a closed-form expression for the nth-order energy correction is well known; however, use of a single perturbed Hamiltonian often leads to divergent energy series, while superior convergence behavior is obtained by expanding the perturbed Hamiltonianmore » in a power series. This report presents a closed-form expression for the nth-order energy correction obtained using Rayleigh-Schroedinger perturbation theory and a power series expansion of the Hamiltonian.« less
Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays.

PubMed

Li, Hongfei; Jiang, Haijun; Hu, Cheng

2016-03-01

In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.
Global exponential stability of positive periodic solution of the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays.

PubMed

Zhao, Kaihong

2018-12-01

In this paper, we study the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.
Solutal and thermal buoyancy effects in self-powered phosphatase micropumps.

PubMed

Valdez, Lyanne; Shum, Henry; Ortiz-Rivera, Isamar; Balazs, Anna C; Sen, Ayusman

2017-04-12

Immobilized enzymes generate net fluid flow when exposed to specific reagents in solution. Thus, they function as self-powered platforms that combine sensing and on-demand fluid pumping. To uncover the mechanism of pumping, we examine the effects of solutal and thermal buoyancy on the behavior of phosphatase-based micropumps, using a series of reactants with known thermodynamic and kinetic parameters. By combining modeling and experiments, we perform the first quantitative comparison of thermal and solutal effects in an enzyme micropump system. Despite the significant exothermicity of the catalyzed reactions, we find that thermal effects play a minimal role in the observed fluid flow. Instead, fluid transport in phosphatase micropumps is governed by the density difference between the reactants and the products of the reaction. This surprising conclusion suggests new design principles for catalytic pumps.
Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.
Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639
Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian

2018-03-01

The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.
Exponential asymptotics of homoclinic snaking

NASA Astrophysics Data System (ADS)

Dean, A. D.; Matthews, P. C.; Cox, S. M.; King, J. R.

2011-12-01

We study homoclinic snaking in the cubic-quintic Swift-Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319-54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement.

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

PubMed

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.
Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping.

PubMed

Salje, Ekhard K H; Planes, Antoni; Vives, Eduard

2017-10-01

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.
Exponential order statistic models of software reliability growth

NASA Technical Reports Server (NTRS)

Miller, D. R.

1985-01-01

Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Using Differentials to Differentiate Trigonometric and Exponential Functions

ERIC Educational Resources Information Center

Dray, Tevian

2013-01-01

Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.
Arima model and exponential smoothing method: A comparison

NASA Astrophysics Data System (ADS)

Wan Ahmad, Wan Kamarul Ariffin; Ahmad, Sabri

2013-04-01

This study shows the comparison between Autoregressive Moving Average (ARIMA) model and Exponential Smoothing Method in making a prediction. The comparison is focused on the ability of both methods in making the forecasts with the different number of data sources and the different length of forecasting period. For this purpose, the data from The Price of Crude Palm Oil (RM/tonne), Exchange Rates of Ringgit Malaysia (RM) in comparison to Great Britain Pound (GBP) and also The Price of SMR 20 Rubber Type (cents/kg) with three different time series are used in the comparison process. Then, forecasting accuracy of each model is measured by examinethe prediction error that producedby using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute deviation (MAD). The study shows that the ARIMA model can produce a better prediction for the long-term forecasting with limited data sources, butcannot produce a better prediction for time series with a narrow range of one point to another as in the time series for Exchange Rates. On the contrary, Exponential Smoothing Method can produce a better forecasting for Exchange Rates that has a narrow range of one point to another for its time series, while itcannot produce a better prediction for a longer forecasting period.
Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO 2 in fractured rocks

DOE PAGES

Zhou, Quanlin; Oldenburg, Curtis M.; Spangler, Lee H.; ...

2017-01-05

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheresmore » and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less
Power estimation using simulations for air pollution time-series studies

PubMed Central

2012-01-01

Background Estimation of power to assess associations of interest can be challenging for time-series studies of the acute health effects of air pollution because there are two dimensions of sample size (time-series length and daily outcome counts), and because these studies often use generalized linear models to control for complex patterns of covariation between pollutants and time trends, meteorology and possibly other pollutants. In general, statistical software packages for power estimation rely on simplifying assumptions that may not adequately capture this complexity. Here we examine the impact of various factors affecting power using simulations, with comparison of power estimates obtained from simulations with those obtained using statistical software. Methods Power was estimated for various analyses within a time-series study of air pollution and emergency department visits using simulations for specified scenarios. Mean daily emergency department visit counts, model parameter value estimates and daily values for air pollution and meteorological variables from actual data (8/1/98 to 7/31/99 in Atlanta) were used to generate simulated daily outcome counts with specified temporal associations with air pollutants and randomly generated error based on a Poisson distribution. Power was estimated by conducting analyses of the association between simulated daily outcome counts and air pollution in 2000 data sets for each scenario. Power estimates from simulations and statistical software (G*Power and PASS) were compared. Results In the simulation results, increasing time-series length and average daily outcome counts both increased power to a similar extent. Our results also illustrate the low power that can result from using outcomes with low daily counts or short time series, and the reduction in power that can accompany use of multipollutant models. Power estimates obtained using standard statistical software were very similar to those from the simulations
Power estimation using simulations for air pollution time-series studies.

PubMed

Winquist, Andrea; Klein, Mitchel; Tolbert, Paige; Sarnat, Stefanie Ebelt

2012-09-20

Estimation of power to assess associations of interest can be challenging for time-series studies of the acute health effects of air pollution because there are two dimensions of sample size (time-series length and daily outcome counts), and because these studies often use generalized linear models to control for complex patterns of covariation between pollutants and time trends, meteorology and possibly other pollutants. In general, statistical software packages for power estimation rely on simplifying assumptions that may not adequately capture this complexity. Here we examine the impact of various factors affecting power using simulations, with comparison of power estimates obtained from simulations with those obtained using statistical software. Power was estimated for various analyses within a time-series study of air pollution and emergency department visits using simulations for specified scenarios. Mean daily emergency department visit counts, model parameter value estimates and daily values for air pollution and meteorological variables from actual data (8/1/98 to 7/31/99 in Atlanta) were used to generate simulated daily outcome counts with specified temporal associations with air pollutants and randomly generated error based on a Poisson distribution. Power was estimated by conducting analyses of the association between simulated daily outcome counts and air pollution in 2000 data sets for each scenario. Power estimates from simulations and statistical software (G*Power and PASS) were compared. In the simulation results, increasing time-series length and average daily outcome counts both increased power to a similar extent. Our results also illustrate the low power that can result from using outcomes with low daily counts or short time series, and the reduction in power that can accompany use of multipollutant models. Power estimates obtained using standard statistical software were very similar to those from the simulations when properly implemented
exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less
Autonomous solutions for powering wireless sensor nodes in rivers

NASA Astrophysics Data System (ADS)

Kamenar, E.; Maćešić, S.; Gregov, G.; Blažević, D.; Zelenika, S.; Marković, K.; Glažar, V.

2015-05-01

There is an evident need for monitoring pollutants and/or other conditions in river flows via wireless sensor networks. In a typical wireless sensor network topography, a series of sensor nodes is to be deployed in the environment, all wirelessly connected to each other and/or their gateways. Each sensor node is composed of active electronic devices that have to be constantly powered. In general, batteries can be used for this purpose, but problems may occur when they have to be replaced. In the case of large networks, when sensor nodes can be placed in hardly accessible locations, energy harvesting can thus be a viable powering solution. The possibility to use three different small-scale river flow energy harvesting principles is hence thoroughly studied in this work: a miniaturized underwater turbine, a so-called `piezoelectric eel' and a hybrid turbine solution coupled with a rigid piezoelectric beam. The first two concepts are then validated experimentally in laboratory as well as in real river conditions. The concept of the miniaturised hydro-generator is finally embedded into the actual wireless sensor node system and its functionality is confirmed.
Plane Symmetric Solutions in f(G) Gravity

NASA Astrophysics Data System (ADS)

Shamir, M. Farasat; Saeed, Atrooba

2017-12-01

The purpose of this document is to investigate the universe in f(G) gravity. A wgeneral static plane symmetric space-time is chosen and exact solutions are explored using a viable f(G) gravity model. In particular, power and exponential law solutions are discussed. In addition, the physical relevance of the solutions with Taub's metric and anti-deSitter space-time is shown. Graphical analysis of energy density and pressure of the universe is done to substantiate the study.
Comparing Exponential and Exponentiated Models of Drug Demand in Cocaine Users

PubMed Central

Strickland, Justin C.; Lile, Joshua A.; Rush, Craig R.; Stoops, William W.

2016-01-01

Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model, but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use), whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values impact demand parameters and their association with drug-use outcomes when using the exponential model, but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency, in addition to demonstrating construct validity and generalizability. PMID:27929347
Analytic solutions to modelling exponential and harmonic functions using Chebyshev polynomials: fitting frequency-domain lifetime images with photobleaching.

PubMed

Malachowski, George C; Clegg, Robert M; Redford, Glen I

2007-12-01

A novel approach is introduced for modelling linear dynamic systems composed of exponentials and harmonics. The method improves the speed of current numerical techniques up to 1000-fold for problems that have solutions of multiple exponentials plus harmonics and decaying components. Such signals are common in fluorescence microscopy experiments. Selective constraints of the parameters being fitted are allowed. This method, using discrete Chebyshev transforms, will correctly fit large volumes of data using a noniterative, single-pass routine that is fast enough to analyse images in real time. The method is applied to fluorescence lifetime imaging data in the frequency domain with varying degrees of photobleaching over the time of total data acquisition. The accuracy of the Chebyshev method is compared to a simple rapid discrete Fourier transform (equivalent to least-squares fitting) that does not take the photobleaching into account. The method can be extended to other linear systems composed of different functions. Simulations are performed and applications are described showing the utility of the method, in particular in the area of fluorescence microscopy.
Comparing exponential and exponentiated models of drug demand in cocaine users.

PubMed

Strickland, Justin C; Lile, Joshua A; Rush, Craig R; Stoops, William W

2016-12-01

Drug purchase tasks provide rapid and efficient measurement of drug demand. Zero values (i.e., prices with zero consumption) present a quantitative challenge when using exponential demand models that exponentiated models may resolve. We aimed to replicate and advance the utility of using an exponentiated model by demonstrating construct validity (i.e., association with real-world drug use) and generalizability across drug commodities. Participants (N = 40 cocaine-using adults) completed Cocaine, Alcohol, and Cigarette Purchase Tasks evaluating hypothetical consumption across changes in price. Exponentiated and exponential models were fit to these data using different treatments of zero consumption values, including retaining zeros or replacing them with 0.1, 0.01, or 0.001. Excellent model fits were observed with the exponentiated model. Means and precision fluctuated with different replacement values when using the exponential model but were consistent for the exponentiated model. The exponentiated model provided the strongest correlation between derived demand intensity (Q0) and self-reported free consumption in all instances (Cocaine r = .88; Alcohol r = .97; Cigarette r = .91). Cocaine demand elasticity was positively correlated with alcohol and cigarette elasticity. Exponentiated parameters were associated with real-world drug use (e.g., weekly cocaine use) whereas these correlations were less consistent for exponential parameters. Our findings show that selection of zero replacement values affects demand parameters and their association with drug-use outcomes when using the exponential model but not the exponentiated model. This work supports the adoption of the exponentiated demand model by replicating improved fit and consistency and demonstrating construct validity and generalizability. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Exact anisotropic viscous fluid solutions of Einstein's equations

NASA Astrophysics Data System (ADS)

Goenner, H. F. M.; Kowalewski, F.

1989-05-01

A method for obtaining anisotropic, rotationless viscous fluid matter solutions of Bianchi type I and Segré type [1, 111] with the barotropic equation of state is presented. Solutions for which the anisotropy decreases exponentially or with a power law as well as solutions with average Hubble parameterH ˜t -1 are discussed. Also, a class of solutions with constant anisotropy and Bianchi type VIh is found. The dominant energy condition holds and the transport coefficients show the right sign.
Matrix exponential-based closures for the turbulent subgrid-scale stress tensor.

PubMed

Li, Yi; Chevillard, Laurent; Eyink, Gregory; Meneveau, Charles

2009-01-01

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.
Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2016-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.
A Solution to the Fundamental Linear Fractional Order Differential Equation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.
Robust Image Regression Based on the Extended Matrix Variate Power Exponential Distribution of Dependent Noise.

PubMed

Luo, Lei; Yang, Jian; Qian, Jianjun; Tai, Ying; Lu, Gui-Fu

2017-09-01

Dealing with partial occlusion or illumination is one of the most challenging problems in image representation and classification. In this problem, the characterization of the representation error plays a crucial role. In most current approaches, the error matrix needs to be stretched into a vector and each element is assumed to be independently corrupted. This ignores the dependence between the elements of error. In this paper, it is assumed that the error image caused by partial occlusion or illumination changes is a random matrix variate and follows the extended matrix variate power exponential distribution. This has the heavy tailed regions and can be used to describe a matrix pattern of l×m dimensional observations that are not independent. This paper reveals the essence of the proposed distribution: it actually alleviates the correlations between pixels in an error matrix E and makes E approximately Gaussian. On the basis of this distribution, we derive a Schatten p -norm-based matrix regression model with L q regularization. Alternating direction method of multipliers is applied to solve this model. To get a closed-form solution in each step of the algorithm, two singular value function thresholding operators are introduced. In addition, the extended Schatten p -norm is utilized to characterize the distance between the test samples and classes in the design of the classifier. Extensive experimental results for image reconstruction and classification with structural noise demonstrate that the proposed algorithm works much more robustly than some existing regression-based methods.
Transition from Exponential to Power Law Income Distributions in a Chaotic Market

NASA Astrophysics Data System (ADS)

Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo

Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.

The Exponential Expansion of Simulation in Research

DTIC Science & Technology

2012-12-01

exponential growth of computing power. Although other analytic approaches also benefit from this trend, keyword searches of several scholarly search ... engines reveal that the reliance on simulation is increasing more rapidly. A descriptive analysis paints a compelling picture: simulation is frequently
Existence and global exponential stability of periodic solution to BAM neural networks with periodic coefficients and continuously distributed delays

NASA Astrophysics Data System (ADS)

Zhou, distributed delays [rapid communication] T.; Chen, A.; Zhou, Y.

2005-08-01

By using the continuation theorem of coincidence degree theory and Liapunov function, we obtain some sufficient criteria to ensure the existence and global exponential stability of periodic solution to the bidirectional associative memory (BAM) neural networks with periodic coefficients and continuously distributed delays. These results improve and generalize the works of papers [J. Cao, L. Wang, Phys. Rev. E 61 (2000) 1825] and [Z. Liu, A. Chen, J. Cao, L. Huang, IEEE Trans. Circuits Systems I 50 (2003) 1162]. An example is given to illustrate that the criteria are feasible.
Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2015-01-01

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.
Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking*

PubMed Central

Hamed, Kaveh Akbari; Gregg, Robert D.

2016-01-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059
Slow synaptic dynamics in a network: From exponential to power-law forgetting

NASA Astrophysics Data System (ADS)

Luck, J. M.; Mehta, A.

2014-09-01

We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modeled from the usual Hebbian perspective, while competition is modeled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal 1/t power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal 1/√t relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most original and important result of our present investigations.
Predictive capabilities of series solutions for laminar free convection boundary layer heat transfer

NASA Technical Reports Server (NTRS)

Lin, F. N.; Chao, B. T.

1978-01-01

Various types of series solutions for predicting laminar, free-convection boundary-layer heat transfer over both isothermal and nonisothermal boundaries are reviewed. The methods include finite difference, Merk series, Blasius series, and Goertler series. Comparative results are presented for heat transfer over an isothermal, horizontal, elliptical cylinder in both slender and blunt configurations.
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
Fluid Power Systems. Energy Technology Series.

ERIC Educational Resources Information Center

Center for Occupational Research and Development, Inc., Waco, TX.

This course in fluid power systems is one of 16 courses in the Energy Technology Series developed for an Energy Conservation-and-Use Technology curriculum. Intended for use in two-year postsecondary technical institutions to prepare technicians for employment, the courses are also useful in industry for updating employees in company-sponsored…
Liver fibrosis: stretched exponential model outperforms mono-exponential and bi-exponential models of diffusion-weighted MRI.

PubMed

Seo, Nieun; Chung, Yong Eun; Park, Yung Nyun; Kim, Eunju; Hwang, Jinwoo; Kim, Myeong-Jin

2018-07-01

To compare the ability of diffusion-weighted imaging (DWI) parameters acquired from three different models for the diagnosis of hepatic fibrosis (HF). Ninety-five patients underwent DWI using nine b values at 3 T magnetic resonance. The hepatic apparent diffusion coefficient (ADC) from a mono-exponential model, the true diffusion coefficient (D t ), pseudo-diffusion coefficient (D p ) and perfusion fraction (f) from a biexponential model, and the distributed diffusion coefficient (DDC) and intravoxel heterogeneity index (α) from a stretched exponential model were compared with the pathological HF stage. For the stretched exponential model, parameters were also obtained using a dataset of six b values (DDC # , α # ). The diagnostic performances of the parameters for HF staging were evaluated with Obuchowski measures and receiver operating characteristics (ROC) analysis. The measurement variability of DWI parameters was evaluated using the coefficient of variation (CoV). Diagnostic accuracy for HF staging was highest for DDC # (Obuchowski measures, 0.770 ± 0.03), and it was significantly higher than that of ADC (0.597 ± 0.05, p < 0.001), D t (0.575 ± 0.05, p < 0.001) and f (0.669 ± 0.04, p = 0.035). The parameters from stretched exponential DWI and D p showed higher areas under the ROC curve (AUCs) for determining significant fibrosis (≥F2) and cirrhosis (F = 4) than other parameters. However, D p showed significantly higher measurement variability (CoV, 74.6%) than DDC # (16.1%, p < 0.001) and α # (15.1%, p < 0.001). Stretched exponential DWI is a promising method for HF staging with good diagnostic performance and fewer b-value acquisitions, allowing shorter acquisition time. • Stretched exponential DWI provides a precise and accurate model for HF staging. • Stretched exponential DWI parameters are more reliable than D p from bi-exponential DWI model • Acquisition of six b values is sufficient to obtain accurate DDC and α.
A Fourier method for the analysis of exponential decay curves.

PubMed

Provencher, S W

1976-01-01

A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions. The Fourier method's usual serious practical limitation of needing high accuracy data over a very wide range is eliminated by the introduction of convergence parameters and a Gaussian taper window. A computer program is described for the analysis of discrete spectra, where the data involves only a sum of exponentials. The program is completely automatic in that the only necessary inputs are the raw data (not necessarily in equal intervals of time); no potentially biased initial guesses concerning either the number or the values of the components are needed. The outputs include the number of components, the amplitudes and time constants together with their estimated errors, and a spectral plot of the solution. The limiting resolving power of the method is studied by analyzing a wide range of simulated two-, three-, and four-component data. The results seem to indicate that the method is applicable over a considerably wider range of conditions than nonlinear least squares or the method of moments.
On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

NASA Astrophysics Data System (ADS)

Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

2018-06-01

In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.
Analytical solutions for systems of partial differential-algebraic equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2014-01-01

This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.
High Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

NASA Technical Reports Server (NTRS)

Scott, James R.; Martini, Michael C.

2008-01-01

Taylor series integration is implemented in a spacecraft trajectory analysis code-the Spacecraft N-body Analysis Program (SNAP) - and compared with the code s existing eighth-order Runge-Kutta Fehlberg time integration scheme. Nine trajectory problems, including near Earth, lunar, Mars and Europa missions, are analyzed. Head-to-head comparison at five different error tolerances shows that, on average, Taylor series is faster than Runge-Kutta Fehlberg by a factor of 15.8. Results further show that Taylor series has superior convergence properties. Taylor series integration proves that it can provide rapid, highly accurate solutions to spacecraft trajectory problems.
Investigation of Noises in GPS Time Series: Case Study on Epn Weekly Solutions

NASA Astrophysics Data System (ADS)

Klos, Anna; Bogusz, Janusz; Figurski, Mariusz; Kosek, Wieslaw; Gruszczynski, Maciej

2014-05-01

The noises in GPS time series are stated to be described the best by the combination of white (Gaussian) and power-law processes. They are mainly the effect of mismodelled satellite orbits, Earth orientation parameters, atmospheric effects, antennae phase centre effects, or of monument instability. Due to the fact, that velocities of permanent stations define the kinematic reference frame, they have to fulfil the requirement of being stable at 0.1 mm/yr. The previously performed researches showed, that the wrong assumption of noise model leads to the underestimation of velocities and their uncertainties from 2 up to even 11, especially in the Up direction. This presentation focuses on more than 200 EPN (EUREF Permanent Network) stations from the area of Europe with various monument types (concrete pillars, buildings, metal masts, with or without domes, placed on the ground or on the rock) and coordinates of weekly changes (GPS weeks 0834-1459). The topocentric components (North, East, Up) in ITRF2005 which come from the EPN Re-Processing made by the Military University of Technology Local Analysis Centre (MUT LAC) were processed with Maximum Likelihood Estimation (MLE) using CATS software. We have assumed the existence of few combinations of noise models (these are: white, flicker and random walk noise with integer spectral indices and power-law noise models with fractional spectral indices) and investigated which of them EPN weekly time series are likely to follow. The results show, that noises in GPS time series are described the best by the combination of white and flicker noise model. It is strictly related to the so-called common mode error (CME) that is spatially correlated error being one of the dominant error source in GPS solutions. We have assumed CME as spatially uniform, what was a good approximation for stations located hundreds of kilometres one to another. Its removal with spatial filtering reduces the amplitudes of white and flicker noise by a
Exponential model normalization for electrical capacitance tomography with external electrodes under gap permittivity conditions

NASA Astrophysics Data System (ADS)

Baidillah, Marlin R.; Takei, Masahiro

2017-06-01

A nonlinear normalization model which is called exponential model for electrical capacitance tomography (ECT) with external electrodes under gap permittivity conditions has been developed. The exponential model normalization is proposed based on the inherently nonlinear relationship characteristic between the mixture permittivity and the measured capacitance due to the gap permittivity of inner wall. The parameters of exponential equation are derived by using an exponential fitting curve based on the simulation and a scaling function is added to adjust the experiment system condition. The exponential model normalization was applied to two dimensional low and high contrast dielectric distribution phantoms by using simulation and experimental studies. The proposed normalization model has been compared with other normalization models i.e. Parallel, Series, Maxwell and Böttcher models. Based on the comparison of image reconstruction results, the exponential model is reliable to predict the nonlinear normalization of measured capacitance in term of low and high contrast dielectric distribution.
Exponentially convergent state estimation for delayed switched recurrent neural networks.

PubMed

Ahn, Choon Ki

2011-11-01

This paper deals with the delay-dependent exponentially convergent state estimation problem for delayed switched neural networks. A set of delay-dependent criteria is derived under which the resulting estimation error system is exponentially stable. It is shown that the gain matrix of the proposed state estimator is characterised in terms of the solution to a set of linear matrix inequalities (LMIs), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.
Application of Krylov exponential propagation to fluid dynamics equations

NASA Technical Reports Server (NTRS)

Saad, Youcef; Semeraro, David

1991-01-01

An application of matrix exponentiation via Krylov subspace projection to the solution of fluid dynamics problems is presented. The main idea is to approximate the operation exp(A)v by means of a projection-like process onto a krylov subspace. This results in a computation of an exponential matrix vector product similar to the one above but of a much smaller size. Time integration schemes can then be devised to exploit this basic computational kernel. The motivation of this approach is to provide time-integration schemes that are essentially of an explicit nature but which have good stability properties.
Scattering of acoustic evanescent waves by circular cylinders: Partial wave series solution

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2002-05-01

Evanescent acoustical waves occur in a variety of situations such as when sound is incident on a fluid interface beyond the critical angle and when flexural waves on a plate are subsonic with respect to the surrounding fluid. The scattering by circular cylinders at normal incidence was calculated to give insight into the consequences on the scattering of the evanescence of the incident wave. To analyze the scattering, it is necessary to express the incident wave using a modified expansion involving cylindrical functions. For plane evanescent waves, the expansion becomes a double summation with products of modified and ordinary Bessel functions. The resulting modified series is found for the scattering by a fluid cylinder in an unbounded medium. The perfectly soft and rigid cases are also examined. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on the transverse coordinate. The associated exponential dependence of the scattering on the location of a scatterer was previously demonstrated [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].
Stable exponential cosmological solutions with 3- and l-dimensional factor spaces in the Einstein-Gauss-Bonnet model with a Λ -term

NASA Astrophysics Data System (ADS)

Ivashchuk, V. D.; Kobtsev, A. A.

2018-02-01

A D-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term Λ is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned Λ , we find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H >0 and h, corresponding to factor spaces of dimensions 3 and l > 2, respectively and D = 1 + 3 + l. The fine-tuned Λ = Λ (x, l, α ) depends upon the ratio h/H = x, l and the ratio α = α _2/α _1 of two constants (α _2 and α _1) of the model. For fixed Λ , α and l > 2 the equation Λ (x,l,α ) = Λ is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals (the example l =3 is presented). For certain restrictions on x we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. A subclass of solutions with small enough variation of the effective gravitational constant G is considered. It is shown that all solutions from this subclass are stable.

Analysis of Air Force Secondary Power Logistics Solution Contract

DTIC Science & Technology

2010-05-21

IL 62225 SUBJECT: Audit. Analysis of Air Force Secondary Power Logistics Solution Contract, 748th Supply Chain Management Group, Hill Air Fon:r... Power Logis.tics Solution Contnict. 748111 Supply Ch.,in Management Group. !-lill Air FOfC! BII.SI!, UT (Project 02009· DOOOCH·0213.000) I. AUlIctlcd...00-00-2010 to 00-00-2010 4. TITLE AND SUBTITLE Analysis of Air Force Secondary Power Logistics Solution Contract 5a. CONTRACT NUMBER 5b. GRANT
High voltage power supply with modular series resonant inverters

DOEpatents

Dreifuerst, Gary R.; Merritt, Bernard T.

1995-01-01

A relatively small and compact high voltage, high current power supply for a laser utilizes a plurality of modules containing series resonant half bridge inverters. A pair of reverse conducting thyristors are incorporated in each series resonant inverter module such that the series resonant inverter modules are sequentially activated in phases 360.degree./n apart, where n=number of modules for n>2. Selective activation of the modules allows precise output control reducing ripple and improving efficiency. Each series resonant half bridge inverter module includes a transformer which has a cooling manifold for actively circulating a coolant such as water, to cool the transformer core as well as selected circuit elements. Conductors connecting and forming various circuit components comprise hollow, electrically conductive tubes such as copper. Coolant circulates through the tubes to remove heat. The conductive tubes act as electrically conductive lines for connecting various components of the power supply. Where it is desired to make electrical isolation breaks, tubes comprised of insulating material such as nylon are used to provide insulation and continue the fluid circuit.
High voltage power supply with modular series resonant inverters

DOEpatents

Dreifuerst, G.R.; Merritt, B.T.

1995-07-18

A relatively small and compact high voltage, high current power supply for a laser utilizes a plurality of modules containing series resonant half bridge inverters. A pair of reverse conducting thyristors are incorporated in each series resonant inverter module such that the series resonant inverter modules are sequentially activated in phases 360{degree}/n apart, where n=number of modules for n>2. Selective activation of the modules allows precise output control reducing ripple and improving efficiency. Each series resonant half bridge inverter module includes a transformer which has a cooling manifold for actively circulating a coolant such as water, to cool the transformer core as well as selected circuit elements. Conductors connecting and forming various circuit components comprise hollow, electrically conductive tubes such as copper. Coolant circulates through the tubes to remove heat. The conductive tubes act as electrically conductive lines for connecting various components of the power supply. Where it is desired to make electrical isolation breaks, tubes comprised of insulating material such as nylon are used to provide insulation and continue the fluid circuit. 11 figs.
A 25-kW Series-Resonant Power Converter

NASA Technical Reports Server (NTRS)

Frye, R. J.; Robson, R. R.

1986-01-01

Prototype exhibited efficiency of 93.9 percent. 25-kW resonant dc/dc power converter designed, developed, fabricated, and tested, using Westinghouse D7ST transistors as high-power switches. D7ST transistor characterized for use as switch in series-resonant converters, and refined base-drive circuit developed. Technical base includes advanced switching magnetic, and filter components, mathematical circuit models, control philosophies, and switch-drive strategies. Power-system benefits such as lower losses when used for high-voltage distribution, and reduced magnetics and filter mass realized.
Stimulation Efficiency With Decaying Exponential Waveforms in a Wirelessly Powered Switched-Capacitor Discharge Stimulation System.

PubMed

Lee, Hyung-Min; Howell, Bryan; Grill, Warren M; Ghovanloo, Maysam

2018-05-01

The purpose of this study was to test the feasibility of using a switched-capacitor discharge stimulation (SCDS) system for electrical stimulation, and, subsequently, determine the overall energy saved compared to a conventional stimulator. We have constructed a computational model by pairing an image-based volume conductor model of the cat head with cable models of corticospinal tract (CST) axons and quantified the theoretical stimulation efficiency of rectangular and decaying exponential waveforms, produced by conventional and SCDS systems, respectively. Subsequently, the model predictions were tested in vivo by activating axons in the posterior internal capsule and recording evoked electromyography (EMG) in the contralateral upper arm muscles. Compared to rectangular waveforms, decaying exponential waveforms with time constants >500 μs were predicted to require 2%-4% less stimulus energy to activate directly models of CST axons and 0.4%-2% less stimulus energy to evoke EMG activity in vivo. Using the calculated wireless input energy of the stimulation system and the measured stimulus energies required to evoke EMG activity, we predict that an SCDS implantable pulse generator (IPG) will require 40% less input energy than a conventional IPG to activate target neural elements. A wireless SCDS IPG that is more energy efficient than a conventional IPG will reduce the size of an implant, require that less wireless energy be transmitted through the skin, and extend the lifetime of the battery in the external power transmitter.
Bounds of memory strength for power-law series.

PubMed

Guo, Fangjian; Yang, Dan; Yang, Zimo; Zhao, Zhi-Dan; Zhou, Tao

2017-05-01

Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents α. By permuting the independently drawn samples from a power-law distribution, we present nontrivial bounds on the memory strength (first-order autocorrelation) as a function of α, which are markedly different from the ordinary ±1 bounds for Gaussian or uniform distributions. When 1<α≤3, as α grows bigger, the upper bound increases from 0 to +1 while the lower bound remains 0; when α>3, the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the posts on Twitter, ratings of MovieLens, calling records of the mobile operator Orange, and the browsing behavior of Taobao, we find that empirical power-law-distributed data produced by human activities obey such constraints. The present findings explain some observed constraints in bursty time series and scale-free networks and challenge the validity of measures such as autocorrelation and assortativity coefficient in heterogeneous systems.
Bounds of memory strength for power-law series

NASA Astrophysics Data System (ADS)

Guo, Fangjian; Yang, Dan; Yang, Zimo; Zhao, Zhi-Dan; Zhou, Tao

2017-05-01

Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents α . By permuting the independently drawn samples from a power-law distribution, we present nontrivial bounds on the memory strength (first-order autocorrelation) as a function of α , which are markedly different from the ordinary ±1 bounds for Gaussian or uniform distributions. When 1 <α ≤3 , as α grows bigger, the upper bound increases from 0 to +1 while the lower bound remains 0; when α >3 , the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the posts on Twitter, ratings of MovieLens, calling records of the mobile operator Orange, and the browsing behavior of Taobao, we find that empirical power-law-distributed data produced by human activities obey such constraints. The present findings explain some observed constraints in bursty time series and scale-free networks and challenge the validity of measures such as autocorrelation and assortativity coefficient in heterogeneous systems.
Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints

NASA Technical Reports Server (NTRS)

Fadel, G. M.

1991-01-01

The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous design history, is tested in this paper on optimization problems with frequency constraints. The aim of the research is to verify the robustness and speed of convergence of the two point exponential approximation method when highly non-linear constraints are used.
Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay

NASA Astrophysics Data System (ADS)

Dai, Qiuyi; Yang, Zhifeng

2014-10-01

In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ 1 and μ 2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561-1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011) by removing the restriction imposed on μ 1 and μ 2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ 1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011).
Summation of power series in particle physics

NASA Astrophysics Data System (ADS)

Fischer, Jan

1999-04-01

The large-order behaviour of power series used in quantum theory (perturbation series and the operator-product expansion) is discussed and relevant summation methods are reviewed. It is emphasised that, in most physically interesting situations, the mere knowledge of the expansion coefficients is not sufficient for a unique determination of the function expanded, and the necessity of some additional, extra-perturbative, input is pointed out. Several possible nonperturbative inputs are suggested. Applications to various problems of quantum chromodynamics are considered. This lecture was presented on the special Memorial Day dedicated to Professor Ryszard R˛czka at this Workshop. The last section is devoted to my personal recollections of this remarkable personality.
General Series Solutions for Stresses and Displacements in an Inner-fixed Ring

NASA Astrophysics Data System (ADS)

Jiao, Yongshu; Liu, Shuo; Qi, Dexuan

2018-03-01

The general series solution approach is provided to get the stress and displacement fields in the inner-fixed ring. After choosing an Airy stress function in series form, stresses are expressed by infinite coefficients. Displacements are obtained by integrating the geometric equations. For an inner-fixed ring, the arbitrary loads acting on outer edge are extended into two sets of Fourier series. The zero displacement boundary conditions on inner surface are utilized. Then the stress (and displacement) coefficients are expressed by loading coefficients. A numerical example shows the validity of this approach.
Exponential convergence through linear finite element discretization of stratified subdomains

NASA Astrophysics Data System (ADS)

Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali

2016-10-01

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.
How exponential are FREDs?

NASA Astrophysics Data System (ADS)

Schaefer, Bradley E.; Dyson, Samuel E.

1996-08-01

A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.
Smarter Grid Solutions Demonstrates Smart Campus Power Control at NREL -

Science.gov Websites

Video Text Version | Energy Systems Integration Facility | NREL Smarter Grid Solutions Demonstrates Smart Campus Power Control at NREL - Video Text Version Smarter Grid Solutions Demonstrates Smart Campus Power Control at NREL - Video Text Version This is the text version for the Smarter Grid Solutions
Properties of branching exponential flights in bounded domains

NASA Astrophysics Data System (ADS)

Zoia, A.; Dumonteil, E.; Mazzolo, A.

2012-11-01

In a series of recent works, important results have been reported concerning the statistical properties of exponential flights evolving in bounded domains, a widely adopted model for finite-speed transport phenomena (Blanco S. and Fournier R., Europhys. Lett., 61 (2003) 168; Mazzolo A., Europhys. Lett., 68 (2004) 350; Bénichou O. et al., Europhys. Lett., 70 (2005) 42). Motivated by physical and biological systems where random spatial displacements are coupled with Galton-Watson birth-death mechanisms, such as neutron multiplication, diffusion of reproducing bacteria or spread of epidemics, in this letter we extend those results in two directions, via a Feynman-Kac formalism. First, we characterize the occupation statistics of exponential flights in the presence of absorption and branching, and give explicit moment formulas for the total length travelled by the walker and the number of performed collisions in a given domain. Then, we show that the survival and escape probability can be derived as well by resorting to a similar approach.
On exponentially suppressed corrections to BMPV black hole entropy

NASA Astrophysics Data System (ADS)

Lal, Shailesh; Narayan, Prithvi

2018-05-01

The microscopic formula for the degeneracy of BMPV black hole microstates contains a series of exponentially suppressed corrections to the leading Bekenstein Hawking expression. We identify saddle points of the quantum entropy function for the BMPV black hole which are natural counterparts to these corrections and discuss the matching of leading and next-to-leading terms from the microscopic and macroscopic sides in a limit where the black hole charges are large.
GRACE RL03-v2 monthly time series of solutions from CNES/GRGS

NASA Astrophysics Data System (ADS)

Lemoine, Jean-Michel; Bourgogne, Stéphane; Bruinsma, Sean; Gégout, Pascal; Reinquin, Franck; Biancale, Richard

2015-04-01

Based on GRACE GPS and KBR Level-1B.v2 data, as well as on LAGEOS-1/2 SLR data, CNES/GRGS has published in 2014 the third full re-iteration of its GRACE gravity field solutions. This monthly time series of solutions, named RL03-v1, complete to spherical harmonics degree/order 80, has displayed interesting performances in terms of spatial resolution and signal amplitude compared to JPL/GFZ/CSR RL05. This is due to a careful selection of the background models (FES2014 ocean tides, ECMWF ERA-interim (atmosphere) and TUGO (non IB-ocean) "dealiasing" models every 3 hours) and to the choice of an original method for gravity field inversion : truncated SVD. Identically to the previous CNES/GRGS releases, no additional filtering of the solutions is necessary before using them. Some problems have however been identified in CNES/GRGS RL03-v1: - an erroneous mass signal located in two small circular rings close to the Earth's poles, leading to the recommendation not to use RL03-v1 above 82° latitudes North and South; - a weakness in the sectorials due to an excessive downweighting of the GRACE GPS observations. These two problems have been understood and addressed, leading to the computation of a corrected time series of solutions, RL03-v2. The corrective steps have been: - to strengthen the determination of the very low degrees by adding Starlette and Stella SLR data to the normal equations; - to increase the weight of the GRACE GPS observations; - to adopt a two steps approach for the computation of the solutions: first a Choleski inversion for the low degrees, followed by a truncated SVD solution. The identification of these problems will be discussed and the performance of the new time series evaluated.
Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods

NASA Astrophysics Data System (ADS)

Monovasilis, Theodore; Kalogiratou, Zacharoula; Simos, T. E.

2014-10-01

In this work we derive exponentially fitted symplectic Runge-Kutta-Nyström (RKN) methods from symplectic exponentially fitted partitioned Runge-Kutta (PRK) methods methods (for the approximate solution of general problems of this category see [18] - [40] and references therein). We construct RKN methods from PRK methods with up to five stages and fourth algebraic order.
Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

NASA Astrophysics Data System (ADS)

Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

2017-03-01

Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.
Nonsimilar Solution for Shock Waves in a Rotational Axisymmetric Perfect Gas with a Magnetic Field and Exponentially Varying Density

NASA Astrophysics Data System (ADS)

Nath, G.; Sinha, A. K.

2017-01-01

The propagation of a cylindrical shock wave in an ideal gas in the presence of a constant azimuthal magnetic field with consideration for the axisymmetric rotational effects is investigated. The ambient medium is assumed to have the radial, axial, and azimuthal velocity components. The fluid velocities and density of the ambient medium are assumed to vary according to an exponential law. Nonsimilar solutions are obtained by taking into account the vorticity vector and its components. The dependences of the characteristics of the problem on the Alfven-Mach number and time are obtained. It is shown that the presence of a magnetic field has a decaying effect on the shock wave. The pressure and density are shown to vanish at the inner surface (piston), and hence a vacuum forms at the line of symmetry.

On Complicated Expansions of Solutions to ODES

NASA Astrophysics Data System (ADS)

Bruno, A. D.

