Adaptive optimal stochastic state feedback control of resistive wall modes in tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2006-01-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least-square method with exponential forgetting factor and covariance resetting is used to identify (experimentally determine) the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.

Adaptive Optimal Stochastic State Feedback Control of Resistive Wall Modes in Tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2007-06-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least square method with exponential forgetting factor and covariance resetting is used to identify the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.

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.

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.

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

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

Ill-posed problem and regularization in reconstruction of radiobiological parameters from serial tumor imaging data

NASA Astrophysics Data System (ADS)

Chvetsov, Alevei V.; Sandison, George A.; Schwartz, Jeffrey L.; Rengan, Ramesh

2015-11-01

The main objective of this article is to improve the stability of reconstruction algorithms for estimation of radiobiological parameters using serial tumor imaging data acquired during radiation therapy. Serial images of tumor response to radiation therapy represent a complex summation of several exponential processes as treatment induced cell inactivation, tumor growth rates, and the rate of cell loss. Accurate assessment of treatment response would require separation of these processes because they define radiobiological determinants of treatment response and, correspondingly, tumor control probability. However, the estimation of radiobiological parameters using imaging data can be considered an inverse ill-posed problem because a sum of several exponentials would produce the Fredholm integral equation of the first kind which is ill posed. Therefore, the stability of reconstruction of radiobiological parameters presents a problem even for the simplest models of tumor response. To study stability of the parameter reconstruction problem, we used a set of serial CT imaging data for head and neck cancer and a simplest case of a two-level cell population model of tumor response. Inverse reconstruction was performed using a simulated annealing algorithm to minimize a least squared objective function. Results show that the reconstructed values of cell surviving fractions and cell doubling time exhibit significant nonphysical fluctuations if no stabilization algorithms are applied. However, after applying a stabilization algorithm based on variational regularization, the reconstruction produces statistical distributions for survival fractions and doubling time that are comparable to published in vitro data. This algorithm is an advance over our previous work where only cell surviving fractions were reconstructed. We conclude that variational regularization allows for an increase in the number of free parameters in our model which enables development of more-advanced parameter reconstruction algorithms.

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.

On stability of discrete composite systems.

NASA Technical Reports Server (NTRS)

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

1973-01-01

Conditions are developed under which exponential stability of a composite discrete system is implied by exponential stability of its subsystems and the nature of their interactions. Stability of the system is determined by testing positive definiteness property of a real symmetric matrix the dimension of which is equal to the number of subsystems.

Destabilizing Effects of Impulse in Delayed Bam Neural Networks

NASA Astrophysics Data System (ADS)

Li, Chuandong; Li, Chaojie; Liu, Chao

This paper further studies the global exponential stability of the equilibrium point of the delayed bidirectional associative memory (DBAM) neural networks with impulse effects. Several results characterizing the aggregated effects of impulse and dynamical property of the impulse-free DBAM on the exponential stability of the considered DBAM have been established. It is shown that the impulsive DBAM will preserve the global exponential stability of the impulse-free DBAM even if the impulses have enlarging effects on the states of neurons.

Non-fragile ?-? control for discrete-time stochastic nonlinear systems under event-triggered protocols

NASA Astrophysics Data System (ADS)

Sun, Ying; Ding, Derui; Zhang, Sunjie; Wei, Guoliang; Liu, Hongjian

2018-07-01

In this paper, the non-fragile ?-? control problem is investigated for a class of discrete-time stochastic nonlinear systems under event-triggered communication protocols, which determine whether the measurement output should be transmitted to the controller or not. The main purpose of the addressed problem is to design an event-based output feedback controller subject to gain variations guaranteeing the prescribed disturbance attenuation level described by the ?-? performance index. By utilizing the Lyapunov stability theory combined with S-procedure, a sufficient condition is established to guarantee both the exponential mean-square stability and the ?-? performance for the closed-loop system. In addition, with the help of the orthogonal decomposition, the desired controller parameter is obtained in terms of the solution to certain linear matrix inequalities. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed event-based controller design scheme.

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)].

Existence and uniqueness, attraction for stochastic age-structured population systems with diffusion and Poisson jump

NASA Astrophysics Data System (ADS)

Chen, Huabin

2013-08-01

In this paper, the problems about the existence and uniqueness, attraction for strong solution of stochastic age-structured population systems with diffusion and Poisson jump are considered. Under the non-Lipschitz condition with the Lipschitz condition being considered as a special case, the existence and uniqueness for such systems is firstly proved by using the Burkholder-Davis-Gundy inequality (B-D-G inequality) and Itô's formula. And then by using a novel inequality technique, some sufficient conditions ensuring the existence for the domain of attraction are established. As another by-product, the exponential stability in mean square moment of strong solution for such systems can be also discussed.

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.

A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization.

PubMed

Zhao, Shouwei

2011-06-01

A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.

On the Time-Dependent Analysis of Gamow Decay

ERIC Educational Resources Information Center

Durr, Detlef; Grummt, Robert; Kolb, Martin

2011-01-01

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any…

Improved result on stability analysis of discrete stochastic neural networks with time delay

NASA Astrophysics Data System (ADS)

Wu, Zhengguang; Su, Hongye; Chu, Jian; Zhou, Wuneng

2009-04-01

This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

Nonholonomic stability aspects of piecewise holonomic systems

NASA Astrophysics Data System (ADS)

Ruina, Andy

1998-10-01

We consider mechanical systems with intermittent contact that are smooth and holonomic except at the instants of transition. Overall such systems can be nonholonomic in that the accessible configuration space can have larger dimension than the instantaneous motions allowed by the constraints. The known examples of such mechanical systems are also dissipative. By virtue of their nonholonomy and of their dissipation such systems are not Hamiltonian. Thus there is no reason to expect them to adhere to the Hamiltonian property that exponential stability of steady motions is impossible. Since nonholonomy and energy dissipation are simultaneously present in these systems, it is usually not clear whether their sometimes-observed exponential stability should be attributed solely to dissipation, to nonholonomy, or to both. However, it is shown here on the basis of one simple example, that the observed exponential stability of such systems can follow solely from the nonholonomic nature of intermittent contact and not from dissipation. In particular, it is shown that a discrete sister model of the Chaplygin sleigh, a rigid body on the plane constrained by one skate, inherits the stability eigenvalues of the smooth system even as the dissipation tends to zero. Thus it seems that discrete nonholonomy can contribute to exponential stability of mechanical systems.

Global synchronization of memristive neural networks subject to random disturbances via distributed pinning control.

PubMed

Guo, Zhenyuan; Yang, Shaofu; Wang, Jun

2016-12-01

This paper presents theoretical results on global exponential synchronization of multiple memristive neural networks in the presence of external noise by means of two types of distributed pinning control. The multiple memristive neural networks are coupled in a general structure via a nonlinear function, which consists of a linear diffusive term and a discontinuous sign term. A pinning impulsive control law is introduced in the coupled system to synchronize all neural networks. Sufficient conditions are derived for ascertaining global exponential synchronization in mean square. In addition, a pinning adaptive control law is developed to achieve global exponential synchronization in mean square. Both pinning control laws utilize only partial state information received from the neighborhood of the controlled neural network. Simulation results are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

A decoupled approach to filter design for stochastic systems

NASA Astrophysics Data System (ADS)

Barbata, A.; Zasadzinski, M.; Ali, H. Souley; Messaoud, H.

2016-08-01

This paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems. This result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept. Two kinds of observers are treated: the full-order and reduced-order cases.

Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems

NASA Astrophysics Data System (ADS)

Mahdi Alavi, S. M.; Saif, Mehrdad

2013-12-01

This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.

Distributed Secure Coordinated Control for Multiagent Systems Under Strategic Attacks.

PubMed

Feng, Zhi; Wen, Guanghui; Hu, Guoqiang

2017-05-01

This paper studies a distributed secure consensus tracking control problem for multiagent systems subject to strategic cyber attacks modeled by a random Markov process. A hybrid stochastic secure control framework is established for designing a distributed secure control law such that mean-square exponential consensus tracking is achieved. A connectivity restoration mechanism is considered and the properties on attack frequency and attack length rate are investigated, respectively. Based on the solutions of an algebraic Riccati equation and an algebraic Riccati inequality, a procedure to select the control gains is provided and stability analysis is studied by using Lyapunov's method.. The effect of strategic attacks on discrete-time systems is also investigated. Finally, numerical examples are provided to illustrate the effectiveness of theoretical analysis.

Stability in Cohen Grossberg-type bidirectional associative memory neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Cao, Jinde; Song, Qiankun

2006-07-01

In this paper, the exponential stability problem is investigated for a class of Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. By using the analysis method, inequality technique and the properties of an M-matrix, several novel sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are derived. Moreover, the exponential convergence rate is estimated. The obtained results are less restrictive than those given in the earlier literature, and the boundedness and differentiability of the activation functions and differentiability of the time-varying delays are removed. Two examples with their simulations are given to show the effectiveness of the obtained results.

Global exponential stability for switched memristive neural networks with time-varying delays.

PubMed

Xin, Youming; Li, Yuxia; Cheng, Zunshui; Huang, Xia

2016-08-01

This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples. Copyright © 2016 Elsevier Ltd. All rights reserved.

Global exponential stability of inertial memristor-based neural networks with time-varying delays and impulses.

PubMed

Zhang, Wei; Huang, Tingwen; He, Xing; Li, Chuandong

2017-11-01

In this study, we investigate the global exponential stability of inertial memristor-based neural networks with impulses and time-varying delays. We construct inertial memristor-based neural networks based on the characteristics of the inertial neural networks and memristor. Impulses with and without delays are considered when modeling the inertial neural networks simultaneously, which are of great practical significance in the current study. Some sufficient conditions are derived under the framework of the Lyapunov stability method, as well as an extended Halanay differential inequality and a new delay impulsive differential inequality, which depend on impulses with and without delays, in order to guarantee the global exponential stability of the inertial memristor-based neural networks. Finally, two numerical examples are provided to illustrate the efficiency of the proposed methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Anomalous yet Brownian.

PubMed

Wang, Bo; Anthony, Stephen M; Bae, Sung Chul; Granick, Steve

2009-09-08

We describe experiments using single-particle tracking in which mean-square displacement is simply proportional to time (Fickian), yet the distribution of displacement probability is not Gaussian as should be expected of a classical random walk but, instead, is decidedly exponential for large displacements, the decay length of the exponential being proportional to the square root of time. The first example is when colloidal beads diffuse along linear phospholipid bilayer tubes whose radius is the same as that of the beads. The second is when beads diffuse through entangled F-actin networks, bead radius being less than one-fifth of the actin network mesh size. We explore the relevance to dynamic heterogeneity in trajectory space, which has been extensively discussed regarding glassy systems. Data for the second system might suggest activated diffusion between pores in the entangled F-actin networks, in the same spirit as activated diffusion and exponential tails observed in glassy systems. But the first system shows exceptionally rapid diffusion, nearly as rapid as for identical colloids in free suspension, yet still displaying an exponential probability distribution as in the second system. Thus, although the exponential tail is reminiscent of glassy systems, in fact, these dynamics are exceptionally rapid. We also compare with particle trajectories that are at first subdiffusive but Fickian at the longest measurement times, finding that displacement probability distributions fall onto the same master curve in both regimes. The need is emphasized for experiments, theory, and computer simulation to allow definitive interpretation of this simple and clean exponential probability distribution.

New exponential stability criteria for stochastic BAM neural networks with impulses

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Samidurai, R.; Anthoni, S. M.

2010-10-01

In this paper, we study the global exponential stability of time-delayed stochastic bidirectional associative memory neural networks with impulses and Markovian jumping parameters. A generalized activation function is considered, and traditional assumptions on the boundedness, monotony and differentiability of activation functions are removed. We obtain a new set of sufficient conditions in terms of linear matrix inequalities, which ensures the global exponential stability of the unique equilibrium point for stochastic BAM neural networks with impulses. The Lyapunov function method with the Itô differential rule is employed for achieving the required result. Moreover, a numerical example is provided to show that the proposed result improves the allowable upper bound of delays over some existing results in the literature.

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.

Propagation of Disturbances in AC Electricity Grids.

PubMed

Tamrakar, Samyak; Conrath, Michael; Kettemann, Stefan

2018-04-24

The energy transition towards high shares of renewable energy will affect the stability of electricity grids in many ways. Here, we aim to study its impact on propagation of disturbances by solving nonlinear swing equations describing coupled rotating masses of synchronous generators and motors on different grid topologies. We consider a tree, a square grid and as a real grid topology, the german transmission grid. We identify ranges of parameters with different transient dynamics: the disturbance decays exponentially in time, superimposed by oscillations with the fast decay rate of a single node, or with a smaller decay rate without oscillations. Most remarkably, as the grid inertia is lowered, nodes may become correlated, slowing down the propagation from ballistic to diffusive motion, decaying with a power law in time. Applying linear response theory we show that tree grids have a spectral gap leading to exponential relaxation as protected by topology and independent on grid size. Meshed grids are found to have a spectral gap which decreases with increasing grid size, leading to slow power law relaxation and collective diffusive propagation of disturbances. We conclude by discussing consequences if no measures are undertaken to preserve the grid inertia in the energy transition.

The validation of a generalized Hooke's law for coronary arteries.

PubMed

Wang, Chong; Zhang, Wei; Kassab, Ghassan S

2008-01-01

The exponential form of constitutive model is widely used in biomechanical studies of blood vessels. There are two main issues, however, with this model: 1) the curve fits of experimental data are not always satisfactory, and 2) the material parameters may be oversensitive. A new type of strain measure in a generalized Hooke's law for blood vessels was recently proposed by our group to address these issues. The new model has one nonlinear parameter and six linear parameters. In this study, the stress-strain equation is validated by fitting the model to experimental data of porcine coronary arteries. Material constants of left anterior descending artery and right coronary artery for the Hooke's law were computed with a separable nonlinear least-squares method with an excellent goodness of fit. A parameter sensitivity analysis shows that the stability of material constants is improved compared with the exponential model and a biphasic model. A boundary value problem was solved to demonstrate that the model prediction can match the measured arterial deformation under experimental loading conditions. The validated constitutive relation will serve as a basis for the solution of various boundary value problems of cardiovascular biomechanics.

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.

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

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.

Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

NASA Astrophysics Data System (ADS)

Raja, R.; Marshal Anthoni, S.

2011-02-01

This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.

An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach

NASA Astrophysics Data System (ADS)

Ma, Zhi-Sai; Liu, Li; Zhou, Si-Da; Yu, Lei; Naets, Frank; Heylen, Ward; Desmet, Wim

2018-01-01

The problem of parametric output-only identification of time-varying structures in a recursive manner is considered. A kernelized time-dependent autoregressive moving average (TARMA) model is proposed by expanding the time-varying model parameters onto the basis set of kernel functions in a reproducing kernel Hilbert space. An exponentially weighted kernel recursive extended least squares TARMA identification scheme is proposed, and a sliding-window technique is subsequently applied to fix the computational complexity for each consecutive update, allowing the method to operate online in time-varying environments. The proposed sliding-window exponentially weighted kernel recursive extended least squares TARMA method is employed for the identification of a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudo-linear regression TARMA method via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics. Furthermore, the comparisons demonstrate the superior achievable accuracy, lower computational complexity and enhanced online identification capability of the proposed kernel recursive extended least squares TARMA approach.

A Study of the Thermal Environment Developed by a Traveling Slipper at High Velocity

DTIC Science & Technology

2013-03-01

Power Partition Function The next partition function takes the same formulation as the powered function but now the exponent is squared. The...function and note the squared term in the exponent . 66 Equation 4.27 (4.36) Thus far the three partition functions each give a predicted...hypothesized that the function would fall somewhere between the first exponential decay function and the power function. However, by squaring the exponent

Discrete-time bidirectional associative memory neural networks with variable delays

NASA Astrophysics Data System (ADS)

Liang, variable delays [rapid communication] J.; Cao, J.; Ho, D. W. C.

2005-02-01

Based on the linear matrix inequality (LMI), some sufficient conditions are presented in this Letter for the existence, uniqueness and global exponential stability of the equilibrium point of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Some of the stability criteria obtained in this Letter are delay-dependent, and some of them are delay-independent, they are less conservative than the ones reported so far in the literature. Furthermore, the results provide one more set of easily verified criteria for determining the exponential stability of discrete-time BAM neural networks.

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.

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.

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.

Nonlinear stability of the 1D Boltzmann equation in a periodic box

NASA Astrophysics Data System (ADS)

Wu, Kung-Chien

2018-05-01

We study the nonlinear stability of the Boltzmann equation in the 1D periodic box with size , where is the Knudsen number. The convergence rate is for small time region and exponential for large time region. Moreover, the exponential rate depends on the size of the domain (Knudsen number). This problem is highly nonlinear and hence we need more careful analysis to control the nonlinear term.

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.

Asynchronous State Estimation for Discrete-Time Switched Complex Networks With Communication Constraints.

PubMed

Zhang, Dan; Wang, Qing-Guo; Srinivasan, Dipti; Li, Hongyi; Yu, Li

2018-05-01

This paper is concerned with the asynchronous state estimation for a class of discrete-time switched complex networks with communication constraints. An asynchronous estimator is designed to overcome the difficulty that each node cannot access to the topology/coupling information. Also, the event-based communication, signal quantization, and the random packet dropout problems are studied due to the limited communication resource. With the help of switched system theory and by resorting to some stochastic system analysis method, a sufficient condition is proposed to guarantee the exponential stability of estimation error system in the mean-square sense and a prescribed performance level is also ensured. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem. Finally, the effectiveness of the proposed design approach is demonstrated by a simulation example.

MRI quantification of diffusion and perfusion in bone marrow by intravoxel incoherent motion (IVIM) and non-negative least square (NNLS) analysis.

PubMed

Marchand, A J; Hitti, E; Monge, F; Saint-Jalmes, H; Guillin, R; Duvauferrier, R; Gambarota, G

2014-11-01

To assess the feasibility of measuring diffusion and perfusion fraction in vertebral bone marrow using the intravoxel incoherent motion (IVIM) approach and to compare two fitting methods, i.e., the non-negative least squares (NNLS) algorithm and the more commonly used Levenberg-Marquardt (LM) non-linear least squares algorithm, for the analysis of IVIM data. MRI experiments were performed on fifteen healthy volunteers, with a diffusion-weighted echo-planar imaging (EPI) sequence at five different b-values (0, 50, 100, 200, 600 s/mm2), in combination with an STIR module to suppress the lipid signal. Diffusion signal decays in the first lumbar vertebra (L1) were fitted to a bi-exponential function using the LM algorithm and further analyzed with the NNLS algorithm to calculate the values of the apparent diffusion coefficient (ADC), pseudo-diffusion coefficient (D*) and perfusion fraction. The NNLS analysis revealed two diffusion components only in seven out of fifteen volunteers, with ADC=0.60±0.09 (10(-3) mm(2)/s), D*=28±9 (10(-3) mm2/s) and perfusion fraction=14%±6%. The values obtained by the LM bi-exponential fit were: ADC=0.45±0.27 (10(-3) mm2/s), D*=63±145 (10(-3) mm2/s) and perfusion fraction=27%±17%. Furthermore, the LM algorithm yielded values of perfusion fraction in cases where the decay was not bi-exponential, as assessed by NNLS analysis. The IVIM approach allows for measuring diffusion and perfusion fraction in vertebral bone marrow; its reliability can be improved by using the NNLS, which identifies the diffusion decays that display a bi-exponential behavior. Copyright © 2014 Elsevier Inc. All rights reserved.

A class of least-squares filtering and identification algorithms with systolic array architectures

NASA Technical Reports Server (NTRS)

Kalson, Seth Z.; Yao, Kung

1991-01-01

A unified approach is presented for deriving a large class of new and previously known time- and order-recursive least-squares algorithms with systolic array architectures, suitable for high-throughput-rate and VLSI implementations of space-time filtering and system identification problems. The geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix. This method utilizes and extends the concept of oblique projections, as used previously in the derivations of the least-squares lattice algorithms. Exponentially weighted least-squares criteria are considered for both sliding and growing memory.

Global exponential stability analysis on impulsive BAM neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Li, Yao-Tang; Yang, Chang-Bo

2006-12-01

Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.

Biological electric fields and rate equations for biophotons.

PubMed

Alvermann, M; Srivastava, Y N; Swain, J; Widom, A

2015-04-01

Biophoton intensities depend upon the squared modulus of the electric field. Hence, we first make some general estimates about the inherent electric fields within various biosystems. Generally, these intensities do not follow a simple exponential decay law. After a brief discussion on the inapplicability of a linear rate equation that leads to strict exponential decay, we study other, nonlinear rate equations that have been successfully used for biosystems along with their physical origins when available.

Impulsive effect on global exponential stability of BAM fuzzy cellular neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Li, Kelin

2010-02-01

In this article, a class of impulsive bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time-varying delays is formulated and investigated. By employing delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time-varying delays are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.

Effects of deterministic and random refuge in a prey-predator model with parasite infection.

PubMed

Mukhopadhyay, B; Bhattacharyya, R

2012-09-01

Most natural ecosystem populations suffer from various infectious diseases and the resulting host-pathogen dynamics is dependent on host's characteristics. On the other hand, empirical evidences show that for most host pathogen systems, a part of the host population always forms a refuge. To study the role of refuge on the host-pathogen interaction, we study a predator-prey-pathogen model where the susceptible and the infected prey can undergo refugia of constant size to evade predator attack. The stability aspects of the model system is investigated from a local and global perspective. The study reveals that the refuge sizes for the susceptible and the infected prey are the key parameters that control possible predator extinction as well as species co-existence. Next we perform a global study of the model system using Lyapunov functions and show the existence of a global attractor. Finally we perform a stochastic extension of the basic model to study the phenomenon of random refuge arising from various intrinsic, habitat-related and environmental factors. The stochastic model is analyzed for exponential mean square stability. Numerical study of the stochastic model shows that increasing the refuge rates has a stabilizing effect on the stochastic dynamics. Copyright © 2012 Elsevier Inc. All rights reserved.

Global exponential stability of bidirectional associative memory neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Song, Qiankun; Cao, Jinde

2007-05-01

A bidirectional associative memory neural network model with distributed delays is considered. By constructing a new Lyapunov functional, employing the homeomorphism theory, M-matrix theory and the inequality (a[greater-or-equal, slanted]0,bk[greater-or-equal, slanted]0,qk>0 with , and r>1), a sufficient condition is obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the model. Moreover, the exponential converging velocity index is estimated, which depends on the delay kernel functions and the system parameters. The results generalize and improve the earlier publications, and remove the usual assumption that the activation functions are bounded . Two numerical examples are given to show the effectiveness of the obtained results.

Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays.

PubMed

Hu, Jin; Wang, Jun

2015-06-01

In recent years, complex-valued recurrent neural networks have been developed and analysed in-depth in view of that they have good modelling performance for some applications involving complex-valued elements. In implementing continuous-time dynamical systems for simulation or computational purposes, it is quite necessary to utilize a discrete-time model which is an analogue of the continuous-time system. In this paper, we analyse a discrete-time complex-valued recurrent neural network model and obtain the sufficient conditions on its global exponential periodicity and exponential stability. Simulation results of several numerical examples are delineated to illustrate the theoretical results and an application on associative memory is also given. Copyright © 2015 Elsevier Ltd. All rights reserved.

Simulation of rare events in quantum error correction

NASA Astrophysics Data System (ADS)

Bravyi, Sergey; Vargo, Alexander

2013-12-01

We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the splitting method widely used in Monte Carlo simulations of rare events and Bennett's acceptance ratio method for estimating the free energy difference between two canonical ensembles. To illustrate the power of these methods in the context of error correction, we calculate the logical error probability PL for the two-dimensional surface code on a square lattice with a pair of holes for all code distances d≤20 and all error rates p below the fault-tolerance threshold. Our numerical results confirm the expected exponential decay PL˜exp[-α(p)d] and provide a simple fitting formula for the decay rate α(p). Both noiseless and noisy syndrome readout circuits are considered.

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 ).

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

Exponential stabilization and synchronization for fuzzy model of memristive neural networks by periodically intermittent control.

PubMed

Yang, Shiju; Li, Chuandong; Huang, Tingwen

2016-03-01

The problem of exponential stabilization and synchronization for fuzzy model of memristive neural networks (MNNs) is investigated by using periodically intermittent control in this paper. Based on the knowledge of memristor and recurrent neural network, the model of MNNs is formulated. Some novel and useful stabilization criteria and synchronization conditions are then derived by using the Lyapunov functional and differential inequality techniques. It is worth noting that the methods used in this paper are also applied to fuzzy model for complex networks and general neural networks. Numerical simulations are also provided to verify the effectiveness of theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Analysis of stability for stochastic delay integro-differential equations.

PubMed

Zhang, Yu; Li, Longsuo

2018-01-01

In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

Threshold of transverse mode coupling instability with arbitrary space charge

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

Balbekov, V.

The threshold of the transverse mode coupling instability is calculated in framework of the square well model at arbitrary value of space charge tune shift. A new method of calculation is developed beyond the traditional expansion technique. The square, resistive, and exponential wakes are investigated. It is shown that the instability threshold goes up indefinitely when the tune shift increases. Finally, a comparison with conventional case of the parabolic potential well is performed.

Threshold of transverse mode coupling instability with arbitrary space charge

DOE PAGES

Balbekov, V.

2017-11-30

The threshold of the transverse mode coupling instability is calculated in framework of the square well model at arbitrary value of space charge tune shift. A new method of calculation is developed beyond the traditional expansion technique. The square, resistive, and exponential wakes are investigated. It is shown that the instability threshold goes up indefinitely when the tune shift increases. Finally, a comparison with conventional case of the parabolic potential well is performed.

Discrete-time BAM neural networks with variable delays

NASA Astrophysics Data System (ADS)

Liu, Xin-Ge; Tang, Mei-Lan; Martin, Ralph; Liu, Xin-Bi

2007-07-01

This Letter deals with the global exponential stability of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Using a Lyapunov functional, and linear matrix inequality techniques (LMI), we derive a new delay-dependent exponential stability criterion for BAM neural networks with variable delays. As this criterion has no extra constraints on the variable delay functions, it can be applied to quite general BAM neural networks with a broad range of time delay functions. It is also easy to use in practice. An example is provided to illustrate the theoretical development.

Resonant acoustic measurement of vapor phase transport phenomenon in porous media

NASA Astrophysics Data System (ADS)

Schuhmann, Richard; Garrett, Steven

2002-05-01

Diffusion of gases through porous media is commonly described using Fick's law and is characterized by a gas diffusion coefficient modified by a media-specific tortuosity parameter. A phase-locked-loop resonance frequency tracker [J. Acoust. Soc. Am. 108, 2520 (2000)] has been upgraded with an insulated copper resonator and a bellows-sealed piston instrumented with an accelerometer. Average system stability (temperature divided by frequency squared) is about 180 ppm. Glass-bead-filled cores of different lengths are fitted into an o-ring sealed opening at the top of the resonator. The rate at which the tracer gas is replaced by air within the resonator is controlled by the core's diffusion constant. Mean molecular weight of the gas mixture in the resonator is determined in real time from the ratio of the absolute temperature to the square of the fundamental acoustic resonance frequency. Molecular weight of the gas mixture is determined approximately six times per minute. Changes in the gas mixture concentration are exponential in time (within 0.1%) over nearly two decades in concentration. We will report diffusion constants for two different sizes of glass beads, in samples of five different lengths, using two different tracer gases, to establish the validity of this approach. [Work supported by ONR.

Locality of the Thomas-Fermi-von Weizsäcker Equations

NASA Astrophysics Data System (ADS)

Nazar, F. Q.; Ortner, C.

2017-06-01

We establish a pointwise stability estimate for the Thomas-Fermi-von Weiz-säcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (The mathematical theory of thermodynamic limits: Thomas-Fermi type models. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, New York, 1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy into exponentially localised site energies (and consequently, exponential locality of forces), and generalised and strengthened results on the charge neutrality of local defects.

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.

Watershed planning, implementation and assessment: the May River Watershed Action Plan case study

Treesearch

Kimberly W. Jones; Christopher L. Ellis; Jeremy S. Ritchie

2016-01-01

Prior to exponential growth in the early to mid-2000s, the Town of Bluffton, SC was one square mile; as of 2015, it is approximately 55 square miles. Associated with this growth was a shellfish harvesting closure for nearly onethird of the May River in 2009. The Town and its partners developed and began to implement the May River Watershed Action Plan in 2011. The plan...

H∞ control problem of linear periodic piecewise time-delay systems

NASA Astrophysics Data System (ADS)

Xie, Xiaochen; Lam, James; Li, Panshuo

2018-04-01

This paper investigates the H∞ control problem based on exponential stability and weighted L2-gain analyses for a class of continuous-time linear periodic piecewise systems with time delay. A periodic piecewise Lyapunov-Krasovskii functional is developed by integrating a discontinuous time-varying matrix function with two global terms. By applying the improved constraints to the stability and L2-gain analyses, sufficient delay-dependent exponential stability and weighted L2-gain criteria are proposed for the periodic piecewise time-delay system. Based on these analyses, an H∞ control scheme is designed under the considerations of periodic state feedback control input and iterative optimisation. Finally, numerical examples are presented to illustrate the effectiveness of our proposed conditions.

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.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking.

PubMed

Hamed, Kaveh Akbari; Gregg, Robert D

2017-07-01

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and [Formula: see text] robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

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

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal 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 and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and H2 robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:28959117

Isothermal magnetostatic atmospheres. III - Similarity solutions with current proportional to the magnetic potential squared. [in solar corona

NASA Technical Reports Server (NTRS)

Webb, G. M.

1988-01-01

A family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is considered. It is assumed that the current (J) is proportional to the square of the magnetostatic potential and falls off exponentially with distance. Results are presented for the contributions of the anisotropic J x B force (where B is the magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.

Mathematics in the Real World.

ERIC Educational Resources Information Center

Borenstein, Matt

1997-01-01

The abstract nature of algebra causes difficulties for many students. Describes "Real-World Data," an algebra course designed for students with low grades in algebra and provides multidisciplinary experiments (linear functions and variations; quadratic, square-root, and inverse relations; and exponential and periodic variation)…

Current pulse amplifier transmits detector signals with minimum distortion and attenuation

NASA Technical Reports Server (NTRS)

Bush, N. E.

1967-01-01

Amplifier translates the square pulses generated by a boron-trifluoride neutron sensitive detector located adjacent to a nuclear reactor to slower, long exponential decay pulses. These pulses are transmitted over long coaxial cables with minimum distortion and loss of frequency.

An accurate and efficient method for evaluating the kernel of the integral equation relating pressure to normalwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

This paper describes an accurate economical method for generating approximations to the kernel of the integral equation relating unsteady pressure to normalwash in nonplanar flow. The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the non elementary integrals in the kernel by exponential approximations and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. Coefficients for 8, 12, 24, and 72 term approximations are tabulated in the report. Also, since the method is automated, it can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Operational modal analysis applied to the concert harp

NASA Astrophysics Data System (ADS)

Chomette, B.; Le Carrou, J.-L.

2015-05-01

Operational modal analysis (OMA) methods are useful to extract modal parameters of operating systems. These methods seem to be particularly interesting to investigate the modal basis of string instruments during operation to avoid certain disadvantages due to conventional methods. However, the excitation in the case of string instruments is not optimal for OMA due to the presence of damped harmonic components and low noise in the disturbance signal. Therefore, the present study investigates the least-square complex exponential (LSCE) and the modified least-square complex exponential methods in the case of a string instrument to identify modal parameters of the instrument when it is played. The efficiency of the approach is experimentally demonstrated on a concert harp excited by some of its strings and the two methods are compared to a conventional modal analysis. The results show that OMA allows us to identify modes particularly present in the instrument's response with a good estimation especially if they are close to the excitation frequency with the modified LSCE method.

Exponential stabilization of magnetoelastic waves in a Mindlin-Timoshenko plate by localized internal damping

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-08-01

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.

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

NASA Technical Reports Server (NTRS)

Wen, John T.; Bayard, David S.

1988-01-01

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

Lévy flight with absorption: A model for diffusing diffusivity with long tails

NASA Astrophysics Data System (ADS)

Jain, Rohit; Sebastian, K. L.

2017-03-01

We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016), 10.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., ∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., πe(D ) ˜e-D /D0 . In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., πe(D ) ˜D-1 -α with 0 <α <1 . We find that in the short time limit, the width of displacement distribution is proportional to √{T }, implying that the diffusion is Fickian. But for long times, the width is proportional to T1 /2 α which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2 α which preserves its shape at all times.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: the square gradient theory and the capillary approach.

PubMed

Wilhelmsen, Øivind; Bedeaux, Dick; Kjelstrup, Signe; Reguera, David

2014-01-14

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

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

Wilhelmsen, Øivind, E-mail: oivind.wilhelmsen@ntnu.no; Bedeaux, Dick; Kjelstrup, Signe

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which showsmore » the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.« less

Well hydraulics in pumping tests with exponentially decayed rates of abstraction in confined aquifers

NASA Astrophysics Data System (ADS)

Wen, Zhang; Zhan, Hongbin; Wang, Quanrong; Liang, Xing; Ma, Teng; Chen, Chen

2017-05-01

Actual field pumping tests often involve variable pumping rates which cannot be handled by the classical constant-rate or constant-head test models, and often require a convolution process to interpret the test data. In this study, we proposed a semi-analytical model considering an exponentially decreasing pumping rate started at a certain (higher) rate and eventually stabilized at a certain (lower) rate for cases with or without wellbore storage. A striking new feature of the pumping test with an exponentially decayed rate is that the drawdowns will decrease over a certain period of time during intermediate pumping stage, which has never been seen before in constant-rate or constant-head pumping tests. It was found that the drawdown-time curve associated with an exponentially decayed pumping rate function was bounded by two asymptotic curves of the constant-rate tests with rates equaling to the starting and stabilizing rates, respectively. The wellbore storage must be considered for a pumping test without an observation well (single-well test). Based on such characteristics of the time-drawdown curve, we developed a new method to estimate the aquifer parameters by using the genetic algorithm.

Boundary control of anti-symmetric vibration of satellite with flexible appendages in planar motion with exponential stability

NASA Astrophysics Data System (ADS)

Rad, Hossein Kaviani; Salarieh, Hassan; Alasty, Aria; Vatankhah, Ramin

2018-06-01

In this research, we have investigated the planar maneuver of a flexible satellite with appendages anti-symmetric vibration. The hybrid governing equations are comprised of coupled partial and ordinary differential equations which are derived by employing Hamilton's principle. In this paper, control goals are the tracking desired pitch angle along with the flexible appendages vibration suppression simultaneously by using only one control torque which is applied to the central hub. The boundary control is proposed to fulfill these control aims; furthermore, this boundary control ensures that spillover instability phenomenon is eliminated, and in-domain sensors and actuators implement are excluded. Indeed, the proposed boundary control is able to stabilize an infinite number of vibration modes, which is one of the important benefits of the proposed control when it is considered that different factors including external disturbances and even the satellite maneuver can excite the various vibration modes of the flexible appendages and consequently the excitement of the high order vibration modes will be possible. Lyapunov's direct method is used to prove the exponential stability; moreover, this Proof is achieved in absence of any damping effect in modeling the vibrations of flexible appendages. In addition, the procedure for finding the boundary control coefficients which ensures the exponential stability is provided. Eventually, numerical simulations are presented to illustrate the effectiveness of the proposed boundary control.

On the analytical determination of relaxation modulus of viscoelastic materials by Prony's interpolation method

NASA Technical Reports Server (NTRS)

Rodriguez, Pedro I.

1986-01-01

A computer implementation to Prony's curve fitting by exponential functions is presented. The method, although more than one hundred years old, has not been utilized to its fullest capabilities due to the restriction that the time range must be given in equal increments in order to obtain the best curve fit for a given set of data. The procedure used in this paper utilizes the 3-dimensional capabilities of the Interactive Graphics Design System (I.G.D.S.) in order to obtain the equal time increments. The resultant information is then input into a computer program that solves directly for the exponential constants yielding the best curve fit. Once the exponential constants are known, a simple least squares solution can be applied to obtain the final form of the equation.

LSPV+7, a branch-point-tolerant reconstructor for strong turbulence adaptive optics.

PubMed

Steinbock, Michael J; Hyde, Milo W; Schmidt, Jason D

2014-06-20

Optical wave propagation through long paths of extended turbulence presents unique challenges to adaptive optics (AO) systems. As scintillation and branch points develop in the beacon phase, challenges arise in accurately unwrapping the received wavefront and optimizing the reconstructed phase with respect to branch cut placement on a continuous facesheet deformable mirror. Several applications are currently restricted by these capability limits: laser communication, laser weapons, remote sensing, and ground-based astronomy. This paper presents a set of temporally evolving AO simulations comparing traditional least-squares reconstruction techniques to a complex-exponential reconstructor and several other reconstructors derived from the postprocessing congruence operation. The reconstructors' behavior in closed-loop operation is compared and discussed, providing several insights into the fundamental strengths and limitations of each reconstructor type. This research utilizes a self-referencing interferometer (SRI) as the high-order wavefront sensor, driving a traditional linear control law in conjunction with a cooperative point source beacon. The SRI model includes practical optical considerations and frame-by-frame fiber coupling effects to allow for realistic noise modeling. The "LSPV+7" reconstructor is shown to offer the best performance in terms of Strehl ratio and correction stability-outperforming the traditional least-squares reconstructed system by an average of 120% in the studied scenarios. Utilizing a continuous facesheet deformable mirror, these reconstructors offer significant AO performance improvements in strong turbulence applications without the need for segmented deformable mirrors.

Fundamental Flux Equations for Fracture-Matrix Interactions with Linear Diffusion

NASA Astrophysics Data System (ADS)

Oldenburg, C. M.; Zhou, Q.; Rutqvist, J.; Birkholzer, J. T.

2017-12-01

The conventional dual-continuum models are only applicable for late-time behavior of pressure propagation in fractured rock, while discrete-fracture-network models may explicitly deal with matrix blocks at high computational expense. To address these issues, we developed a unified-form diffusive flux equation for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular matrix blocks (squares, cubes, rectangles, and rectangular parallelepipeds) by partitioning the entire dimensionless-time domain (Zhou et al., 2017a, b). For each matrix block, this flux equation consists of the early-time solution up until a switch-over time after which the late-time solution is applied to create continuity from early to late time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the coefficients dependent on dimensionless area-to-volume ratio and aspect ratios for rectangular blocks. For the late-time solutions, one exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic blocks. The time-partitioning method was also used for calculating pressure/concentration/temperature distribution within a matrix block. The approximate solution contains an error-function solution for early times and an exponential solution for late times, with relative errors less than 0.003. These solutions form the kernel of multirate and multidimensional hydraulic, solute and thermal diffusion in fractured reservoirs.

Development Towards a Space Qualified Laser Stabilization System in Support of Space-Based Optical Interferometers

NASA Technical Reports Server (NTRS)

Seidel, David J.; Dubovitsky, Serge

2000-01-01

We report on the development, functional performance and space-qualification status of a laser stabilization system supporting a space-based metrology source used to measure changes in optical path lengths in space-based stellar interferometers. The Space Interferometry Mission (SIM) and Deep Space 3 (DS-3) are two missions currently funded by the National Aeronautics and Space Administration (NASA) that are space-based optical interferometers. In order to properly recombine the starlight received at each telescope of the interferometer it is necessary to perform high resolution laser metrology to stabilize the interferometer. A potentially significant error source in performing high resolution metrology length measurements is the potential for fluctuations in the laser gauge itself. If the laser frequency or wavelength is changing over time it will be misinterpreted as a length change in one of the legs of the interferometer. An analysis of the frequency stability requirement for SIM resulted in a fractional frequency stability requirement of square root (S(sub y)(f)) = <2 x 10(exp -12)/square root(Hz) at Fourier frequencies between 10 Hz and 1000 Hz. The DS-3 mission stability requirement is further increased to square root (S(sub y)(f)) = <5 x 10(exp -14)/Square root(Hz) at Fourier frequencies between 0.2 Hz and 10 kHz with a goal of extending the low frequency range to 0.05 Hz. The free running performance of the Lightwave Electronics NPRO lasers, which are the baseline laser for both SIM and DS-3 vary in stability and we have measured them to perform as follows (9 x l0(exp -11)/ f(Hz))(Hz)/square root(Hz)) = <( square root (S(sub y)(f)) = <(1.3 x l0(exp -8)/ f(Hz))/Square root(Hz). In order to improve the frequency stability of the laser we stabilize the laser to a high finesse optical cavity by locking the optical frequency of the laser to one of the transmission modes of the cavity. At JPL we have built a prototype space-qualifiable system meeting the stability requirements of SIM, which has been delivered to one of the SIM testbeds. We have also started on the development of a system to meet the stability needs of DS-3.

Stability analysis of switched cellular neural networks: A mode-dependent average dwell time approach.

PubMed

Huang, Chuangxia; Cao, Jie; Cao, Jinde

2016-10-01

This paper addresses the exponential stability of switched cellular neural networks by using the mode-dependent average dwell time (MDADT) approach. This method is quite different from the traditional average dwell time (ADT) method in permitting each subsystem to have its own average dwell time. Detailed investigations have been carried out for two cases. One is that all subsystems are stable and the other is that stable subsystems coexist with unstable subsystems. By employing Lyapunov functionals, linear matrix inequalities (LMIs), Jessen-type inequality, Wirtinger-based inequality, reciprocally convex approach, we derived some novel and less conservative conditions on exponential stability of the networks. Comparing to ADT, the proposed MDADT show that the minimal dwell time of each subsystem is smaller and the switched system stabilizes faster. The obtained results extend and improve some existing ones. Moreover, the validness and effectiveness of these results are demonstrated through numerical simulations. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

A Spectral Lyapunov Function for Exponentially Stable LTV Systems

NASA Technical Reports Server (NTRS)

Zhu, J. Jim; Liu, Yong; Hang, Rui

2010-01-01

This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.

Analysis of volumetric response of pituitary adenomas receiving adjuvant CyberKnife stereotactic radiosurgery with the application of an exponential fitting model.

PubMed

Yu, Yi-Lin; Yang, Yun-Ju; Lin, Chin; Hsieh, Chih-Chuan; Li, Chiao-Zhu; Feng, Shao-Wei; Tang, Chi-Tun; Chung, Tzu-Tsao; Ma, Hsin-I; Chen, Yuan-Hao; Ju, Da-Tong; Hueng, Dueng-Yuan

2017-01-01

Tumor control rates of pituitary adenomas (PAs) receiving adjuvant CyberKnife stereotactic radiosurgery (CK SRS) are high. However, there is currently no uniform way to estimate the time course of the disease. The aim of this study was to analyze the volumetric responses of PAs after CK SRS and investigate the application of an exponential decay model in calculating an accurate time course and estimation of the eventual outcome.A retrospective review of 34 patients with PAs who received adjuvant CK SRS between 2006 and 2013 was performed. Tumor volume was calculated using the planimetric method. The percent change in tumor volume and tumor volume rate of change were compared at median 4-, 10-, 20-, and 36-month intervals. Tumor responses were classified as: progression for >15% volume increase, regression for ≤15% decrease, and stabilization for ±15% of the baseline volume at the time of last follow-up. For each patient, the volumetric change versus time was fitted with an exponential model.The overall tumor control rate was 94.1% in the 36-month (range 18-87 months) follow-up period (mean volume change of -43.3%). Volume regression (mean decrease of -50.5%) was demonstrated in 27 (79%) patients, tumor stabilization (mean change of -3.7%) in 5 (15%) patients, and tumor progression (mean increase of 28.1%) in 2 (6%) patients (P = 0.001). Tumors that eventually regressed or stabilized had a temporary volume increase of 1.07% and 41.5% at 4 months after CK SRS, respectively (P = 0.017). The tumor volume estimated using the exponential fitting equation demonstrated high positive correlation with the actual volume calculated by magnetic resonance imaging (MRI) as tested by Pearson correlation coefficient (0.9).Transient progression of PAs post-CK SRS was seen in 62.5% of the patients receiving CK SRS, and it was not predictive of eventual volume regression or progression. A three-point exponential model is of potential predictive value according to relative distribution. An exponential decay model can be used to calculate the time course of tumors that are ultimately controlled.

Feasibility study on the least square method for fitting non-Gaussian noise data

NASA Astrophysics Data System (ADS)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

Prediction of Unsteady Aerodynamic Coefficients at High Angles of Attack

NASA Technical Reports Server (NTRS)

Pamadi, Bandu N.; Murphy, Patrick C.; Klein, Vladislav; Brandon, Jay M.

2001-01-01

The nonlinear indicial response method is used to model the unsteady aerodynamic coefficients in the low speed longitudinal oscillatory wind tunnel test data of the 0.1 scale model of the F-16XL aircraft. Exponential functions are used to approximate the deficiency function in the indicial response. Using one set of oscillatory wind tunnel data and parameter identification method, the unknown parameters in the exponential functions are estimated. The genetic algorithm is used as a least square minimizing algorithm. The assumed model structures and parameter estimates are validated by comparing the predictions with other sets of available oscillatory wind tunnel test data.

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.

The evaluation of anthropogenic impact on the ecological stability of landscape.