2018-03-01

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

PubMed

Hirono, Yuhei; Nonaka, Kunihiko

2016-02-01

Radiocaesium ((134)Cs and (137)Cs) release following the accident at the Fukushima Dai-ichi Nuclear Power Plant, belonging to the Tokyo Electric Power Company caused severe contamination of new tea plant (Camellia sinensis (L.)) shoots by radiocaesium in many prefectures in eastern Japan. Because tea plants are perennial crops, there is the fear that the contamination might last for a long time. The objectives of this study were to reveal time series changes in the distribution of radiocaesium in tea plants after radioactive fallout and to evaluate the effect of pruning on reduction of radiocaesium concentrations in new shoots growing next year. The experimental tea field was located in Shizuoka, Japan, approximately 400 km away from the Fukushima Dai-ichi Nuclear Power Plant in a southwest direction. Time series changes in radiocaesium concentrations in unrefined tea, a tea product primarily produced for making Japanese green tea, from May 2011 to June 2013 and distribution of radiocaesium in tea plants from May 2011 to May 2012 were monitored. The radiocaesium concentrations in unrefined tea exponentially decreased; the effective half-lives for (134)Cs and (137)Cs were 0.30 and 0.36 y during the first 2 y after the accident, respectively. With time, the highest concentrations of (137)Cs moved from the upper to the lower parts of plants. Medium pruning 2-3 months after the accident reduced the concentration of (137)Cs in new shoots harvested in the first crop season of the following year by 56% compared with unpruned tea plants; thus, pruning is an effective measure for reducing radiocaesium concentration in tea. Copyright © 2015 Elsevier Ltd. All rights reserved.
Electrical Power and Illumination Systems. Energy Technology Series.

ERIC Educational Resources Information Center

Center for Occupational Research and Development, Inc., Waco, TX.

This course in electrical power and illumination systems is one of 16 courses in the Energy Technology Series developed for an Energy Conservation-and-Use Technology curriculum. Intended for use in two-year postsecondary technical institutions to prepare technicians for employment, the courses are also useful in industry for updating employees in…
Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

NASA Astrophysics Data System (ADS)

Bakker, Mark

2010-08-01

A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.
On the non-exponentiality of the dielectric Debye-like relaxation of monoalcohols

NASA Astrophysics Data System (ADS)

Arrese-Igor, S.; Alegría, A.; Colmenero, J.

2017-03-01

We have investigated the Debye-like relaxation in a series of monoalcohols (MAs) by broadband dielectric spectroscopy and thermally stimulated depolarization current techniques in order to get further insight on the time dispersion of this intriguing relaxation. Results indicate that the Debye-like relaxation of MAs is not always of exponential type and conforms well to a dispersion of Cole-Davidson type. Apart from the already reported non-exponentiality of the Debye-like relaxation in 2-hexyl-1-decanol and 2-butyl-1-octanol, a detailed analysis of the dielectric permittivity of 5-methyl-3-heptanol shows that this MA also presents some extent of dispersion on its Debye-like relaxation which strongly depends on the temperature. Results suggest that the non-exponential character of the Debye-like relaxation might be a general characteristic in the case of not so intense Debye-like relaxations relative to the α relaxation. Finally, we briefly discuss on the T-dependence and possible origin for the observed dispersion.
Ammonium Removal from Aqueous Solutions by Clinoptilolite: Determination of Isotherm and Thermodynamic Parameters and Comparison of Kinetics by the Double Exponential Model and Conventional Kinetic Models

PubMed Central

Tosun, İsmail

2012-01-01

The adsorption isotherm, the adsorption kinetics, and the thermodynamic parameters of ammonium removal from aqueous solution by using clinoptilolite in aqueous solution was investigated in this study. Experimental data obtained from batch equilibrium tests have been analyzed by four two-parameter (Freundlich, Langmuir, Tempkin and Dubinin-Radushkevich (D-R)) and four three-parameter (Redlich-Peterson (R-P), Sips, Toth and Khan) isotherm models. D-R and R-P isotherms were the models that best fitted to experimental data over the other two- and three-parameter models applied. The adsorption energy (E) from the D-R isotherm was found to be approximately 7 kJ/mol for the ammonium-clinoptilolite system, thereby indicating that ammonium is adsorbed on clinoptilolite by physisorption. Kinetic parameters were determined by analyzing the nth-order kinetic model, the modified second-order model and the double exponential model, and each model resulted in a coefficient of determination (R2) of above 0.989 with an average relative error lower than 5%. A Double Exponential Model (DEM) showed that the adsorption process develops in two stages as rapid and slow phase. Changes in standard free energy (∆G°), enthalpy (∆H°) and entropy (∆S°) of ammonium-clinoptilolite system were estimated by using the thermodynamic equilibrium coefficients. PMID:22690177
Ammonium removal from aqueous solutions by clinoptilolite: determination of isotherm and thermodynamic parameters and comparison of kinetics by the double exponential model and conventional kinetic models.

PubMed

Tosun, Ismail

2012-03-01

The adsorption isotherm, the adsorption kinetics, and the thermodynamic parameters of ammonium removal from aqueous solution by using clinoptilolite in aqueous solution was investigated in this study. Experimental data obtained from batch equilibrium tests have been analyzed by four two-parameter (Freundlich, Langmuir, Tempkin and Dubinin-Radushkevich (D-R)) and four three-parameter (Redlich-Peterson (R-P), Sips, Toth and Khan) isotherm models. D-R and R-P isotherms were the models that best fitted to experimental data over the other two- and three-parameter models applied. The adsorption energy (E) from the D-R isotherm was found to be approximately 7 kJ/mol for the ammonium-clinoptilolite system, thereby indicating that ammonium is adsorbed on clinoptilolite by physisorption. Kinetic parameters were determined by analyzing the nth-order kinetic model, the modified second-order model and the double exponential model, and each model resulted in a coefficient of determination (R(2)) of above 0.989 with an average relative error lower than 5%. A Double Exponential Model (DEM) showed that the adsorption process develops in two stages as rapid and slow phase. Changes in standard free energy (∆G°), enthalpy (∆H°) and entropy (∆S°) of ammonium-clinoptilolite system were estimated by using the thermodynamic equilibrium coefficients.
Reliability analysis using an exponential power model with bathtub-shaped failure rate function: a Bayes study.

PubMed

Shehla, Romana; Khan, Athar Ali

2016-01-01

Models with bathtub-shaped hazard function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this paper, the exponential power model capable of assuming increasing as well as bathtub-shape, is studied. This article makes a Bayesian study of the same model and simultaneously shows how posterior simulations based on Markov chain Monte Carlo algorithms can be straightforward and routine in R. The study is carried out for complete as well as censored data, under the assumption of weakly-informative priors for the parameters. In addition to this, inference interest focuses on the posterior distribution of non-linear functions of the parameters. Also, the model has been extended to include continuous explanatory variables and R-codes are well illustrated. Two real data sets are considered for illustrative purposes.
Effective calculation of power system low-voltage solutions

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

Overbye, T.J.; Klump, R.P.

1996-02-01

This paper develops a method for reliably determining the set of low-voltage solutions which are closest to the operable power flow solution. These solutions are often used in conjunction with techniques such as energy methods and the voltage instability proximity index (VIPI) for assessing system voltage stability. This paper presents an algorithm which provides good initial guesses for these solutions. The results are demonstrated on a small system and on larger systems with up to 2,000 buses.
Modeling the full-bridge series-resonant power converter

NASA Technical Reports Server (NTRS)

King, R. J.; Stuart, T. A.

1982-01-01

A steady state model is derived for the full-bridge series-resonant power converter. Normalized parametric curves for various currents and voltages are then plotted versus the triggering angle of the switching devices. The calculations are compared with experimental measurements made on a 50 kHz converter and a discussion of certain operating problems is presented.
Duality between QCD perturbative series and power corrections

NASA Astrophysics Data System (ADS)

Narison, S.; Zakharov, V. I.

2009-08-01

We elaborate on the relation between perturbative and power-like corrections to short-distance sensitive QCD observables. We confront theoretical expectations with explicit perturbative calculations existing in literature. As is expected, the quadratic correction is dual to a long perturbative series and one should use one of them but not both. However, this might be true only for very long perturbative series, with number of terms needed in most cases exceeding the number of terms available. What has not been foreseen, the quartic corrections might also be dual to the perturbative series. If confirmed, this would imply a crucial modification of the dogma. We confront this quadratic correction against existing phenomenology (QCD (spectral) sum rules scales, determinations of light quark masses and of αs from τ-decay). We find no contradiction and (to some extent) better agreement with the data and with recent lattice calculations.
Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.
A study on stimulation of DC high voltage power of LCC series parallel resonant in projectile velocity measurement system

NASA Astrophysics Data System (ADS)

Lu, Dong-dong; Gu, Jin-liang; Luo, Hong-e.; Xia, Yan

2017-10-01

According to specific requirements of the X-ray machine system for measuring velocity of outfield projectile, a DC high voltage power supply system is designed for the high voltage or the smaller current. The system comprises: a series resonant circuit is selected as a full-bridge inverter circuit; a high-frequency zero-current soft switching of a high-voltage power supply is realized by PWM output by STM32; a nanocrystalline alloy transformer is chosen as a high-frequency booster transformer; and the related parameters of an LCC series-parallel resonant are determined according to the preset parameters of the transformer. The concrete method includes: a LCC series parallel resonant circuit and a voltage doubling circuit are stimulated by using MULTISM and MATLAB; selecting an optimal solution and an optimal parameter of all parts after stimulation analysis; and finally verifying the correctness of the parameter by stimulation of the whole system. Through stimulation analysis, the output voltage of the series-parallel resonant circuit gets to 10KV in 28s: then passing through the voltage doubling circuit, the output voltage gets to 120KV in one hour. According to the system, the wave range of the output voltage is so small as to provide the stable X-ray supply for the X-ray machine for measuring velocity of outfield projectile. It is fast in charging and high in efficiency.
On the performance of exponential integrators for problems in magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Einkemmer, Lukas; Tokman, Mayya; Loffeld, John

2017-02-01

Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin-Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.
Building Alliances Series: Workforce Development

ERIC Educational Resources Information Center

Brady, Cecilia

2009-01-01

Public-private partnerships done right are a powerful tool for development, providing enduring solutions to some of the greatest challenges. To help familiarize readers with the art of alliance building, the Global Development Alliance (GDA) office has created a series of practical guides that highlight proven practices in partnerships,…
Applications of an exponential finite difference technique

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

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.
A representation of solution of stochastic differential equations

NASA Astrophysics Data System (ADS)

Kim, Yoon Tae; Jeon, Jong Woo

2006-03-01

We prove that the logarithm of the formal power series, obtained from a stochastic differential equation, is an element in the closure of the Lie algebra generated by vector fields being coefficients of equations. By using this result, we obtain a representation of the solution of stochastic differential equations in terms of Lie brackets and iterated Stratonovich integrals in the algebra of formal power series.
Effect of growth solution, membrane size and array connection on microbial fuel cell power supply for medical devices.

PubMed

Roxby, Daniel N; Nham Tran; Pak-Lam Yu; Nguyen, Hung T

2016-08-01

Implanted biomedical devices typically last a number of years before their batteries are depleted and a surgery is required to replace them. A Microbial Fuel Cell (MFC) is a device which by using bacteria, directly breaks down sugars to generate electricity. Conceptually there is potential to continually power implanted medical devices for the lifetime of a patient. To investigate the practical potential of this technology, H-Cell Dual Chamber MFCs were evaluated with two different growth solutions and measurements recorded for maximum power output both of individual MFCs and connected MFCs. Using Luria-Bertani media and connecting MFCs in a hybrid series and parallel arrangement with larger membrane sizes showed the highest power output and the greatest potential for replacing implanted batteries.
An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.
Exponential Decay of Dispersion-Managed Solitons for General Dispersion Profiles

NASA Astrophysics Data System (ADS)

Green, William R.; Hundertmark, Dirk

2016-02-01

We show that any weak solution of the dispersion management equation describing dispersion-managed solitons together with its Fourier transform decay exponentially. This strong regularity result extends a recent result of Erdoğan, Hundertmark, and Lee in two directions, to arbitrary non-negative average dispersion and, more importantly, to rather general dispersion profiles, which cover most, if not all, physically relevant cases.

Thermal fluctuations and elastic relaxation in the compressed exponential dynamics of colloidal gels

NASA Astrophysics Data System (ADS)

Bouzid, Mehdi; Colombo, Jader; Del Gado, Emanuela

Colloidal gels belong to the class of amorphous systems, they are disordered elastic solids that can form at very low volume fraction, via aggregation into a rich variety of networks. They exhibit a slow relaxation process in the aging regime similar to the glassy dynamics. A wide range of experiments on colloidal gels show unusual compressed exponential of the relaxation dynamical properties. We use molecular dynamics simulation to investigate how the dynamic change with the age of the system. Upon breaking and reorganization of the network structure, the system may display stretched or compressed exponential relaxation. We show that the transition between these two regimes is associated to the interplay between thermally activated rearrangements and the elastic relaxation of internal stresses. In particular, ballistic-like displacements emerge from the non local relaxation of internal stresses mediated by a series of ''micro-collapses''. When thermal fluctuations dominate, the gel restructuring involves instead more homogeneous displacements across the heterogeneous gel network, leading to a stretched exponential type of relaxation.
The symbolic computation of series solutions to ordinary differential equations using trees (extended abstract)

NASA Technical Reports Server (NTRS)

Grossman, Robert

1991-01-01

Algorithms previously developed by the author give formulas which can be used for the efficient symbolic computation of series expansions to solutions of nonlinear systems of ordinary differential equations. As a by product of this analysis, formulas are derived which relate to trees to the coefficients of the series expansions, similar to the work of Leroux and Viennot, and Lamnabhi, Leroux and Viennot.
A general solution strategy of modified power method for higher mode solutions

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

Zhang, Peng; Lee, Hyunsuk; Lee, Deokjung, E-mail: deokjung@unist.ac.kr

2016-01-15

A general solution strategy of the modified power iteration method for calculating higher eigenmodes has been developed and applied in continuous energy Monte Carlo simulation. The new approach adopts four features: 1) the eigen decomposition of transfer matrix, 2) weight cancellation for higher modes, 3) population control with higher mode weights, and 4) stabilization technique of statistical fluctuations using multi-cycle accumulations. The numerical tests of neutron transport eigenvalue problems successfully demonstrate that the new strategy can significantly accelerate the fission source convergence with stable convergence behavior while obtaining multiple higher eigenmodes at the same time. The advantages of the newmore » strategy can be summarized as 1) the replacement of the cumbersome solution step of high order polynomial equations required by Booth's original method with the simple matrix eigen decomposition, 2) faster fission source convergence in inactive cycles, 3) more stable behaviors in both inactive and active cycles, and 4) smaller variances in active cycles. Advantages 3 and 4 can be attributed to the lower sensitivity of the new strategy to statistical fluctuations due to the multi-cycle accumulations. The application of the modified power method to continuous energy Monte Carlo simulation and the higher eigenmodes up to 4th order are reported for the first time in this paper. -- Graphical abstract: -- Highlights: •Modified power method is applied to continuous energy Monte Carlo simulation. •Transfer matrix is introduced to generalize the modified power method. •All mode based population control is applied to get the higher eigenmodes. •Statistic fluctuation can be greatly reduced using accumulated tally results. •Fission source convergence is accelerated with higher mode solutions.« less
Multi-exponential analysis of magnitude MR images using a quantitative multispectral edge-preserving filter.

PubMed

Bonny, Jean Marie; Boespflug-Tanguly, Odile; Zanca, Michel; Renou, Jean Pierre

2003-03-01

A solution for discrete multi-exponential analysis of T(2) relaxation decay curves obtained in current multi-echo imaging protocol conditions is described. We propose a preprocessing step to improve the signal-to-noise ratio and thus lower the signal-to-noise ratio threshold from which a high percentage of true multi-exponential detection is detected. It consists of a multispectral nonlinear edge-preserving filter that takes into account the signal-dependent Rician distribution of noise affecting magnitude MR images. Discrete multi-exponential decomposition, which requires no a priori knowledge, is performed by a non-linear least-squares procedure initialized with estimates obtained from a total least-squares linear prediction algorithm. This approach was validated and optimized experimentally on simulated data sets of normal human brains.
An Exponential Growth Learning Trajectory: Students' Emerging Understanding of Exponential Growth through Covariation

ERIC Educational Resources Information Center

Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel

2016-01-01

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…
Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation. Part 2; Constant Stress Rate Experiments

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Nemeth, Noel N.; Gyekenyesi, John P.

2002-01-01

The previously determined life prediction analysis based on an exponential crack-velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress rate and preload testing at ambient and elevated temperatures. The data fit to the relation of strength versus the log of the stress rate was very reasonable for most of the materials. Also, the preloading technique was determined equally applicable to the case of slow-crack-growth (SCG) parameter n greater than 30 for both the power-law and exponential formulations. The major limitation in the exponential crack-velocity formulation, however, was that the inert strength of a material must be known a priori to evaluate the important SCG parameter n, a significant drawback as compared with the conventional power-law crack-velocity formulation.
Electrostatic screening in classical Coulomb fluids: exponential or power-law decay or both? An investigation into the effect of dispersion interactions

NASA Astrophysics Data System (ADS)

Kjellander, Roland

2006-04-01

It is shown that the nature of the non-electrostatic part of the pair interaction potential in classical Coulomb fluids can have a profound influence on the screening behaviour. Two cases are compared: (i) when the non-electrostatic part equals an arbitrary finite-ranged interaction and (ii) when a dispersion r-6 interaction potential is included. A formal analysis is done in exact statistical mechanics, including an investigation of the bridge function. It is found that the Coulombic r-1 and the dispersion r-6 potentials are coupled in a very intricate manner as regards the screening behaviour. The classical one-component plasma (OCP) is a particularly clear example due to its simplicity and is investigated in detail. When the dispersion r-6 potential is turned on, the screened electrostatic potential from a particle goes from a monotonic exponential decay, exp(-κr)/r, to a power-law decay, r-8, for large r. The pair distribution function acquire, at the same time, an r-10 decay for large r instead of the exponential one. There still remains exponentially decaying contributions to both functions, but these contributions turn oscillatory when the r-6 interaction is switched on. When the Coulomb interaction is turned off but the dispersion r-6 pair potential is kept, the decay of the pair distribution function for large r goes over from the r-10 to an r-6 behaviour, which is the normal one for fluids of electroneutral particles with dispersion interactions. Differences and similarities compared to binary electrolytes are pointed out.
Exponentially accurate approximations to piece-wise smooth periodic functions

NASA Technical Reports Server (NTRS)

Greer, James; Banerjee, Saheb

1995-01-01

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.
Design of Passive Power Filter for Hybrid Series Active Power Filter using Estimation, Detection and Classification Method

NASA Astrophysics Data System (ADS)

Swain, Sushree Diptimayee; Ray, Pravat Kumar; Mohanty, K. B.

2016-06-01

This research paper discover the design of a shunt Passive Power Filter (PPF) in Hybrid Series Active Power Filter (HSAPF) that employs a novel analytic methodology which is superior than FFT analysis. This novel approach consists of the estimation, detection and classification of the signals. The proposed method is applied to estimate, detect and classify the power quality (PQ) disturbance such as harmonics. This proposed work deals with three methods: the harmonic detection through wavelet transform method, the harmonic estimation by Kalman Filter algorithm and harmonic classification by decision tree method. From different type of mother wavelets in wavelet transform method, the db8 is selected as suitable mother wavelet because of its potency on transient response and crouched oscillation at frequency domain. In harmonic compensation process, the detected harmonic is compensated through Hybrid Series Active Power Filter (HSAPF) based on Instantaneous Reactive Power Theory (IRPT). The efficacy of the proposed method is verified in MATLAB/SIMULINK domain and as well as with an experimental set up. The obtained results confirm the superiority of the proposed methodology than FFT analysis. This newly proposed PPF is used to make the conventional HSAPF more robust and stable.
Nuclear Power and the Environment, Understanding the Atom Series.

ERIC Educational Resources Information Center

Atomic Energy Commission, Oak Ridge, TN. Div. of Technical Information.

This booklet is one of the booklets in the "Understanding the Atom Series" published by the U. S. Atomic Energy Commission for high school science teachers and their students. Discussion concentrates on the radiological and thermal aspects of the environmental effects of nuclear power plants; on the procedures followed by the Atomic Energy…
Self similar flow behind an exponential shock wave in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux

NASA Astrophysics Data System (ADS)

Bajargaan, Ruchi; Patel, Arvind

2018-04-01

One-dimensional unsteady adiabatic flow behind an exponential shock wave propagating in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux, which has exponentially varying azimuthal and axial fluid velocities, is investigated. The shock wave is driven out by a piston moving with time according to an exponential law. The dusty gas is taken to be a mixture of a non-ideal gas and small solid particles. The density of the ambient medium is assumed to be constant. The equilibrium flow conditions are maintained and energy is varying exponentially, which is continuously supplied by the piston. The heat conduction is expressed in the terms of Fourier's law, and the radiation is assumed of diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density according to a power law. The effects of the variation of heat transfer parameters, gravitation parameter and dusty gas parameters on the shock strength, the distance between the piston and the shock front, and on the flow variables are studied out in detail. It is interesting to note that the similarity solution exists under the constant initial angular velocity, and the shock strength is independent from the self gravitation, heat conduction and radiation heat flux.
Efficient Algorithm for Locating and Sizing Series Compensation Devices in Large Transmission Grids: Solutions and Applications (PART II)

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

Frolov, Vladimir; Backhaus, Scott N.; Chertkov, Michael

2014-01-14

In a companion manuscript, we developed a novel optimization method for placement, sizing, and operation of Flexible Alternating Current Transmission System (FACTS) devices to relieve transmission network congestion. Specifically, we addressed FACTS that provide Series Compensation (SC) via modification of line inductance. In this manuscript, this heuristic algorithm and its solutions are explored on a number of test cases: a 30-bus test network and a realistically-sized model of the Polish grid (~2700 nodes and ~3300 lines). The results on the 30-bus network are used to study the general properties of the solutions including non-locality and sparsity. The Polish grid ismore » used as a demonstration of the computational efficiency of the heuristics that leverages sequential linearization of power flow constraints and cutting plane methods that take advantage of the sparse nature of the SC placement solutions. Using these approaches, the algorithm is able to solve an instance of Polish grid in tens of seconds. We explore the utility of the algorithm by analyzing transmission networks congested by (a) uniform load growth, (b) multiple overloaded configurations, and (c) sequential generator retirements« less
On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Herve

1992-01-01

It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.
First-order analytic propagation of satellites in the exponential atmosphere of an oblate planet

NASA Astrophysics Data System (ADS)

Martinusi, Vladimir; Dell'Elce, Lamberto; Kerschen, Gaëtan

2017-04-01

The paper offers the fully analytic solution to the motion of a satellite orbiting under the influence of the two major perturbations, due to the oblateness and the atmospheric drag. The solution is presented in a time-explicit form, and takes into account an exponential distribution of the atmospheric density, an assumption that is reasonably close to reality. The approach involves two essential steps. The first one concerns a new approximate mathematical model that admits a closed-form solution with respect to a set of new variables. The second step is the determination of an infinitesimal contact transformation that allows to navigate between the new and the original variables. This contact transformation is obtained in exact form, and afterwards a Taylor series approximation is proposed in order to make all the computations explicit. The aforementioned transformation accommodates both perturbations, improving the accuracy of the orbit predictions by one order of magnitude with respect to the case when the atmospheric drag is absent from the transformation. Numerical simulations are performed for a low Earth orbit starting at an altitude of 350 km, and they show that the incorporation of drag terms into the contact transformation generates an error reduction by a factor of 7 in the position vector. The proposed method aims at improving the accuracy of analytic orbit propagation and transforming it into a viable alternative to the computationally intensive numerical methods.
Water movement through plant roots - exact solutions of the water flow equation in roots with linear or exponential piecewise hydraulic properties

NASA Astrophysics Data System (ADS)

Meunier, Félicien; Couvreur, Valentin; Draye, Xavier; Zarebanadkouki, Mohsen; Vanderborght, Jan; Javaux, Mathieu

2017-12-01

In 1978, Landsberg and Fowkes presented a solution of the water flow equation inside a root with uniform hydraulic properties. These properties are root radial conductivity and axial conductance, which control, respectively, the radial water flow between the root surface and xylem and the axial flow within the xylem. From the solution for the xylem water potential, functions that describe the radial and axial flow along the root axis were derived. These solutions can also be used to derive root macroscopic parameters that are potential input parameters of hydrological and crop models. In this paper, novel analytical solutions of the water flow equation are developed for roots whose hydraulic properties vary along their axis, which is the case for most plants. We derived solutions for single roots with linear or exponential variations of hydraulic properties with distance to root tip. These solutions were subsequently combined to construct single roots with complex hydraulic property profiles. The analytical solutions allow one to verify numerical solutions and to get a generalization of the hydric behaviour with the main influencing parameters of the solutions. The resulting flow distributions in heterogeneous roots differed from those in uniform roots and simulations led to more regular, less abrupt variations of xylem suction or radial flux along root axes. The model could successfully be applied to maize effective root conductance measurements to derive radial and axial hydraulic properties. We also show that very contrasted root water uptake patterns arise when using either uniform or heterogeneous root hydraulic properties in a soil-root model. The optimal root radius that maximizes water uptake under a carbon cost constraint was also studied. The optimal radius was shown to be highly dependent on the root hydraulic properties and close to observed properties in maize roots. We finally used the obtained functions for evaluating the impact of root maturation
Effects of turbulent hyporheic mixing on reach-scale solute transport

NASA Astrophysics Data System (ADS)

Roche, K. R.; Li, A.; Packman, A. I.

2017-12-01

Turbulence rapidly mixes solutes and fine particles into coarse-grained streambeds. Both hyporheic exchange rates and spatial variability of hyporheic mixing are known to be controlled by turbulence, but it is unclear how turbulent mixing influences mass transport at the scale of stream reaches. We used a process-based particle-tracking model to simulate local- and reach-scale solute transport for a coarse-bed stream. Two vertical mixing profiles, one with a smooth transition from in-stream to hyporheic transport conditions and a second with enhanced turbulent transport at the sediment-water interface, were fit to steady-state subsurface concentration profiles observed in laboratory experiments. The mixing profile with enhanced interfacial transport better matched the observed concentration profiles and overall mass retention in the streambed. The best-fit mixing profiles were then used to simulate upscaled solute transport in a stream. Enhanced mixing coupled in-stream and hyporheic solute transport, causing solutes exchanged into the shallow subsurface to have travel times similar to the water column. This extended the exponential region of the in-stream solute breakthrough curve, and delayed the onset of the heavy power-law tailing induced by deeper and slower hyporheic porewater velocities. Slopes of observed power-law tails were greater than those predicted from stochastic transport theory, and also changed in time. In addition, rapid hyporheic transport velocities truncated the hyporheic residence time distribution by causing mass to exit the stream reach via subsurface advection, yielding strong exponential tempering in the in-stream breakthrough curves at the timescale of advective hyporheic transport through the reach. These results show that strong turbulent mixing across the sediment-water interface violates the conventional separation of surface and subsurface flows used in current models for solute transport in rivers. Instead, the full distribution of
Rheological and micro-Raman time-series characterization of enzyme sol–gel solution toward morphological control of electrospun fibers

PubMed Central

Oriero, Dennis A; Weakley, Andrew T; Aston, D Eric

2012-01-01

Rheological and micro-Raman time-series characterizations were used to investigate the chemical evolutionary changes of silica sol–gel mixtures for electrospinning fibers to immobilize an enzyme (tyrosinase). Results of dynamic rheological measurements agreed with the expected structural transitions associated with reacting sol–gel systems. The electrospinning sols exhibited shear-thinning behavior typical of a power law model. Ultrafine (200–300 nm diameter) fibers were produced at early and late times within the reaction window of approximately one hour from initial mixing of sol solutions with and without enzyme; diameter distributions of these fibers showed much smaller deviations than expected. The enzyme markedly increased magnitudes of both elastic and viscous moduli but had no significant impact on final fiber diameters, suggesting that the shear-thinning behavior of both sol–gel mixtures is dominant in the fiber elongation process. The time course and scale for the electrospinning batch fabrication show strong correlations between the magnitudes in rheological property changes over time and the chemical functional group evolution obtained from micro-Raman time-series analysis of the reacting sol–gel systems. PMID:27877486
Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.
Univariate Time Series Prediction of Solar Power Using a Hybrid Wavelet-ARMA-NARX Prediction Method

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

Nazaripouya, Hamidreza; Wang, Yubo; Chu, Chi-Cheng

This paper proposes a new hybrid method for super short-term solar power prediction. Solar output power usually has a complex, nonstationary, and nonlinear characteristic due to intermittent and time varying behavior of solar radiance. In addition, solar power dynamics is fast and is inertia less. An accurate super short-time prediction is required to compensate for the fluctuations and reduce the impact of solar power penetration on the power system. The objective is to predict one step-ahead solar power generation based only on historical solar power time series data. The proposed method incorporates discrete wavelet transform (DWT), Auto-Regressive Moving Average (ARMA)more » models, and Recurrent Neural Networks (RNN), while the RNN architecture is based on Nonlinear Auto-Regressive models with eXogenous inputs (NARX). The wavelet transform is utilized to decompose the solar power time series into a set of richer-behaved forming series for prediction. ARMA model is employed as a linear predictor while NARX is used as a nonlinear pattern recognition tool to estimate and compensate the error of wavelet-ARMA prediction. The proposed method is applied to the data captured from UCLA solar PV panels and the results are compared with some of the common and most recent solar power prediction methods. The results validate the effectiveness of the proposed approach and show a considerable improvement in the prediction precision.« less
The Exponential Expansion of Simulation: How Simulation has Grown as a Research Tool

DTIC Science & Technology

2012-09-01

exponential growth of computing power. Although other analytic approaches also benefit from this trend, keyword searches of several scholarly search ... engines reveal that the reliance on simulation is increasing more rapidly. A descriptive analysis paints a compelling picture: simulation is frequently

Calculation of power spectrums from digital time series with missing data points

NASA Technical Reports Server (NTRS)

Murray, C. W., Jr.

1980-01-01

Two algorithms are developed for calculating power spectrums from the autocorrelation function when there are missing data points in the time series. Both methods use an average sampling interval to compute lagged products. One method, the correlation function power spectrum, takes the discrete Fourier transform of the lagged products directly to obtain the spectrum, while the other, the modified Blackman-Tukey power spectrum, takes the Fourier transform of the mean lagged products. Both techniques require fewer calculations than other procedures since only 50% to 80% of the maximum lags need be calculated. The algorithms are compared with the Fourier transform power spectrum and two least squares procedures (all for an arbitrary data spacing). Examples are given showing recovery of frequency components from simulated periodic data where portions of the time series are missing and random noise has been added to both the time points and to values of the function. In addition the methods are compared using real data. All procedures performed equally well in detecting periodicities in the data.
Evidence of the Exponential Decay Emission in the Swift Gamma-ray Bursts

NASA Technical Reports Server (NTRS)

Sakamoto, T.; Sato, G.; Hill, J.E.; Krimm, H.A.; Yamazaki, R.; Takami, K.; Swindell, S.; Osborne, J.P.

2007-01-01

We present a systematic study of the steep decay emission of gamma-ray bursts (GRBs) observed by the Swift X-Ray Telescope (XRT). In contrast to the analysis in recent literature, instead of extrapolating the data of Burst Alert Telescope (BAT) down into the XRT energy range, we extrapolated the XRT data up to the BAT energy range, 15-25 keV, to produce the BAT and XRT composite light curve. Based on our composite light curve fitting, we have confirmed the existence of an exponential decay component which smoothly connects the BAT prompt data to the XRT steep decay for several GRBs. We also find that the XRT steep decay for some of the bursts can be well fitted by a combination of a power-law with an exponential decay model. We discuss that this exponential component may be the emission from an external shock and a sign of the deceleration of the outflow during the prompt phase.
A series-resonant silicon-controlled-rectifier power processor for ion thrusters

NASA Technical Reports Server (NTRS)

Shumaker, H. A.; Biess, J. J.; Goldin, D. S.

1973-01-01

A program to develop a power processing system for ion thrusters is presented. Basic operation of the silicon controlled rectifier series inverter circuitry is examined. The approach for synthesizing such circuits into a system which limits the electrical stress levels on the power source, semiconductor switching elements, and the ion thruster load is described. Experimental results are presented for a 2.5-kW breadboard system designed to operate a 20-cm ion thruster.
The true quantum face of the "exponential" decay: Unstable systems in rest and in motion

NASA Astrophysics Data System (ADS)

Urbanowski, K.

2017-12-01

Results of theoretical studies and numerical calculations presented in the literature suggest that the survival probability P0(t) has the exponential form starting from times much smaller than the lifetime τ up to times t ⪢τ and that P0(t) exhibits inverse power-law behavior at the late time region for times longer than the so-called crossover time T ⪢ τ (The crossover time T is the time when the late time deviations of P0(t) from the exponential form begin to dominate). More detailed analysis of the problem shows that in fact the survival probability P0(t) can not take the pure exponential form at any time interval including times smaller than the lifetime τ or of the order of τ and it has has an oscillating form. We also study the survival probability of moving relativistic unstable particles with definite momentum . These studies show that late time deviations of the survival probability of these particles from the exponential-like form of the decay law, that is the transition times region between exponential-like and non-exponential form of the survival probability, should occur much earlier than it follows from the classical standard considerations.
Power Mobility Training for Young Children with Multiple, Severe Impairments: A Case Series.

PubMed

Kenyon, Lisa K; Farris, John P; Gallagher, Cailee; Hammond, Lyndsay; Webster, Lauren M; Aldrich, Naomi J

2017-02-01

Young children with neurodevelopmental conditions are often limited in their ability to explore and learn from their environment. The purposes of this case series were to (1) describe the outcomes of using an alternative power mobility device with young children who had multiple, severe impairments; (2) develop power mobility training methods for use with these children; and (3) determine the feasibility of using various outcome measures. Three children with cerebral palsy (Gross Motor Function Classification System Levels IV, V, and V) ages 17 months to 3.5 years participated in the case series. Examination included the Pediatric Evaluation of Disability Inventory-Computer Adaptive Test (PEDI-CAT) and the Dimensions of Mastery Questionnaire (DMQ). An individualized, engaging power mobility training environment was created for each participant. Intervention was provided for 60 minutes per week over 12 weeks. All participants exhibited improvements in power mobility skills. Post-intervention PEDI-CAT scores increased in various domains for all participants. Post-intervention DMQ scores improved in Participants 1 and 2. The participants appeared to make improvements in their beginning power mobility skills. Additional research is planned to further explore the impact of power mobility training in this unique population.
CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

PubMed

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2013-04-01

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling , or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.
CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS

PubMed Central

Shalizi, Cosma Rohilla; Rinaldo, Alessandro

2015-01-01

The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM’s expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses. PMID:26166910
Synthesis and characterization of the LDH hydrotalcite-pyroaurite solid-solution series

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

Rozov, K., E-mail: urs.berner@psi.c; Rock-Water Interaction Group, Institute of Geological Sciences, University of Bern, Baltzerstrasse 3, CH-3012; Berner, U.

2010-08-15

A layered double hydroxide (LDH) hydrotalcite-pyroaurite solid-solution series Mg{sub 3}(Al{sub x}Fe{sub 1-x})(CO{sub 3}){sub 0.5}(OH){sub 8} with 1 - x = 0.0, 0.1...1.0 was prepared by co-precipitation at 23 {+-} 2 {sup o}C and pH = 11.40 {+-} 0.03. The compositions of the solids and the reaction solutions were determined using ICP-OES (Mg, Al, Fe, and Na) and TGA techniques (CO{sub 3}{sup 2-}, OH{sup -}, and H{sub 2}O). Powder X-ray diffraction was employed for phase identification and determination of the unit cell parameters a{sub o} and c{sub o} from peak profile analysis. The parameter a{sub o} = b{sub o} was foundmore » to be a linear function of the composition. This dependency confirms Vegard's law and indicates the presence of a continuous solid-solution series in the hydrotalcite-pyroaurite system. TGA data show that the temperatures at which interlayer H{sub 2}O molecules and CO{sub 3}{sup 2-} anions are lost, and at which dehydroxylation of the layers occurs, all decrease with increasing mole fraction of iron within the hydroxide layers. Features of the Raman spectra also depend on the iron content. The absence of Raman bands for Fe-rich members (x{sub Fe} > 0.5) is attributed to possible fluorescence phenomena. Based on chemical analysis of both the solids and the reaction solutions after synthesis, preliminary Gibbs free energies of formation have been estimated. Values of {Delta}G{sup o}{sub f}(hydrotalcite) = - 3773.3 {+-} 51.4 kJ/mol and {Delta}G{sup o}{sub f}(pyroaurite) = - 3294.5 {+-} 95.8 kJ/mol were found at 296.15 K. The formal uncertainties of these formations constants are very high. Derivation of more precise values would require carefully designed solubility experiments and improved analytical techniques.« less
Theory, computation, and application of exponential splines

NASA Technical Reports Server (NTRS)

Mccartin, B. J.

1981-01-01

A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Rotating flow of a nanofluid due to an exponentially stretching surface with suction

NASA Astrophysics Data System (ADS)

Salleh, Siti Nur Alwani; Bachok, Norfifah; Arifin, Norihan Md

2017-08-01

An analysis of the rotating nanofluid flow past an exponentially stretched surface with the presence of suction is studied in this work. Three different types of nanoparticles, namely, copper, titania and alumina are considered. The system of ordinary differential equations is computed numerically using a shooting method in Maple software after being transformed from the partial differential equations. This transformation has considered the similarity transformations in exponential form. The physical effect of the rotation, suction and nanoparticle volume fraction parameters on the rotating flow and heat transfer phenomena is investigated and has been described in detail through graphs. The dual solutions are found to appear when the governing parameters reach a certain range.
How bootstrap can help in forecasting time series with more than one seasonal pattern

NASA Astrophysics Data System (ADS)

Cordeiro, Clara; Neves, M. Manuela

2012-09-01

The search for the future is an appealing challenge in time series analysis. The diversity of forecasting methodologies is inevitable and is still in expansion. Exponential smoothing methods are the launch platform for modelling and forecasting in time series analysis. Recently this methodology has been combined with bootstrapping revealing a good performance. The algorithm (Boot. EXPOS) using exponential smoothing and bootstrap methodologies, has showed promising results for forecasting time series with one seasonal pattern. In case of more than one seasonal pattern, the double seasonal Holt-Winters methods and the exponential smoothing methods were developed. A new challenge was now to combine these seasonal methods with bootstrap and carry over a similar resampling scheme used in Boot. EXPOS procedure. The performance of such partnership will be illustrated for some well-know data sets existing in software.
Quantum decay model with exact explicit analytical solution

NASA Astrophysics Data System (ADS)

Marchewka, Avi; Granot, Er'El

2009-01-01

A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.
An exact solution on unsteady MHD free convection chemically reacting silver nanofluid flow past an exponentially accelerated vertical plate through porous medium

NASA Astrophysics Data System (ADS)

Kumaresan, E.; Vijaya Kumar, A. G.; Rushi Kumar, B.