PubMed

Michaeli, Eva; Ivanová, Monika; Koco, Štefan

2015-01-01

The model area is the northern surrounding of the water reservoir Zemplinska Irava in the east of Slovakia. Selection of the examined territory and the time horizons was not random. The aim was to capture the intensity level of anthropogenic impact on the values of the coefficient of ecological stability after the construction of water reservoir, Zempifnska Irava. The contribution evaluates ecological stability of landscape in the years 1956 and 2009 by GIS technology, using two methods. The first method determines the rate of ecological stability of landscape on the basis of the significance of land cover classes in the regular network of squares (the real size of the square is 0.5 square km). The second method determines the ecological stability of landscape secondary on the basis of the man influence on the landscape. A comparison of two methods has been made, as well as interpretation of the output data (e.g., monitoring the impact of marginal land cover classes with the minimal surfaces in the grid of square at the fluctuation of the index of ecological stability, respectively, it considers the possibilities to streamline the research results using homogeneous spatial units) and it also allows to track the changes in the ecological stability of the landscape in chronological development.

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.

Facilities Management in Higher Education: Doing More with Less.

ERIC Educational Resources Information Center

Casey, John M.

This analysis looked at higher education facilities management that, despite exponential growth in responsibilities since the 1960s, has seen reduced resources for operations and maintenance. By extrapolating 1988 data from the National Center for Education Statistics, the review estimated that there are now 3.4 billion square feet of higher…

Analytical model of coincidence resolving time in TOF-PET

NASA Astrophysics Data System (ADS)

Wieczorek, H.; Thon, A.; Dey, T.; Khanin, V.; Rodnyi, P.

2016-06-01

The coincidence resolving time (CRT) of scintillation detectors is the parameter determining noise reduction in time-of-flight PET. We derive an analytical CRT model based on the statistical distribution of photons for two different prototype scintillators. For the first one, characterized by single exponential decay, CRT is proportional to the decay time and inversely proportional to the number of photons, with a square root dependence on the trigger level. For the second scintillator prototype, characterized by exponential rise and decay, CRT is proportional to the square root of the product of rise time and decay time divided by the doubled number of photons, and it is nearly independent of the trigger level. This theory is verified by measurements of scintillation time constants, light yield and CRT on scintillator sticks. Trapping effects are taken into account by defining an effective decay time. We show that in terms of signal-to-noise ratio, CRT is as important as patient dose, imaging time or PET system sensitivity. The noise reduction effect of better timing resolution is verified and visualized by Monte Carlo simulation of a NEMA image quality phantom.

Statistical steady states in turbulent droplet condensation

NASA Astrophysics Data System (ADS)

Bec, Jeremie; Krstulovic, Giorgio; Siewert, Christoph

2017-11-01

We investigate the general problem of turbulent condensation. Using direct numerical simulations we show that the fluctuations of the supersaturation field offer different conditions for the growth of droplets which evolve in time due to turbulent transport and mixing. This leads to propose a Lagrangian stochastic model consisting of a set of integro-differential equations for the joint evolution of the squared radius and the supersaturation along droplet trajectories. The model has two parameters fixed by the total amount of water and the thermodynamic properties, as well as the Lagrangian integral timescale of the turbulent supersaturation. The model reproduces very well the droplet size distributions obtained from direct numerical simulations and their time evolution. A noticeable result is that, after a stage where the squared radius simply diffuses, the system converges exponentially fast to a statistical steady state independent of the initial conditions. The main mechanism involved in this convergence is a loss of memory induced by a significant number of droplets undergoing a complete evaporation before growing again. The statistical steady state is characterised by an exponential tail in the droplet mass distribution.

A Modified Tri-Exponential Model for Multi-b-value Diffusion-Weighted Imaging: A Method to Detect the Strictly Diffusion-Limited Compartment in Brain

PubMed Central

Zeng, Qiang; Shi, Feina; Zhang, Jianmin; Ling, Chenhan; Dong, Fei; Jiang, Biao

2018-01-01

Purpose: To present a new modified tri-exponential model for diffusion-weighted imaging (DWI) to detect the strictly diffusion-limited compartment, and to compare it with the conventional bi- and tri-exponential models. Methods: Multi-b-value diffusion-weighted imaging (DWI) with 17 b-values up to 8,000 s/mm2 were performed on six volunteers. The corrected Akaike information criterions (AICc) and squared predicted errors (SPE) were calculated to compare these three models. Results: The mean f0 values were ranging 11.9–18.7% in white matter ROIs and 1.2–2.7% in gray matter ROIs. In all white matter ROIs: the AICcs of the modified tri-exponential model were the lowest (p < 0.05 for five ROIs), indicating the new model has the best fit among these models; the SPEs of the bi-exponential model were the highest (p < 0.05), suggesting the bi-exponential model is unable to predict the signal intensity at ultra-high b-value. The mean ADCvery−slow values were extremely low in white matter (1–7 × 10−6 mm2/s), but not in gray matter (251–445 × 10−6 mm2/s), indicating that the conventional tri-exponential model fails to represent a special compartment. Conclusions: The strictly diffusion-limited compartment may be an important component in white matter. The new model fits better than the other two models, and may provide additional information. PMID:29535599

Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

NASA Astrophysics Data System (ADS)

Chunodkar, Apurva A.; Akella, Maruthi R.

2013-12-01

This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

46 CFR 178.330 - Simplified stability proof test.

Code of Federal Regulations, 2010 CFR

2010-10-01

...-meters (foot-pounds); P = wind pressure of: (1) 36.6 kilograms/square meter (7.5 pounds/square foot) for operation on protected waters; (2) 48.8 kilogram/square meter (10.0 pounds/square foot) for operation on partially protected waters; or (3) 73.3 kilograms/square meter (15.0 pounds/square foot) for operation on...

Vibration waveform effects on dynamic stabilization of ablative Rayleigh-Taylor instability

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

Piriz, A. R.; Lucchio, L. Di; Rodriguez Prieto, G.

2011-08-15

An analysis of dynamic stabilization of Rayleigh-Taylor instability in an ablation front is performed by considering a general square wave for modulating the vertical acceleration of the front. Such a kind of modulation allows for clarifying the role of thermal conduction in the mechanism of dynamic stabilization. In addition, the study of the effect of different modulations by varying the duration and amplitude of the square wave in each half-period provides insight on the optimum performance of dynamic stabilization.

Two-stage unified stretched-exponential model for time-dependence of threshold voltage shift under positive-bias-stresses in amorphous indium-gallium-zinc oxide thin-film transistors

NASA Astrophysics Data System (ADS)

Jeong, Chan-Yong; Kim, Hee-Joong; Hong, Sae-Young; Song, Sang-Hun; Kwon, Hyuck-In

2017-08-01

In this study, we show that the two-stage unified stretched-exponential model can more exactly describe the time-dependence of threshold voltage shift (ΔV TH) under long-term positive-bias-stresses compared to the traditional stretched-exponential model in amorphous indium-gallium-zinc oxide (a-IGZO) thin-film transistors (TFTs). ΔV TH is mainly dominated by electron trapping at short stress times, and the contribution of trap state generation becomes significant with an increase in the stress time. The two-stage unified stretched-exponential model can provide useful information not only for evaluating the long-term electrical stability and lifetime of the a-IGZO TFT but also for understanding the stress-induced degradation mechanism in a-IGZO TFTs.

Stabilization of time domain acoustic boundary element method for the exterior problem avoiding the nonuniqueness.

PubMed

Jang, Hae-Won; Ih, Jeong-Guon

2013-03-01

The time domain boundary element method (TBEM) to calculate the exterior sound field using the Kirchhoff integral has difficulties in non-uniqueness and exponential divergence. In this work, a method to stabilize TBEM calculation for the exterior problem is suggested. The time domain CHIEF (Combined Helmholtz Integral Equation Formulation) method is newly formulated to suppress low order fictitious internal modes. This method constrains the surface Kirchhoff integral by forcing the pressures at the additional interior points to be zero when the shortest retarded time between boundary nodes and an interior point elapses. However, even after using the CHIEF method, the TBEM calculation suffers the exponential divergence due to the remaining unstable high order fictitious modes at frequencies higher than the frequency limit of the boundary element model. For complete stabilization, such troublesome modes are selectively adjusted by projecting the time response onto the eigenspace. In a test example for a transiently pulsating sphere, the final average error norm of the stabilized response compared to the analytic solution is 2.5%.

How enzymes can capture and transmit free energy from an oscillating electric field.

PubMed

Westerhoff, H V; Tsong, T Y; Chock, P B; Chen, Y D; Astumian, R D

1986-07-01

Recently, it has been demonstrated that free energy from an alternating electric field can drive the active transport of Rb+ by way of the Na+, K+-ATPase. In the present work, it is shown why many transmembrane enzymes can be expected to absorb free energy from an oscillating electric field and transduce that to chemical or transport work. In the theoretical analysis it turned out to be sufficient that (i) the catalytic process be accompanied by either net or cyclic charge translocation across the membrane and (ii) the stability of the enzyme states involved be asymmetric. Calculations based on a four-state model reveal that free-energy transduction occurs with sinusoidal, square-wave, and positive-only oscillating electric fields and for cases that exhibit either linear or exponential field-dependent rate constants. The results suggest that in addition to oscillating electric field-driven transport, the proposed mechanism can also be used to explain, in part, the "missing" free energy term in the cases in which ATP synthesis has been observed with insufficient transmembrane proton electrochemical potential difference.

How enzymes can capture and transmit free energy from an oscillating electric field.

PubMed Central

Westerhoff, H V; Tsong, T Y; Chock, P B; Chen, Y D; Astumian, R D

1986-01-01

Recently, it has been demonstrated that free energy from an alternating electric field can drive the active transport of Rb+ by way of the Na+, K+-ATPase. In the present work, it is shown why many transmembrane enzymes can be expected to absorb free energy from an oscillating electric field and transduce that to chemical or transport work. In the theoretical analysis it turned out to be sufficient that (i) the catalytic process be accompanied by either net or cyclic charge translocation across the membrane and (ii) the stability of the enzyme states involved be asymmetric. Calculations based on a four-state model reveal that free-energy transduction occurs with sinusoidal, square-wave, and positive-only oscillating electric fields and for cases that exhibit either linear or exponential field-dependent rate constants. The results suggest that in addition to oscillating electric field-driven transport, the proposed mechanism can also be used to explain, in part, the "missing" free energy term in the cases in which ATP synthesis has been observed with insufficient transmembrane proton electrochemical potential difference. PMID:2941758

New model of the average neutron and proton pairing gaps

NASA Astrophysics Data System (ADS)

Madland, David G.; Nix, J. Rayford

1988-01-01

By use of the BCS approximation applied to a distribution of dense, equally spaced levels, we derive new expressions for the average neutron pairing gap ¯gD n and average proton pairing gap ¯gD p. These expressions, which contain exponential terms, take into account the dependencies of ¯gD n and ¯gD p upon both the relative neutron excess and shape of the nucleus. The three constants that appear are determined by a least-squares adjustment to experimental pairing gaps obtained by use of fourth-order differences of measured masses. For this purpose we use the 1986 Audi-Wapstra mid-stream mass evaluation and take into account experimental uncertainties. Our new model explains not only the dependencies of ¯gD n and ¯gD p upon relative neutron excess and nuclear shape, but also the experimental result that for medium and heavy nuclei ¯gD n is generally smaller than ¯gD p. We also introduce a new expression for the average residual neutron-proton interaction energy ¯gd that appears in the masses of odd-odd nuclei, and determine the constant that appears by an analogous least-squares adjustment to experimental mass differences. Our new expressions for ¯gD n, ¯gD p and ¯gd should permit extrapolation of these quantities to heavier nuclei and to nuclei farther removed from the valley of β stability than do previous parameterizations.

Moisture Influence Reducing Method for Heavy Metals Detection in Plant Materials Using Laser-Induced Breakdown Spectroscopy: A Case Study for Chromium Content Detection in Rice Leaves.

PubMed

Peng, Jiyu; He, Yong; Ye, Lanhan; Shen, Tingting; Liu, Fei; Kong, Wenwen; Liu, Xiaodan; Zhao, Yun

2017-07-18

Fast detection of heavy metals in plant materials is crucial for environmental remediation and ensuring food safety. However, most plant materials contain high moisture content, the influence of which cannot be simply ignored. Hence, we proposed moisture influence reducing method for fast detection of heavy metals using laser-induced breakdown spectroscopy (LIBS). First, we investigated the effect of moisture content on signal intensity, stability, and plasma parameters (temperature and electron density) and determined the main influential factors (experimental parameters F and the change of analyte concentration) on the variations of signal. For chromium content detection, the rice leaves were performed with a quick drying procedure, and two strategies were further used to reduce the effect of moisture content and shot-to-shot fluctuation. An exponential model based on the intensity of background was used to correct the actual element concentration in analyte. Also, the ratio of signal-to-background for univariable calibration and partial least squared regression (PLSR) for multivariable calibration were used to compensate the prediction deviations. The PLSR calibration model obtained the best result, with the correlation coefficient of 0.9669 and root-mean-square error of 4.75 mg/kg in the prediction set. The preliminary results indicated that the proposed method allowed for the detection of heavy metals in plant materials using LIBS, and it could be possibly used for element mapping in future work.

Estimation of liver T₂ in transfusion-related iron overload in patients with weighted least squares T₂ IDEAL.

PubMed

Vasanawala, Shreyas S; Yu, Huanzhou; Shimakawa, Ann; Jeng, Michael; Brittain, Jean H

2012-01-01

MRI imaging of hepatic iron overload can be achieved by estimating T(2) values using multiple-echo sequences. The purpose of this work is to develop and clinically evaluate a weighted least squares algorithm based on T(2) Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation (IDEAL) technique for volumetric estimation of hepatic T(2) in the setting of iron overload. The weighted least squares T(2) IDEAL technique improves T(2) estimation by automatically decreasing the impact of later, noise-dominated echoes. The technique was evaluated in 37 patients with iron overload. Each patient underwent (i) a standard 2D multiple-echo gradient echo sequence for T(2) assessment with nonlinear exponential fitting, and (ii) a 3D T(2) IDEAL technique, with and without a weighted least squares fit. Regression and Bland-Altman analysis demonstrated strong correlation between conventional 2D and T(2) IDEAL estimation. In cases of severe iron overload, T(2) IDEAL without weighted least squares reconstruction resulted in a relative overestimation of T(2) compared with weighted least squares. Copyright © 2011 Wiley-Liss, Inc.

Analysis of volumetric response of pituitary adenomas receiving adjuvant CyberKnife stereotactic radiosurgery with the application of an exponential fitting model

PubMed Central

Yu, Yi-Lin; Yang, Yun-Ju; Lin, Chin; Hsieh, Chih-Chuan; Li, Chiao-Zhu; Feng, Shao-Wei; Tang, Chi-Tun; Chung, Tzu-Tsao; Ma, Hsin-I; Chen, Yuan-Hao; Ju, Da-Tong; Hueng, Dueng-Yuan

2017-01-01

Abstract Tumor control rates of pituitary adenomas (PAs) receiving adjuvant CyberKnife stereotactic radiosurgery (CK SRS) are high. However, there is currently no uniform way to estimate the time course of the disease. The aim of this study was to analyze the volumetric responses of PAs after CK SRS and investigate the application of an exponential decay model in calculating an accurate time course and estimation of the eventual outcome. A retrospective review of 34 patients with PAs who received adjuvant CK SRS between 2006 and 2013 was performed. Tumor volume was calculated using the planimetric method. The percent change in tumor volume and tumor volume rate of change were compared at median 4-, 10-, 20-, and 36-month intervals. Tumor responses were classified as: progression for >15% volume increase, regression for ≤15% decrease, and stabilization for ±15% of the baseline volume at the time of last follow-up. For each patient, the volumetric change versus time was fitted with an exponential model. The overall tumor control rate was 94.1% in the 36-month (range 18–87 months) follow-up period (mean volume change of −43.3%). Volume regression (mean decrease of −50.5%) was demonstrated in 27 (79%) patients, tumor stabilization (mean change of −3.7%) in 5 (15%) patients, and tumor progression (mean increase of 28.1%) in 2 (6%) patients (P = 0.001). Tumors that eventually regressed or stabilized had a temporary volume increase of 1.07% and 41.5% at 4 months after CK SRS, respectively (P = 0.017). The tumor volume estimated using the exponential fitting equation demonstrated high positive correlation with the actual volume calculated by magnetic resonance imaging (MRI) as tested by Pearson correlation coefficient (0.9). Transient progression of PAs post-CK SRS was seen in 62.5% of the patients receiving CK SRS, and it was not predictive of eventual volume regression or progression. A three-point exponential model is of potential predictive value according to relative distribution. An exponential decay model can be used to calculate the time course of tumors that are ultimately controlled. PMID:28121913

Recursive least squares estimation and its application to shallow trench isolation

NASA Astrophysics Data System (ADS)

Wang, Jin; Qin, S. Joe; Bode, Christopher A.; Purdy, Matthew A.

2003-06-01

In recent years, run-to-run (R2R) control technology has received tremendous interest in semiconductor manufacturing. One class of widely used run-to-run controllers is based on the exponentially weighted moving average (EWMA) statistics to estimate process deviations. Using an EWMA filter to smooth the control action on a linear process has been shown to provide good results in a number of applications. However, for a process with severe drifts, the EWMA controller is insufficient even when large weights are used. This problem becomes more severe when there is measurement delay, which is almost inevitable in semiconductor industry. In order to control drifting processes, a predictor-corrector controller (PCC) and a double EWMA controller have been developed. Chen and Guo (2001) show that both PCC and double-EWMA controller are in effect Integral-double-Integral (I-II) controllers, which are able to control drifting processes. However, since offset is often within the noise of the process, the second integrator can actually cause jittering. Besides, tuning the second filter is not as intuitive as a single EWMA filter. In this work, we look at an alternative way Recursive Least Squares (RLS), to estimate and control the drifting process. EWMA and double-EWMA are shown to be the least squares estimate for locally constant mean model and locally constant linear trend model. Then the recursive least squares with exponential factor is applied to shallow trench isolation etch process to predict the future etch rate. The etch process, which is a critical process in the flash memory manufacturing, is known to suffer from significant etch rate drift due to chamber seasoning. In order to handle the metrology delay, we propose a new time update scheme. RLS with the new time update method gives very good result. The estimate error variance is smaller than that from EWMA, and mean square error decrease more than 10% compared to that from EWMA.

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.

Almost periodic cellular neural networks with neutral-type proportional delays

NASA Astrophysics Data System (ADS)

Xiao, Songlin

2018-03-01

This paper presents a new result on the existence, uniqueness and generalised exponential stability of almost periodic solutions for cellular neural networks with neutral-type proportional delays and D operator. Based on some novel differential inequality techniques, a testable condition is derived to ensure that all the state trajectories of the system converge to an almost periodic solution with a positive exponential convergence rate. The effectiveness of the obtained result is illustrated by a numerical example.

A neural-network-based exponential H∞ synchronisation for chaotic secure communication via improved genetic algorithm

NASA Astrophysics Data System (ADS)

Hsiao, Feng-Hsiag

2016-10-01

In this study, a novel approach via improved genetic algorithm (IGA)-based fuzzy observer is proposed to realise exponential optimal H∞ synchronisation and secure communication in multiple time-delay chaotic (MTDC) systems. First, an original message is inserted into the MTDC system. Then, a neural-network (NN) model is employed to approximate the MTDC system. Next, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion derived in terms of Lyapunov's direct method, thus ensuring that the trajectories of the slave system approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Due to GA's random global optimisation search capabilities, the lower and upper bounds of the search space can be set so that the GA will seek better fuzzy observer feedback gains, accelerating feedback gain-based synchronisation via the LMI-based approach. IGA, which exhibits better performance than traditional GA, is used to synthesise a fuzzy observer to not only realise the exponential synchronisation, but also achieve optimal H∞ performance by minimizing the disturbance attenuation level and recovering the transmitted message. Finally, a numerical example with simulations is given in order to demonstrate the effectiveness of our approach.

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.

Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability

NASA Technical Reports Server (NTRS)

Ito, K.

1984-01-01

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

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.

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.

On Superstability of Semigroups

NASA Technical Reports Server (NTRS)

Balakrishnan. A. V.

1997-01-01

This paper presents a brief report on superstable semigroups - abstract theory and some applications thereof. The notion of super stability is a strengthening of exponential stability and occurs in Timoshenko models of structures with self-straining material using pure (idealized) rate feed- back. It is also relevant to the problem of Riesz bases of eigenfunctions of infinitesimal generators under perturbation.

Stability of the Markov operator and synchronization of Markovian random products

NASA Astrophysics Data System (ADS)

Díaz, Lorenzo J.; Matias, Edgar

2018-05-01

We study Markovian random products on a large class of ‘m-dimensional’ connected compact metric spaces (including products of closed intervals and trees). We introduce a splitting condition, generalizing the classical one by Dubins and Freedman, and prove that this condition implies the asymptotic stability of the corresponding Markov operator and (exponentially fast) synchronization.

Investigation of hyperelastic models for nonlinear elastic behavior of demineralized and deproteinized bovine cortical femur bone.

PubMed

Hosseinzadeh, M; Ghoreishi, M; Narooei, K

2016-06-01

In this study, the hyperelastic models of demineralized and deproteinized bovine cortical femur bone were investigated and appropriate models were developed. Using uniaxial compression test data, the strain energy versus stretch was calculated and the appropriate hyperelastic strain energy functions were fitted on data in order to calculate the material parameters. To obtain the mechanical behavior in other loading conditions, the hyperelastic strain energy equations were investigated for pure shear and equi-biaxial tension loadings. The results showed the Mooney-Rivlin and Ogden models cannot predict the mechanical response of demineralized and deproteinized bovine cortical femur bone accurately, while the general exponential-exponential and general exponential-power law models have a good agreement with the experimental results. To investigate the sensitivity of the hyperelastic models, a variation of 10% in material parameters was performed and the results indicated an acceptable stability for the general exponential-exponential and general exponential-power law models. Finally, the uniaxial tension and compression of cortical femur bone were studied using the finite element method in VUMAT user subroutine of ABAQUS software and the computed stress-stretch curves were shown a good agreement with the experimental data. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Nonlinear Spacecraft Attitude Controller and Observer with an Unknown Constant Gyro Bias and Gyro Noise

NASA Technical Reports Server (NTRS)

Deutschmann, Julie; Sanner, Robert M.

2001-01-01

A nonlinear control scheme for attitude control of a spacecraft is combined with a nonlinear gyro bias observer for the case of constant gyro bias, in the presence of gyro noise. The observer bias estimates converge exponentially to a mean square bound determined by the standard deviation of the gyro noise. The resulting coupled, closed loop dynamics are proven to be globally stable, with asymptotic tracking which is also mean square bounded. A simulation of the proposed observer-controller design is given for a rigid spacecraft tracking a specified, time-varying attitude sequence to illustrate the theoretical claims.

Arrhenius time-scaled least squares: a simple, robust approach to accelerated stability data analysis for bioproducts.

PubMed

Rauk, Adam P; Guo, Kevin; Hu, Yanling; Cahya, Suntara; Weiss, William F

2014-08-01

Defining a suitable product presentation with an acceptable stability profile over its intended shelf-life is one of the principal challenges in bioproduct development. Accelerated stability studies are routinely used as a tool to better understand long-term stability. Data analysis often employs an overall mass action kinetics description for the degradation and the Arrhenius relationship to capture the temperature dependence of the observed rate constant. To improve predictive accuracy and precision, the current work proposes a least-squares estimation approach with a single nonlinear covariate and uses a polynomial to describe the change in a product attribute with respect to time. The approach, which will be referred to as Arrhenius time-scaled (ATS) least squares, enables accurate, precise predictions to be achieved for degradation profiles commonly encountered during bioproduct development. A Monte Carlo study is conducted to compare the proposed approach with the common method of least-squares estimation on the logarithmic form of the Arrhenius equation and nonlinear estimation of a first-order model. The ATS least squares method accommodates a range of degradation profiles, provides a simple and intuitive approach for data presentation, and can be implemented with ease. © 2014 Wiley Periodicals, Inc. and the American Pharmacists Association.

Periodic bidirectional associative memory neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Chen, Anping; Huang, Lihong; Liu, Zhigang; Cao, Jinde

2006-05-01

Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin's coincidence degree theory and the Lyapunov functional method and the Young's inequality technique. These results are helpful for designing a globally exponentially stable and periodic oscillatory BAM neural network, and the conditions can be easily verified and be applied in practice. An example is also given to illustrate our results.

Rural Student Entrepreneurs: Linking Commerce and Community. (Benefits)[Squared]: The Exponential Results of Linking School Improvement and Community Development, Issue Number Three.

ERIC Educational Resources Information Center

Boethel, Martha

In many rural areas, both communities and schools are threatened by decreasing population and changing economic conditions. To boost both the local economy and student achievement, a growing number of rural schools are turning to entrepreneurial education. In school entrepreneurship programs, students create small businesses under the guidance of…

Gaussian quadrature exponential sum modeling of near infrared methane laboratory spectra obtained at temperatures from 106 to 297 K

NASA Technical Reports Server (NTRS)

Giver, Lawrence P.; Benner, D. C.; Tomasko, M. G.; Fink, U.; Kerola, D.

1990-01-01

Transmission measurements made on near-infrared laboratory methane spectra have previously been fit using a Malkmus band model. The laboratory spectra were obtained in three groups at temperatures averaging 112, 188, and 295 K; band model fitting was done separately for each temperature group. These band model parameters cannot be used directly in scattering atmosphere model computations, so an exponential sum model is being developed which includes pressure and temperature fitting parameters. The goal is to obtain model parameters by least square fits at 10/cm intervals from 3800 to 9100/cm. These results will be useful in the interpretation of current planetary spectra and also NIMS spectra of Jupiter anticipated from the Galileo mission.

Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

NASA Astrophysics Data System (ADS)

Wan, Li; Zhou, Qinghua

2007-10-01

The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem.

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.

Thermal Noise Limit in Frequency Stabilization of Lasers with Rigid Cavities

NASA Technical Reports Server (NTRS)

Numata, Kenji; Kemery, Amy; Camp, Jordan

2004-01-01

We evaluated thermal noise (Brownian motion) in a rigid reference cavity used for frequency stabilization of lasers, based on the mechanical loss of cavity materials and the numerical analysis of the mirror-spacer mechanics with t.he direct application of the fluctuation dissipation theorem. This noise sets a fundamental limit for the frequency stability achieved with a rigid frequency- reference cavity of order 1 Hz/square root Hz(0.01 Hz/square root Hz) at 10 mHz (100 Hz) at room temperature. This level coincides with the world-highest level stabilization results.

Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay.

PubMed

Korkmaz, Erdal

2017-01-01

In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

Stability of phases of a square-well fluid within superposition approximation

NASA Astrophysics Data System (ADS)

Piasecki, Jarosław; Szymczak, Piotr; Kozak, John J.

2013-04-01

The analytic and numerical methods introduced previously to study the phase behavior of hard sphere fluids starting from the Yvon-Born-Green (YBG) equation under the Kirkwood superposition approximation (KSA) are adapted to the square-well fluid. We are able to show conclusively that the YBG equation under the KSA closure when applied to the square-well fluid: (i) predicts the existence of an absolute stability limit corresponding to freezing where undamped oscillations appear in the long-distance behavior of correlations, (ii) in accordance with earlier studies reveals the existence of a liquid-vapor transition by the appearance of a "near-critical region" where monotonically decaying correlations acquire very long range, although the system never loses stability.

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

NASA Technical Reports Server (NTRS)

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

1987-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.

Chem Ed Compacts

ERIC Educational Resources Information Center

Wolf, Walter A., Ed.

1976-01-01

Presents three activities: (1) the investigation of the purity and stability of nicotinamide and flavin coenzymes; (2) desk-computer fitting of a two-exponential function; and (3) an interesting and inexpensive solubility product experiment for introductory chemistry. (RH)

An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of Delay

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

Apalara, Tijani A., E-mail: tijani@kfupm.edu.sa; Messaoudi, Salim A., E-mail: messaoud@kfupm.edu.sa

In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in themore » presence of a small delay is an open question.« less

Asymptotic stability estimates near an equilibrium point

NASA Astrophysics Data System (ADS)

Dumas, H. Scott; Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia

2017-07-01

We use the error bounds for adiabatic invariants found in the work of Chartier, Murua and Sanz-Serna [3] to bound the solutions of a Hamiltonian system near an equilibrium over exponentially long times. Our estimates depend only on the linearized system and not on the higher order terms as in KAM theory, nor do we require any steepness or convexity conditions as in Nekhoroshev theory. We require that the equilibrium point where our estimate applies satisfy a type of formal stability called Lie stability.

Determinism in synthesized chaotic waveforms.

PubMed

Corron, Ned J; Blakely, Jonathan N; Hayes, Scott T; Pethel, Shawn D

2008-03-01

The output of a linear filter driven by a randomly polarized square wave, when viewed backward in time, is shown to exhibit determinism at all times when embedded in a three-dimensional state space. Combined with previous results establishing exponential divergence equivalent to a positive Lyapunov exponent, this result rigorously shows that such reverse-time synthesized waveforms appear equally to have been produced by a deterministic chaotic system.

Stability of the thermodynamic equilibrium - A test of the validity of dynamic models as applied to gyroviscous perpendicular magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Faghihi, Mustafa; Scheffel, Jan; Spies, Guenther O.

1988-05-01

Stability of the thermodynamic equilibrium is put forward as a simple test of the validity of dynamic equations, and is applied to perpendicular gyroviscous magnetohydrodynamics (i.e., perpendicular magnetohydrodynamics with gyroviscosity added). This model turns out to be invalid because it predicts exponentially growing Alfven waves in a spatially homogeneous static equilibrium with scalar pressure.

Design of vibration isolation systems using multiobjective optimization techniques

NASA Technical Reports Server (NTRS)

Rao, S. S.

1984-01-01

The design of vibration isolation systems is considered using multicriteria optimization techniques. The integrated values of the square of the force transmitted to the main mass and the square of the relative displacement between the main mass and the base are taken as the performance indices. The design of a three degrees-of-freedom isolation system with an exponentially decaying type of base disturbance is considered for illustration. Numerical results are obtained using the global criterion, utility function, bounded objective, lexicographic, goal programming, goal attainment and game theory methods. It is found that the game theory approach is superior in finding a better optimum solution with proper balance of the various objective functions.

Calibration of Lévy Processes with American Options

NASA Astrophysics Data System (ADS)

Achdou, Yves

We study options on financial assets whose discounted prices are exponential of Lévy processes. The price of an American vanilla option as a function of the maturity and the strike satisfies a linear complementarity problem involving a non-local partial integro-differential operator. It leads to a variational inequality in a suitable weighted Sobolev space. Calibrating the Lévy process may be done by solving an inverse least square problem where the state variable satisfies the previously mentioned variational inequality. We first assume that the volatility is positive: after carefully studying the direct problem, we propose necessary optimality conditions for the least square inverse problem. We also consider the direct problem when the volatility is zero.

Stability of post-fertilization traveling waves

NASA Astrophysics Data System (ADS)

Flores, Gilberto; Plaza, Ramón G.

This paper studies the stability of a family of traveling wave solutions to the system proposed by Lane et al. [D.C. Lane, J.D. Murray, V.S. Manoranjan, Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs, IMA J. Math. Appl. Med. Biol. 4 (4) (1987) 309-331], to model a pair of mechanochemical phenomena known as post-fertilization waves on eggs. The waves consist of an elastic deformation pulse on the egg's surface, and a free calcium concentration front. The family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration. This work establishes the spectral, linear and nonlinear orbital stability of these post-fertilization waves for small values of the coupling parameter. The usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation. Nonetheless, exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established. We show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase-modulated traveling wave.

Orthogonality catastrophe and fractional exclusion statistics

NASA Astrophysics Data System (ADS)

Ares, Filiberto; Gupta, Kumar S.; de Queiroz, Amilcar R.

2018-02-01

We show that the N -particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the N -body ground state wave functions with two different values of the inverse-square interaction term goes to zero in the thermodynamic limit. When the two values of the inverse-square coupling differ by an infinitesimal amount, the wave function overlap shows an exponential suppression. This is qualitatively different from the usual power law suppression observed in the Anderson's orthogonality catastrophe. We also obtain an analytic expression for the wave function overlaps for an arbitrary set of couplings, whose properties are analyzed numerically. The quasiparticles constituting the ground state wave functions of the Sutherland model are known to obey fractional exclusion statistics. Our analysis indicates that the orthogonality catastrophe may be valid in systems with more general kinds of statistics than just the fermionic type.

Orthogonality catastrophe and fractional exclusion statistics.

PubMed

Ares, Filiberto; Gupta, Kumar S; de Queiroz, Amilcar R

2018-02-01

We show that the N-particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the N-body ground state wave functions with two different values of the inverse-square interaction term goes to zero in the thermodynamic limit. When the two values of the inverse-square coupling differ by an infinitesimal amount, the wave function overlap shows an exponential suppression. This is qualitatively different from the usual power law suppression observed in the Anderson's orthogonality catastrophe. We also obtain an analytic expression for the wave function overlaps for an arbitrary set of couplings, whose properties are analyzed numerically. The quasiparticles constituting the ground state wave functions of the Sutherland model are known to obey fractional exclusion statistics. Our analysis indicates that the orthogonality catastrophe may be valid in systems with more general kinds of statistics than just the fermionic type.

46 CFR 178.340 - Stability standards for pontoon vessels on protected waters.

Code of Federal Regulations, 2011 CFR

2011-10-01

... = 2.0 feet (0.61 meters); Mw = Wind heeling moment in foot-pounds (kilogram-meters) P = Wind pressure of 7.5 pounds/square foot (36.6 kilograms/square meter); A = Area, in square feet (square meters), of the projected lateral surface of the vessel above the waterline (including each projected area of the...

46 CFR 178.340 - Stability standards for pontoon vessels on protected waters.

Code of Federal Regulations, 2014 CFR

2014-10-01

... = 2.0 feet (0.61 meters); Mw = Wind heeling moment in foot-pounds (kilogram-meters) P = Wind pressure of 7.5 pounds/square foot (36.6 kilograms/square meter); A = Area, in square feet (square meters), of the projected lateral surface of the vessel above the waterline (including each projected area of the...

46 CFR 178.340 - Stability standards for pontoon vessels on protected waters.

Code of Federal Regulations, 2012 CFR

2012-10-01

... = 2.0 feet (0.61 meters); Mw = Wind heeling moment in foot-pounds (kilogram-meters) P = Wind pressure of 7.5 pounds/square foot (36.6 kilograms/square meter); A = Area, in square feet (square meters), of the projected lateral surface of the vessel above the waterline (including each projected area of the...

46 CFR 178.340 - Stability standards for pontoon vessels on protected waters.

Code of Federal Regulations, 2013 CFR

2013-10-01

... = 2.0 feet (0.61 meters); Mw = Wind heeling moment in foot-pounds (kilogram-meters) P = Wind pressure of 7.5 pounds/square foot (36.6 kilograms/square meter); A = Area, in square feet (square meters), of the projected lateral surface of the vessel above the waterline (including each projected area of the...

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.

Optimization of the geometrical stability in square ring laser gyroscopes

NASA Astrophysics Data System (ADS)

Santagata, R.; Beghi, A.; Belfi, J.; Beverini, N.; Cuccato, D.; Di Virgilio, A.; Ortolan, A.; Porzio, A.; Solimeno, S.

2015-03-01

Ultra-sensitive ring laser gyroscopes are regarded as potential detectors of the general relativistic frame-dragging effect due to the rotation of the Earth. Our project for this goal is called GINGER (gyroscopes in general relativity), and consists of a ground-based triaxial array of ring lasers aimed at measuring the rotation rate of the Earth with an accuracy of {{10}-14} rad {{s}-1}. Such an ambitious goal is now within reach, as large-area ring lasers are very close to the required sensitivity and stability. However, demanding constraints on the geometrical stability of the optical path of the laser inside the ring cavity are required. Thus, we have begun a detailed study of the geometry of an optical cavity in order to find a control strategy for its geometry that could meet the specifications of the GINGER project. As the cavity perimeter has a stationary point for the square configuration, we identify a set of transformations on the mirror positions that allows us to adjust the laser beam steering to the shape of a square. We show that the geometrical stability of a square cavity strongly increases by implementing a suitable system to measure the mirror distances, and that the geometry stabilization can be achieved by measuring the absolute lengths of the two diagonals and the perimeter of the ring.

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.

Spectral Study of Measles Epidemics: The Dependence of Spectral Gradient on the Population Size of the Community

NASA Astrophysics Data System (ADS)

Sumi, Ayako; Olsen, Lars Folke; Ohtomo, Norio; Tanaka, Yukio; Sawamura, Sadashi

2003-02-01

We have carried out spectral analysis of measles notifications in several communities in Denmark, UK and USA. The results confirm that each power spectral density (PSD) shows exponential characteristics, which are universally observed in the PSD for time series generated from nonlinear dynamical system. The exponential gradient increases with the population size. For almost all communities, many spectral lines observed in each PSD can be fully assigned to linear combinations of several fundamental periods, suggesting that the measles data are substantially noise-free. The optimum least squares fitting curve calculated using these fundamental periods essentially reproduces an underlying variation of the measles data, and an extension of the curve can be used to predict measles epidemics. For the communities with large population sizes, some PSD patterns obtained from segment time series analysis show a close resemblance to the PSD patterns at the initial stages of a period-doubling bifurcation process for the so-called susceptible/exposed/infectious/recovered (SEIR) model with seasonal forcing. The meaning of the relationship between the exponential gradient and the population size is discussed.

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.

Scaling in the distribution of intertrade durations of Chinese stocks

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Chen, Wei; Zhou, Wei-Xing

2008-10-01

The distribution of intertrade durations, defined as the waiting times between two consecutive transactions, is investigated based upon the limit order book data of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. A scaling pattern is observed in the distributions of intertrade durations, where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve. The scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions. The ensemble distributions for all stocks are modeled by the Weibull and the Tsallis q-exponential distributions. Maximum likelihood estimation shows that the Weibull distribution outperforms the q-exponential for not-too-large intertrade durations which account for more than 98.5% of the data. Alternatively, nonlinear least-squares estimation selects the q-exponential as a better model, in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities. The distribution of intertrade durations is Weibull followed by a power-law tail with an asymptotic tail exponent close to 3.

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.

The Steep Nekhoroshev's Theorem

NASA Astrophysics Data System (ADS)

Guzzo, M.; Chierchia, L.; Benettin, G.

2016-03-01

Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.

The Inverse-Square Law and the Exponential Attenuation Law Used to the Shielding Calculation in Radiotherapy on a High School Level

ERIC Educational Resources Information Center

de Paiva, Eduardo

2016-01-01

Every year millions of people contract cancer in the world, and according to prediction of the World Health Organization by the year 2030 there will be about 27 million new cases. Because of these figures and the resulting social and economic implications of this disease, radiotherapy, which is one form of treatment that uses ionizing radiation,…

Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays.

PubMed

Rakkiyappan, R; Sakthivel, N; Cao, Jinde

2015-06-01

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods. Copyright © 2015 Elsevier Ltd. All rights reserved.

On the nature of dissipative Timoshenko systems at light of the second spectrum of frequency

NASA Astrophysics Data System (ADS)

Almeida Júnior, D. S.; Ramos, A. J. A.

2017-12-01

In the present work, we prove that there exists a relation between a physical inconsistence known as second spectrum of frequency or non-physical spectrum and the exponential decay of a dissipative Timoshenko system where the damping mechanism acts on angle rotation. The so-called second spectrum is addressed into stabilization scenario and, in particular, we show that the second spectrum of the classical Timoshenko model can be truncated by taking a damping mechanism. Also, we show that dissipative Timoshenko type systems which are free of the second spectrum [based on important physical and historical observations made by Elishakoff (Advances mathematical modeling and experimental methods for materials and structures, solid mechanics and its applications, Springer, Berlin, pp 249-254, 2010), Elishakoff et al. (ASME Am Soc Mech Eng Appl Mech Rev 67(6):1-11 2015) and Elishakoff et al. (Int J Solids Struct 109:143-151, 2017)] are exponential stable for any values of the coefficients of system. In this direction, we provide physical explanations why weakly dissipative Timoshenko systems decay exponentially according to equality between velocity of wave propagation as proved in pioneering works by Soufyane (C R Acad Sci 328(8):731-734, 1999) and also by Muñoz Rivera and Racke (Discrete Contin Dyn Syst B 9:1625-1639, 2003). Therefore, the second spectrum of the classical Timoshenko beam model plays an important role in explaining some results on exponential decay and our investigations suggest to pay attention to the eventual consequences of this spectrum on stabilization setting for dissipative Timoshenko type systems.

Non Lyapunov stability of the constant spatially developing 1-D gas flow in presence of solutions having strictly positive exponential growth rate

NASA Astrophysics Data System (ADS)

Balint, Stefan; Balint, Agneta M.

2017-01-01

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].

Stability analysis for stochastic BAM nonlinear neural network with delays

NASA Astrophysics Data System (ADS)

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

2008-02-01

In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

NASA Astrophysics Data System (ADS)

Do, K. D.

2018-05-01

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

Razumikhin-Type Stability Criteria for Differential Equations with Delayed Impulses.

PubMed

Wang, Qing; Zhu, Quanxin

2013-01-01

This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations. Based on the method of Lyapunov functions, Razumikhin technique and mathematical induction, several stability criteria are obtained for differential equations with delayed impulses. Our results show that some systems with delayed impulses may be exponentially stabilized by impulses even if the system matrices are unstable. Some less restrictive sufficient conditions are also given to keep the good stability property of systems subject to certain type of impulsive perturbations. Examples with numerical simulations are discussed to illustrate the theorems. Our results may be applied to complex problems where impulses depend on both current and past states.

Applying the methodology of Design of Experiments to stability studies: a Partial Least Squares approach for evaluation of drug stability.

PubMed

Jordan, Nika; Zakrajšek, Jure; Bohanec, Simona; Roškar, Robert; Grabnar, Iztok

2018-05-01

The aim of the present research is to show that the methodology of Design of Experiments can be applied to stability data evaluation, as they can be seen as multi-factor and multi-level experimental designs. Linear regression analysis is usually an approach for analyzing stability data, but multivariate statistical methods could also be used to assess drug stability during the development phase. Data from a stability study for a pharmaceutical product with hydrochlorothiazide (HCTZ) as an unstable drug substance was used as a case example in this paper. The design space of the stability study was modeled using Umetrics MODDE 10.1 software. We showed that a Partial Least Squares model could be used for a multi-dimensional presentation of all data generated in a stability study and for determination of the relationship among factors that influence drug stability. It might also be used for stability predictions and potentially for the optimization of the extent of stability testing needed to determine shelf life and storage conditions, which would be time and cost-effective for the pharmaceutical industry.

The size distribution of Pacific Seamounts

NASA Astrophysics Data System (ADS)

Smith, Deborah K.; Jordan, Thomas H.

1987-11-01

An analysis of wide-beam, Sea Beam and map-count data in the eastern and southern Pacific confirms the hypothesis that the average number of "ordinary" seamounts with summit heights h ≥ H can be approximated by the exponential frequency-size distribution: v(H) = vo e-βH. The exponential model, characterized by the single scale parameter β-1, is found to be superior to a power-law (self-similar) model. The exponential model provides a good first-order description of the summit-height distribution over a very broad spectrum of seamount sizes, from small cones (h < 300 m) to tall composite volcanoes (h > 3500 m). The distribution parameters obtained from 157,000 km of wide-beam profiles in the eastern and southern Pacific Ocean are vo = (5.4 ± 0.65) × 10-9m-2 and β = (3.5 ± 0.21) × 10-3 m-1, yielding an average of 5400 ± 650 seamounts per million square kilometers, of which 170 ± 17 are greater than one kilometer in height. The exponential distribution provides a reference for investigating the populations of not-so-ordinary seamounts, such as those on hotspot swells and near fracture zones, and seamounts in other ocean basins. If we assume that volcano height is determined by a hydraulic head proportional to the source depth of the magma column, then our observations imply an approximately exponential distribution of source depths. For reasonable values of magma and crustal densities, a volcano with the characteristic height β-1 = 285 m has an apparent source depth on the order of the crustal thickness.

Master-slave exponential synchronization of delayed complex-valued memristor-based neural networks via impulsive control.

PubMed

Li, Xiaofan; Fang, Jian-An; Li, Huiyuan

2017-09-01

This paper investigates master-slave exponential synchronization for a class of complex-valued memristor-based neural networks with time-varying delays via discontinuous impulsive control. Firstly, the master and slave complex-valued memristor-based neural networks with time-varying delays are translated to two real-valued memristor-based neural networks. Secondly, an impulsive control law is constructed and utilized to guarantee master-slave exponential synchronization of the neural networks. Thirdly, the master-slave synchronization problems are transformed into the stability problems of the master-slave error system. By employing linear matrix inequality (LMI) technique and constructing an appropriate Lyapunov-Krasovskii functional, some sufficient synchronization criteria are derived. Finally, a numerical simulation is provided to illustrate the effectiveness of the obtained theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Proposal for a standardised identification of the mono-exponential terminal phase for orally administered drugs.

PubMed

Scheerans, Christian; Derendorf, Hartmut; Kloft, Charlotte

2008-04-01

The area under the plasma concentration-time curve from time zero to infinity (AUC(0-inf)) is generally considered to be the most appropriate measure of total drug exposure for bioavailability/bioequivalence studies of orally administered drugs. However, the lack of a standardised method for identifying the mono-exponential terminal phase of the concentration-time curve causes variability for the estimated AUC(0-inf). The present investigation introduces a simple method, called the two times t(max) method (TTT method) to reliably identify the mono-exponential terminal phase in the case of oral administration. The new method was tested by Monte Carlo simulation in Excel and compared with the adjusted r squared algorithm (ARS algorithm) frequently used in pharmacokinetic software programs. Statistical diagnostics of three different scenarios, each with 10,000 hypothetical patients showed that the new method provided unbiased average AUC(0-inf) estimates for orally administered drugs with a monophasic concentration-time curve post maximum concentration. In addition, the TTT method generally provided more precise estimates for AUC(0-inf) compared with the ARS algorithm. It was concluded that the TTT method is a most reasonable tool to be used as a standardised method in pharmacokinetic analysis especially bioequivalence studies to reliably identify the mono-exponential terminal phase for orally administered drugs showing a monophasic concentration-time profile.

Adiabatic approximation with exponential accuracy for many-body systems and quantum computation

NASA Astrophysics Data System (ADS)

Lidar, Daniel A.; Rezakhani, Ali T.; Hamma, Alioscia

2009-10-01

We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real-time axis, that some number of its time derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is nondegenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time derivative of the Hamiltonian divided by the cube of the minimal gap.

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

Longitudinal Proximity Effects in Superconducting Transition-Edge Sensors

NASA Technical Reports Server (NTRS)

Sadleir, John E.; Smith, Stephen J.; Bandler, SImon R.; Chervenak, James A.; Clem, John R.

2009-01-01

We have found experimentally that the critical current of a square superconducting transition-edge sensor (TES) depends exponentially upon the side length L and the square root of the temperature T. As a consequence, the effective transition temperature T(sub c) of the TES is current-dependent and at fixed current scales as 1/L(sup 2). We also have found that the critical current can show clear Fraunhofer-like oscillations in an applied magnetic field, similar to those found in Josephson junctions. The observed behavior has a natural theoretical explanation in terms of longitudinal proximity effects if the TES is regarded as a weak link between superconducting leads. We have observed the proximity effect in these devices over extraordinarily long lengths exceeding 100 microns.

Simulating the Stability of Colloidal Amorphous Iron Oxide in Natural Waters

EPA Science Inventory

Anecdotal evidence suggests that there are more than 800 commercial products containing manufactured nanomaterials in commercial production and that this number is expected to increase in an exponential fashion. Unfortunately, existing standardized test guidelines designed to as...

Investigation on Stability in Roll of Square Section Missile at High Angle of Attack

NASA Astrophysics Data System (ADS)

Tao, Yang; Fan, Zhaolin; Wu, Jifei; Wu, Wenhua

An experimental investigation of the stability in roll of a square section missile at high incidence was conducted in FL-23 wind tunnel. Dynamic motions were obtained on a square section missile that is free to rotate about its longitudinal axis. Different dynamic rolling motions were observed depending on the incidence of the model sting. These dynamic regimes include damped oscillations, quasi-limit-cycle wing-rock motion, and constant rolling. A coupling numerical method was established by solving the fluid dynamics equations and the rigid-body dynamics equations synchronously in order to predict the onset and the development of uncommented motions and then explore the unsteady movement characteristics of the aircraft. The study indicates that the aircraft loss stability at high incidence is caused by the asymmetric vertex on the level fin tip liftoff and attach alternately. The computation results are in line with the experiment results.

Low frequency AC waveform generator

DOEpatents

Bilharz, Oscar W.

1986-01-01

Low frequency sine, cosine, triangle and square waves are synthesized in circuitry which allows variation in the waveform amplitude and frequency while exhibiting good stability and without requiring significant stabilization time. A triangle waveform is formed by a ramped integration process controlled by a saturation amplifier circuit which produces the necessary hysteresis for the triangle waveform. The output of the saturation circuit is tapped to produce the square waveform. The sine waveform is synthesized by taking the absolute value of the triangular waveform, raising this absolute value to a predetermined power, multiplying the raised absolute value of the triangle wave with the triangle wave itself and properly scaling the resultant waveform and subtracting it from the triangular waveform itself. The cosine is synthesized by squaring the triangular waveform, raising the triangular waveform to a predetermined power and adding the squared waveform raised to the predetermined power with a DC reference and subtracting the squared waveform therefrom, with all waveforms properly scaled. The resultant waveform is then multiplied with a square wave in order to correct the polarity and produce the resultant cosine waveform.

Structure of the nucleoid in cells of Streptococcus faecalis.

PubMed Central

Daneo-Moore, L; Dicker, D; Higgins, M L

1980-01-01

The structure of the nucleoid of Streptococcus faecalis (ATCC 9790) was examined and compared in the unfixed and fixed states by immersive refractometry and electron microscopy. It appears from these studies that the nucleoid structure is much more centralized in unfixed chloramphenicol-treated (stationary-phase) cells than it is in cells in the exponential phase of growth. The more dispersed configuration of the exponential-phase nucleoid could be preserved by fixation in glutaraldehyde, but not in Formalin or in osmium tetroxide. One important factor in explaining these differences in preservation is that glutaraldehyde (but not Formalin or osmium tetroxide) can rapidly cross-link the amino groups of macromolecules in cells. It was also observed that osmium tetroxide resulted in a preferential breakdown of nascent ribonucleic acid. These results are interpreted as indicating that glutaraldehyde is able to stabilize the exponential-phase nucleoid before it assumes the more central appearance seen in osmium tetroxide- and Formalin-fixed cells. These results are discussed in terms of the proposed organization of the exponential-phase nucleoid in unfixed cells. Images PMID:6767695

Turbulence and the Stabilization Principle

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Control of three-dimensional waves on thin liquid films

NASA Astrophysics Data System (ADS)

Tomlin, Ruben; Gomes, Susana; Pavliotis, Greg; Papageorgiou, Demetrios

2017-11-01

We consider a weakly nonlinear model for interfacial waves on three-dimensional thin films on inclined flat planes - the Kuramoto-Sivashinsky equation. The flow is driven by gravity, and is allowed to be overlying or hanging on the flat substrate. Blowing and suction controls are applied at the substrate surface. We explore the instability of the transverse modes for hanging arrangements, which are unbounded and grow exponentially. The structure of the equations allows us to construct optimal transverse controls analytically to prevent this transverse growth. We also may consider the influence of transverse modes on overlying film flows, these modes are damped out if uncontrolled. We also consider the more physical concept of point actuated controls which are modelled using Dirac delta functions. We first study the case of proportional control, where the actuation at a point depends on the local interface height alone. Here, we study the influence of control strength and number/location of actuators on the possible stabilization of the zero solution. We also consider the full feedback problem, which assumes that we can observe the full interface and allow communication between actuators. Using these controls we can obtain exponential stability where proportional controls fail, and stabilize non-trivial solutions.

Exponential stability preservation in semi-discretisations of BAM networks with nonlinear impulses

NASA Astrophysics Data System (ADS)

Mohamad, Sannay; Gopalsamy, K.

2009-01-01

This paper demonstrates the reliability of a discrete-time analogue in preserving the exponential convergence of a bidirectional associative memory (BAM) network that is subject to nonlinear impulses. The analogue derived from a semi-discretisation technique with the value of the time-step fixed is treated as a discrete-time dynamical system while its exponential convergence towards an equilibrium state is studied. Thereby, a family of sufficiency conditions governing the network parameters and the impulse magnitude and frequency is obtained for the convergence. As special cases, one can obtain from our results, those corresponding to the non-impulsive discrete-time BAM networks and also those corresponding to continuous-time (impulsive and non-impulsive) systems. A relation between the Lyapunov exponent of the non-impulsive system and that of the impulsive system involving the size of the impulses and the inter-impulse intervals is obtained.

Multistability of second-order competitive neural networks with nondecreasing saturated activation functions.

PubMed

Nie, Xiaobing; Cao, Jinde

2011-11-01

In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2N equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)N locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis.

Exponential Synchronization of Networked Chaotic Delayed Neural Network by a Hybrid Event Trigger Scheme.

PubMed

Fei, Zhongyang; Guan, Chaoxu; Gao, Huijun; Zhongyang Fei; Chaoxu Guan; Huijun Gao; Fei, Zhongyang; Guan, Chaoxu; Gao, Huijun

2018-06-01

This paper is concerned with the exponential synchronization for master-slave chaotic delayed neural network with event trigger control scheme. The model is established on a network control framework, where both external disturbance and network-induced delay are taken into consideration. The desired aim is to synchronize the master and slave systems with limited communication capacity and network bandwidth. In order to save the network resource, we adopt a hybrid event trigger approach, which not only reduces the data package sending out, but also gets rid of the Zeno phenomenon. By using an appropriate Lyapunov functional, a sufficient criterion for the stability is proposed for the error system with extended ( , , )-dissipativity performance index. Moreover, hybrid event trigger scheme and controller are codesigned for network-based delayed neural network to guarantee the exponential synchronization between the master and slave systems. The effectiveness and potential of the proposed results are demonstrated through a numerical example.

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 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.

Non-stationary least-squares complex decomposition for microseismic noise attenuation

NASA Astrophysics Data System (ADS)

Chen, Yangkang

2018-06-01

Microseismic data processing and imaging are crucial for subsurface real-time monitoring during hydraulic fracturing process. Unlike the active-source seismic events or large-scale earthquake events, the microseismic event is usually of very small magnitude, which makes its detection challenging. The biggest trouble of microseismic data is the low signal-to-noise ratio issue. Because of the small energy difference between effective microseismic signal and ambient noise, the effective signals are usually buried in strong random noise. I propose a useful microseismic denoising algorithm that is based on decomposing a microseismic trace into an ensemble of components using least-squares inversion. Based on the predictive property of useful microseismic event along the time direction, the random noise can be filtered out via least-squares fitting of multiple damping exponential components. The method is flexible and almost automated since the only parameter needed to be defined is a decomposition number. I use some synthetic and real data examples to demonstrate the potential of the algorithm in processing complicated microseismic data sets.

Stabilization of model-based networked control systems

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

Miranda, Francisco; Instituto Politécnico de Viana do Castelo, Viana do Castelo; Abreu, Carlos

2016-06-08

A class of networked control systems called Model-Based Networked Control Systems (MB-NCSs) is considered. Stabilization of MB-NCSs is studied using feedback controls and simulation of stabilization for different feedbacks is made with the purpose to reduce the network trafic. The feedback control input is applied in a compensated model of the plant that approximates the plant dynamics and stabilizes the plant even under slow network conditions. Conditions for global exponential stabilizability and for the choosing of a feedback control input for a given constant time between the information moments of the network are derived. An optimal control problem to obtainmore » an optimal feedback control is also presented.« less

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

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

Metastable dynamical patterns and their stabilization in arrays of bidirectionally coupled sigmoidal neurons

NASA Astrophysics Data System (ADS)

Horikawa, Yo

2013-12-01

Transient patterns in a bistable ring of bidirectionally coupled sigmoidal neurons were studied. When the system had a pair of spatially uniform steady solutions, the instability of unstable spatially nonuniform steady solutions decreased exponentially with the number of neurons because of the symmetry of the system. As a result, transient spatially nonuniform patterns showed dynamical metastability: Their duration increased exponentially with the number of neurons and the duration of randomly generated patterns obeyed a power-law distribution. However, these metastable dynamical patterns were easily stabilized in the presence of small variations in coupling strength. Metastable rotating waves and their pinning in the presence of asymmetry in the direction of coupling and the disappearance of metastable dynamical patterns due to asymmetry in the output function of a neuron were also examined. Further, in a two-dimensional array of neurons with nearest-neighbor coupling, intrinsically one-dimensional patterns were dominant in transients, and self-excitation in these neurons affected the metastable dynamical patterns.

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

NASA Astrophysics Data System (ADS)

Tice, Ian

2018-04-01

This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which arises in modeling the motion of such a fluid down an inclined plane, after a coordinate change. We consider the problem both with and without surface tension for horizontally periodic flows. This problem gives rise to shear-flow equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of the equilibria in certain parameter regimes. We prove that there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time t=0 give rise to global-in-time solutions that return to equilibrium exponentially in the case with surface tension and almost exponentially in the case without surface tension. We also establish a vanishing surface tension limit, which connects the solutions with and without surface tension.

Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays.

PubMed

Wang, Dongshu; Huang, Lihong

2014-03-01

In this paper, we investigate the periodic dynamical behaviors for a class of general Cohen-Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and the fixed point theorem of multi-valued maps, the existence of periodic solutions for the neural networks is obtained. After that, we derive some sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of nonsmooth analysis theory with generalized Lyapunov approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, our results will also be valid. Moreover, our results extend previous works not only on discrete time-varying and distributed delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete time-varying and distributed delayed neural networks with discontinuous activations. We give some numerical examples to show the applicability and effectiveness of our main results. Copyright © 2013 Elsevier Ltd. All rights reserved.

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models

NASA Astrophysics Data System (ADS)

Wang, Xiaoqiang; Ju, Lili; Du, Qiang

2016-07-01

The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.

Cyberinfrastructure for the NSF Ocean Observatories Initiative

NASA Astrophysics Data System (ADS)

Orcutt, J. A.; Vernon, F. L.; Arrott, M.; Chave, A.; Krueger, I.; Schofield, O.; Glenn, S.; Peach, C.; Nayak, A.

2007-12-01

The Internet today is vastly different than the Internet that we knew even five years ago and the changes that will be evident five years from now, when the NSF Ocean Observatories Initiative (OOI) prototype has been installed, are nearly unpredictable. Much of this progress is based on the exponential growth in capabilities of consumer electronics and information technology; the reality of this exponential behavior is rarely appreciated. For example, the number of transistors on a square cm of silicon will continue to double every 18 months, the density of disk storage will double every year, and network bandwidth will double every eight months. Today's desktop 2TB RAID will be 64TB and the 10Gbps Regional Scale Network fiber optical connection will be running at 1.8Tbps. The same exponential behavior characterizes the future of genome sequencing. The first two sequences of composites of individuals' genes cost tens of millions of dollars in 2001. Dr. Craig Venter just published a more accurate complete human genome (his own) at a cost on the order of 100,000. The J. Craig Venter Institute has provided support for the X Prize for Genomics offering 10M to the first successful sequencing of a human genome for $1,000. It's anticipated that the prize will be won within five years. Major advances in technology that are broadly viewed as disruptive or revolutionary rather than evolutionary will often depend upon the exploitation of exponential expansions in capability. Applications of these ideas to the OOI will be discussed. Specifically, the agile ability to scale cyberinfrastructure commensurate with the exponential growth of sensors, networks and computational capability and demand will be described.

Pore‐Scale Hydrodynamics in a Progressively Bioclogged Three‐Dimensional Porous Medium: 3‐D Particle Tracking Experiments and Stochastic Transport Modeling

PubMed Central

Carrel, M.; Dentz, M.; Derlon, N.; Morgenroth, E.

2018-01-01

Abstract Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play a central role in services ranging from degradation of pollutants to water purification. Biofilms dynamically change the pore structure of the medium through selective clogging of pores, a process known as bioclogging. This affects how solutes are transported and spread through the porous matrix, but the temporal changes to transport behavior during bioclogging are not well understood. To address this uncertainty, we experimentally study the hydrodynamic changes of a transparent 3‐D porous medium as it experiences progressive bioclogging. Statistical analyses of the system's hydrodynamics at four time points of bioclogging (0, 24, 36, and 48 h in the exponential growth phase) reveal exponential increases in both average and variance of the flow velocity, as well as its correlation length. Measurements for spreading, as mean‐squared displacements, are found to be non‐Fickian and more intensely superdiffusive with progressive bioclogging, indicating the formation of preferential flow pathways and stagnation zones. A gamma distribution describes well the Lagrangian velocity distributions and provides parameters that quantify changes to the flow, which evolves from a parallel pore arrangement under unclogged conditions, toward a more serial arrangement with increasing clogging. Exponentially evolving hydrodynamic metrics agree with an exponential bacterial growth phase and are used to parameterize a correlated continuous time random walk model with a stochastic velocity relaxation. The model accurately reproduces transport observations and can be used to resolve transport behavior at intermediate time points within the exponential growth phase considered. PMID:29780184

Pore-Scale Hydrodynamics in a Progressively Bioclogged Three-Dimensional Porous Medium: 3-D Particle Tracking Experiments and Stochastic Transport Modeling

NASA Astrophysics Data System (ADS)

Carrel, M.; Morales, V. L.; Dentz, M.; Derlon, N.; Morgenroth, E.; Holzner, M.

2018-03-01

Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play a central role in services ranging from degradation of pollutants to water purification. Biofilms dynamically change the pore structure of the medium through selective clogging of pores, a process known as bioclogging. This affects how solutes are transported and spread through the porous matrix, but the temporal changes to transport behavior during bioclogging are not well understood. To address this uncertainty, we experimentally study the hydrodynamic changes of a transparent 3-D porous medium as it experiences progressive bioclogging. Statistical analyses of the system's hydrodynamics at four time points of bioclogging (0, 24, 36, and 48 h in the exponential growth phase) reveal exponential increases in both average and variance of the flow velocity, as well as its correlation length. Measurements for spreading, as mean-squared displacements, are found to be non-Fickian and more intensely superdiffusive with progressive bioclogging, indicating the formation of preferential flow pathways and stagnation zones. A gamma distribution describes well the Lagrangian velocity distributions and provides parameters that quantify changes to the flow, which evolves from a parallel pore arrangement under unclogged conditions, toward a more serial arrangement with increasing clogging. Exponentially evolving hydrodynamic metrics agree with an exponential bacterial growth phase and are used to parameterize a correlated continuous time random walk model with a stochastic velocity relaxation. The model accurately reproduces transport observations and can be used to resolve transport behavior at intermediate time points within the exponential growth phase considered.

New broadband square-law detector

NASA Technical Reports Server (NTRS)

Reid, M. S.; Gardner, R. A.; Stelzried, C. T.

1975-01-01

Compact device has wide dynamic range, accurate square-law response, good thermal stability, high-level dc output with immunity to ground-loop problems, ability to insert known time constants for radiometric applications, and fast response times compatible with computer systems.

Comparative Analyses of Creep Models of a Solid Propellant

NASA Astrophysics Data System (ADS)

Zhang, J. B.; Lu, B. J.; Gong, S. F.; Zhao, S. P.

2018-05-01

The creep experiments of a solid propellant samples under five different stresses are carried out at 293.15 K and 323.15 K. In order to express the creep properties of this solid propellant, the viscoelastic model i.e. three Parameters solid, three Parameters fluid, four Parameters solid, four Parameters fluid and exponential model are involved. On the basis of the principle of least squares fitting, and different stress of all the parameters for the models, the nonlinear fitting procedure can be used to analyze the creep properties. The study shows that the four Parameters solid model can best express the behavior of creep properties of the propellant samples. However, the three Parameters solid and exponential model cannot very well reflect the initial value of the creep process, while the modified four Parameters models are found to agree well with the acceleration characteristics of the creep process.

NMR investigation of the short-chain ionic surfactant-water systems.

PubMed

Popova, M V; Tchernyshev, Y S; Michel, D

2004-02-03

The structure and dynamics of surfactant molecules [CH3(CH2)7COOK] in heavy water solutions were investigated by 1H and 2H NMR. A double-exponential attenuation of the spin-echo amplitude in a Carr-Purcell-Meiboom-Gill experiment was found. We expect correspondence to both bounded and monomeric states. At high concentrations in the NMR self-diffusion measurements also a double-exponential decay of the spin-echo signal versus the square of the dc magnetic gradient was observed. The slow component of the diffusion process is caused by micellar aggregates, while the fast component is the result of the self-diffusion of the monomers through the micelles. The self-diffusion studies indicate that the form of micelles changes with increasing total surfactant concentration. The critical temperature range for self-association is reflected in the 1H transverse relaxation.

Genetic attack on neural cryptography.

PubMed

Ruttor, Andreas; Kinzel, Wolfgang; Naeh, Rivka; Kanter, Ido

2006-03-01

Different scaling properties for the complexity of bidirectional synchronization and unidirectional learning are essential for the security of neural cryptography. Incrementing the synaptic depth of the networks increases the synchronization time only polynomially, but the success of the geometric attack is reduced exponentially and it clearly fails in the limit of infinite synaptic depth. This method is improved by adding a genetic algorithm, which selects the fittest neural networks. The probability of a successful genetic attack is calculated for different model parameters using numerical simulations. The results show that scaling laws observed in the case of other attacks hold for the improved algorithm, too. The number of networks needed for an effective attack grows exponentially with increasing synaptic depth. In addition, finite-size effects caused by Hebbian and anti-Hebbian learning are analyzed. These learning rules converge to the random walk rule if the synaptic depth is small compared to the square root of the system size.

Concentration dependence of molal conductivity and dielectric constant of 1-alcohol electrolytes using the compensated arrhenius formalism.

PubMed

Fleshman, Allison M; Petrowsky, Matt; Frech, Roger

2013-05-02

The molal conductivity of liquid electrolytes with low static dielectric constants (ε(s) < 10) decreases to a minimum at low concentrations (region I) and increases to a maximum at higher concentrations (region II) when plotted against the square root of the concentration. This behavior is investigated by applying the compensated Arrhenius formalism (CAF) to the molal conductivity, Λ, of a family of 1-alcohol electrolytes over a broad concentration range. A scaling procedure is applied that results in an energy of activation (E(a)) and an exponential prefactor (Λ0) that are both concentration dependent. It is shown that the increasing molal conductivity in region II results from the combined effect of (1) a decrease in the energy of activation calculated from the CAF, and (2) an inherent concentration dependence in the exponential prefactor that is partly due to the dielectric constant.

Edge Extraction by an Exponential Function Considering X-ray Transmission Characteristics

NASA Astrophysics Data System (ADS)

Kim, Jong Hyeong; Youp Synn, Sang; Cho, Sung Man; Jong Joo, Won

2011-04-01

3-D radiographic methodology has been into the spotlight for quality inspection of mass product or in-service inspection of aging product. To locate a target object in 3-D space, its characteristic contours such as edge length, edge angle, and vertices are very important. In spite of a simple geometry product, it is very difficult to get clear shape contours from a single radiographic image. The image contains scattering noise at the edges and ambiguity coming from X-Ray absorption within the body. This article suggests a concise method to extract whole edges from a single X-ray image. At the edge point of the object, the intensity of the X-ray decays exponentially as the X-ray penetrates the object. Considering this X-Ray decaying property, edges are extracted by using the least square fitting with the control of Coefficient of Determination.

An optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization and its application in prediction for the incidence of Hepatitis B in Xinjiang, China.

PubMed

Zhang, Liping; Zheng, Yanling; Wang, Kai; Zhang, Xueliang; Zheng, Yujian

2014-06-01

In this paper, by using a particle swarm optimization algorithm to solve the optimal parameter estimation problem, an improved Nash nonlinear grey Bernoulli model termed PSO-NNGBM(1,1) is proposed. To test the forecasting performance, the optimized model is applied for forecasting the incidence of hepatitis B in Xinjiang, China. Four models, traditional GM(1,1), grey Verhulst model (GVM), original nonlinear grey Bernoulli model (NGBM(1,1)) and Holt-Winters exponential smoothing method, are also established for comparison with the proposed model under the criteria of mean absolute percentage error and root mean square percent error. The prediction results show that the optimized NNGBM(1,1) model is more accurate and performs better than the traditional GM(1,1), GVM, NGBM(1,1) and Holt-Winters exponential smoothing method. Copyright © 2014. Published by Elsevier Ltd.

Identical superdeformed bands in yrast 152Dy: a systematic description

NASA Astrophysics Data System (ADS)

Dadwal, Anshul; Mittal, H. M.

2018-06-01

The nuclear softness (NS) formula, semiclassical particle rotor model (PRM) and modified exponential model with pairing attenuation are used for the systematic study of the identical superdeformed bands in the A ∼ 150 mass region. These formulae/models are employed to study the identical superdeformed bands relative to the yrast SD band 152Dy(1), {152Dy(1), 151Tb(2)}, {152Dy(1), 151Dy(4)} (midpoint), {152Dy(1), 153Dy(2)} (quarter point), {152Dy(1), 153Dy(3)} (three-quarter point). The parameters, baseline moment of inertia ({{I}}0), alignment (i) and effective pairing parameter (Δ0) are calculated using the least-squares fitting of the γ-ray transitions energies in the NS formula, semiclassical-PRM and modified exponential model with pairing attenuation, respectively. The calculated parameters are found to depend sensitively on the proposed baseline spin (I 0).

Genetic attack on neural cryptography

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

Ruttor, Andreas; Kinzel, Wolfgang; Naeh, Rivka

2006-03-15

Different scaling properties for the complexity of bidirectional synchronization and unidirectional learning are essential for the security of neural cryptography. Incrementing the synaptic depth of the networks increases the synchronization time only polynomially, but the success of the geometric attack is reduced exponentially and it clearly fails in the limit of infinite synaptic depth. This method is improved by adding a genetic algorithm, which selects the fittest neural networks. The probability of a successful genetic attack is calculated for different model parameters using numerical simulations. The results show that scaling laws observed in the case of other attacks hold formore » the improved algorithm, too. The number of networks needed for an effective attack grows exponentially with increasing synaptic depth. In addition, finite-size effects caused by Hebbian and anti-Hebbian learning are analyzed. These learning rules converge to the random walk rule if the synaptic depth is small compared to the square root of the system size.« less

Genetic attack on neural cryptography

NASA Astrophysics Data System (ADS)

Ruttor, Andreas; Kinzel, Wolfgang; Naeh, Rivka; Kanter, Ido

2006-03-01

Different scaling properties for the complexity of bidirectional synchronization and unidirectional learning are essential for the security of neural cryptography. Incrementing the synaptic depth of the networks increases the synchronization time only polynomially, but the success of the geometric attack is reduced exponentially and it clearly fails in the limit of infinite synaptic depth. This method is improved by adding a genetic algorithm, which selects the fittest neural networks. The probability of a successful genetic attack is calculated for different model parameters using numerical simulations. The results show that scaling laws observed in the case of other attacks hold for the improved algorithm, too. The number of networks needed for an effective attack grows exponentially with increasing synaptic depth. In addition, finite-size effects caused by Hebbian and anti-Hebbian learning are analyzed. These learning rules converge to the random walk rule if the synaptic depth is small compared to the square root of the system size.

Low-Temperature Crystal Structures of the Hard Core Square Shoulder Model.

PubMed

Gabriëlse, Alexander; Löwen, Hartmut; Smallenburg, Frank

2017-11-07

In many cases, the stability of complex structures in colloidal systems is enhanced by a competition between different length scales. Inspired by recent experiments on nanoparticles coated with polymers, we use Monte Carlo simulations to explore the types of crystal structures that can form in a simple hard-core square shoulder model that explicitly incorporates two favored distances between the particles. To this end, we combine Monte Carlo-based crystal structure finding algorithms with free energies obtained using a mean-field cell theory approach, and draw phase diagrams for two different values of the square shoulder width as a function of the density and temperature. Moreover, we map out the zero-temperature phase diagram for a broad range of shoulder widths. Our results show the stability of a rich variety of crystal phases, such as body-centered orthogonal (BCO) lattices not previously considered for the square shoulder model.

Longitudinal Proximity Effects in Superconducting Transition-Edge Sensors

NASA Technical Reports Server (NTRS)

Sadlier, John E.; Smith, Stephen J.; Bandler, Simon R.; Chervenak, James A.; Clem, John R.

2009-01-01

We have found experimentally that the critical current of a square thin-film superconducting transition-edge sensor (TES) depends exponentially upon the side length L and the square root of the temperature T, a behavior that has a natural theoretical explanation in terms of longitudinal proximity effects if the TES is regarded as a weak link between superconducting leads. As a consequence, the effective transition temperature T(sub c) of the TES is current-dependent and at fixed current scales as 1/L(sup 2). We also have found that the critical current can show clear Fraunhofer-like oscillations in an applied magnetic field, similar to those found in Josephson junctions. We have observed the longitudinal proximity effect in these devices over extraordinarily long lengths up to 290 micrometers, 1450 times the mean-free path.

Energy-optimal electrical excitation of nerve fibers.

PubMed

Jezernik, Saso; Morari, Manfred

2005-04-01

We derive, based on an analytical nerve membrane model and optimal control theory of dynamical systems, an energy-optimal stimulation current waveform for electrical excitation of nerve fibers. Optimal stimulation waveforms for nonleaky and leaky membranes are calculated. The case with a leaky membrane is a realistic case. Finally, we compare the waveforms and energies necessary for excitation of a leaky membrane in the case where the stimulation waveform is a square-wave current pulse, and in the case of energy-optimal stimulation. The optimal stimulation waveform is an exponentially rising waveform and necessitates considerably less energy to excite the nerve than a square-wave pulse (especially true for larger pulse durations). The described theoretical results can lead to drastically increased battery lifetime and/or decreased energy transmission requirements for implanted biomedical systems.

Longitudinal Proximity Effects in Superconducting Transition-Edge Sensors

NASA Technical Reports Server (NTRS)

Sadleir, John E.; Smith, Stephen J.; Bandler, Simon R.; Chervenak, James A.; Clem, John R.

2010-01-01

We have found experimentally that the critical current of a square thin-film superconducting transition-edge sensor (TES) depends exponentially upon the side length L and the square root of the temperature T, a behavior that has a natural theoretical explanation in terms of longitudinal proximity effects if the TES is regarded as a weak link between superconducting leads. As a consequence, the effective transition temperature T(sub c) of the TES is current-dependent and at fixed current scales as 1/L(sup 2). We also have found that the critical current can show clear Fraunhofer-like oscillations in an applied magnetic field, similar to those found in Josephson junctions. We have observed the longitudinal proximity effect in these devices over extraordinarily long lengths up to 290 micrometers, 1450 times the mean-free path.

Laser frequency stabilization for LISA

NASA Technical Reports Server (NTRS)

Mueller, Guido; McNamara, Paul; Thorpe, Ira; Camp, Jordan

2005-01-01

The requirement on laser frequency noise in the Laser Interferometer Space Antenna (LISA) depends on the velocity and our knowledge of the position of each spacecraft of the interferometer. Currently it is assumed that the lasers must have a pre-stabilized frequency stability of 30Hz/square root of Hz over LISA'S most sensitive frequency band (3 mHz - 30 mHz). The intrinsic frequency stability of even the most stable com- mercial lasers is several orders of magnitude above this level. Therefore it is necessary to stabilize the laser frequency to an ultra-stable frequency reference which meets the LISA requirements. The baseline frequency reference for the LISA lasers are high finesse optical cavities based on ULE spacers. We measured the stability of two ULE spacer cavities with respect to each other. Our current best results show a noise floor at, or below, 30 Hz/square root of Hz above 3 mHz. In this report we describe the experimental layout of the entire experiment and discuss the limiting noise sources.

Transient statistics in stabilizing periodic orbits

NASA Astrophysics Data System (ADS)

Meucci, R.; Gadomski, W.; Ciofini, M.; Arecchi, F. T.

1995-11-01

The statistics of chaotic and periodic transient time intervals preceding the stabilization of a given periodic orbit have been experimentally studied in a CO2 laser with modulated losses, subjected to a small subharmonic perturbation. As predicted by the theory, an exponential tail has been found in the probability distribution of chaotic transients. Furthermore, a fine periodic structure in the distributions of the periodic transients, resulting from the interaction of the control signal and the local structure of the chaotic attractor, has been revealed.

46 CFR 171.057 - Intact stability requirements for a sailing catamaran.

Code of Federal Regulations, 2011 CFR

2011-10-01

... displacement of the vessel, in kilograms (pounds). X=4.88 kilograms/square meter (1.0 pounds/square foot). (b... sail area above the deck, in meters (feet). W=the total displacement of the vessel, in kilograms...

46 CFR 171.057 - Intact stability requirements for a sailing catamaran.

Code of Federal Regulations, 2013 CFR

2013-10-01

... displacement of the vessel, in kilograms (pounds). X=4.88 kilograms/square meter (1.0 pounds/square foot). (b... sail area above the deck, in meters (feet). W=the total displacement of the vessel, in kilograms...

46 CFR 171.057 - Intact stability requirements for a sailing catamaran.

Code of Federal Regulations, 2012 CFR

2012-10-01

... displacement of the vessel, in kilograms (pounds). X=4.88 kilograms/square meter (1.0 pounds/square foot). (b... sail area above the deck, in meters (feet). W=the total displacement of the vessel, in kilograms...

46 CFR 171.057 - Intact stability requirements for a sailing catamaran.

Code of Federal Regulations, 2014 CFR

2014-10-01

... displacement of the vessel, in kilograms (pounds). X=4.88 kilograms/square meter (1.0 pounds/square foot). (b... sail area above the deck, in meters (feet). W=the total displacement of the vessel, in kilograms...

Stability of an abstract system of coupled hyperbolic and parabolic equations

NASA Astrophysics Data System (ADS)

Hao, Jianghao; Liu, Zhuangyi

2013-08-01

In this paper, we provide a complete stability analysis for an abstract system of coupled hyperbolic and parabolic equations = -Au + γ A^{α} θ, quad θ_t = -γ A^{α}u_t - kA^{β}θ, u(0) = u_0, quad u_t(0) = v_0, quad θ(0) = θ_0 where A is a self-adjoint, positive definite operator on a Hilbert space H. For {(α,β) in [0,1] × [0,1]} , the region of exponential stability had been identified in Ammar-Khodja et al. (ESAIM Control Optim Calc Var 4:577-593,1999). Our contribution is to show that the rest of the region can be classified as region of polynomial stability and region of instability. Moreover, we obtain the optimality of the order of polynomial stability.

Random matrix theory filters in portfolio optimisation: A stability and risk assessment

NASA Astrophysics Data System (ADS)

Daly, J.; Crane, M.; Ruskin, H. J.

2008-07-01

Random matrix theory (RMT) filters, applied to covariance matrices of financial returns, have recently been shown to offer improvements to the optimisation of stock portfolios. This paper studies the effect of three RMT filters on the realised portfolio risk, and on the stability of the filtered covariance matrix, using bootstrap analysis and out-of-sample testing. We propose an extension to an existing RMT filter, (based on Krzanowski stability), which is observed to reduce risk and increase stability, when compared to other RMT filters tested. We also study a scheme for filtering the covariance matrix directly, as opposed to the standard method of filtering correlation, where the latter is found to lower the realised risk, on average, by up to 6.7%. We consider both equally and exponentially weighted covariance matrices in our analysis, and observe that the overall best method out-of-sample was that of the exponentially weighted covariance, with our Krzanowski stability-based filter applied to the correlation matrix. We also find that the optimal out-of-sample decay factors, for both filtered and unfiltered forecasts, were higher than those suggested by Riskmetrics [J.P. Morgan, Reuters, Riskmetrics technical document, Technical Report, 1996. http://www.riskmetrics.com/techdoc.html], with those for the latter approaching a value of α=1. In conclusion, RMT filtering reduced the realised risk, on average, and in the majority of cases when tested out-of-sample, but increased the realised risk on a marked number of individual days-in some cases more than doubling it.

Stability of Capillary Surfaces in Rectangular Containers: The Right Square Cylinder

NASA Technical Reports Server (NTRS)

Weislogel, M. M.; Hsieh, K. C.

1998-01-01

The linearized governing equations for an ideal fluid are presented for numerical analysis for the stability of free capillary surfaces in rectangular containers against unfavorable disturbances (accelerations,i.e. Rayleigh-Taylor instability). The equations are solved for the case of the right square cylinder. The results are expressed graphically in term of a critical Bond number as a function of system contact angle. A critical wetting phenomena in the corners is shown to significantly alter the region of stability for such containers in contrast to simpler geometries such as the right circular cylinder or the infinite rectangular slot. Such computational results provide additional constraints for the design of fluids systems for space-based applications.

Quantum mechanical generalized phase-shift approach to atom-surface scattering: a Feshbach projection approach to dealing with closed channel effects.

PubMed

Maji, Kaushik; Kouri, Donald J

2011-03-28

We have developed a new method for solving quantum dynamical scattering problems, using the time-independent Schrödinger equation (TISE), based on a novel method to generalize a "one-way" quantum mechanical wave equation, impose correct boundary conditions, and eliminate exponentially growing closed channel solutions. The approach is readily parallelized to achieve approximate N(2) scaling, where N is the number of coupled equations. The full two-way nature of the TISE is included while propagating the wave function in the scattering variable and the full S-matrix is obtained. The new algorithm is based on a "Modified Cayley" operator splitting approach, generalizing earlier work where the method was applied to the time-dependent Schrödinger equation. All scattering variable propagation approaches to solving the TISE involve solving a Helmholtz-type equation, and for more than one degree of freedom, these are notoriously ill-behaved, due to the unavoidable presence of exponentially growing contributions to the numerical solution. Traditionally, the method used to eliminate exponential growth has posed a major obstacle to the full parallelization of such propagation algorithms. We stabilize by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing closed channels, while retaining all of the propagating open channel components, as well as exponentially decaying closed channel components.

Square-Wave Model for a Pendulum with Oscillating Suspension

ERIC Educational Resources Information Center

Yorke, Ellen D.

1978-01-01

Demonstrates that if a sinusoidal oscillation of the point of support of a pendulum is approximated by a square wave, a matrix method may be used to discuss parametric resonance and the stability of the inverted pendulum. (Author/SL)

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.

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2018-05-01

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.

Transmission problems for Mindlin–Timoshenko plates: frictional versus viscous damping mechanisms

NASA Astrophysics Data System (ADS)

Ferreira, Marcio V.; Muñoz Rivera, Jaime E.; Suárez, Fredy M. S.

2018-06-01

In this article, we make a comparative analysis of the stabilizing effect of the frictional dissipation with the dissipation produced by viscous materials of Kelvin-Voigt type both located in a part of a Mindlin-Timoshenko plate. We model these dissipative mechanisms through transmission problems and show that localized frictional damping, when effective over a strategic component of the plate, produces exponential stability of the corresponding semigroup. On the other hand, although the dissipation of Kelvin-Voigt is considered a strong dissipation, we prove that it loses its uniform stabilizing properties when localized over a component of the material and provides only a slower polynomial decay.

Ising model simulation in directed lattices and networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.; Stauffer, D.

2006-01-01

On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabási-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.

Simulation and study of small numbers of random events

NASA Technical Reports Server (NTRS)

Shelton, R. D.

1986-01-01

Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.

Function algorithms for MPP scientific subroutines, volume 1

NASA Technical Reports Server (NTRS)

Gouch, J. G.

1984-01-01

Design documentation and user documentation for function algorithms for the Massively Parallel Processor (MPP) are presented. The contract specifies development of MPP assembler instructions to perform the following functions: natural logarithm; exponential (e to the x power); square root; sine; cosine; and arctangent. To fulfill the requirements of the contract, parallel array and solar implementations for these functions were developed on the PDP11/34 Program Development and Management Unit (PDMU) that is resident at the MPP testbed installation located at the NASA Goddard facility.

Constrained Chebyshev approximations to some elementary functions suitable for evaluation with floating point arithmetic

NASA Technical Reports Server (NTRS)

Manos, P.; Turner, L. R.

1972-01-01

Approximations which can be evaluated with precision using floating-point arithmetic are presented. The particular set of approximations thus far developed are for the function TAN and the functions of USASI FORTRAN excepting SQRT and EXPONENTIATION. These approximations are, furthermore, specialized to particular forms which are especially suited to a computer with a small memory, in that all of the approximations can share one general purpose subroutine for the evaluation of a polynomial in the square of the working argument.

Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

PubMed

Stamova, Ivanka; Stamov, Gani

2017-12-01

In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stability of uncertain impulsive complex-variable chaotic systems with time-varying delays.

PubMed

Zheng, Song

2015-09-01

In this paper, the robust exponential stabilization of uncertain impulsive complex-variable chaotic delayed systems is considered with parameters perturbation and delayed impulses. It is assumed that the considered complex-variable chaotic systems have bounded parametric uncertainties together with the state variables on the impulses related to the time-varying delays. Based on the theories of adaptive control and impulsive control, some less conservative and easily verified stability criteria are established for a class of complex-variable chaotic delayed systems with delayed impulses. Some numerical simulations are given to validate the effectiveness of the proposed criteria of impulsive stabilization for uncertain complex-variable chaotic delayed systems. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Control over self-assembly of diblock copolymers on hexagonal and square templates for high area density circuit boards.

PubMed

Feng, Jie; Cavicchi, Kevin A; Heinz, Hendrik

2011-12-27

Self-assembled diblock copolymer melts on patterned substrates can induce a smaller characteristic domain spacing compared to predefined lithographic patterns and enable the manufacture of circuit boards with a high area density of computing and storage units. Monte Carlo simulation using coarse-grain models of polystyrene-b-polydimethylsiloxane shows that the generation of high-density hexagonal and square patterns is controlled by the ratio N(D) of the surface area per post and the surface area per spherical domain of neat block copolymer. N(D) represents the preferred number of block copolymer domains per post. Selected integer numbers support the formation of ordered structures on hexagonal (1, 3, 4, 7, 9) and square (1, 2, 5, 7) templates. On square templates, only smaller numbers of block copolymer domains per post support the formation of ordered arrays with significant stabilization energies relative to hexagonal morphology. Deviation from suitable integer numbers N(D) increases the likelihood of transitional morphologies between square and hexagonal. Upon increasing the spacing of posts on the substrate, square arrays, nested square arrays, and disordered hexagonal morphologies with multiple coordination numbers were identified, accompanied by a decrease in stabilization energy. Control over the main design parameter N(D) may allow an up to 7-fold increase in density of spherical block copolymer domains per surface area in comparison to the density of square posts and provide access to a wide range of high-density nanostructures to pattern electronic devices.

Non-exponential resistive switching in Ag2S memristors: a key to nanometer-scale non-volatile memory devices.

PubMed

Gubicza, Agnes; Csontos, Miklós; Halbritter, András; Mihály, György

2015-03-14

The dynamics of resistive switchings in nanometer-scale metallic junctions formed between an inert metallic tip and an Ag film covered by a thin Ag2S layer are investigated. Our thorough experimental analysis and numerical simulations revealed that the resistance change upon a switching bias voltage pulse exhibits a strongly non-exponential behaviour yielding markedly different response times at different bias levels. Our results demonstrate the merits of Ag2S nanojunctions as nanometer-scale non-volatile memory cells with stable switching ratios, high endurance as well as fast response to write/erase, and an outstanding stability against read operations at technologically optimal bias and current levels.

Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller.

PubMed

Gong, Shuqing; Yang, Shaofu; Guo, Zhenyuan; Huang, Tingwen

2018-06-01

The paper is concerned with the synchronization problem of inertial memristive neural networks with time-varying delay. First, by choosing a proper variable substitution, inertial memristive neural networks described by second-order differential equations can be transformed into first-order differential equations. Then, a novel controller with a linear diffusive term and discontinuous sign term is designed. By using the controller, the sufficient conditions for assuring the global exponential synchronization of the derive and response neural networks are derived based on Lyapunov stability theory and some inequality techniques. Finally, several numerical simulations are provided to substantiate the effectiveness of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Interpreting Popov criteria in Lure´ systems with complex scaling stability analysis

NASA Astrophysics Data System (ADS)

Zhou, J.

2018-06-01

The paper presents a novel frequency-domain interpretation of Popov criteria for absolute stability in Lure´ systems by means of what we call complex scaling stability analysis. The complex scaling technique is developed for exponential/asymptotic stability in LTI feedback systems, which dispenses open-loop poles distribution, contour/locus orientation and prior frequency sweeping. Exploiting the technique for alternatively revealing positive realness of transfer functions, re-interpreting Popov criteria is explicated. More specifically, the suggested frequency-domain stability conditions are conformable both in scalar and multivariable cases, and can be implemented either graphically with locus plotting or numerically without; in particular, the latter is suitable as a design tool with auxiliary parameter freedom. The interpretation also reveals further frequency-domain facts about Lure´ systems. Numerical examples are included to illustrate the main results.

Influence of unbalance on the nonlinear dynamical response and stability of flexible rotor-bearing systems

NASA Technical Reports Server (NTRS)

Gunter, E. J.; Humphris, R. R.; Springer, H.

1983-01-01

In this paper, some of the effects of unbalance on the nonlinear response and stability of flexible rotor-bearing systems is presented from both a theoretical and experimental standpoint. In a linear system, operating above its stability threshold, the amplitude of motion grows exponentially with time and the orbits become unbounded. In an actual system, this is not necessarily the case. The actual amplitudes of motion may be bounded due to various nonlinear effects in the system. These nonlinear effects cause limit cycles of motion. Nonlinear effects are inherent in fluid film bearings and seals. Other contributors to nonlinear effects are shafts, couplings and foundations. In addition to affecting the threshold of stability, the nonlinear effects can cause jump phenomena to occur at not only the critical speeds, but also at stability onset or restabilization speeds.

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

Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

PubMed

Liu, Meiqin

2009-09-01

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Diffusive processes in a stochastic magnetic field

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

Wang, H.; Vlad, M.; Vanden Eijnden, E.