2017-11-01

This article studies, an exact solution of unsteady MHD free convection boundary-layer flow of a silver nanofluid past an exponentially accelerated moving vertical plate through aporous medium in the presence of thermal radiation, transverse applied amagnetic field, radiation absorption and Heat generation or absorption with chemical reaction are investigated theoretically. We consider nanofluids contain spherical shaped nanoparticle of silverwith a nanoparticle volume concentration range smaller than or equal to 0.04. This phenomenon is modeled in the form of partial differential equations with initial boundary conditions. Some suitable dimensional variables are introduced. The corresponding dimensionless equations with boundary conditions are solved by using Laplace transform technique. The exact solutions for velocity, energy, and species are obtained, also the corresponding numerical values of nanofluid velocity, temperature and concentration profiles are represented graphically. The expressions for skin friction coefficient, the rate of heat transfer and mass transfer are derived. The present study finds applications involving heat transfer, enhancement of thermal conductivity and other applications like transportation, industrial cooling applications, heating buildings and reducing pollution, energy applications and solar absorption. The effect of heat transfer is found to be more pronounced in a silver-water nanofluid than in the other nanofluids.
A new approach for measuring power spectra and reconstructing time series in active galactic nuclei

NASA Astrophysics Data System (ADS)

Li, Yan-Rong; Wang, Jian-Min

2018-05-01

We provide a new approach to measure power spectra and reconstruct time series in active galactic nuclei (AGNs) based on the fact that the Fourier transform of AGN stochastic variations is a series of complex Gaussian random variables. The approach parametrizes a stochastic series in frequency domain and transforms it back to time domain to fit the observed data. The parameters and their uncertainties are derived in a Bayesian framework, which also allows us to compare the relative merits of different power spectral density models. The well-developed fast Fourier transform algorithm together with parallel computation enables an acceptable time complexity for the approach.
On the Matrix Exponential Function

ERIC Educational Resources Information Center

Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai

2006-01-01

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.
A stochastic evolutionary model generating a mixture of exponential distributions

NASA Astrophysics Data System (ADS)

Fenner, Trevor; Levene, Mark; Loizou, George

2016-02-01

Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in [T. Fenner, M. Levene, G. Loizou, J. Stat. Mech. 2015, P08015 (2015)] so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.
Determination of the functioning parameters in asymmetrical flow field-flow fractionation with an exponential channel.

PubMed

Déjardin, P

2013-08-30

The flow conditions in normal mode asymmetric flow field-flow fractionation are determined to approach the high retention limit with the requirement d≪l≪w, where d is the particle diameter, l the characteristic length of the sample exponential distribution and w the channel height. The optimal entrance velocity is determined from the solute characteristics, the channel geometry (exponential to rectangular) and the membrane properties, according to a model providing the velocity fields all over the cell length. In addition, a method is proposed for in situ determination of the channel height. Copyright © 2013 Elsevier B.V. All rights reserved.
Regulation of Renewable Energy Sources to Optimal Power Flow Solutions Using ADMM

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

Dall-Anese, Emiliano; Zhang, Yijian; Hong, Mingyi

This paper considers power distribution systems featuring renewable energy sources (RESs), and develops a distributed optimization method to steer the RES output powers to solutions of AC optimal power flow (OPF) problems. The design of the proposed method leverages suitable linear approximations of the AC-power flow equations, and is based on the Alternating Direction Method of Multipliers (ADMM). Convergence of the RES-inverter output powers to solutions of the OPF problem is established under suitable conditions on the stepsize as well as mismatches between the commanded setpoints and actual RES output powers. In a broad sense, the methods and results proposedmore » here are also applicable to other distributed optimization problem setups with ADMM and inexact dual updates.« less
On the origin of non-exponential fluorescence decays in enzyme-ligand complex

NASA Astrophysics Data System (ADS)

Wlodarczyk, Jakub; Kierdaszuk, Borys

2004-05-01

Complex fluorescence decays have usually been analyzed with the aid of a multi-exponential model, but interpretation of the individual exponential terms has not been adequately characterized. In such cases the intensity decays were also analyzed in terms of the continuous lifetime distribution as a consequence of an interaction of fluorophore with environment, conformational heterogeneity or their dynamical nature. We show that non-exponential fluorescence decay of the enzyme-ligand complexes may results from time dependent energy transport. The latter, to our opinion, may be accounted for by electron transport from the protein tyrosines to their neighbor residues. We introduce the time-dependent hopping rate in the form v(t)~(a+bt)-1. This in turn leads to the luminescence decay function in the form I(t)=Ioexp(-t/τ1)(1+lt/γτ2)-γ. Such a decay function provides good fits to highly complex fluorescence decays. The power-like tail implies the time hierarchy in migration energy process due to the hierarchical energy-level structure. Moreover, such a power-like term is a manifestation of so called Tsallis nonextensive statistic and is suitable for description of the systems with long-range interactions, memory effect as well as with fluctuations of characteristic lifetime of fluorescence. The proposed decay function was applied in analysis of fluorescence decays of tyrosine protein, i.e. the enzyme purine nucleoside phosphorylase from E. coli in a complex with formycin A (an inhibitor) and orthophosphate (a co-substrate).
A General Exponential Framework for Dimensionality Reduction.

PubMed

Wang, Su-Jing; Yan, Shuicheng; Yang, Jian; Zhou, Chun-Guang; Fu, Xiaolan

2014-02-01

As a general framework, Laplacian embedding, based on a pairwise similarity matrix, infers low dimensional representations from high dimensional data. However, it generally suffers from three issues: 1) algorithmic performance is sensitive to the size of neighbors; 2) the algorithm encounters the well known small sample size (SSS) problem; and 3) the algorithm de-emphasizes small distance pairs. To address these issues, here we propose exponential embedding using matrix exponential and provide a general framework for dimensionality reduction. In the framework, the matrix exponential can be roughly interpreted by the random walk over the feature similarity matrix, and thus is more robust. The positive definite property of matrix exponential deals with the SSS problem. The behavior of the decay function of exponential embedding is more significant in emphasizing small distance pairs. Under this framework, we apply matrix exponential to extend many popular Laplacian embedding algorithms, e.g., locality preserving projections, unsupervised discriminant projections, and marginal fisher analysis. Experiments conducted on the synthesized data, UCI, and the Georgia Tech face database show that the proposed new framework can well address the issues mentioned above.

Performance of time-series methods in forecasting the demand for red blood cell transfusion.

PubMed

Pereira, Arturo

2004-05-01

Planning the future blood collection efforts must be based on adequate forecasts of transfusion demand. In this study, univariate time-series methods were investigated for their performance in forecasting the monthly demand for RBCs at one tertiary-care, university hospital. Three time-series methods were investigated: autoregressive integrated moving average (ARIMA), the Holt-Winters family of exponential smoothing models, and one neural-network-based method. The time series consisted of the monthly demand for RBCs from January 1988 to December 2002 and was divided into two segments: the older one was used to fit or train the models, and the younger to test for the accuracy of predictions. Performance was compared across forecasting methods by calculating goodness-of-fit statistics, the percentage of months in which forecast-based supply would have met the RBC demand (coverage rate), and the outdate rate. The RBC transfusion series was best fitted by a seasonal ARIMA(0,1,1)(0,1,1)(12) model. Over 1-year time horizons, forecasts generated by ARIMA or exponential smoothing laid within the +/- 10 percent interval of the real RBC demand in 79 percent of months (62% in the case of neural networks). The coverage rate for the three methods was 89, 91, and 86 percent, respectively. Over 2-year time horizons, exponential smoothing largely outperformed the other methods. Predictions by exponential smoothing laid within the +/- 10 percent interval of real values in 75 percent of the 24 forecasted months, and the coverage rate was 87 percent. Over 1-year time horizons, predictions of RBC demand generated by ARIMA or exponential smoothing are accurate enough to be of help in the planning of blood collection efforts. For longer time horizons, exponential smoothing outperforms the other forecasting methods.
Equivalences between nonuniform exponential dichotomy and admissibility

NASA Astrophysics Data System (ADS)

Zhou, Linfeng; Lu, Kening; Zhang, Weinian

2017-01-01

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

NASA Astrophysics Data System (ADS)

Wan, Li; Zhou, Qinghua

2007-11-01

The stability property of bidirectional associate memory (BAM) neural networks with time-varying delays and diffusion terms are considered. By using the method of variation parameter and inequality technique, the delay-independent sufficient conditions to guarantee the uniqueness and global exponential stability of the equilibrium solution of such networks are established.
The Prediction of Teacher Turnover Employing Time Series Analysis.

ERIC Educational Resources Information Center

Costa, Crist H.

The purpose of this study was to combine knowledge of teacher demographic data with time-series forecasting methods to predict teacher turnover. Moving averages and exponential smoothing were used to forecast discrete time series. The study used data collected from the 22 largest school districts in Iowa, designated as FACT schools. Predictions…
Power-balancing instantaneous optimization energy management for a novel series-parallel hybrid electric bus

NASA Astrophysics Data System (ADS)

Sun, Dongye; Lin, Xinyou; Qin, Datong; Deng, Tao

2012-11-01

Energy management(EM) is a core technique of hybrid electric bus(HEB) in order to advance fuel economy performance optimization and is unique for the corresponding configuration. There are existing algorithms of control strategy seldom take battery power management into account with international combustion engine power management. In this paper, a type of power-balancing instantaneous optimization(PBIO) energy management control strategy is proposed for a novel series-parallel hybrid electric bus. According to the characteristic of the novel series-parallel architecture, the switching boundary condition between series and parallel mode as well as the control rules of the power-balancing strategy are developed. The equivalent fuel model of battery is implemented and combined with the fuel of engine to constitute the objective function which is to minimize the fuel consumption at each sampled time and to coordinate the power distribution in real-time between the engine and battery. To validate the proposed strategy effective and reasonable, a forward model is built based on Matlab/Simulink for the simulation and the dSPACE autobox is applied to act as a controller for hardware in-the-loop integrated with bench test. Both the results of simulation and hardware-in-the-loop demonstrate that the proposed strategy not only enable to sustain the battery SOC within its operational range and keep the engine operation point locating the peak efficiency region, but also the fuel economy of series-parallel hybrid electric bus(SPHEB) dramatically advanced up to 30.73% via comparing with the prototype bus and a similar improvement for PBIO strategy relative to rule-based strategy, the reduction of fuel consumption is up to 12.38%. The proposed research ensures the algorithm of PBIO is real-time applicability, improves the efficiency of SPHEB system, as well as suite to complicated configuration perfectly.
Exponential approximations in optimal design

NASA Technical Reports Server (NTRS)

Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

1990-01-01

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Analysis of Operating Modes of Stand-Alone Series Controller of Power Flows for Overhead Power Transmission Lines

NASA Astrophysics Data System (ADS)

Astashev, M. G.; Panfilov, D. I.; Seregin, D. A.; Chernyshev, A. A.

2017-12-01

The features of using the bridge voltage inverter in small-size stand-alone series controllers of power flows (PFSC) for overhead power transmission lines (OPTL) are examined. The basic processes in the converter during transient and steady state modes were analyzed. The basic relations for calculating the electromagnetic processes taking into account the energy loss in the circuit and without it were received. A simulation model is proposed of a converter that makes it possible to study its operating modes during the formation of reactance introduced into the overhead power transmission line. The results of simulation of operating modes of the PFSC are presented.
Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.
Early-Time Solution of the Horizontal Unconfined Aquifer in the Buildup Phase

NASA Astrophysics Data System (ADS)

Gravanis, Elias; Akylas, Evangelos

2017-10-01

We derive the early-time solution of the Boussinesq equation for the horizontal unconfined aquifer in the buildup phase under constant recharge and zero inflow. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turns out to be asymptotic and it is regularized by resummation techniques that are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self-similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution.
Design of Distributed Controllers Seeking Optimal Power Flow Solutions Under Communication Constraints

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

Dall'Anese, Emiliano; Simonetto, Andrea; Dhople, Sairaj

This paper focuses on power distribution networks featuring inverter-interfaced distributed energy resources (DERs), and develops feedback controllers that drive the DER output powers to solutions of time-varying AC optimal power flow (OPF) problems. Control synthesis is grounded on primal-dual-type methods for regularized Lagrangian functions, as well as linear approximations of the AC power-flow equations. Convergence and OPF-solution-tracking capabilities are established while acknowledging: i) communication-packet losses, and ii) partial updates of control signals. The latter case is particularly relevant since it enables asynchronous operation of the controllers where DER setpoints are updated at a fast time scale based on local voltagemore » measurements, and information on the network state is utilized if and when available, based on communication constraints. As an application, the paper considers distribution systems with high photovoltaic integration, and demonstrates that the proposed framework provides fast voltage-regulation capabilities, while enabling the near real-time pursuit of solutions of AC OPF problems.« less
Series Connected Converter for Control of Multi-Bus Spacecraft Power Utility

NASA Technical Reports Server (NTRS)

Beach, Raymond F. (Inventor); Brush, Andy (Inventor)

1997-01-01

The invention provides a power system using series connected regulators. Power from a source, such as a solar array, is processed through the regulators and provided to corresponding buses used to charge a battery and supply loads. The regulators employ a bypass loop around a DC-DC converter. The bypass loop connects a hot input of the converter to a return output, preferably though an inductor. Part of the current from the source passes through the bypass loop to the power bus. The converter bucks or boosts the voltage from the source to maintain the desired voltage at the bus. Thus, only part of the power is processed through the converter. The converter can also be used without the bypass loop to provide isolation. All of the converters can be substantially identical.
Fully solution-processed, transparent organic power-generating polarizer

NASA Astrophysics Data System (ADS)

Chou, Wei-Yu; Hsu, Fang-Chi; Chen, Yang-Fang

2017-03-01

We fabricate transparent organic power-generating polarizer by all solution process. Based on the conventional indium-tin-oxide-coated glass as the bottom cathode, the subsequent layers are prepared by a combination of solution processing methods. Sprayed silver nanowires film serves as the top anode and can transmit greater than 80% of the visible light with sheet resistance of 16 Ω/□. By adopting the quasi-bilayer structure for the photoactive layer composed of rubbed polymer donors to produce anisotropic optical property underneath fullerene acceptors, the finished device demonstrates a power conversion efficiency of 1.36% with unpolarized light, a dichroic ratio of 3.2, and a high short circuit current ratio of 2.6 with polarized light. Our proposed fabrication procedures of devices take into account not only the cost-effective production, but also the flexibility of devices for applying in flexible, scalable circuits to advance the development of future technology.
Three-Dimensional Flow of Nanofluid Induced by an Exponentially Stretching Sheet: An Application to Solar Energy

PubMed Central

Khan, Junaid Ahmad; Mustafa, M.; Hayat, T.; Sheikholeslami, M.; Alsaedi, A.

2015-01-01

This work deals with the three-dimensional flow of nanofluid over a bi-directional exponentially stretching sheet. The effects of Brownian motion and thermophoretic diffusion of nanoparticles are considered in the mathematical model. The temperature and nanoparticle volume fraction at the sheet are also distributed exponentially. Local similarity solutions are obtained by an implicit finite difference scheme known as Keller-box method. The results are compared with the existing studies in some limiting cases and found in good agreement. The results reveal the existence of interesting Sparrow-Gregg-type hills for temperature distribution corresponding to some range of parametric values. PMID:25785857
A new modification in the exponential rational function method for nonlinear fractional differential equations

NASA Astrophysics Data System (ADS)

Ahmed, Naveed; Bibi, Sadaf; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-02-01

We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.
AN EMPIRICAL FORMULA FOR THE DISTRIBUTION FUNCTION OF A THIN EXPONENTIAL DISC

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

Sharma, Sanjib; Bland-Hawthorn, Joss

2013-08-20

An empirical formula for a Shu distribution function that reproduces a thin disc with exponential surface density to good accuracy is presented. The formula has two free parameters that specify the functional form of the velocity dispersion. Conventionally, this requires the use of an iterative algorithm to produce the correct solution, which is computationally taxing for applications like Markov Chain Monte Carlo model fitting. The formula has been shown to work for flat, rising, and falling rotation curves. Application of this methodology to one of the Dehnen distribution functions is also shown. Finally, an extension of this formula to reproducemore » velocity dispersion profiles that are an exponential function of radius is also presented. Our empirical formula should greatly aid the efficient comparison of disc models with large stellar surveys or N-body simulations.« less
Exponential Methods for the Time Integration of Schroedinger Equation

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

Cano, B.; Gonzalez-Pachon, A.

2010-09-30

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.
Testing predictions of the quantum landscape multiverse 2: the exponential inflationary potential

NASA Astrophysics Data System (ADS)

Di Valentino, Eleonora; Mersini-Houghton, Laura

2017-03-01

The 2015 Planck data release tightened the region of the allowed inflationary models. Inflationary models with convex potentials have now been ruled out since they produce a large tensor to scalar ratio. Meanwhile the same data offers interesting hints on possible deviations from the standard picture of CMB perturbations. Here we revisit the predictions of the theory of the origin of the universe from the landscape multiverse for the case of exponential inflation, for two reasons: firstly to check the status of the anomalies associated with this theory, in the light of the recent Planck data; secondly, to search for a counterexample whereby new physics modifications may bring convex inflationary potentials, thought to have been ruled out, back into the region of potentials allowed by data. Using the exponential inflation as an example of convex potentials, we find that the answer to both tests is positive: modifications to the perturbation spectrum and to the Newtonian potential of the universe originating from the quantum entanglement, bring the exponential potential, back within the allowed region of current data; and, the series of anomalies previously predicted in this theory, is still in good agreement with current data. Hence our finding for this convex potential comes at the price of allowing for additional thermal relic particles, equivalently dark radiation, in the early universe.
Hardware accelerator of convolution with exponential function for image processing applications

NASA Astrophysics Data System (ADS)

Panchenko, Ivan; Bucha, Victor

2015-12-01

In this paper we describe a Hardware Accelerator (HWA) for fast recursive approximation of separable convolution with exponential function. This filter can be used in many Image Processing (IP) applications, e.g. depth-dependent image blur, image enhancement and disparity estimation. We have adopted this filter RTL implementation to provide maximum throughput in constrains of required memory bandwidth and hardware resources to provide a power-efficient VLSI implementation.
The Secular Evolution Of Disc Galaxies And The Origin Of Exponential And Double Exponential Surface Density Profiles

NASA Astrophysics Data System (ADS)

Elmegreen, Bruce G.

2016-10-01

Exponential radial profiles are ubiquitous in spiral and dwarf Irregular galaxies, but the origin of this structural form is not understood. This talk will review the observations of exponential and double exponential disks, considering both the light and the mass profiles, and the contributions from stars and gas. Several theories for this structure will also be reviewed, including primordial collapse, bar and spiral torques, clump torques, galaxy interactions, disk viscosity and other internal processes of angular momentum exchange, and stellar scattering off of clumpy structure. The only process currently known that can account for this structure in the most theoretically difficult case is stellar scattering off disks clumps. Stellar orbit models suggest that such scattering can produce exponentials even in isolated dwarf irregulars that have no bars or spirals, little shear or viscosity, and profiles that go out too far for the classical Mestel case of primordial collapse with specific angular momentum conservation.
Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation. Part 3; Constant Stress and Cyclic Stress Experiments

NASA Technical Reports Server (NTRS)

Choi, Sung R.; Nemeth, Noel N.; Gyekenyesi, John P.

2002-01-01

The previously determined life prediction analysis based on an exponential crack-velocity formulation was examined using a variety of experimental data on advanced structural ceramics tested under constant stress and cyclic stress loading at ambient and elevated temperatures. The data fit to the relation between the time to failure and applied stress (or maximum applied stress in cyclic loading) was very reasonable for most of the materials studied. It was also found that life prediction for cyclic stress loading from data of constant stress loading in the exponential formulation was in good agreement with the experimental data, resulting in a similar degree of accuracy as compared with the power-law formulation. The major limitation in the exponential crack-velocity formulation, however, was that the inert strength of a material must be known a priori to evaluate the important slow-crack-growth (SCG) parameter n, a significant drawback as compared with the conventional power-law crack-velocity formulation.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.
Rapid growth of seed black holes in the early universe by supra-exponential accretion.

PubMed

Alexander, Tal; Natarajan, Priyamvada

2014-09-12

Mass accretion by black holes (BHs) is typically capped at the Eddington rate, when radiation's push balances gravity's pull. However, even exponential growth at the Eddington-limited e-folding time t(E) ~ few × 0.01 billion years is too slow to grow stellar-mass BH seeds into the supermassive luminous quasars that are observed when the universe is 1 billion years old. We propose a dynamical mechanism that can trigger supra-exponential accretion in the early universe, when a BH seed is bound in a star cluster fed by the ubiquitous dense cold gas flows. The high gas opacity traps the accretion radiation, while the low-mass BH's random motions suppress the formation of a slowly draining accretion disk. Supra-exponential growth can thus explain the puzzling emergence of supermassive BHs that power luminous quasars so soon after the Big Bang. Copyright © 2014, American Association for the Advancement of Science.
Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.
Comparison of Parallel and Series Hybrid Power Trains for Transit Bus Applications

DOE PAGES

Gao, Zhiming; Daw, C. Stuart; Smith, David E.; ...

2016-08-01

The fuel economy and emissions of conventional and hybrid buses equipped with emissions after treatment were evaluated via computational simulation for six representative city bus drive cycles. Both series and parallel configurations for the hybrid case were studied. The simulation results indicated that series hybrid buses have the greatest overall advantage in fuel economy. The series and parallel hybrid buses were predicted to produce similar carbon monoxide and hydrocarbon tailpipe emissions but were also predicted to have reduced tailpipe emissions of nitrogen oxides compared with the conventional bus in higher speed cycles. For the New York bus cycle, which hasmore » the lowest average speed among the cycles evaluated, the series bus tailpipe emissions were somewhat higher than they were for the conventional bus; the parallel hybrid bus had significantly lower tailpipe emissions. All three bus power trains were found to require periodic active diesel particulate filter regeneration to maintain control of particulate matter. Finally, plug-in operation of series hybrid buses appears to offer significant fuel economy benefits and is easily employed because of the relatively large battery capacity that is typical of the series hybrid configuration.« less
Comparison of Parallel and Series Hybrid Power Trains for Transit Bus Applications

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

Gao, Zhiming; Daw, C. Stuart; Smith, David E.

The fuel economy and emissions of conventional and hybrid buses equipped with emissions after treatment were evaluated via computational simulation for six representative city bus drive cycles. Both series and parallel configurations for the hybrid case were studied. The simulation results indicated that series hybrid buses have the greatest overall advantage in fuel economy. The series and parallel hybrid buses were predicted to produce similar carbon monoxide and hydrocarbon tailpipe emissions but were also predicted to have reduced tailpipe emissions of nitrogen oxides compared with the conventional bus in higher speed cycles. For the New York bus cycle, which hasmore » the lowest average speed among the cycles evaluated, the series bus tailpipe emissions were somewhat higher than they were for the conventional bus; the parallel hybrid bus had significantly lower tailpipe emissions. All three bus power trains were found to require periodic active diesel particulate filter regeneration to maintain control of particulate matter. Finally, plug-in operation of series hybrid buses appears to offer significant fuel economy benefits and is easily employed because of the relatively large battery capacity that is typical of the series hybrid configuration.« less
Stretched exponential distributions in nature and economy: ``fat tails'' with characteristic scales

NASA Astrophysics Data System (ADS)

Laherrère, J.; Sornette, D.

1998-04-01

To account quantitatively for many reported "natural" fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power law distributions. It has many advantages, among which to be economical with only two adjustable parameters with clear physical interpretation. Furthermore, it derives from a simple and generic mechanism in terms of multiplicative processes. We show that stretched exponentials describe very well the distributions of radio and light emissions from galaxies, of US GOM OCS oilfield reserve sizes, of World, US and French agglomeration sizes, of country population sizes, of daily Forex US-Mark and Franc-Mark price variations, of Vostok (near the south pole) temperature variations over the last 400 000 years, of the Raup-Sepkoski's kill curve and of citations of the most cited physicists in the world. We also discuss its potential for the distribution of earthquake sizes and fault displacements. We suggest physical interpretations of the parameters and provide a short toolkit of the statistical properties of the stretched exponentials. We also provide a comparison with other distributions, such as the shifted linear fractal, the log-normal and the recently introduced parabolic fractal distributions.
Stretched-to-compressed-exponential crossover observed in the electrical degradation kinetics of some spinel-metallic screen-printed structures

NASA Astrophysics Data System (ADS)

Balitska, V.; Shpotyuk, O.; Brunner, M.; Hadzaman, I.

2018-02-01

Thermally-induced (170 °C) degradation-relaxation kinetics is examined in screen-printed structures composed of spinel Cu0.1Ni0.1Co1.6Mn1.2O4 ceramics with conductive Ag or Ag-Pd layered electrodes. Structural inhomogeneities due to Ag and Ag-Pd diffusants in spinel phase environment play a decisive role in non-exponential kinetics of negative relative resistance drift. If Ag migration in spinel is inhibited by Pd addition due to Ag-Pd alloy, the kinetics attains stretched exponential behavior with ∼0.58 exponent, typical for one-stage diffusion in structurally-dispersive media. Under deep Ag penetration into spinel ceramics, as for thick films with Ag-layered electrodes, the degradation kinetics drastically changes, attaining features of two-step diffusing process governed by compressed-exponential dependence with power index of ∼1.68. Crossover from stretched- to compressed-exponential kinetics in spinel-metallic structures is mapped on free energy landscape of non-barrier multi-well system under strong perturbation from equilibrium, showing transition with a character downhill scenario resulting in faster than exponential decaying.
Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

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

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com; Wang, Jie, E-mail: wangjie@iun.edu

2015-07-15

We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system.
A mechanism producing power law etc. distributions

NASA Astrophysics Data System (ADS)

Li, Heling; Shen, Hongjun; Yang, Bin

2017-07-01

Power law distribution is playing an increasingly important role in the complex system study. Based on the insolvability of complex systems, the idea of incomplete statistics is utilized and expanded, three different exponential factors are introduced in equations about the normalization condition, statistical average and Shannon entropy, with probability distribution function deduced about exponential function, power function and the product form between power function and exponential function derived from Shannon entropy and maximal entropy principle. So it is shown that maximum entropy principle can totally replace equal probability hypothesis. Owing to the fact that power and probability distribution in the product form between power function and exponential function, which cannot be derived via equal probability hypothesis, can be derived by the aid of maximal entropy principle, it also can be concluded that maximal entropy principle is a basic principle which embodies concepts more extensively and reveals basic principles on motion laws of objects more fundamentally. At the same time, this principle also reveals the intrinsic link between Nature and different objects in human society and principles complied by all.
A comparative study of mixed exponential and Weibull distributions in a stochastic model replicating a tropical rainfall process

NASA Astrophysics Data System (ADS)

Abas, Norzaida; Daud, Zalina M.; Yusof, Fadhilah

2014-11-01

A stochastic rainfall model is presented for the generation of hourly rainfall data in an urban area in Malaysia. In view of the high temporal and spatial variability of rainfall within the tropical rain belt, the Spatial-Temporal Neyman-Scott Rectangular Pulse model was used. The model, which is governed by the Neyman-Scott process, employs a reasonable number of parameters to represent the physical attributes of rainfall. A common approach is to attach each attribute to a mathematical distribution. With respect to rain cell intensity, this study proposes the use of a mixed exponential distribution. The performance of the proposed model was compared to a model that employs the Weibull distribution. Hourly and daily rainfall data from four stations in the Damansara River basin in Malaysia were used as input to the models, and simulations of hourly series were performed for an independent site within the basin. The performance of the models was assessed based on how closely the statistical characteristics of the simulated series resembled the statistics of the observed series. The findings obtained based on graphical representation revealed that the statistical characteristics of the simulated series for both models compared reasonably well with the observed series. However, a further assessment using the AIC, BIC and RMSE showed that the proposed model yields better results. The results of this study indicate that for tropical climates, the proposed model, using a mixed exponential distribution, is the best choice for generation of synthetic data for ungauged sites or for sites with insufficient data within the limit of the fitted region.
Problems in Analyzing Time Series with Gaps and Their Solution with the WinABD Software Package

NASA Astrophysics Data System (ADS)

Desherevskii, A. V.; Zhuravlev, V. I.; Nikolsky, A. N.; Sidorin, A. Ya.

2017-12-01

Technologies for the analysis of time series with gaps are considered. Some algorithms of signal extraction (purification) and evaluation of its characteristics, such as rhythmic components, are discussed for series with gaps. Examples are given for the analysis of data obtained during long-term observations at the Garm geophysical test site and in other regions. The technical solutions used in the WinABD software are considered to most efficiently arrange the operation of relevant algorithms in the presence of observational defects.
Short-time microscopic dynamics of aqueous methanol solutions

NASA Astrophysics Data System (ADS)

Kalampounias, A. G.; Tsilomelekis, G.; Boghosian, S.

2012-12-01

In this paper we present the picosecond vibrational dynamics of a series of methanol aqueous solutions over a wide concentration range from dense to dilute solutions. We studied the vibrational dephasing and vibrational frequency modulation by calculating the time correlation functions of vibrational relaxation by fits in the frequency domain. This method is applied to aqueous methanol solutions xMeOH-(1 - x)H2O, where x = 0, 0.2, 0.4, 0.6, 0.8 and 1. The important finding is that the vibrational dynamics of the system become slower with increasing methanol concentration. The removal of many-body effects by having the molecules in less-crowded environments seems to be the key factor. The interpretation of the vibrational correlation function in the context of Kubo theory, which is based on the assumption that the environmental modulation arises from a single relaxation process and applied to simple liquids, is inadequate for all solutions studied. We found that the vibrational correlation functions of the solutions over the whole concentration range comply with the Rothschild approach, assuming that the environmental modulation is described by a stretched exponential decay. The evolution of the dispersion parameter α with dilution indicates the deviation of the solutions from the model simple liquid and the results are discussed in the framework of the current phenomenological status of the field.
A solid solution series of atacamite type Ni{sub 2x}Mg{sub 2−2x}Cl(OH){sub 3}

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

Bette, Sebastian; Dinnebier, Robert E.; Röder, Christian

2015-08-15

For the first time a complete solid solution series Ni{sub 2x}Mg{sub 2−2x}Cl(OH){sub 3} of an atacamite type alkaline main group metal chloride, Mg{sub 2}Cl(OH){sub 3}, and a transition group metal chloride, Ni{sub 2}Cl(OH){sub 3}, was prepared and characterized by chemical and thermal analysis as well as by Raman and IR spectroscopy, and high resolution laboratory X-ray powder diffraction. All members of the solid solution series crystallize in space group Pnam (62). The main building units of these crystal structures are distorted, edge-linked Ni/MgO{sub 4}Cl{sub 2} and Ni/MgO{sub 5}Cl octahedra. The distribution of Ni{sup 2+}- and Mg{sup 2+}-ions among these twomore » metal-sites within the solid solution series is discussed in detail. The crystallization of the solid solution phases occurs via an intermediate solid solution series, (Ni/Mg)Cl{sub 2x}(OH){sub 2−2x}, with variable Cl: OH ratio up to the 1:3 ratio according to the formula Ni{sub 2x}Mg{sub 2−2x} Cl(OH){sub 3}. For one isolated intermediate solid solution member, Ni{sub 0.70}Mg{sub 0.30}Cl{sub 0.58}(OH){sub 1.42}, the formation and crystal structure is presented as well. - Graphical abstract: For the first time a complete solid solution series, Ni{sub 2x}Mg{sub 2−2x} Cl(OH){sub 3}, was synthesized and characterized. Structure solution by revealed that Ni{sup 2+} prefers to occupy the Jahn–Teller-like distorted hole, out of two available cation sites. Substitution of Ni{sup 2+} by Mg{sup 2+} in atacamite type Ni{sub 2}Cl(OH){sub 3} results in systematic band shifts in Raman and IR spectra as well as in systematic changes in thermal properties. The α-polymorphs M{sub 2}Cl(OH){sub 3} with M=Mg{sup 2+}, Ni{sup 2+} and other divalent transition metal ions, as described in literature, were identified as separate compounds. - Highlights: • First synthesis of solid solution series between main and transition metal chloride. • Ni{sup 2+} prefers to occupy Jahn–Teller-like distorted
Design of Distributed Controllers Seeking Optimal Power Flow Solutions under Communication Constraints: Preprint

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

Dall'Anese, Emiliano; Simonetto, Andrea; Dhople, Sairaj

This paper focuses on power distribution networks featuring inverter-interfaced distributed energy resources (DERs), and develops feedback controllers that drive the DER output powers to solutions of time-varying AC optimal power flow (OPF) problems. Control synthesis is grounded on primal-dual-type methods for regularized Lagrangian functions, as well as linear approximations of the AC power-flow equations. Convergence and OPF-solution-tracking capabilities are established while acknowledging: i) communication-packet losses, and ii) partial updates of control signals. The latter case is particularly relevant since it enables asynchronous operation of the controllers where DER setpoints are updated at a fast time scale based on local voltagemore » measurements, and information on the network state is utilized if and when available, based on communication constraints. As an application, the paper considers distribution systems with high photovoltaic integration, and demonstrates that the proposed framework provides fast voltage-regulation capabilities, while enabling the near real-time pursuit of solutions of AC OPF problems.« less
Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R

USGS Publications Warehouse

Asquith, William H.

2014-01-01

The implementation characteristics of two method of L-moments (MLM) algorithms for parameter estimation of the 4-parameter Asymmetric Exponential Power (AEP4) distribution are studied using the R environment for statistical computing. The objective is to validate the algorithms for general application of the AEP4 using R. An algorithm was introduced in the original study of the L-moments for the AEP4. A second or alternative algorithm is shown to have a larger L-moment-parameter domain than the original. The alternative algorithm is shown to provide reliable parameter production and recovery of L-moments from fitted parameters. A proposal is made for AEP4 implementation in conjunction with the 4-parameter Kappa distribution to create a mixed-distribution framework encompassing the joint L-skew and L-kurtosis domains. The example application provides a demonstration of pertinent algorithms with L-moment statistics and two 4-parameter distributions (AEP4 and the Generalized Lambda) for MLM fitting to a modestly asymmetric and heavy-tailed dataset using R.
Effects of Heat Source/Sink and Chemical Reaction on MHD Maxwell Nanofluid Flow Over a Convectively Heated Exponentially Stretching Sheet Using Homotopy Analysis Method

NASA Astrophysics Data System (ADS)

Sravanthi, C. S.; Gorla, R. S. R.

2018-02-01

The aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.
Exponential Sum-Fitting of Dwell-Time Distributions without Specifying Starting Parameters

PubMed Central

Landowne, David; Yuan, Bin; Magleby, Karl L.

2013-01-01

Fitting dwell-time distributions with sums of exponentials is widely used to characterize histograms of open- and closed-interval durations recorded from single ion channels, as well as for other physical phenomena. However, it can be difficult to identify the contributing exponential components. Here we extend previous methods of exponential sum-fitting to present a maximum-likelihood approach that consistently detects all significant exponentials without the need for user-specified starting parameters. Instead of searching for exponentials, the fitting starts with a very large number of initial exponentials with logarithmically spaced time constants, so that none are missed. Maximum-likelihood fitting then determines the areas of all the initial exponentials keeping the time constants fixed. In an iterative manner, with refitting after each step, the analysis then removes exponentials with negligible area and combines closely spaced adjacent exponentials, until only those exponentials that make significant contributions to the dwell-time distribution remain. There is no limit on the number of significant exponentials and no starting parameters need be specified. We demonstrate fully automated detection for both experimental and simulated data, as well as for classical exponential-sum-fitting problems. PMID:23746510
Is it growing exponentially fast? -- Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics.

PubMed

Chowell, Gerardo; Viboud, Cécile

2016-10-01

The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing models that capture the baseline transmission characteristics in order to generate reliable epidemic forecasts. Improved models for epidemic forecasting could be achieved by identifying signature features of epidemic growth, which could inform the design of models of disease spread and reveal important characteristics of the transmission process. In particular, it is often taken for granted that the early growth phase of different growth processes in nature follow early exponential growth dynamics. In the context of infectious disease spread, this assumption is often convenient to describe a transmission process with mass action kinetics using differential equations and generate analytic expressions and estimates of the reproduction number. In this article, we carry out a simulation study to illustrate the impact of incorrectly assuming an exponential-growth model to characterize the early phase (e.g., 3-5 disease generation intervals) of an infectious disease outbreak that follows near-exponential growth dynamics. Specifically, we assess the impact on: 1) goodness of fit, 2) bias on the growth parameter, and 3) the impact on short-term epidemic forecasts. Designing transmission models and statistical approaches that more flexibly capture the profile of epidemic growth could lead to enhanced model fit, improved estimates of key transmission parameters, and more realistic epidemic forecasts.
Simulation-based power calculation for designing interrupted time series analyses of health policy interventions.

PubMed

Zhang, Fang; Wagner, Anita K; Ross-Degnan, Dennis

2011-11-01

Interrupted time series is a strong quasi-experimental research design to evaluate the impacts of health policy interventions. Using simulation methods, we estimated the power requirements for interrupted time series studies under various scenarios. Simulations were conducted to estimate the power of segmented autoregressive (AR) error models when autocorrelation ranged from -0.9 to 0.9 and effect size was 0.5, 1.0, and 2.0, investigating balanced and unbalanced numbers of time periods before and after an intervention. Simple scenarios of autoregressive conditional heteroskedasticity (ARCH) models were also explored. For AR models, power increased when sample size or effect size increased, and tended to decrease when autocorrelation increased. Compared with a balanced number of study periods before and after an intervention, designs with unbalanced numbers of periods had less power, although that was not the case for ARCH models. The power to detect effect size 1.0 appeared to be reasonable for many practical applications with a moderate or large number of time points in the study equally divided around the intervention. Investigators should be cautious when the expected effect size is small or the number of time points is small. We recommend conducting various simulations before investigation. Copyright © 2011 Elsevier Inc. All rights reserved.
Stochastic exponential synchronization of memristive neural networks with time-varying delays via quantized control.

PubMed

Zhang, Wanli; Yang, Shiju; Li, Chuandong; Zhang, Wei; Yang, Xinsong

2018-08-01

This paper focuses on stochastic exponential synchronization of delayed memristive neural networks (MNNs) by the aid of systems with interval parameters which are established by using the concept of Filippov solution. New intermittent controller and adaptive controller with logarithmic quantization are structured to deal with the difficulties induced by time-varying delays, interval parameters as well as stochastic perturbations, simultaneously. Moreover, not only control cost can be reduced but also communication channels and bandwidth are saved by using these controllers. Based on novel Lyapunov functions and new analytical methods, several synchronization criteria are established to realize the exponential synchronization of MNNs with stochastic perturbations via intermittent control and adaptive control with or without logarithmic quantization. Finally, numerical simulations are offered to substantiate our theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Theoretical analysis of exponential transversal method of lines for the diffusion equation

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

Salazar, A.; Raydan, M.; Campo, A.

1996-12-31

Recently a new approximate technique to solve the diffusion equation was proposed by Campo and Salazar. This new method is inspired on the Method of Lines (MOL) with some insight coming from the method of separation of variables. The proposed method, the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly good numerical results. In this paper, the authors study the theoretical properties of ETMOL in depth. In particular, consistency,more » stability and convergence are established in the framework of the heat/mass diffusion equation. In most practical applications the method presents a very reduced truncation error in time and its different versions are proven to be unconditionally stable in the Fourier sense. Convergence of the solutions is then established. The theory is corroborated by several analytical/numerical experiments.« less
Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory

NASA Astrophysics Data System (ADS)

Wang, Na; Li, Dong; Wang, Qiwen

2012-12-01

The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government
Power and Roots by Recursion.

ERIC Educational Resources Information Center

Aieta, Joseph F.