1995-05-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing,more » in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.« less

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.

Long-wave theory for a new convective instability with exponential growth normal to the wall.

PubMed

Healey, J J

2005-05-15

A linear stability theory is presented for the boundary-layer flow produced by an infinite disc rotating at constant angular velocity in otherwise undisturbed fluid. The theory is developed in the limit of long waves and when the effects of viscosity on the waves can be neglected. This is the parameter regime recently identified by the author in a numerical stability investigation where a curious new type of instability was found in which disturbances propagate and grow exponentially in the direction normal to the disc, (i.e. the growth takes place in a region of zero mean shear). The theory describes the mechanisms controlling the instability, the role and location of critical points, and presents a saddle-point analysis describing the large-time evolution of a wave packet in frames of reference moving normal to the disc. The theory also shows that the previously obtained numerical solutions for numerically large wavelengths do indeed lie in the asymptotic long-wave regime, and so the behaviour and mechanisms described here may apply to a number of cross-flow instability problems.

Global exponential stability of octonion-valued neural networks with leakage delay and mixed delays.

PubMed

Popa, Călin-Adrian

2018-06-08

This paper discusses octonion-valued neural networks (OVNNs) with leakage delay, time-varying delays, and distributed delays, for which the states, weights, and activation functions belong to the normed division algebra of octonions. The octonion algebra is a nonassociative and noncommutative generalization of the complex and quaternion algebras, but does not belong to the category of Clifford algebras, which are associative. In order to avoid the nonassociativity of the octonion algebra and also the noncommutativity of the quaternion algebra, the Cayley-Dickson construction is used to decompose the OVNNs into 4 complex-valued systems. By using appropriate Lyapunov-Krasovskii functionals, with double and triple integral terms, the free weighting matrix method, and simple and double integral Jensen inequalities, delay-dependent criteria are established for the exponential stability of the considered OVNNs. The criteria are given in terms of complex-valued linear matrix inequalities, for two types of Lipschitz conditions which are assumed to be satisfied by the octonion-valued activation functions. Finally, two numerical examples illustrate the feasibility, effectiveness, and correctness of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

A New Local Bipolar Autoassociative Memory Based on External Inputs of Discrete Recurrent Neural Networks With Time Delay.

PubMed

Zhou, Caigen; Zeng, Xiaoqin; Luo, Chaomin; Zhang, Huaguang

In this paper, local bipolar auto-associative memories are presented based on discrete recurrent neural networks with a class of gain type activation function. The weight parameters of neural networks are acquired by a set of inequalities without the learning procedure. The global exponential stability criteria are established to ensure the accuracy of the restored patterns by considering time delays and external inputs. The proposed methodology is capable of effectively overcoming spurious memory patterns and achieving memory capacity. The effectiveness, robustness, and fault-tolerant capability are validated by simulated experiments.In this paper, local bipolar auto-associative memories are presented based on discrete recurrent neural networks with a class of gain type activation function. The weight parameters of neural networks are acquired by a set of inequalities without the learning procedure. The global exponential stability criteria are established to ensure the accuracy of the restored patterns by considering time delays and external inputs. The proposed methodology is capable of effectively overcoming spurious memory patterns and achieving memory capacity. The effectiveness, robustness, and fault-tolerant capability are validated by simulated experiments.

Obstructive sleep apnea alters sleep stage transition dynamics.

PubMed

Bianchi, Matt T; Cash, Sydney S; Mietus, Joseph; Peng, Chung-Kang; Thomas, Robert

2010-06-28

Enhanced characterization of sleep architecture, compared with routine polysomnographic metrics such as stage percentages and sleep efficiency, may improve the predictive phenotyping of fragmented sleep. One approach involves using stage transition analysis to characterize sleep continuity. We analyzed hypnograms from Sleep Heart Health Study (SHHS) participants using the following stage designations: wake after sleep onset (WASO), non-rapid eye movement (NREM) sleep, and REM sleep. We show that individual patient hypnograms contain insufficient number of bouts to adequately describe the transition kinetics, necessitating pooling of data. We compared a control group of individuals free of medications, obstructive sleep apnea (OSA), medical co-morbidities, or sleepiness (n = 374) with mild (n = 496) or severe OSA (n = 338). WASO, REM sleep, and NREM sleep bout durations exhibited multi-exponential temporal dynamics. The presence of OSA accelerated the "decay" rate of NREM and REM sleep bouts, resulting in instability manifesting as shorter bouts and increased number of stage transitions. For WASO bouts, previously attributed to a power law process, a multi-exponential decay described the data well. Simulations demonstrated that a multi-exponential process can mimic a power law distribution. OSA alters sleep architecture dynamics by decreasing the temporal stability of NREM and REM sleep bouts. Multi-exponential fitting is superior to routine mono-exponential fitting, and may thus provide improved predictive metrics of sleep continuity. However, because a single night of sleep contains insufficient transitions to characterize these dynamics, extended monitoring of sleep, probably at home, would be necessary for individualized clinical application.

Field Performance of an Optimized Stack of YBCO Square “Annuli” for a Compact NMR Magnet

PubMed Central

Hahn, Seungyong; Voccio, John; Bermond, Stéphane; Park, Dong-Keun; Bascuñán, Juan; Kim, Seok-Beom; Masaru, Tomita; Iwasa, Yukikazu

2011-01-01

The spatial field homogeneity and time stability of a trapped field generated by a stack of YBCO square plates with a center hole (square “annuli”) was investigated. By optimizing stacking of magnetized square annuli, we aim to construct a compact NMR magnet. The stacked magnet consists of 750 thin YBCO plates, each 40-mm square and 80- μm thick with a 25-mm bore, and has a Ø10 mm room-temperature access for NMR measurement. To improve spatial field homogeneity of the 750-plate stack (YP750) a three-step optimization was performed: 1) statistical selection of best plates from supply plates; 2) field homogeneity measurement of multi-plate modules; and 3) optimal assembly of the modules to maximize field homogeneity. In this paper, we present analytical and experimental results of field homogeneity and temporal stability at 77 K, performed on YP750 and those of a hybrid stack, YPB750, in which two YBCO bulk annuli, each Ø46 mm and 16-mm thick with a 25-mm bore, are added to YP750, one at the top and the other at the bottom. PMID:22081753

Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks.

PubMed

Chen, Wu-Hua; Lu, Xiaomei; Zheng, Wei Xing

2015-04-01

This paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs). Two types of DDNNs with stabilizing impulses are studied. By introducing the time-varying Lyapunov functional to capture the dynamical characteristics of discrete-time impulsive delayed neural networks (DIDNNs) and by using a convex combination technique, new exponential stability criteria are derived in terms of linear matrix inequalities. The stability criteria for DIDNNs are independent of the size of time delay but rely on the lengths of impulsive intervals. With the newly obtained stability results, sufficient conditions on the existence of linear-state feedback impulsive controllers are derived. Moreover, a novel impulsive synchronization scheme for two identical DDNNs is proposed. The novel impulsive synchronization scheme allows synchronizing two identical DDNNs with unknown delays. Simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of DDNNs. Finally, an application of the obtained impulsive synchronization result for two identical chaotic DDNNs to a secure communication scheme is presented.

Socio-Economic Instability and the Scaling of Energy Use with Population Size

PubMed Central

DeLong, John P.; Burger, Oskar

2015-01-01

The size of the human population is relevant to the development of a sustainable world, yet the forces setting growth or declines in the human population are poorly understood. Generally, population growth rates depend on whether new individuals compete for the same energy (leading to Malthusian or density-dependent growth) or help to generate new energy (leading to exponential and super-exponential growth). It has been hypothesized that exponential and super-exponential growth in humans has resulted from carrying capacity, which is in part determined by energy availability, keeping pace with or exceeding the rate of population growth. We evaluated the relationship between energy use and population size for countries with long records of both and the world as a whole to assess whether energy yields are consistent with the idea of an increasing carrying capacity. We find that on average energy use has indeed kept pace with population size over long time periods. We also show, however, that the energy-population scaling exponent plummets during, and its temporal variability increases preceding, periods of social, political, technological, and environmental change. We suggest that efforts to increase the reliability of future energy yields may be essential for stabilizing both population growth and the global socio-economic system. PMID:26091499

Socio-Economic Instability and the Scaling of Energy Use with Population Size.

PubMed

DeLong, John P; Burger, Oskar

2015-01-01

The size of the human population is relevant to the development of a sustainable world, yet the forces setting growth or declines in the human population are poorly understood. Generally, population growth rates depend on whether new individuals compete for the same energy (leading to Malthusian or density-dependent growth) or help to generate new energy (leading to exponential and super-exponential growth). It has been hypothesized that exponential and super-exponential growth in humans has resulted from carrying capacity, which is in part determined by energy availability, keeping pace with or exceeding the rate of population growth. We evaluated the relationship between energy use and population size for countries with long records of both and the world as a whole to assess whether energy yields are consistent with the idea of an increasing carrying capacity. We find that on average energy use has indeed kept pace with population size over long time periods. We also show, however, that the energy-population scaling exponent plummets during, and its temporal variability increases preceding, periods of social, political, technological, and environmental change. We suggest that efforts to increase the reliability of future energy yields may be essential for stabilizing both population growth and the global socio-economic system.

Statistical Characteristics of the Gaussian-Noise Spikes Exceeding the Specified Threshold as Applied to Discharges in a Thundercloud

NASA Astrophysics Data System (ADS)

Klimenko, V. V.

2017-12-01

We obtain expressions for the probabilities of the normal-noise spikes with the Gaussian correlation function and for the probability density of the inter-spike intervals. As distinct from the delta-correlated noise, in which the intervals are distributed by the exponential law, the probability of the subsequent spike depends on the previous spike and the interval-distribution law deviates from the exponential one for a finite noise-correlation time (frequency-bandwidth restriction). This deviation is the most pronounced for a low detection threshold. Similarity of the behaviors of the distributions of the inter-discharge intervals in a thundercloud and the noise spikes for the varying repetition rate of the discharges/spikes, which is determined by the ratio of the detection threshold to the root-mean-square value of noise, is observed. The results of this work can be useful for the quantitative description of the statistical characteristics of the noise spikes and studying the role of fluctuations for the discharge emergence in a thundercloud.

Planetary cores, their energy flux relationship, and its implications

NASA Astrophysics Data System (ADS)

Johnson, Fred M.

2018-02-01

Integrated surface heat flux data from each planet in our solar system plus over 50 stars, including our Sun, was plotted against each object's known mass to generate a continuous exponential curve at an R-squared value of 0.99. The unexpected yet undeniable implication of this study is that all planets and celestial objects have a similar mode of energy production. It is widely accepted that proton-proton reactions require hydrogen gas at temperatures of about 15 million degrees, neither of which can plausibly exist inside a terrestrial planet. Hence, this paper proposes a nuclear fission mechanism for all luminous celestial objects, and uses this mechanism to further suggest a developmental narrative for all celestial bodies, including our Sun. This narrative was deduced from an exponential curve drawn adjacent to the first and passing through the Earth's solid core (as a known prototype). This trend line was used to predict the core masses for each planet as a function of its luminosity.

Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi-Ulam model

NASA Astrophysics Data System (ADS)

Livorati, André L. P.; Palmero, Matheus S.; Díaz-I, Gabriel; Dettmann, Carl P.; Caldas, Iberê L.; Leonel, Edson D.

2018-02-01

We study the dynamics of an ensemble of non interacting particles constrained by two infinitely heavy walls, where one of them is moving periodically in time, while the other is fixed. The system presents mixed dynamics, where the accessible region for the particle to diffuse chaotically is bordered by an invariant spanning curve. Statistical analysis for the root mean square velocity, considering high and low velocity ensembles, leads the dynamics to the same steady state plateau for long times. A transport investigation of the dynamics via escape basins reveals that depending of the initial velocity ensemble, the decay rates of the survival probability present different shapes and bumps, in a mix of exponential, power law and stretched exponential decays. After an analysis of step-size averages, we found that the stable manifolds play the role of a preferential path for faster escape, being responsible for the bumps and different shapes of the survival probability.

A study on industrial accident rate forecasting and program development of estimated zero accident time in Korea.

PubMed

Kim, Tae-gu; Kang, Young-sig; Lee, Hyung-won

2011-01-01

To begin a zero accident campaign for industry, the first thing is to estimate the industrial accident rate and the zero accident time systematically. This paper considers the social and technical change of the business environment after beginning the zero accident campaign through quantitative time series analysis methods. These methods include sum of squared errors (SSE), regression analysis method (RAM), exponential smoothing method (ESM), double exponential smoothing method (DESM), auto-regressive integrated moving average (ARIMA) model, and the proposed analytic function method (AFM). The program is developed to estimate the accident rate, zero accident time and achievement probability of an efficient industrial environment. In this paper, MFC (Microsoft Foundation Class) software of Visual Studio 2008 was used to develop a zero accident program. The results of this paper will provide major information for industrial accident prevention and be an important part of stimulating the zero accident campaign within all industrial environments.

Forecasting hotspots in East Kutai, Kutai Kartanegara, and West Kutai as early warning information

NASA Astrophysics Data System (ADS)

Wahyuningsih, S.; Goejantoro, R.; Rizki, N. A.

2018-04-01

The aims of this research are to model hotspots and forecast hotspot 2017 in East Kutai, Kutai Kartanegara and West Kutai. The methods which used in this research were Holt exponential smoothing, Holt’s additive dump trend method, Holt-Winters’ additive method, additive decomposition method, multiplicative decomposition method, Loess decomposition method and Box-Jenkins method. For smoothing techniques, additive decomposition is better than Holt’s exponential smoothing. The hotspots model using Box-Jenkins method were Autoregressive Moving Average ARIMA(1,1,0), ARIMA(0,2,1), and ARIMA(0,1,0). Comparing the results from all methods which were used in this research, and based on Root of Mean Squared Error (RMSE), show that Loess decomposition method is the best times series model, because it has the least RMSE. Thus the Loess decomposition model used to forecast the number of hotspot. The forecasting result indicatethat hotspots pattern tend to increase at the end of 2017 in Kutai Kartanegara and West Kutai, but stationary in East Kutai.

Flash spectroscopy of purple membrane.

PubMed Central

Xie, A H; Nagle, J F; Lozier, R H

1987-01-01

Flash spectroscopy data were obtained for purple membrane fragments at pH 5, 7, and 9 for seven temperatures from 5 degrees to 35 degrees C, at the magic angle for actinic versus measuring beam polarizations, at fifteen wavelengths from 380 to 700 nm, and for about five decades of time from 1 microsecond to completion of the photocycle. Signal-to-noise ratios are as high as 500. Systematic errors involving beam geometries, light scattering, absorption flattening, photoselection, temperature fluctuations, partial dark adaptation of the sample, unwanted actinic effects, and cooperativity were eliminated, compensated for, or are shown to be irrelevant for the conclusions. Using nonlinear least squares techniques, all data at one temperature and one pH were fitted to sums of exponential decays, which is the form required if the system obeys conventional first-order kinetics. The rate constants obtained have well behaved Arrhenius plots. Analysis of the residual errors of the fitting shows that seven exponentials are required to fit the data to the accuracy of the noise level. PMID:3580488

Flash spectroscopy of purple membrane.

PubMed

Xie, A H; Nagle, J F; Lozier, R H

1987-04-01

Flash spectroscopy data were obtained for purple membrane fragments at pH 5, 7, and 9 for seven temperatures from 5 degrees to 35 degrees C, at the magic angle for actinic versus measuring beam polarizations, at fifteen wavelengths from 380 to 700 nm, and for about five decades of time from 1 microsecond to completion of the photocycle. Signal-to-noise ratios are as high as 500. Systematic errors involving beam geometries, light scattering, absorption flattening, photoselection, temperature fluctuations, partial dark adaptation of the sample, unwanted actinic effects, and cooperativity were eliminated, compensated for, or are shown to be irrelevant for the conclusions. Using nonlinear least squares techniques, all data at one temperature and one pH were fitted to sums of exponential decays, which is the form required if the system obeys conventional first-order kinetics. The rate constants obtained have well behaved Arrhenius plots. Analysis of the residual errors of the fitting shows that seven exponentials are required to fit the data to the accuracy of the noise level.

Formation stability analysis of unmanned multi-vehicles under interconnection topologies

NASA Astrophysics Data System (ADS)

Yang, Aolei; Naeem, Wasif; Fei, Minrui

2015-04-01

In this paper, the overall formation stability of an unmanned multi-vehicle is mathematically presented under interconnection topologies. A novel definition of formation error is first given and followed by the proposed formation stability hypothesis. Based on this hypothesis, a unique extension-decomposition-aggregation scheme is then employed to support the stability analysis for the overall multi-vehicle formation under a mesh topology. It is proved that the overall formation control system consisting of N number of nonlinear vehicles is not only asymptotically stable, but also exponentially stable in the sense of Lyapunov within a neighbourhood of the desired formation. This technique is shown to be applicable for a mesh topology but is equally applicable for other topologies. A simulation study of the formation manoeuvre of multiple Aerosonde UAVs (unmanned aerial vehicles), in 3-D space, is finally carried out verifying the achieved formation stability result.

Vacuum statistics and stability in axionic landscapes

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

Masoumi, Ali; Vilenkin, Alexander, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu

2016-03-01

We investigate vacuum statistics and stability in random axionic landscapes. For this purpose we developed an algorithm for a quick evaluation of the tunneling action, which in most cases is accurate within 10%. We find that stability of a vacuum is strongly correlated with its energy density, with lifetime rapidly growing as the energy density is decreased. On the other hand, the probability P(B) for a vacuum to have a tunneling action B greater than a given value declines as a slow power law in B. This is in sharp contrast with the studies of random quartic potentials, which foundmore » a fast exponential decline of P(B). Our results suggest that the total number of relatively stable vacua (say, with B>100) grows exponentially with the number of fields N and can get extremely large for N∼> 100. The problem with this kind of model is that the stable vacua are concentrated near the absolute minimum of the potential, so the observed value of the cosmological constant cannot be explained without fine-tuning. To address this difficulty, we consider a modification of the model, where the axions acquire a quadratic mass term, due to their mixing with 4-form fields. This results in a larger landscape with a much broader distribution of vacuum energies. The number of relatively stable vacua in such models can still be extremely large.« less

Study on Parameter Identification of Assembly Robot based on Screw Theory

NASA Astrophysics Data System (ADS)

Yun, Shi; Xiaodong, Zhang

2017-11-01

The kinematic model of assembly robot is one of the most important factors affecting repetitive precision. In order to improve the accuracy of model positioning, this paper first establishes the exponential product model of ER16-1600 assembly robot on the basis of screw theory, and then based on iterative least squares method, using ER16-1600 model robot parameter identification. By comparing the experiment before and after the calibration, it is proved that the method has obvious improvement on the positioning accuracy of the assembly robot.

A Study of the Application of the Lognormal and Gamma Distributions to Corrective Maintenance Repair Time Data.

DTIC Science & Technology

1982-10-01

K-S A R A j 1 10 23 R 3 8 11 16 18 For the lognormal methods the test methods sometimes give different results. The K-S test and the chi-square...significant difference among the three test methods . A previous study has been done using 24 data sets of electronic systems and equipments, using only the W...are suitable descriptors for corrective maintenance repair times, and to estimate the difference caused in assuming an exponential distribution for

The ultimate quantum limits on the accuracy of measurements

NASA Technical Reports Server (NTRS)

Yuen, Horace P.

1992-01-01

A quantum generalization of rate-distortion theory from standard communication and information theory is developed for application to determining the ultimate performance limit of measurement systems in physics. For the estimation of a real or a phase parameter, it is shown that the root-mean-square error obtained in a measurement with a single-mode photon level N cannot do better than approximately N exp -1, while approximately exp(-N) may be obtained for multi-mode fields with the same photon level N. Possible ways to achieve the remarkable exponential performance are indicated.

Demand forecasting of electricity in Indonesia with limited historical data

NASA Astrophysics Data System (ADS)

Dwi Kartikasari, Mujiati; Rohmad Prayogi, Arif

2018-03-01

Demand forecasting of electricity is an important activity for electrical agents to know the description of electricity demand in future. Prediction of demand electricity can be done using time series models. In this paper, double moving average model, Holt’s exponential smoothing model, and grey model GM(1,1) are used to predict electricity demand in Indonesia under the condition of limited historical data. The result shows that grey model GM(1,1) has the smallest value of MAE (mean absolute error), MSE (mean squared error), and MAPE (mean absolute percentage error).

Geographic Resources Analysis Support System (GRASS) Version 4.0 User’s Reference Manual

DTIC Science & Technology

1992-06-01

inpur-image need not be square; before processing, the X and Y dimensions of the input-image are padded with zeroes to the next highest power of two in...structures an input kowledge /control script with an appropriate combination of map layer category values (GRASS raster map layers that contain data on...F cos(x) cosine of x (x is in degrees) F exp(x) exponential function of x F exp(x,y) x to the power y F float(x) convert x to floating point F if

Light scattering and dynamics of interacting Brownian particles

NASA Technical Reports Server (NTRS)

Tsang, T.; Tang, H. T.

1982-01-01

The relative motions of interacting Brownian particles in liquids may be described as radial diffusion in an effective potential of the mean force. By using a harmonic approximation for the effective potential, the intermediate scattering function may also be evaluated. For polystyrene spheres of 250 A mean radius in aqueous environment at 0.00125 g/cu cm concentration, the results for the calculated mean square displacement are in qualitative agreement with experimental data from photon correlation spectroscopy. Because of the interactions, the functions deviate considerably from the exponential forms for the free particles.

Nonlinear analogue of the May−Wigner instability transition

PubMed Central

Fyodorov, Yan V.; Khoruzhenko, Boris A.

2016-01-01

We study a system of N≫1 degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium with rate μ. We show that, while increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically nontrivial regime characterized by an exponential number of equilibria, the vast majority of which are expected to be unstable. It is suggested that this picture provides a global view on the nature of the May−Wigner instability transition originally discovered by local linear stability analysis. PMID:27274077

Unusually large Stokes shift for a near-infrared emitting DNA-stabilized silver nanocluster

NASA Astrophysics Data System (ADS)

Ammitzbøll Bogh, Sidsel; Carro-Temboury, Miguel R.; Cerretani, Cecilia; Swasey, Steven M.; Copp, Stacy M.; Gwinn, Elisabeth G.; Vosch, Tom

2018-04-01

In this paper we present a new near-IR emitting silver nanocluster (NIR-DNA-AgNC) with an unusually large Stokes shift between absorption and emission maximum (211 nm or 5600 cm-1). We studied the effect of viscosity and temperature on the steady state and time-resolved emission. The time-resolved results on NIR-DNA-AgNC show that the relaxation dynamics slow down significantly with increasing viscosity of the solvent. In high viscosity solution, the spectral relaxation stretches well into the nanosecond scale. As a result of this slow spectral relaxation in high viscosity solutions, a multi-exponential fluorescence decay time behavior is observed, in contrast to the more mono-exponential decay in low viscosity solution.

Exponential H ∞ Synchronization of Chaotic Cryptosystems Using an Improved Genetic Algorithm

PubMed Central

Hsiao, Feng-Hsiag

2015-01-01

This paper presents a systematic design methodology for neural-network- (NN-) based secure communications in multiple time-delay chaotic (MTDC) systems with optimal H ∞ performance and cryptography. On the basis of the Improved Genetic Algorithm (IGA), which is demonstrated to have better performance than that of a traditional GA, a model-based fuzzy controller is then synthesized to stabilize the MTDC systems. A fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H ∞ performance by minimizing the disturbance attenuation level. Furthermore, the error of the recovered message is stated by using the n-shift cipher and key. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach. PMID:26366432

Spatial Prediction and Optimized Sampling Design for Sodium Concentration in Groundwater

PubMed Central

Shabbir, Javid; M. AbdEl-Salam, Nasser; Hussain, Tajammal

2016-01-01

Sodium is an integral part of water, and its excessive amount in drinking water causes high blood pressure and hypertension. In the present paper, spatial distribution of sodium concentration in drinking water is modeled and optimized sampling designs for selecting sampling locations is calculated for three divisions in Punjab, Pakistan. Universal kriging and Bayesian universal kriging are used to predict the sodium concentrations. Spatial simulated annealing is used to generate optimized sampling designs. Different estimation methods (i.e., maximum likelihood, restricted maximum likelihood, ordinary least squares, and weighted least squares) are used to estimate the parameters of the variogram model (i.e, exponential, Gaussian, spherical and cubic). It is concluded that Bayesian universal kriging fits better than universal kriging. It is also observed that the universal kriging predictor provides minimum mean universal kriging variance for both adding and deleting locations during sampling design. PMID:27683016

Transitionless driving on adiabatic search algorithm

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

Oh, Sangchul, E-mail: soh@qf.org.qa; Kais, Sabre, E-mail: kais@purdue.edu; Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907

We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian,more » approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.« less

Non-perturbative reheating and Nnaturalness

NASA Astrophysics Data System (ADS)

Hardy, Edward

2017-11-01

We study models in which reheating happens only through non-perturbative processes. The energy transferred can be exponentially suppressed unless the inflaton is coupled to a particle with a parametrically small mass. Additionally, in some models a light scalar with a negative mass squared parameter leads to much more efficient reheating than one with a positive mass squared of the same magnitude. If a theory contains many sectors similar to the Standard Model coupled to the inflaton via their Higgses, such dynamics can realise the Nnaturalness solution to the hierarchy problem. A sector containing a light Higgs with a non-zero vacuum expectation value is dominantly reheated and there is little energy transferred to the other sectors, consistent with cosmological constraints. The inflaton must decouple from other particles and have a flat potential at large field values, in which case the visible sector UV cutoff can be raised to 10 TeV in a simple model.

Stability of peatland carbon to rising temperatures

Treesearch

R. M. Wilson; A. M. Hopple; M. M. Tfaily; S. D. Sebestyen; C. W. Schadt; L. Pfeifer-Meister; C. Medvedeff; K. J. McFarlane; J. E. Kostka; M. Kolton; R.K. Kolka; L. A. Kluber; J. K. Keller; T. P. Guilderson; N. A. Griffiths; J. P. Chanton; S. D. Bridgham; P. J. Hanson

2016-01-01

Peatlands contain one-third of soil carbon (C), mostly buried in deep, saturated anoxic zones (catotelm). The response of catotelm C to climate forcing is uncertain, because prior experiments have focused on surface warming. We show that deep peat heating of a 2 m-thick peat column results in an exponential increase in CH4 emissions. However,...

Any Ontological Model of the Single Qubit Stabilizer Formalism must be Contextual

NASA Astrophysics Data System (ADS)

Lillystone, Piers; Wallman, Joel J.

Quantum computers allow us to easily solve some problems classical computers find hard. Non-classical improvements in computational power should be due to some non-classical property of quantum theory. Contextuality, a more general notion of non-locality, is a necessary, but not sufficient, resource for quantum speed-up. Proofs of contextuality can be constructed for the classically simulable stabilizer formalism. Previous proofs of stabilizer contextuality are known for 2 or more qubits, for example the Mermin-Peres magic square. In the work presented we extend these results and prove that any ontological model of the single qubit stabilizer theory must be contextual, as defined by R. Spekkens, and give a relation between our result and the Mermin-Peres square. By demonstrating that contextuality is present in the qubit stabilizer formalism we provide further insight into the contextuality present in quantum theory. Understanding the contextuality of classical sub-theories will allow us to better identify the physical properties of quantum theory required for computational speed up. This research was supported by CIFAR, the Government of Ontario, and the Government of Canada through NSERC and Industry Canada.

On Using the Average Intercorrelation Among Predictor Variables and Eigenvector Orientation to Choose a Regression Solution.

ERIC Educational Resources Information Center

Mugrage, Beverly; And Others

Three ridge regression solutions are compared with ordinary least squares regression and with principal components regression using all components. Ridge regression, particularly the Lawless-Wang solution, out-performed ordinary least squares regression and the principal components solution on the criteria of stability of coefficient and closeness…

Stability properties of solitary waves for fractional KdV and BBM equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime

2018-03-01

This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.

Effect of Fuel Particle Size on the Stability of Swirl Stabilized Flame in a Gas Turbine Combustor

NASA Astrophysics Data System (ADS)

Mishra, R. K.; Kishore Kumar, S.; Chandel, Sunil

2015-05-01

Combustion stability is examined in a swirl stabilized aero gas turbine combustor using computational fluid dynamics. A 22.5° sector of an annular combustor is modeled for the study. Unstructured tetrahedral meshes comprising 1.2 × 106 elements are employed in the model where the governing equations are solved using CFD flow solver CFX using eddy dissipation combustion model. The effect of fuel particle size on the combustion and its stability has been studied at steady state and transient conditions. The time for complete evaporation is increased exponentially when drop size increases. It delays heating up the mixture and subsequent ignition. This strongly affects the stability of the combustion flame as the incoming fresh mixture will have a quenching effect on the existing temperature field. Transient analysis at low fuel-air ratio and high particle size shows that there is a series of flame extinction and re-ignition prior to complete extinction which is observed from the fluctuation of gas temperature in the primary zone.

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

NASA Technical Reports Server (NTRS)

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

1972-01-01

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

Causes and consequences of a tropical forest gold rush in the Guiana Shield, South America.

PubMed

Hammond, David S; Gond, Valéry; de Thoisy, Benoit; Forget, Pierre-Michel; DeDijn, Bart P E

2007-12-01

Statistical and spatial analyses of both historical time series and remotely sensed data show a link between the spatial distribution and growth of gold production across the Guiana Shield in northeast Amazonia. Results indicate that an exponential rise in production across an expanding area is primarily a delayed response to the 1971-1978 market flotation of international gold prices. The subsequent 10-fold (2-fold) average nominal (real) price increase has provided a compelling economic incentive to mass exploitation of lower-grade gold deposits. The ground-based and remotely sensed distributions of mining activity are strongly attached to these deposits that dominate the region's gold geology. The presence of these gold-bearing formations in conservation and sustainable timber zones has sparked social conflict and environmental degradation across the region. Left unmanaged, more than a quarter-million square-kilometer area of tropical forest zoned for protection and sustainable management could ultimately be compromised by the price-driven boom in gold mining through poorly integrated resource use planning, lack of reclamation effort, and control of illegal operations. Serious public health issues propagated through the unregulated mining environment further erode the financial benefits achieved through gold extraction. This study demonstrates in part how international economic policies successfully stabilizing more conspicuous centers of the global economy can have unintended but profound environmental and social impacts on remote commodity frontiers.

Advances of the smooth variable structure filter: square-root and two-pass formulations

NASA Astrophysics Data System (ADS)

Gadsden, S. Andrew; Lee, Andrew S.

2017-01-01

The smooth variable structure filter (SVSF) has seen significant development and research activity in recent years. It is based on sliding mode concepts, which utilize a switching gain that brings an inherent amount of stability to the estimation process. In an effort to improve upon the numerical stability of the SVSF, a square-root formulation is derived. The square-root SVSF is based on Potter's algorithm. The proposed formulation is computationally more efficient and reduces the risks of failure due to numerical instability. The new strategy is applied on target tracking scenarios for the purposes of state estimation, and the results are compared with the popular Kalman filter. In addition, the SVSF is reformulated to present a two-pass smoother based on the SVSF gain. The proposed method is applied on an aerospace flight surface actuator, and the results are compared with the Kalman-based two-pass smoother.

Stability analysis for uncertain switched neural networks with time-varying delay.

PubMed

Shen, Wenwen; Zeng, Zhigang; Wang, Leimin

2016-11-01

In this paper, stability for a class of uncertain switched neural networks with time-varying delay is investigated. By exploring the mode-dependent properties of each subsystem, all the subsystems are categorized into stable and unstable ones. Based on Lyapunov-like function method and average dwell time technique, some delay-dependent sufficient conditions are derived to guarantee the exponential stability of considered uncertain switched neural networks. Compared with general results, our proposed approach distinguishes the stable and unstable subsystems rather than viewing all subsystems as being stable, thus getting less conservative criteria. Finally, two numerical examples are provided to show the validity and the advantages of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Scoring Methods in the International Land Benchmarking (ILAMB) Package

NASA Astrophysics Data System (ADS)

Collier, N.; Hoffman, F. M.; Keppel-Aleks, G.; Lawrence, D. M.; Mu, M.; Riley, W. J.; Randerson, J. T.

2017-12-01

The International Land Model Benchmarking (ILAMB) project is a model-data intercomparison and integration project designed to improve the performance of the land component of Earth system models. This effort is disseminated in the form of a python package which is openly developed (https://bitbucket.org/ncollier/ilamb). ILAMB is more than a workflow system that automates the generation of common scalars and plot comparisons to observational data. We aim to provide scientists and model developers with a tool to gain insight into model behavior. Thus, a salient feature of the ILAMB package is our synthesis methodology, which provides users with a high-level understanding of model performance. Within ILAMB, we calculate a non-dimensional score of a model's performance in a given dimension of the physics, chemistry, or biology with respect to an observational dataset. For example, we compare the Fluxnet-MTE Gross Primary Productivity (GPP) product against model output in the corresponding historical period. We compute common statistics such as the bias, root mean squared error, phase shift, and spatial distribution. We take these measures and find relative errors by normalizing the values, and then use the exponential to map this relative error to the unit interval. This allows for the scores to be combined into an overall score representing multiple aspects of model performance. In this presentation we give details of this process as well as a proposal for tuning the exponential mapping to make scores more cross comparable. However, as many models are calibrated using these scalar measures with respect to observational datasets, we also score the relationships among relevant variables in the model. For example, in the case of GPP, we also consider its relationship to precipitation, evapotranspiration, and temperature. We do this by creating a mean response curve and a two-dimensional distribution based on the observational data and model results. The response curves are then scored using a relative measure of the root mean squared error and the exponential as before. The distributions are scored using the so-called Hellinger distance, a statistical measure for how well one distribution is represented by another, and included in the model's overall score.

A Long-Lived Oscillatory Space-Time Correlation Function of Two Dimensional Colloids

NASA Astrophysics Data System (ADS)

Kim, Jeongmin; Sung, Bong June

2014-03-01

Diffusion of a colloid in solution has drawn significant attention for a century. A well-known behavior of the colloid is called Brownian motion : the particle displacement probability distribution (PDPD) is Gaussian and the mean-square displacement (MSD) is linear with time. However, recent simulation and experimental studies revealed the heterogeneous dynamics of colloids near glass transitions or in complex environments such as entangled actin, PDPD exhibited the exponential tail at a large length instead of being Gaussian at all length scales. More interestingly, PDPD is still exponential even when MSD was still linear with time. It requires a refreshing insight on the colloidal diffusion in the complex environments. In this work, we study heterogeneous dynamics of two dimensional (2D) colloids using molecular dynamics simulations. Unlike in three dimensions, 2D solids do not follow the Lindemann melting criterion. The Kosterlitz-Thouless-Halperin-Nelson-Young theory predicts two-step phase transitions with an intermediate phase, the hexatic phase between isotropic liquids and solids. Near solid-hexatic transition, PDPD shows interesting oscillatory behavior between a central Gaussian part and an exponential tail. Until 12 times longer than translational relaxation time, the oscillatory behavior still persists even after entering the Fickian regime. We also show that multi-layered kinetic clusters account for heterogeneous dynamics of 2D colloids with the long-lived anomalous oscillatory PDPD.

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

Anomalous T2 relaxation in normal and degraded cartilage.

PubMed

Reiter, David A; Magin, Richard L; Li, Weiguo; Trujillo, Juan J; Pilar Velasco, M; Spencer, Richard G

2016-09-01

To compare the ordinary monoexponential model with three anomalous relaxation models-the stretched Mittag-Leffler, stretched exponential, and biexponential functions-using both simulated and experimental cartilage relaxation data. Monte Carlo simulations were used to examine both the ability of identifying a given model under high signal-to-noise ratio (SNR) conditions and the accuracy and precision of parameter estimates under more modest SNR as would be encountered clinically. Experimental transverse relaxation data were analyzed from normal and enzymatically degraded cartilage samples under high SNR and rapid echo sampling to compare each model. Both simulation and experimental results showed improvement in signal representation with the anomalous relaxation models. The stretched exponential model consistently showed the lowest mean squared error in experimental data and closely represents the signal decay over multiple decades of the decay time (e.g., 1-10 ms, 10-100 ms, and >100 ms). The stretched exponential parameter αse showed an inverse correlation with biochemically derived cartilage proteoglycan content. Experimental results obtained at high field suggest potential application of αse as a measure of matrix integrity. Simulation reflecting more clinical imaging conditions, indicate the ability to robustly estimate αse and distinguish between normal and degraded tissue, highlighting its potential as a biomarker for human studies. Magn Reson Med 76:953-962, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Temporal and spatial binning of TCSPC data to improve signal-to-noise ratio and imaging speed

NASA Astrophysics Data System (ADS)

Walsh, Alex J.; Beier, Hope T.

2016-03-01

Time-correlated single photon counting (TCSPC) is the most robust method for fluorescence lifetime imaging using laser scanning microscopes. However, TCSPC is inherently slow making it ineffective to capture rapid events due to the single photon product per laser pulse causing extensive acquisition time limitations and the requirement of low fluorescence emission efficiency to avoid bias of measurement towards short lifetimes. Furthermore, thousands of photons per pixel are required for traditional instrument response deconvolution and fluorescence lifetime exponential decay estimation. Instrument response deconvolution and fluorescence exponential decay estimation can be performed in several ways including iterative least squares minimization and Laguerre deconvolution. This paper compares the limitations and accuracy of these fluorescence decay analysis techniques to accurately estimate double exponential decays across many data characteristics including various lifetime values, lifetime component weights, signal-to-noise ratios, and number of photons detected. Furthermore, techniques to improve data fitting, including binning data temporally and spatially, are evaluated as methods to improve decay fits and reduce image acquisition time. Simulation results demonstrate that binning temporally to 36 or 42 time bins, improves accuracy of fits for low photon count data. Such a technique reduces the required number of photons for accurate component estimation if lifetime values are known, such as for commercial fluorescent dyes and FRET experiments, and improve imaging speed 10-fold.

Exponential Modelling for Mutual-Cohering of Subband Radar Data

NASA Astrophysics Data System (ADS)

Siart, U.; Tejero, S.; Detlefsen, J.

2005-05-01

Increasing resolution and accuracy is an important issue in almost any type of radar sensor application. However, both resolution and accuracy are strongly related to the available signal bandwidth and energy that can be used. Nowadays, often several sensors operating in different frequency bands become available on a sensor platform. It is an attractive goal to use the potential of advanced signal modelling and optimization procedures by making proper use of information stemming from different frequency bands at the RF signal level. An important prerequisite for optimal use of signal energy is coherence between all contributing sensors. Coherent multi-sensor platforms are greatly expensive and are thus not available in general. This paper presents an approach for accurately estimating object radar responses using subband measurements at different RF frequencies. An exponential model approach allows to compensate for the lack of mutual coherence between independently operating sensors. Mutual coherence is recovered from the a-priori information that both sensors have common scattering centers in view. Minimizing the total squared deviation between measured data and a full-range exponential signal model leads to more accurate pole angles and pole magnitudes compared to single-band optimization. The model parameters (range and magnitude of point scatterers) after this full-range optimization process are also more accurate than the parameters obtained from a commonly used super-resolution procedure (root-MUSIC) applied to the non-coherent subband data.

Least-Squares Regression and Spectral Residual Augmented Classical Least-Squares Chemometric Models for Stability-Indicating Analysis of Agomelatine and Its Degradation Products: A Comparative Study.

PubMed

Naguib, Ibrahim A; Abdelrahman, Maha M; El Ghobashy, Mohamed R; Ali, Nesma A

2016-01-01

Two accurate, sensitive, and selective stability-indicating methods are developed and validated for simultaneous quantitative determination of agomelatine (AGM) and its forced degradation products (Deg I and Deg II), whether in pure forms or in pharmaceutical formulations. Partial least-squares regression (PLSR) and spectral residual augmented classical least-squares (SRACLS) are two chemometric models that are being subjected to a comparative study through handling UV spectral data in range (215-350 nm). For proper analysis, a three-factor, four-level experimental design was established, resulting in a training set consisting of 16 mixtures containing different ratios of interfering species. An independent test set consisting of eight mixtures was used to validate the prediction ability of the suggested models. The results presented indicate the ability of mentioned multivariate calibration models to analyze AGM, Deg I, and Deg II with high selectivity and accuracy. The analysis results of the pharmaceutical formulations were statistically compared to the reference HPLC method, with no significant differences observed regarding accuracy and precision. The SRACLS model gives comparable results to the PLSR model; however, it keeps the qualitative spectral information of the classical least-squares algorithm for analyzed components.

A non-Boltzmannian behavior of the energy distribution for quasi-stationary regimes of the Fermi–Pasta–Ulam β system

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

Leo, Mario, E-mail: mario.leo@le.infn.it; Leo, Rosario Antonio, E-mail: leora@le.infn.it; Tempesta, Piergiulio, E-mail: p.tempesta@fis.ucm.es

2013-06-15

In a recent paper [M. Leo, R.A. Leo, P. Tempesta, C. Tsallis, Phys. Rev. E 85 (2012) 031149], the existence of quasi-stationary states for the Fermi–Pasta–Ulam β system has been shown numerically, by analyzing the stability properties of the N/4-mode exact nonlinear solution. Here we study the energy distribution of the modes N/4, N/3 and N/2, when they are unstable, as a function of N and of the initial excitation energy. We observe that the classical Boltzmann weight is replaced by a different weight, expressed by a q-exponential function. -- Highlights: ► New statistical properties of the Fermi–Pasta–Ulam beta systemmore » are found. ► The energy distribution of specific observables are studied: a deviation from the standard Boltzmann behavior is found. ► A q-exponential weight should be used instead. ► The classical exponential weight is restored in the large particle limit (mesoscopic nature of the phenomenon)« less

The gap of the area-weighted Motzkin spin chain is exponentially small

NASA Astrophysics Data System (ADS)

Levine, Lionel; Movassagh, Ramis

2017-06-01

We prove that the energy gap of the model proposed by Zhang et al (2016 arXiv:1606.07795) is exponentially small in the square of the system size. In Movassagh and Shor (2016 Proc. Natl Acad. Sci. USA) a class of exactly solvable quantum spin chain models was proposed that have integer spins (s), with a nearest neighbors Hamiltonian, and a unique ground state. The ground state can be seen as a uniform superposition of all s-colored Motzkin walks. The half-chain entanglement entropy provably violates the area law by a square root factor in the system’s size (˜\\sqrt{n} ) for s  >  1. For s  =  1, the violation is logarithmic (Bravyi et al 2012 Phys. Rev. Lett. 109 207202). Moreover in Movassagh and Shor (2016 Proc. Natl Acad. Sci. USA) it was proved that the gap vanishes polynomially and is O(n -c ) with c≥slant2 . Recently, a deformation of Movassagh and Shor (2016 Proc. Natl Acad. Sci. USA), which we call ‘weighted Motzkin quantum spin chain’ was proposed Zhang et al (2016 arXiv:1606.07795). This model has a unique ground state that is a superposition of the s-colored Motzkin walks weighted by tarea\\{Motzkin walk\\} with t  >  1. The most surprising feature of this model is that it violates the area law by a factor of n. Here we prove that the gap of this model is upper bounded by 8ns t-n2/3 for t  >  1 and s  >  1.

Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application

PubMed Central

Tutty, O.

2015-01-01

With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterizing the magnitude of the Coriolis force. By converting the original Navier–Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares of polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterizing the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study, several results meaningful in the context of the method used were also obtained. Overall, the results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach. PMID:26730219

Physicochemically Tunable Polyfunctionalized RNA Square Architecture with Fluorogenic and Ribozymatic Properties

PubMed Central

2015-01-01

Recent advances in RNA nanotechnology allow the rational design of various nanoarchitectures. Previous methods utilized conserved angles from natural RNA motifs to form geometries with specific sizes. However, the feasibility of producing RNA architecture with variable sizes using native motifs featuring fixed sizes and angles is limited. It would be advantageous to display RNA nanoparticles of diverse shape and size derived from a given primary sequence. Here, we report an approach to construct RNA nanoparticles with tunable size and stability. Multifunctional RNA squares with a 90° angle were constructed by tuning the 60° angle of the three-way junction (3WJ) motif from the packaging RNA (pRNA) of the bacteriophage phi29 DNA packaging motor. The physicochemical properties and size of the RNA square were also easily tuned by modulating the “core” strand and adjusting the length of the sides of the square via predictable design. Squares of 5, 10, and 20 nm were constructed, each showing diverse thermodynamic and chemical stabilities. Four “arms” extending from the corners of the square were used to incorporate siRNA, ribozyme, and fluorogenic RNA motifs. Unique intramolecular contact using the pre-existing intricacy of the 3WJ avoids relatively weaker intermolecular interactions via kissing loops or sticky ends. Utilizing the 3WJ motif, we have employed a modular design technique to construct variable-size RNA squares with controllable properties and functionalities for diverse and versatile applications with engineering, pharmaceutical, and medical potential. This technique for simple design to finely tune physicochemical properties adds a new angle to RNA nanotechnology. PMID:24971772

Stabilization of a system with saturating, non-monotone hysteresis and frequency dependent power losses by a PD controller

NASA Astrophysics Data System (ADS)

Ekanayake, D. B.; Iyer, R. V.

2015-02-01

We prove the closed loop stability of a PD controller for certain systems with saturating, non-monotone hysteresis and frequency dependent power losses. Most controllers use inverse compensators to cancel out actuator hysteresis nonlinearity. We show that we can achieve stability of the closed-loop system without an explicit inverse computation (using least squares minimization or otherwise).

Regimes of stability and scaling relations for the removal time in the asteroid belt: a simple kinetic model and numerical tests

NASA Astrophysics Data System (ADS)

Cubrovic, Mihailo

2005-02-01

We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws) between the removal time (the time for an asteroid to experience a qualitative change of dynamical behavior and enter a wide chaotic zone) and the Lyapunov time. The correlations are shown to arise in two different regimes, characterized by exponential and power-law scalings. We also show how is the so-called “stable chaos” (exponential regime) related to anomalous diffusion. Finally, we check our results numerically and discuss their possible applications in analyzing the motion of particular asteroids.

Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control.

PubMed

Wang, Leimin; Shen, Yi; Zhang, Guodong

2016-10-01

This paper is concerned with the synchronization problem for a class of switched neural networks (SNNs) with time-varying delays. First, a new crucial lemma which includes and extends the classical exponential stability theorem is constructed. Then by using the lemma, new algebraic criteria of ψ -type synchronization (synchronization with general decay rate) for SNNs are established via the designed nonlinear feedback control. The ψ -type synchronization which is in a general framework is obtained by introducing a ψ -type function. It contains exponential synchronization, polynomial synchronization, and other synchronization as its special cases. The results of this paper are general, and they also complement and extend some previous results. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling.

PubMed

Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian

2012-09-01

This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.

On Using Exponential Parameter Estimators with an Adaptive Controller

NASA Technical Reports Server (NTRS)

Patre, Parag; Joshi, Suresh M.

2011-01-01

Typical adaptive controllers are restricted to using a specific update law to generate parameter estimates. This paper investigates the possibility of using any exponential parameter estimator with an adaptive controller such that the system tracks a desired trajectory. The goal is to provide flexibility in choosing any update law suitable for a given application. The development relies on a previously developed concept of controller/update law modularity in the adaptive control literature, and the use of a converse Lyapunov-like theorem. Stability analysis is presented to derive gain conditions under which this is possible, and inferences are made about the tracking error performance. The development is based on a class of Euler-Lagrange systems that are used to model various engineering systems including space robots and manipulators.

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.

Suzaku observation of IGR J16318-4848

NASA Technical Reports Server (NTRS)

Barragan, Laura; Wilms, Joern; Pottschmidt, Katja; Nowak, Michael A.; Kreykenbohm, Ingo; Walter, Roland; Tomsick, John A.

2009-01-01

We report on the first Suzaku observation of IGR J16318-4848, the most extreme example of a new group of highly absorbed X-ray binaries that have recently been discovered by the International Gamma-Ray Astrophysics Laboratory (INTEGRAL). The Suzaku observation was carried out between 2006 August 14 and 17, with a net exposure time of 97 ks. The average X-ray spectrum of the source can be well described (chi-square (sub red)= 0.99) with a continuum model typical for neutron stars i.e., a strongly absorbed power law continuum with a photon index of 0.676(42) and an exponential cutoff at 20.5(6) keY. The absorbing column is N(sub H) = 1.95(3) X 10(exp 24)/square cm. Consistent with earlier work, strong fluorescent emission lines of Fe K-alpha, Fe K-beta, and Ni K-alpha are observed. Despite the large N(sub H), no Compton shoulder is seen in the lines, arguing for a non-spherical and inhomogeneous absorber. Seen at an average 5-60 keV absorbed flux of 3.4 x 10(exp -10) erg/square cm/second, the source exhibits significant variability on timescales of hours.

A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains

NASA Astrophysics Data System (ADS)

Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto

2016-05-01

This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.

Stability of the discretization of the electron avalanche phenomenon

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

Villa, Andrea, E-mail: andrea.villa@rse-web.it; Barbieri, Luca, E-mail: luca.barbieri@rse-web.it; Gondola, Marco, E-mail: marco.gondola@rse-web.it

2015-09-01

The numerical simulation of the discharge inception is an active field of applied physics with many industrial applications. In this work we focus on the drift-reaction equation that describes the electron avalanche. This phenomenon is one of the basic building blocks of the streamer model. The main difficulty of the electron avalanche equation lies in the fact that the reaction term is positive when a high electric field is applied. It leads to exponentially growing solutions and this has a major impact on the behavior of numerical schemes. We analyze the stability of a reference finite volume scheme applied tomore » this latter problem. The stability of the method may impose a strict mesh spacing, therefore a proper stabilized scheme, which is stable whatever spacing is used, has been developed. The convergence of the scheme is treated as well as some numerical experiments.« less

Stabilization of flow past a rounded cylinder

NASA Astrophysics Data System (ADS)

Samtaney, Ravi; Zhang, Wei

2016-11-01

We perform global linear stability analysis on low-Re flow past a rounded cylinder. The cylinder corners are rounded with a radius R, normalized as R+ = R / D where D is the cylinder diameter, and its effect on the flow stability characteristics is investigated. We compute the critical Reynolds number (Recr) for the onset of first instability, and quantify the perturbation growth rate for the super-critical flows. It is found that the flow can be stabilized by partially rounding the cylinder. Compared with the square and circular cylinders, the partially rounded cylinder has a higher Recr , attaining a maximum at around R+ = 0 . 30 , and the perturbation growth rate of the super-critical flows is reduced for Re <= 100 . We perform sensitivity analysis to explore the source of the stabilization. The growth rate sensitivity to base flow modification has two different spatial structures: the growth rate is sensitive to the wake backflow in a large region for square-like cylinders (R+ -> 0 . 00), while only the near-wake backflow is crucial for circular-like cylinders (R+ -> 0 . 50). The stability analysis results are also verified with those of the direct simulations and very good agreement is achieved. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1394-01. The supercomputer Shaheen at KAUST was utilized for the simulations.

Is the Milky Way's hot halo convectively unstable?

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

Henley, David B.; Shelton, Robin L., E-mail: dbh@physast.uga.edu

2014-03-20

We investigate the convective stability of two popular types of model of the gas distribution in the hot Galactic halo. We first consider models in which the halo density and temperature decrease exponentially with height above the disk. These halo models were created to account for the fact that, on some sight lines, the halo's X-ray emission lines and absorption lines yield different temperatures, implying that the halo is non-isothermal. We show that the hot gas in these exponential models is convectively unstable if γ < 3/2, where γ is the ratio of the temperature and density scale heights. Usingmore » published measurements of γ and its uncertainty, we use Bayes' theorem to infer posterior probability distributions for γ, and hence the probability that the halo is convectively unstable for different sight lines. We find that, if these exponential models are good descriptions of the hot halo gas, at least in the first few kiloparsecs from the plane, the hot halo is reasonably likely to be convectively unstable on two of the three sight lines for which scale height information is available. We also consider more extended models of the halo. While isothermal halo models are convectively stable if the density decreases with distance from the Galaxy, a model of an extended adiabatic halo in hydrostatic equilibrium with the Galaxy's dark matter is on the boundary between stability and instability. However, we find that radiative cooling may perturb this model in the direction of convective instability. If the Galactic halo is indeed convectively unstable, this would argue in favor of supernova activity in the Galactic disk contributing to the heating of the hot halo gas.« less

Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2016-12-01

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5 n equilibrium points located in ℜ n , and 3 n of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Ballooning instabilities in tokamaks with sheared toroidal flows

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

Waelbroeck, F.L.; Chen, L.

1990-11-01

The stability of ballooning modes in the presence of sheared toroidal flows is investigated. The eigenmodes are shown to be related by a Fourier transformation to the non-exponentially growing Floquet solutions found by Cooper. It is further shown that the problem cannot be reduced further than to a two dimensional partial differential equation. Next, the generalized ballooning equation is solved analytically for a circular tokamak equilibrium with sonic flows, but with a small rotation shear compared to the sound speed. With this ordering, the centrifugal forces are comparable to the pressure gradient forces driving the instability, but coupling of themore » mode with the sound wave is avoided. A new stability criterion is derived which explicitly demonstrates that flow shear is stabilizing at constant centrifugal force gradient. 34 refs.« less

Stochastic functional evolution equations with monotone nonlinearity: Existence and stability of the mild solutions

NASA Astrophysics Data System (ADS)

Jahanipur, Ruhollah

In this paper, we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone condition. We prove the existence, uniqueness and exponentially asymptotic stability of the mild solutions. Our approach is to apply a convenient version of Burkholder inequality for convolution integrals and an iteration method based on the existence and measurability results for the functional integral equations in Hilbert spaces. An Itô-type inequality is the main tool to study the uniqueness, p-th moment and almost sure sample path asymptotic stability of the mild solutions. We also give some examples to illustrate the applications of the theorems and meanwhile we compare the results obtained in this paper with some others appeared in the literature.

Long time stability of small-amplitude Breathers in a mixed FPU-KG model

NASA Astrophysics Data System (ADS)

Paleari, Simone; Penati, Tiziano

2016-12-01

In the limit of small couplings in the nearest neighbor interaction, and small total energy, we apply the resonant normal form result of a previous paper of ours to a finite but arbitrarily large mixed Fermi-Pasta-Ulam Klein-Gordon chain, i.e., with both linear and nonlinear terms in both the on-site and interaction potential, with periodic boundary conditions. An existence and orbital stability result for Breathers of such a normal form, which turns out to be a generalized discrete nonlinear Schrödinger model with exponentially decaying all neighbor interactions, is first proved. Exploiting such a result as an intermediate step, a long time stability theorem for the true Breathers of the KG and FPU-KG models, in the anti-continuous limit, is proven.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

NASA Astrophysics Data System (ADS)

Brown, J. S.; Shaheen, S. E.

2018-04-01

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics.

PubMed

Brown, J S; Shaheen, S E

2018-04-04

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Stochastic modelling of intermittent fluctuations in the scrape-off layer: Correlations, distributions, level crossings, and moment estimation

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

Garcia, O. E., E-mail: odd.erik.garcia@uit.no; Kube, R.; Theodorsen, A.

A stochastic model is presented for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas. The fluctuations in the plasma density are modeled by a super-position of uncorrelated pulses with fixed shape and duration, describing radial motion of blob-like structures. In the case of an exponential pulse shape and exponentially distributed pulse amplitudes, predictions are given for the lowest order moments, probability density function, auto-correlation function, level crossings, and average times for periods spent above and below a given threshold level. Also, the mean squared errors on estimators of sample mean and variance for realizations of the process bymore » finite time series are obtained. These results are discussed in the context of single-point measurements of fluctuations in the scrape-off layer, broad density profiles, and implications for plasma–wall interactions due to the transient transport events in fusion grade plasmas. The results may also have wide applications for modelling fluctuations in other magnetized plasmas such as basic laboratory experiments and ionospheric irregularities.« less

The stationary non-equilibrium plasma of cosmic-ray electrons and positrons

NASA Astrophysics Data System (ADS)

Tomaschitz, Roman

2016-06-01

The statistical properties of the two-component plasma of cosmic-ray electrons and positrons measured by the AMS-02 experiment on the International Space Station and the HESS array of imaging atmospheric Cherenkov telescopes are analyzed. Stationary non-equilibrium distributions defining the relativistic electron-positron plasma are derived semi-empirically by performing spectral fits to the flux data and reconstructing the spectral number densities of the electronic and positronic components in phase space. These distributions are relativistic power-law densities with exponential cutoff, admitting an extensive entropy variable and converging to the Maxwell-Boltzmann or Fermi-Dirac distributions in the non-relativistic limit. Cosmic-ray electrons and positrons constitute a classical (low-density high-temperature) plasma due to the low fugacity in the quantized partition function. The positron fraction is assembled from the flux densities inferred from least-squares fits to the electron and positron spectra and is subjected to test by comparing with the AMS-02 flux ratio measured in the GeV interval. The calculated positron fraction extends to TeV energies, predicting a broad spectral peak at about 1 TeV followed by exponential decay.

Quantitative photoplethysmography: Lambert-Beer law or inverse function incorporating light scatter.

PubMed

Cejnar, M; Kobler, H; Hunyor, S N

1993-03-01

Finger blood volume is commonly determined from measurement of infra-red (IR) light transmittance using the Lambert-Beer law of light absorption derived for use in non-scattering media, even when such transmission involves light scatter around the phalangeal bone. Simultaneous IR transmittance and finger volume were measured over the full dynamic range of vascular volumes in seven subjects and outcomes compared with data fitted according to the Lambert-Beer exponential function and an inverse function derived for light attenuation by scattering materials. Curves were fitted by the least-squares method and goodness of fit was compared using standard errors of estimate (SEE). The inverse function gave a better data fit in six of the subjects: mean SEE 1.9 (SD 0.7, range 0.7-2.8) and 4.6 (2.2, 2.0-8.0) respectively (p < 0.02, paired t-test). Thus, when relating IR transmittance to blood volume, as occurs in the finger during measurements of arterial compliance, an inverse function derived from a model of light attenuation by scattering media gives more accurate results than the traditional exponential fit.

Multivariate Time Series Forecasting of Crude Palm Oil Price Using Machine Learning Techniques

NASA Astrophysics Data System (ADS)

Kanchymalay, Kasturi; Salim, N.; Sukprasert, Anupong; Krishnan, Ramesh; Raba'ah Hashim, Ummi

2017-08-01

The aim of this paper was to study the correlation between crude palm oil (CPO) price, selected vegetable oil prices (such as soybean oil, coconut oil, and olive oil, rapeseed oil and sunflower oil), crude oil and the monthly exchange rate. Comparative analysis was then performed on CPO price forecasting results using the machine learning techniques. Monthly CPO prices, selected vegetable oil prices, crude oil prices and monthly exchange rate data from January 1987 to February 2017 were utilized. Preliminary analysis showed a positive and high correlation between the CPO price and soy bean oil price and also between CPO price and crude oil price. Experiments were conducted using multi-layer perception, support vector regression and Holt Winter exponential smoothing techniques. The results were assessed by using criteria of root mean square error (RMSE), means absolute error (MAE), means absolute percentage error (MAPE) and Direction of accuracy (DA). Among these three techniques, support vector regression(SVR) with Sequential minimal optimization (SMO) algorithm showed relatively better results compared to multi-layer perceptron and Holt Winters exponential smoothing method.

Chemical networks with inflows and outflows: a positive linear differential inclusions approach.

PubMed

Angeli, David; De Leenheer, Patrick; Sontag, Eduardo D

2009-01-01

Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. 2009 American Institute of Chemical Engineers

Dynamic stability of passive dynamic walking on an irregular surface.

PubMed

Su, Jimmy Li-Shin; Dingwell, Jonathan B

2007-12-01

Falls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously "correct" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., "local") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r(2)=2.43%; p=0.280) or long-term local instability (r(2)=1.0%; p=0.441). These measures essentially reflected the fact that the model never actually "fell" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r(2)>or=99.6%; p<0.001) and short-term local instability increased linearly (r(2)=88.1%; p<0.001). These measures thus predicted the increased risk of falling exhibited by the model. For all simulated conditions, the walker remained orbitally stable, while exhibiting substantial local instability. This was because very small initial perturbations diverged away from the limit cycle, while larger initial perturbations converged toward the limit cycle. These results provide insight into how these different proposed measures of walking stability are related to each other and to risk of falling.

Square tracking sensor for autonomous helicopter hover stabilization

NASA Astrophysics Data System (ADS)

Oertel, Carl-Henrik

1995-06-01

Sensors for synthetic vision are needed to extend the mission profiles of helicopters. A special task for various applications is the autonomous position hold of a helicopter above a ground fixed or moving target. As a proof of concept for a general synthetic vision solution a restricted machine vision system, which is capable of locating and tracking a special target, was developed by the Institute of Flight Mechanics of Deutsche Forschungsanstalt fur Luft- und Raumfahrt e.V. (i.e., German Aerospace Research Establishment). This sensor, which is specialized to detect and track a square, was integrated in the fly-by-wire helicopter ATTHeS (i.e., Advanced Technology Testing Helicopter System). An existing model following controller for the forward flight condition was adapted for the hover and low speed requirements of the flight vehicle. The special target, a black square with a length of one meter, was mounted on top of a car. Flight tests demonstrated the automatic stabilization of the helicopter above the moving car by synthetic vision.

Modeling steady-state dynamics of macromolecules in exponential-stretching flow using multiscale molecular-dynamics-multiparticle-collision simulations.

PubMed

Ghatage, Dhairyasheel; Chatterji, Apratim

2013-10-01

We introduce a method to obtain steady-state uniaxial exponential-stretching flow of a fluid (akin to extensional flow) in the incompressible limit, which enables us to study the response of suspended macromolecules to the flow by computer simulations. The flow field in this flow is defined by v(x) = εx, where v(x) is the velocity of the fluid and ε is the stretch flow gradient. To eliminate the effect of confining boundaries, we produce the flow in a channel of uniform square cross section with periodic boundary conditions in directions perpendicular to the flow, but simultaneously maintain uniform density of fluid along the length of the tube. In experiments a perfect elongational flow is obtained only along the axis of symmetry in a four-roll geometry or a filament-stretching rheometer. We can reproduce flow conditions very similar to extensional flow near the axis of symmetry by exponential-stretching flow; we do this by adding the right amounts of fluid along the length of the flow in our simulations. The fluid particles added along the length of the tube are the same fluid particles which exit the channel due to the flow; thus mass conservation is maintained in our model by default. We also suggest a scheme for possible realization of exponential-stretching flow in experiments. To establish our method as a useful tool to study various soft matter systems in extensional flow, we embed (i) spherical colloids with excluded volume interactions (modeled by the Weeks-Chandler potential) as well as (ii) a bead-spring model of star polymers in the fluid to study their responses to the exponential-stretched flow and show that the responses of macromolecules in the two flows are very similar. We demonstrate that the variation of number density of the suspended colloids along the direction of flow is in tune with our expectations. We also conclude from our study of the deformation of star polymers with different numbers of arms f that the critical flow gradient ε(c) at which the star undergoes the coil-to-stretch transition is independent of f for f = 2,5,10, and 20.

Methane exchange at the peatland forest floor - automatic chamber system exposes the dynamics of small fluxes

NASA Astrophysics Data System (ADS)

Korkiakoski, Mika; Tuovinen, Juha-Pekka; Aurela, Mika; Koskinen, Markku; Minkkinen, Kari; Ojanen, Paavo; Penttilä, Timo; Rainne, Juuso; Laurila, Tuomas; Lohila, Annalea

2017-04-01

We measured methane (CH4) exchange rates with automatic chambers at the forest floor of a nutrient-rich drained peatland in 2011-2013. The fen, located in southern Finland, was drained for forestry in 1969 and the tree stand is now a mixture of Scots pine, Norway spruce, and pubescent birch. Our measurement system consisted of six transparent chambers and stainless steel frames, positioned on a number of different field and moss layer compositions. Gas concentrations were measured with an online cavity ring-down spectroscopy gas analyzer. Fluxes were calculated with both linear and exponential regression. The use of linear regression resulted in systematically smaller CH4 fluxes by 10-45 % as compared to exponential regression. However, the use of exponential regression with small fluxes ( < 2.5 µg CH4 m-2 h-1) typically resulted in anomalously large absolute fluxes and high hour-to-hour deviations. Therefore, we recommend that fluxes are initially calculated with linear regression to determine the threshold for low fluxes and that higher fluxes are then recalculated using exponential regression. The exponential flux was clearly affected by the length of the fitting period when this period was < 190 s, but stabilized with longer periods. Thus, we also recommend the use of a fitting period of several minutes to stabilize the results and decrease the flux detection limit. There were clear seasonal dynamics in the CH4 flux: the forest floor acted as a CH4 sink particularly from early summer until the end of the year, while in late winter the flux was very small and fluctuated around zero. However, the magnitude of fluxes was relatively small throughout the year, ranging mainly from -130 to +100 µg CH4 m-2 h-1. CH4 emission peaks were observed occasionally, mostly in summer during heavy rainfall events. Diurnal variation, showing a lower CH4 uptake rate during the daytime, was observed in all of the chambers, mainly in the summer and late spring, particularly in dry conditions. It was attributed more to changes in wind speed than air or soil temperature, which suggest that physical rather than biological phenomena are responsible for the observed variation. The annual net CH4 exchange varied from -104 ± 30 to -505 ± 39 mg CH4 m-2 yr-1 among the six chambers, with an average of -219 mg CH4 m-2 yr-1 over the 2-year measurement period.

The Relationship of Core Strength and Activation and Performance on Three Functional Movement Screens.

PubMed

Johnson, Caleb D; Whitehead, Paul N; Pletcher, Erin R; Faherty, Mallory S; Lovalekar, Mita T; Eagle, Shawn R; Keenan, Karen A

2018-04-01

Johnson, CD, Whitehead, PN, Pletcher, ER, Faherty, MS, Lovalekar, MT, Eagle, SR, and Keenan, KA. The relationship of core strength and activation and performance on three functional movement screens. J Strength Cond Res 32(4): 1166-1173, 2018-Current measures of core stability used by clinicians and researchers suffer from several shortcomings. Three functional movement screens appear, at face-value, to be dependent on the ability to activate and control core musculature. These 3 screens may present a viable alternative to current measures of core stability. Thirty-nine subjects completed a deep squat, trunk stability push-up, and rotary stability screen. Scores on the 3 screens were summed to calculate a composite score (COMP). During the screens, muscle activity was collected to determine the length of time that the bilateral erector spinae, rectus abdominis, external oblique, and gluteus medius muscles were active. Strength was assessed for core muscles (trunk flexion and extension, trunk rotation, and hip abduction and adduction) and accessory muscles (knee flexion and extension and pectoralis major). Two ordinal logistic regression equations were calculated with COMP as the outcome variable, and: (a) core strength and accessory strength, (b) only core strength. The first model was significant in predicting COMP (p = 0.004) (Pearson's Chi-Square = 149.132, p = 0.435; Nagelkerke's R-Squared = 0.369). The second model was significant in predicting COMP (p = 0.001) (Pearson's Chi-Square = 148.837, p = 0.488; Nagelkerke's R-Squared = 0.362). The core muscles were found to be active for most screens, with percentages of "time active" for each muscle ranging from 54-86%. In conclusion, performance on the 3 screens is predicted by core strength, even when accounting for "accessory" strength variables. Furthermore, it seems the screens elicit wide-ranging activation of core muscles. Although more investigation is needed, these screens, collectively, seem to be a good assessment of core strength.

Exponential instability in the fractional Calderón problem

NASA Astrophysics Data System (ADS)

Rüland, Angkana; Salo, Mikko

2018-04-01

In this paper we prove the exponential instability of the fractional Calderón problem and thus prove the optimality of the logarithmic stability estimate from Rüland and Salo (2017 arXiv:1708.06294). In order to infer this result, we follow the strategy introduced by Mandache in (2001 Inverse Problems 17 1435) for the standard Calderón problem. Here we exploit a close relation between the fractional Calderón problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in Rüland and Salo (2017 arXiv:1708.06294). Finally, in one dimension, we show a close relation between the fractional Calderón problem and the truncated Hilbert transform.

Astronomical Verification of a Stabilized Frequency Reference Transfer System for the Square Kilometer Array

NASA Astrophysics Data System (ADS)

Gozzard, David R.; Schediwy, Sascha W.; Dodson, Richard; Rioja, María J.; Hill, Mike; Lennon, Brett; McFee, Jock; Mirtschin, Peter; Stevens, Jamie; Grainge, Keith

2017-07-01

In order to meet its cutting-edge scientific objectives, the Square Kilometre Array (SKA) telescope requires high-precision frequency references to be distributed to each of its antennas. The frequency references are distributed via fiber-optic links and must be actively stabilized to compensate for phase noise imposed on the signals by environmental perturbations on the links. SKA engineering requirements demand that any proposed frequency reference distribution system be proved in “astronomical verification” tests. We present results of the astronomical verification of a stabilized frequency reference transfer system proposed for SKA-mid. The dual-receiver architecture of the Australia Telescope Compact Array was exploited to subtract the phase noise of the sky signal from the data, allowing the phase noise of observations performed using a standard frequency reference, as well as the stabilized frequency reference transfer system transmitting over 77 km of fiber-optic cable, to be directly compared. Results are presented for the fractional frequency stability and phase drift of the stabilized frequency reference transfer system for celestial calibrator observations at 5 and 25 GHz. These observations plus additional laboratory results for the transferred signal stability over a 166 km metropolitan fiber-optic link are used to show that the stabilized transfer system under test exceeds all SKA phase-stability requirements within a broad range of observing conditions. Furthermore, we have shown that alternative reference dissemination systems that use multiple synthesizers to supply reference signals to sub-sections of an array may limit the imaging capability of the telescope.

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

Spectroscopic investigations of Nd3+ doped Lithium Lead Alumino Borate glasses for 1.06 μm laser applications

NASA Astrophysics Data System (ADS)

Deopa, Nisha; Rao, A. S.; Gupta, Mohini; Vijaya Prakash, G.

2018-01-01

Neodymium doped lithium lead alumino borate glasses were synthesized with the molar composition 10Li2Osbnd 10PbOsbnd (10-x) Al2O3sbnd 70B2O3sbnd x Nd2O3 (where, x = 0.1, 0.5, 1.0, 1.5, 2.0 and 2.5 mol %) via conventional melt quenching technique to understand their lasing potentialities using the absorption, emission and photoluminescence decay spectral measurements. The oscillator strengths measured from the absorption spectra were used to estimate the Judd-Ofelt intensity parameters using least square fitting procedure. The emission spectra recorded for the as-prepared glasses under investigation exhibit two emission transitions 4F3/2 → 4I11/2 (1063 nm) and 4F3/2 → 4I9/2 (1350 nm) for which radiative parameters have been evaluated. The emission intensity increases with increase in Nd3+ ion concentration up to 1 mol % and beyond concentration quenching took place. The decay profile shows single exponential nature for lower Nd3+ ion concentration and non-exponential for higher concentration. To elucidate the nature of energy transfer process, the non-exponential decay curves were well fitted to Inokuti-Hirayama model. The relatively higher values of emission cross-sections, branching ratios and quantum efficiency values obtained for 1.0 mol% of Nd3+ ions in LiPbAlB glass suggests it's aptness in generating lasing action at 1063 nm in NIR region.

The square lattice Ising model on the rectangle II: finite-size scaling limit

NASA Astrophysics Data System (ADS)

Hucht, Alfred

2017-06-01

Based on the results published recently (Hucht 2017 J. Phys. A: Math. Theor. 50 065201), the universal finite-size contributions to the free energy of the square lattice Ising model on the L× M rectangle, with open boundary conditions in both directions, are calculated exactly in the finite-size scaling limit L, M\\to∞ , T\\to Tc , with fixed temperature scaling variable x\\propto(T/Tc-1)M and fixed aspect ratio ρ\\propto L/M . We derive exponentially fast converging series for the related Casimir potential and Casimir force scaling functions. At the critical point T=Tc we confirm predictions from conformal field theory (Cardy and Peschel 1988 Nucl. Phys. B 300 377, Kleban and Vassileva 1991 J. Phys. A: Math. Gen. 24 3407). The presence of corners and the related corner free energy has dramatic impact on the Casimir scaling functions and leads to a logarithmic divergence of the Casimir potential scaling function at criticality.

Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels

NASA Technical Reports Server (NTRS)

Fromme, J. A.; Golberg, M. A.

1979-01-01

Lift interference effects are discussed based on Bland's (1968) integral equation. A mathematical existence theory is utilized for which convergence of the numerical method has been proved for general (square-integrable) downwashes. Airloads are computed using orthogonal airfoil polynomial pairs in conjunction with a collocation method which is numerically equivalent to Galerkin's method and complex least squares. Convergence exhibits exponentially decreasing error with the number n of collocation points for smooth downwashes, whereas errors are proportional to 1/n for discontinuous downwashes. The latter can be reduced to 1/n to the m+1 power with mth-order Richardson extrapolation (by using m = 2, hundredfold error reductions were obtained with only a 13% increase of computer time). Numerical results are presented showing acoustic resonance, as well as the effect of Mach number, ventilation, height-to-chord ratio, and mode shape on wind-tunnel interference. Excellent agreement with experiment is obtained in steady flow, and good agreement is obtained for unsteady flow.

Phase transition in 2-d system of quadrupoles on square lattice with anisotropic field

NASA Astrophysics Data System (ADS)

Sallabi, A. K.; Alkhttab, M.

2014-12-01

Monte Carlo method is used to study a simple model of two-dimensional interacting quadrupoles on ionic square lattice with anisotropic strength provided by the ionic lattice. Order parameter, susceptibility and correlation function data, show that this system form an ordered structure with p(2×1) symmetry at low temperature. The p(2×1) structure undergoes an order-disorder phase transition into disordered (1×1) phase at 8.3K. The two-point correlation function show exponential dependence on distance both above and below the transition temperature. At Tc the two-point correlation function shows a power law dependence on distance, e.g. C(r) ~ 1η. The value of the exponent η at Tc shows small deviation from the Ising value and indicates that this system falls into the same universality class as the XY model with cubic anisotropy. This model can be applied to prototypical quadrupoles physisorbed systems as N2 on NaCl(100).

Charge transport study in bis{2-(2-hydroxyphenyl) benzoxazolate} zinc [Zn(hpb)2

NASA Astrophysics Data System (ADS)

Rai, Virendra Kumar; Srivastava, Ritu; Chauhan, Gayatri; Kumar, Arunandan; Kamalasanan, M. N.

2008-10-01

The nature of the electrical transport mechanism for carrier transport in pure bis {2-(2-hydroxyphenyl) benzoxazolate} zinc [Zn(hpb)2] has been studied by current voltage measurements of samples at different thicknesses and at different temperatures. Hole-only devices show ohmic conduction at low voltages and space charge conduction at high voltages. The space charge conduction is clearly identifiable with a square law dependence of current on voltage as well as the scaling of current inversely with the cube of thickness. With a further increase in voltage, the current increases with a Vm dependence with m varying with temperature typical of trap limited conduction with an exponential distribution of trap states. From the square law region the effective charge carrier mobility of holes has been evaluated as 2.5 × 10-11 m2 V-1 s-1. Electron-only devices however show electrode limited conduction, which was found to obey the Scott Malliaras model of charge injection.

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

Optimal Frequency-Domain System Realization with Weighting

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Maghami, Peiman G.

1999-01-01

Several approaches are presented to identify an experimental system model directly from frequency response data. The formulation uses a matrix-fraction description as the model structure. Frequency weighting such as exponential weighting is introduced to solve a weighted least-squares problem to obtain the coefficient matrices for the matrix-fraction description. A multi-variable state-space model can then be formed using the coefficient matrices of the matrix-fraction description. Three different approaches are introduced to fine-tune the model using nonlinear programming methods to minimize the desired cost function. The first method uses an eigenvalue assignment technique to reassign a subset of system poles to improve the identified model. The second method deals with the model in the real Schur or modal form, reassigns a subset of system poles, and adjusts the columns (rows) of the input (output) influence matrix using a nonlinear optimizer. The third method also optimizes a subset of poles, but the input and output influence matrices are refined at every optimization step through least-squares procedures.

Monte Carlo point process estimation of electromyographic envelopes from motor cortical spikes for brain-machine interfaces

NASA Astrophysics Data System (ADS)

Liao, Yuxi; She, Xiwei; Wang, Yiwen; Zhang, Shaomin; Zhang, Qiaosheng; Zheng, Xiaoxiang; Principe, Jose C.

2015-12-01

Objective. Representation of movement in the motor cortex (M1) has been widely studied in brain-machine interfaces (BMIs). The electromyogram (EMG) has greater bandwidth than the conventional kinematic variables (such as position, velocity), and is functionally related to the discharge of cortical neurons. As the stochastic information of EMG is derived from the explicit spike time structure, point process (PP) methods will be a good solution for decoding EMG directly from neural spike trains. Previous studies usually assume linear or exponential tuning curves between neural firing and EMG, which may not be true. Approach. In our analysis, we estimate the tuning curves in a data-driven way and find both the traditional functional-excitatory and functional-inhibitory neurons, which are widely found across a rat’s motor cortex. To accurately decode EMG envelopes from M1 neural spike trains, the Monte Carlo point process (MCPP) method is implemented based on such nonlinear tuning properties. Main results. Better reconstruction of EMG signals is shown on baseline and extreme high peaks, as our method can better preserve the nonlinearity of the neural tuning during decoding. The MCPP improves the prediction accuracy (the normalized mean squared error) 57% and 66% on average compared with the adaptive point process filter using linear and exponential tuning curves respectively, for all 112 data segments across six rats. Compared to a Wiener filter using spike rates with an optimal window size of 50 ms, MCPP decoding EMG from a point process improves the normalized mean square error (NMSE) by 59% on average. Significance. These results suggest that neural tuning is constantly changing during task execution and therefore, the use of spike timing methodologies and estimation of appropriate tuning curves needs to be undertaken for better EMG decoding in motor BMIs.

Robust Variable Selection with Exponential Squared Loss.

PubMed

Wang, Xueqin; Jiang, Yunlu; Huang, Mian; Zhang, Heping

2013-04-01

Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness that has not been done for the existing procedures, while its performance is near optimal and superior to some recently developed methods. Specifically, under defined regularity conditions, our estimators are [Formula: see text] and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed method with some recent methods, using the oracle method as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error and the positive selection rate even in the presence of influential points. In contrast, other existing procedures have a much lower non-causal selection rate. Furthermore, we re-analyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Dataset that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods.

Robust Variable Selection with Exponential Squared Loss

PubMed Central

Wang, Xueqin; Jiang, Yunlu; Huang, Mian; Zhang, Heping

2013-01-01

Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness that has not been done for the existing procedures, while its performance is near optimal and superior to some recently developed methods. Specifically, under defined regularity conditions, our estimators are n-consistent and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed method with some recent methods, using the oracle method as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error and the positive selection rate even in the presence of influential points. In contrast, other existing procedures have a much lower non-causal selection rate. Furthermore, we re-analyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Dataset that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods. PMID:23913996

Mass transport in micellar surfactant solutions: 2. Theoretical modeling of adsorption at a quiescent interface.

PubMed

Danov, K D; Kralchevsky, P A; Denkov, N D; Ananthapadmanabhan, K P; Lips, A

2006-01-31

Here, we apply the detailed theoretical model of micellar kinetics from part 1 of this study to the case of surfactant adsorption at a quiescent interface, i.e., to the relaxation of surface tension and adsorption after a small initial perturbation. Our goal is to understand why for some surfactant solutions the surface tension relaxes as inverse-square-root of time, 1/t(1/2), but two different expressions for the characteristic relaxation time are applicable to different cases. In addition, our aim is to clarify why for other surfactant solutions the surface tension relaxes exponentially. For this goal, we carried out a computer modeling of the adsorption process, based on the general system of equations derived in part 1. This analysis reveals the existence of four different consecutive relaxation regimes (stages) for a given micellar solution: two exponential regimes and two inverse-square-root regimes, following one after another in alternating order. Experimentally, depending on the specific surfactant and method, one usually registers only one of these regimes. Therefore, to interpret properly the data, one has to identify which of these four kinetic regimes is observed in the given experiment. Our numerical results for the relaxation of the surface tension, micelle concentration and aggregation number are presented in the form of kinetic diagrams, which reveal the stages of the relaxation process. At low micelle concentrations, "rudimentary" kinetic diagrams could be observed, which are characterized by merging of some stages. Thus, the theoretical modeling reveals a general and physically rich picture of the adsorption process. To facilitate the interpretation of experimental data, we have derived convenient theoretical expressions for the time dependence of surface tension and adsorption in each of the four regimes.

Correlation of porous and functional properties of food materials by NMR relaxometry and multivariate analysis.

PubMed

Haiduc, Adrian Marius; van Duynhoven, John

2005-02-01

The porous properties of food materials are known to determine important macroscopic parameters such as water-holding capacity and texture. In conventional approaches, understanding is built from a long process of establishing macrostructure-property relations in a rational manner. Only recently, multivariate approaches were introduced for the same purpose. The model systems used here are oil-in-water emulsions, stabilised by protein, and form complex structures, consisting of fat droplets dispersed in a porous protein phase. NMR time-domain decay curves were recorded for emulsions with varied levels of fat, protein and water. Hardness, dry matter content and water drainage were determined by classical means and analysed for correlation with the NMR data with multivariate techniques. Partial least squares can calibrate and predict these properties directly from the continuous NMR exponential decays and yields regression coefficients higher than 82%. However, the calibration coefficients themselves belong to the continuous exponential domain and do little to explain the connection between NMR data and emulsion properties. Transformation of the NMR decays into a discreet domain with non-negative least squares permits the use of multilinear regression (MLR) on the resulting amplitudes as predictors and hardness or water drainage as responses. The MLR coefficients show that hardness is highly correlated with the components that have T2 distributions of about 20 and 200 ms whereas water drainage is correlated with components that have T2 distributions around 400 and 1800 ms. These T2 distributions very likely correlate with water populations present in pores with different sizes and/or wall mobility. The results for the emulsions studied demonstrate that NMR time-domain decays can be employed to predict properties and to provide insight in the underlying microstructural features.

Comparison of least squares and exponential sine sweep methods for Parallel Hammerstein Models estimation

NASA Astrophysics Data System (ADS)

Rebillat, Marc; Schoukens, Maarten

2018-05-01

Linearity is a common assumption for many real-life systems, but in many cases the nonlinear behavior of systems cannot be ignored and must be modeled and estimated. Among the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are interesting as they are at the same time easy to interpret as well as to estimate. One way to estimate PHM relies on the fact that the estimation problem is linear in the parameters and thus that classical least squares (LS) estimation algorithms can be used. In that area, this article introduces a regularized LS estimation algorithm inspired on some of the recently developed regularized impulse response estimation techniques. Another mean to estimate PHM consists in using parametric or non-parametric exponential sine sweeps (ESS) based methods. These methods (LS and ESS) are founded on radically different mathematical backgrounds but are expected to tackle the same issue. A methodology is proposed here to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii) their robustness to noise. Tests are performed on simulated systems for several values of methods respective parameters and of signal to noise ratio. Results show that, for a given set of data points, the ESS method is less demanding in computational resources than the LS method but that it is also less accurate. Furthermore, the LS method needs parameters to be set in advance whereas the ESS method is not subject to conditioning issues and can be fully non-parametric. In summary, for a given set of data points, ESS method can provide a first, automatic, and quick overview of a nonlinear system than can guide more computationally demanding and precise methods, such as the regularized LS one proposed here.

Ion temperature gradient driven transport in tokamaks with square shaping

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

Joiner, N.; Dorland, W.

2010-06-15

Advanced tokamak schemes which may offer significant improvement to plasma confinement on the usual large aspect ratio Dee-shaped flux surface configuration are of great interest to the fusion community. One possibility is to introduce square shaping to the flux surfaces. The gyrokinetic code GS2[Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1996)] is used to study linear stability and the resulting nonlinear thermal transport of the ion temperature gradient driven (ITG) mode in tokamak equilibria with square shaping. The maximum linear growth rate of ITG modes is increased by negative squareness (diamond shaping) and reduced by positive values (square shaping).more » The dependence of thermal transport produced by saturated ITG instabilities on squareness is not as clear. The overall trend follows that of the linear instability, heat and particle fluxes increase with negative squareness and decrease with positive squareness. This is contradictory to recent experimental results [Holcomb et al., Phys. Plasmas 16, 056116 (2009)] which show a reduction in transport with negative squareness. This may be reconciled as a reduction in transport (consistent with the experiment) is observed at small negative values of the squareness parameter.« less

Microscale Synthesis, Reactions, and (Super 1)H NMR Spectroscopic Investigations of Square Planar Macrocyclic, Tetramido-N Co(III) Complexes Relevant to Green Chemistry

ERIC Educational Resources Information Center

Watson, Tanya T.; Uffelman, Erich S.; Lee, Daniel W., III; Doherty, Jonathan R.; Schulze, Carl; Burke, Amy L.; Bonnema, Kristen, R.

2004-01-01

The microscale preparation, characterization, and reactivity of a square planar Co(III) complex that has grown out of a program to introduce experiments of relevance to green chemistry into the undergraduate curriculum is presented. The given experiments illustrate the remarkable redox and aqueous acid-base stability that make the macrocycles very…

Stability Criteria Analysis for Landing Craft Utility

DTIC Science & Technology

2017-12-01

Square meter m/s Meters per Second m/s2 Meters per Second Squared n Vertical Displacement of Sea Water Free Surface n3 Ship’s Heave... Displacement n5 Ship’s Pitch Angle p(ξ) Rayleigh Distribution Probability Function POSSE Program of Ship Salvage Engineering pk...Spectrum Constant γ JONSWAP Wave Spectrum Peak Factor Γ(λ) Gamma Probability Function Δ Ship’s Displacement Δω Small Frequency

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.

Switched impulsive control of the endocrine disruptor diethylstilbestrol singular model

NASA Astrophysics Data System (ADS)

Zamani, Iman; Shafiee, Masoud; Ibeas, Asier; de la Sen, M.

2014-12-01

In this work, a switched and impulsive controller is designed to control the Endocrine Disruptor Diethylstilbestrol mechanism which is usually modeled as a singular system. Then the exponential stabilization property of the proposed switched and impulsive singular model is discussed under matrix inequalities. A design algorithm is given and applied for the physiological process of endocrine disruptor diethylstilbestrol model to illustrate the effectiveness of the results.

Comparative Studies of the Pyrolytic and Kinetic Characteristics of Maize Straw and the Seaweed Ulva pertusa

PubMed Central

Ye, Naihao; Li, Demao; Chen, Limei; Zhang, Xiaowen; Xu, Dong

2010-01-01

Seaweed has attracted considerable attention as a potential biofuel feedstock. The pyrolytic and kinetic characteristics of maize straw and the seaweed Ulva pertusa were studied and compared using heating rates of 10, 30 and 50°C min−1 under an inert atmosphere. The activation energy, and pre-exponential factors were calculated by the Flynn-Wall-Ozawa (FWO), Kissinger-Akahira-Sunose (KAS) and Popescu methods. The kinetic mechanism was deduced by the Popescu method. The results indicate that there are three stages to the pyrolysis; dehydration, primary devolatilization and residual decomposition. There were significant differences in average activation energy, thermal stability, final residuals and reaction rates between the two materials. The primary devolatilization stage of U. pertusa can be described by the Avramic-Erofeev equation (n = 3), whereas that of maize straw can be described by the Mampel Power Law (n = 2). The average activation energy of maize straw and U. pertusa were 153.0 and 148.7 KJ mol−1, respectively. The pyrolysis process of U.pertusa would be easier than maize straw. And co-firing of the two biomass may be require less external heat input and improve process stability. There were minor kinetic compensation effects between the pre-exponential factors and the activation energy. PMID:20844751

Extension of Liouville Formalism to Postinstability Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A mathematical formalism has been developed for predicting the postinstability motions of a dynamic system governed by a system of nonlinear equations and subject to initial conditions. Previously, there was no general method for prediction and mathematical modeling of postinstability behaviors (e.g., chaos and turbulence) in such a system. The formalism of nonlinear dynamics does not afford means to discriminate between stable and unstable motions: an additional stability analysis is necessary for such discrimination. However, an additional stability analysis does not suggest any modifications of a mathematical model that would enable the model to describe postinstability motions efficiently. The most important type of instability that necessitates a postinstability description is associated with positive Lyapunov exponents. Such an instability leads to exponential growth of small errors in initial conditions or, equivalently, exponential divergence of neighboring trajectories. The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Characterizing ISI and sub-threshold membrane potential distributions: Ensemble of IF neurons with random squared-noise intensity.

PubMed

Kumar, Sanjeev; Karmeshu

2018-04-01

A theoretical investigation is presented that characterizes the emerging sub-threshold membrane potential and inter-spike interval (ISI) distributions of an ensemble of IF neurons that group together and fire together. The squared-noise intensity σ 2 of the ensemble of neurons is treated as a random variable to account for the electrophysiological variations across population of nearly identical neurons. Employing superstatistical framework, both ISI distribution and sub-threshold membrane potential distribution of neuronal ensemble are obtained in terms of generalized K-distribution. The resulting distributions exhibit asymptotic behavior akin to stretched exponential family. Extensive simulations of the underlying SDE with random σ 2 are carried out. The results are found to be in excellent agreement with the analytical results. The analysis has been extended to cover the case corresponding to independent random fluctuations in drift in addition to random squared-noise intensity. The novelty of the proposed analytical investigation for the ensemble of IF neurons is that it yields closed form expressions of probability distributions in terms of generalized K-distribution. Based on a record of spiking activity of thousands of neurons, the findings of the proposed model are validated. The squared-noise intensity σ 2 of identified neurons from the data is found to follow gamma distribution. The proposed generalized K-distribution is found to be in excellent agreement with that of empirically obtained ISI distribution of neuronal ensemble. Copyright © 2018 Elsevier B.V. All rights reserved.

Specimen charging in X-ray absorption spectroscopy: correction of total electron yield data from stabilized zirconia in the energy range 250-915 eV.