1987-01-01

This article illustrates how questions from elementary finance can serve as motivation for studying high order powers, roots, and exponential functions using Logo procedures. A second discussion addresses a relatively unknown algorithm for the trigonometric exponential and hyperbolic functions. (PK)
Local perturbations perturb—exponentially-locally

NASA Astrophysics Data System (ADS)

De Roeck, W.; Schütz, M.

2015-06-01

We elaborate on the principle that for gapped quantum spin systems with local interaction, "local perturbations [in the Hamiltonian] perturb locally [the groundstate]." This principle was established by Bachmann et al. [Commun. Math. Phys. 309, 835-871 (2012)], relying on the "spectral flow technique" or "quasi-adiabatic continuation" [M. B. Hastings, Phys. Rev. B 69, 104431 (2004)] to obtain locality estimates with sub-exponential decay in the distance to the spatial support of the perturbation. We use ideas of Hamza et al. [J. Math. Phys. 50, 095213 (2009)] to obtain similarly a transformation between gapped eigenvectors and their perturbations that is local with exponential decay. This allows to improve locality bounds on the effect of perturbations on the low lying states in certain gapped models with a unique "bulk ground state" or "topological quantum order." We also give some estimate on the exponential decay of correlations in models with impurities where some relevant correlations decay faster than one would naively infer from the global gap of the system, as one also expects in disordered systems with a localized groundstate.
Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

NASA Technical Reports Server (NTRS)

Mirels, Harold

1959-01-01

Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.
A new approach to the extraction of single exponential diode model parameters

NASA Astrophysics Data System (ADS)

Ortiz-Conde, Adelmo; García-Sánchez, Francisco J.

2018-06-01

A new integration method is presented for the extraction of the parameters of a single exponential diode model with series resistance from the measured forward I-V characteristics. The extraction is performed using auxiliary functions based on the integration of the data which allow to isolate the effects of each of the model parameters. A differentiation method is also presented for data with low level of experimental noise. Measured and simulated data are used to verify the applicability of both proposed method. Physical insight about the validity of the model is also obtained by using the proposed graphical determinations of the parameters.
Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

NASA Astrophysics Data System (ADS)

Huang, Juntao; Shu, Chi-Wang

2018-05-01

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu [43]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.
Propagation of exponential shock wave in an axisymmetric rotating non-ideal dusty gas

NASA Astrophysics Data System (ADS)

Nath, G.

2016-09-01

One-dimensional unsteady isothermal and adiabatic flow behind a strong exponential shock wave propagating in a rotational axisymmetric mixture of non-ideal gas and small solid particles, which has variable azimuthal and axial fluid velocities, is analyzed. The shock wave is driven out by a piston moving with time according to exponential law. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to be varying and obeying exponential laws. In the present work, small solid particles are considered as pseudo-fluid with the assumption that the equilibrium flow-conditions are maintained in the flow-field, and the viscous-stress and heat conduction of the mixture are negligible. Solutions are obtained in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector and compressibility. It is found that the assumption of zero temperature gradient brings a profound change in the density, axial component of vorticity vector and compressibility distributions as compared to that of the adiabatic case. To investigate the behavior of the flow variables and the influence on the shock wave propagation by the parameter of non-idealness of the gas overline{b} in the mixture as well as by the mass concentration of solid particles in the mixture Kp and by the ratio of the density of solid particles to the initial density of the gas G1 are worked out in detail. It is interesting to note that the shock strength increases with an increase in G1 ; whereas it decreases with an increase in overline{b} . Also, a comparison between the solutions in the cases of isothermal and adiabatic flows is made.
Photovoltaic Inverter Controllers Seeking AC Optimal Power Flow Solutions

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

Dall'Anese, Emiliano; Dhople, Sairaj V.; Giannakis, Georgios B.

This paper considers future distribution networks featuring inverter-interfaced photovoltaic (PV) systems, and addresses the synthesis of feedback controllers that seek real- and reactive-power inverter setpoints corresponding to AC optimal power flow (OPF) solutions. The objective is to bridge the temporal gap between long-term system optimization and real-time inverter control, and enable seamless PV-owner participation without compromising system efficiency and stability. The design of the controllers is grounded on a dual ..epsilon..-subgradient method, while semidefinite programming relaxations are advocated to bypass the non-convexity of AC OPF formulations. Global convergence of inverter output powers is analytically established for diminishing stepsize rules formore » cases where: i) computational limits dictate asynchronous updates of the controller signals, and ii) inverter reference inputs may be updated at a faster rate than the power-output settling time.« less
Implementation of Four-Phase Interleaved Balance Charger for Series-Connected Batteries with Power Factor Correction

NASA Astrophysics Data System (ADS)

Juan, Y. L.; Lee, Y. T.; Lee, Y. L.; Chen, L. L.; Huang, M. L.

2017-11-01

A four-phase interleaved balance charger for series-connected batteries with power factor correction is proposed in this dissertation. In the two phases of two buckboost converters, the rectified ac power is firstly converted to a dc link capacitor. In the other two phases of two flyback converters, the rectified ac power is directly converted to charge the corresponding batteries. Additionally, the energy on the leakage inductance of flyback converter is bypassed to the dc link capacitor. Then, a dual-output balance charging circuit is connected to the dc link to deliver the dc link power to charge two batteries in the series-connected batteries module. The constant-current/constant-voltage charging strategy is adopted. Finally, a prototype of the proposed charger with rated power 500 W is constructed. From the experimental results, the performance and validity of the proposed topology are verified. Compared to the conventional topology with passive RCD snubber, the efficiency of the proposed topology is improved about 3% and the voltage spike on the active switch is also reduced. The efficiency of the proposed charger is at least 83.6 % within the CC/CV charging progress.
Analysis of temporal decay of diffuse broadband sound fields in enclosures by decomposition in powers of an absorption parameter

NASA Astrophysics Data System (ADS)

Bliss, Donald; Franzoni, Linda; Rouse, Jerry; Manning, Ben

2005-09-01

An analysis method for time-dependent broadband diffuse sound fields in enclosures is described. Beginning with a formulation utilizing time-dependent broadband intensity boundary sources, the strength of these wall sources is expanded in a series in powers of an absorption parameter, thereby giving a separate boundary integral problem for each power. The temporal behavior is characterized by a Taylor expansion in the delay time for a source to influence an evaluation point. The lowest-order problem has a uniform interior field proportional to the reciprocal of the absorption parameter, as expected, and exhibits relatively slow exponential decay. The next-order problem gives a mean-square pressure distribution that is independent of the absorption parameter and is primarily responsible for the spatial variation of the reverberant field. This problem, which is driven by input sources and the lowest-order reverberant field, depends on source location and the spatial distribution of absorption. Additional problems proceed at integer powers of the absorption parameter, but are essentially higher-order corrections to the spatial variation. Temporal behavior is expressed in terms of an eigenvalue problem, with boundary source strength distributions expressed as eigenmodes. Solutions exhibit rapid short-time spatial redistribution followed by long-time decay of a predominant spatial mode.
Deviations from uniform power law scaling in nonstationary time series

NASA Technical Reports Server (NTRS)

Viswanathan, G. M.; Peng, C. K.; Stanley, H. E.; Goldberger, A. L.

1997-01-01

A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.
Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Kofane, T. C.; Fokou, M.; Mohamadou, A.; Yomba, E.

2017-11-01

In this work, the lump solution and the kink solitary wave solution from the (2 + 1) -dimensional third-order evolution equation, using the Hirota bilinear method are obtained through symbolic computation with Maple. We have assumed that the lump solution is centered at the origin, when t = 0 . By considering a mixing positive quadratic function with exponential function, as well as a mixing positive quadratic function with hyperbolic cosine function, interaction solutions like lump-exponential and lump-hyperbolic cosine are presented. A completely non-elastic interaction between a lump and kink soliton is observed, showing that a lump solution can be swallowed by a kink soliton.
PAWS/STEM - PADE APPROXIMATION WITH SCALING AND SCALED TAYLOR EXPONENTIAL MATRIX (SUN VERSION)

NASA Technical Reports Server (NTRS)

Butler, R. W.

1994-01-01

Traditional fault-tree techniques for analyzing the reliability of large, complex systems fail to model the dynamic reconfiguration capabilities of modern computer systems. Markov models, on the other hand, can describe fault-recovery (via system reconfiguration) as well as fault-occurrence. The Pade Approximation with Scaling (PAWS) and Scaled Taylor Exponential Matrix (STEM) programs provide a flexible, user-friendly, language-based interface for the creation and evaluation of Markov models describing the behavior of fault-tolerant reconfigurable computer systems. PAWS and STEM produce exact solutions for the probability of system failure and provide a conservative estimate of the number of significant digits in the solution. The calculation of the probability of entering a death state of a Markov model (representing system failure) requires the solution of a set of coupled differential equations. Because of the large disparity between the rates of fault arrivals and system recoveries, Markov models of fault-tolerant architectures inevitably lead to numerically stiff differential equations. Both PAWS and STEM have the capability to solve numerically stiff models. These complementary programs use separate methods to determine the matrix exponential in the solution of the model's system of differential equations. In general, PAWS is better suited to evaluate small and dense models. STEM operates at lower precision, but works faster than PAWS for larger models. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. Although different solution techniques are utilized on different programs, it is possible to have a common input language. The Systems Validation Methods group at NASA Langley Research Center has created a set of programs that form the basis for a reliability analysis workstation. The set of programs are: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST
Second-order small-disturbance solutions for hypersonic flow over power-law bodies

NASA Technical Reports Server (NTRS)

Townsend, J. C.

1975-01-01

Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
Transfer of control system interface solutions from other domains to the thermal power industry.

PubMed

Bligård, L-O; Andersson, J; Osvalder, A-L

2012-01-01

In a thermal power plant the operators' roles are to control and monitor the process to achieve efficient and safe production. To achieve this, the human-machine interfaces have a central part. The interfaces need to be updated and upgraded together with the technical functionality to maintain optimal operation. One way of achieving relevant updates is to study other domains and see how they have solved similar issues in their design solutions. The purpose of this paper is to present how interface design solution ideas can be transferred from domains with operator control to thermal power plants. In the study 15 domains were compared using a model for categorisation of human-machine systems. The result from the domain comparison showed that nuclear power, refinery and ship engine control were most similar to thermal power control. From the findings a basic interface structure and three specific display solutions were proposed for thermal power control: process parameter overview, plant overview, and feed water view. The systematic comparison of the properties of a human-machine system allowed interface designers to find suitable objects, structures and navigation logics in a range of domains that could be transferred to the thermal power domain.
Are infant mortality rate declines exponential? The general pattern of 20th century infant mortality rate decline

PubMed Central

Bishai, David; Opuni, Marjorie

2009-01-01

Background Time trends in infant mortality for the 20th century show a curvilinear pattern that most demographers have assumed to be approximately exponential. Virtually all cross-country comparisons and time series analyses of infant mortality have studied the logarithm of infant mortality to account for the curvilinear time trend. However, there is no evidence that the log transform is the best fit for infant mortality time trends. Methods We use maximum likelihood methods to determine the best transformation to fit time trends in infant mortality reduction in the 20th century and to assess the importance of the proper transformation in identifying the relationship between infant mortality and gross domestic product (GDP) per capita. We apply the Box Cox transform to infant mortality rate (IMR) time series from 18 countries to identify the best fitting value of lambda for each country and for the pooled sample. For each country, we test the value of λ against the null that λ = 0 (logarithmic model) and against the null that λ = 1 (linear model). We then demonstrate the importance of selecting the proper transformation by comparing regressions of ln(IMR) on same year GDP per capita against Box Cox transformed models. Results Based on chi-squared test statistics, infant mortality decline is best described as an exponential decline only for the United States. For the remaining 17 countries we study, IMR decline is neither best modelled as logarithmic nor as a linear process. Imposing a logarithmic transform on IMR can lead to bias in fitting the relationship between IMR and GDP per capita. Conclusion The assumption that IMR declines are exponential is enshrined in the Preston curve and in nearly all cross-country as well as time series analyses of IMR data since Preston's 1975 paper, but this assumption is seldom correct. Statistical analyses of IMR trends should assess the robustness of findings to transformations other than the log transform. PMID:19698144
Power law expansion of the early universe for a V (a) = kan potential

NASA Astrophysics Data System (ADS)

Freitas, Augusto S.

2018-01-01

In a recent paper, He, Gao and Cai [Phys. Rev. D 89, 083510 (2014)], found a rigorous proof, based on analytical solutions of the Wheeler-DeWitt (WDWE) equation, of the spontaneous creation of the universe from nothing. The solutions were obtained from a classical potential V = ka2, where a is the scale factor. In this paper, we present a complementary (to that of He, Gao and Cai) solution to the WDWE equation with V = kan. I have found an exponential expansion of the true vacuum bubble for all scenarios. In all scenarios, we found a power law behavior of the scale factor result which is in agreement with another studies.
On the gap between an empirical distribution and an exponential distribution of waiting times for price changes in a financial market

NASA Astrophysics Data System (ADS)

Sazuka, Naoya

2007-03-01

We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high-frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between trades are not exponentially distributed. Here we show that our data is well approximated by a Weibull distribution rather than an exponential distribution in the non-asymptotic regime. Moreover, we quantitatively evaluate how much an empirical data is far from an exponential distribution using a Weibull fit. Finally, we discuss a transition between a Weibull-law and a power-law in the long time asymptotic regime.
Test Exponential Pile

NASA Astrophysics Data System (ADS)

Fermi, Enrico

The Patent contains an extremely detailed description of an atomic pile employing natural uranium as fissile material and graphite as moderator. It starts with the discussion of the theory of the intervening phenomena, in particular the evaluation of the reproduction or multiplication factor, K, that is the ratio of the number of fast neutrons produced in one generation by the fissions to the original number of fast neutrons, in a system of infinite size. The possibility of having a self-maintaining chain reaction in a system of finite size depends both on the facts that K is greater than unity and the overall size of the system is sufficiently large to minimize the percentage of neutrons escaping from the system. After the description of a possible realization of such a pile (with many detailed drawings), the various kinds of neutron losses in a pile are depicted. Particularly relevant is the reported "invention" of the exponential experiment: since theoretical calculations can determine whether or not a chain reaction will occur in a give system, but can be invalidated by uncertainties in the parameters of the problem, an experimental test of the pile is proposed, aimed at ascertaining if the pile under construction would be divergent (i.e. with a neutron multiplication factor K greater than 1) by making measurements on a smaller pile. The idea is to measure, by a detector containing an indium foil, the exponential decrease of the neutron density along the length of a column of uranium-graphite lattice, where a neutron source is placed near its base. Such an exponential decrease is greater or less than that expected due to leakage, according to whether the K factor is less or greater than 1, so that this experiment is able to test the criticality of the pile, its accuracy increasing with the size of the column. In order to perform this measure a mathematical description of the effect of neutron production, diffusion, and absorption on the neutron density in the

Fluid particles only separate exponentially in the dissipation range of turbulence after extremely long times

NASA Astrophysics Data System (ADS)

Dhariwal, Rohit; Bragg, Andrew D.

2018-03-01

In this paper, we consider how the statistical moments of the separation between two fluid particles grow with time when their separation lies in the dissipation range of turbulence. In this range, the fluid velocity field varies smoothly and the relative velocity of two fluid particles depends linearly upon their separation. While this may suggest that the rate at which fluid particles separate is exponential in time, this is not guaranteed because the strain rate governing their separation is a strongly fluctuating quantity in turbulence. Indeed, Afik and Steinberg [Nat. Commun. 8, 468 (2017), 10.1038/s41467-017-00389-8] argue that there is no convincing evidence that the moments of the separation between fluid particles grow exponentially with time in the dissipation range of turbulence. Motivated by this, we use direct numerical simulations (DNS) to compute the moments of particle separation over very long periods of time in a statistically stationary, isotropic turbulent flow to see if we ever observe evidence for exponential separation. Our results show that if the initial separation between the particles is infinitesimal, the moments of the particle separation first grow as power laws in time, but we then observe convincing evidence that at sufficiently long times the moments do grow exponentially. However, this exponential growth is only observed after extremely long times ≳200 τη , where τη is the Kolmogorov time scale. This is due to fluctuations in the strain rate about its mean value measured along the particle trajectories, the effect of which on the moments of the particle separation persists for very long times. We also consider the backward-in-time (BIT) moments of the article separation, and observe that they too grow exponentially in the long-time regime. However, a dramatic consequence of the exponential separation is that at long times the difference between the rate of the particle separation forward in time (FIT) and BIT grows
Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.
General solution of the Bagley-Torvik equation with fractional-order derivative

NASA Astrophysics Data System (ADS)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.
Polymer relaxation and stretching dynamics in semi-dilute DNA solutions: a single molecule study

NASA Astrophysics Data System (ADS)

Hsiao, Kai-Wen; Brockman, Christopher; Schroeder, Charles

2015-03-01

In this work, we study polymer relaxation and stretching dynamics in semi-dilute DNA solutions using single molecule techniques. Using this approach, we uncover a unique scaling relation for longest polymer relaxation time that falls in the crossover regime described by semi-flexible polymer solutions, which is distinct from truly flexible polymer chains. In addition, we performed a series of step-strain experiments on single polymers in semi-dilute solutions in planar extensional flow using an automated microfluidic trap. In this way, we are able to precisely control the flow strength and the amount of strain applied to single polymer chains, thereby enabling direct observation of the full stretching and relaxation process in semi-dilute solutions during transient start-up and flow cessation. Interestingly, we observe polymer individualism in the conformation of single chains in semi-dilute solutions, which to our knowledge has not yet been observed. In addition, we observe the relaxation data can be explained by a multi-exponential decay process after flow cessation in semi-dilute solutions. Overall, our work reports key advance in non-dilute polymer systems from a molecular perspective via direct observation of dynamics in strong flows. DOW fellowship.
Gasoline-powered series hybrid cars cause lower life cycle carbon emissions than battery cars

NASA Astrophysics Data System (ADS)

Meinrenken, Christoph; Lackner, Klaus S.

2012-02-01

Battery cars powered by grid electricity promise reduced life cycle green house gas (GHG) emissions from the automotive sector. Such scenarios usually point to the much higher emissions from conventional, internal combustion engine cars. However, today's commercially available series hybrid technology achieves the well known efficiency gains in electric drivetrains (regenerative breaking, lack of gearbox) even if the electricity is generated onboard, from conventional fuels. Here, we analyze life cycle GHG emissions for commercially available, state-of the-art plug-in battery cars (e.g. Nissan Leaf) and those of commercially available series hybrid cars (e.g., GM Volt, at same size and performance). Crucially, we find that series hybrid cars driven on (fossil) gasoline cause fewer emissions (126g CO2eq per km) than battery cars driven on current US grid electricity (142g CO2eq per km). We attribute this novel finding to the significant incremental emissions from plug-in battery cars due to losses during grid transmission and battery dis-/charging, and manufacturing larger batteries. We discuss crucial implications for strategic policy decisions towards a low carbon automotive sector as well as relative land intensity when powering cars by biofuel vs. bioelectricity.
Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen-Grossberg BAM neural networks with impulses.

PubMed

Yang, Wengui; Yu, Wenwu; Cao, Jinde; Alsaadi, Fuad E; Hayat, Tasawar

2018-02-01

This paper investigates the stability and lag synchronization for memristor-based fuzzy Cohen-Grossberg bidirectional associative memory (BAM) neural networks with mixed delays (asynchronous time delays and continuously distributed delays) and impulses. By applying the inequality analysis technique, homeomorphism theory and some suitable Lyapunov-Krasovskii functionals, some new sufficient conditions for the uniqueness and global exponential stability of equilibrium point are established. Furthermore, we obtain several sufficient criteria concerning globally exponential lag synchronization for the proposed system based on the framework of Filippov solution, differential inclusion theory and control theory. In addition, some examples with numerical simulations are given to illustrate the feasibility and validity of obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.
Core follow calculation with the nTRACER numerical reactor and verification using power reactor measurement data

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

Jung, Y. S.; Joo, H. G.; Yoon, J. I.

The nTRACER direct whole core transport code employing the planar MOC solution based 3-D calculation method, the subgroup method for resonance treatment, the Krylov matrix exponential method for depletion, and a subchannel thermal/hydraulic calculation solver was developed for practical high-fidelity simulation of power reactors. Its accuracy and performance is verified by comparing with the measurement data obtained for three pressurized water reactor cores. It is demonstrated that accurate and detailed multi-physic simulation of power reactors is practically realizable without any prior calculations or adjustments. (authors)
Pedagogical Implications in the Thermal Analysis of Uniform Annular Fins: Alternative Analytic Solutions by Series.

ERIC Educational Resources Information Center

Campo, Antonio; Rodriguez, Franklin

1998-01-01

Presents two alternative computational procedures for solving the modified Bessel equation of zero order: the Frobenius method, and the power series method coupled with a curve fit. Students in heat transfer courses can benefit from these alternative procedures; a course on ordinary differential equations is the only mathematical background that…
Compact exponential product formulas and operator functional derivative

NASA Astrophysics Data System (ADS)

Suzuki, Masuo

1997-02-01

A new scheme for deriving compact expressions of the logarithm of the exponential product is proposed and it is applied to several exponential product formulas. A generalization of the Dynkin-Specht-Wever (DSW) theorem on free Lie elements is given, and it is used to study the relation between the traditional method (based on the DSW theorem) and the present new scheme. The concept of the operator functional derivative is also proposed, and it is applied to ordered exponentials, such as time-evolution operators for time-dependent Hamiltonians.
Multimedia Language Learning Courseware: A Design Solution to the Production of a Series of CD-ROMs.

ERIC Educational Resources Information Center

Brett, P. A.; Nash, M.

1999-01-01

Discusses multimedia software and describes the production and the learning rationale of a series of six multimedia CD-ROMs that develop the listening skills of learners of Business English. Describes problems of cost, time, and quality in producing multiple courseware and explains the programming solution which gives control to subject experts.…
Recurrence formulas for fully exponentially correlated four-body wave functions

NASA Astrophysics Data System (ADS)

Harris, Frank E.

2009-03-01

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (≥-1) of all the interparticle distances rij , multiplied by an exponential containing an arbitrary linear combination of all the rij . These integrals are generalizations of those encountered using Hylleraas basis functions and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill plus some easily evaluated three-body “boundary” integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.
Method for exponentiating in cryptographic systems

DOEpatents

Brickell, Ernest F.; Gordon, Daniel M.; McCurley, Kevin S.

1994-01-01

An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computi The United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.
The propagation of the shock wave from a strong explosion in a plane-parallel stratified medium: the Kompaneets approximation

NASA Astrophysics Data System (ADS)

Olano, C. A.

2009-11-01

Context: Using certain simplifications, Kompaneets derived a partial differential equation that states the local geometrical and kinematical conditions that each surface element of a shock wave, created by a point blast in a stratified gaseous medium, must satisfy. Kompaneets could solve his equation analytically for the case of a wave propagating in an exponentially stratified medium, obtaining the form of the shock front at progressive evolutionary stages. Complete analytical solutions of the Kompaneets equation for shock wave motion in further plane-parallel stratified media were not found, except for radially stratified media. Aims: We aim to analytically solve the Kompaneets equation for the motion of a shock wave in different plane-parallel stratified media that can reflect a wide variety of astrophysical contexts. We were particularly interested in solving the Kompaneets equation for a strong explosion in the interstellar medium of the Galactic disk, in which, due to intense winds and explosions of stars, gigantic gaseous structures known as superbubbles and supershells are formed. Methods: Using the Kompaneets approximation, we derived a pair of equations that we call adapted Kompaneets equations, that govern the propagation of a shock wave in a stratified medium and that permit us to obtain solutions in parametric form. The solutions provided by the system of adapted Kompaneets equations are equivalent to those of the Kompaneets equation. We solved the adapted Kompaneets equations for shock wave propagation in a generic stratified medium by means of a power-series method. Results: Using the series solution for a shock wave in a generic medium, we obtained the series solutions for four specific media whose respective density distributions in the direction perpendicular to the stratification plane are of an exponential, power-law type (one with exponent k=-1 and the other with k =-2) and a quadratic hyperbolic-secant. From these series solutions, we deduced
Cascade DNA nanomachine and exponential amplification biosensing.

PubMed

Xu, Jianguo; Wu, Zai-Sheng; Shen, Weiyu; Xu, Huo; Li, Hongling; Jia, Lee

2015-11-15

DNA is a versatile scaffold for the assembly of multifunctional nanostructures, and potential applications of various DNA nanodevices have been recently demonstrated for disease diagnosis and treatment. In the current study, a powerful cascade DNA nanomachine was developed that can execute the exponential amplification of p53 tumor suppressor gene. During the operation of the newly-proposed DNA nanomachine, dual-cyclical nucleic acid strand-displacement polymerization (dual-CNDP) was ingeniously introduced, where the target trigger is repeatedly used as the fuel molecule and the nicked fragments are dramatically accumulated. Moreover, each displaced nicked fragment is able to activate the another type of cyclical strand-displacement amplification, increasing exponentially the value of fluorescence intensity. Essentially, one target binding event can induce considerable number of subsequent reactions, and the nanodevice was called cascade DNA nanomachine. It can implement several functions, including recognition element, signaling probe, polymerization primer and template. Using the developed autonomous operation of DNA nanomachine, the p53 gene can be quantified in the wide concentration range from 0.05 to 150 nM with the detection limit of 50 pM. If taking into account the final volume of mixture, the detection limit is calculated as lower as 6.2 pM, achieving an desirable assay ability. More strikingly, the mutant gene can be easily distinguished from the wild-type one. The proof-of-concept demonstrations reported herein is expected to promote the development and application of DNA nanomachine, showing great potential value in basic biology and medical diagnosis. Copyright © 2015 Elsevier B.V. All rights reserved.
An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function.

PubMed

Aggarwal, Ankush

2017-08-01

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress-strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.
Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: a basis for q-exponential distributions.

PubMed

Abe, Sumiyoshi

2002-10-01

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Rényi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.
Solutions for transients in arbitrarily branching cables: III. Voltage clamp problems.

PubMed

Major, G

1993-07-01

Branched cable voltage recording and voltage clamp analytical solutions derived in two previous papers are used to explore practical issues concerning voltage clamp. Single exponentials can be fitted reasonably well to the decay phase of clamped synaptic currents, although they contain many underlying components. The effective time constant depends on the fit interval. The smoothing effects on synaptic clamp currents of dendritic cables and series resistance are explored with a single cylinder + soma model, for inputs with different time courses. "Soma" and "cable" charging currents cannot be separated easily when the soma is much smaller than the dendrites. Subtractive soma capacitance compensation and series resistance compensation are discussed. In a hippocampal CA1 pyramidal neurone model, voltage control at most dendritic sites is extremely poor. Parameter dependencies are illustrated. The effects of series resistance compound those of dendritic cables and depend on the "effective capacitance" of the cell. Plausible combinations of parameters can cause order-of-magnitude distortions to clamp current waveform measures of simulated Schaeffer collateral inputs. These voltage clamp problems are unlikely to be solved by the use of switch clamp methods.
Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.
A multi-pixel InSAR time series analysis method: Simultaneous estimation of atmospheric noise, orbital errors and deformation

NASA Astrophysics Data System (ADS)

Jolivet, R.; Simons, M.

2016-12-01

InSAR time series analysis allows reconstruction of ground deformation with meter-scale spatial resolution and high temporal sampling. For instance, the ESA Sentinel-1 Constellation is capable of providing 6-day temporal sampling, thereby opening a new window on the spatio-temporal behavior of tectonic processes. However, due to computational limitations, most time series methods rely on a pixel-by-pixel approach. This limitation is a concern because (1) accounting for orbital errors requires referencing all interferograms to a common set of pixels before reconstruction of the time series and (2) spatially correlated atmospheric noise due to tropospheric turbulence is ignored. Decomposing interferograms into statistically independent wavelets will mitigate issues of correlated noise, but prior estimation of orbital uncertainties will still be required. Here, we explore a method that considers all pixels simultaneously when solving for the spatio-temporal evolution of interferometric phase Our method is based on a massively parallel implementation of a conjugate direction solver. We consider an interferogram as the sum of the phase difference between 2 SAR acquisitions and the corresponding orbital errors. In addition, we fit the temporal evolution with a physically parameterized function while accounting for spatially correlated noise in the data covariance. We assume noise is isotropic for any given InSAR pair with a covariance described by an exponential function that decays with increasing separation distance between pixels. We regularize our solution in space using a similar exponential function as model covariance. Given the problem size, we avoid matrix multiplications of the full covariances by computing convolutions in the Fourier domain. We first solve the unregularized least squares problem using the LSQR algorithm to approach the final solution, then run our conjugate direction solver to account for data and model covariances. We present synthetic tests
The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

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

Ganapol, B.; Picca, P.; Previti, A.

This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making usemore » of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)« less

PAWS/STEM - PADE APPROXIMATION WITH SCALING AND SCALED TAYLOR EXPONENTIAL MATRIX (VAX VMS VERSION)

NASA Technical Reports Server (NTRS)

Butler, R. W.

1994-01-01

Traditional fault-tree techniques for analyzing the reliability of large, complex systems fail to model the dynamic reconfiguration capabilities of modern computer systems. Markov models, on the other hand, can describe fault-recovery (via system reconfiguration) as well as fault-occurrence. The Pade Approximation with Scaling (PAWS) and Scaled Taylor Exponential Matrix (STEM) programs provide a flexible, user-friendly, language-based interface for the creation and evaluation of Markov models describing the behavior of fault-tolerant reconfigurable computer systems. PAWS and STEM produce exact solutions for the probability of system failure and provide a conservative estimate of the number of significant digits in the solution. The calculation of the probability of entering a death state of a Markov model (representing system failure) requires the solution of a set of coupled differential equations. Because of the large disparity between the rates of fault arrivals and system recoveries, Markov models of fault-tolerant architectures inevitably lead to numerically stiff differential equations. Both PAWS and STEM have the capability to solve numerically stiff models. These complementary programs use separate methods to determine the matrix exponential in the solution of the model's system of differential equations. In general, PAWS is better suited to evaluate small and dense models. STEM operates at lower precision, but works faster than PAWS for larger models. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. Although different solution techniques are utilized on different programs, it is possible to have a common input language. The Systems Validation Methods group at NASA Langley Research Center has created a set of programs that form the basis for a reliability analysis workstation. The set of programs are: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST
Exact three-dimensional spectral solution to surface-groundwater interactions with arbitrary surface topography

USGS Publications Warehouse

Worman, A.; Packman, A.I.; Marklund, L.; Harvey, J.W.; Stone, S.H.

2006-01-01

It has been long known that land surface topography governs both groundwater flow patterns at the regional-to-continental scale and on smaller scales such as in the hyporheic zone of streams. Here we show that the surface topography can be separated in a Fourier-series spectrum that provides an exact solution of the underlying three-dimensional groundwater flows. The new spectral solution offers a practical tool for fast calculation of subsurface flows in different hydrological applications and provides a theoretical platform for advancing conceptual understanding of the effect of landscape topography on subsurface flows. We also show how the spectrum of surface topography influences the residence time distribution for subsurface flows. The study indicates that the subsurface head variation decays exponentially with depth faster than it would with equivalent two-dimensional features, resulting in a shallower flow interaction. Copyright 2006 by the American Geophysical Union.
Calculation of Rate Spectra from Noisy Time Series Data

PubMed Central

Voelz, Vincent A.; Pande, Vijay S.

2011-01-01

As the resolution of experiments to measure folding kinetics continues to improve, it has become imperative to avoid bias that may come with fitting data to a predetermined mechanistic model. Towards this end, we present a rate spectrum approach to analyze timescales present in kinetic data. Computing rate spectra of noisy time series data via numerical discrete inverse Laplace transform is an ill-conditioned inverse problem, so a regularization procedure must be used to perform the calculation. Here, we show the results of different regularization procedures applied to noisy multi-exponential and stretched exponential time series, as well as data from time-resolved folding kinetics experiments. In each case, the rate spectrum method recapitulates the relevant distribution of timescales present in the data, with different priors on the rate amplitudes naturally corresponding to common biases toward simple phenomenological models. These results suggest an attractive alternative to the “Occam’s razor” philosophy of simply choosing models with the fewest number of relaxation rates. PMID:22095854
Predictability of monthly temperature and precipitation using automatic time series forecasting methods

NASA Astrophysics Data System (ADS)

Papacharalampous, Georgia; Tyralis, Hristos; Koutsoyiannis, Demetris

2018-02-01

We investigate the predictability of monthly temperature and precipitation by applying automatic univariate time series forecasting methods to a sample of 985 40-year-long monthly temperature and 1552 40-year-long monthly precipitation time series. The methods include a naïve one based on the monthly values of the last year, as well as the random walk (with drift), AutoRegressive Fractionally Integrated Moving Average (ARFIMA), exponential smoothing state-space model with Box-Cox transformation, ARMA errors, Trend and Seasonal components (BATS), simple exponential smoothing, Theta and Prophet methods. Prophet is a recently introduced model inspired by the nature of time series forecasted at Facebook and has not been applied to hydrometeorological time series before, while the use of random walk, BATS, simple exponential smoothing and Theta is rare in hydrology. The methods are tested in performing multi-step ahead forecasts for the last 48 months of the data. We further investigate how different choices of handling the seasonality and non-normality affect the performance of the models. The results indicate that: (a) all the examined methods apart from the naïve and random walk ones are accurate enough to be used in long-term applications; (b) monthly temperature and precipitation can be forecasted to a level of accuracy which can barely be improved using other methods; (c) the externally applied classical seasonal decomposition results mostly in better forecasts compared to the automatic seasonal decomposition used by the BATS and Prophet methods; and (d) Prophet is competitive, especially when it is combined with externally applied classical seasonal decomposition.
Compact exponential product formulas and operator functional derivative

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

Suzuki, M.

1997-02-01

A new scheme for deriving compact expressions of the logarithm of the exponential product is proposed and it is applied to several exponential product formulas. A generalization of the Dynkin{endash}Specht{endash}Wever (DSW) theorem on free Lie elements is given, and it is used to study the relation between the traditional method (based on the DSW theorem) and the present new scheme. The concept of the operator functional derivative is also proposed, and it is applied to ordered exponentials, such as time-evolution operators for time-dependent Hamiltonians. {copyright} {ital 1997 American Institute of Physics.}
Development of Multi-physics (Multiphase CFD + MCNP) simulation for generic solution vessel power calculation

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

Kim, Seung Jun; Buechler, Cynthia Eileen

The current study aims to predict the steady state power of a generic solution vessel and to develop a corresponding heat transfer coefficient correlation for a Moly99 production facility by conducting a fully coupled multi-physics simulation. A prediction of steady state power for the current application is inherently interconnected between thermal hydraulic characteristics (i.e. Multiphase computational fluid dynamics solved by ANSYS-Fluent 17.2) and the corresponding neutronic behavior (i.e. particle transport solved by MCNP6.2) in the solution vessel. Thus, the development of a coupling methodology is vital to understand the system behavior at a variety of system design and postulated operatingmore » scenarios. In this study, we report on the k-effective (keff) calculation for the baseline solution vessel configuration with a selected solution concentration using MCNP K-code modeling. The associated correlation of thermal properties (e.g. density, viscosity, thermal conductivity, specific heat) at the selected solution concentration are developed based on existing experimental measurements in the open literature. The numerical coupling methodology between multiphase CFD and MCNP is successfully demonstrated, and the detailed coupling procedure is documented. In addition, improved coupling methods capturing realistic physics in the solution vessel thermal-neutronic dynamics are proposed and tested further (i.e. dynamic height adjustment, mull-cell approach). As a key outcome of the current study, a multi-physics coupling methodology between MCFD and MCNP is demonstrated and tested for four different operating conditions. Those different operating conditions are determined based on the neutron source strength at a fixed geometry condition. The steady state powers for the generic solution vessel at various operating conditions are reported, and a generalized correlation of the heat transfer coefficient for the current application is discussed. The assessment of
Statistical power for detecting trends with applications to seabird monitoring

USGS Publications Warehouse

Hatch, Shyla A.

2003-01-01

Power analysis is helpful in defining goals for ecological monitoring and evaluating the performance of ongoing efforts. I examined detection standards proposed for population monitoring of seabirds using two programs (MONITOR and TRENDS) specially designed for power analysis of trend data. Neither program models within- and among-years components of variance explicitly and independently, thus an error term that incorporates both components is an essential input. Residual variation in seabird counts consisted of day-to-day variation within years and unexplained variation among years in approximately equal parts. The appropriate measure of error for power analysis is the standard error of estimation (S.E.est) from a regression of annual means against year. Replicate counts within years are helpful in minimizing S.E.est but should not be treated as independent samples for estimating power to detect trends. Other issues include a choice of assumptions about variance structure and selection of an exponential or linear model of population change. Seabird count data are characterized by strong correlations between S.D. and mean, thus a constant CV model is appropriate for power calculations. Time series were fit about equally well with exponential or linear models, but log transformation ensures equal variances over time, a basic assumption of regression analysis. Using sample data from seabird monitoring in Alaska, I computed the number of years required (with annual censusing) to detect trends of -1.4% per year (50% decline in 50 years) and -2.7% per year (50% decline in 25 years). At ??=0.05 and a desired power of 0.9, estimated study intervals ranged from 11 to 69 years depending on species, trend, software, and study design. Power to detect a negative trend of 6.7% per year (50% decline in 10 years) is suggested as an alternative standard for seabird monitoring that achieves a reasonable match between statistical and biological significance.
Power law inflation with electromagnetism

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

Luo, Xianghui; Isenberg, James, E-mail: isenberg@uoregon.edu

2013-07-15

We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M{sup n+1},g{sup -hat}, ϕ{sup -hat}) considered by Ringström (2009) in [11] are solutions of the Einstein–Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as inmore » Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}⊂U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (M{sup n+1},g{sup -hat}, ϕ{sup -hat}, A{sup -hat} = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results.« less
Complex motion of a vehicle through a series of signals controlled by power-law phase

NASA Astrophysics Data System (ADS)

Nagatani, Takashi

2017-07-01

We study the dynamic motion of a vehicle moving through the series of traffic signals controlled by the position-dependent phase of power law. All signals are controlled by both cycle time and position-dependent phase. The dynamic model of the vehicular motion is described in terms of the nonlinear map. The vehicular motion varies in a complex manner by varying cycle time for various values of the power of the position-dependent phase. The vehicle displays the periodic motion with a long cycle for the integer power of the phase, while the vehicular motion exhibits the very complex behavior for the non-integer power of the phase.
Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

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

Dall-Anese, Emiliano; Zhao, Changhong; Zamzam, Admed S.