PubMed

Vlachos, Dimitrios; Craven, Alan J; McComb, David W

2005-03-01

The effects of specimen charging on X-ray absorption spectroscopy using total electron yield have been investigated using powder samples of zirconia stabilized by a range of oxides. The stabilized zirconia powder was mixed with graphite to minimize the charging but significant modifications of the intensities of features in the X-ray absorption near-edge fine structure (XANES) still occurred. The time dependence of the charging was measured experimentally using a time scan, and an algorithm was developed to use this measured time dependence to correct the effects of the charging. The algorithm assumes that the system approaches the equilibrium state by an exponential decay. The corrected XANES show improved agreement with the electron energy-loss near-edge fine structure obtained from the same samples.

A multidimensional stability model for predicting shallow landslide size and shape across landscapes.

PubMed

Milledge, David G; Bellugi, Dino; McKean, Jim A; Densmore, Alexander L; Dietrich, William E

2014-11-01

The size of a shallow landslide is a fundamental control on both its hazard and geomorphic importance. Existing models are either unable to predict landslide size or are computationally intensive such that they cannot practically be applied across landscapes. We derive a model appropriate for natural slopes that is capable of predicting shallow landslide size but simple enough to be applied over entire watersheds. It accounts for lateral resistance by representing the forces acting on each margin of potential landslides using earth pressure theory and by representing root reinforcement as an exponential function of soil depth. We test our model's ability to predict failure of an observed landslide where the relevant parameters are well constrained by field data. The model predicts failure for the observed scar geometry and finds that larger or smaller conformal shapes are more stable. Numerical experiments demonstrate that friction on the boundaries of a potential landslide increases considerably the magnitude of lateral reinforcement, relative to that due to root cohesion alone. We find that there is a critical depth in both cohesive and cohesionless soils, resulting in a minimum size for failure, which is consistent with observed size-frequency distributions. Furthermore, the differential resistance on the boundaries of a potential landslide is responsible for a critical landslide shape which is longer than it is wide, consistent with observed aspect ratios. Finally, our results show that minimum size increases as approximately the square of failure surface depth, consistent with observed landslide depth-area data.

A multidimensional stability model for predicting shallow landslide size and shape across landscapes

PubMed Central

Milledge, David G; Bellugi, Dino; McKean, Jim A; Densmore, Alexander L; Dietrich, William E

2014-01-01

The size of a shallow landslide is a fundamental control on both its hazard and geomorphic importance. Existing models are either unable to predict landslide size or are computationally intensive such that they cannot practically be applied across landscapes. We derive a model appropriate for natural slopes that is capable of predicting shallow landslide size but simple enough to be applied over entire watersheds. It accounts for lateral resistance by representing the forces acting on each margin of potential landslides using earth pressure theory and by representing root reinforcement as an exponential function of soil depth. We test our model's ability to predict failure of an observed landslide where the relevant parameters are well constrained by field data. The model predicts failure for the observed scar geometry and finds that larger or smaller conformal shapes are more stable. Numerical experiments demonstrate that friction on the boundaries of a potential landslide increases considerably the magnitude of lateral reinforcement, relative to that due to root cohesion alone. We find that there is a critical depth in both cohesive and cohesionless soils, resulting in a minimum size for failure, which is consistent with observed size-frequency distributions. Furthermore, the differential resistance on the boundaries of a potential landslide is responsible for a critical landslide shape which is longer than it is wide, consistent with observed aspect ratios. Finally, our results show that minimum size increases as approximately the square of failure surface depth, consistent with observed landslide depth-area data. PMID:26213663

Least square neural network model of the crude oil blending process.

PubMed

Rubio, José de Jesús

2016-06-01

In this paper, the recursive least square algorithm is designed for the big data learning of a feedforward neural network. The proposed method as the combination of the recursive least square and feedforward neural network obtains four advantages over the alone algorithms: it requires less number of regressors, it is fast, it has the learning ability, and it is more compact. Stability, convergence, boundedness of parameters, and local minimum avoidance of the proposed technique are guaranteed. The introduced strategy is applied for the modeling of the crude oil blending process. Copyright © 2016 Elsevier Ltd. All rights reserved.

On Liapunov and Exponential Stability of Rossby-Haurwitz Waves in Invariant Sets of Perturbations

NASA Astrophysics Data System (ADS)

Skiba, Yuri N.

2018-01-01

In this work, the stability of the Rossby-Haurwitz (RH) waves from the subspace H1\\oplus Hn is considered (n≥2 ) where Hk is the subspace of the homogeneous spherical polynomials of degree k. A conservation law for arbitrary perturbations of the RH wave is derived, and all perturbations are divided into three invariant sets M-n , M0n and M+n in which the mean spectral number χ (ψ ^' }) of any perturbation ψ ^' } is less than, equal to or greater than n(n+1) , respectively. In turn, the set M0n is divided into the invariant subsets Hn and M0n{\\setminus } Hn . Quotient spaces and norms of the perturbations are introduced, a hyperbolic law for the perturbations belonging to the sets M-n and M+n is derived, and a geometric interpretation of variations in the kinetic energy of perturbations is given. It is proved that any non-zonal RH wave from H1\\oplus Hn (n≥2 ) is Liapunov unstable in the invariant set M-n . Also, it is shown that a stationary RH wave from H1\\oplus Hn may be exponentially unstable only in the invariant set M0n{\\setminus } Hn , while any perturbation of the invariant set Hn conserves its form with time and hence is neutral. Since a Legendre polynomial flow aPn(μ ) and zonal RH wave - ω μ +aPn(μ ) are particular cases of the RH waves of H1\\oplus Hn , the major part of the stability results obtained here is also true for them.

Surface properties and exponential stress relaxations of mammalian meibum films.

PubMed

Eftimov, Petar; Yokoi, Norihiko; Tonchev, Vesselin; Nencheva, Yana; Georgiev, Georgi As

2017-03-01

The surface properties of meibomian secretion (MGS), the major constituent of the tear film (TF) lipid layer, are of key importance for TF stability. The interfacial properties of canine, cMGS, and feline, fMGS, meibum films were studied using a Langmuir surface balance. These species were selected because they have blinking frequency and TF stability similar to those of humans. The sample's performance during dynamic area changes was evaluated by surface pressure (π)-area (A) isocycles and the layer structure was monitored with Brewster angle microscopy. The films' dilatational rheology was probed via the stress-relaxation technique. The animal MGS showed similar behavior both between each other and with human MGS (studied previously). They form reversible, non-collapsible, multilayer thick films. The relaxations of canine, feline, and human MGS films were well described by double exponential decay reflecting the presence of two processes: (1) fast elastic process, with characteristic time τ < 10 s and (2) slow viscous process, with τ > 100 s-emphasizing the meibum layers viscoelasticity. The temperature decrease from 35 to 25 °C resulted in decreased thickness and lateral expansion of all MGS layers accompanied with increase of the π/A hysteresis and of the elastic process contribution to π relaxation transients. Thus, MGS films of mammals with similar blinking frequency and TF stability have similar surface properties and stress relaxations unaltered by the interspecies MGS compositional variations. Such knowledge may impact the selection of animal mimics of human MGS and on a better understanding of lipid classes' impact on meibum functionality.

Soil erosion-runoff relationships: insights from laboratory studies

NASA Astrophysics Data System (ADS)

Mamedov, Amrakh; Warrington, David; Levy, Guy

2016-04-01

Understanding the processes and mechanisms affecting runoff generation and subsequent soil erosion in semi-arid regions is essential for the development of improved soil and water conservation management practices. Using a drip type laboratory rain simulator, we studied runoff and soil erosion, and the relationships between them, in 60 semi-arid region soils varying in their intrinsic properties (e.g., texture, organic matter) under differing extrinsic conditions (e.g., rain properties, and conditions prevailing in the field soil). Both runoff and soil erosion were significantly affected by the intrinsic soil and rain properties, and soil conditions within agricultural fields or watersheds. The relationship between soil erosion and runoff was stronger when the rain kinetic energy was higher rather than lower, and could be expressed either as a linear or exponential function. Linear functions applied to certain limited cases associated with conditions that enhanced soil structure stability, (e.g., slow wetting, amending with soil stabilizers, minimum tillage in clay soils, and short duration exposure to rain). Exponential functions applied to most of the cases under conditions that tended to harm soil stability (e.g., fast wetting of soils, a wide range of antecedent soil water contents and rain kinetic energies, conventional tillage, following biosolid applications, irrigation with water of poor quality, consecutive rain simulations). The established relationships between runoff and soil erosion contributed to a better understanding of the mechanisms governing overland flow and soil loss, and could assist in (i) further development of soil erosion models and research techniques, and (ii) the design of more suitable management practices for soil and water conservation.

Organic light-emitting diodes from homoleptic square planar complexes

DOEpatents

Omary, Mohammad A

2013-11-12

Homoleptic square planar complexes [M(N.LAMBDA.N).sub.2], wherein two identical N.LAMBDA.N bidentate anionic ligands are coordinated to the M(II) metal center, including bidentate square planar complexes of triazolates, possess optical and electrical properties that make them useful for a wide variety of optical and electrical devices and applications. In particular, the complexes are useful for obtaining white or monochromatic organic light-emitting diodes ("OLEDs"). Improved white organic light emitting diode ("WOLED") designs have improved efficacy and/or color stability at high brightness in single- or two-emitter white or monochrome OLEDs that utilize homoleptic square planar complexes, including bis[3,5-bis(2-pyridyl)-1,2,4-triazolato]platinum(II) ("Pt(ptp).sub.2").

Lattice distortion of square iron nitride monolayers induced by changing symmetry of substrate

NASA Astrophysics Data System (ADS)

Hattori, Takuma; Iimori, Takushi; Miyamachi, Toshio; Komori, Fumio

2018-04-01

Rectangular iron nitride monatomic layers are fabricated on the threefold symmetric Cu(111) substrate by taking advantage of the stability of the square nitride film. Two different ordered structures are observed on the Cu(111) substrate by scanning tunneling microscopy after annealing at 510 K and 580 K. Their chemical composition and lattice symmetry are investigated by x-ray photoelectron spectroscopy and low energy electron diffraction. The monolayer film prepared at 580 K is a distorted Fe2N monolayer analogous to a ferromagnetic square Fe2N monolayer with a clock reconstruction on the Cu(001) substrate. The lattice deformation of the square Fe2N monolayer is induced by using Cu(111) with threefold symmetry.

Stabilization of the Inverse Laplace Transform of Multiexponential Decay through Introduction of a Second Dimension

PubMed Central

Celik, Hasan; Bouhrara, Mustapha; Reiter, David A.; Fishbein, Kenneth W.; Spencer, Richard G.

2013-01-01

We propose a new approach to stabilizing the inverse Laplace transform of a multiexponential decay signal, a classically ill-posed problem, in the context of nuclear magnetic resonance relaxometry. The method is based on extension to a second, indirectly detected, dimension, that is, use of the established framework of two-dimensional relaxometry, followed by projection onto the desired axis. Numerical results for signals comprised of discrete T1 and T2 relaxation components and experiments performed on agarose gel phantoms are presented. We find markedly improved accuracy, and stability with respect to noise, as well as insensitivity to regularization in quantifying underlying relaxation components through use of the two-dimensional as compared to the one-dimensional inverse Laplace transform. This improvement is demonstrated separately for two different inversion algorithms, nonnegative least squares and non-linear least squares, to indicate the generalizability of this approach. These results may have wide applicability in approaches to the Fredholm integral equation of the first kind. PMID:24035004

Sznajd Opinion Dynamics with Global and Local Neighborhood

NASA Astrophysics Data System (ADS)

Schulze, Christian

In this modification of the Sznajd consensus model on the square lattice, two people of arbitrary distance who agree in their opinions convince their nearest neighbors of this opinion. Similarly to the mean field theory of Slanina and Lavicka, the times needed to reach consensus are distributed exponentially and are quite small. The width of the phase transition vanishes reciprocally to the linear lattice dimension. Advertising has effects independent of the system size. For more than two opinions, three opinions reach a consensus in roughly half of the samples, and four only rarely and only for small lattices. Up to 109 agents were simulated.

Design of sliding-mode observer for a class of uncertain neutral stochastic systems

NASA Astrophysics Data System (ADS)

Liu, Zhen; Zhao, Lin; Zhu, Quanmin; Gao, Cunchen

2017-05-01

The problem of robust ? control for a class of uncertain neutral stochastic systems (NSS) is investigated by utilising the sliding-mode observer (SMO) technique. This paper presents a novel observer and integral-type sliding-surface design, based on which a new sufficient condition guaranteeing the resultant sliding-mode dynamics (SMDs) to be mean-square exponentially stable with a prescribed level of ? performance is derived. Then, an adaptive reaching motion controller is synthesised to lead the system to the predesigned sliding surface in finite-time almost surely. Finally, two illustrative examples are exhibited to verify the validity and superiority of the developed scheme.

Gaussian process regression for geometry optimization

NASA Astrophysics Data System (ADS)

Denzel, Alexander; Kästner, Johannes

2018-03-01

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Matérn kernel and the squared exponential kernel. The Matérn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the Limited-memory Broyden-Fletcher-Goldfarb-Shanno optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps.

Revisiting the environmental Kuznets curve hypothesis in a tourism development context.

PubMed

de Vita, Glauco; Katircioglu, Salih; Altinay, Levent; Fethi, Sami; Mercan, Mehmet

2015-11-01

This study investigates empirically an extended version of the Environmental Kuznets Curve model that controls for tourism development. We find that international tourist arrivals into Turkey alongside income, squared income and energy consumption, cointegrate with CO2 emissions. Tourist arrivals, growth, and energy consumption exert a positive and significant impact on CO2 emissions in the long-run. Our results provide empirical support to EKC hypothesis showing that at exponential levels of growth, CO2 emissions decline. The findings suggest that despite the environmental degradation stemming from tourism development, policies aimed at environmental protection should not be pursued at the expense of tourism-led growth.

A Gaussian measure of quantum phase noise

NASA Technical Reports Server (NTRS)

Schleich, Wolfgang P.; Dowling, Jonathan P.

1992-01-01

We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.

Characterization of Titan III-D Acoustic Pressure Spectra by Least-Squares Fit to Theoretical Model

DTIC Science & Technology

1980-01-01

P(f) for a set value of P0 and f0" Mhe inverse transform was taken and the result multiplied by a decaying exponential which modelled the envelope of...0 FORWARD TRANSFORM C IF=1 INVERSE TRANSFORM c C M 0 XREAL AND XIMAG RETURNED AS REAL AND IMAG. FOR FORWARD Xr"RM9; C M= " " " MAGNITUDE AND PHASE...34 .. .. C (PHASE IN DEGREE9) C M=2 XREAL RETURNED AS ’PSD’ XIMAG =0. C HERE ’DSD’ MEANS SUM OF N VALUES OF XREAL = MEAN SQU\\Riz OF INPUT C C FOR INVERSE

The Homotopic Probability Distribution and the Partition Function for the Entangled System Around a Ribbon Segment Chain

NASA Astrophysics Data System (ADS)

Qian, Shang-Wu; Gu, Zhi-Yu

2001-12-01

Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution P_L^n for the winding number n and the partition function P_L of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.

The Inverse-Square Law and the Exponential Attenuation Law Used to the Shielding Calculation in Radiotherapy on a High School Level

NASA Astrophysics Data System (ADS)

de Paiva, Eduardo

2016-04-01

Every year millions of people contract cancer in the world, and according to prediction of the World Health Organization by the year 2030 there will be about 27 million new cases. Because of these figures and the resulting social and economic implications of this disease, radiotherapy, which is one form of treatment that uses ionizing radiation, has a great importance. In the classroom the teacher can introduce the subject of the use of ionizing radiation in medicine and the basic physical principles to calculate the thickness of the walls of the rooms that house ionizing radiation sources.

Neutron skyshine measurements at Fermilab.

PubMed

Cossairt, J D; Coulson, L V

1985-02-01

Neutron skyshine has been a significant source of environmental radiation exposure at many high-energy proton accelerators. A particularly troublesome source of skyshine neutrons has existed at Fermilab during operation of the 400-GeV high-energy physics program. This paper reports on several measurements of this source made with a DePangher precision long counter at large distances. The spatial distribution of the neutron skyshine can approximately be described as an inverse square law dependence multiplied by an exponential with an approximate attenuation length of 1200 +/- 300 m. The absolute magnitude of the distributions can be matched directly to the conventionally measured absorbed dose distribution near the source.

Stability and phase transition of skyrmion crystals generated by Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

El Hog, Sahbi; Bailly-Reyre, Aurélien; Diep, H. T.

2018-06-01

We generate a crystal of skyrmions in two dimensions using a Heisenberg Hamiltonian including the ferromagnetic interaction J, the Dzyaloshinskii-Moriya interaction D, and an applied magnetic field H. The ground state (GS) is determined by minimizing the interaction energy. We show that the GS is a skyrmion crystal in a region of (D, H) . The stability of this skyrmion crystalline phase at finite temperatures is shown by a study of the time-dependence of the order parameter using Monte Carlo simulations. We observe that the relaxation is very slow and follows a stretched exponential law. The skyrmion crystal phase is shown to undergo a transition to the paramagnetic state at a finite temperature.

Expression stability of two housekeeping genes (18S rRNA and G3PDH) during in vitro maturation of follicular oocytes in buffalo (Bubalus bubalis).

PubMed

Aswal, Ajay Pal Singh; Raghav, Sarvesh; De, Sachinandan; Thakur, Manish; Goswami, Surender Lal; Datta, Tirtha Kumar

2008-01-15

The present study was undertaken to evaluate the expression stability of two housekeeping genes (HKGs), 18S rRNA and G3PDH during in vitro maturation (IVM) of oocytes in buffalo, which qualifies their use as internal controls for valid qRT-PCR estimation of other oocyte transcripts. A semi quantitative RT-PCR system was used with optimised qRT-PCR parameters at exponential PCR cycle for evaluation of temporal expression pattern of these genes over 24 h of IVM. 18S rRNA was found more stable in its expression pattern than G3PDH.

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

Modeling the pressure inactivation of Escherichia coli and Salmonella typhimurium in sapote mamey ( Pouteria sapota (Jacq.) H.E. Moore & Stearn) pulp.

PubMed

Saucedo-Reyes, Daniela; Carrillo-Salazar, José A; Román-Padilla, Lizbeth; Saucedo-Veloz, Crescenciano; Reyes-Santamaría, María I; Ramírez-Gilly, Mariana; Tecante, Alberto

2018-03-01

High hydrostatic pressure inactivation kinetics of Escherichia coli ATCC 25922 and Salmonella enterica subsp. enterica serovar Typhimurium ATCC 14028 ( S. typhimurium) in a low acid mamey pulp at four pressure levels (300, 350, 400, and 450 MPa), different exposure times (0-8 min), and temperature of 25 ± 2℃ were obtained. Survival curves showed deviations from linearity in the form of a tail (upward concavity). The primary models tested were the Weibull model, the modified Gompertz equation, and the biphasic model. The Weibull model gave the best goodness of fit ( R 2 adj  > 0.956, root mean square error < 0.290) in the modeling and the lowest Akaike information criterion value. Exponential-logistic and exponential decay models, and Bigelow-type and an empirical models for b'( P) and n( P) parameters, respectively, were tested as alternative secondary models. The process validation considered the two- and one-step nonlinear regressions for making predictions of the survival fraction; both regression types provided an adequate goodness of fit and the one-step nonlinear regression clearly reduced fitting errors. The best candidate model according to the Akaike theory information, with better accuracy and more reliable predictions was the Weibull model integrated by the exponential-logistic and exponential decay secondary models as a function of time and pressure (two-step procedure) or incorporated as one equation (one-step procedure). Both mathematical expressions were used to determine the t d parameter, where the desired reductions ( 5D) (considering d = 5 ( t 5 ) as the criterion of 5 Log 10 reduction (5 D)) in both microorganisms are attainable at 400 MPa for 5.487 ± 0.488 or 5.950 ± 0.329 min, respectively, for the one- or two-step nonlinear procedure.

Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models

PubMed Central

Marias, Kostas; Lambregts, Doenja M. J.; Nikiforaki, Katerina; van Heeswijk, Miriam M.; Bakers, Frans C. H.; Beets-Tan, Regina G. H.

2017-01-01

Purpose The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Material and methods Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. Results All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. Conclusion No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior. PMID:28863161

Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models.

PubMed

Manikis, Georgios C; Marias, Kostas; Lambregts, Doenja M J; Nikiforaki, Katerina; van Heeswijk, Miriam M; Bakers, Frans C H; Beets-Tan, Regina G H; Papanikolaou, Nikolaos

2017-01-01

The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.

Breathers in a locally resonant granular chain with precompression

DOE PAGES

Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; ...

2016-09-01

Here we study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS) modulation equation. In turn, this leads us to provide analytical evidence, subsequently corroborated numerically, for the existence of two distinct types of discrete breathers related to acoustic or optical modes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b) stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on top of a non-vanishing background. Moreover, the stability and bifurcation structure of numerically computedmore » exact stationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLS equation, which is defocusing at the upper edges of the phonon bands and becomes linear at the lower edge of the optical band.« less

Effects of variable electrical conductivity and thermal conductivity on unsteady MHD free convection flow past an exponential accelerated inclined plate

NASA Astrophysics Data System (ADS)

Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.

2017-06-01

An analysis is carried out to investigate the effects of variable viscosity, thermal radiation, absorption of radiation and cross diffusion past an inclined exponential accelerated plate under the influence of variable heat and mass transfer. A set of suitable transformations has been used to obtain the non-dimensional coupled governing equations. Explicit finite difference technique has been used to solve the obtained numerical solutions of the present problem. Stability and convergence of the finite difference scheme have been carried out for this problem. Compaq Visual Fortran 6.6a has been used to calculate the numerical results. The effects of various physical parameters on the fluid velocity, temperature, concentration, coefficient of skin friction, rate of heat transfer, rate of mass transfer, streamlines and isotherms on the flow field have been presented graphically and discussed in details.

An invariability-area relationship sheds new light on the spatial scaling of ecological stability.

PubMed

Wang, Shaopeng; Loreau, Michel; Arnoldi, Jean-Francois; Fang, Jingyun; Rahman, K Abd; Tao, Shengli; de Mazancourt, Claire

2017-05-19

The spatial scaling of stability is key to understanding ecological sustainability across scales and the sensitivity of ecosystems to habitat destruction. Here we propose the invariability-area relationship (IAR) as a novel approach to investigate the spatial scaling of stability. The shape and slope of IAR are largely determined by patterns of spatial synchrony across scales. When synchrony decays exponentially with distance, IARs exhibit three phases, characterized by steeper increases in invariability at both small and large scales. Such triphasic IARs are observed for primary productivity from plot to continental scales. When synchrony decays as a power law with distance, IARs are quasilinear on a log-log scale. Such quasilinear IARs are observed for North American bird biomass at both species and community levels. The IAR provides a quantitative tool to predict the effects of habitat loss on population and ecosystem stability and to detect regime shifts in spatial ecological systems, which are goals of relevance to conservation and policy.

An Efficient Method for Studying the Stability and Dynamics of the Rotational Motions of Celestial Bodies

NASA Astrophysics Data System (ADS)

Pavlov, A. I.; Maciejewski, A. J.

2003-08-01

We use the alternative MEGNO (Mean Exponential Growth of Nearby Orbits) technique developed by Cincotta and Simo to study the stability of orbital-rotational motions for plane oscillations and three-dimensional rotations. We present a detailed numerical-analytical study of a rigid body in the case where the proper rotation of the body is synchronized with its orbital motion as 3: 2 (Mercurian-type synchronism). For plane rotations, the loss of stability of the periodic solution that corresponds to a 3: 2 resonance is shown to be soft, which should be taken into account to estimate the upper limit for the ellipticity of Mercury. In studying stable and chaotic translational-rotational motions, we point out that the MEGNO criterion can be effectively used. This criterion gives a clear picture of the resonant structures and allows the calculations to be conveniently presented in the form of the corresponding MEGNO stability maps for multidimensional systems. We developed an appropriate software package.

Comparison principle for impulsive functional differential equations with infinite delays and applications

NASA Astrophysics Data System (ADS)

Li, Xiaodi; Shen, Jianhua; Akca, Haydar; Rakkiyappan, R.

2018-04-01

We introduce the Razumikhin technique to comparison principle and establish some comparison results for impulsive functional differential equations (IFDEs) with infinite delays, where the infinite delays may be infinite time-varying delays or infinite distributed delays. The idea is, under the help of Razumikhin technique, to reduce the study of IFDEs with infinite delays to the study of scalar impulsive differential equations (IDEs) in which the solutions are easy to deal with. Based on the comparison principle, we study the qualitative properties of IFDEs with infinite delays , which include stability, asymptotic stability, exponential stability, practical stability, boundedness, etc. It should be mentioned that the developed results in this paper can be applied to IFDEs with not only infinite delays but also persistent impulsive perturbations. Moreover, even for the special cases of non-impulsive effects or/and finite delays, the criteria prove to be simpler and less conservative than some existing results. Finally, two examples are given to illustrate the effectiveness and advantages of the proposed results.

The impact of loss sensitivity on a mobile phone supply chain system stability based on the chaos theory

NASA Astrophysics Data System (ADS)

Ma, Junhai; Xie, Lei

2018-02-01

This paper, based on the China's communications and the current situation of the mobile phone industry, focuses on the stability of a supply chain system that consists of one supplier and one bounded rational retailer. We explore the influence of the decision makers' loss sensitivity and decision adjustment speed on the stability of the supply chain. It is found that when the retailer is not sensitive to the loss or adjusts decisions cautiously, the system can be stable. The single-retailer model is extended to a multi-retailer one to study the influence of competition on the system stability. The results show that the market share of each retailer does not affect the system stability when it is fixed. The decision of each retailer does not affect that of any other retailer and the system stability. We present two decision adjustment rules (;bounded rationality expectation (BRE); and "adaptive exponential smoothing (AES)") and compare their performances on the system stability, and find that the AES rule does not affect the system stability, while the BRE rule will make the system stability be sensitive to the retailers' loss sensitivity and the decision adjustment speed. We also reveal the unstable system's negative impact on the retailers' decisions and profits, to emphasize the importance to maintain the system stability.

Existence and energy decay of a nonuniform Timoshenko system with second sound

NASA Astrophysics Data System (ADS)

Hamadouche, Taklit; Messaoudi, Salim A.

2018-02-01

In this paper, we consider a linear thermoelastic Timoshenko system with variable physical parameters, where the heat conduction is given by Cattaneo's law and the coupling is via the displacement equation. We discuss the well-posedness and the regularity of solution using the semigroup theory. Moreover, we establish the exponential decay result provided that the stability function χ r(x)=0. Otherwise, we show that the solution decays polynomially.

Energy Decay and Boundary Control for Distributed Parameter Systems with Viscoelastic Damping

DTIC Science & Technology

1989-07-24

for the evolution variational 2 inequality for a rigid-visco-plastic (Bingham) fluid [4, 11-13J. Other work involved numerical and theoretical analysis...dimensional parabolic -elliptic interface problem, submitted to Quart. Appl. Math. 16. W. Desch and R. K. Miller, Exponential Stabilization of Volterra ...17 16. SUPPLEMENTARY NOTATION 17, COSATI CODES 18. SUBJECT TERMS (Continue an revemu of necessay and kdeftOi by block number) FIELD IGROUP ISUB-GROUP

Centralized Multi-Sensor Square Root Cubature Joint Probabilistic Data Association

PubMed Central

Liu, Jun; Li, Gang; Qi, Lin; Li, Yaowen; He, You

2017-01-01

This paper focuses on the tracking problem of multiple targets with multiple sensors in a nonlinear cluttered environment. To avoid Jacobian matrix computation and scaling parameter adjustment, improve numerical stability, and acquire more accurate estimated results for centralized nonlinear tracking, a novel centralized multi-sensor square root cubature joint probabilistic data association algorithm (CMSCJPDA) is proposed. Firstly, the multi-sensor tracking problem is decomposed into several single-sensor multi-target tracking problems, which are sequentially processed during the estimation. Then, in each sensor, the assignment of its measurements to target tracks is accomplished on the basis of joint probabilistic data association (JPDA), and a weighted probability fusion method with square root version of a cubature Kalman filter (SRCKF) is utilized to estimate the targets’ state. With the measurements in all sensors processed CMSCJPDA is derived and the global estimated state is achieved. Experimental results show that CMSCJPDA is superior to the state-of-the-art algorithms in the aspects of tracking accuracy, numerical stability, and computational cost, which provides a new idea to solve multi-sensor tracking problems. PMID:29113085

Centralized Multi-Sensor Square Root Cubature Joint Probabilistic Data Association.

PubMed

Liu, Yu; Liu, Jun; Li, Gang; Qi, Lin; Li, Yaowen; He, You

2017-11-05

This paper focuses on the tracking problem of multiple targets with multiple sensors in a nonlinear cluttered environment. To avoid Jacobian matrix computation and scaling parameter adjustment, improve numerical stability, and acquire more accurate estimated results for centralized nonlinear tracking, a novel centralized multi-sensor square root cubature joint probabilistic data association algorithm (CMSCJPDA) is proposed. Firstly, the multi-sensor tracking problem is decomposed into several single-sensor multi-target tracking problems, which are sequentially processed during the estimation. Then, in each sensor, the assignment of its measurements to target tracks is accomplished on the basis of joint probabilistic data association (JPDA), and a weighted probability fusion method with square root version of a cubature Kalman filter (SRCKF) is utilized to estimate the targets' state. With the measurements in all sensors processed CMSCJPDA is derived and the global estimated state is achieved. Experimental results show that CMSCJPDA is superior to the state-of-the-art algorithms in the aspects of tracking accuracy, numerical stability, and computational cost, which provides a new idea to solve multi-sensor tracking problems.

Fault-tolerant conversion between adjacent Reed-Muller quantum codes based on gauge fixing

NASA Astrophysics Data System (ADS)

Quan, Dong-Xiao; Zhu, Li-Li; Pei, Chang-Xing; Sanders, Barry C.

2018-03-01

We design forward and backward fault-tolerant conversion circuits, which convert between the Steane code and the 15-qubit Reed-Muller quantum code so as to provide a universal transversal gate set. In our method, only seven out of a total 14 code stabilizers need to be measured, and we further enhance the circuit by simplifying some stabilizers; thus, we need only to measure eight weight-4 stabilizers for one round of forward conversion and seven weight-4 stabilizers for one round of backward conversion. For conversion, we treat random single-qubit errors and their influence on syndromes of gauge operators, and our novel single-step process enables more efficient fault-tolerant conversion between these two codes. We make our method quite general by showing how to convert between any two adjacent Reed-Muller quantum codes \\overline{\\textsf{RM}}(1,m) and \\overline{\\textsf{RM}}≤ft(1,m+1\\right) , for which we need only measure stabilizers whose number scales linearly with m rather than exponentially with m obtained in previous work. We provide the explicit mathematical expression for the necessary stabilizers and the concomitant resources required.

Gas production in the Barnett Shale obeys a simple scaling theory

PubMed Central

Patzek, Tad W.; Male, Frank; Marder, Michael

2013-01-01

Natural gas from tight shale formations will provide the United States with a major source of energy over the next several decades. Estimates of gas production from these formations have mainly relied on formulas designed for wells with a different geometry. We consider the simplest model of gas production consistent with the basic physics and geometry of the extraction process. In principle, solutions of the model depend upon many parameters, but in practice and within a given gas field, all but two can be fixed at typical values, leading to a nonlinear diffusion problem we solve exactly with a scaling curve. The scaling curve production rate declines as 1 over the square root of time early on, and it later declines exponentially. This simple model provides a surprisingly accurate description of gas extraction from 8,294 wells in the United States’ oldest shale play, the Barnett Shale. There is good agreement with the scaling theory for 2,057 horizontal wells in which production started to decline exponentially in less than 10 y. The remaining 6,237 horizontal wells in our analysis are too young for us to predict when exponential decline will set in, but the model can nevertheless be used to establish lower and upper bounds on well lifetime. Finally, we obtain upper and lower bounds on the gas that will be produced by the wells in our sample, individually and in total. The estimated ultimate recovery from our sample of 8,294 wells is between 10 and 20 trillion standard cubic feet. PMID:24248376

Gas production in the Barnett Shale obeys a simple scaling theory.

PubMed

Patzek, Tad W; Male, Frank; Marder, Michael

2013-12-03

Natural gas from tight shale formations will provide the United States with a major source of energy over the next several decades. Estimates of gas production from these formations have mainly relied on formulas designed for wells with a different geometry. We consider the simplest model of gas production consistent with the basic physics and geometry of the extraction process. In principle, solutions of the model depend upon many parameters, but in practice and within a given gas field, all but two can be fixed at typical values, leading to a nonlinear diffusion problem we solve exactly with a scaling curve. The scaling curve production rate declines as 1 over the square root of time early on, and it later declines exponentially. This simple model provides a surprisingly accurate description of gas extraction from 8,294 wells in the United States' oldest shale play, the Barnett Shale. There is good agreement with the scaling theory for 2,057 horizontal wells in which production started to decline exponentially in less than 10 y. The remaining 6,237 horizontal wells in our analysis are too young for us to predict when exponential decline will set in, but the model can nevertheless be used to establish lower and upper bounds on well lifetime. Finally, we obtain upper and lower bounds on the gas that will be produced by the wells in our sample, individually and in total. The estimated ultimate recovery from our sample of 8,294 wells is between 10 and 20 trillion standard cubic feet.

Three-dimensional convection of binary mixtures in porous media.

PubMed

Umla, R; Augustin, M; Huke, B; Lücke, M

2011-11-01

We investigate convection patterns of binary mixtures with a positive separation ratio in porous media. As setup, we choose the Rayleigh-Bénard system of a fluid layer heated from below. Results are obtained by a multimode Galerkin method. Using this method, we compute square and crossroll patterns, and we analyze their structural, bifurcation, and stability properties. Evidence is provided that, for a strong enough Soret effect, both structures exist as stable forms of convection. Some of their properties are found to be similar to square and crossroll convection in the system without porous medium. However, there are also qualitative differences. For example, squares can be destabilized by oscillatory perturbations with square symmetry in porous media, and their velocity isolines are deformed in the so-called Soret regime.

Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field

DOE PAGES

Prathama, Aditya Heru; Pantano, Carlos

2017-08-09

Here, we study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin–Helmholtz configuration, show that even in the presence of surface tension, the interfacemore » is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.« less

Numerical simulation of stability and stability control of high speed compressible rotating couette flow

NASA Technical Reports Server (NTRS)

Biringen, Sedat; Hatay, Ferhat F.

1993-01-01

The nonlinear temporal evolution of disturbances in compressible flow between infinitely long, concentric cylinders is investigated through direct numerical simulations of the full, three-dimensional Navier-Stokes and energy equations. Counter-rotating cylinders separated by wide gaps are considered with supersonic velocities of the inner cylinder. Initially, the primary disturbance grows exponentially in accordance with linear stability theory. As the disturbances evolve, higher harmonics and subharmonics are generated in a cascading order eventually reaching a saturation state. Subsequent highly nonlinear stages of the evolution are governed by the interaction of the disturbance modes, particularly the axial subharmonics. Nonlinear evolution of the disturbance field is characterized by the formation of high-shear layers extending from the inner cylinder towards the center of the gap in the form of jets similar to the ejection events in transitional and turbulent wall-bounded shear flows.

Modelling and finite-time stability analysis of psoriasis pathogenesis

NASA Astrophysics Data System (ADS)

Oza, Harshal B.; Pandey, Rakesh; Roper, Daniel; Al-Nuaimi, Yusur; Spurgeon, Sarah K.; Goodfellow, Marc

2017-08-01

A new systems model of psoriasis is presented and analysed from the perspective of control theory. Cytokines are treated as actuators to the plant model that govern the cell population under the reasonable assumption that cytokine dynamics are faster than the cell population dynamics. The analysis of various equilibria is undertaken based on singular perturbation theory. Finite-time stability and stabilisation have been studied in various engineering applications where the principal paradigm uses non-Lipschitz functions of the states. A comprehensive study of the finite-time stability properties of the proposed psoriasis dynamics is carried out. It is demonstrated that the dynamics are finite-time convergent to certain equilibrium points rather than asymptotically or exponentially convergent. This feature of finite-time convergence motivates the development of a modified version of the Michaelis-Menten function, frequently used in biology. This framework is used to model cytokines as fast finite-time actuators.

Exponential parameter and tracking error convergence guarantees for adaptive controllers without persistency of excitation

NASA Astrophysics Data System (ADS)

Chowdhary, Girish; Mühlegg, Maximilian; Johnson, Eric

2014-08-01

In model reference adaptive control (MRAC) the modelling uncertainty is often assumed to be parameterised with time-invariant unknown ideal parameters. The convergence of parameters of the adaptive element to these ideal parameters is beneficial, as it guarantees exponential stability, and makes an online learned model of the system available. Most MRAC methods, however, require persistent excitation of the states to guarantee that the adaptive parameters converge to the ideal values. Enforcing PE may be resource intensive and often infeasible in practice. This paper presents theoretical analysis and illustrative examples of an adaptive control method that leverages the increasing ability to record and process data online by using specifically selected and online recorded data concurrently with instantaneous data for adaptation. It is shown that when the system uncertainty can be modelled as a combination of known nonlinear bases, simultaneous exponential tracking and parameter error convergence can be guaranteed if the system states are exciting over finite intervals such that rich data can be recorded online; PE is not required. Furthermore, the rate of convergence is directly proportional to the minimum singular value of the matrix containing online recorded data. Consequently, an online algorithm to record and forget data is presented and its effects on the resulting switched closed-loop dynamics are analysed. It is also shown that when radial basis function neural networks (NNs) are used as adaptive elements, the method guarantees exponential convergence of the NN parameters to a compact neighbourhood of their ideal values without requiring PE. Flight test results on a fixed-wing unmanned aerial vehicle demonstrate the effectiveness of the method.

Braid Entropy of Two-Dimensional Turbulence

NASA Astrophysics Data System (ADS)

Francois, Nicolas; Xia, Hua; Punzmann, Horst; Faber, Benjamin; Shats, Michael

2015-12-01

The evolving shape of material fluid lines in a flow underlies the quantitative prediction of the dissipation and material transport in many industrial and natural processes. However, collecting quantitative data on this dynamics remains an experimental challenge in particular in turbulent flows. Indeed the deformation of a fluid line, induced by its successive stretching and folding, can be difficult to determine because such description ultimately relies on often inaccessible multi-particle information. Here we report laboratory measurements in two-dimensional turbulence that offer an alternative topological viewpoint on this issue. This approach characterizes the dynamics of a braid of Lagrangian trajectories through a global measure of their entanglement. The topological length of material fluid lines can be derived from these braids. This length is found to grow exponentially with time, giving access to the braid topological entropy . The entropy increases as the square root of the turbulent kinetic energy and is directly related to the single-particle dispersion coefficient. At long times, the probability distribution of is positively skewed and shows strong exponential tails. Our results suggest that may serve as a measure of the irreversibility of turbulence based on minimal principles and sparse Lagrangian data.

PLEMT: A NOVEL PSEUDOLIKELIHOOD BASED EM TEST FOR HOMOGENEITY IN GENERALIZED EXPONENTIAL TILT MIXTURE MODELS.

PubMed

Hong, Chuan; Chen, Yong; Ning, Yang; Wang, Shuang; Wu, Hao; Carroll, Raymond J

2017-01-01

Motivated by analyses of DNA methylation data, we propose a semiparametric mixture model, namely the generalized exponential tilt mixture model, to account for heterogeneity between differentially methylated and non-differentially methylated subjects in the cancer group, and capture the differences in higher order moments (e.g. mean and variance) between subjects in cancer and normal groups. A pairwise pseudolikelihood is constructed to eliminate the unknown nuisance function. To circumvent boundary and non-identifiability problems as in parametric mixture models, we modify the pseudolikelihood by adding a penalty function. In addition, the test with simple asymptotic distribution has computational advantages compared with permutation-based test for high-dimensional genetic or epigenetic data. We propose a pseudolikelihood based expectation-maximization test, and show the proposed test follows a simple chi-squared limiting distribution. Simulation studies show that the proposed test controls Type I errors well and has better power compared to several current tests. In particular, the proposed test outperforms the commonly used tests under all simulation settings considered, especially when there are variance differences between two groups. The proposed test is applied to a real data set to identify differentially methylated sites between ovarian cancer subjects and normal subjects.

Theoretical results on fractionally integrated exponential generalized autoregressive conditional heteroskedastic processes

NASA Astrophysics Data System (ADS)

Lopes, Sílvia R. C.; Prass, Taiane S.

2014-05-01

Here we present a theoretical study on the main properties of Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedastic (FIEGARCH) processes. We analyze the conditions for the existence, the invertibility, the stationarity and the ergodicity of these processes. We prove that, if { is a FIEGARCH(p,d,q) process then, under mild conditions, { is an ARFIMA(q,d,0) with correlated innovations, that is, an autoregressive fractionally integrated moving average process. The convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes { and { are discussed. Expressions for the kurtosis and the asymmetry measures for any stationary FIEGARCH(p,d,q) process are also derived. The h-step ahead forecast for the processes {, { and { are given with their respective mean square error of forecast. The work also presents a Monte Carlo simulation study showing how to generate, estimate and forecast based on six different FIEGARCH models. The forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models (namely, ARCH-type models) and radial basis models is compared through an empirical application to Brazilian stock market exchange index.

Inventory control of raw material using silver meal heuristic method in PR. Trubus Alami Malang

NASA Astrophysics Data System (ADS)

Ikasari, D. M.; Lestari, E. R.; Prastya, E.

2018-03-01

The purpose of this study was to compare the total inventory cost calculated using the method applied by PR. Trubus Alami and Silver Meal Heuristic (SMH) method. The study was started by forecasting the cigarette demand from July 2016 to June 2017 (48 weeks) using additive decomposition forecasting method. The additive decomposition was used because it has the lowest value of Mean Abosolute Deviation (MAD) and Mean Squared Deviation (MSD) compared to other methods such as multiplicative decomposition, moving average, single exponential smoothing, and double exponential smoothing. The forcasting results was then converted as a raw material needs and further calculated using SMH method to obtain inventory cost. As expected, the result shows that the order frequency of using SMH methods was smaller than that of using the method applied by Trubus Alami. This affected the total inventory cost. The result suggests that using SMH method gave a 29.41% lower inventory cost, giving the cost different of IDR 21,290,622. The findings, is therefore, indicated that the PR. Trubus Alami should apply the SMH method if the company wants to reduce the total inventory cost.

Braid Entropy of Two-Dimensional Turbulence

PubMed Central

Francois, Nicolas; Xia, Hua; Punzmann, Horst; Faber, Benjamin; Shats, Michael

2015-01-01

The evolving shape of material fluid lines in a flow underlies the quantitative prediction of the dissipation and material transport in many industrial and natural processes. However, collecting quantitative data on this dynamics remains an experimental challenge in particular in turbulent flows. Indeed the deformation of a fluid line, induced by its successive stretching and folding, can be difficult to determine because such description ultimately relies on often inaccessible multi-particle information. Here we report laboratory measurements in two-dimensional turbulence that offer an alternative topological viewpoint on this issue. This approach characterizes the dynamics of a braid of Lagrangian trajectories through a global measure of their entanglement. The topological length of material fluid lines can be derived from these braids. This length is found to grow exponentially with time, giving access to the braid topological entropy . The entropy increases as the square root of the turbulent kinetic energy and is directly related to the single-particle dispersion coefficient. At long times, the probability distribution of is positively skewed and shows strong exponential tails. Our results suggest that may serve as a measure of the irreversibility of turbulence based on minimal principles and sparse Lagrangian data. PMID:26689261

Heterogeneous Link Weight Promotes the Cooperation in Spatial Prisoner's Dilemma

NASA Astrophysics Data System (ADS)

Ma, Zhi-Qin; Xia, Cheng-Yi; Sun, Shi-Wen; Wang, Li; Wang, Huai-Bin; Wang, Juan

The spatial structure has often been identified as a prominent mechanism that substantially promotes the cooperation level in prisoner's dilemma game. In this paper we introduce a weighting mechanism into the spatial prisoner's dilemma game to explore the cooperative behaviors on the square lattice. Here, three types of weight distributions: exponential, power-law and uniform distributions are considered, and the weight is assigned to links between players. Through large-scale numerical simulations we find, compared with the traditional spatial game, that this mechanism can largely enhance the frequency of cooperators. For most ranges of b, we find that the power-law distribution enables the highest promotion of cooperation and the uniform one leads to the lowest enhancement, whereas the exponential one lies often between them. The great improvement of cooperation can be caused by the fact that the distributional link weight yields inhomogeneous interaction strength among individuals, which can facilitate the formation of cooperative clusters to resist the defector's invasion. In addition, the impact of amplitude of the undulation of weight distribution and noise strength on cooperation is also investigated for three kinds of weight distribution. Current researches can aid in the further understanding of evolutionary cooperation in biological and social science.