This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successivemore » convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.« less
Exponential integrators in time-dependent density-functional calculations

NASA Astrophysics Data System (ADS)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.
Modeling of magnitude distributions by the generalized truncated exponential distribution

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2015-01-01

The probability distribution of the magnitude can be modeled by an exponential distribution according to the Gutenberg-Richter relation. Two alternatives are the truncated exponential distribution (TED) and the cutoff exponential distribution (CED). The TED is frequently used in seismic hazard analysis although it has a weak point: when two TEDs with equal parameters except the upper bound magnitude are mixed, then the resulting distribution is not a TED. Inversely, it is also not possible to split a TED of a seismic region into TEDs of subregions with equal parameters except the upper bound magnitude. This weakness is a principal problem as seismic regions are constructed scientific objects and not natural units. We overcome it by the generalization of the abovementioned exponential distributions: the generalized truncated exponential distribution (GTED). Therein, identical exponential distributions are mixed by the probability distribution of the correct cutoff points. This distribution model is flexible in the vicinity of the upper bound magnitude and is equal to the exponential distribution for smaller magnitudes. Additionally, the exponential distributions TED and CED are special cases of the GTED. We discuss the possible ways of estimating its parameters and introduce the normalized spacing for this purpose. Furthermore, we present methods for geographic aggregation and differentiation of the GTED and demonstrate the potential and universality of our simple approach by applying it to empirical data. The considerable improvement by the GTED in contrast to the TED is indicated by a large difference between the corresponding values of the Akaike information criterion.
Confronting quasi-exponential inflation with WMAP seven

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

Pal, Barun Kumar; Pal, Supratik; Basu, B., E-mail: barunp1985@rediffmail.com, E-mail: pal@th.physik.uni-bonn.de, E-mail: banasri@isical.ac.in

2012-04-01

We confront quasi-exponential models of inflation with WMAP seven years dataset using Hamilton Jacobi formalism. With a phenomenological Hubble parameter, representing quasi exponential inflation, we develop the formalism and subject the analysis to confrontation with WMAP seven using the publicly available code CAMB. The observable parameters are found to fair extremely well with WMAP seven. We also obtain a ratio of tensor to scalar amplitudes which may be detectable in PLANCK.
Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

PubMed

Yuste, S Bravo; Borrego, R; Abad, E

2010-02-01

We consider various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry. The motion of particles is described by a fractional diffusion equation. Their mean-square displacement is given by r(2) proportional, variant t(gamma)(0series appear when the concentration or survival probabilities are evaluated via the method of separation of variables. While the solution for normal diffusion problems is, at most, divergent as t-->0 , the emergence of such series in the long-time domain is a specific feature of subdiffusion problems. We present a method to regularize such series, and, in some cases, validate the procedure by using alternative techniques (Laplace transform method and numerical simulations). In the normal diffusion case, we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single (the main) decay mode in the long-time regime. In remarkable contrast, long-time memory of the initial condition is present in the subdiffusive case as the spatial part Psi1(r) describing the long-time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem, the weight being dependent on the initial condition. Interestingly, Psi1(r) turns out to be independent of the anomalous diffusion exponent gamma .
Research on the exponential growth effect on network topology: Theoretical and empirical analysis

NASA Astrophysics Data System (ADS)

Li, Shouwei; You, Zongjun

Integrated circuit (IC) industry network has been built in Yangtze River Delta with the constant expansion of IC industry. The IC industry network grows exponentially with the establishment of new companies and the establishment of contacts with old firms. Based on preferential attachment and exponential growth, the paper presents the analytical results in which the vertices degree of scale-free network follows power-law distribution p(k)˜k‑γ (γ=2β+1) and parameter β satisfies 0.5≤β≤1. At the same time, we find that the preferential attachment takes place in a dynamic local world and the size of the dynamic local world is in direct proportion to the size of whole networks. The paper also gives the analytical results of no-preferential attachment and exponential growth on random networks. The computer simulated results of the model illustrate these analytical results. Through some investigations on the enterprises, this paper at first presents the distribution of IC industry, composition of industrial chain and service chain firstly. Then, the correlative network and its analysis of industrial chain and service chain are presented. The correlative analysis of the whole IC industry is also presented at the same time. Based on the theory of complex network, the analysis and comparison of industrial chain network and service chain network in Yangtze River Delta are provided in the paper.
Recurrent Neural Network Applications for Astronomical Time Series

NASA Astrophysics Data System (ADS)

Protopapas, Pavlos

2017-06-01

The benefits of good predictive models in astronomy lie in early event prediction systems and effective resource allocation. Current time series methods applicable to regular time series have not evolved to generalize for irregular time series. In this talk, I will describe two Recurrent Neural Network methods, Long Short-Term Memory (LSTM) and Echo State Networks (ESNs) for predicting irregular time series. Feature engineering along with a non-linear modeling proved to be an effective predictor. For noisy time series, the prediction is improved by training the network on error realizations using the error estimates from astronomical light curves. In addition to this, we propose a new neural network architecture to remove correlation from the residuals in order to improve prediction and compensate for the noisy data. Finally, I show how to set hyperparameters for a stable and performant solution correctly. In this work, we circumvent this obstacle by optimizing ESN hyperparameters using Bayesian optimization with Gaussian Process priors. This automates the tuning procedure, enabling users to employ the power of RNN without needing an in-depth understanding of the tuning procedure.
Intravoxel water diffusion heterogeneity MR imaging of nasopharyngeal carcinoma using stretched exponential diffusion model.

PubMed

Lai, Vincent; Lee, Victor Ho Fun; Lam, Ka On; Sze, Henry Chun Kin; Chan, Queenie; Khong, Pek Lan

2015-06-01

To determine the utility of stretched exponential diffusion model in characterisation of the water diffusion heterogeneity in different tumour stages of nasopharyngeal carcinoma (NPC). Fifty patients with newly diagnosed NPC were prospectively recruited. Diffusion-weighted MR imaging was performed using five b values (0-2,500 s/mm(2)). Respective stretched exponential parameters (DDC, distributed diffusion coefficient; and alpha (α), water heterogeneity) were calculated. Patients were stratified into low and high tumour stage groups based on the American Joint Committee on Cancer (AJCC) staging for determination of the predictive powers of DDC and α using t test and ROC curve analyses. The mean ± standard deviation values were DDC = 0.692 ± 0.199 (×10(-3) mm(2)/s) for low stage group vs 0.794 ± 0.253 (×10(-3) mm(2)/s) for high stage group; α = 0.792 ± 0.145 for low stage group vs 0.698 ± 0.155 for high stage group. α was significantly lower in the high stage group while DDC was negatively correlated. DDC and α were both reliable independent predictors (p < 0.001), with α being more powerful. Optimal cut-off values were (sensitivity, specificity, positive likelihood ratio, negative likelihood ratio) DDC = 0.692 × 10(-3) mm(2)/s (94.4 %, 64.3 %, 2.64, 0.09), α = 0.720 (72.2 %, 100 %, -, 0.28). The heterogeneity index α is robust and can potentially help in staging and grading prediction in NPC. • Stretched exponential diffusion models can help in tissue characterisation in nasopharyngeal carcinoma • α and distributed diffusion coefficient (DDC) are negatively correlated • α is a robust heterogeneity index marker • α can potentially help in staging and grading prediction.
A Stochastic Super-Exponential Growth Model for Population Dynamics

NASA Astrophysics Data System (ADS)

Avila, P.; Rekker, A.

2010-11-01

A super-exponential growth model with environmental noise has been studied analytically. Super-exponential growth rate is a property of dynamical systems exhibiting endogenous nonlinear positive feedback, i.e., of self-reinforcing systems. Environmental noise acts on the growth rate multiplicatively and is assumed to be Gaussian white noise in the Stratonovich interpretation. An analysis of the stochastic super-exponential growth model with derivations of exact analytical formulae for the conditional probability density and the mean value of the population abundance are presented. Interpretations and various applications of the results are discussed.
An approach for the regularization of a power flow solution around the maximum loading point

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

Kataoka, Y.

1992-08-01

In the conventional power flow solution, the boundary conditions are directly specified by active power and reactive power at each node, so that the singular point coincided with the maximum loading point. For this reason, the computations are often disturbed by ill-condition. This paper proposes a new method for getting the wide-range regularity by giving some modifications to the conventional power flow solution method, thereby eliminating the singular point or shifting it to the region with the voltage lower than that of the maximum loading point. Then, the continuous execution of V-P curves including maximum loading point is realized. Themore » efficiency and effectiveness of the method are tested in practical 598-nodes system in comparison with the conventional method.« less
pth moment exponential stability of stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays.

PubMed

Wang, Fen; Chen, Yuanlong; Liu, Meichun

2018-02-01

Stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays play an increasingly important role in the design and implementation of neural network systems. Under the framework of Filippov solutions, the issues of the pth moment exponential stability of stochastic memristor-based BAM neural networks are investigated. By using the stochastic stability theory, Itô's differential formula and Young inequality, the criteria are derived. Meanwhile, with Lyapunov approach and Cauchy-Schwarz inequality, we derive some sufficient conditions for the mean square exponential stability of the above systems. The obtained results improve and extend previous works on memristor-based or usual neural networks dynamical systems. Four numerical examples are provided to illustrate the effectiveness of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Multivariable Time Series Prediction for the Icing Process on Overhead Power Transmission Line

PubMed Central

Li, Peng; Zhao, Na; Zhou, Donghua; Cao, Min; Li, Jingjie; Shi, Xinling

2014-01-01

The design of monitoring and predictive alarm systems is necessary for successful overhead power transmission line icing. Given the characteristics of complexity, nonlinearity, and fitfulness in the line icing process, a model based on a multivariable time series is presented here to predict the icing load of a transmission line. In this model, the time effects of micrometeorology parameters for the icing process have been analyzed. The phase-space reconstruction theory and machine learning method were then applied to establish the prediction model, which fully utilized the history of multivariable time series data in local monitoring systems to represent the mapping relationship between icing load and micrometeorology factors. Relevant to the characteristic of fitfulness in line icing, the simulations were carried out during the same icing process or different process to test the model's prediction precision and robustness. According to the simulation results for the Tao-Luo-Xiong Transmission Line, this model demonstrates a good accuracy of prediction in different process, if the prediction length is less than two hours, and would be helpful for power grid departments when deciding to take action in advance to address potential icing disasters. PMID:25136653
Exponential localization of Wannier functions in insulators.

PubMed

Brouder, Christian; Panati, Gianluca; Calandra, Matteo; Mourougane, Christophe; Marzari, Nicola

2007-01-26

The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of analytic quasi-Bloch functions and the nullity of the Chern numbers (or of the Hall current) for the system under consideration. The same equivalence implies that Chern insulators cannot display exponentially localized Wannier functions. An explicit condition for the reality of the Wannier functions is identified.
Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-04-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.
Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-06-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.
Multiserver Queueing Model subject to Single Exponential Vacation

NASA Astrophysics Data System (ADS)

Vijayashree, K. V.; Janani, B.

2018-04-01

A multi-server queueing model subject to single exponential vacation is considered. The arrivals are allowed to join the queue according to a Poisson distribution and services takes place according to an exponential distribution. Whenever the system becomes empty, all the servers goes for a vacation and returns back after a fixed interval of time. The servers then starts providing service if there are waiting customers otherwise they will wait to complete the busy period. The vacation times are also assumed to be exponentially distributed. In this paper, the stationary and transient probabilities for the number of customers during ideal and functional state of the server are obtained explicitly. Also, numerical illustrations are added to visualize the effect of various parameters.
An exponential decay model for mediation.

PubMed

Fritz, Matthew S

2014-10-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.
An Exponential Decay Model for Mediation

PubMed Central

Fritz, Matthew S.

2013-01-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, addresses many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed. PMID:23625557
de Sitter and power-law solutions in some models of modified gravity

NASA Astrophysics Data System (ADS)

Zhong, Yi; Elizalde, Emilio

2016-11-01

Inspired by some recent works of Lovelock Brans-Dicke (BD) gravity and mimetic gravity, cosmology solutions in extensions of these two modified gravities are investigated. A nonlocal term is added to the Lovelock BD action and Gauss-Bonnet (GB) terms to the mimetic action, correspondingly. de Sitter and power scale factor solutions are then obtained in both theories. They can provide natural new approaches to a more accurate description of the unverse evolution.
Ground state energies from converging and diverging power series expansions

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

Lisowski, C.; Norris, S.; Pelphrey, R.

2016-10-15

It is often assumed that bound states of quantum mechanical systems are intrinsically non-perturbative in nature and therefore any power series expansion methods should be inapplicable to predict the energies for attractive potentials. However, if the spatial domain of the Schrödinger Hamiltonian for attractive one-dimensional potentials is confined to a finite length L, the usual Rayleigh–Schrödinger perturbation theory can converge rapidly and is perfectly accurate in the weak-binding region where the ground state’s spatial extension is comparable to L. Once the binding strength is so strong that the ground state’s extension is less than L, the power expansion becomes divergent,more » consistent with the expectation that bound states are non-perturbative. However, we propose a new truncated Borel-like summation technique that can recover the bound state energy from the diverging sum. We also show that perturbation theory becomes divergent in the vicinity of an avoided-level crossing. Here the same numerical summation technique can be applied to reproduce the energies from the diverging perturbative sums.« less
Calculating Formulae of Proportion Factor and Mean Neutron Exposure in the Exponential Expression of Neutron Exposure Distribution

NASA Astrophysics Data System (ADS)

Feng-Hua, Zhang; Gui-De, Zhou; Kun, Ma; Wen-Juan, Ma; Wen-Yuan, Cui; Bo, Zhang

2016-07-01

Previous studies have shown that, for the three main stages of the development and evolution of asymptotic giant branch (AGB) star s-process models, the neutron exposure distribution (DNE) in the nucleosynthesis region can always be considered as an exponential function, i.e., ρAGB(τ) = C/τ0 exp(-τ/τ0) in an effective range of the neutron exposure values. However, the specific expressions of the proportion factor C and the mean neutron exposure τ0 in the exponential distribution function for different models are not completely determined in the related literature. Through dissecting the basic method to obtain the exponential DNE, and systematically analyzing the solution procedures of neutron exposure distribution functions in different stellar models, the general formulae, as well as their auxiliary equations, for calculating C and τ0 are derived. Given the discrete neutron exposure distribution Pk, the relationships of C and τ0 with the model parameters can be determined. The result of this study has effectively solved the problem to analytically calculate the DNE in the current low-mass AGB star s-process nucleosynthesis model of 13C-pocket radiative burning.
Motion of Molecular Probes and Viscosity Scaling in Polyelectrolyte Solutions at Physiological Ionic Strength

PubMed Central

Sozanski, Krzysztof; Wisniewska, Agnieszka; Kalwarczyk, Tomasz; Sznajder, Anna; Holyst, Robert

2016-01-01

We investigate transport properties of model polyelectrolyte systems at physiological ionic strength (0.154 M). Covering a broad range of flow length scales—from diffusion of molecular probes to macroscopic viscous flow—we establish a single, continuous function describing the scale dependent viscosity of high-salt polyelectrolyte solutions. The data are consistent with the model developed previously for electrically neutral polymers in a good solvent. The presented approach merges the power-law scaling concepts of de Gennes with the idea of exponential length scale dependence of effective viscosity in complex liquids. The result is a simple and applicable description of transport properties of high-salt polyelectrolyte solutions at all length scales, valid for motion of single molecules as well as macroscopic flow of the complex liquid. PMID:27536866
A gamma variate model that includes stretched exponential is a better fit for gastric emptying data from mice

PubMed Central

Bajzer, Željko; Gibbons, Simon J.; Coleman, Heidi D.; Linden, David R.

2015-01-01

Noninvasive breath tests for gastric emptying are important techniques for understanding the changes in gastric motility that occur in disease or in response to drugs. Mice are often used as an animal model; however, the gamma variate model currently used for data analysis does not always fit the data appropriately. The aim of this study was to determine appropriate mathematical models to better fit mouse gastric emptying data including when two peaks are present in the gastric emptying curve. We fitted 175 gastric emptying data sets with two standard models (gamma variate and power exponential), with a gamma variate model that includes stretched exponential and with a proposed two-component model. The appropriateness of the fit was assessed by the Akaike Information Criterion. We found that extension of the gamma variate model to include a stretched exponential improves the fit, which allows for a better estimation of T1/2 and Tlag. When two distinct peaks in gastric emptying are present, a two-component model is required for the most appropriate fit. We conclude that use of a stretched exponential gamma variate model and when appropriate a two-component model will result in a better estimate of physiologically relevant parameters when analyzing mouse gastric emptying data. PMID:26045615
Exponential gain of randomness certified by quantum contextuality

NASA Astrophysics Data System (ADS)

Um, Mark; Zhang, Junhua; Wang, Ye; Wang, Pengfei; Kim, Kihwan

2017-04-01

We demonstrate the protocol of exponential gain of randomness certified by quantum contextuality in a trapped ion system. The genuine randomness can be produced by quantum principle and certified by quantum inequalities. Recently, randomness expansion protocols based on inequality of Bell-text and Kochen-Specker (KS) theorem, have been demonstrated. These schemes have been theoretically innovated to exponentially expand the randomness and amplify the randomness from weak initial random seed. Here, we report the experimental evidence of such exponential expansion of randomness. In the experiment, we use three states of a 138Ba + ion between a ground state and two quadrupole states. In the 138Ba + ion system, we do not have detection loophole and we apply a methods to rule out certain hidden variable models that obey a kind of extended noncontextuality.
Mutant number distribution in an exponentially growing population

NASA Astrophysics Data System (ADS)

Keller, Peter; Antal, Tibor

2015-01-01

We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.
A series of simple oligomer-like small molecules based on oligothiophenes for solution-processed solar cells with high efficiency.

PubMed

Kan, Bin; Li, Miaomiao; Zhang, Qian; Liu, Feng; Wan, Xiangjian; Wang, Yunchuang; Ni, Wang; Long, Guankui; Yang, Xuan; Feng, Huanran; Zuo, Yi; Zhang, Mingtao; Huang, Fei; Cao, Yong; Russell, Thomas P; Chen, Yongsheng

2015-03-25

A series of acceptor-donor-acceptor simple oligomer-like small molecules based on oligothiophenes, namely, DRCN4T-DRCN9T, were designed and synthesized. Their optical, electrical, and thermal properties and photovoltaic performances were systematically investigated. Except for DRCN4T, excellent performances were obtained for DRCN5T-DRCN9T. The devices based on DRCN5T, DRCN7T, and DRCN9T with axisymmetric chemical structures exhibit much higher short-circuit current densities than those based on DRCN6T and DRCN8T with centrosymmetric chemical structures, which is attributed to their well-developed fibrillar network with a feature size less than 20 nm. The devices based on DRCN5T/PC71BM showed a notable certified power conversion efficiency (PCE) of 10.10% under AM 1.5G irradiation (100 mW cm(-2)) using a simple solution spin-coating fabrication process. This is the highest PCE for single-junction small-molecule-based organic photovoltaics (OPVs) reported to date. DRCN5T is a rather simpler molecule compared with all of the other high-performance molecules in OPVs to date, and this might highlight its advantage in the future possible commercialization of OPVs. These results demonstrate that a fine and balanced modification/design of chemical structure can make significant performance differences and that the performance of solution-processed small-molecule-based solar cells can be comparable to or even surpass that of their polymer counterparts.
Exponentially decaying interaction potential of cavity solitons

NASA Astrophysics Data System (ADS)

Anbardan, Shayesteh Rahmani; Rimoldi, Cristina; Kheradmand, Reza; Tissoni, Giovanna; Prati, Franco

2018-03-01

We analyze the interaction of two cavity solitons in an optically injected vertical cavity surface emitting laser above threshold. We show that they experience an attractive force even when their distance is much larger than their diameter, and eventually they merge. Since the merging time depends exponentially on the initial distance, we suggest that the attraction could be associated with an exponentially decaying interaction potential, similarly to what is found for hydrophobic materials. We also show that the merging time is simply related to the characteristic times of the laser, photon lifetime, and carrier lifetime.
Using Solution Strategies to Examine and Promote High-School Students' Understanding of Exponential Functions: One Teacher's Attempt

ERIC Educational Resources Information Center

Brendefur, Jonathan

2014-01-01

Much research has been conducted on how elementary students develop mathematical understanding and subsequently how teachers might use this information. This article builds on this type of work by investigating how one high-school algebra teacher designs and conducts a lesson on exponential functions. Through a lesson study format she studies with…
Decay of homogeneous turbulence from a specified state

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1972-01-01

The homogeneous turbulence problem is formulated by first specifying the multipoint velocity correlations or their spectral equivalents at an initial time. Those quantities, together with the correlation or spectral equations, are then used to calculate initial time derivatives of correlations or spectra. The derivatives in turn are used in time series to calculate the evolution of turbulence quantities with time. When the problem is treated in this way, the correlation equations are closed by the initial specification of the turbulence and no closure assumption is necessary. An exponential series which is an iterative solution of the Navier stokes equations gave much better results than a Taylor power series when used with the limited available initial data. In general, the agreement between theory and experiment was good.
Dynamic equations for an isotropic spherical shell using the power series method and surface differential operators

NASA Astrophysics Data System (ADS)

Okhovat, Reza; Boström, Anders

2017-04-01

Dynamic equations for an isotropic spherical shell are derived by using a series expansion technique. The displacement field is split into a scalar (radial) part and a vector (tangential) part. Surface differential operators are introduced to decrease the length of all equations. The starting point is a power series expansion of the displacement components in the thickness coordinate relative to the mid-surface of the shell. By using the expansions of the displacement components, the three-dimensional elastodynamic equations yield a set of recursion relations among the expansion functions that can be used to eliminate all but the four of lowest order and to express higher order expansion functions in terms of those of lowest orders. Applying the boundary conditions on the surfaces of the spherical shell and eliminating all but the four lowest order expansion functions give the shell equations as a power series in the shell thickness. After lengthy manipulations, the final four shell equations are obtained in a relatively compact form which are given to second order in shell thickness explicitly. The eigenfrequencies are compared to exact three-dimensional theory with excellent agreement and to membrane theory.
Exponential smoothing weighted correlations

NASA Astrophysics Data System (ADS)

Pozzi, F.; Di Matteo, T.; Aste, T.

2012-06-01

In many practical applications, correlation matrices might be affected by the "curse of dimensionality" and by an excessive sensitiveness to outliers and remote observations. These shortcomings can cause problems of statistical robustness especially accentuated when a system of dynamic correlations over a running window is concerned. These drawbacks can be partially mitigated by assigning a structure of weights to observational events. In this paper, we discuss Pearson's ρ and Kendall's τ correlation matrices, weighted with an exponential smoothing, computed on moving windows using a data-set of daily returns for 300 NYSE highly capitalized companies in the period between 2001 and 2003. Criteria for jointly determining optimal weights together with the optimal length of the running window are proposed. We find that the exponential smoothing can provide more robust and reliable dynamic measures and we discuss that a careful choice of the parameters can reduce the autocorrelation of dynamic correlations whilst keeping significance and robustness of the measure. Weighted correlations are found to be smoother and recovering faster from market turbulence than their unweighted counterparts, helping also to discriminate more effectively genuine from spurious correlations.

How do output growth-rate distributions look like? Some cross-country, time-series evidence

NASA Astrophysics Data System (ADS)

Fagiolo, G.; Napoletano, M.; Roventini, A.

2007-05-01

This paper investigates the statistical properties of within-country gross domestic product (GDP) and industrial production (IP) growth-rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether also within-country, time-series GDP and IP growth rates can be approximated by tent-shaped distributions. We fit output growth rates with the exponential-power (Subbotin) family of densities, which includes as particular cases both Gaussian and Laplace distributions. We find that, for a large number of OECD (Organization for Economic Cooperation and Development) countries including the US, both GDP and IP growth rates are Laplace distributed. Moreover, we show that fat-tailed distributions robustly emerge even after controlling for outliers, autocorrelation and heteroscedasticity.
An exact formulation of the time-ordered exponential using path-sums

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

Giscard, P.-L., E-mail: p.giscard1@physics.ox.ac.uk; Lui, K.; Thwaite, S. J.

2015-05-15

We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitudemore » of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.« less
Complex network approach to fractional time series

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

Manshour, Pouya

In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacencymore » matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.« less
Modelling and Simulation of Single-Phase Series Active Compensator for Power Quality Improvement

NASA Astrophysics Data System (ADS)

Verma, Arun Kumar; Mathuria, Kirti; Singh, Bhim; Bhuvaneshwari, G.

2017-10-01

A single-phase active series compensator is proposed in this work to reduce harmonic currents at the ac mains and to regulate the dc link voltage of a diode bridge rectifier (DBR) that acts as the front end converter for a voltage source inverter feeding an ac motor. This ac motor drive is used in any of the domestic, commercial or industrial appliances. Under fluctuating ac mains voltages, the dc link voltage of the DBR depicts wide variations and hence the ac motor is used at reduced rating as compared to its name-plate rating. The active series compensator proposed here provides dual functions of improving the power quality at the ac mains and regulating the dc link voltage thus averting the need for derating of the ac motor.
Analysis of series resonant converter with series-parallel connection

NASA Astrophysics Data System (ADS)

Lin, Bor-Ren; Huang, Chien-Lan

2011-02-01

In this study, a parallel inductor-inductor-capacitor (LLC) resonant converter series-connected on the primary side and parallel-connected on the secondary side is presented for server power supply systems. Based on series resonant behaviour, the power metal-oxide-semiconductor field-effect transistors are turned on at zero voltage switching and the rectifier diodes are turned off at zero current switching. Thus, the switching losses on the power semiconductors are reduced. In the proposed converter, the primary windings of the two LLC converters are connected in series. Thus, the two converters have the same primary currents to ensure that they can supply the balance load current. On the output side, two LLC converters are connected in parallel to share the load current and to reduce the current stress on the secondary windings and the rectifier diodes. In this article, the principle of operation, steady-state analysis and design considerations of the proposed converter are provided and discussed. Experiments with a laboratory prototype with a 24 V/21 A output for server power supply were performed to verify the effectiveness of the proposed converter.
A Systematic Multi-Time Scale Solution for Regional Power Grid Operation

NASA Astrophysics Data System (ADS)

Zhu, W. J.; Liu, Z. G.; Cheng, T.; Hu, B. Q.; Liu, X. Z.; Zhou, Y. F.

2017-10-01

Many aspects need to be taken into consideration in a regional grid while making schedule plans. In this paper, a systematic multi-time scale solution for regional power grid operation considering large scale renewable energy integration and Ultra High Voltage (UHV) power transmission is proposed. In the time scale aspect, we discuss the problem from month, week, day-ahead, within-day to day-behind, and the system also contains multiple generator types including thermal units, hydro-plants, wind turbines and pumped storage stations. The 9 subsystems of the scheduling system are described, and their functions and relationships are elaborated. The proposed system has been constructed in a provincial power grid in Central China, and the operation results further verified the effectiveness of the system.
Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and variational approaches

NASA Astrophysics Data System (ADS)

Gambino, G.; Tanriver, U.; Guha, P.; Choudhury, A. Ghose; Choudhury, S. Roy

2015-02-01

In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding traveling-wave equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic/heteroclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. And finally, variational methods are employed to generate families of both regular and embedded solitary wave solutions for the SPE PDE. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and it is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the assumed ansatz for the trial functions). Thus, a direct error analysis is performed, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that not much is known about solutions of the family of generalized SPE equations considered here, the results obtained are both new and timely.
The Western Africa ebola virus disease epidemic exhibits both global exponential and local polynomial growth rates.

PubMed

Chowell, Gerardo; Viboud, Cécile; Hyman, James M; Simonsen, Lone

2015-01-21

While many infectious disease epidemics are initially characterized by an exponential growth in time, we show that district-level Ebola virus disease (EVD) outbreaks in West Africa follow slower polynomial-based growth kinetics over several generations of the disease. We analyzed epidemic growth patterns at three different spatial scales (regional, national, and subnational) of the Ebola virus disease epidemic in Guinea, Sierra Leone and Liberia by compiling publicly available weekly time series of reported EVD case numbers from the patient database available from the World Health Organization website for the period 05-Jan to 17-Dec 2014. We found significant differences in the growth patterns of EVD cases at the scale of the country, district, and other subnational administrative divisions. The national cumulative curves of EVD cases in Guinea, Sierra Leone, and Liberia show periods of approximate exponential growth. In contrast, local epidemics are asynchronous and exhibit slow growth patterns during 3 or more EVD generations, which can be better approximated by a polynomial than an exponential function. The slower than expected growth pattern of local EVD outbreaks could result from a variety of factors, including behavior changes, success of control interventions, or intrinsic features of the disease such as a high level of clustering. Quantifying the contribution of each of these factors could help refine estimates of final epidemic size and the relative impact of different mitigation efforts in current and future EVD outbreaks.
The Western Africa Ebola Virus Disease Epidemic Exhibits Both Global Exponential and Local Polynomial Growth Rates

PubMed Central

Chowell, Gerardo; Viboud, Cécile; Hyman, James M; Simonsen, Lone

2015-01-01

Background: While many infectious disease epidemics are initially characterized by an exponential growth in time, we show that district-level Ebola virus disease (EVD) outbreaks in West Africa follow slower polynomial-based growth kinetics over several generations of the disease. Methods: We analyzed epidemic growth patterns at three different spatial scales (regional, national, and subnational) of the Ebola virus disease epidemic in Guinea, Sierra Leone and Liberia by compiling publicly available weekly time series of reported EVD case numbers from the patient database available from the World Health Organization website for the period 05-Jan to 17-Dec 2014. Results: We found significant differences in the growth patterns of EVD cases at the scale of the country, district, and other subnational administrative divisions. The national cumulative curves of EVD cases in Guinea, Sierra Leone, and Liberia show periods of approximate exponential growth. In contrast, local epidemics are asynchronous and exhibit slow growth patterns during 3 or more EVD generations, which can be better approximated by a polynomial than an exponential function. Conclusions: The slower than expected growth pattern of local EVD outbreaks could result from a variety of factors, including behavior changes, success of control interventions, or intrinsic features of the disease such as a high level of clustering. Quantifying the contribution of each of these factors could help refine estimates of final epidemic size and the relative impact of different mitigation efforts in current and future EVD outbreaks. PMID:25685633
Power law f(𝒢,T) gravity models supporting wormhole solutions

NASA Astrophysics Data System (ADS)

Shamir, M. Farasat; Ahmad, Mushtaq

This work provides some feasible regions for the existence of traversable wormhole geometries in modified f(𝒢,T) gravity. For this purpose, three different matter contents have been studied with special emphasis on anisotropic fluid by considering a specific f(𝒢,T) gravity power law model. It has been shown that the null energy conditions for the effective energy-momentum tensor are widely violated for the ordinary matter content. However, some small feasible regions to support the wormhole solutions have been noted. Furthermore, the stability of the anisotropic feasible regions for the wormhole solutions has been discussed. It is concluded that the wormhole geometries threaded by the ordinary matter actually exist and are well stable in f(𝒢,T) gravity.
Exponential Correlation of IQ and the Wealth of Nations

ERIC Educational Resources Information Center

Dickerson, Richard E.

2006-01-01

Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…
A Simulation To Model Exponential Growth.

ERIC Educational Resources Information Center

Appelbaum, Elizabeth Berman

2000-01-01

Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)
Analytical time-domain Green’s functions for power-law media

PubMed Central

Kelly, James F.; McGough, Robert J.; Meerschaert, Mark M.

2008-01-01

Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation [“Time domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green’s functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1∕3, 1∕2, 2∕3, 3∕2, and 2, the Green’s function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green’s functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green’s functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green’s function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green’s function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774
Autoregressive processes with exponentially decaying probability distribution functions: applications to daily variations of a stock market index.

PubMed

Porto, Markus; Roman, H Eduardo

2002-04-01

We consider autoregressive conditional heteroskedasticity (ARCH) processes in which the variance sigma(2)(y) depends linearly on the absolute value of the random variable y as sigma(2)(y) = a+b absolute value of y. While for the standard model, where sigma(2)(y) = a + b y(2), the corresponding probability distribution function (PDF) P(y) decays as a power law for absolute value of y-->infinity, in the linear case it decays exponentially as P(y) approximately exp(-alpha absolute value of y), with alpha = 2/b. We extend these results to the more general case sigma(2)(y) = a+b absolute value of y(q), with 0 < q < 2. We find stretched exponential decay for 1 < q < 2 and stretched Gaussian behavior for 0 < q < 1. As an application, we consider the case q=1 as our starting scheme for modeling the PDF of daily (logarithmic) variations in the Dow Jones stock market index. When the history of the ARCH process is taken into account, the resulting PDF becomes a stretched exponential even for q = 1, with a stretched exponent beta = 2/3, in a much better agreement with the empirical data.
Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface

NASA Astrophysics Data System (ADS)

Zaigham Zia, Q. M.; Ullah, Ikram; Waqas, M.; Alsaedi, A.; Hayat, T.

2018-03-01

This research intends to elaborate Soret-Dufour characteristics in mixed convective radiated Casson liquid flow by exponentially heated surface. Novel features of exponential space dependent heat source are introduced. Appropriate variables are implemented for conversion of partial differential frameworks into a sets of ordinary differential expressions. Homotopic scheme is employed for construction of analytic solutions. Behavior of various embedding variables on velocity, temperature and concentration distributions are plotted graphically and analyzed in detail. Besides, skin friction coefficients and heat and mass transfer rates are also computed and interpreted. The results signify the pronounced characteristics of temperature corresponding to convective and radiation variables. Concentration bears opposite response for Soret and Dufour variables.
Linear or Exponential Number Lines

ERIC Educational Resources Information Center

Stafford, Pat

2011-01-01

Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather…
The series-elastic shock absorber: tendons attenuate muscle power during eccentric actions.

PubMed

Roberts, Thomas J; Azizi, Emanuel

2010-08-01

Elastic tendons can act as muscle power amplifiers or energy-conserving springs during locomotion. We used an in situ muscle-tendon preparation to examine the mechanical function of tendons during lengthening contractions, when muscles absorb energy. Force, length, and power were measured in the lateral gastrocnemius muscle of wild turkeys. Sonomicrometry was used to measure muscle fascicle length independently from muscle-tendon unit (MTU) length, as measured by a muscle lever system (servomotor). A series of ramp stretches of varying velocities was applied to the MTU in fully activated muscles. Fascicle length changes were decoupled from length changes imposed on the MTU by the servomotor. Under most conditions, muscle fascicles shortened on average, while the MTU lengthened. Energy input to the MTU during the fastest lengthenings was -54.4 J/kg, while estimated work input to the muscle fascicles during this period was only -11.24 J/kg. This discrepancy indicates that energy was first absorbed by elastic elements, then released to do work on muscle fascicles after the lengthening phase of the contraction. The temporary storage of energy by elastic elements also resulted in a significant attenuation of power input to the muscle fascicles. At the fastest lengthening rates, peak instantaneous power input to the MTU reached -2,143.9 W/kg, while peak power input to the fascicles was only -557.6 W/kg. These results demonstrate that tendons may act as mechanical buffers by limiting peak muscle forces, lengthening rates, and power inputs during energy-absorbing contractions.
The series-elastic shock absorber: tendons attenuate muscle power during eccentric actions

PubMed Central

Azizi, Emanuel

2010-01-01

Elastic tendons can act as muscle power amplifiers or energy-conserving springs during locomotion. We used an in situ muscle-tendon preparation to examine the mechanical function of tendons during lengthening contractions, when muscles absorb energy. Force, length, and power were measured in the lateral gastrocnemius muscle of wild turkeys. Sonomicrometry was used to measure muscle fascicle length independently from muscle-tendon unit (MTU) length, as measured by a muscle lever system (servomotor). A series of ramp stretches of varying velocities was applied to the MTU in fully activated muscles. Fascicle length changes were decoupled from length changes imposed on the MTU by the servomotor. Under most conditions, muscle fascicles shortened on average, while the MTU lengthened. Energy input to the MTU during the fastest lengthenings was −54.4 J/kg, while estimated work input to the muscle fascicles during this period was only −11.24 J/kg. This discrepancy indicates that energy was first absorbed by elastic elements, then released to do work on muscle fascicles after the lengthening phase of the contraction. The temporary storage of energy by elastic elements also resulted in a significant attenuation of power input to the muscle fascicles. At the fastest lengthening rates, peak instantaneous power input to the MTU reached −2,143.9 W/kg, while peak power input to the fascicles was only −557.6 W/kg. These results demonstrate that tendons may act as mechanical buffers by limiting peak muscle forces, lengthening rates, and power inputs during energy-absorbing contractions. PMID:20507964
Quark mixing and exponential form of the Cabibbo-Kobayashi-Maskawa matrix

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

Zhukovsky, K. V., E-mail: zhukovsk@phys.msu.ru; Dattoli, D., E-mail: dattoli@frascati.enea.i

2008-10-15

Various forms of representation of the mixing matrix are discussed. An exponential parametrization e{sup A} of the Cabibbo-Kobayashi-Maskawa matrix is considered in the context of the unitarity requirement, this parametrization being the most general form of the mixing matrix. An explicit representation for the exponential mixing matrix in terms of the first and second degrees of the matrix A exclusively is obtained. This representation makes it possible to calculate this exponential mixing matrix readily in any order of the expansion in the small parameter {lambda}. The generation of new unitary parametric representations of the mixing matrix with the aid ofmore » the exponential matrix is demonstrated.« less
Photocounting distributions for exponentially decaying sources.

PubMed

Teich, M C; Card, H C

1979-05-01

Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model.

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

DOE PAGES

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

2016-10-21

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less
Power Distribution at the Bottom of the Pyramid: Illumination through Affordable and Sustainable Solution of Gram Power

NASA Astrophysics Data System (ADS)

Pandey, Nisha; Sarswat, Prashant

2016-03-01

Energy plays a vital role in the socio -economic development, mainly due to the dependency of indispensable amenities on electricity. However, a matter of concern is developing country domestic power needs and inadequate supply. One of the cases is Indian subcontinent, where more than 50,000 villages still not have access to uninterrupted electric power. `Power theft' is a major challenge due to the lack of adequate energy supply and the financial constraints. Long distances, inaccurate and inflated electricity bills are the other issues lead to default on payments. Gram Power, a social enterprise, is providing a smart metering and affordable solution in areas where the extension of existing grid supply is economically not viable. India's first solar powered micro-grid (centralized array of solar panels) in Rajasthan was established by this initiative. The core innovation is a smart distribution technology that consists of smart meters with recharging facility and grid monitoring, to provide on-demand, theft-proof power through centralized servers with a pay-as-you-use schedule. The details of the changes, socio-economic transformation, and operational sustainability of such a community engagement model will be discussed in this study.
On the parallel solution of parabolic equations

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Youcef

1989-01-01

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.
Analytical solution for the diffusion of a capacitor discharge generated magnetic field pulse in a conductor

NASA Astrophysics Data System (ADS)

Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter

2016-06-01

Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
Exponential Sensitivity and its Cost in Quantum Physics

PubMed Central

Gilyén, András; Kiss, Tamás; Jex, Igor

2016-01-01

State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed. PMID:26861076
Exponential Sensitivity and its Cost in Quantum Physics.

PubMed

Gilyén, András; Kiss, Tamás; Jex, Igor

2016-02-10

State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed.
Early-time solution of the horizontal unconfined aquifer in the build-up phase

NASA Astrophysics Data System (ADS)

Gravanis, Elias; Akylas, Evangelos

2017-04-01

The Boussinesq equation is a dynamical equation for the free surface of saturated subsurface flows over an impervious bed. Boussinesq equation is non-linear. The non-linearity comes from the reduction of the dimensionality of the problem: The flow is assumed to be vertically homogeneous, therefore the flow rate through a cross section of the flow is proportional to the free surface height times the hydraulic gradient, which is assumed to be equal to the slope of the free surface (Dupuit approximation). In general, 'vertically' means normally on the bed; combining the Dupuit approximation with the continuity equation leads to the Boussinesq equation. There are very few transient exact solutions. Self- similar solutions have been constructed in the past by various authors. A power series type of solution was derived for a self-similar Boussinesq equation by Barenblatt in 1990. That type of solution has generated a certain amount of literature. For the unconfined flow case for zero recharge rate Boussinesq derived for the horizontal aquifer an exact solution assuming separation of variables. This is actually an exact asymptotic solution of the horizontal aquifer recession phase for late times. The kinematic wave is an interesting solution obtained by dropping the non-linear term in the Boussinesq equation. Although it is an approximate solution, and holds well only for small values of the Henderson and Wooding λ parameter (that is, for steep slopes, high conductivity or small recharge rate), it becomes less and less approximate for smaller values of the parameter, that is, it is asymptotically exact with respect to that parameter. In the present work we consider the case of the unconfined subsurface flow over horizontal bed in the build-up phase under constant recharge rate. This is a case with an infinite Henderson and Wooding parameter, that is, it is the limiting case where the non-linear term is present in the Boussinesq while the linear spatial derivative term
Solution-processed small-molecule solar cells: breaking the 10% power conversion efficiency.

PubMed

Liu, Yongsheng; Chen, Chun-Chao; Hong, Ziruo; Gao, Jing; Yang, Yang Michael; Zhou, Huanping; Dou, Letian; Li, Gang; Yang, Yang

2013-11-28

A two-dimensional conjugated small molecule (SMPV1) was designed and synthesized for high performance solution-processed organic solar cells. This study explores the photovoltaic properties of this molecule as a donor, with a fullerene derivative as an acceptor, using solution processing in single junction and double junction tandem solar cells. The single junction solar cells based on SMPV1 exhibited a certified power conversion efficiency of 8.02% under AM 1.5 G irradiation (100 mW cm(-2)). A homo-tandem solar cell based on SMPV1 was constructed with a novel interlayer (or tunnel junction) consisting of bilayer conjugated polyelectrolyte, demonstrating an unprecedented PCE of 10.1%. These results strongly suggest solution-processed small molecular materials are excellent candidates for organic solar cells.
Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-01-01

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.
Possible stretched exponential parametrization for humidity absorption in polymers.

PubMed

Hacinliyan, A; Skarlatos, Y; Sahin, G; Atak, K; Aybar, O O

2009-04-01

Polymer thin films have irregular transient current characteristics under constant voltage. In hydrophilic and hydrophobic polymers, the irregularity is also known to depend on the humidity absorbed by the polymer sample. Different stretched exponential models are studied and it is shown that the absorption of humidity as a function of time can be adequately modelled by a class of these stretched exponential absorption models.
A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

NASA Technical Reports Server (NTRS)

Solakiewicz, Richard; Attele, Rohan; Koshak, William

2011-01-01

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.
Contribution of Lattice Distortion to Solid Solution Strengthening in a Series of Refractory High Entropy Alloys

NASA Astrophysics Data System (ADS)

Chen, H.; Kauffmann, A.; Laube, S.; Choi, I.-C.; Schwaiger, R.; Huang, Y.; Lichtenberg, K.; Müller, F.; Gorr, B.; Christ, H.-J.; Heilmaier, M.

2018-03-01

We present an experimental approach for revealing the impact of lattice distortion on solid solution strengthening in a series of body-centered-cubic (bcc) Al-containing, refractory high entropy alloys (HEAs) from the Nb-Mo-Cr-Ti-Al system. By systematically varying the Nb and Cr content, a wide range of atomic size difference as a common measure for the lattice distortion was obtained. Single-phase, bcc solid solutions were achieved by arc melting and homogenization as well as verified by means of scanning electron microscopy and X-ray diffraction. The atomic radii of the alloying elements for determination of atomic size difference were recalculated on the basis of the mean atomic radii in and the chemical compositions of the solid solutions. Microhardness (μH) at room temperature correlates well with the deduced atomic size difference. Nevertheless, the mechanisms of microscopic slip lead to pronounced temperature dependence of mechanical strength. In order to account for this particular feature, we present a combined approach, using μH, nanoindentation, and compression tests. The athermal proportion to the yield stress of the investigated equimolar alloys is revealed. These parameters support the universality of this aforementioned correlation. Hence, the pertinence of lattice distortion for solid solution strengthening in bcc HEAs is proven.
Analysis of log-periodic power law singularity patterns in time series related to credit risk

NASA Astrophysics Data System (ADS)

Wosnitza, Jan Henrik; Sornette, Didier

2015-04-01

The log-periodic (super-exponential) power law singularity (LPPLS) has become a promising tool for predicting extreme behavior of self-organizing systems in natural sciences and finance. Some researchers have recently proposed to employ the LPPLS on credit risk markets. The review article at hand summarizes four papers in this field and shows how they are linked. After structuring the research questions, we collect the corresponding answers from the four articles. This eventually gives us an overall picture of the application of the LPPLS to credit risk data. Our literature review begins with grounding the view that credit default swap (CDS) spreads are hotbeds for LPPLS patterns and it ends up with drawing attention to the recently proposed alarm index for the prediction of institutional bank runs. By presenting a new field of application for the LPPLS, the reviewed strand of literature further substantiates the LPPLS hypothesis. Moreover, the results suggest that CDS spread trajectories belong to a different universality class than, for instance, stock prices.
Review of "Going Exponential: Growing the Charter School Sector's Best"

ERIC Educational Resources Information Center

Garcia, David

2011-01-01

This Progressive Policy Institute report argues that charter schools should be expanded rapidly and exponentially. Citing exponential growth organizations, such as Starbucks and Apple, as well as the rapid growth of molds, viruses and cancers, the report advocates for similar growth models for charter schools. However, there is no explanation of…
[Application of exponential smoothing method in prediction and warning of epidemic mumps].

PubMed

Shi, Yun-ping; Ma, Jia-qi

2010-06-01

To analyze the daily data of epidemic Mumps in a province from 2004 to 2008 and set up exponential smoothing model for the prediction. To predict and warn the epidemic mumps in 2008 through calculating 7-day moving summation and removing the effect of weekends to the data of daily reported mumps cases during 2005-2008 and exponential summation to the data from 2005 to 2007. The performance of Holt-Winters exponential smoothing is good. The result of warning sensitivity was 76.92%, specificity was 83.33%, and timely rate was 80%. It is practicable to use exponential smoothing method to warn against epidemic Mumps.
Modelling and stability analysis of switching impulsive power systems with multiple equilibria

NASA Astrophysics Data System (ADS)

Zhu, Liying; Qiu, Jianbin; Chadli, Mohammed

2017-12-01

This paper tries to model power systems accompanied with a series of faults in the form of switched impulsive Hamiltonian systems (SIHSs) with multiple equilibria (ME) and unstable subsystems (US), and then analyze long-term stability issues of the power systems from the viewpoint of mathematics. According to the complex phenomena of switching actions of stages and generators, impulses of state, and existence of multiple equilibria, this paper first introduces an SIHS with ME and US to formulate a switching impulsive power system composed of an active generator, a standby generator, and an infinite load. Then, based on special system structures, a unique compact region containing all ME is determined, and novel stability concepts of region stability (RS), asymptotic region stability (ARS), and exponential region stability (ERS) are defined for such SIHS with respect to the region. Third, based on the introduced stability concepts, this paper proposes a necessary and sufficient condition of RS and ARS and a sufficient condition of ERS for the power system with respect to the region via the maximum energy function method. Finally, numerical simulations are carried out for a power system to show the effectiveness and practicality of the obained novel results.
Power function decay of hydraulic conductivity for a TOPMODEL-based infiltration routine

NASA Astrophysics Data System (ADS)

Wang, Jun; Endreny, Theodore A.; Hassett, James M.

2006-11-01

TOPMODEL rainfall-runoff hydrologic concepts are based on soil saturation processes, where soil controls on hydrograph recession have been represented by linear, exponential, and power function decay with soil depth. Although these decay formulations have been incorporated into baseflow decay and topographic index computations, only the linear and exponential forms have been incorporated into infiltration subroutines. This study develops a power function formulation of the Green and Ampt infiltration equation for the case where the power n = 1 and 2. This new function was created to represent field measurements in the New York City, USA, Ward Pound Ridge drinking water supply area, and provide support for similar sites reported by other researchers. Derivation of the power-function-based Green and Ampt model begins with the Green and Ampt formulation used by Beven in deriving an exponential decay model. Differences between the linear, exponential, and power function infiltration scenarios are sensitive to the relative difference between rainfall rates and hydraulic conductivity. Using a low-frequency 30 min design storm with 4.8 cm h-1 rain, the n = 2 power function formulation allows for a faster decay of infiltration and more rapid generation of runoff. Infiltration excess runoff is rare in most forested watersheds, and advantages of the power function infiltration routine may primarily include replication of field-observed processes in urbanized areas and numerical consistency with power function decay of baseflow and topographic index distributions. Equation development is presented within a TOPMODEL-based Ward Pound Ridge rainfall-runoff simulation. Copyright
Exponential Potential versus Dark Matter

DTIC Science & Technology

1993-10-15

scale of the solar system. Galaxy, Dark matter , Galaxy cluster, Gravitation, Quantum gravity...A two parameter exponential potential explains the anomalous kinematics of galaxies and galaxy clusters without need for the myriad ad hoc dark ... matter models currently in vogue. It also explains much about the scales and structures of galaxies and galaxy clusters while being quite negligible on the
Ultrasound degradation of xanthan polymer in aqueous solution: Its scission mechanism and the effect of NaCl incorporation.

PubMed

Saleh, H M; Annuar, M S M; Simarani, K

2017-11-01

Degradation of xanthan polymer in aqueous solution by ultrasonic irradiation was investigated. The effects of selected variables i.e. sonication intensity, irradiation time, concentration of xanthan gum and molar concentration of NaCl in solution were studied. Combined approach of full factorial design and conventional one-factor-at-a-time was applied to obtain optimum degradation at sonication power intensity of 11.5Wcm -2 , irradiation time 120min and 0.1gL -1 xanthan in a salt-free solution. Molecular weight reduction of xanthan gum under sonication was described by an exponential decay function with higher rate constant for polymer degradation in the salt free solution. The limiting molecular weight where fragments no longer undergo scission was determined from the function. The incorporation of NaCl in xanthan solution resulted in a lower limiting molecular weight. The ultrasound-mediated degradation of aqueous xanthan polymer chain agreed with a random scission model. Side chain of xanthan polymer is proposed to be the primary site of scission action. Copyright © 2017 Elsevier B.V. All rights reserved.
A Nonlinear Digital Control Solution for a DC/DC Power Converter

NASA Technical Reports Server (NTRS)

Zhu, Minshao

2002-01-01

A digital Nonlinear Proportional-Integral-Derivative (NPID) control algorithm was proposed to control a 1-kW, PWM, DC/DC, switching power converter. The NPID methodology is introduced and a practical hardware control solution is obtained. The design of the controller was completed using Matlab (trademark) Simulink, while the hardware-in-the-loop testing was performed using both the dSPACE (trademark) rapid prototyping system, and a stand-alone Texas Instruments (trademark) Digital Signal Processor (DSP)-based system. The final Nonlinear digital control algorithm was implemented and tested using the ED408043-1 Westinghouse DC-DC switching power converter. The NPID test results are discussed and compared to the results of a standard Proportional-Integral (PI) controller.

Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles

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

Warshaw, S I

2001-07-15

In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resultedmore » from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.« less
Rational approximations from power series of vector-valued meromorphic functions

NASA Technical Reports Server (NTRS)

Sidi, Avram

1992-01-01

Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.
Fast Modular Exponentiation and Elliptic Curve Group Operation in Maple

ERIC Educational Resources Information Center

Yan, S. Y.; James, G.

2006-01-01

The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…
Generalized recursive solutions to Ornstein-Zernike integral equations

NASA Astrophysics Data System (ADS)

Rossky, Peter J.; Dale, William D. T.

1980-09-01

Recursive procedures for the solution of a class of integral equations based on the Ornstein-Zernike equation are developed; the hypernetted chain and Percus-Yevick equations are two special cases of the class considered. It is shown that certain variants of the new procedures developed here are formally equivalent to those recently developed by Dale and Friedman, if the new recursive expressions are initialized in the same way as theirs. However, the computational solution of the new equations is significantly more efficient. Further, the present analysis leads to the identification of various graphical quantities arising in the earlier study with more familiar quantities related to pair correlation functions. The analysis is greatly facilitated by the use of several identities relating simple chain sums whose graphical elements can be written as a sum of two or more parts. In particular, the use of these identities permits renormalization of the equivalent series solution to the integral equation to be directly incorporated into the recursive solution in a straightforward manner. Formulas appropriate to renormalization with respect to long and short range parts of the pair potential, as well as more general components of the direct correlation function, are obtained. To further illustrate the utility of this approach, we show that a simple generalization of the hypernetted chain closure relation for the direct correlation function leads directly to the reference hypernetted chain (RHNC) equation due to Lado. The form of the correlation function used in the exponential approximation of Andersen and Chandler is then seen to be equivalent to the first estimate obtained from a renormalized RHNC equation.
The exponentiated Hencky energy: anisotropic extension and case studies

NASA Astrophysics Data System (ADS)

Schröder, Jörg; von Hoegen, Markus; Neff, Patrizio

2017-10-01

In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants. Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient \\varvec{F} to the group of rotations. We formally extend this approach towards anisotropy by defining additional anisotropic logarithmic strain invariants with the help of suitable structural tensors and consider our findings for selected case studies.
Turbulent particle transport in streams: can exponential settling be reconciled with fluid mechanics?

PubMed

McNair, James N; Newbold, J Denis

2012-05-07

Most ecological studies of particle transport in streams that focus on fine particulate organic matter or benthic invertebrates use the Exponential Settling Model (ESM) to characterize the longitudinal pattern of particle settling on the bed. The ESM predicts that if particles are released into a stream, the proportion that have not yet settled will decline exponentially with transport time or distance and will be independent of the release elevation above the bed. To date, no credible basis in fluid mechanics has been established for this model, nor has it been rigorously tested against more-mechanistic alternative models. One alternative is the Local Exchange Model (LEM), which is a stochastic advection-diffusion model that includes both longitudinal and vertical spatial dimensions and is based on classical fluid mechanics. The LEM predicts that particle settling will be non-exponential in the near field but will become exponential in the far field, providing a new theoretical justification for far-field exponential settling that is based on plausible fluid mechanics. We review properties of the ESM and LEM and compare these with available empirical evidence. Most evidence supports the prediction of both models that settling will be exponential in the far field but contradicts the ESM's prediction that a single exponential distribution will hold for all transport times and distances. Copyright Â© 2012 Elsevier Ltd. All rights reserved.
Approximate solution to the Hopf Phi equation for isotropic homogeneous fluid turbulence

NASA Technical Reports Server (NTRS)

Rosen, G.

1982-01-01

Consistent with the observed t to the -n decay laws for isotropic homogeneous turbulence and the form of the longitudinal correlation function f(r, t) for small r, the Hopf Phi equation is shown to be satisfied approximately by an asymptotic power series in t to the -n. This solution features a self-similar universal equilibrium functional which manifests Kolmogoroff-type scaling.
A Decreasing Failure Rate, Mixed Exponential Model Applied to Reliability.

DTIC Science & Technology

1981-06-01

Trident missile systems have been observed. The mixed exponential distribu- tion has been shown to fit the life data for the electronic equipment on...these systems . This paper discusses some of the estimation problems which occur with the decreasing failure rate mixed exponential distribution when...assumption of constant or increasing failure rate seemed to be incorrect. 2. However, the design of this electronic equipment indicated that
Exponentially Stabilizing Robot Control Laws

NASA Technical Reports Server (NTRS)

Wen, John T.; Bayard, David S.

1990-01-01

New class of exponentially stabilizing laws for joint-level control of robotic manipulators introduced. In case of set-point control, approach offers simplicity of proportion/derivative control architecture. In case of tracking control, approach provides several important alternatives to completed-torque method, as far as computational requirements and convergence. New control laws modified in simple fashion to obtain asymptotically stable adaptive control, when robot model and/or payload mass properties unknown.
Discrete breathers in an array of self-excited oscillators: Exact solutions and stability.

PubMed

Shiroky, I B; Gendelman, O V

2016-10-01

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions-discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self-excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.
Longitudinal aerodynamic performance of a series of power-law and minimum wave drag bodies at Mach 6 and several Reynolds numbers

NASA Technical Reports Server (NTRS)

Ashby, G. C., Jr.

1974-01-01

Experimental data have been obtained for two series of bodies at Mach 6 and Reynolds numbers, based on model length, from 1.4 million to 9.5 million. One series consisted of axisymmetric power-law bodies geometrically constrained for constant length and base diameter with values of the exponent n of 0.25, 0.5, 0.6, 0.667, 0.75, and 1.0. The other series consisted of positively and negatively cambered bodies of polygonal cross section, each having a constant longitudinal area distribution conforming to that required for minimizing zero-lift wave drag at hypersonic speeds under the geometric constraints of given length and volume. At the highest Reynolds number, the power-law body for minimum drag is blunter (exponent n lower) than predicted by inviscid theory (n approximately 0.6 instead of n = 0.667); however, the peak value of lift-drag ratio occurs at n = 0.667. Viscous effects were present on the bodies of polygonal cross section but were less pronounced than those on the power-law bodies. The trapezoidal bodies with maximum width at the bottom were found to have the highest maximum lift-drag ratio and the lowest mimimum drag.
Powers and Roots. Fundamentals of Occupational Mathematics. Module 11.

ERIC Educational Resources Information Center

Engelbrecht, Nancy; And Others

This module is the 11th in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include multiplication, powers, calculator use, and roots.…
A note on free and forced Rossby wave solutions: The case of a straight coast and a channel

NASA Astrophysics Data System (ADS)

Graef, Federico

2017-03-01

The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l1) and reflected (l2) wave are equal or complex are discussed. If l1 = l2 the energy streams along the coast and a uniformly valid solution cannot be found; if l1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes. If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed. The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially ;decaying; and exponentially ;growing; RW could be excited in the channel.
Cohomogeneity-one solutions in Einstein-Maxwell-dilaton gravity

NASA Astrophysics Data System (ADS)

Lim, Yen-Kheng

2017-05-01

The field equations for Einstein-Maxwell-dilaton gravity in D dimensions are reduced to an effective one-dimensional system under the influence of exponential potentials. Various cases where exact solutions can be found are explored. With this procedure, we present interesting solutions such as a one-parameter generalization of the dilaton-Melvin spacetime and a three-parameter solution that interpolates between the Reissner-Nordström and Bertotti-Robinson solutions. This procedure also allows simple, alternative derivations of known solutions such as the Lifshitz spacetime and the planar anti-de Sitter naked singularity. In the latter case, the metric is cast in a simpler form which reveals the presence of an additional curvature singularity.
Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods.

PubMed

Ye, Jun

2016-01-01

An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems. As a supplement, this paper firstly introduces new exponential operational laws of INSs, where the bases are crisp values or interval numbers and the exponents are interval neutrosophic numbers (INNs), which are basic elements in INSs. Then, we propose an interval neutrosophic weighted exponential aggregation (INWEA) operator and a dual interval neutrosophic weighted exponential aggregation (DINWEA) operator based on these exponential operational laws and introduce comparative methods based on cosine measure functions for INNs and dual INNs. Further, we develop decision-making methods based on the INWEA and DINWEA operators. Finally, a practical example on the selecting problem of global suppliers is provided to illustrate the applicability and rationality of the proposed methods.
Geometric Series: A New Solution to the Dog Problem

ERIC Educational Resources Information Center

Dion, Peter; Ho, Anthony

2013-01-01

This article describes what is often referred to as the dog, beetle, mice, ant, or turtle problem. Solutions to this problem exist, some being variations of each other, which involve mathematics of a wide range of complexity. Herein, the authors describe the intuitive solution and the calculus solution and then offer a completely new solution…
Spray-on polyvinyl alcohol separators and impact on power production in air-cathode microbial fuel cells with different solution conductivities.

PubMed

Hoskins, Daniel L; Zhang, Xiaoyuan; Hickner, Michael A; Logan, Bruce E

2014-11-01

Separators are used to protect cathodes from biofouling and to avoid electrode short-circuiting, but they can adversely affect microbial fuel cell (MFC) performance. A spray method was used to apply a polyvinyl alcohol (PVA) separator to the cathode. Power densities were unaffected by the PVA separator (339±29mW/m(2)), compared to a control lacking a separator in a low conductivity solution (1mS/cm) similar to wastewater. Power was reduced with separators in solutions typical of laboratory tests (7-13mS/cm), compared to separatorless controls. The PVA separator produced more power in a separator assembly (SEA) configuration (444±8mW/m(2)) in the 1mS/cm solution, but power was reduced if a PVA or wipe separator was used in higher conductivity solutions with either Pt or activated carbon catalysts. Spray and cast PVA separators performed similarly, but the spray method is preferred as it was easier to apply and use. Copyright © 2014 Elsevier Ltd. All rights reserved.
An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

NASA Technical Reports Server (NTRS)

Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

1974-01-01

The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.
Classification of the line-soliton solutions of KPII

NASA Astrophysics Data System (ADS)

Chakravarty, Sarbarish; Kodama, Yuji

2008-07-01

In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| → ∞. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.
Optical solitons, explicit solutions and modulation instability analysis with second-order spatio-temporal dispersion

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Isa Aliyu, Aliyu; Yusuf, Abdullahi; Baleanu, Dumitru

2017-12-01

This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the nonlinear Schrödinger equation (NLSE) with group velocity dispersion coefficient and second-order spatio-temporal dispersion coefficient, which arises in photonics and waveguide optics and in optical fibers. The integration algorithm is the sine-Gordon equation method (SGEM). Furthermore, the explicit solutions of the equation are derived by considering the power series solutions (PSS) theory and the convergence of the solutions is guaranteed. Lastly, the modulation instability analysis (MI) is studied based on the standard linear-stability analysis and the MI gain spectrum is obtained.

Exploring Exponential Decay Using Limited Resources

ERIC Educational Resources Information Center

DePierro, Ed; Garafalo, Fred; Gordon, Patrick

2018-01-01

Science students need exposure to activities that will help them to become familiar with phenomena exhibiting exponential decay. This paper describes an experiment that allows students to determine the rate of thermal energy loss by a hot object to its surroundings. It requires limited equipment, is safe, and gives reasonable results. Students…
A solution to Schroder's equation in several variables

DOE PAGES

Bridges, Robert A.

2016-03-04

For this paper, let φ be an analytic self-map of the n -ball, having 0 as the attracting fixed point and having full-rank near 0. We consider the generalized Schroder's equation, F °φ=φ'(0) kF with ka positive integer and prove there is always a solution F with linearly independent component functions, but that such an F cannot have full rank except possibly when k=1. Furthermore, when k=1 (Schroder's equation), necessary and sufficient conditions on φ are given to ensure F has full rank near 0 without the added assumption of diagonalizability as needed in the 2003 Cowen/MacCluer paper. In responsemore » to Enoch's 2007 paper, it is proven that any formal power series solution indeed represents an analytic function on the whole unit ball. Finally, how exactly resonance can lead to an obstruction of a full rank solution is discussed as well as some consequences of having solutions to Schroder's equation.« less
On the conditions of exponential stability in active disturbance rejection control based on singular perturbation analysis

NASA Astrophysics Data System (ADS)

Shao, S.; Gao, Z.

2017-10-01

Stability of active disturbance rejection control (ADRC) is analysed in the presence of unknown, nonlinear, and time-varying dynamics. In the framework of singular perturbations, the closed-loop error dynamics are semi-decoupled into a relatively slow subsystem (the feedback loop) and a relatively fast subsystem (the extended state observer), respectively. It is shown, analytically and geometrically, that there exists a unique exponential stable solution if the size of the initial observer error is sufficiently small, i.e. in the same order of the inverse of the observer bandwidth. The process of developing the uniformly asymptotic solution of the system reveals the condition on the stability of the ADRC and the relationship between the rate of change in the total disturbance and the size of the estimation error. The differentiability of the total disturbance is the only assumption made.
Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.
Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.
Time-fractional Cahn-Allen and time-fractional Klein-Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Isa Aliyu, Aliyu; Baleanu, Dumitru

2018-03-01

This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn-Allen (CA) and time-fractional Klein-Gordon (KG) equations with Riemann-Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented.
Optimal Low-Thrust Limited-Power Transfers between Arbitrary Elliptic Coplanar Orbits

NASA Technical Reports Server (NTRS)

daSilvaFernandes, Sandro; dasChagasCarvalho, Francisco

2007-01-01

In this work, a complete first order analytical solution, which includes the short periodic terms, for the problem of optimal low-thrust limited-power transfers between arbitrary elliptic coplanar orbits in a Newtonian central gravity field is obtained through Hamilton-Jacobi theory and a perturbation method based on Lie series.
Cycle Analysis of Two-stage Planar SOFC Power Generation by Series Connection of Low and High Temperature SOFCs

NASA Astrophysics Data System (ADS)

Ohba, Takahiro; Takezawa, Shinya; Araki, Takuto; Onda, Kazuo; Sakaki, Yoshinori

Solid Oxide Fuel Cell (SOFC) can be composed by solid components, and high power generation efficiency of a whole cycle is obtained by using high temperature exhaust heat for fuel reforming and bottoming power generation. Recently, the low temperature SOFC, which runs in the temperature range of around 600°C or above, has been developed with the high efficiency of power generation. On the other hand, multi-stage power generation system has been proposed by the United States DOE. In this study, a power generation system of two-stage SOFC by series connection of low and high temperature SOFCs has been studied. Overpotential data for low-temperature SOFC used in this study are based on recent published data, and those for high temperature SOFC arhaihe based on our previous study. The analytical results show the two-stage SOFC power generation efficiency of 50.3% and the total power generation efficiency of 56.1% under a standard operating condition.
Exponential inflation with F (R ) gravity

NASA Astrophysics Data System (ADS)

Oikonomou, V. K.

2018-03-01

In this paper, we shall consider an exponential inflationary model in the context of vacuum F (R ) gravity. By using well-known reconstruction techniques, we shall investigate which F (R ) gravity can realize the exponential inflation scenario at leading order in terms of the scalar curvature, and we shall calculate the slow-roll indices and the corresponding observational indices, in the context of slow-roll inflation. We also provide some general formulas of the slow-roll and the corresponding observational indices in terms of the e -foldings number. In addition, for the calculation of the slow-roll and of the observational indices, we shall consider quite general formulas, for which it is not necessary for the assumption that all the slow-roll indices are much smaller than unity to hold true. Finally, we investigate the phenomenological viability of the model by comparing it with the latest Planck and BICEP2/Keck-Array observational data. As we demonstrate, the model is compatible with the current observational data for a wide range of the free parameters of the model.
Transient electromagnetic scattering by a radially uniaxial dielectric sphere: Debye series, Mie series and ray tracing methods

NASA Astrophysics Data System (ADS)

Yazdani, Mohsen

Transient electromagnetic scattering by a radially uniaxial dielectric sphere is explored using three well-known methods: Debye series, Mie series, and ray tracing theory. In the first approach, the general solutions for the impulse and step responses of a uniaxial sphere are evaluated using the inverse Laplace transformation of the generalized Mie series solution. Following high frequency scattering solution of a large uniaxial sphere, the Mie series summation is split into the high frequency (HF) and low frequency terms where the HF term is replaced by its asymptotic expression allowing a significant reduction in computation time of the numerical Bromwich integral. In the second approach, the generalized Debye series for a radially uniaxial dielectric sphere is introduced and the Mie series coefficients are replaced by their equivalent Debye series formulations. The results are then applied to examine the transient response of each individual Debye term allowing the identification of impulse returns in the transient response of the uniaxial sphere. In the third approach, the ray tracing theory in a uniaxial sphere is investigated to evaluate the propagation path as well as the arrival time of the ordinary and extraordinary returns in the transient response of the uniaxial sphere. This is achieved by extracting the reflection and transmission angles of a plane wave obliquely incident on the radially oriented air-uniaxial and uniaxial-air boundaries, and expressing the phase velocities as well as the refractive indices of the ordinary and extraordinary waves in terms of the incident angle, optic axis and propagation direction. The results indicate a satisfactory agreement between Debye series, Mie series and ray tracing methods.
Power-law tails and non-Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory

NASA Astrophysics Data System (ADS)

Chakraborty, Ahana; Sensarma, Rajdeep

2018-03-01

The Born-Markov approximation is widely used to study the dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to a noninteracting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has nonanalyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power-law tails. The Green's functions show a short-time "quasi"-Markovian exponential decay before crossing over to a power-law tail governed by the nonanalyticity of the spectral function. We study a system of bosons (fermions) hopping on a one-dimensional lattice, where each site is coupled linearly to an independent bath of noninteracting bosons (fermions). We obtain exact expressions for the Green's functions of this system, which show power-law decay ˜|t - t'|-3 /2 . We use these to calculate the density and current profile, as well as unequal-time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long-time power-law tails |t - t'|-3 characteristic of non-Markovian dynamics. We show that the power-law decays survive in the presence of interparticle interaction in the system, but the crossover time scale is shifted to larger values with increasing interaction strength.
Exponential rise of dynamical complexity in quantum computing through projections.

PubMed

Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya

2014-10-10

The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.
Baecklund transformation, Lax pair, and solutions for the Caudrey-Dodd-Gibbon equation

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

Qu Qixing; Sun Kun; Jiang Yan

2011-01-15

By using Bell polynomials and symbolic computation, we investigate the Caudrey-Dodd-Gibbon equation analytically. Through a generalization of Bells polynomials, its bilinear form is derived, based on which, the periodic wave solution and soliton solutions are presented. And the soliton solutions with graphic analysis are also given. Furthermore, Baecklund transformation and Lax pair are derived via the Bells exponential polynomials. Finally, the Ablowitz-Kaup-Newell-Segur system is constructed.
Analytical solution for boundary heat fluxes from a radiating rectangular medium

NASA Technical Reports Server (NTRS)

Siegel, R.

1991-01-01

Reference is made to the work of Shah (1979) which demonstrated the possibility of partially integrating the radiative equations analytically to obtain an 'exact' solution. Shah's solution was given as a double integration of the modified Bessel function of order zero. Here, it is shown that the 'exact' solution for a rectangular region radiating to cold black walls can be conveniently derived, and expressed in simple form, by using an integral function, Sn, analogous to the exponential integral function appearing in plane-layer solutions.
A solar power plant for Curtin University Malaysia

NASA Astrophysics Data System (ADS)

Palanichamy, C.

2016-03-01

The Curtin University, Sarawak Malaysia (Curtin Sarawak) is the first and largest offshore campus of Curtin University in Perth, Western Australia, and the first foreign university to be established in East Malaysia in partnership with the Sarawak State Government. Today's major concern of Curtin is its monthly electrical energy consumption and the electricity bill since its monthly energy consumption exceeds 0.3 Million kWh, and the corresponding electricity bill surpasses RM 95000. Such a situation necessitates Curtin to curtail the heavy energy consumption with immediate effect. Introducing Renewable Energy Source such as PV Solar Systems is a cost-effective and environmental friendly solution to reduce the exponential increase in energy consumption charges of Curtin. Hence, this paper proposes a 90 kW solar power plant for Curtin Sarawak.
Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

NASA Technical Reports Server (NTRS)

Cockrell, C. R.

1989-01-01

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.
Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham-Broer-Kaup-Like Equations

NASA Astrophysics Data System (ADS)

Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian

2017-03-01

In this article, a generalised Whitham-Broer-Kaup-Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham-Broer-Kaup-Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Quanlin; Oldenburg, Curtis M.; Spangler, Lee H.

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheresmore » and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less
The exponential function transforms the Abbreviated Injury Scale, which both improves accuracy and simplifies scoring.

PubMed

Wang, M D; Fan, W H; Qiu, W S; Zhang, Z L; Mo, Y N; Qiu, F

2014-06-01

We present here the exponential function which transforms the Abbreviated Injury Scale (AIS). It is called the Exponential Injury Severity Score (EISS), and significantly outperforms the venerable but dated New Injury Severity Score (NISS) and Injury Severity Score (ISS) as a predictor of mortality. The EISS is defined as a change of AIS values by raising each AIS severity score (1-6) by 3 taking a power of AIS minus 2 and then summing the three most severe injuries (i.e., highest AIS), regardless of body regions. EISS values were calculated for every patient in two large independent data sets: 3,911 and 4,129 patients treated during a 6-year period at the Class A tertiary hospitals in China. The power of the EISS to predict mortality was then compared with previously calculated NISS values for the same patients in each of the two data sets. We found that the EISS is more predictive of survival [Zhejiang: area under the receiver operating characteristic curve (AUC): NISS = 0.932, EISS = 0.949, P = 0.0115; Liaoning: AUC: NISS = 0.924, EISS = 0.942, P = 0.0139]. Moreover, the EISS provides a better fit throughout its entire range of prediction (Hosmer-Lemeshow statistic for Zhejiang: NISS = 21.86, P = 0.0027, EISS = 13.52, P = 0.0604; Liaoning: NISS = 23.27, P = 0.0015, EISS = 15.55, P = 0.0164). The EISS may be used as the standard summary measure of human trauma.
The investigation of trapped thickness shear modes in a contoured AT-cut quartz plate using the power series expansion technique

NASA Astrophysics Data System (ADS)

Li, Peng; Jin, Feng

2018-01-01

The dynamic model about the anti-plane vibration of a contoured quartz plate with thickness changing continuously is established by ignoring the effect of small elastic constant c 56. The governing equation is solved using the power series expansion technique, and the trapped thickness shear modes caused by bulge thickness are revealed. Theoretically, the proposed method is more general, which can be capable of handling various thickness profiles defined mathematically. After the convergence of the series is demonstrated and the correctness is numerically validated with the aid of finite element method results, systematic parametric studies are subsequently carried out to quantify the effects of the geometry parameter upon the trapped modes, including resonant frequency and mode shape. After that, the band structures of thickness shear waves propagation in a periodically contoured quartz plate, as well as the power transmission spectra, are obtained based on the power series expansion technique. It is revealed that broad stop bands below cut-off frequency exist owing to the trapped modes excited by the geometry inhomogeneity, which has little relationship with the structural periodicity, and its physical mechanism is different from the Bragg scattering effect. The outcome is widely applicable, and can be utilized to provide theoretical and practical guidance for the design and manufacturing of quartz resonators and wave filters.

Blip decomposition of the path integral: exponential acceleration of real-time calculations on quantum dissipative systems.

PubMed

Makri, Nancy

2014-10-07

The real-time path integral representation of the reduced density matrix for a discrete system in contact with a dissipative medium is rewritten in terms of the number of blips, i.e., elementary time intervals over which the forward and backward paths are not identical. For a given set of blips, it is shown that the path sum with respect to the coordinates of all remaining time points is isomorphic to that for the wavefunction of a system subject to an external driving term and thus can be summed by an inexpensive iterative procedure. This exact decomposition reduces the number of terms by a factor that increases exponentially with propagation time. Further, under conditions (moderately high temperature and/or dissipation strength) that lead primarily to incoherent dynamics, the "fully incoherent limit" zero-blip term of the series provides a reasonable approximation to the dynamics, and the blip series converges rapidly to the exact result. Retention of only the blips required for satisfactory convergence leads to speedup of full-memory path integral calculations by many orders of magnitude.
CMB constraints on β-exponential inflationary models

NASA Astrophysics Data System (ADS)

Santos, M. A.; Benetti, M.; Alcaniz, J. S.; Brito, F. A.; Silva, R.

2018-03-01

We analyze a class of generalized inflationary models proposed in ref. [1], known as β-exponential inflation. We show that this kind of potential can arise in the context of brane cosmology, where the field describing the size of the extra-dimension is interpreted as the inflaton. We discuss the observational viability of this class of model in light of the latest Cosmic Microwave Background (CMB) data from the Planck Collaboration through a Bayesian analysis, and impose tight constraints on the model parameters. We find that the CMB data alone prefer weakly the minimal standard model (ΛCDM) over the β-exponential inflation. However, when current local measurements of the Hubble parameter, H0, are considered, the β-inflation model is moderately preferred over the ΛCDM cosmology, making the study of this class of inflationary models interesting in the context of the current H0 tension.
Scaling behaviour of Fisher and Shannon entropies for the exponential-cosine screened coulomb potential

NASA Astrophysics Data System (ADS)

Abdelmonem, M. S.; Abdel-Hady, Afaf; Nasser, I.

2017-07-01

The scaling laws are given for the entropies in the information theory, including the Shannon's entropy, its power, the Fisher's information and the Fisher-Shannon product, using the exponential-cosine screened Coulomb potential. The scaling laws are specified, in the r-space, as a function of |μ - μc, nℓ|, where μ is the screening parameter and μc, nℓ its critical value for the specific quantum numbers n and ℓ. Scaling laws for other physical quantities, such as energy eigenvalues, the moments, static polarisability, transition probabilities, etc. are also given. Some of these are reported for the first time. The outcome is compared with the available literatures' results.
The mechanism of double-exponential growth in hyper-inflation

NASA Astrophysics Data System (ADS)

Mizuno, T.; Takayasu, M.; Takayasu, H.

2002-05-01

Analyzing historical data of price indices, we find an extraordinary growth phenomenon in several examples of hyper-inflation in which, price changes are approximated nicely by double-exponential functions of time. In order to explain such behavior we introduce the general coarse-graining technique in physics, the Monte Carlo renormalization group method, to the price dynamics. Starting from a microscopic stochastic equation describing dealers’ actions in open markets, we obtain a macroscopic noiseless equation of price consistent with the observation. The effect of auto-catalytic shortening of characteristic time caused by mob psychology is shown to be responsible for the double-exponential behavior.
Exponential stability of stochastic complex networks with multi-weights based on graph theory

NASA Astrophysics Data System (ADS)

Zhang, Chunmei; Chen, Tianrui

2018-04-01

In this paper, a novel approach to exponential stability of stochastic complex networks with multi-weights is investigated by means of the graph-theoretical method. New sufficient conditions are provided to ascertain the moment exponential stability and almost surely exponential stability of stochastic complex networks with multiple weights. It is noted that our stability results are closely related with multi-weights and the intensity of stochastic disturbance. Numerical simulations are also presented to substantiate the theoretical results.
Memory feedback PID control for exponential synchronisation of chaotic Lur'e systems

NASA Astrophysics Data System (ADS)

Zhang, Ruimei; Zeng, Deqiang; Zhong, Shouming; Shi, Kaibo

2017-09-01

This paper studies the problem of exponential synchronisation of chaotic Lur'e systems (CLSs) via memory feedback proportional-integral-derivative (PID) control scheme. First, a novel augmented Lyapunov-Krasovskii functional (LKF) is constructed, which can make full use of the information on time delay and activation function. Second, improved synchronisation criteria are obtained by using new integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. In comparison with existing results, in which only proportional control or proportional derivative (PD) control is used, less conservative results are derived for CLSs by PID control. Third, the desired memory feedback controllers are designed in terms of the solution to linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to show the effectiveness and advantages of the proposed results.
Conditional optimal spacing in exponential distribution.

PubMed

Park, Sangun

2006-12-01

In this paper, we propose the conditional optimal spacing defined as the optimal spacing after specifying a predetermined order statistic. If we specify a censoring time, then the optimal inspection times for grouped inspection can be determined from this conditional optimal spacing. We take an example of exponential distribution, and provide a simple method of finding the conditional optimal spacing.
Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations.