A Novel Method for Age Estimation in Solar-Type Stars Through GALEX FUV Magnitudes

NASA Astrophysics Data System (ADS)

Ho, Kelly; Subramonian, Arjun; Smith, Graeme; Shouru Shieh

2018-01-01

Utilizing an inverse association known to exist between Galaxy Evolution Explorer (GALEX) far ultraviolet (FUV) magnitudes and the chromospheric activity of F, G, and K dwarfs, we explored a method of age estimation in solar-type stars through GALEX FUV magnitudes. Sample solar-type star data were collected from refereed publications and filtered by B-V and absolute visual magnitude to ensure similarities in temperature and luminosity to the Sun. We determined FUV-B and calculated a residual index Q for all the stars, using the temperature-induced upper bound on FUV-B as the fiducial. Plotting current age estimates for the stars against Q, we discovered a strong and significant association between the variables. By applying a log-linear transformation to the data to produce a strong correlation between Q and loge Age, we confirmed the association between Q and age to be exponential. Thus, least-squares regression was used to generate an exponential model relating Q to age in solar-type stars, which can be used by astronomers. The Q-method of stellar age estimation is simple and more efficient than existing spectroscopic methods and has applications to galactic archaeology and stellar chemical composition analysis.

A case study demonstration of the soil temperature extrema recovery rates after precipitation cooling at 10-cm soil depth

NASA Technical Reports Server (NTRS)

Welker, Jean Edward

1991-01-01

Since the invention of maximum and minimum thermometers in the 18th century, diurnal temperature extrema have been taken for air worldwide. At some stations, these extrema temperatures were collected at various soil depths also, and the behavior of these temperatures at a 10-cm depth at the Tifton Experimental Station in Georgia is presented. After a precipitation cooling event, the diurnal temperature maxima drop to a minimum value and then start a recovery to higher values (similar to thermal inertia). This recovery represents a measure of response to heating as a function of soil moisture and soil property. Eight different curves were fitted to a wide variety of data sets for different stations and years, and both power and exponential curves were fitted to a wide variety of data sets for different stations and years. Both power and exponential curve fits were consistently found to be statistically accurate least-square fit representations of the raw data recovery values. The predictive procedures used here were multivariate regression analyses, which are applicable to soils at a variety of depths besides the 10-cm depth presented.

Model based on GRID-derived descriptors for estimating CYP3A4 enzyme stability of potential drug candidates

NASA Astrophysics Data System (ADS)

Crivori, Patrizia; Zamora, Ismael; Speed, Bill; Orrenius, Christian; Poggesi, Italo

2004-03-01

A number of computational approaches are being proposed for an early optimization of ADME (absorption, distribution, metabolism and excretion) properties to increase the success rate in drug discovery. The present study describes the development of an in silico model able to estimate, from the three-dimensional structure of a molecule, the stability of a compound with respect to the human cytochrome P450 (CYP) 3A4 enzyme activity. Stability data were obtained by measuring the amount of unchanged compound remaining after a standardized incubation with human cDNA-expressed CYP3A4. The computational method transforms the three-dimensional molecular interaction fields (MIFs) generated from the molecular structure into descriptors (VolSurf and Almond procedures). The descriptors were correlated to the experimental metabolic stability classes by a partial least squares discriminant procedure. The model was trained using a set of 1800 compounds from the Pharmacia collection and was validated using two test sets: the first one including 825 compounds from the Pharmacia collection and the second one consisting of 20 known drugs. This model correctly predicted 75% of the first and 85% of the second test set and showed a precision above 86% to correctly select metabolically stable compounds. The model appears a valuable tool in the design of virtual libraries to bias the selection toward more stable compounds. Abbreviations: ADME - absorption, distribution, metabolism and excretion; CYP - cytochrome P450; MIFs - molecular interaction fields; HTS - high throughput screening; DDI - drug-drug interactions; 3D - three-dimensional; PCA - principal components analysis; CPCA - consensus principal components analysis; PLS - partial least squares; PLSD - partial least squares discriminant; GRIND - grid independent descriptors; GRID - software originally created and developed by Professor Peter Goodford.

μ SR studies of the extended kagome systems YBaCo4O7+δ (δ = 0 and 0.1)

NASA Astrophysics Data System (ADS)

Lee, Suheon; Lee, Wonjun; Mitchell, John; Choi, Kwang-Yong

We present a μSR study of the extended kagome systems YBaCo4O7+δ (δ = 0 and 0.1), which are made up of an alternating stacking of triangular and kagome layers. The parent material YBaCo4O7.0 undergoes a structural phase transition at 310 K, releasing geometrical frustration and thereby stabilizing an antiferromagnetically ordered state below TN = 106 K. The μSR spectra of YBaCo4O7.0 exhibit the loss of initial asymmetry and the development of a fast relaxation component below TN = 111 K. This indicates that the Co spins in the kagome planes remain in an inhomogeneous and dynamically fluctuating state down to 4 K, while the triangular spins order antiferromagnetically below TN. The nonstoichiometric YBaCo4O7.1 compound with no magnetic ordering exhibits a disparate spin dynamics between the fast cooling (10 K/min) and slow cooling (1 K/min) procedures. While the fast-cooled μSR spectra show a simple exponential decay, the slow-cooled spectra are described with a sum of a simple exponential function and a stretched exponential function. These are in agreements with the occurrence of the phase separation between interstitial oxygen-rich and poor regions in the slow-cooling measurements.

Validation of Reference Genes for Real-Time Quantitative PCR (qPCR) Analysis of Avibacterium paragallinarum.

PubMed

Wen, Shuxiang; Chen, Xiaoling; Xu, Fuzhou; Sun, Huiling

2016-01-01

Real-time quantitative reverse transcription PCR (qRT-PCR) offers a robust method for measurement of gene expression levels. Selection of reliable reference gene(s) for gene expression study is conducive to reduce variations derived from different amounts of RNA and cDNA, the efficiency of the reverse transcriptase or polymerase enzymes. Until now reference genes identified for other members of the family Pasteurellaceae have not been validated for Avibacterium paragallinarum. The aim of this study was to validate nine reference genes of serovars A, B, and C strains of A. paragallinarum in different growth phase by qRT-PCR. Three of the most widely used statistical algorithms, geNorm, NormFinder and ΔCT method were used to evaluate the expression stability of reference genes. Data analyzed by overall rankings showed that in exponential and stationary phase of serovar A, the most stable reference genes were gyrA and atpD respectively; in exponential and stationary phase of serovar B, the most stable reference genes were atpD and recN respectively; in exponential and stationary phase of serovar C, the most stable reference genes were rpoB and recN respectively. This study provides recommendations for stable endogenous control genes for use in further studies involving measurement of gene expression levels.

Antisense transcriptional interference mediates condition-specific gene repression in budding yeast.

PubMed

Nevers, Alicia; Doyen, Antonia; Malabat, Christophe; Néron, Bertrand; Kergrohen, Thomas; Jacquier, Alain; Badis, Gwenael

2018-05-18

Pervasive transcription generates many unstable non-coding transcripts in budding yeast. The transcription of such noncoding RNAs, in particular antisense RNAs (asRNAs), has been shown in a few examples to repress the expression of the associated mRNAs. Yet, such mechanism is not known to commonly contribute to the regulation of a given class of genes. Using a mutant context that stabilized pervasive transcripts, we observed that the least expressed mRNAs during the exponential phase were associated with high levels of asRNAs. These asRNAs also overlapped their corresponding gene promoters with a much higher frequency than average. Interrupting antisense transcription of a subset of genes corresponding to quiescence-enriched mRNAs restored their expression. The underlying mechanism acts in cis and involves several chromatin modifiers. Our results convey that transcription interference represses up to 30% of the 590 least expressed genes, which includes 163 genes with quiescence-enriched mRNAs. We also found that pervasive transcripts constitute a higher fraction of the transcriptome in quiescence relative to the exponential phase, consistent with gene expression itself playing an important role to suppress pervasive transcription. Accordingly, the HIS1 asRNA, normally only present in quiescence, is expressed in exponential phase upon HIS1 mRNA transcription interruption.

Scalable analysis of nonlinear systems using convex optimization

NASA Astrophysics Data System (ADS)

Papachristodoulou, Antonis

In this thesis, we investigate how convex optimization can be used to analyze different classes of nonlinear systems at various scales algorithmically. The methodology is based on the construction of appropriate Lyapunov-type certificates using sum of squares techniques. After a brief introduction on the mathematical tools that we will be using, we turn our attention to robust stability and performance analysis of systems described by Ordinary Differential Equations. A general framework for constrained systems analysis is developed, under which stability of systems with polynomial, non-polynomial vector fields and switching systems, as well estimating the region of attraction and the L2 gain can be treated in a unified manner. We apply our results to examples from biology and aerospace. We then consider systems described by Functional Differential Equations (FDEs), i.e., time-delay systems. Their main characteristic is that they are infinite dimensional, which complicates their analysis. We first show how the complete Lyapunov-Krasovskii functional can be constructed algorithmically for linear time-delay systems. Then, we concentrate on delay-independent and delay-dependent stability analysis of nonlinear FDEs using sum of squares techniques. An example from ecology is given. The scalable stability analysis of congestion control algorithms for the Internet is investigated next. The models we use result in an arbitrary interconnection of FDE subsystems, for which we require that stability holds for arbitrary delays, network topologies and link capacities. Through a constructive proof, we develop a Lyapunov functional for FAST---a recently developed network congestion control scheme---so that the Lyapunov stability properties scale with the system size. We also show how other network congestion control schemes can be analyzed in the same way. Finally, we concentrate on systems described by Partial Differential Equations. We show that axially constant perturbations of the Navier-Stokes equations for Hagen-Poiseuille flow are globally stable, even though the background noise is amplified as R3 where R is the Reynolds number, giving a 'robust yet fragile' interpretation. We also propose a sum of squares methodology for the analysis of systems described by parabolic PDEs. We conclude this work with an account for future research.

Delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing

NASA Astrophysics Data System (ADS)

Chi, Fudong; Wang, Jinting; Jin, Feng

2010-09-01

It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing (RTDHT). This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT. The exponential delay term is transferred into a rational fraction by the Padé approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique. First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure. The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness. For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay. For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable. Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.

Kernel machines for epilepsy diagnosis via EEG signal classification: a comparative study.

PubMed

Lima, Clodoaldo A M; Coelho, André L V

2011-10-01

We carry out a systematic assessment on a suite of kernel-based learning machines while coping with the task of epilepsy diagnosis through automatic electroencephalogram (EEG) signal classification. The kernel machines investigated include the standard support vector machine (SVM), the least squares SVM, the Lagrangian SVM, the smooth SVM, the proximal SVM, and the relevance vector machine. An extensive series of experiments was conducted on publicly available data, whose clinical EEG recordings were obtained from five normal subjects and five epileptic patients. The performance levels delivered by the different kernel machines are contrasted in terms of the criteria of predictive accuracy, sensitivity to the kernel function/parameter value, and sensitivity to the type of features extracted from the signal. For this purpose, 26 values for the kernel parameter (radius) of two well-known kernel functions (namely, Gaussian and exponential radial basis functions) were considered as well as 21 types of features extracted from the EEG signal, including statistical values derived from the discrete wavelet transform, Lyapunov exponents, and combinations thereof. We first quantitatively assess the impact of the choice of the wavelet basis on the quality of the features extracted. Four wavelet basis functions were considered in this study. Then, we provide the average accuracy (i.e., cross-validation error) values delivered by 252 kernel machine configurations; in particular, 40%/35% of the best-calibrated models of the standard and least squares SVMs reached 100% accuracy rate for the two kernel functions considered. Moreover, we show the sensitivity profiles exhibited by a large sample of the configurations whereby one can visually inspect their levels of sensitiveness to the type of feature and to the kernel function/parameter value. Overall, the results evidence that all kernel machines are competitive in terms of accuracy, with the standard and least squares SVMs prevailing more consistently. Moreover, the choice of the kernel function and parameter value as well as the choice of the feature extractor are critical decisions to be taken, albeit the choice of the wavelet family seems not to be so relevant. Also, the statistical values calculated over the Lyapunov exponents were good sources of signal representation, but not as informative as their wavelet counterparts. Finally, a typical sensitivity profile has emerged among all types of machines, involving some regions of stability separated by zones of sharp variation, with some kernel parameter values clearly associated with better accuracy rates (zones of optimality). Copyright © 2011 Elsevier B.V. All rights reserved.

Growth rate for blackhole instabilities

NASA Astrophysics Data System (ADS)

Prabhu, Kartik; Wald, Robert

2015-04-01

Hollands and Wald showed that dynamic stability of stationary axisymmetric black holes is equivalent to positivity of canonical energy on a space of linearised axisymmetric perturbations satisfying certain boundary and gauge conditions. Using a reflection isometry of the background, we split the energy into kinetic and potential parts. We show that the kinetic energy is positive. In the case that potential energy is negative, we show existence of exponentially growing perturbations and further obtain a variational formula for the growth rate.

Stability of infinite derivative Abelian Higgs models

NASA Astrophysics Data System (ADS)

Ghoshal, Anish; Mazumdar, Anupam; Okada, Nobuchika; Villalba, Desmond

2018-04-01

Motivated by the stringy effects by modifying the local kinetic term of an Abelian Higgs field by the Gaussian kinetic term, we show that the Higgs field does not possess any instability; the Yukawa coupling between the scalar and the fermion, the gauge coupling, and the self interaction of the Higgs yields exponentially suppressed running at high energies, showing that such class of theory never suffers from vacuum instability. We briefly discuss its implications for the early Universe cosmology.

Stochastic processes in cosmology

NASA Astrophysics Data System (ADS)

Cáceres, Manuel O.; Diaz, Mario C.; Pullin, Jorge A.

1987-08-01

The behavior of a radiation filled de Sitter universe in which the equation of state is perturbed by a stochastic term is studied. The corresponding two-dimensional Fokker-Planck equation is solved. The finiteness of the cosmological constant appears to be a necessary condition for the stability of the model which undergoes an exponentially expanding state. Present address: Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Laprida 854, 5000 Códoba, Argentina.

Punctuated evolution and robustness in morphogenesis

PubMed Central

Grigoriev, D.; Reinitz, J.; Vakulenko, S.; Weber, A.

2014-01-01

This paper presents an analytic approach to the pattern stability and evolution problem in morphogenesis. The approach used here is based on the ideas from the gene and neural network theory. We assume that gene networks contain a number of small groups of genes (called hubs) controlling morphogenesis process. Hub genes represent an important element of gene network architecture and their existence is empirically confirmed. We show that hubs can stabilize morphogenetic pattern and accelerate the morphogenesis. The hub activity exhibits an abrupt change depending on the mutation frequency. When the mutation frequency is small, these hubs suppress all mutations and gene product concentrations do not change, thus, the pattern is stable. When the environmental pressure increases and the population needs new genotypes, the genetic drift and other effects increase the mutation frequency. For the frequencies that are larger than a critical amount the hubs turn off; and as a result, many mutations can affect phenotype. This effect can serve as an engine for evolution. We show that this engine is very effective: the evolution acceleration is an exponential function of gene redundancy. Finally, we show that the Eldredge-Gould concept of punctuated evolution results from the network architecture, which provides fast evolution, control of evolvability, and pattern robustness. To describe analytically the effect of exponential acceleration, we use mathematical methods developed recently for hard combinatorial problems, in particular, for so-called k-SAT problem, and numerical simulations. PMID:24996115

Nature of the wiggle instability of galactic spiral shocks

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

Kim, Woong-Tae; Kim, Yonghwi; Kim, Jeong-Gyu, E-mail: wkim@astro.snu.ac.kr, E-mail: kimyh@astro.snu.ac.kr, E-mail: jgkim@astro.snu.ac.kr

Gas in disk galaxies interacts nonlinearly with an underlying stellar spiral potential to form galactic spiral shocks. While numerical simulations typically show that spiral shocks are unstable to wiggle instability (WI) even in the absence of magnetic fields and self-gravity, its physical nature has remained uncertain. To clarify the mechanism behind the WI, we conduct a normal-mode linear stability analysis and nonlinear simulations assuming that the disk is isothermal and infinitesimally thin. We find that the WI is physical, originating from the generation of potential vorticity at a deformed shock front, rather than Kelvin-Helmholtz instabilities as previously thought. Since gasmore » in galaxy rotation periodically passes through the shocks multiple times, the potential vorticity can accumulate successively, setting up a normal mode that grows exponentially with time. Eigenfunctions of the WI decay exponentially downstream from the shock front. Both shock compression of acoustic waves and a discontinuity of shear across the shock stabilize the WI. The wavelength and growth time of the WI depend on the arm strength quite sensitively. When the stellar-arm forcing is moderate at 5%, the wavelength of the most unstable mode is about 0.07 times the arm-to-arm spacing, with the growth rate comparable to the orbital angular frequency, which is found to be in good agreement with the results of numerical simulations.« less

On the Nonlinear Stability of Plane Parallel Shear Flow in a Coplanar Magnetic Field

NASA Astrophysics Data System (ADS)

Xu, Lanxi; Lan, Wanli

2017-12-01

Lyapunov direct method has been used to study the nonlinear stability of laminar flow between two parallel planes in the presence of a coplanar magnetic field for streamwise perturbations with stress-free boundary planes. Two Lyapunov functions are defined. By means of the first, it is proved that the transverse components of the perturbations decay unconditionally and asymptotically to zero for all Reynolds numbers and magnetic Reynolds numbers. By means of the second, it is showed that the other components of the perturbations decay conditionally and exponentially to zero for all Reynolds numbers and the magnetic Reynolds numbers below π ^2/2M, where M is the maximum of the absolute value of the velocity field of the laminar flow.

Complete stability of delayed recurrent neural networks with Gaussian activation functions.

PubMed

Liu, Peng; Zeng, Zhigang; Wang, Jun

2017-01-01

This paper addresses the complete stability of delayed recurrent neural networks with Gaussian activation functions. By means of the geometrical properties of Gaussian function and algebraic properties of nonsingular M-matrix, some sufficient conditions are obtained to ensure that for an n-neuron neural network, there are exactly 3 k equilibrium points with 0≤k≤n, among which 2 k and 3 k -2 k equilibrium points are locally exponentially stable and unstable, respectively. Moreover, it concludes that all the states converge to one of the equilibrium points; i.e., the neural networks are completely stable. The derived conditions herein can be easily tested. Finally, a numerical example is given to illustrate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Groundwater dynamics in a two-dimensional aquifer

NASA Astrophysics Data System (ADS)

Jules, Valentin; Devauchelle, Olivier; Lajeunesse, Eric

2017-11-01

During a rain event, water infiltrates into the ground where it flows slowly towards a river. The time scale and the geometry of this flow control the chemical composition and the discharge of the river. We use a tank filled with glass beads to simulate this process in a simplified laboratory experiment. A sprinkler pipe generates rain, which infiltrates into the porous material. Groundwater exits this laboratory aquifer through a side of the tank. Guérin et al. (2014) investigated the case of a quasi-horizontal flow. In nature, however, groundwater often follows non-horizontal flowlines. To create a vertical flow, we place the outlet of our experiment high above its bottom. We find that, during rainfall, the discharge Q increases as the rainfall rate R times the square root of time t (Q Rt 1 / 2). This laboratory aquifer thus responds linearly to the forcing. However, long after the rain has stopped, the discharge decreases as the inverse square of time (Q t-2), although linear systems of finite size typically relax exponentially. We investigate this surprising behavior using a combination of complex analysis and numerical methods.

[Restoration filtering based on projection power spectrum for single-photon emission computed tomography].

PubMed

Kubo, N

1995-04-01

To improve the quality of single-photon emission computed tomographic (SPECT) images, a restoration filter has been developed. This filter was designed according to practical "least squares filter" theory. It is necessary to know the object power spectrum and the noise power spectrum. The power spectrum is estimated from the power spectrum of a projection, when the high-frequency power spectrum of a projection is adequately approximated as a polynomial exponential expression. A study of the restoration with the filter based on a projection power spectrum was conducted, and compared with that of the "Butterworth" filtering method (cut-off frequency of 0.15 cycles/pixel), and "Wiener" filtering (signal-to-noise power spectrum ratio was a constant). Normalized mean-squared errors (NMSE) of the phantom, two line sources located in a 99mTc filled cylinder, were used. NMSE of the "Butterworth" filter, "Wiener" filter, and filtering based on a power spectrum were 0.77, 0.83, and 0.76 respectively. Clinically, brain SPECT images utilizing this new restoration filter improved the contrast. Thus, this filter may be useful in diagnosis of SPECT images.

Diffusion of chains in a periodic potential

NASA Astrophysics Data System (ADS)

Terranova, G. R.; Mártin, H. O.; Aldao, C. M.

2017-09-01

We studied the diffusion of 1D rigid chains in a square wave potential of period T. We considered chains of type A (composed of N particles A) and chains of type A-B (composed of N/2 particles A and N/2 particles B). The square wave potential represents domains, a lamellar structure observed for block copolymers, in which the repulsive δ energy between each A particle (B particle) of the chain and B particles (A particles) of the medium where the chains diffuse. From Monte Carlo simulations and analytical results it is found that the normalized diffusivity D, for N\\ll T , presents a universal behavior as a function of X  =  Nδ for chains of type A and X  =  (Nδ  -  lnT 2) for chains of type A-B, with and exponential decay for large values of X. For fixed values of δ and T, D is a periodic function of N with period T and 2T for chains of type A and type A-B, respectively.

Phase stability in the two-dimensional anisotropic boson Hubbard Hamiltonian

DOE PAGES

Ying, T.; Batrouni, G. G.; Rousseau, V. G.; ...

2013-05-15

The two dimensional square lattice hard-core boson Hubbard model with near neighbor interactions has a ‘checkerboard’ charge density wave insulating phase at half-filling and sufficiently large intersite repulsion. When doped, rather than forming a supersolid phase in which long range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near neighbor repulsion might similarly stabilize the square lattice supersolid. Lastly, by consideringmore » the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the ˆx and ˆy directions, we conclude that phase separation still occurs.« less

Finite-temperature mechanical instability in disordered lattices.

PubMed

Zhang, Leyou; Mao, Xiaoming

2016-02-01

Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered systems. We use this theory to study two disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice. These two lattices belong to two different universality classes as they approach mechanical instability at T=0. We show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as G∼T(1/2), whereas the square lattice shows G∼T(2/3). We discuss generic scaling laws for finite-T mechanical instabilities and relate them to experimental systems.

Steering Concept of a 2-Blade Heliogyro Solar Sail Spacecraft

NASA Technical Reports Server (NTRS)

Wiwattananon, Peerawan; Bryant, Robert G.

2017-01-01

Solar sails can be classified into two groups based on their method of stabilization: 1) truss supported, and 2) centrifugally (spin) supported. The truss configuration requires masts or booms to deploy, support, and rigidize the sails whereas the spin type uses the spacecraft’s centrifugal force to deploy and stabilize the sails. The truss-supported type sail has a scaling limitation because as the sail area gets larger, the sail is increasingly more difficult to make and stow: the masts and booms get heavier, occupying more volume, and have increased risk during deployment. This major disadvantage limits the size of the sail area. The spin type comes in two configurations: 1) spinning square/disk sail and 2) heliogyro sail. This spinning square/disk sail architecture suffers the same sail area limitation as the truss-supported sail.

Estimation of gloss from rough surface parameters

NASA Astrophysics Data System (ADS)

Simonsen, Ingve; Larsen, Åge G.; Andreassen, Erik; Ommundsen, Espen; Nord-Varhaug, Katrin

2005-12-01

Gloss is a quantity used in the optical industry to quantify and categorize materials according to how well they scatter light specularly. With the aid of phase perturbation theory, we derive an approximate expression for this quantity for a one-dimensional randomly rough surface. It is demonstrated that gloss depends in an exponential way on two dimensionless quantities that are associated with the surface randomness: the root-mean-square roughness times the perpendicular momentum transfer for the specular direction, and a correlation function dependent factor times a lateral momentum variable associated with the collection angle. Rigorous Monte Carlo simulations are used to access the quality of this approximation, and good agreement is observed over large regions of parameter space.

Controlling dynamical entanglement in a Josephson tunneling junction

NASA Astrophysics Data System (ADS)

Ziegler, K.

2017-12-01

We analyze the evolution of an entangled many-body state in a Josephson tunneling junction and its dependence on the number of bosons and interaction strength. A N00N state, which is a superposition of two complementary Fock states, appears in the evolution with sufficient probability only for a moderate many-body interaction on an intermediate time scale. This time scale is inversely proportional to the tunneling rate. Many-body interaction strongly supports entanglement: The probability for creating an entangled state decays exponentially with the number of particles without many-body interaction, whereas it decays only like the inverse square root of the number of particles in the presence of many-body interaction.

Quantum algorithm for support matrix machines

NASA Astrophysics Data System (ADS)

Duan, Bojia; Yuan, Jiabin; Liu, Ying; Li, Dan

2017-09-01

We propose a quantum algorithm for support matrix machines (SMMs) that efficiently addresses an image classification problem by introducing a least-squares reformulation. This algorithm consists of two core subroutines: a quantum matrix inversion (Harrow-Hassidim-Lloyd, HHL) algorithm and a quantum singular value thresholding (QSVT) algorithm. The two algorithms can be implemented on a universal quantum computer with complexity O[log(npq) ] and O[log(pq)], respectively, where n is the number of the training data and p q is the size of the feature space. By iterating the algorithms, we can find the parameters for the SMM classfication model. Our analysis shows that both HHL and QSVT algorithms achieve an exponential increase of speed over their classical counterparts.

A recursive solution for a fading memory filter derived from Kalman filter theory

NASA Technical Reports Server (NTRS)

Statman, J. I.

1986-01-01

A simple recursive solution for a class of fading memory tracking filters is presented. A fading memory filter provides estimates of filter states based on past measurements, similar to a traditional Kalman filter. Unlike a Kalman filter, an exponentially decaying weight is applied to older measurements, discounting their effect on present state estimates. It is shown that Kalman filters and fading memory filters are closely related solutions to a general least squares estimator problem. Closed form filter transfer functions are derived for a time invariant, steady state, fading memory filter. These can be applied in loop filter implementation of the Deep Space Network (DSN) Advanced Receiver carrier phase locked loop (PLL).

Optimization of power systems with voltage security constraints

NASA Astrophysics Data System (ADS)

Rosehart, William Daniel

As open access market principles are applied to power systems, significant changes in their operation and control are occurring. In the new marketplace, power systems are operating under higher loading conditions as market influences demand greater attention to operating cost versus stability margins. Since stability continues to be a basic requirement in the operation of any power system, new tools are being considered to analyze the effect of stability on the operating cost of the system, so that system stability can be incorporated into the costs of operating the system. In this thesis, new optimal power flow (OPF) formulations are proposed based on multi-objective methodologies to optimize active and reactive power dispatch while maximizing voltage security in power systems. The effects of minimizing operating costs, minimizing reactive power generation and/or maximizing voltage stability margins are analyzed. Results obtained using the proposed Voltage Stability Constrained OPF formulations are compared and analyzed to suggest possible ways of costing voltage security in power systems. When considering voltage stability margins the importance of system modeling becomes critical, since it has been demonstrated, based on bifurcation analysis, that modeling can have a significant effect of the behavior of power systems, especially at high loading levels. Therefore, this thesis also examines the effects of detailed generator models and several exponential load models. Furthermore, because of its influence on voltage stability, a Static Var Compensator model is also incorporated into the optimization problems.

A new finite element formulation for computational fluid dynamics. IX - Fourier analysis of space-time Galerkin/least-squares algorithms

NASA Technical Reports Server (NTRS)

Shakib, Farzin; Hughes, Thomas J. R.

1991-01-01

A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.

Generation of dual-wavelength square pulse in a figure-eight erbium-doped fiber laser with ultra-large net-anomalous dispersion.

PubMed

Shao, Zhihua; Qiao, Xueguang; Rong, Qiangzhou; Su, Dan

2015-08-01

A type of wave-breaking-free mode-locked dual-wavelength square pulse was experimentally observed in a figure-eight erbium-doped fiber laser with ultra-large net-anomalous dispersion. A 2.7 km long single-mode fiber (SMF) was incorporated as a nonlinear optical loop mirror (NOLM) and provided largely nonlinear phase accumulation and anomalous dispersion, which enhanced the four-wave-mixing effect to improve the stability of the dual-wavelength operation. In the NOLM, the long SMF with small birefringence supported the Sagnac interference as a filter to manage the dual-wavelength lasing. The dual-wavelength operation was made switchable by adjusting the intra-cavity polarization loss and phase delay corresponding to two square pulses. When the pump power was increased, the duration of the square pulse increased continuously while the peak pulse power gradually decreased. This square-type pulse can potentially be utilized for signal transmission and sensing.

Low frequency ac waveform generator

DOEpatents

Bilharz, O.W.

1983-11-22

Low frequency sine, cosine, triangle and square waves are synthesized in circuitry which allows variation in the waveform amplitude and frequency while exhibiting good stability and without requiring significant stablization time. A triangle waveform is formed by a ramped integration process controlled by a saturation amplifier circuit which produces the necessary hysteresis for the triangle waveform. The output of the saturation circuit is tapped to produce the square waveform. The sine waveform is synthesized by taking the absolute value of the triangular waveform, raising this absolute value to a predetermined power, multiplying the raised absolute value of the triangle wave with the triangle wave itself and properly scaling the resultant waveform and subtracting it from the triangular waveform to a predetermined power and adding the squared waveform raised to the predetermined power with a DC reference and subtracting the squared waveform therefrom, with all waveforms properly scaled. The resultant waveform is then multiplied with a square wave in order to correct the polarity and produce the resultant cosine waveform.

Design of robust reliable control for T-S fuzzy Markovian jumping delayed neutral type neural networks with probabilistic actuator faults and leakage delays: An event-triggered communication scheme.

PubMed

Syed Ali, M; Vadivel, R; Saravanakumar, R

2018-06-01

This study examines the problem of robust reliable control for Takagi-Sugeno (T-S) fuzzy Markovian jumping delayed neural networks with probabilistic actuator faults and leakage terms. An event-triggered communication scheme. First, the randomly occurring actuator faults and their failures rates are governed by two sets of unrelated random variables satisfying certain probabilistic failures of every actuator, new type of distribution based event triggered fault model is proposed, which utilize the effect of transmission delay. Second, Takagi-Sugeno (T-S) fuzzy model is adopted for the neural networks and the randomness of actuators failures is modeled in a Markov jump model framework. Third, to guarantee the considered closed-loop system is exponential mean square stable with a prescribed reliable control performance, a Markov jump event-triggered scheme is designed in this paper, which is the main purpose of our study. Fourth, by constructing appropriate Lyapunov-Krasovskii functional, employing Newton-Leibniz formulation and integral inequalities, several delay-dependent criteria for the solvability of the addressed problem are derived. The obtained stability criteria are stated in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones, among them one example was supported by real-life application of the benchmark problem. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Efficient Levenberg-Marquardt minimization of the maximum likelihood estimator for Poisson deviates

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

Laurence, T; Chromy, B

2009-11-10

Histograms of counted events are Poisson distributed, but are typically fitted without justification using nonlinear least squares fitting. The more appropriate maximum likelihood estimator (MLE) for Poisson distributed data is seldom used. We extend the use of the Levenberg-Marquardt algorithm commonly used for nonlinear least squares minimization for use with the MLE for Poisson distributed data. In so doing, we remove any excuse for not using this more appropriate MLE. We demonstrate the use of the algorithm and the superior performance of the MLE using simulations and experiments in the context of fluorescence lifetime imaging. Scientists commonly form histograms ofmore » counted events from their data, and extract parameters by fitting to a specified model. Assuming that the probability of occurrence for each bin is small, event counts in the histogram bins will be distributed according to the Poisson distribution. We develop here an efficient algorithm for fitting event counting histograms using the maximum likelihood estimator (MLE) for Poisson distributed data, rather than the non-linear least squares measure. This algorithm is a simple extension of the common Levenberg-Marquardt (L-M) algorithm, is simple to implement, quick and robust. Fitting using a least squares measure is most common, but it is the maximum likelihood estimator only for Gaussian-distributed data. Non-linear least squares methods may be applied to event counting histograms in cases where the number of events is very large, so that the Poisson distribution is well approximated by a Gaussian. However, it is not easy to satisfy this criterion in practice - which requires a large number of events. It has been well-known for years that least squares procedures lead to biased results when applied to Poisson-distributed data; a recent paper providing extensive characterization of these biases in exponential fitting is given. The more appropriate measure based on the maximum likelihood estimator (MLE) for the Poisson distribution is also well known, but has not become generally used. This is primarily because, in contrast to non-linear least squares fitting, there has been no quick, robust, and general fitting method. In the field of fluorescence lifetime spectroscopy and imaging, there have been some efforts to use this estimator through minimization routines such as Nelder-Mead optimization, exhaustive line searches, and Gauss-Newton minimization. Minimization based on specific one- or multi-exponential models has been used to obtain quick results, but this procedure does not allow the incorporation of the instrument response, and is not generally applicable to models found in other fields. Methods for using the MLE for Poisson-distributed data have been published by the wider spectroscopic community, including iterative minimization schemes based on Gauss-Newton minimization. The slow acceptance of these procedures for fitting event counting histograms may also be explained by the use of the ubiquitous, fast Levenberg-Marquardt (L-M) fitting procedure for fitting non-linear models using least squares fitting (simple searches obtain {approx}10000 references - this doesn't include those who use it, but don't know they are using it). The benefits of L-M include a seamless transition between Gauss-Newton minimization and downward gradient minimization through the use of a regularization parameter. This transition is desirable because Gauss-Newton methods converge quickly, but only within a limited domain of convergence; on the other hand the downward gradient methods have a much wider domain of convergence, but converge extremely slowly nearer the minimum. L-M has the advantages of both procedures: relative insensitivity to initial parameters and rapid convergence. Scientists, when wanting an answer quickly, will fit data using L-M, get an answer, and move on. Only those that are aware of the bias issues will bother to fit using the more appropriate MLE for Poisson deviates. However, since there is a simple, analytical formula for the appropriate MLE measure for Poisson deviates, it is inexcusable that least squares estimators are used almost exclusively when fitting event counting histograms. There have been ways found to use successive non-linear least squares fitting to obtain similarly unbiased results, but this procedure is justified by simulation, must be re-tested when conditions change significantly, and requires two successive fits. There is a great need for a fitting routine for the MLE estimator for Poisson deviates that has convergence domains and rates comparable to the non-linear least squares L-M fitting. We show in this report that a simple way to achieve that goal is to use the L-M fitting procedure not to minimize the least squares measure, but the MLE for Poisson deviates.« less

Rimonabant reduces the essential value of food in the genetically obese Zucker rat: an exponential demand analysis.

PubMed

Rasmussen, Erin B; Reilly, William; Buckley, Jessica; Boomhower, Steven R

2012-02-01

Research on free-food intake suggests that cannabinoids are implicated in the regulation of feeding. Few studies, however, have characterized how environmental factors that affect food procurement interact with cannabinoid drugs that reduce food intake. Demand analysis provides a framework to understand how cannabinoid blockers, such as rimonabant, interact with effort in reducing demand for food. The present study examined the effects rimonabant had on demand for sucrose in obese Zucker rats when effort to obtain food varied and characterized the data using the exponential ("essential value") model of demand. Twenty-nine male (15 lean, 14 obese) Zucker rats lever-pressed under eight fixed ratio (FR) schedules of sucrose reinforcement, in which the number of lever-presses to gain access to a single sucrose pellet varied between 1 and 300. After behavior stabilized under each FR schedule, acute doses of rimonabant (1-10mg/kg) were administered prior to some sessions. The number of food reinforcers and responses in each condition was averaged and the exponential and linear demand equations were fit to the data. These demand equations quantify the value of a reinforcer by its sensitivity to price (FR) increases. Under vehicle conditions, obese Zucker rats consumed more sucrose pellets than leans at smaller fixed ratios; however, they were equally sensitive to price increases with both models of demand. Rimonabant dose-dependently reduced reinforcers and responses for lean and obese rats across all FR schedules. Data from the exponential analysis suggest that rimonabant dose-dependently increased elasticity, i.e., reduced the essential value of sucrose, a finding that is consistent with graphical depictions of normalized demand curves. Copyright © 2011 Elsevier Inc. All rights reserved.

Spectral Cauchy Characteristic Extraction: Gravitational Waves and Gauge Free News

NASA Astrophysics Data System (ADS)

Handmer, Casey; Szilagyi, Bela; Winicour, Jeff

2015-04-01

We present a fast, accurate spectral algorithm for the characteristic evolution of the full non-linear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate how spectral Cauchy characteristic extraction produces gravitational News without confounding gauge effects. We explain several numerical innovations and demonstrate speed, stability, accuracy, exponential convergence, and consistency with existing methods. We highlight its capability to deliver physical insights in the study of black hole binaries.

On the stabilization of viscoelastic laminated beams with interfacial slip

NASA Astrophysics Data System (ADS)

Mustafa, Muhammad I.

2018-04-01

In this paper, we consider a viscoelastic laminated beam model. This structure is given by two identical uniform layers on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. We use viscoelastic damping with general assumptions on the relaxation function and establish explicit energy decay result from which we can recover the optimal exponential and polynomial rates. Our result generalizes the earlier related results in the literature.

Multiple μ-stability of neural networks with unbounded time-varying delays.

PubMed

Wang, Lili; Chen, Tianping

2014-05-01

In this paper, we are concerned with a class of recurrent neural networks with unbounded time-varying delays. Based on the geometrical configuration of activation functions, the phase space R(n) can be divided into several Φη-type subsets. Accordingly, a new set of regions Ωη are proposed, and rigorous mathematical analysis is provided to derive the existence of equilibrium point and its local μ-stability in each Ωη. It concludes that the n-dimensional neural networks can exhibit at least 3(n) equilibrium points and 2(n) of them are μ-stable. Furthermore, due to the compatible property, a set of new conditions are presented to address the dynamics in the remaining 3(n)-2(n) subset regions. As direct applications of these results, we can get some criteria on the multiple exponential stability, multiple power stability, multiple log-stability, multiple log-log-stability and so on. In addition, the approach and results can also be extended to the neural networks with K-level nonlinear activation functions and unbounded time-varying delays, in which there can store (2K+1)(n) equilibrium points, (K+1)(n) of them are locally μ-stable. Numerical examples are given to illustrate the effectiveness of our results. Copyright © 2014 Elsevier Ltd. All rights reserved.

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.

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

Estimating Distances from Parallaxes. II. Performance of Bayesian Distance Estimators on a Gaia-like Catalogue

NASA Astrophysics Data System (ADS)

Astraatmadja, Tri L.; Bailer-Jones, Coryn A. L.

2016-12-01

Estimating a distance by inverting a parallax is only valid in the absence of noise. As most stars in the Gaia catalog will have non-negligible fractional parallax errors, we must treat distance estimation as a constrained inference problem. Here we investigate the performance of various priors for estimating distances, using a simulated Gaia catalog of one billion stars. We use three minimalist, isotropic priors, as well an anisotropic prior derived from the observability of stars in a Milky Way model. The two priors that assume a uniform distribution of stars—either in distance or in space density—give poor results: The root mean square fractional distance error, {f}{rms}, grows far in excess of 100% once the fractional parallax error, {f}{true}, is larger than 0.1. A prior assuming an exponentially decreasing space density with increasing distance performs well once its single parameter—the scale length— has been set to an appropriate value: {f}{rms} is roughly equal to {f}{true} for {f}{true}\\lt 0.4, yet does not increase further as {f}{true} increases up to to 1.0. The Milky Way prior performs well except toward the Galactic center, due to a mismatch with the (simulated) data. Such mismatches will be inevitable (and remain unknown) in real applications, and can produce large errors. We therefore suggest adopting the simpler exponentially decreasing space density prior, which is also less time-consuming to compute. Including Gaia photometry improves the distance estimation significantly for both the Milky Way and exponentially decreasing space density prior, yet doing so requires additional assumptions about the physical nature of stars.

Deriving sulfamethoxazole dissipation endpoints in pasture soils using first order and biphasic kinetic models.

PubMed

Srinivasan, Prakash; Sarmah, Ajit K; Rohan, Maheswaran

2014-08-01

Single first-order (SFO) kinetic model is often used to derive the dissipation endpoints of an organic chemical in soil. This model is used due to its simplicity and requirement by regulatory agencies. However, using the SFO model for all types of decay pattern could lead to under- or overestimation of dissipation endpoints when the deviation from first-order is significant. In this study the performance of three biphasic kinetic models - bi-exponential decay (BEXP), first-order double exponential decay (FODED), and first-order two-compartment (FOTC) models was evaluated using dissipation datasets of sulfamethoxazole (SMO) antibiotic in three different soils under varying concentration, depth, temperature, and sterile conditions. Corresponding 50% (DT50) and 90% (DT90) dissipation times for the antibiotics were numerically obtained and compared against those obtained using the SFO model. The fit of each model to the measured values was evaluated based on an array of statistical measures such as coefficient of determination (R(2)adj), root mean square error (RMSE), chi-square (χ(2)) test at 1% significance, Bayesian Information Criteria (BIC) and % model error. Box-whisker residual plots were also used to compare the performance of each model to the measured datasets. The antibiotic dissipation was successfully predicted by all four models. However, the nonlinear biphasic models improved the goodness-of-fit parameters for all datasets. Deviations from datasets were also often less evident with the biphasic models. The fits of FOTC and FODED models for SMO dissipation datasets were identical in most cases, and were found to be superior to the BEXP model. Among the biphasic models, the FOTC model was found to be the most suitable for obtaining the endpoints and could provide a mechanistic explanation for SMO dissipation in the soils. Copyright © 2014 Elsevier B.V. All rights reserved.

Squared ligament of the elbow: anatomy and contribution to forearm stability.

PubMed

Otayek, Salma; Tayeb, Abd-el-Kader Ait; Assabah, Bouchra; Viard, Brice; Dayan, Romain; Lazure, Thierry; Soubeyrand, Marc

2016-03-01

The present study describes the macroscopic and microscopic features of the squared ligament of the elbow (SLE). In addition, the SLE biomechanical behavior and contribution to the forearm stability were also examined. Ten forearms from freshly frozen cadavers were used for this work. Each forearm was mounted in an experimental frame for quantification of longitudinal and transverse stability. Macroscopic features and biomechanical behavior were analyzed on dynamic videos obtained during forearm rotation. Then, the SLE was harvested from the 10 forearms for microscopic analysis on histological slices stained with hematoxylin-eosin-saffron. Two main SLE configurations were identified. One in which the SLE had three distinct bundles (anterior, middle, posterior) and another in which it was homogeneous. The anterior part of the SLE had a mean length of 11.2 mm (±2.4 mm) and a mean width of 1.2 mm (±0.2 mm) while the posterior part had a mean length of 9.9 mm (±2.2 mm) and a mean width of 1 mm (±0.2 mm). Microscopic examination showed that the SLE is composed of a thin layer of arranged collagen fibers. During forearm rotation, the SLE progressively tightens upon pronation and supination by wrapping around the radial neck. Tightening of the SLE during forearm rotation provides transverse and longitudinal stability to the forearm, mainly in maximal pronation and supination. The SLE is a true ligament and provides forearm stability when it is stretched in pronation and supination.

Importance sampling large deviations in nonequilibrium steady states. I.

PubMed

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T

2018-03-28

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

Importance sampling large deviations in nonequilibrium steady states. I

NASA Astrophysics Data System (ADS)

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.

2018-03-01

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

Signal transmissibility in marginal granular materials

NASA Astrophysics Data System (ADS)

Pinson, Matthew B.; Witten, Thomas A.

2016-12-01

We examine the ‘transmissibility’ of a simulated two-dimensional pack of frictionless disks formed by confining dilute disks in a shrinking, periodic box to the point of mechanical stability. Two opposite boundaries are then removed, thus allowing a set of free motions. Small free displacements on one boundary then induce proportional displacements on the opposite boundary. Transmissibility is the ability to distinguish different perturbations by their distant responses. We assess transmissibility by successively identifying free orthonormal modes of motion that have the smallest distant responses. The last modes to be identified in this ‘pessimistic’ basis are the most transmissive. The transmitted amplitudes of these most transmissive modes fall off exponentially with mode number. Similar exponential falloff is seen in a simple elastic medium, though the responsible modes differ greatly in structure in the two systems. Thus the marginal pack’s transmissibility is qualitatively similar to that of a simple elastic medium. We compare our results with recent findings based on the projection of the space of free motion onto interior sites.