PubMed

Gu, Yongyi; Qi, Jianming

2017-01-01

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

NASA Astrophysics Data System (ADS)

Herdiani, Erna Tri; Fandrilla, Geysa; Sunusi, Nurtiti

2018-03-01

In general, observations of the statistical process control are assumed to be mutually independence. However, this assumption is often violated in practice. Consequently, statistical process controls were developed for interrelated processes, including Shewhart, Cumulative Sum (CUSUM), and exponentially weighted moving average (EWMA) control charts in the data that were autocorrelation. One researcher stated that this chart is not suitable if the same control limits are used in the case of independent variables. For this reason, it is necessary to apply the time series model in building the control chart. A classical control chart for independent variables is usually applied to residual processes. This procedure is permitted provided that residuals are independent. In 1978, Shewhart modification for the autoregressive process was introduced by using the distance between the sample mean and the target value compared to the standard deviation of the autocorrelation process. In this paper we will examine the mean of EWMA for autocorrelation process derived from Montgomery and Patel. Performance to be investigated was investigated by examining Average Run Length (ARL) based on the Markov Chain Method.
Clinical proteomics in kidney disease as an exponential technology: heading towards the disruptive phase.

PubMed

Sanchez-Niño, Maria Dolores; Sanz, Ana B; Ramos, Adrian M; Fernandez-Fernandez, Beatriz; Ortiz, Alberto

2017-04-01

Exponential technologies double in power or processing speed every year, whereas their cost halves. Deception and disruption are two key stages in the development of exponential technologies. Deception occurs when, after initial introduction, technologies are dismissed as irrelevant, while they continue to progress, perhaps not as fast or with so many immediate practical applications as initially thought. Twenty years after the first publications, clinical proteomics is still not available in most hospitals and some clinicians have felt deception at unfulfilled promises. However, there are indications that clinical proteomics may be entering the disruptive phase, where, once refined, technologies disrupt established industries or procedures. In this regard, recent manuscripts in CKJ illustrate how proteomics is entering the clinical realm, with applications ranging from the identification of amyloid proteins in the pathology lab, to a new generation of urinary biomarkers for chronic kidney disease (CKD) assessment and outcome prediction. Indeed, one such panel of urinary peptidomics biomarkers, CKD273, recently received a Food and Drug Administration letter of support, the first ever in the CKD field. In addition, a must-read resource providing information on kidney disease-related proteomics and systems biology databases and how to access and use them in clinical decision-making was also recently published in CKJ .
The generalized truncated exponential distribution as a model for earthquake magnitudes

NASA Astrophysics Data System (ADS)

Raschke, Mathias

2015-04-01

The random distribution of small, medium and large earthquake magnitudes follows an exponential distribution (ED) according to the Gutenberg-Richter relation. But a magnitude distribution is truncated in the range of very large magnitudes because the earthquake energy is finite and the upper tail of the exponential distribution does not fit well observations. Hence the truncated exponential distribution (TED) is frequently applied for the modelling of the magnitude distributions in the seismic hazard and risk analysis. The TED has a weak point: when two TEDs with equal parameters, except the upper bound magnitude, are mixed, then the resulting distribution is not a TED. Inversely, it is also not possible to split a TED of a seismic region into TEDs of subregions with equal parameters, except the upper bound magnitude. This weakness is a principal problem as seismic regions are constructed scientific objects and not natural units. It also applies to alternative distribution models. The presented generalized truncated exponential distribution (GTED) overcomes this weakness. The ED and the TED are special cases of the GTED. Different issues of the statistical inference are also discussed and an example of empirical data is presented in the current contribution.
Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.
CORONAL FOURIER POWER SPECTRA: IMPLICATIONS FOR CORONAL SEISMOLOGY AND CORONAL HEATING

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

Ireland, J.; McAteer, R. T. J.; Inglis, A. R., E-mail: jack.ireland@nasa.gov

The dynamics of regions of the solar corona are investigated using Atmospheric Imaging Assembly 171 Å and 193 Å data. The coronal emission from the quiet Sun, coronal loop footprints, coronal moss, and from above a sunspot is studied. It is shown that the mean Fourier power spectra in these regions can be described by a power law at lower frequencies that tails to a flat spectrum at higher frequencies, plus a Gaussian-shaped contribution that varies depending on the region studied. This Fourier spectral shape is in contrast to the commonly held assumption that coronal time series are well describedmore » by the sum of a long timescale background trend plus Gaussian-distributed noise, with some specific locations also showing an oscillatory signal. The implications of the observed spectral shape on the fields of coronal seismology and the automated detection of oscillations in the corona are discussed. The power-law contribution to the shape of the Fourier power spectrum is interpreted as being due to the summation of a distribution of exponentially decaying emission events along the line of sight. This is consistent with the idea that the solar atmosphere is heated everywhere by small energy deposition events.« less
High-titer and productivity of l-(+)-lactic acid using exponential fed-batch fermentation with Bacillus coagulans arr4, a new thermotolerant bacterial strain.

PubMed

Coelho, Luciana Fontes; Beitel, Susan Michelz; Sass, Daiane Cristina; Neto, Paulo Marcelo Avila; Contiero, Jonas

2018-04-01

Bacillus coagulans arr4 is a thermotolerant microorganism with great biotechnological potential for l-(+)-lactic acid production from granulated sugar and yeast extract. The highest l-(+)-lactic acid production was obtained with Ca(OH) 2 . The maximum production of l-(+)-lactic acid (206.81 g/L) was observed in exponential feeding using granulated sugar solution (900 g/L) and yeast extract (1%) at 50 °C, pH 6.5, and initial granulated sugar concentration of 100 g/L at 39 h. 5.3 g/L h productivity and 97% yield were observed, and no sugar remained. Comparing the simple batch with exponential fed-batch fermentation, the l(+) lactic acid production was improved in 133.22% and dry cell weight was improved in 83.29%, using granulated sugar and yeast extract. This study presents the highest productivity of lactic acid ever observed in the literature, on the fermentation of thermotolerant Bacillus sp. as well as an innovative and high-efficiency purification technology, using low-cost substances as Celite and charcoal. The recovery of lactic acid was 86%, with 100% protein removal, and the fermentation medium (brown color) became a colorless solution.
Analysis on the Operation Strategy of the 220kV External Transmission Channel for the Nujiang Power Grid after the Installation of Series Compensation

NASA Astrophysics Data System (ADS)

Liu, Xiaoxin; Feng, Peilei; Jan, Lisheng; Dai, Xiaozhong; Cai, Pengcheng

2018-01-01

In recent years, Nujiang Prefecture vigorously develop hydropower, the grid structure in the northwest of Yunnan Province is not perfect, which leads to the research and construction of the power grid lags behind the development of the hydropower. In 2015, the company in view of the nu river hydropower dilemma decided to change outside the nu river to send out a passage with series compensation device in order to improve the transmission capacity, the company to the main problems related to the system plan, but not too much in the region distribution network and detailed study. Nujiang power grid has unique structure and properties of the nujiang power grid after respectively, a whole rack respectively into two parts, namely power delivery channels, load power supply, the whole grid occurred fundamental changes, the original strategy of power network is not applicable, especially noteworthy is the main failure after network of independent operation problem, how to avoid the local series, emergency problem is more urgent, very tolerance test area power grid, this paper aims at the analysis of existing data, simulation, provide a reference for respectively after the operation for the stable operation of the power grid.
Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2016-06-01

Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.
Cooperative bi-exponential decay of dye emission coupled via plasmons.

PubMed

Lyvers, David P; Moazzezi, Mojtaba; de Silva, Vashista C; Brown, Dean P; Urbas, Augustine M; Rostovtsev, Yuri V; Drachev, Vladimir P

2018-06-22

Bi-exponential decay of dye fluorescence near the surface of plasmonic metamaterials and core-shell nanoparticles is shown to be an intrinsic property of the coupled system. Indeed, the Dicke, cooperative states involve two groups of transitions: super-radiant, from the most excited to the ground states and sub-radiant, which cannot reach the ground state. The relaxation in the sub-radiant system occurs mainly due to the interaction with the plasmon modes. Our theory shows that the relaxation leads to the population of the sub-radiant states by dephasing the super-radiant Dicke states giving rise to the bi-exponential decay in agreement with the experiments. We use a set of metamaterial samples consisting of gratings of paired silver nanostrips coated with Rh800 dye molecules, having resonances in the same spectral range. The bi-exponential decay is demonstrated for Au\\SiO 2 \\ATTO655 core-shell nanoparticles as well, which persists even when averaging over a broad range of the coupling parameter.
Exact analytical solutions of continuity equation for electron beams precipitating in Coulomb collisions

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

Dobranskis, R. R.; Zharkova, V. V., E-mail: valentina.zharkova@northumbria.ac.uk

2014-06-10

The original continuity equation (CE) used for the interpretation of the power law energy spectra of beam electrons in flares was written and solved for an electron beam flux while ignoring an additional free term with an electron density. In order to remedy this omission, the original CE for electron flux, considering beam's energy losses in Coulomb collisions, was first differentiated by the two independent variables: depth and energy leading to partial differential equation for an electron beam density instead of flux with the additional free term. The analytical solution of this partial differential continuity equation (PDCE) is obtained bymore » using the method of characteristics. This solution is further used to derive analytical expressions for mean electron spectra for Coulomb collisions and to carry out numeric calculations of hard X-ray (HXR) photon spectra for beams with different parameters. The solutions revealed a significant departure of electron densities at lower energies from the original results derived from the CE for the flux obtained for Coulomb collisions. This departure is caused by the additional exponential term that appeared in the updated solutions for electron differential density leading to its faster decrease at lower energies (below 100 keV) with every precipitation depth similar to the results obtained with numerical Fokker-Planck solutions. The effects of these updated solutions for electron densities on mean electron spectra and HXR photon spectra are also discussed.« less
On the Occurrence of Mass Inflation for the Einstein-Maxwell-Scalar Field System with a Cosmological Constant and an Exponential Price Law

NASA Astrophysics Data System (ADS)

Costa, João L.; Girão, Pedro M.; Natário, José; Silva, Jorge Drumond

2018-03-01

In this paper we study the spherically symmetric characteristic initial data problem for the Einstein-Maxwell-scalar field system with a positive cosmological constant in the interior of a black hole, assuming an exponential Price law along the event horizon. More precisely, we construct open sets of characteristic data which, on the outgoing initial null hypersurface (taken to be the event horizon), converges exponentially to a reference Reissner-Nördstrom black hole at infinity. We prove the stability of the radius function at the Cauchy horizon, and show that, depending on the decay rate of the initial data, mass inflation may or may not occur. In the latter case, we find that the solution can be extended across the Cauchy horizon with continuous metric and Christoffel symbols in {L^2_{loc}} , thus violating the Christodoulou-Chruściel version of strong cosmic censorship.
A nanostructured surface increases friction exponentially at the solid-gas interface.

PubMed

Phani, Arindam; Putkaradze, Vakhtang; Hawk, John E; Prashanthi, Kovur; Thundat, Thomas

2016-09-06

According to Stokes' law, a moving solid surface experiences viscous drag that is linearly related to its velocity and the viscosity of the medium. The viscous interactions result in dissipation that is known to scale as the square root of the kinematic viscosity times the density of the gas. We observed that when an oscillating surface is modified with nanostructures, the experimentally measured dissipation shows an exponential dependence on kinematic viscosity. The surface nanostructures alter solid-gas interplay greatly, amplifying the dissipation response exponentially for even minute variations in viscosity. Nanostructured resonator thus allows discrimination of otherwise narrow range of gaseous viscosity making dissipation an ideal parameter for analysis of a gaseous media. We attribute the observed exponential enhancement to the stochastic nature of interactions of many coupled nanostructures with the gas media.

A nanostructured surface increases friction exponentially at the solid-gas interface

NASA Astrophysics Data System (ADS)

Phani, Arindam; Putkaradze, Vakhtang; Hawk, John E.; Prashanthi, Kovur; Thundat, Thomas

2016-09-01

According to Stokes’ law, a moving solid surface experiences viscous drag that is linearly related to its velocity and the viscosity of the medium. The viscous interactions result in dissipation that is known to scale as the square root of the kinematic viscosity times the density of the gas. We observed that when an oscillating surface is modified with nanostructures, the experimentally measured dissipation shows an exponential dependence on kinematic viscosity. The surface nanostructures alter solid-gas interplay greatly, amplifying the dissipation response exponentially for even minute variations in viscosity. Nanostructured resonator thus allows discrimination of otherwise narrow range of gaseous viscosity making dissipation an ideal parameter for analysis of a gaseous media. We attribute the observed exponential enhancement to the stochastic nature of interactions of many coupled nanostructures with the gas media.
Exponential integration algorithms applied to viscoplasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Walker, Kevin P.

1991-01-01

Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.
Power from Radioisotopes, Understanding the Atom Series.

ERIC Educational Resources Information Center

Corliss, William R.; Mead, Robert L.

This 1971 revision deals with radioisotopes and their use in power generators. Early developments and applications for the Systems for Nuclear Auxiliary Power (SNAP) and Radioisotope Thermoelectric Generators (RTGs) are reviewed. Present uses in space and on earth are included. Uses in space are as power sources in various satellites and space…
Interferometric measurements of a dendritic growth front solutal diffusion layer

NASA Technical Reports Server (NTRS)

Hopkins, John A.; Mccay, T. D.; Mccay, Mary H.

1991-01-01

An experimental study was undertaken to measure solutal distributions in the diffusion layer produced during the vertical directional solidification (VDS) of an ammonium chloride - water (NH4Cl-H2O) solution. Interferometry was used to obtain concentration measurements in the 1-2 millimeter region defining the diffusion layer. These measurements were fitted to an exponential form to extract the characteristic diffusion parameter for various times after the start of solidification. The diffusion parameters are within the limits predicted by steady state theory and suggest that the effective solutal diffusivity is increasing as solidification progresses.
Exponential Thurston maps and limits of quadratic differentials

NASA Astrophysics Data System (ADS)

Hubbard, John; Schleicher, Dierk; Shishikura, Mitsuhiro

2009-01-01

We give a topological characterization of postsingularly finite topological exponential maps, i.e., universal covers g\\colon{C}to{C}setminus\\{0\\} such that 0 has a finite orbit. Such a map either is Thurston equivalent to a unique holomorphic exponential map λ e^z or it has a topological obstruction called a degenerate Levy cycle. This is the first analog of Thurston's topological characterization theorem of rational maps, as published by Douady and Hubbard, for the case of infinite degree. One main tool is a theorem about the distribution of mass of an integrable quadratic differential with a given number of poles, providing an almost compact space of models for the entire mass of quadratic differentials. This theorem is given for arbitrary Riemann surfaces of finite type in a uniform way.
Efficient algorithm for locating and sizing series compensation devices in large power transmission grids: I. Model implementation

NASA Astrophysics Data System (ADS)

Frolov, Vladimir; Backhaus, Scott; Chertkov, Misha

2014-10-01

We explore optimization methods for planning the placement, sizing and operations of flexible alternating current transmission system (FACTS) devices installed to relieve transmission grid congestion. We limit our selection of FACTS devices to series compensation (SC) devices that can be represented by modification of the inductance of transmission lines. Our master optimization problem minimizes the l1 norm of the inductance modification subject to the usual line thermal-limit constraints. We develop heuristics that reduce this non-convex optimization to a succession of linear programs (LP) that are accelerated further using cutting plane methods. The algorithm solves an instance of the MatPower Polish Grid model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard laptop—a speed that allows the sizing and placement of a family of SC devices to correct a large set of anticipated congestions. We observe that our algorithm finds feasible solutions that are always sparse, i.e., SC devices are placed on only a few lines. In a companion manuscript, we demonstrate our approach on realistically sized networks that suffer congestion from a range of causes, including generator retirement. In this manuscript, we focus on the development of our approach, investigate its structure on a small test system subject to congestion from uniform load growth, and demonstrate computational efficiency on a realistically sized network.
Memory and betweenness preference in temporal networks induced from time series

NASA Astrophysics Data System (ADS)

Weng, Tongfeng; Zhang, Jie; Small, Michael; Zheng, Rui; Hui, Pan

2017-02-01

We construct temporal networks from time series via unfolding the temporal information into an additional topological dimension of the networks. Thus, we are able to introduce memory entropy analysis to unravel the memory effect within the considered signal. We find distinct patterns in the entropy growth rate of the aggregate network at different memory scales for time series with different dynamics ranging from white noise, 1/f noise, autoregressive process, periodic to chaotic dynamics. Interestingly, for a chaotic time series, an exponential scaling emerges in the memory entropy analysis. We demonstrate that the memory exponent can successfully characterize bifurcation phenomenon, and differentiate the human cardiac system in healthy and pathological states. Moreover, we show that the betweenness preference analysis of these temporal networks can further characterize dynamical systems and separate distinct electrocardiogram recordings. Our work explores the memory effect and betweenness preference in temporal networks constructed from time series data, providing a new perspective to understand the underlying dynamical systems.
A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.
Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions

NASA Astrophysics Data System (ADS)

Merzon, A.; Zhevandrov, P.; Romero Rodríguez, M. I.; De la Paz Méndez, J. E.

2018-06-01

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.
Theory for Transitions Between Exponential and Stationary Phases: Universal Laws for Lag Time

NASA Astrophysics Data System (ADS)

Himeoka, Yusuke; Kaneko, Kunihiko

2017-04-01

The quantitative characterization of bacterial growth has attracted substantial attention since Monod's pioneering study. Theoretical and experimental works have uncovered several laws for describing the exponential growth phase, in which the number of cells grows exponentially. However, microorganism growth also exhibits lag, stationary, and death phases under starvation conditions, in which cell growth is highly suppressed, for which quantitative laws or theories are markedly underdeveloped. In fact, the models commonly adopted for the exponential phase that consist of autocatalytic chemical components, including ribosomes, can only show exponential growth or decay in a population; thus, phases that halt growth are not realized. Here, we propose a simple, coarse-grained cell model that includes an extra class of macromolecular components in addition to the autocatalytic active components that facilitate cellular growth. These extra components form a complex with the active components to inhibit the catalytic process. Depending on the nutrient condition, the model exhibits typical transitions among the lag, exponential, stationary, and death phases. Furthermore, the lag time needed for growth recovery after starvation follows the square root of the starvation time and is inversely related to the maximal growth rate. This is in agreement with experimental observations, in which the length of time of cell starvation is memorized in the slow accumulation of molecules. Moreover, the lag time distributed among cells is skewed with a long time tail. If the starvation time is longer, an exponential tail appears, which is also consistent with experimental data. Our theory further predicts a strong dependence of lag time on the speed of substrate depletion, which can be tested experimentally. The present model and theoretical analysis provide universal growth laws beyond the exponential phase, offering insight into how cells halt growth without entering the death phase.
Discrete breathers in an array of self-excited oscillators: Exact solutions and stability

NASA Astrophysics Data System (ADS)

Shiroky, I. B.; Gendelman, O. V.

2016-10-01

We consider dynamics of array of coupled self-excited oscillators. The model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs) and exploration of their stability in the space of parameters. The DB solutions exist for all frequencies in the attenuation zone but lose stability via Neimark-Sacker bifurcation in the vicinity of the bandgap boundary. Besides the well-known DBs with exponential localization, the considered system possesses novel type of solutions—discrete breathers with main frequency in the propagation zone of the chain. In these regimes, the energy irradiation into the chain is balanced by the self-excitation. The amplitude of oscillations is maximal at the localization site and then exponentially approaches constant value at infinity. We also derive these solutions in the closed analytic form. They are stable in a narrow region of system parameters bounded by Neimark-Sacker and pitchfork bifurcations.
Stochastic modeling of neurobiological time series: Power, coherence, Granger causality, and separation of evoked responses from ongoing activity

NASA Astrophysics Data System (ADS)

Chen, Yonghong; Bressler, Steven L.; Knuth, Kevin H.; Truccolo, Wilson A.; Ding, Mingzhou

2006-06-01

In this article we consider the stochastic modeling of neurobiological time series from cognitive experiments. Our starting point is the variable-signal-plus-ongoing-activity model. From this model a differentially variable component analysis strategy is developed from a Bayesian perspective to estimate event-related signals on a single trial basis. After subtracting out the event-related signal from recorded single trial time series, the residual ongoing activity is treated as a piecewise stationary stochastic process and analyzed by an adaptive multivariate autoregressive modeling strategy which yields power, coherence, and Granger causality spectra. Results from applying these methods to local field potential recordings from monkeys performing cognitive tasks are presented.
Progress, Exponential Growth and Post-Growth Education

ERIC Educational Resources Information Center

Irwin, Ruth

2017-01-01

Teleological progress is the underlying motif of modern culture, and informs education, innovation, and economic development. Progress includes a gradual increase in consumerism. Since the 1940s, the Keynesian Settlement and its embedded belief in progress is legislated in exponential 2-3% economic growth. Unfortunately, climate change is a direct…
Comparison of VLBI TRF solutions based on Kalman filtering and recent ITRS realizations

NASA Astrophysics Data System (ADS)

Soja, Benedikt; Nilsson, Tobias; Glaser, Susanne; Balidakis, Kyriakos; Karbon, Maria; Heinkelmann, Robert; Gross, Richard; Schuh, Harald

2016-04-01

Compared to previous prominent global terrestrial reference frames (TRF) solutions, such as the ITRF2008 or DTRF2008, the current accuracy requirements demand among other things extended parameterization to account for various non-linear signals present in the time series of station coordinates. The next generation of TRFs, built upon geodetic data until the end of 2014, employs different approaches to tackle in particular seasonal variations and post-seismic deformations. The ITRF2014, developed at the International Earth Rotation and Reference Systems Service (IERS) Combination Center (CC) at Institut Géographique National, introduces harmonic, exponential and logarithmic functions to take into account aforementioned effects. In contrast, the ITRS realization of the IERS CC at Jet Propulsion Laboratory is based on Kalman filtering, which allows coordinate variations to be modeled in a stochastic sense besides the parameterized linear and seasonal signals. In our study, we compare these multi-technique TRFs with solutions solely based on VLBI data, including 104 radio telescopes and 4239 VLBI sessions, covering a time span of 34 years. We calculated a VLBI TRF based on the traditional least-squares adjustment of session-wise normal equations, and an ensemble of Kalman filter and smoother solutions with different parameterizations and stochastic models. In particular, we investigate the impact of different process noise levels for station coordinates, the choice of stochastic processes, e.g. random walks, and the application of time- and station-dependent noise models. For instance, we find that the estimation of seasonal signals, while important for predictions, does not affect the filtered coordinate time series when observational data is available. Furthermore, post-seismic deformations after major earthquakes require the process noise to be scaled accordingly. For instance, we detected coordinate differences of up to 5 cm immediately after the Chile 2010
Power System Decomposition for Practical Implementation of Bulk-Grid Voltage Control Methods

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

Vallem, Mallikarjuna R.; Vyakaranam, Bharat GNVSR; Holzer, Jesse T.

Power system algorithms such as AC optimal power flow and coordinated volt/var control of the bulk power system are computationally intensive and become difficult to solve in operational time frames. The computational time required to run these algorithms increases exponentially as the size of the power system increases. The solution time for multiple subsystems is less than that for solving the entire system simultaneously, and the local nature of the voltage problem lends itself to such decomposition. This paper describes an algorithm that can be used to perform power system decomposition from the point of view of the voltage controlmore » problem. Our approach takes advantage of the dominant localized effect of voltage control and is based on clustering buses according to the electrical distances between them. One of the contributions of the paper is to use multidimensional scaling to compute n-dimensional Euclidean coordinates for each bus based on electrical distance to perform algorithms like K-means clustering. A simple coordinated reactive power control of photovoltaic inverters for voltage regulation is used to demonstrate the effectiveness of the proposed decomposition algorithm and its components. The proposed decomposition method is demonstrated on the IEEE 118-bus system.« less
Exponential model for option prices: Application to the Brazilian market

NASA Astrophysics Data System (ADS)

Ramos, Antônio M. T.; Carvalho, J. A.; Vasconcelos, G. L.

2016-03-01

In this paper we report an empirical analysis of the Ibovespa index of the São Paulo Stock Exchange and its respective option contracts. We compare the empirical data on the Ibovespa options with two option pricing models, namely the standard Black-Scholes model and an empirical model that assumes that the returns are exponentially distributed. It is found that at times near the option expiration date the exponential model performs better than the Black-Scholes model, in the sense that it fits the empirical data better than does the latter model.
On exponential stability of linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Tien Dung, Nguyen

2015-02-01

The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].
Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement

PubMed Central

Gustman, Alan L.; Steinmeier, Thomas L.

2012-01-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest. Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used. PMID:22711946
Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement.

PubMed

Gustman, Alan L; Steinmeier, Thomas L

2012-06-01

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest.Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used.
Detecting chaos in irregularly sampled time series.

PubMed

Kulp, C W

2013-09-01

Recently, Wiebe and Virgin [Chaos 22, 013136 (2012)] developed an algorithm which detects chaos by analyzing a time series' power spectrum which is computed using the Discrete Fourier Transform (DFT). Their algorithm, like other time series characterization algorithms, requires that the time series be regularly sampled. Real-world data, however, are often irregularly sampled, thus, making the detection of chaotic behavior difficult or impossible with those methods. In this paper, a characterization algorithm is presented, which effectively detects chaos in irregularly sampled time series. The work presented here is a modification of Wiebe and Virgin's algorithm and uses the Lomb-Scargle Periodogram (LSP) to compute a series' power spectrum instead of the DFT. The DFT is not appropriate for irregularly sampled time series. However, the LSP is capable of computing the frequency content of irregularly sampled data. Furthermore, a new method of analyzing the power spectrum is developed, which can be useful for differentiating between chaotic and non-chaotic behavior. The new characterization algorithm is successfully applied to irregularly sampled data generated by a model as well as data consisting of observations of variable stars.

Convergence of a Catalan Series

ERIC Educational Resources Information Center

Koshy, Thomas; Gao, Zhenguang

2012-01-01

This article studies the convergence of the infinite series of the reciprocals of the Catalan numbers. We extract the sum of the series as well as some related ones, illustrating the power of the calculus in the study of the Catalan numbers.
78 FR 11904 - Zion Nuclear Power Station, Units 1 and 2; ZionSolutions, LLC; Consideration of Indirect Transfer

Federal Register 2010, 2011, 2012, 2013, 2014

2013-02-20

... NUCLEAR REGULATORY COMMISSION [Docket Nos. 50-295 and 50-304; NRC-2013-0034] Zion Nuclear Power Station, Units 1 and 2; ZionSolutions, LLC; Consideration of Indirect Transfer AGENCY: Nuclear Regulatory... the indirect transfer of Facility Operating License Nos. DPR-39 and DPR-48 for Zion Nuclear Power...
Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory

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

Cid, Antonella; Leon, Genly; Leyva, Yoelsy, E-mail: acidm@ubiobio.cl, E-mail: genly.leon@ucv.cl, E-mail: yoelsy.leyva@uta.cl

2016-02-01

In this paper we investigate the evolution of a Jordan-Brans-Dicke scalar field, Φ, with a power-law potential in the presence of a second scalar field, φ, with an exponential potential, in both the Jordan and the Einstein frames. We present the relation of our model with the induced gravity model with power-law potential and the integrability of this kind of models is discussed when the quintessence field φ is massless, and has a small velocity. The fact that for some fine-tuned values of the parameters we may get some integrable cosmological models, makes our choice of potentials very interesting. Wemore » prove that in Jordan-Brans-Dicke theory, the de Sitter solution is not a natural attractor. Instead, we show that the attractor in the Jordan frame corresponds to an ''intermediate accelerated'' solution of the form a(t) ≅ e{sup α{sub 1} t{sup p{sup {sub 1}}}}, as t → ∞ where α{sub 1} > 0 and 0 < p{sub 1} < 1, for a wide range of parameters. Furthermore, when we work in the Einstein frame we get that the attractor is also an ''intermediate accelerated'' solution of the form a(t) ≅ e{sup α{sub 2} tp{sub 2}} as t → ∞ where α{sub 2} > 0 and 0« less
Optimal power flow with optimal placement TCSC device on 500 kV Java-Bali electrical power system using genetic Algorithm-Taguchi method

NASA Astrophysics Data System (ADS)

Apribowo, Chico Hermanu Brillianto; Ibrahim, Muhammad Hamka; Wicaksono, F. X. Rian

2018-02-01

The growing burden of the load and the complexity of the power system has had an impact on the need for optimization of power system operation. Optimal power flow (OPF) with optimal location placement and rating of thyristor controlled series capacitor (TCSC) is an effective solution used to determine the economic cost of operating the plant and regulate the power flow in the power system. The purpose of this study is to minimize the total cost of generation by placing the location and the optimal rating of TCSC using genetic algorithm-design of experiment techniques (GA-DOE). Simulation on Java-Bali system 500 kV with the amount of TCSC used by 5 compensator, the proposed method can reduce the generation cost by 0.89% compared to OPF without using TCSC.
Exact solution of corner-modified banded block-Toeplitz eigensystems

NASA Astrophysics Data System (ADS)

Cobanera, Emilio; Alase, Abhijeet; Ortiz, Gerardo; Viola, Lorenza

2017-05-01

Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified. Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz, independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix, whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev.
High precision series solutions of differential equations: Ordinary and regular singular points of second order ODEs

NASA Astrophysics Data System (ADS)

Noreen, Amna; Olaussen, Kåre

2012-10-01

A subroutine for a very-high-precision numerical solution of a class of ordinary differential equations is provided. For a given evaluation point and equation parameters the memory requirement scales linearly with precision P, and the number of algebraic operations scales roughly linearly with P when P becomes sufficiently large. We discuss results from extensive tests of the code, and how one, for a given evaluation point and equation parameters, may estimate precision loss and computing time in advance. Program summary Program title: seriesSolveOde1 Catalogue identifier: AEMW_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 991 No. of bytes in distributed program, including test data, etc.: 488116 Distribution format: tar.gz Programming language: C++ Computer: PC's or higher performance computers. Operating system: Linux and MacOS RAM: Few to many megabytes (problem dependent). Classification: 2.7, 4.3 External routines: CLN — Class Library for Numbers [1] built with the GNU MP library [2], and GSL — GNU Scientific Library [3] (only for time measurements). Nature of problem: The differential equation -s2({d2}/{dz2}+{1-ν+-ν-}/{z}{d}/{dz}+{ν+ν-}/{z2})ψ(z)+{1}/{z} ∑n=0N vnznψ(z)=0, is solved numerically to very high precision. The evaluation point z and some or all of the equation parameters may be complex numbers; some or all of them may be represented exactly in terms of rational numbers. Solution method: The solution ψ(z), and optionally ψ'(z), is evaluated at the point z by executing the recursion A(z)={s-2}/{(m+1+ν-ν+)(m+1+ν-ν-)} ∑n=0N Vn(z)A(z), ψ(z)=ψ(z)+A(z), to sufficiently large m. Here ν is either ν+ or ν-, and Vn(z)=vnz. The recursion is initialized by A(z)=δzν,for n
Lump solutions with interaction phenomena in the (2+1)-dimensional Ito equation

NASA Astrophysics Data System (ADS)

Zou, Li; Yu, Zong-Bing; Tian, Shou-Fu; Feng, Lian-Li; Li, Jin

2018-03-01

In this paper, we consider the (2+1)-dimensional Ito equation, which was introduced by Ito. By considering the Hirota’s bilinear method, and using the positive quadratic function, we obtain some lump solutions of the Ito equation. In order to ensure rational localization and analyticity of these lump solutions, some sufficient and necessary conditions are provided on the parameters that appeared in the solutions. Furthermore, the interaction solutions between lump solutions and the stripe solitons are discussed by combining positive quadratic function with exponential function. Finally, the dynamic properties of these solutions are shown via the way of graphical analysis by selecting appropriate values of the parameters.
Automatic selection of arterial input function using tri-exponential models

NASA Astrophysics Data System (ADS)

Yao, Jianhua; Chen, Jeremy; Castro, Marcelo; Thomasson, David

2009-02-01

Dynamic Contrast Enhanced MRI (DCE-MRI) is one method for drug and tumor assessment. Selecting a consistent arterial input function (AIF) is necessary to calculate tissue and tumor pharmacokinetic parameters in DCE-MRI. This paper presents an automatic and robust method to select the AIF. The first stage is artery detection and segmentation, where knowledge about artery structure and dynamic signal intensity temporal properties of DCE-MRI is employed. The second stage is AIF model fitting and selection. A tri-exponential model is fitted for every candidate AIF using the Levenberg-Marquardt method, and the best fitted AIF is selected. Our method has been applied in DCE-MRIs of four different body parts: breast, brain, liver and prostate. The success rates in artery segmentation for 19 cases are 89.6%+/-15.9%. The pharmacokinetic parameters computed from the automatically selected AIFs are highly correlated with those from manually determined AIFs (R2=0.946, P(T<=t)=0.09). Our imaging-based tri-exponential AIF model demonstrated significant improvement over a previously proposed bi-exponential model.
Reduced Heme Levels Underlie the Exponential Growth Defect of the Shewanella oneidensis hfq Mutant

PubMed Central

Mezoian, Taylor; Hunt, Taylor M.; Keane, Meaghan L.; Leonard, Jessica N.; Scola, Shelby E.; Beer, Emma N.; Perdue, Sarah; Pellock, Brett J.

2014-01-01

The RNA chaperone Hfq fulfills important roles in small regulatory RNA (sRNA) function in many bacteria. Loss of Hfq in the dissimilatory metal reducing bacterium Shewanella oneidensis strain MR-1 results in slow exponential phase growth and a reduced terminal cell density at stationary phase. We have found that the exponential phase growth defect of the hfq mutant in LB is the result of reduced heme levels. Both heme levels and exponential phase growth of the hfq mutant can be completely restored by supplementing LB medium with 5-aminolevulinic acid (5-ALA), the first committed intermediate synthesized during heme synthesis. Increasing expression of gtrA, which encodes the enzyme that catalyzes the first step in heme biosynthesis, also restores heme levels and exponential phase growth of the hfq mutant. Taken together, our data indicate that reduced heme levels are responsible for the exponential growth defect of the S. oneidensis hfq mutant in LB medium and suggest that the S. oneidensis hfq mutant is deficient in heme production at the 5-ALA synthesis step. PMID:25356668
Square Root Graphical Models: Multivariate Generalizations of Univariate Exponential Families that Permit Positive Dependencies

PubMed Central

Inouye, David I.; Ravikumar, Pradeep; Dhillon, Inderjit S.

2016-01-01

We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models (Yang et al., 2015) did not allow positive dependencies for the exponential and Poisson generalizations. However, in many real-world datasets, variables clearly have positive dependencies. For example, the airport delay time in New York—modeled as an exponential distribution—is positively related to the delay time in Boston. With this motivation, we give an example of our model class derived from the univariate exponential distribution that allows for almost arbitrary positive and negative dependencies with only a mild condition on the parameter matrix—a condition akin to the positive definiteness of the Gaussian covariance matrix. Our Poisson generalization allows for both positive and negative dependencies without any constraints on the parameter values. We also develop parameter estimation methods using node-wise regressions with ℓ1 regularization and likelihood approximation methods using sampling. Finally, we demonstrate our exponential generalization on a synthetic dataset and a real-world dataset of airport delay times. PMID:27563373
Statistical analyses support power law distributions found in neuronal avalanches.

PubMed

Klaus, Andreas; Yu, Shan; Plenz, Dietmar

2011-01-01

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.
Exponential evolution: implications for intelligent extraterrestrial life.

PubMed

Russell, D A

1983-01-01

Some measures of biologic complexity, including maximal levels of brain development, are exponential functions of time through intervals of 10(6) to 10(9) yrs. Biological interactions apparently stimulate evolution but physical conditions determine the time required to achieve a given level of complexity. Trends in brain evolution suggest that other organisms could attain human levels within approximately 10(7) yrs. The number (N) and longevity (L) terms in appropriate modifications of the Drake Equation, together with trends in the evolution of biological complexity on Earth, could provide rough estimates of the prevalence of life forms at specified levels of complexity within the Galaxy. If life occurs throughout the cosmos, exponential evolutionary processes imply that higher intelligence will soon (10(9) yrs) become more prevalent than it now is. Changes in the physical universe become less rapid as time increases from the Big Bang. Changes in biological complexity may be most rapid at such later times. This lends a unique and symmetrical importance to early and late universal times.
Domestic wastewater treatment and power generation in continuous flow air-cathode stacked microbial fuel cell: Effect of series and parallel configuration.

PubMed

Estrada-Arriaga, Edson Baltazar; Hernández-Romano, Jesús; García-Sánchez, Liliana; Guillén Garcés, Rosa Angélica; Bahena-Bahena, Erick Obed; Guadarrama-Pérez, Oscar; Moeller Chavez, Gabriela Eleonora

2018-05-15

In this study, a continuous flow stack consisting of 40 individual air-cathode MFC units was used to determine the performance of stacked MFC during domestic wastewater treatment operated with unconnected individual MFC and in series and parallel configuration. The voltages obtained from individual MFC units were of 0.08-1.1 V at open circuit voltage, while in series connection, the maximum power and current density were 2500 mW/m 2 and 500 mA/m 2 (4.9 V), respectively. In parallel connection, the maximum power and current density was 5.8 mW/m 2 and 24 mA/m 2 , respectively. When the cells were not connected to each other MFC unit, the main bacterial species found in the anode biofilms were Bacillus and Lysinibacillus. After switching from unconnected to series and parallel connections, the most abundant species in the stacked MFC were Pseudomonas aeruginosa, followed by different Bacilli classes. This study demonstrated that when the stacked MFC was switched from unconnected to series and parallel connections, the pollutants removal, performance electricity and microbial community changed significantly. Voltages drops were observed in the stacked MFC, which was mainly limited by the cathodes. These voltages loss indicated high resistances within the stacked MFC, generating a parasitic cross current. Copyright © 2018 Elsevier Ltd. All rights reserved.
A Simple Mechanical Experiment on Exponential Growth

ERIC Educational Resources Information Center

McGrew, Ralph

2015-01-01

With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…
Formulation and Stability of Solutions.

PubMed

Akers, Michael J

2016-01-01

Ready-to-use solutions are the most preferable and most common dosage forms for injectable and topical ophthalmic products. Drugs formulated as solution almost always have chemical and physical stability challenges as well as solubility limitations and the need to prevent inadvertent microbial contamination issues. The first in this series of articles took us through a discussion of optimizing the physical stability of solutions. This article concludes this series of articles with a discussion on foreign particles, protein aggregation, and immunogenicity; optimizing microbiological activity; and osmolality (tonicity) agents, and discusses how these challenges and issues are addressed.
Exact, E = 0, classical and quantum solutions for general power-law oscillators

NASA Technical Reports Server (NTRS)

Nieto, Michael Martin; Daboul, Jamil

1995-01-01

For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.
Teaching Exponential Growth and Decay: Examples from Medicine

ERIC Educational Resources Information Center

Hobbie, Russell K.

1973-01-01

A treatment of exponential growth and decay is sketched which does not require knowledge of calculus, and hence, it can be applied to many cases in the biological and medical sciences. Some examples are bacterial growth, sterilization, clearance, and drug absorption. (DF)
Historical remarks on exponential product and quantum analysis

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

Suzuki, Masuo

2015-03-10

The exponential product formula [1, 2] was substantially introduced in physics by the present author [2]. Its systematic applications to quantum Monte Carlo Methods [3] were preformed [4, 5] first in 1977. Many interesting applications [6] of the quantum-classical correspondence (namely S-T transformation) have been reported. Systematic higher-order decomposition formulae were also discovered by the present author [7-11], using the recursion scheme [7, 9]. Physically speaking, these exponential product formulae play a conceptual role of separation of procedures [3,14]. Mathematical aspects of these formulae have been integrated in quantum analysis [15], in which non-commutative differential calculus is formulated and amore » general quantum Taylor expansion formula is given. This yields many useful operator expansion formulae such as the Feynman expansion formula and the resolvent expansion. Irreversibility and entropy production are also studied using quantum analysis [15].« less
Technical and economic feasibility of development innovative technological solutions for expansion the adjustment range of high-power CCP

NASA Astrophysics Data System (ADS)

Arakelyan, E. K.; Andryushin, A. V.; Burtsev, S. Y.; Andryushin, K. A.

2017-11-01

The analysis of technical and parametric constraints on the adjustment range of highpower CCP and recommended technological solutions in the technical literature for their elimination. Established that in the conditions of toughening the requirements for economy, reliability and maneuverability on the part of the system operator with the participation of CCP in control the frequency and power in the power system, existing methods do not ensure the fulfillment of these requirements. The current situation in the energy sector — the lack of highly manoeuvrable power equipment leads to the need participate in control of power consumption diagrams for all types of power plants, including CCP, although initially they were intended primarily for basic loads. Large-scale research conducted at the department of Automated control systems of technological processes, showed the possibility of a significant expansion of the adjustment range of CCP when it operating in the condensing mode and in the heating mode. The report presents the main results of these research for example the CCP-450 and CCP-450T. Various technological solutions are considered: when CCP in the condensation mode — the use of bypass steam distribution schemes, the transfer of a part of the steam turbine into a low-steam mode; when CCP operation in the heating mode — bypass steam distribution and the transfer CCP to gas turbine unit — power heating plants mode with the transfer the steam turbine to the motor mode. Data on the evaluation of the technical and economic feasibility of the proposed innovative technological solutions are presented in comparison with the methods used to solve this problem, which are used in practice, such as passing through the failures of the electric load graphs by transferring the CCP to the mode of operation with incomplete equipment. When comparing, both the economics, and the maneuverability and reliability of the equipment are considered.
Non-exponential kinetics of unfolding under a constant force.

PubMed

Bell, Samuel; Terentjev, Eugene M

2016-11-14

We examine the population dynamics of naturally folded globular polymers, with a super-hydrophobic "core" inserted at a prescribed point in the polymer chain, unfolding under an application of external force, as in AFM force-clamp spectroscopy. This acts as a crude model for a large class of folded biomolecules with hydrophobic or hydrogen-bonded cores. We find that the introduction of super-hydrophobic units leads to a stochastic variation in the unfolding rate, even when the positions of the added monomers are fixed. This leads to the average non-exponential population dynamics, which is consistent with a variety of experimental data and does not require any intrinsic quenched disorder that was traditionally thought to be at the origin of non-exponential relaxation laws.

Non-exponential kinetics of unfolding under a constant force

NASA Astrophysics Data System (ADS)

Bell, Samuel; Terentjev, Eugene M.

2016-11-01

We examine the population dynamics of naturally folded globular polymers, with a super-hydrophobic "core" inserted at a prescribed point in the polymer chain, unfolding under an application of external force, as in AFM force-clamp spectroscopy. This acts as a crude model for a large class of folded biomolecules with hydrophobic or hydrogen-bonded cores. We find that the introduction of super-hydrophobic units leads to a stochastic variation in the unfolding rate, even when the positions of the added monomers are fixed. This leads to the average non-exponential population dynamics, which is consistent with a variety of experimental data and does not require any intrinsic quenched disorder that was traditionally thought to be at the origin of non-exponential relaxation laws.
A modified exponential behavioral economic demand model to better describe consumption data.

PubMed

Koffarnus, Mikhail N; Franck, Christopher T; Stein, Jeffrey S; Bickel, Warren K

2015-12-01

Behavioral economic demand analyses that quantify the relationship between the consumption of a commodity and its price have proven useful in studying the reinforcing efficacy of many commodities, including drugs of abuse. An exponential equation proposed by Hursh and Silberberg (2008) has proven useful in quantifying the dissociable components of demand intensity and demand elasticity, but is limited as an analysis technique by the inability to correctly analyze consumption values of zero. We examined an exponentiated version of this equation that retains all the beneficial features of the original Hursh and Silberberg equation, but can accommodate consumption values of zero and improves its fit to the data. In Experiment 1, we compared the modified equation with the unmodified equation under different treatments of zero values in cigarette consumption data collected online from 272 participants. We found that the unmodified equation produces different results depending on how zeros are treated, while the exponentiated version incorporates zeros into the analysis, accounts for more variance, and is better able to estimate actual unconstrained consumption as reported by participants. In Experiment 2, we simulated 1,000 datasets with demand parameters known a priori and compared the equation fits. Results indicated that the exponentiated equation was better able to replicate the true values from which the test data were simulated. We conclude that an exponentiated version of the Hursh and Silberberg equation provides better fits to the data, is able to fit all consumption values including zero, and more accurately produces true parameter values. (PsycINFO Database Record (c) 2015 APA, all rights reserved).
Statistical assessment of bi-exponential diffusion weighted imaging signal characteristics induced by intravoxel incoherent motion in malignant breast tumors

PubMed Central

Wong, Oi Lei; Lo, Gladys G.; Chan, Helen H. L.; Wong, Ting Ting; Cheung, Polly S. Y.

2016-01-01

Background The purpose of this study is to statistically assess whether bi-exponential intravoxel incoherent motion (IVIM) model better characterizes diffusion weighted imaging (DWI) signal of malignant breast tumor than mono-exponential Gaussian diffusion model. Methods 3 T DWI data of 29 malignant breast tumors were retrospectively included. Linear least-square mono-exponential fitting and segmented least-square bi-exponential fitting were used for apparent diffusion coefficient (ADC) and IVIM parameter quantification, respectively. F-test and Akaike Information Criterion (AIC) were used to statistically assess the preference of mono-exponential and bi-exponential model using region-of-interests (ROI)-averaged and voxel-wise analysis. Results For ROI-averaged analysis, 15 tumors were significantly better fitted by bi-exponential function and 14 tumors exhibited mono-exponential behavior. The calculated ADC, D (true diffusion coefficient) and f (pseudo-diffusion fraction) showed no significant differences between mono-exponential and bi-exponential preferable tumors. Voxel-wise analysis revealed that 27 tumors contained more voxels exhibiting mono-exponential DWI decay while only 2 tumors presented more bi-exponential decay voxels. ADC was consistently and significantly larger than D for both ROI-averaged and voxel-wise analysis. Conclusions Although the presence of IVIM effect in malignant breast tumors could be suggested, statistical assessment shows that bi-exponential fitting does not necessarily better represent the DWI signal decay in breast cancer under clinically typical acquisition protocol and signal-to-noise ratio (SNR). Our study indicates the importance to statistically examine the breast cancer DWI signal characteristics in practice. PMID:27709078
Adaptive exponential integrate-and-fire model as an effective description of neuronal activity.

PubMed

Brette, Romain; Gerstner, Wulfram

2005-11-01

We introduce a two-dimensional integrate-and-fire model that combines an exponential spike mechanism with an adaptation equation, based on recent theoretical findings. We describe a systematic method to estimate its parameters with simple electrophysiological protocols (current-clamp injection of pulses and ramps) and apply it to a detailed conductance-based model of a regular spiking neuron. Our simple model predicts correctly the timing of 96% of the spikes (+/-2 ms) of the detailed model in response to injection of noisy synaptic conductances. The model is especially reliable in high-conductance states, typical of cortical activity in vivo, in which intrinsic conductances were found to have a reduced role in shaping spike trains. These results are promising because this simple model has enough expressive power to reproduce qualitatively several electrophysiological classes described in vitro.
Ratio-based lengths of intervals to improve fuzzy time series forecasting.

PubMed

Huarng, Kunhuang; Yu, Tiffany Hui-Kuang

2006-04-01

The objective of this study is to explore ways of determining the useful lengths of intervals in fuzzy time series. It is suggested that ratios, instead of equal lengths of intervals, can more properly represent the intervals among observations. Ratio-based lengths of intervals are, therefore, proposed to improve fuzzy time series forecasting. Algebraic growth data, such as enrollments and the stock index, and exponential growth data, such as inventory demand, are chosen as the forecasting targets, before forecasting based on the various lengths of intervals is performed. Furthermore, sensitivity analyses are also carried out for various percentiles. The ratio-based lengths of intervals are found to outperform the effective lengths of intervals, as well as the arbitrary ones in regard to the different statistical measures. The empirical analysis suggests that the ratio-based lengths of intervals can also be used to improve fuzzy time series forecasting.
Correlating the stretched-exponential and super-Arrhenius behaviors in the structural relaxation of glass-forming liquids.

PubMed

Wang, Lianwen; Li, Jiangong; Fecht, Hans-Jörg

2011-04-20

Following the report of a single-exponential activation behavior behind the super-Arrhenius structural relaxation of glass-forming liquids in our preceding paper, we find that the non-exponentiality in the structural relaxation of glass-forming liquids is straightforwardly determined by the relaxation time, and could be calculated from the measured relaxation data. Comparisons between the calculated and measured non-exponentialities for typical glass-forming liquids, from fragile to intermediate, convincingly support the present analysis. Hence the origin of the non-exponentiality and its correlation with liquid fragility become clearer.
GPS coordinate time series measurements in Ontario and Quebec, Canada

NASA Astrophysics Data System (ADS)

Samadi Alinia, Hadis; Tiampo, Kristy F.; James, Thomas S.

2017-06-01

New precise network solutions for continuous GPS (cGPS) stations distributed in eastern Ontario and western Québec provide constraints on the regional three-dimensional crustal velocity field. Five years of continuous observations at fourteen cGPS sites were analyzed using Bernese GPS processing software. Several different sub-networks were chosen from these stations, and the data were processed and compared to in order to select the optimal configuration to accurately estimate the vertical and horizontal station velocities and minimize the associated errors. The coordinate time series were then compared to the crustal motions from global solutions and the optimized solution is presented here. A noise analysis model with power-law and white noise, which best describes the noise characteristics of all three components, was employed for the GPS time series analysis. The linear trend, associated uncertainties, and the spectral index of the power-law noise were calculated using a maximum likelihood estimation approach. The residual horizontal velocities, after removal of rigid plate motion, have a magnitude consistent with expected glacial isostatic adjustment (GIA). The vertical velocities increase from subsidence of almost 1.9 mm/year south of the Great Lakes to uplift near Hudson Bay, where the highest rate is approximately 10.9 mm/year. The residual horizontal velocities range from approximately 0.5 mm/year, oriented south-southeastward, at the Great Lakes to nearly 1.5 mm/year directed toward the interior of Hudson Bay at stations adjacent to its shoreline. Here, the velocity uncertainties are estimated at less than 0.6 mm/year for the horizontal component and 1.1 mm/year for the vertical component. A comparison between the observed velocities and GIA model predictions, for a limited range of Earth models, shows a better fit to the observations for the Earth model with the smallest upper mantle viscosity and the largest lower mantle viscosity. However, the
A time series analysis performed on a 25-year period of kidney transplantation activity in a single center.

PubMed

Santori, G; Fontana, I; Bertocchi, M; Gasloli, G; Valente, U

2010-05-01

Following the example of many Western countries, where a "minimum volume rule" policy has been adopted as a quality parameter for complex surgical procedures, the Italian National Transplant Centre set the minimum number of kidney transplantation procedures/y at 30/center. The number of procedures performed in a single center over a large period may be treated as a time series to evaluate trends, seasonal cycles, and nonsystematic fluctuations. Between January 1, 1983, and December 31, 2007, we performed 1376 procedures in adult or pediatric recipients from living or cadaveric donors. The greatest numbers of cases/y were performed in 1998 (n = 86) followed by 2004 (n = 82), 1996 (n = 75), and 2003 (n = 73). A time series analysis performed using R Statistical Software (Foundation for Statistical Computing, Vienna, Austria), a free software environment for statistical computing and graphics, showed a whole incremental trend after exponential smoothing as well as after seasonal decomposition. However, starting from 2005, we observed a decreased trend in the series. The number of kidney transplants expected to be performed for 2008 by using the Holt-Winters exponential smoothing applied to the period 1983 to 2007 suggested 58 procedures, while in that year there were 52. The time series approach may be helpful to establish a minimum volume/y at a single-center level. Copyright (c) 2010 Elsevier Inc. All rights reserved.
Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth

ERIC Educational Resources Information Center

Castillo-Garsow, Carlos

2010-01-01

Both Thompson and the duo of Confrey and Smith describe how students might be taught to build "ways of thinking" about exponential behavior by coordinating the covariation of two changing quantities, however, these authors build exponential behavior from different meanings of covariation. Confrey and Smith advocate beginning with discrete additive…
Prony series spectra of structural relaxation in N-BK7 for finite element modeling.

PubMed

Koontz, Erick; Blouin, Vincent; Wachtel, Peter; Musgraves, J David; Richardson, Kathleen

2012-12-20

Structural relaxation behavior of N-BK7 glass was characterized at temperatures 20 °C above and below T(12) for this glass, using a thermo mechanical analyzer (TMA). T(12) is a characteristic temperature corresponding to a viscosity of 10(12) Pa·s. The glass was subject to quick temperature down-jumps preceded and followed by long isothermal holds. The exponential-like decay of the sample height was recorded and fitted using a unique Prony series method. The result of his method was a plot of the fit parameters revealing the presence of four distinct peaks or distributions of relaxation times. The number of relaxation times decreased as final test temperature was increased. The relaxation times did not shift significantly with changing temperature; however, the Prony weight terms varied essentially linearly with temperature. It was also found that the structural relaxation behavior of the glass trended toward single exponential behavior at temperatures above the testing range. The result of the analysis was a temperature-dependent Prony series model that can be used in finite element modeling of glass behavior in processes such as precision glass molding (PGM).
Time series dataset of fish assemblages near thermal discharges at nuclear power plants in northern Taiwan.

PubMed

Chen, Hungyen; Chen, Ching-Yi; Shao, Kwang-Tsao

2018-05-08

Long-term time series datasets with consistent sampling methods are rather rare, especially the ones of non-target coastal fishes. Here we described a long-term time series dataset of fish collected by trammel net fish sampling and observed by an underwater diving visual census near the thermal discharges at two nuclear power plants on the northern coast of Taiwan. Both experimental and control stations of these two investigations were monitored four times per year in the surrounding seas at both plants from 2000 to 2017. The underwater visual census mainly monitored reef fish assemblages and trammel net samples monitored pelagic or demersal fishes above the muddy/sandy bottom. In total, 508 samples containing 203,863 individuals from 347 taxa were recorded in both investigations at both plants. These data can be used by ecologists and fishery biologists interested in the elucidation of the temporal patterns of species abundance and composition.
Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function

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

Peng, Bo; Kowalski, Karol

In this paper we derive basic properties of the Green’s function matrix elements stemming from the exponential coupled cluster (CC) parametrization of the ground-state wave function. We demon- strate that all intermediates used to express retarded (or equivalently, ionized) part of the Green’s function in the ω-representation can be expressed through connected diagrams only. Similar proper- ties are also shared by the first order ω-derivatives of the retarded part of the CC Green’s function. This property can be extended to any order ω-derivatives of the Green’s function. Through the Dyson equation of CC Green’s function, the derivatives of corresponding CCmore » self-energy can be evaluated analytically. In analogy to the CC Green’s function, the corresponding CC self-energy is expressed in terms of connected diagrams only. Moreover, the ionized part of the CC Green’s func- tion satisfies the non-homogeneous linear system of ordinary differential equations, whose solution may be represented in the exponential form. Our analysis can be easily generalized to the advanced part of the CC Green’s function.« less
Exponential Stellar Disks in Low Surface Brightness Galaxies: A Critical Test of Viscous Evolution

NASA Astrophysics Data System (ADS)

Bell, Eric F.

2002-12-01

Viscous redistribution of mass in Milky Way-type galactic disks is an appealing way of generating an exponential stellar profile over many scale lengths, almost independent of initial conditions, requiring only that the viscous timescale and star formation timescale are approximately equal. However, galaxies with solid-body rotation curves cannot undergo viscous evolution. Low surface brightness (LSB) galaxies have exponential surface brightness profiles, yet have slowly rising, nearly solid-body rotation curves. Because of this, viscous evolution may be inefficient in LSB galaxies: the exponential profiles, instead, would give important insight into initial conditions for galaxy disk formation. Using star formation laws from the literature and tuning the efficiency of viscous processes to reproduce an exponential stellar profile in Milky Way-type galaxies, I test the role of viscous evolution in LSB galaxies. Under the conservative and not unreasonable condition that LSB galaxies are gravitationally unstable for at least a part of their lives, I find that it is impossible to rule out a significant role for viscous evolution. This type of model still offers an attractive way of producing exponential disks, even in LSB galaxies with slowly rising rotation curves.
Fourier series expansion for nonlinear Hamiltonian oscillators.

PubMed

Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac

2010-06-01

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.
Numerical modelling of series-parallel cooling systems in power plant

NASA Astrophysics Data System (ADS)

Regucki, Paweł; Lewkowicz, Marek; Kucięba, Małgorzata

2017-11-01

The paper presents a mathematical model allowing one to study series-parallel hydraulic systems like, e.g., the cooling system of a power boiler's auxiliary devices or a closed cooling system including condensers and cooling towers. The analytical approach is based on a set of non-linear algebraic equations solved using numerical techniques. As a result of the iterative process, a set of volumetric flow rates of water through all the branches of the investigated hydraulic system is obtained. The calculations indicate the influence of changes in the pipeline's geometrical parameters on the total cooling water flow rate in the analysed installation. Such an approach makes it possible to analyse different variants of the modernization of the studied systems, as well as allowing for the indication of its critical elements. Basing on these results, an investor can choose the optimal variant of the reconstruction of the installation from the economic point of view. As examples of such a calculation, two hydraulic installations are described. One is a boiler auxiliary cooling installation including two screw ash coolers. The other is a closed cooling system consisting of cooling towers and condensers.
A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

PubMed

Stuebner, Michael; Haider, Mansoor A

2010-06-18

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage. Copyright (c) 2010 Elsevier Ltd. All rights reserved.
Diagrammatic exponentiation for products of Wilson lines

NASA Astrophysics Data System (ADS)

Mitov, Alexander; Sterman, George; Sung, Ilmo

2010-11-01

We provide a recursive diagrammatic prescription for the exponentiation of gauge theory amplitudes involving products of Wilson lines and loops. This construction generalizes the concept of webs, originally developed for eikonal form factors and cross sections with two eikonal lines, to general soft functions in QCD and related gauge theories. Our coordinate space arguments apply to arbitrary paths for the lines.
Approximation of the exponential integral (well function) using sampling methods

NASA Astrophysics Data System (ADS)

Baalousha, Husam Musa

2015-04-01

Exponential integral (also known as well function) is often used in hydrogeology to solve Theis and Hantush equations. Many methods have been developed to approximate the exponential integral. Most of these methods are based on numerical approximations and are valid for a certain range of the argument value. This paper presents a new approach to approximate the exponential integral. The new approach is based on sampling methods. Three different sampling methods; Latin Hypercube Sampling (LHS), Orthogonal Array (OA), and Orthogonal Array-based Latin Hypercube (OA-LH) have been used to approximate the function. Different argument values, covering a wide range, have been used. The results of sampling methods were compared with results obtained by Mathematica software, which was used as a benchmark. All three sampling methods converge to the result obtained by Mathematica, at different rates. It was found that the orthogonal array (OA) method has the fastest convergence rate compared with LHS and OA-LH. The root mean square error RMSE of OA was in the order of 1E-08. This method can be used with any argument value, and can be used to solve other integrals in hydrogeology such as the leaky aquifer integral.
Predicting High-Power Performance in Professional Cyclists.

PubMed

Sanders, Dajo; Heijboer, Mathieu; Akubat, Ibrahim; Meijer, Kenneth; Hesselink, Matthijs K

2017-03-01

To assess if short-duration (5 to ~300 s) high-power performance can accurately be predicted using the anaerobic power reserve (APR) model in professional cyclists. Data from 4 professional cyclists from a World Tour cycling team were used. Using the maximal aerobic power, sprint peak power output, and an exponential constant describing the decrement in power over time, a power-duration relationship was established for each participant. To test the predictive accuracy of the model, several all-out field trials of different durations were performed by each cyclist. The power output achieved during the all-out trials was compared with the predicted power output by the APR model. The power output predicted by the model showed very large to nearly perfect correlations to the actual power output obtained during the all-out trials for each cyclist (r = .88 ± .21, .92 ± .17, .95 ± .13, and .97 ± .09). Power output during the all-out trials remained within an average of 6.6% (53 W) of the predicted power output by the model. This preliminary pilot study presents 4 case studies on the applicability of the APR model in professional cyclists using a field-based approach. The decrement in all-out performance during high-intensity exercise seems to conform to a general relationship with a single exponential-decay model describing the decrement in power vs increasing duration. These results are in line with previous studies using the APR model to predict performance during brief all-out trials. Future research should evaluate the APR model with a larger sample size of elite cyclists.
State-space forecasting of Schistosoma haematobium time-series in Niono, Mali.

PubMed

Medina, Daniel C; Findley, Sally E; Doumbia, Seydou

2008-08-13

Much of the developing world, particularly sub-Saharan Africa, exhibits high levels of morbidity and mortality associated with infectious diseases. The incidence of Schistosoma sp.-which are neglected tropical diseases exposing and infecting more than 500 and 200 million individuals in 77 countries, respectively-is rising because of 1) numerous irrigation and hydro-electric projects, 2) steady shifts from nomadic to sedentary existence, and 3) ineffective control programs. Notwithstanding the colossal scope of these parasitic infections, less than 0.5% of Schistosoma sp. investigations have attempted to predict their spatial and or temporal distributions. Undoubtedly, public health programs in developing countries could benefit from parsimonious forecasting and early warning systems to enhance management of these parasitic diseases. In this longitudinal retrospective (01/1996-06/2004) investigation, the Schistosoma haematobium time-series for the district of Niono, Mali, was fitted with general-purpose exponential smoothing methods to generate contemporaneous on-line forecasts. These methods, which are encapsulated within a state-space framework, accommodate seasonal and inter-annual time-series fluctuations. Mean absolute percentage error values were circa 25% for 1- to 5-month horizon forecasts. The exponential smoothing state-space framework employed herein produced reasonably accurate forecasts for this time-series, which reflects the incidence of S. haematobium-induced terminal hematuria. It obliquely captured prior non-linear interactions between disease dynamics and exogenous covariates (e.g., climate, irrigation, and public health interventions), thus obviating the need for more complex forecasting methods in the district of Niono, Mali. Therefore, this framework could assist with managing and assessing S. haematobium transmission and intervention impact, respectively, in this district and potentially elsewhere in the Sahel.

The petroleum exponential (again)

NASA Astrophysics Data System (ADS)

Bell, Peter M.

The U.S. production and reserves of liquid and gaseous petroleum have declined since 1960, at least in the lower 48 states. This decline stems from decreased discovery rates, as predicted by M. King Hubbert in the mid-1950's. Hubbert's once unpopular views were based on statistical analysis of the production history of the petroleum industry, and now, even with inclusion of the statistical perturbation caused by the Prudhoe Bay-North Alaskan Slope discovery (the largest oil field ever found in the United States), it seems clear again that production is following the exponential curve to depletion of the resource—to the end of the ultimate yield of petroleum from wells in the United States.In a recent report, C. Hall and C. Cleveland of Cornell University show that large atypical discoveries, such as the Prudhoe Bay find, are but minor influences on what now appears to be the crucial intersection of two exponentials [Science, 211, 576-579, 1981]: the production-per-drilled-foot curve of Hubbert, which crosses zero production no later than the year 2005; the other, a curve that plots the energy cost of drilling and extraction with time; that is, the cost-time rate of how much oil is used to drill and extract oil from the ground. The intersection, if no other discoveries the size of the Prudhoe Bay field are made, could be as early as 1990, the end of the present decade. The inclusion of each Prudhoe-Bay-size find extends the year of intersection by only about 6 years. Beyond that point, more than one barrel of petroleum would be expended for each barrel extracted from the ground. The oil exploration-extraction and refining industry is currently the second most energy-intensive industry in the U.S., and the message seems clear. Either more efficient drilling and production techniques are discovered, or domestic production will cease well before the end of this century if the Hubbert analysis modified by Hall and Cleveland is correct.
Monoclinic structure of hydroxylpyromorphite Pb10(PO4)6(OH)2 - hydroxylmimetite Pb10(AsO4)6(OH)2 solid solution series

NASA Astrophysics Data System (ADS)

Giera, Alicja; Manecki, Maciej; Borkiewicz, Olaf; Zelek, Sylwia; Rakovan, John; Bajda, Tomasz; Marchlewski, Tomasz

2016-04-01

Seven samples of hydroxyl analogues of pyromorphite-mimetite solid solutions series were synthesized from aqueous solutions at 80° C in a computer-controlled chemistate: 200 mL aqueous solutions of 0.05M Pb(NO3)2 and 0.03M KH2AsO4 and/or KH2PO4 were dosed with a 0.25 mL/min rate to a glass beaker, which initially contained 100 mL of distilled water. Constant pH of 8 was maintained using 2M KOH. The syntheses yielded homogeneous fine-grained white precipitates composition of which was close to theoretical Pb10[(PO4)6-x(AsO4)x](OH)2, where x = 0, 1, 2, 3, 4, 5, 6. High-resolution powder X-ray diffraction data were obtained in transmission geometry at the beamline 11-BM at the Advanced Photon Source (Argonne National Laboratory in Illinois, USA). The structure Rietveld refinements based on starting parameters of either hexagonal hydroxylpyromorphite or monoclinic mimetite-M were performed using GSAS+EXPGUI software. Apatite usually crystallizes in the hexagonal crystal system with the space group P63/m. For the first time, however, the lowering of the hexagonal to monoclinic crystal symmetry was observed in the hydroxyl variety of pyromorphite-mimetite solid solution series. This is indicated by better fitting of the modeled monoclinic structure to the experimental data. The same is not the case for analogous calcium hydroxylapatite series Ca5(PO4)3OH - Ca5(AsO4)3OH (Lee et al. 2009). Systematical linear increase of unit cell parameters is observed with As substitution from a=9.88, b=19.75, and c=7.43 for Pb10(PO4)6(OH)2 to a=10.23, b=20.32, and c=7.51 for Pb10(AsO4)6(OH)2. A strong pseudohexagonal character (γ ≈ 120° and b ≈ 2a) of the analyzed monoclinic phases was established. This work is partially funded by AGH research grant no 11.11.140.319 and partially by Polish NCN grant No 2011/01/M/ST10/06999. Lee Y.J., Stephens P.W., Tang Y., Li W., Philips B.L., Parise J.B., Reeder R.J., 2009. Arsenate substitution in hydroxylapatite: Structural characterization
Holographic insulator/superconductor transition with exponential nonlinear electrodynamics probed by entanglement entropy

NASA Astrophysics Data System (ADS)

Yao, Weiping; Yang, Chaohui; Jing, Jiliang

2018-05-01

From the viewpoint of holography, we study the behaviors of the entanglement entropy in insulator/superconductor transition with exponential nonlinear electrodynamics (ENE). We find that the entanglement entropy is a good probe to the properties of the holographic phase transition. Both in the half space and the belt space, the non-monotonic behavior of the entanglement entropy in superconducting phase versus the chemical potential is general in this model. Furthermore, the behavior of the entanglement entropy for the strip geometry shows that the confinement/deconfinement phase transition appears in both insulator and superconductor phases. And the critical width of the confinement/deconfinement phase transition depends on the chemical potential and the exponential coupling term. More interestingly, the behaviors of the entanglement entropy in their corresponding insulator phases are independent of the exponential coupling factor but depends on the width of the subsystem A.
Determining Parameters of Fractional-Exponential Heredity Kernels of Nonlinear Viscoelastic Materials

NASA Astrophysics Data System (ADS)

Golub, V. P.; Pavlyuk, Ya. V.; Fernati, P. V.

2017-07-01

The problem of determining the parameters of fractional-exponential heredity kernels of nonlinear viscoelastic materials is solved. The methods for determining the parameters that are used in the cubic theory of viscoelasticity and the nonlinear theories based on the conditions of similarity of primary creep curves and isochronous creep diagrams are analyzed. The parameters of fractional-exponential heredity kernels are determined and experimentally validated for the oriented polypropylene, FM3001 and FM10001 nylon fibers, microplastics, TC 8/3-250 glass-reinforced plastic, SWAM glass-reinforced plastic, and contact molding glass-reinforced plastic.
Concept of the Exponential Law Prior to 1900

ERIC Educational Resources Information Center

Curtis, Lorenzo J.

1978-01-01

Presents the historical development of perceptions and applications of the exponential law, tracing it from its ancient origins until the year 1900. Shows that many concepts such as mean life and half life and their relationships to differential equations were known long before their application to nuclear radioactivity. (GA)
W-transform for exponential stability of second order delay differential equations without damping terms.

PubMed

Domoshnitsky, Alexander; Maghakyan, Abraham; Berezansky, Leonid

2017-01-01

In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.
Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.
Exponential Formulae and Effective Operations

NASA Technical Reports Server (NTRS)

Mielnik, Bogdan; Fernandez, David J. C.

1996-01-01

One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).
Flow behind an exponential shock wave in a rotational axisymmetric perfect gas with magnetic field and variable density.

PubMed

Nath, G; Sahu, P K

2016-01-01

A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere. The ambient medium is assumed to possess radial, axial and azimuthal component of fluid velocities. The initial density, the fluid velocities and magnetic field of the ambient medium are assumed to be varying with time according to an exponential law. The gas is taken to be non-viscous having infinite electrical conductivity. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector. The effects of the variation of the initial density index, adiabatic exponent of the gas and the Alfven-Mach number on the flow-field behind the shock wave are investigated. It is found that the presence of the magnetic field have decaying effects on the shock wave. Also, it is observed that the effect of an increase in the magnetic field strength is more impressive in the case of adiabatic flow than in the case of isothermal flow. The assumption of zero temperature gradient brings a profound change in the density, non-dimensional azimuthal and axial components of vorticity vector distributions in comparison to those in the case of adiabatic flow. A comparison is made between isothermal and adiabatic flows. It is obtained that an increase in the initial density variation index, adiabatic exponent and strength of the magnetic field decrease the shock strength.
Learning curves in highly skilled chess players: a test of the generality of the power law of practice.

PubMed

Howard, Robert W

2014-09-01

The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development. Copyright © 2014 Elsevier B.V. All rights reserved.
Diffusion-weighted MR imaging of pancreatic cancer: A comparison of mono-exponential, bi-exponential and non-Gaussian kurtosis models.

PubMed

Kartalis, Nikolaos; Manikis, Georgios C; Loizou, Louiza; Albiin, Nils; Zöllner, Frank G; Del Chiaro, Marco; Marias, Kostas; Papanikolaou, Nikolaos

2016-01-01

To compare two Gaussian diffusion-weighted MRI (DWI) models including mono-exponential and bi-exponential, with the non-Gaussian kurtosis model in patients with pancreatic ductal adenocarcinoma. After written informed consent, 15 consecutive patients with pancreatic ductal adenocarcinoma underwent free-breathing DWI (1.5T, b-values: 0, 50, 150, 200, 300, 600 and 1000 s/mm 2 ). Mean values of DWI-derived metrics ADC, D, D*, f, K and D K were calculated from multiple regions of interest in all tumours and non-tumorous parenchyma and compared. Area under the curve was determined for all metrics. Mean ADC and D K showed significant differences between tumours and non-tumorous parenchyma (both P < 0.001). Area under the curve for ADC, D, D*, f, K, and D K were 0.77, 0.52, 0.53, 0.62, 0.42, and 0.84, respectively. ADC and D K could differentiate tumours from non-tumorous parenchyma with the latter showing a higher diagnostic accuracy. Correction for kurtosis effects has the potential to increase the diagnostic accuracy of DWI in patients with pancreatic ductal adenocarcinoma.
A New Insight into the Earthquake Recurrence Studies from the Three-parameter Generalized Exponential Distributions

NASA Astrophysics Data System (ADS)

Pasari, S.; Kundu, D.; Dikshit, O.

2012-12-01

Earthquake recurrence interval is one of the important ingredients towards probabilistic seismic hazard assessment (PSHA) for any location. Exponential, gamma, Weibull and lognormal distributions are quite established probability models in this recurrence interval estimation. However, they have certain shortcomings too. Thus, it is imperative to search for some alternative sophisticated distributions. In this paper, we introduce a three-parameter (location, scale and shape) exponentiated exponential distribution and investigate the scope of this distribution as an alternative of the afore-mentioned distributions in earthquake recurrence studies. This distribution is a particular member of the exponentiated Weibull distribution. Despite of its complicated form, it is widely accepted in medical and biological applications. Furthermore, it shares many physical properties with gamma and Weibull family. Unlike gamma distribution, the hazard function of generalized exponential distribution can be easily computed even if the shape parameter is not an integer. To contemplate the plausibility of this model, a complete and homogeneous earthquake catalogue of 20 events (M ≥ 7.0) spanning for the period 1846 to 1995 from North-East Himalayan region (20-32 deg N and 87-100 deg E) has been used. The model parameters are estimated using maximum likelihood estimator (MLE) and method of moment estimator (MOME). No geological or geophysical evidences have been considered in this calculation. The estimated conditional probability reaches quite high after about a decade for an elapsed time of 17 years (i.e. 2012). Moreover, this study shows that the generalized exponential distribution fits the above data events more closely compared to the conventional models and hence it is tentatively concluded that generalized exponential distribution can be effectively considered in earthquake recurrence studies.
Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

ERIC Educational Resources Information Center

Winkel, Brian

2015-01-01

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…
S-Wave Dispersion Relations: Exact Left Hand E-Plane Discontinuity from the Born Series

NASA Technical Reports Server (NTRS)

Bessis, D.; Temkin, A.

1999-01-01

We show, for a superposition of Yukawa potentials, that the left hand cut discontinuity in the complex E plane of the (S-wave) scattering amplitude is given exactly, in an interval depending on n, by the discontinuity of the Born series stopped at order n. This also establishes an inverse and unexpected correspondence of the Born series at positive high energies and negative low energies. We can thus construct a viable dispersion relation (DR) for the partial (S-) wave amplitude. The high numerical precision achievable by the DR is demonstrated for the exponential potential at zero scattering energy. We also briefly discuss the extension of our results to Field Theory.
Effect of Hofmeister series salts on Absorptivity of aqueous solutions on Sodium polyacrylate

NASA Astrophysics Data System (ADS)

Korrapati, Swathi; Pullela, Phani Kumar; Vijayalakshmi, U.

2017-11-01

Sodium polyacrylate (SPA) is a popular super absorbent commonly used in children diapers, sanitary pads, adult diapers etc. The use of SPA is in force from past 30 years and the newer applications like as food preservant are evolving. SPA is recently discovered by our group for improvement of sensitivity of colorimetric agents. Though the discovery of improvement in sensitivity is phenomenal, the mechanism still remains a puzzle. A typical assay reagent contains colorimetric/fluorescent reagents, buffers, salts, stabilizers etc. These chemicals are known to influence the water absorptivity of SPA. If we were to perform chemical/biochemical assays on SPA absorbed reagents effect of salts and other excipients on colorimetric/fluorescence compounds absorbed on SPA is very important. The hofmeister series are standard for studying effect of salts on permeability, stability, aggregation, fluorescence quenching etc. We recently studied affect of urea, sodium chloride, ammonium sulfate, guanidine thiocayanate on fluorescence characteristics of fluorescence compounds and noted that except urea all other reagents have resulted in fluorescence quenching and urea had an opposite effect and increased the fluorescence intensity. This result was attributed to the different water structure around fluorescent in urea solution versus other chaotropic agents.
Transient photoresponse in amorphous In-Ga-Zn-O thin films under stretched exponential analysis

NASA Astrophysics Data System (ADS)

Luo, Jiajun; Adler, Alexander U.; Mason, Thomas O.; Bruce Buchholz, D.; Chang, R. P. H.; Grayson, M.

2013-04-01

We investigated transient photoresponse and Hall effect in amorphous In-Ga-Zn-O thin films and observed a stretched exponential response which allows characterization of the activation energy spectrum with only three fit parameters. Measurements of as-grown films and 350 K annealed films were conducted at room temperature by recording conductivity, carrier density, and mobility over day-long time scales, both under illumination and in the dark. Hall measurements verify approximately constant mobility, even as the photoinduced carrier density changes by orders of magnitude. The transient photoconductivity data fit well to a stretched exponential during both illumination and dark relaxation, but with slower response in the dark. The inverse Laplace transforms of these stretched exponentials yield the density of activation energies responsible for transient photoconductivity. An empirical equation is introduced, which determines the linewidth of the activation energy band from the stretched exponential parameter β. Dry annealing at 350 K is observed to slow the transient photoresponse.
Use of Continuous Exponential Families to Link Forms via Anchor Tests. Research Report. ETS RR-11-11

ERIC Educational Resources Information Center

Haberman, Shelby J.; Yan, Duanli

2011-01-01

Continuous exponential families are applied to linking test forms via an internal anchor. This application combines work on continuous exponential families for single-group designs and work on continuous exponential families for equivalent-group designs. Results are compared to those for kernel and equipercentile equating in the case of chained…
Extended q -Gaussian and q -exponential distributions from gamma random variables

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2015-05-01

The family of q -Gaussian and q -exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q -Gaussian and q -exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q -Gaussian and modified q -exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.
Exact solution of the Lifshitz equations governing the growth of fluctuations in cosmology

NASA Technical Reports Server (NTRS)

Adams, P. J.; Canuto, V.

1975-01-01

The exact solution of the Lifshitz equations governing the cosmological evolution of an initial fluctuation is presented. Lifshitz results valid for squares of the sound velocity equal to zero and 1/3 are extended in closed form to any equation of state where the pressure equals the total energy density times the square of the sound velocity. The solutions embody all the results found previously for special cases of the square of the sound velocity. It is found that the growth of any initial fluctuation is only an exponential function of time with an exponent of not more than 4/3 and is insufficient to produce galaxies unless the initial fluctuation is very large. A possible way to produce very large initial fluctuations by modifying the equation of state by including gravitational interactions is also examined. It is found that a phase transition can occur at baryonic density of 1 nucleon per cubic Planck length or equivalently, at a time of about 10 to the -43rd power sec. At those early times, the masses allowed by causality requirements are too small to be of interest in galaxy formation.
Program THEK energy production units of average power and using thermal conversion of solar radiation

NASA Technical Reports Server (NTRS)

1978-01-01

General studies undertaken by the C.N.R.S. in the field of solar power plants have generated the problem of building energy production units in the medium range of electrical power, in the order of 100 kW. Among the possible solutions, the principle of the use of distributed heliothermal converters has been selected as being, with the current status of things, the most advantageous solution. This principle consists of obtaining the conversion of concentrated radiation into heat by using a series of heliothermal conversion modules scattered over the ground; the produced heat is collected by a heat-carrying fluid circulating inside a thermal loop leading to a device for both regulation and storage.

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