First Demonstration of Electrostatic Damping of Parametric Instability at Advanced LIGO

NASA Astrophysics Data System (ADS)

Blair, Carl; Gras, Slawek; Abbott, Richard; Aston, Stuart; Betzwieser, Joseph; Blair, David; DeRosa, Ryan; Evans, Matthew; Frolov, Valera; Fritschel, Peter; Grote, Hartmut; Hardwick, Terra; Liu, Jian; Lormand, Marc; Miller, John; Mullavey, Adam; O'Reilly, Brian; Zhao, Chunnong; Abbott, B. P.; Abbott, T. D.; Adams, C.; Adhikari, R. X.; Anderson, S. B.; Ananyeva, A.; Appert, S.; Arai, K.; Ballmer, S. W.; Barker, D.; Barr, B.; Barsotti, L.; Bartlett, J.; Bartos, I.; Batch, J. C.; Bell, A. S.; Billingsley, G.; Birch, J.; Biscans, S.; Biwer, C.; Bork, R.; Brooks, A. F.; Ciani, G.; Clara, F.; Countryman, S. T.; Cowart, M. J.; Coyne, D. C.; Cumming, A.; Cunningham, L.; Danzmann, K.; Da Silva Costa, C. F.; Daw, E. J.; DeBra, D.; DeSalvo, R.; Dooley, K. L.; Doravari, S.; Driggers, J. C.; Dwyer, S. E.; Effler, A.; Etzel, T.; Evans, T. M.; Factourovich, M.; Fair, H.; Fernández Galiana, A.; Fisher, R. P.; Fulda, P.; Fyffe, M.; Giaime, J. A.; Giardina, K. D.; Goetz, E.; Goetz, R.; Gray, C.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hall, E. D.; Hammond, G.; Hanks, J.; Hanson, J.; Harry, G. M.; Heintze, M. C.; Heptonstall, A. W.; Hough, J.; Izumi, K.; Jones, R.; Kandhasamy, S.; Karki, S.; Kasprzack, M.; Kaufer, S.; Kawabe, K.; Kijbunchoo, N.; King, E. J.; King, P. J.; Kissel, J. S.; Korth, W. Z.; Kuehn, G.; Landry, M.; Lantz, B.; Lockerbie, N. A.; Lundgren, A. P.; MacInnis, M.; Macleod, D. M.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martin, I. W.; Martynov, D. V.; Mason, K.; Massinger, T. J.; Matichard, F.; Mavalvala, N.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McIntyre, G.; McIver, J.; Mendell, G.; Merilh, E. L.; Meyers, P. M.; Mittleman, R.; Moreno, G.; Mueller, G.; Munch, J.; Nuttall, L. K.; Oberling, J.; Oppermann, P.; Oram, Richard J.; Ottaway, D. J.; Overmier, H.; Palamos, J. R.; Paris, H. R.; Parker, W.; Pele, A.; Penn, S.; Phelps, M.; Pierro, V.; Pinto, I.; Principe, M.; Prokhorov, L. G.; Puncken, O.; Quetschke, V.; Quintero, E. A.; Raab, F. J.; Radkins, H.; Raffai, P.; Reid, S.; Reitze, D. H.; Robertson, N. A.; Rollins, J. G.; Roma, V. J.; Romie, J. H.; Rowan, S.; Ryan, K.; Sadecki, T.; Sanchez, E. J.; Sandberg, V.; Savage, R. L.; Schofield, R. M. S.; Sellers, D.; Shaddock, D. A.; Shaffer, T. J.; Shapiro, B.; Shawhan, P.; Shoemaker, D. H.; Sigg, D.; Slagmolen, B. J. J.; Smith, B.; Smith, J. R.; Sorazu, B.; Staley, A.; Strain, K. A.; Tanner, D. B.; Taylor, R.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thrane, E.; Torrie, C. I.; Traylor, G.; Vajente, G.; Valdes, G.; van Veggel, A. A.; Vecchio, A.; Veitch, P. J.; Venkateswara, K.; Vo, T.; Vorvick, C.; Walker, M.; Ward, R. L.; Warner, J.; Weaver, B.; Weiss, R.; Weßels, P.; Willke, B.; Wipf, C. C.; Worden, J.; Wu, G.; Yamamoto, H.; Yancey, C. C.; Yu, Hang; Yu, Haocun; Zhang, L.; Zucker, M. E.; Zweizig, J.; LSC Instrument Authors

2017-04-01

Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of three-mode parametric instabilities, in which the laser field in the arm cavities is scattered into higher-order optical modes by acoustic modes of the cavity mirrors. The optical modes can further drive the acoustic modes via radiation pressure, potentially producing an exponential buildup. One proposed technique to stabilize parametric instability is active damping of acoustic modes. We report here the first demonstration of damping a parametrically unstable mode using active feedback forces on the cavity mirror. A 15 538 Hz mode that grew exponentially with a time constant of 182 sec was damped using electrostatic actuation, with a resulting decay time constant of 23 sec. An average control force of 0.03 nN was required to maintain the acoustic mode at its minimum amplitude.

Large deviations and mixing for dissipative PDEs with unbounded random kicks

NASA Astrophysics Data System (ADS)

Jakšić, V.; Nersesyan, V.; Pillet, C.-A.; Shirikyan, A.

2018-02-01

We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic dynamics and a non-degeneracy condition for the driving random force, we discuss the existence and uniqueness of a stationary measure and its exponential stability in the Kantorovich-Wasserstein metric. We next turn to the large deviations principle (LDP) and establish its validity for the occupation measures of the Markov processes in question. The proof is based on Kifer’s criterion for non-compact spaces, a result on large-time asymptotics for generalised Markov semigroup, and a coupling argument. These tools combined together constitute a new approach to LDP for infinite-dimensional processes without strong Feller property in a non-compact space. The results obtained can be applied to the two-dimensional Navier-Stokes system in a bounded domain and to the complex Ginzburg-Landau equation.

Region of attraction analysis for nonlinear vehicle lateral dynamics using sum-of-squares programming

NASA Astrophysics Data System (ADS)

Imani Masouleh, Mehdi; Limebeer, David J. N.

2018-07-01

In this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates.

A Galerkin least squares approach to viscoelastic flow.

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

Rao, Rekha R.; Schunk, Peter Randall

2015-10-01

A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity andmore » pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.« less

A multi-channel isolated power supply in non-equipotential circuit

NASA Astrophysics Data System (ADS)

Li, Xiang; Zhao, Bo-Wen; Zhang, Yan-Chi; Xie, Da

2018-04-01

A multi-channel isolation power supply is designed for the problems of different MOSFET or IGBT in the non-equipotential circuit in this paper. It mainly includes the square wave generation circuit, the high-frequency transformer and the three-terminal stabilized circuit. The first part is used to generate the 24V square wave, and as the input of the magnetic ring transformer. In the second part, the magnetic ring transformer consists of one input and three outputs to realize multi-channel isolation output. The third part can output different potential and realize non-equal potential function through the three-terminal stabilized chip. In addition, the multi-channel isolation power source proposed in this paper is Small size, high reliability and low price, and it is convenient for power electronic switches that operate on multiple different potentials. Therefore, the research on power supply of power electronic circuit has practical significance.

Post-ExSELEX stabilization of an unnatural-base DNA aptamer targeting VEGF165 toward pharmaceutical applications.

PubMed

Kimoto, Michiko; Nakamura, Mana; Hirao, Ichiro

2016-09-06

A new technology, genetic alphabet expansion using artificial bases (unnatural bases), has created high-affinity DNA ligands (aptamers) that specifically bind to target proteins by ExSELEX (genetic alphabet Expansion for Systematic Evolution of Ligands by EXponential enrichment). We recently found that the unnatural-base DNA aptamers can be stabilized against nucleases, by introducing an extraordinarily stable, unique hairpin DNA (mini-hairpin DNA) and by reinforcing the stem region with G-C pairs. Here, to establish this aptamer generation method, we examined the stabilization of a high-affinity anti-VEGF165 unnatural-base DNA aptamer. The stabilized aptamers displayed significantly increased thermal and nuclease stabilities, and furthermore, exhibited higher affinity to the target. As compared to the well-known anti-VEGF165 RNA aptamer, pegaptanib (Macugen), our aptamers did not require calcium ions for binding to VEGF165 Biological experiments using cultured cells revealed that our stabilized aptamers efficiently inhibited the interaction between VEGF165 and its receptor, with the same or slightly higher efficiency than that of the pegaptanib RNA aptamer. The development of cost-effective and calcium ion-independent high-affinity anti-VEGF165 DNA aptamers encourages further progress in diagnostic and therapeutic applications. In addition, the stabilization process provided additional information about the key elements required for aptamer binding to VEGF165. © The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.

The Effects of Different Electrode Types for Obtaining Surface Machining Shape on Shape Memory Alloy Using Electrochemical Machining

NASA Astrophysics Data System (ADS)

Choi, S. G.; Kim, S. H.; Choi, W. K.; Moon, G. C.; Lee, E. S.

2017-06-01

Shape memory alloy (SMA) is important material used for the medicine and aerospace industry due to its characteristics called the shape memory effect, which involves the recovery of deformed alloy to its original state through the application of temperature or stress. Consumers in modern society demand stability in parts. Electrochemical machining is one of the methods for obtained these stabilities in parts requirements. These parts of shape memory alloy require fine patterns in some applications. In order to machine a fine pattern, the electrochemical machining method is suitable. For precision electrochemical machining using different shape electrodes, the current density should be controlled precisely. And electrode shape is required for precise electrochemical machining. It is possible to obtain precise square holes on the SMA if the insulation layer controlled the unnecessary current between electrode and workpiece. If it is adjusting the unnecessary current to obtain the desired shape, it will be a great contribution to the medical industry and the aerospace industry. It is possible to process a desired shape to the shape memory alloy by micro controlling the unnecessary current. In case of the square electrode without insulation layer, it derives inexact square holes due to the unnecessary current. The results using the insulated electrode in only side show precise square holes. The removal rate improved in case of insulated electrode than others because insulation layer concentrate the applied current to the machining zone.

Laser frequency stabilization and control through offset sideband locking to optical cavities.

PubMed

Thorpe, J I; Numata, K; Livas, J

2008-09-29

We describe a class of techniques whereby a laser frequency can be stabilized to a fixed optical cavity resonance with an adjustable offset, providing a wide tuning range for the central frequency. These techniques require only minor modifications to the standard Pound-Drever-Hall locking techniques and have the advantage of not altering the intrinsic stability of the frequency reference. We discuss the expected performance and limitations of these techniques and present a laboratory investigation in which both the sideband techniques and the standard, on-tunable Pound-Drever- Hall technique reached the 100Hz/square root(Hz) level.

Simulation evaluation of a speed-guidance law for Harrier approach transitions

NASA Technical Reports Server (NTRS)

Merrick, Vernon K.; Moralez, Ernesto; Stortz, Michael W.; Hardy, Gordon H.; Gerdes, Ronald M.

1991-01-01

An exponential-deceleration speed guidance law is formulated which mimics the technique currently used by Harrier pilots to perform decelerating approaches to a hover. This guidance law was tested along with an existing two-step constant deceleration speed guidance law, using a fixed-base piloted simulator programmed to represent a YAV-8B Harrier. Decelerating approaches to a hover at a predetermined station-keeping point were performed along a straight (-3 deg glideslope) path in headwinds up to 40 knots and turbulence up to 6 ft./sec. Visibility was fixed at one-quarter nautical mile and 100 ft. cloud ceiling. Three Harrier pilots participated in the experiment. Handling qualities with the aircraft equipped with the standard YAV-8B rate damped attitude stability augmentation system were adequate (level 2) using either speed guidance law. However, the exponential deceleration speed guidance law was rated superior to the constant-deceleration speed guidance law by a Cooper-Harper handling qualities rating of about one unit independent of the level of wind and turbulence. Replacing the attitude control system of the YAV-8B with a high fidelity model following attitude flight controller increased the approach accuracy and reduced the pilot workload. With one minor exception, the handling qualities for the approach were rated satisfactory (level 1). It is concluded that the exponential deceleration speed guidance law is the most cost effective.

Aquarius L-Band Microwave Radiometer: Three Years of Radiometric Performance and Systematic Effects

NASA Technical Reports Server (NTRS)

Piepmeier, Jeffrey R.; Hong, Liang; Pellerano, Fernando A.

2015-01-01

The Aquarius L-band microwave radiometer is a three-beam pushbroom instrument designed to measure sea surface salinity. Results are analyzed for performance and systematic effects over three years of operation. The thermal control system maintains tight temperature stability promoting good gain stability. The gain spectrum exhibits expected orbital variations with 1f noise appearing at longer time periods. The on-board detection and integration scheme coupled with the calibration algorithm produce antenna temperatures with NEDT 0.16 K for 1.44-s samples. Nonlinearity is characterized before launch and the derived correction is verified with cold-sky calibration data. Finally, long-term drift is discovered in all channels with 1-K amplitude and 100-day time constant. Nonetheless, it is adeptly corrected using an exponential model.

On the modeling of breath-by-breath oxygen uptake kinetics at the onset of high-intensity exercises: simulated annealing vs. GRG2 method.

PubMed

Bernard, Olivier; Alata, Olivier; Francaux, Marc

2006-03-01

Modeling in the time domain, the non-steady-state O2 uptake on-kinetics of high-intensity exercises with empirical models is commonly performed with gradient-descent-based methods. However, these procedures may impair the confidence of the parameter estimation when the modeling functions are not continuously differentiable and when the estimation corresponds to an ill-posed problem. To cope with these problems, an implementation of simulated annealing (SA) methods was compared with the GRG2 algorithm (a gradient-descent method known for its robustness). Forty simulated Vo2 on-responses were generated to mimic the real time course for transitions from light- to high-intensity exercises, with a signal-to-noise ratio equal to 20 dB. They were modeled twice with a discontinuous double-exponential function using both estimation methods. GRG2 significantly biased two estimated kinetic parameters of the first exponential (the time delay td1 and the time constant tau1) and impaired the precision (i.e., standard deviation) of the baseline A0, td1, and tau1 compared with SA. SA significantly improved the precision of the three parameters of the second exponential (the asymptotic increment A2, the time delay td2, and the time constant tau2). Nevertheless, td2 was significantly biased by both procedures, and the large confidence intervals of the whole second component parameters limit their interpretation. To compare both algorithms on experimental data, 26 subjects each performed two transitions from 80 W to 80% maximal O2 uptake on a cycle ergometer and O2 uptake was measured breath by breath. More than 88% of the kinetic parameter estimations done with the SA algorithm produced the lowest residual sum of squares between the experimental data points and the model. Repeatability coefficients were better with GRG2 for A1 although better with SA for A2 and tau2. Our results demonstrate that the implementation of SA improves significantly the estimation of most of these kinetic parameters, but a large inaccuracy remains in estimating the parameter values of the second exponential.

Pattern formation based on complex coupling mechanism in dielectric barrier discharge

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

Liu, Weibo; College of Aeronautical Engineering, Binzhou University, Binzhou 256603; Dong, Lifang, E-mail: donglfhbu@163.com, E-mail: pyy1616@163.com

2016-08-15

The pattern formation of cinque-dice square superlattice pattern (CDSSP) is investigated based on the complex coupling mechanism in a dielectric barrier discharge (DBD) system. The spatio-temporal structure of CDSSP obtained by using an intensified-charge coupled device indicates that CDSSP is an interleaving of two kinds of subpatterns (mixture of rectangle and square, and dot-line square) which discharge twice in one half voltage, respectively. Selected by the complex coupling of two subpatterns, the CDSSP can be formed and shows good stability. This investigation based on gas discharge theory together with nonlinear theory may provide a deeper understanding for the nonlinear characteristicsmore » and even the formation mechanism of patterns in DBD.« less

Clinical variables related to antidepressant-induced mania in bipolar disorder.

PubMed

Mundo, Emanuela; Cattaneo, Elisabetta; Russo, Michela; Altamura, A Carlo

2006-06-01

The development of mania or hypomania during antidepressant treatment is a serious complication of the clinical management of bipolar disorder (BP). The primary aim of this study was to evaluate the clinical variables related to antidepressant-induced mania or hypomania (AIM) in patients with BP. DSM-IV BP-I or BP-II patients who had had at least one depressive episode treated with antidepressants were considered. Patients were subdivided into two groups according to the presence (n = 30) or absence (n = 106) of manic or hypomanic episodes occurring during antidepressant treatment. Possible predictive clinical variables of AIM were considered: gender, diagnostic subtype, age at onset, duration of illness, duration of untreated illness, type of antidepressant administered, number of previous spontaneous hypomanic or manic episodes, number of previous depressive episodes, presence of lifetime suicide attempts, presence of mood stabilizer treatments, presence of psychotic symptoms during spontaneous episodes, family history for psychiatric disorders in first degree relatives. Data were compared between the two groups, with (AIM+) and without (AIM-) antidepressant-induced mania, using Student's t tests and chi-square tests. The lack of mood stabilizer treatments during antidepressant therapy (chi-square = 37.602, df = 1, p < 0.001) and the exposure to tricyclic antidepressants (chi-square = 4.901, df = 1, p < 0.05) resulted significantly associated to the development of AIM. This study was not done under controlled conditions and the relatively small sample studied warrants further replications. These results point out the risk of mania induction associated to the use of tricyclic antidepressants in BP patients, mainly in absence of adequate mood stabilizers.

Tidal Volume Estimation Using the Blanket Fractal Dimension of the Tracheal Sounds Acquired by Smartphone

PubMed Central

Reljin, Natasa; Reyes, Bersain A.; Chon, Ki H.

2015-01-01

In this paper, we propose the use of blanket fractal dimension (BFD) to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5) healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE) is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE). The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained). The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation) was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days. PMID:25923929

Tidal volume estimation using the blanket fractal dimension of the tracheal sounds acquired by smartphone.

PubMed

Reljin, Natasa; Reyes, Bersain A; Chon, Ki H

2015-04-27

In this paper, we propose the use of blanket fractal dimension (BFD) to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5) healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE) is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE). The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained). The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation) was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days.

Short range shooting distance estimation using variable pressure SEM images of the surroundings of bullet holes in textiles.

PubMed

Hinrichs, Ruth; Frank, Paulo Ricardo Ost; Vasconcellos, M A Z

2017-03-01

Modifications of cotton and polyester textiles due to shots fired at short range were analyzed with a variable pressure scanning electron microscope (VP-SEM). Different mechanisms of fiber rupture as a function of fiber type and shooting distance were detected, namely fusing, melting, scorching, and mechanical breakage. To estimate the firing distance, the approximately exponential decay of GSR coverage as a function of radial distance from the entrance hole was determined from image analysis, instead of relying on chemical analysis with EDX, which is problematic in the VP-SEM. A set of backscattered electron images, with sufficient magnification to discriminate micrometer wide GSR particles, was acquired at different radial distances from the entrance hole. The atomic number contrast between the GSR particles and the organic fibers allowed to find a robust procedure to segment the micrographs into binary images, in which the white pixel count was attributed to GSR coverage. The decrease of the white pixel count followed an exponential decay, and it was found that the reciprocal of the decay constant, obtained from the least-square fitting of the coverage data, showed a linear dependence on the shooting distance. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.

TIME-DOMAIN METHODS FOR DIFFUSIVE TRANSPORT IN SOFT MATTER

PubMed Central

Fricks, John; Yao, Lingxing; Elston, Timothy C.; Gregory Forest, And M.

2015-01-01

Passive microrheology [12] utilizes measurements of noisy, entropic fluctuations (i.e., diffusive properties) of micron-scale spheres in soft matter to infer bulk frequency-dependent loss and storage moduli. Here, we are concerned exclusively with diffusion of Brownian particles in viscoelastic media, for which the Mason-Weitz theoretical-experimental protocol is ideal, and the more challenging inference of bulk viscoelastic moduli is decoupled. The diffusive theory begins with a generalized Langevin equation (GLE) with a memory drag law specified by a kernel [7, 16, 22, 23]. We start with a discrete formulation of the GLE as an autoregressive stochastic process governing microbead paths measured by particle tracking. For the inverse problem (recovery of the memory kernel from experimental data) we apply time series analysis (maximum likelihood estimators via the Kalman filter) directly to bead position data, an alternative to formulas based on mean-squared displacement statistics in frequency space. For direct modeling, we present statistically exact GLE algorithms for individual particle paths as well as statistical correlations for displacement and velocity. Our time-domain methods rest upon a generalization of well-known results for a single-mode exponential kernel [1, 7, 22, 23] to an arbitrary M-mode exponential series, for which the GLE is transformed to a vector Ornstein-Uhlenbeck process. PMID:26412904

Improving positive and negative bias illumination stress stability in parylene passivated IGZO transistors

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

Kiazadeh, Asal; Universidade do Algarve, FCT, 8000-139 Faro; Gomes, Henrique L.

The impact of a parylene top-coating layer on the illumination and bias stress instabilities of indium-gallium-zinc oxide thin-film transistors (TFTs) is presented and discussed. The parylene coating substantially reduces the threshold voltage shift caused by continuous application of a gate bias and light exposure. The operational stability improves by 75%, and the light induced instability is reduced by 35%. The operational stability is quantified by fitting the threshold voltage shift with a stretched exponential model. Storage time as long as 7 months does not cause any measurable degradation on the electrical performance. It is proposed that parylene plays not onlymore » the role of an encapsulation layer but also of a defect passivation on the top semiconductor surface. It is also reported that depletion-mode TFTs are less sensitive to light induced instabilities. This is attributed to a defect neutralization process in the presence of free electrons.« less

New class of de Sitter vacua in string theory compactifications

NASA Astrophysics Data System (ADS)

Achúcarro, Ana; Ortiz, Pablo; Sousa, Kepa

2016-10-01

String theory contains few known working examples of de Sitter vacua, four-dimensional universes with a positive cosmological constant. A notorious obstacle is the stabilization of a large number—sometimes hundreds—of moduli fields that characterize the compact dimensions. We study the stability of a class of supersymmetric moduli (the complex structure moduli and dilaton in type-IIB flux compactifications) in the regime where the volume of the compact space is large but not exponentially large. We show that, if the number of moduli is very large, random matrix theory provides a new stability condition, a lower bound on the volume. We find a new class of stable vacua where the mass spectrum of these supersymmetric moduli is gapped, without requiring a large mass hierarchy between moduli sectors or any fine-tuning of the superpotential. We provide the first explicit example of this class of vacua in the P[1,1 ,1 ,6 ,9 ] 4 model. A distinguishing feature is that all fermions in the supersymmetric sector are lighter than the gravitino.

Periodicity and stability for variable-time impulsive neural networks.

PubMed

Li, Hongfei; Li, Chuandong; Huang, Tingwen

2017-10-01

The paper considers a general neural networks model with variable-time impulses. It is shown that each solution of the system intersects with every discontinuous surface exactly once via several new well-proposed assumptions. Moreover, based on the comparison principle, this paper shows that neural networks with variable-time impulse can be reduced to the corresponding neural network with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the variable-time impulsive neural networks. Furthermore, a series of sufficient criteria are derived to ensure the existence and global exponential stability of periodic solution of variable-time impulsive neural networks, and to illustrate the same stability properties between variable-time impulsive neural networks and the fixed-time ones. The new criteria are established by applying Schaefer's fixed point theorem combined with the use of inequality technique. Finally, a numerical example is presented to show the effectiveness of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

On the convergence of local approximations to pseudodifferential operators with applications

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1994-01-01

We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.

Entanglement properties of the two-dimensional SU(3) Affleck-Kennedy-Lieb-Tasaki state

NASA Astrophysics Data System (ADS)

Gauthé, Olivier; Poilblanc, Didier

2017-09-01

Two-dimensional (spin-2) Affleck-Kennedy-Lieb-Tasaki (AKLT) type valence bond solids on a square lattice are known to be symmetry-protected topological (SPT) gapped spin liquids [S. Takayoshi, P. Pujol, and A. Tanaka Phys. Rev. B 94, 235159 (2016), 10.1103/PhysRevB.94.235159]. Using the projected entangled pair state framework, we extend the construction of the AKLT state to the case of SU(3 ) , relevant for cold atom systems. The entanglement spectrum is shown to be described by an alternating SU(3 ) chain of "quarks" and "antiquarks", subject to exponentially decaying (with distance) Heisenberg interactions, in close similarity with its SU(2 ) analog. We discuss the SPT feature of the state.

Spectral properties of the massless relativistic quartic oscillator

NASA Astrophysics Data System (ADS)

Durugo, Samuel O.; Lőrinczi, József

2018-03-01

An explicit solution of the spectral problem of the non-local Schrödinger operator obtained as the sum of the square root of the Laplacian and a quartic potential in one dimension is presented. The eigenvalues are obtained as zeroes of special functions related to the fourth order Airy function, and closed formulae for the Fourier transform of the eigenfunctions are derived. These representations allow to derive further spectral properties such as estimates of spectral gaps, heat trace and the asymptotic distribution of eigenvalues, as well as a detailed analysis of the eigenfunctions. A subtle spectral effect is observed which manifests in an exponentially tight approximation of the spectrum by the zeroes of the dominating term in the Fourier representation of the eigenfunctions and its derivative.

Development of a winter wheat adjustable crop calendar model. [Colorado, Idaho, Oklahoma, Montana, Kansas, Missouri, North Dakota and Texas

NASA Technical Reports Server (NTRS)

Baker, J. R. (Principal Investigator)

1979-01-01

The author has identified the following significant results. Least squares techniques were applied for parameter estimation of functions to predict winter wheat phenological stage with daily maximum temperature, minimum temperature, daylength, and precipitation as independent variables. After parameter estimation, tests were conducted using independent data. It may generally be concluded that exponential functions have little advantage over polynomials. Precipitation was not found to significantly affect the fits. The Robertson triquadratic form, in general use for spring wheat, yielded good results, but special techniques and care are required. In most instances, equations with nonlinear effects were found to yield erratic results when utilized with averaged daily environmental values as independent variables.

Generation kinetics of boron-oxygen complexes in p-type compensated c-Si

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

Wu, Yichao; Yu, Xuegong, E-mail: yuxuegong@zju.edu.cn; Chen, Peng

2014-03-10

Kinetics characteristics of boron-oxygen complexes responsible for light-induced degradation in p-type compensated c-Si have been investigated. The generation of B-O complexes is well fitted by a fast-forming process and a slow-forming one. Activation energies of complexes generation during the fast-forming process are determined to be 0.29 and 0.24 eV in compensated and non-compensated c-Si, respectively, and those during the slow-forming process are the same, about 0.44 eV. Moreover, it is found that the pre-exponential factors of complexes generation in compensated c-Si is proportional to the square of the net doping concentration, which suggests that the latent centers should exist.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner

NASA Astrophysics Data System (ADS)

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner.

PubMed

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

The Phosphorolytic Exoribonucleases Polynucleotide Phosphorylase and RNase PH Stabilize sRNAs and Facilitate Regulation of Their mRNA Targets

PubMed Central

2016-01-01

ABSTRACT Gene regulation by base pairing between small noncoding RNAs (sRNAs) and their mRNA targets is an important mechanism that allows bacteria to maintain homeostasis and respond to dynamic environments. In Gram-negative bacteria, sRNA pairing and regulation are mediated by several RNA-binding proteins, including the sRNA chaperone Hfq and polynucleotide phosphorylase (PNPase). PNPase and its homolog RNase PH together represent the two 3′ to 5′ phosphorolytic exoribonucleases found in Escherichia coli; however, the role of RNase PH in sRNA regulation has not yet been explored and reported. Here, we have examined in detail how PNPase and RNase PH interact to support sRNA stability, activity, and base pairing in exponential and stationary growth conditions. Our results indicate that these proteins facilitate the stability and regulatory function of the sRNAs RyhB, CyaR, and MicA during exponential growth. PNPase further appears to contribute to pairing between RyhB and its mRNA targets. During stationary growth, each sRNA responded differently to the absence or presence of PNPase and RNase PH. Finally, our results suggest that PNPase and RNase PH stabilize only Hfq-bound sRNAs. Taken together, these results confirm and extend previous findings that PNPase participates in sRNA regulation and reveal that RNase PH serves a similar, albeit more limited, role as well. These proteins may, therefore, act to protect sRNAs from spurious degradation while also facilitating regulatory pairing with their targets. IMPORTANCE In many bacteria, Hfq-dependent base-pairing sRNAs facilitate rapid changes in gene expression that are critical for maintaining homeostasis and responding to stress and environmental changes. While a role for Hfq in this process was identified more than 2 decades ago, the identity and function of the other proteins required for Hfq-dependent regulation by sRNAs have not been resolved. Here, we demonstrate that PNPase and RNase PH, the two phosphorolytic RNases in E. coli, stabilize sRNAs against premature degradation and, in the case of PNPase, also accelerate regulation by sRNA-mRNA pairings for certain sRNAs. These findings are the first to demonstrate that RNase PH influences and supports sRNA regulation and suggest shared and distinct roles for these phosphorolytic RNases in this process. PMID:27698082

On a variational approach to some parameter estimation problems

NASA Technical Reports Server (NTRS)

Banks, H. T.

1985-01-01

Examples (1-D seismic, large flexible structures, bioturbation, nonlinear population dispersal) in which a variation setting can provide a convenient framework for convergence and stability arguments in parameter estimation problems are considered. Some of these examples are 1-D seismic, large flexible structures, bioturbation, and nonlinear population dispersal. Arguments for convergence and stability via a variational approach of least squares formulations of parameter estimation problems for partial differential equations is one aspect of the problem considered.

Deciphering the Dynamics of Non-Covalent Interactions Affecting Thermal Stability of a Protein: Molecular Dynamics Study on Point Mutant of Thermus thermophilus Isopropylmalate Dehydrogenase.

PubMed

Sharma, Reetu; Sastry, G Narahari

2015-01-01

Thermus thermophilius isopropylmalate dehydrogenase catalyzes oxidative decarboxylation and dehydrogenation of isopropylmalate. Substitution of leucine to alanine at position 172 enhances the thermal stability among the known point mutants. Exploring the dynamic properties of non-covalent interactions such as saltbridges, hydrogen bonds and hydrophobic interactions to explain thermal stability of a protein is interesting in its own right. In this study dynamic changes in the non-covalent interactions are studied to decipher the deterministic features of thermal stability of a protein considering a case study of a point mutant in Thermus thermophilus isopropylmalate dehydrogenase. A total of four molecular dynamic simulations of 0.2 μs were carried out on wild type and mutant's functional dimers at 300 K and 337 K. Higher thermal stability of the mutant as compared to wild type is revealed by root mean square deviation, root mean square fluctuations and Cα-Cα distance with an increase in temperature from 300 K to 337 K. Most of the regions of wild type fluctuate higher than the corresponding regions of mutant with an increase in temperature. Cα-Cα distance analysis suggests that long distance networks are significantly affected in wild type as compared to the mutant. Short lived contacts are higher in wild type, while long lived contacts are lost at 337 K. The mutant forms less hydrogen bonds with water as compared to wild type at 337 K. In contrast to wild type, the mutant shows significant increase in unique saltbridges, hydrogen bonds and hydrophobic contacts at 337 K. The current study indicates that there is a strong inter-dependence of thermal stability on the way in which non-covalent interactions reorganize, and it is rewarding to explore this connection in single mutant studies.

Simple Chaotic Flow with Circle and Square Equilibrium

NASA Astrophysics Data System (ADS)

Gotthans, Tomas; Sprott, Julien Clinton; Petrzela, Jiri

Simple systems of third-order autonomous nonlinear differential equations can exhibit chaotic behavior. In this paper, we present a new class of chaotic flow with a square-shaped equilibrium. This unique property has apparently not yet been described. Such a system belongs to a newly introduced category of chaotic systems with hidden attractors that are interesting and important in engineering applications. The mathematical model is accompanied by an electrical circuit implementation, demonstrating structural stability of the strange attractor. The circuit is simulated with PSpice, constructed, and analyzed (measured).

Symmetric factorization of the conformation tensor in viscoelastic fluid models

NASA Astrophysics Data System (ADS)

Thomases, Becca; Balci, Nusret; Renardy, Michael; Doering, Charles

2010-11-01

The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.

Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

NASA Astrophysics Data System (ADS)

Yu, Gwo-Ruey; Huang, Yu-Chia; Cheng, Chih-Yung

2016-07-01

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi-Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.

Dynamic stability of spinning pretwisted beams subjected to axial random forces

NASA Astrophysics Data System (ADS)

Young, T. H.; Gau, C. Y.

2003-11-01

This paper studies the dynamic stability of a pretwisted cantilever beam spinning along its longitudinal axis and subjected to an axial random force at the free end. The axial force is assumed as the sum of a constant force and a random process with a zero mean. Due to this axial force, the beam may experience parametric random instability. In this work, the finite element method is first applied to yield discretized system equations. The stochastic averaging method is then adopted to obtain Ito's equations for the response amplitudes of the system. Finally the mean-square stability criterion is utilized to determine the stability condition of the system. Numerical results show that the stability boundary of the system converges as the first three modes are taken into calculation. Before the convergence is reached, the stability condition predicted is not conservative enough.

Repeatability of paired counts.

PubMed

Alexander, Neal; Bethony, Jeff; Corrêa-Oliveira, Rodrigo; Rodrigues, Laura C; Hotez, Peter; Brooker, Simon

2007-08-30

The Bland and Altman technique is widely used to assess the variation between replicates of a method of clinical measurement. It yields the repeatability, i.e. the value within which 95 per cent of repeat measurements lie. The valid use of the technique requires that the variance is constant over the data range. This is not usually the case for counts of items such as CD4 cells or parasites, nor is the log transformation applicable to zero counts. We investigate the properties of generalized differences based on Box-Cox transformations. For an example, in a data set of hookworm eggs counted by the Kato-Katz method, the square root transformation is found to stabilize the variance. We show how to back-transform the repeatability on the square root scale to the repeatability of the counts themselves, as an increasing function of the square mean root egg count, i.e. the square of the average of square roots. As well as being more easily interpretable, the back-transformed results highlight the dependence of the repeatability on the sample volume used.

Analysis of Nonlinear Dynamics by Square Matrix Method

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

Yu, Li Hua

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. Andmore » more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.« less

Measuring dose from radiotherapy treatments in the vicinity of a cardiac pacemaker.

PubMed

Peet, Samuel C; Wilks, Rachael; Kairn, Tanya; Crowe, Scott B

2016-12-01

This study investigated the dose absorbed by tissues surrounding artificial cardiac pacemakers during external beam radiotherapy procedures. The usefulness of out-of-field reference data, treatment planning systems, and skin dose measurements to estimate the dose in the vicinity of a pacemaker was also examined. Measurements were performed by installing a pacemaker onto an anthropomorphic phantom, and using radiochromic film and optically stimulated luminescence dosimeters to measure the dose in the vicinity of the device during the delivery of square fields and clinical treatment plans. It was found that the dose delivered in the vicinity of the cardiac device was unevenly distributed both laterally and anteroposteriorly. As the device was moved distally from the square field, the dose dropped exponentially, in line with out-of-field reference data in the literature. Treatment planning systems were found to substantially underestimate the dose for volumetric modulated arc therapy, helical tomotherapy, and 3D conformal treatments. The skin dose was observed to be either greater or lesser than the dose received at the depth of the device, depending on the treatment site, and so care should be if skin dose measurements are to be used to estimate the dose to a pacemaker. Square field reference data may be used as an upper estimate of absorbed dose per monitor unit in the vicinity of a cardiac device for complex treatments involving multiple gantry angles. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Magnetic properties of NdFeB-coated rubberwood composites

NASA Astrophysics Data System (ADS)

Noodam, Jureeporn; Sirisathitkul, Chitnarong; Matan, Nirundorn; Rattanasakulthong, Watcharee; Jantaratana, Pongsakorn

2013-01-01

Magnetic properties of composites prepared by coating lacquer containing neodymium iron boron (Nd-Fe-B) powders on rubberwood were characterized by vibrating sample magnetometry (VSM), magnetic moment measurements, and attraction tests with an iron-core solenoid. The Nd-Fe-B powders were recycled from electronic wastes by the ball-milling technique. Varying the milling time from 20 to 300 min, the magnetic squareness and the coercive field of the Nd-Fe-B powders were at the minimum when the powders were milled for 130 min. It followed that the coercive field of the magnetic wood composites was increased with the milling time increasing from 130 to 300 min. For the magnetic wood composites using Nd-Fe-B obtained from the same milling time, the magnetic squareness and the coercive field were rather insensitive to the variation of Nd-Fe-B concentration in coating lacquer from 0.43 to 1.00 g/cm3. By contrast, the magnetization and magnetic moment were increased with the Nd-Fe-B concentration increasing. Furthermore, the electrical current in the solenoid required for the attraction of the magnetic wood composites was exponentially reduced with the increase in the amount of Nd-Fe-B used in the coating.

Etching of germanium-tin using ammonia peroxide mixture

NASA Astrophysics Data System (ADS)

Dong, Yuan; Ong, Bin Leong; Wang, Wei; Zhang, Zheng; Pan, Jisheng; Gong, Xiao; Tok, Eng-Soon; Liang, Gengchiau; Yeo, Yee-Chia

2015-12-01

The wet etching of germanium-tin (Ge1-xSnx) alloys (4.2% < x < 16.0%) in ammonia peroxide mixture (APM) is investigated. Empirical fitting of the data points indicates that the etch depth of Ge1-xSnx is proportional to the square root of the etch time t and decreases exponentially with increasing x for a given t. In addition, X-ray photoelectron spectroscopy results show that increasing t increases the intensity of the Sn oxide peak, whereas no obvious change is observed for the Ge oxide peak. This indicates that an accumulation of Sn oxide on the Ge1-xSnx surface decreases the amount of Ge atoms exposed to the etchant, which accounts for the decrease in etch rate with increasing etch time. Atomic force microscopy was used to examine the surface morphologies of the Ge0.918Sn0.082 samples. Both root-mean-square roughness and undulation periods of the Ge1-xSnx surface were observed to increase with increasing t. This work provides further understanding of the wet etching of Ge1-xSnx using APM and may be used for the fabrication of Ge1-xSnx-based electronic and photonic devices.

Generalised observer design for dissipative Lipschitz nonlinear systems in the presence of measurement noise

NASA Astrophysics Data System (ADS)

Vijayaraghavan, Krishna

2014-11-01

This paper presents two novel observer concepts. First, it develops a globally exponentially stable nonlinear observer for noise-free dissipative nonlinear systems. Second, for a dissipative nonlinear system with measurement noise, the paper develops an observer to guarantee a desired performance, namely an upper limit on the ratio of the square of the weighted L2 norm of the error to the square of the weighted L2 norm of the measurement noise. The necessary and sufficient conditions for both observers are reformulated as algebraic Riccati equations (AREs) so that standard solvers can be utilised. In addition, the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the ARE (and hence the observer design problem) has a solution. The use of the methodology developed in this paper is demonstrated through illustrative examples. In literature, there is no previous observer for dissipative system that provides both necessary and sufficient conditions. Results for noisy system either rely on linearising the system about state trajectory (requiring initial estimates to be close to the actual states) or are for specialised systems that cannot be extended to dissipative systems.

Experimental evaluation of leaky least-mean-square algorithms for active noise reduction in communication headsets.

PubMed

Cartes, David A; Ray, Laura R; Collier, Robert D

2002-04-01

An adaptive leaky normalized least-mean-square (NLMS) algorithm has been developed to optimize stability and performance of active noise cancellation systems. The research addresses LMS filter performance issues related to insufficient excitation, nonstationary noise fields, and time-varying signal-to-noise ratio. The adaptive leaky NLMS algorithm is based on a Lyapunov tuning approach in which three candidate algorithms, each of which is a function of the instantaneous measured reference input, measurement noise variance, and filter length, are shown to provide varying degrees of tradeoff between stability and noise reduction performance. Each algorithm is evaluated experimentally for reduction of low frequency noise in communication headsets, and stability and noise reduction performance are compared with that of traditional NLMS and fixed-leakage NLMS algorithms. Acoustic measurements are made in a specially designed acoustic test cell which is based on the original work of Ryan et al. ["Enclosure for low frequency assessment of active noise reducing circumaural headsets and hearing protection," Can. Acoust. 21, 19-20 (1993)] and which provides a highly controlled and uniform acoustic environment. The stability and performance of the active noise reduction system, including a prototype communication headset, are investigated for a variety of noise sources ranging from stationary tonal noise to highly nonstationary measured F-16 aircraft noise over a 20 dB dynamic range. Results demonstrate significant improvements in stability of Lyapunov-tuned LMS algorithms over traditional leaky or nonleaky normalized algorithms, while providing noise reduction performance equivalent to that of the NLMS algorithm for idealized noise fields.

Tangential acceleration feedback control of friction induced vibration

NASA Astrophysics Data System (ADS)

Nath, Jyayasi; Chatterjee, S.

2016-09-01

Tangential control action is studied on a phenomenological mass-on-belt model exhibiting friction-induced self-excited vibration attributed to the low-velocity drooping characteristics of friction which is also known as Stribeck effect. The friction phenomenon is modelled by the exponential model. Linear stability analysis is carried out near the equilibrium point and local stability boundary is delineated in the plane of control parameters. The system is observed to undergo a Hopf bifurcation as the eigenvalues determined from the linear stability analysis are found to cross the imaginary axis transversally from RHS s-plane to LHS s-plane or vice-versa as one varies the control parameters, namely non-dimensional belt velocity and the control gain. A nonlinear stability analysis by the method of Averaging reveals the subcritical nature of the Hopf bifurcation. Thus, a global stability boundary is constructed so that any choice of control parameters from the globally stable region leads to a stable equilibrium. Numerical simulations in a MATLAB SIMULINK model and bifurcation diagrams obtained in AUTO validate these analytically obtained results. Pole crossover design is implemented to optimize the filter parameters with an independent choice of belt velocity and control gain. The efficacy of this optimization (based on numerical results) in the delicate low velocity region is also enclosed.

DSS 13 frequency stability tests

NASA Technical Reports Server (NTRS)

Otoshi, T. Y.; Franco, M. M.

1987-01-01

In a previous article, the results of frequency stability tests at DSS 13 were presented in table form for tau = 1000 s for the test period May 1985 through March 1986. This article is a continuation of that initial report and presents specially selected Allan sigma (square root of variance) plots of each of the subsystem test previously reported. An additional result obtained from tests performed during July 1986 was included for completeness. The Allan sigma plots are useful in that frequency stability information is not only given for tau = 1000 s, but for tau values in the regions of 1, 100, 500, and 2000 s as well.

Black holes and Higgs stability

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

Tetradis, Nikolaos; Physics Department, Theory Unit, CERN,CH-1211 Geneva 23

We study the effect of primordial black holes on the classical rate of nucleation of AdS regions within the standard electroweak vacuum. We find that the energy barrier for transitions to the new vacuum, which characterizes the exponential suppression of the nucleation rate, can be reduced significantly in the black-hole background. A precise analysis is required in order to determine whether the the existence of primordial black holes is compatible with the form of the Higgs potential at high temperature or density in the Standard Model or its extensions.

Effects of wall suction/blowing on two-dimensional flow past a confined square cylinder.

PubMed

Zhang, Wei; Jiang, Yanqun; Li, Lang; Chen, Guoping

2016-01-01

A numerical simulation is conducted to study the laminar flow past a square cylinder confined in a channel (the ratio of side length of the square to channel width is fixed at 1/4) subjected to a locally uniform blowing/suction speed placed at the top and bottom channel walls. Governing equations with boundary conditions are resolved using a finite volume method in pressure-velocity formulation. The flow patterns relevant to the critical spacing values are investigated. Numerical results show that wall blowing has a stabilizing effect on the flow, and the corresponding critical Reynolds number increases monotonically with increasing blowing velocity. Remarkably, steady asymmetric solutions and hysteretic mode transitions exist in a certain range of parameters (Reynolds number and suction speed) in the case of suction.

On the Stability of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs

NASA Technical Reports Server (NTRS)

Patilkulkarni, Sudarshan; Herencia-Zapana, Heber; Gray, W. Steven; Gonzalez, Oscar R.

2004-01-01

This paper presents two mean-square stability tests for a jump-linear system driven by a finite-state machine with a first-order Markovian input process. The first test is based on conventional Markov jump-linear theory and avoids the use of any higher-order statistics. The second test is developed directly using the higher-order statistics of the machine s output process. The two approaches are illustrated with a simple model for a recoverable computer control system.

Robust interval-based regulation for anaerobic digestion processes.

PubMed

Alcaraz-González, V; Harmand, J; Rapaport, A; Steyer, J P; González-Alvarez, V; Pelayo-Ortiz, C

2005-01-01

A robust regulation law is applied to the stabilization of a class of biochemical reactors exhibiting partially known highly nonlinear dynamic behavior. An uncertain environment with the presence of unknown inputs is considered. Based on some structural and operational conditions, this regulation law is shown to exponentially stabilize the aforementioned bioreactors around a desired set-point. This approach is experimentally applied and validated on a pilot-scale (1 m3) anaerobic digestion process for the treatment of raw industrial wine distillery wastewater where the objective is the regulation of the chemical oxygen demand (COD) by using the dilution rate as the manipulated variable. Despite large disturbances on the input COD and state and parametric uncertainties, this regulation law gave excellent performances leading the output COD towards its set-point and keeping it inside a pre-specified interval.

Dynamics of a New 5D Hyperchaotic System of Lorenz Type

NASA Astrophysics Data System (ADS)

Zhang, Fuchen; Chen, Rui; Wang, Xingyuan; Chen, Xiusu; Mu, Chunlai; Liao, Xiaofeng

Ultimate boundedness of chaotic dynamical systems is one of the fundamental concepts in dynamical systems, which plays an important role in investigating the stability of the equilibrium, estimating the Lyapunov dimension of attractors and the Hausdorff dimension of attractors, the existence of periodic solutions, chaos control, chaos synchronization. However, it is often difficult to obtain the bounds of the hyperchaotic systems due to the complex algebraic structure of the hyperchaotic systems. This paper has investigated the boundedness of solutions of a nonlinear hyperchaotic system. We have obtained the global exponential attractive set and the ultimate bound set for this system. To obtain the ellipsoidal ultimate bound, the ultimate bound of the proposed system is theoretically estimated using Lagrange multiplier method, Lyapunov stability theory and optimization theory. To show the ultimate bound region, numerical simulations are provided.