Locally Stationary Processes - A Review
Dahlhaus, Rainer
2011-01-01
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the next section a general framework for time series with time varying finite dimensional parameters is discussed with special emphasis on nonlinear locally stationary processes. Then the paper focusses on linear processes where a more general theory is possible. First a general definition for linear processes is given and time varying spectral densities are discussed in detail. Then the Gaussian likelihood theory is presented for locally stationary processes. In the next section the relevance of empirical spectral processes for locally stationary time series is discussed. Empirical spectral processes play a major role in proving theoretical results and provide a deeper understanding of many techniques. The article concludes with an overview of other results for locally stationar...
Piecewise quartic polynomial curves with a local shape parameter
Han, Xuli
2006-10-01
Piecewise quartic polynomial curves with a local shape parameter are presented in this paper. The given blending function is an extension of the cubic uniform B-splines. The changes of a local shape parameter will only change two curve segments. With the increase of the value of a shape parameter, the curves approach a corresponding control point. The given curves possess satisfying shape-preserving properties. The given curve can also be used to interpolate locally the control points with GC2 continuity. Thus, the given curves unify the representation of the curves for interpolating and approximating the control polygon. As an application, the piecewise polynomial curves can intersect an ellipse at different knot values by choosing the value of the shape parameter. The given curve can approximate an ellipse from the both sides and can then yield a tight envelope for an ellipse. Some computing examples for curve design are given.
Local identification of piecewise deterministic models of genetic networks
Cinquemani, Eugenio; Milias-Argeitis, Andreas; Summers, Sean; Lygeros, John
2009-01-01
We address the identification of genetic networks under stationary conditions. A stochastic hybrid description of the genetic interactions is considered and an approximation of it in stationary conditions is derived. Contrary to traditional structure identification methods based on fitting determini
Inference for local autocorrelations in locally stationary models.
Zhao, Zhibiao
2015-04-01
For non-stationary processes, the time-varying correlation structure provides useful insights into the underlying model dynamics. We study estimation and inferences for local autocorrelation process in locally stationary time series. Our constructed simultaneous confidence band can be used to address important hypothesis testing problems, such as whether the local autocorrelation process is indeed time-varying and whether the local autocorrelation is zero. In particular, our result provides an important generalization of the R function acf() to locally stationary Gaussian processes. Simulation studies and two empirical applications are developed. For the global temperature series, we find that the local autocorrelations are time-varying and have a "V" shape during 1910-1960. For the S&P 500 index, we conclude that the returns satisfy the efficient-market hypothesis whereas the magnitudes of returns show significant local autocorrelations.
Local polynomial Whittle estimation covering non-stationary fractional processes
DEFF Research Database (Denmark)
Nielsen, Frank
This paper extends the local polynomial Whittle estimator of Andrews & Sun (2004) to fractionally integrated processes covering stationary and non-stationary regions. We utilize the notion of the extended discrete Fourier transform and periodogram to extend the local polynomial Whittle estimator ...... study illustrates the performance of the proposed estimator compared to the classical local Whittle estimator and the local polynomial Whittle estimator. The empirical justi.cation of the proposed estimator is shown through an analysis of credit spreads....
On the Causality between Multiple Locally Stationary Processes
Directory of Open Access Journals (Sweden)
Junichi Hirukawa
2012-01-01
Full Text Available When one would like to describe the relations between multivariate time series, the concepts of dependence and causality are of importance. These concepts also appear to be useful when one is describing the properties of an engineering or econometric model. Although the measures of dependence and causality under stationary assumption are well established, empirical studies show that these measures are not constant in time. Recently one of the most important classes of nonstationary processes has been formulated in a rigorous asymptotic framework by Dahlhaus in (1996, (1997, and (2000, called locally stationary processes. Locally stationary processes have time-varying spectral densities whose spectral structures smoothly change in time. Here, we generalize measures of linear dependence and causality to multiple locally stationary processes. We give the measures of linear dependence, linear causality from one series to the other, and instantaneous linear feedback, at time t and frequency λ.
Lascola, Robert; O'Rourke, Patrick E; Kyser, Edward A
2017-01-01
We have developed a piecewise local (PL) partial least squares (PLS) analysis method for total plutonium measurements by absorption spectroscopy in nitric acid-based nuclear material processing streams. Instead of using a single PLS model that covers all expected solution conditions, the method selects one of several local models based on an assessment of solution absorbance, acidity, and Pu oxidation state distribution. The local models match the global model for accuracy against the calibration set, but were observed in several instances to be more robust to variations associated with measurements in the process. The improvements are attributed to the relative parsimony of the local models. Not all of the sources of spectral variation are uniformly present at each part of the calibration range. Thus, the global model is locally overfitting and susceptible to increased variance when presented with new samples. A second set of models quantifies the relative concentrations of Pu(III), (IV), and (VI). Standards containing a mixture of these species were not at equilibrium due to a disproportionation reaction. Therefore, a separate principal component analysis is used to estimate of the concentrations of the individual oxidation states in these standards in the absence of independent confirmatory analysis. The PL analysis approach is generalizable to other systems where the analysis of chemically complicated systems can be aided by rational division of the overall range of solution conditions into simpler sub-regions.
STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS
FELLNER, KLEMENS
2010-12-01
In this paper, we are interested in the large-time behaviour of a solution to a non-local interaction equation, where a density of particles/individuals evolves subject to an interaction potential and an external potential. It is known that for regular interaction potentials, stable stationary states of these equations are generically finite sums of Dirac masses. For a finite sum of Dirac masses, we give (i) a condition to be a stationary state, (ii) two necessary conditions of linear stability w.r.t. shifts and reallocations of individual Dirac masses, and (iii) show that these linear stability conditions imply local non-linear stability. Finally, we show that for regular repulsive interaction potential Wε converging to a singular repulsive interaction potential W, the Dirac-type stationary states ρ̄ ε approximate weakly a unique stationary state ρ̄ ∈ L∞. We illustrate our results with numerical examples. © 2010 World Scientific Publishing Company.
Global equilibrium and local thermodynamics in stationary spacetimes
Panerai, R
2015-01-01
In stationary spacetimes global equilibrium states can be defined, applying the maximum entropy principle, by the introduction of local thermodynamic fields determined solely by geometry. As an example, we study a class of equilibrium states for a scalar field in the Einstein's static universe, characterized by inhomogeneous thermodynamic properties and non-vanishing angular momentum.
Institute of Scientific and Technical Information of China (English)
ZHAO Yuchun; LI Zechun; XIAO Ziniu
2008-01-01
A 4-day persistent rainstorm resulting in serious flooding disasters occurred in the north of Fujian Province under the influences of a quasi-stationary Meiyu front during 5-8 June 2006. With 1°×1°latitude and longitude NCEP reanalysis data and the ground surface rainfall, using the potential vorticity (PV) analysis and PV inversion method, the evolution of main synoptic systems, and the corresponding PV and PV perturbation (or PV anomalies) and their relationship with heavy rainfall along the Meiyu front are analyzed in order to investigate the physical mechanism of the formation, development, and maintenance of the Meiyu front. Furthermore, the PV perturbations related to different physics are separated to investigate their different roles in the formation and development of the Meiyu front. The results show: the formation and persistence of the Meiyu front in a quasi-WE orientation are mainly due to the maintenance of the high-pressure systems in its south/north sides (the West Pacific subtropical high/ the high pressure band extending from the Korean Peninsula to east of North China). The Meiyu front is closely associated with the PV in the lower troposphere. The location of the positive PV perturbation on the Meiyu front matches well with the main heavy rainfall area along the Meiyu front. The PV inversion reveals that the balanced winds satisfying the nonlinear balanced assumption represent to a large extent the real atmospheric flow and its evolution basically reflects the variation of stream flow associated with the Meiyu front. The unbalanced flow forms the convergence band of the Meiyu front and it mainly comes from the high-pressure system in the north side of the Meiyu front. The positive PV perturbation related to latent heat release in the middle-lower troposphere is one of the main factors influencing the formation and development of the Meiyu front. The positive vorticity band from the total balanced winds is in accordance with the Meiyu front
Directory of Open Access Journals (Sweden)
Haiyan Hu
1996-01-01
Full Text Available One critical case for the motion of a periodically excited oscillator with continuous and piecewise-linear restoring force is that the motion happens to graze a switching plane between two linear regions of the restoring force. This article presents a numerical scheme for locating the periodic grazing orbit first. Then, through a brief analysis, the article shows that the grazing phenomenon turns the stability trend of the periodic orbit so abruptly that it may be impossible to predict an incident local bifurcation with the variation of a control parameter from the concept of smooth dynamic systems. The numerical simulation in the article well supports the scheme and the analysis, and shows an abundance of grazing phenomena in an engineering range of the excitation frequency.
Estimation for Non-Gaussian Locally Stationary Processes with Empirical Likelihood Method
Directory of Open Access Journals (Sweden)
Hiroaki Ogata
2012-01-01
Full Text Available An application of the empirical likelihood method to non-Gaussian locally stationary processes is presented. Based on the central limit theorem for locally stationary processes, we give the asymptotic distributions of the maximum empirical likelihood estimator and the empirical likelihood ratio statistics, respectively. It is shown that the empirical likelihood method enables us to make inferences on various important indices in a time series analysis. Furthermore, we give a numerical study and investigate a finite sample property.
Stationary Source Related Documents for State and Local Transportation
State and Local Transporation Resources is an EPA/OTAQ web page for state and local air quality regulators and transportation planners that offers guidance on how to reduce air pollution from cars, diesel trucks, city and school buses
Large-Deviation Results for Discriminant Statistics of Gaussian Locally Stationary Processes
Directory of Open Access Journals (Sweden)
Junichi Hirukawa
2012-01-01
Full Text Available This paper discusses the large-deviation principle of discriminant statistics for Gaussian locally stationary processes. First, large-deviation theorems for quadratic forms and the log-likelihood ratio for a Gaussian locally stationary process with a mean function are proved. Their asymptotics are described by the large deviation rate functions. Second, we consider the situations where processes are misspecified to be stationary. In these misspecified cases, we formally make the log-likelihood ratio discriminant statistics and derive the large deviation theorems of them. Since they are complicated, they are evaluated and illustrated by numerical examples. We realize the misspecification of the process to be stationary seriously affecting our discrimination.
Local invariants vanishing on stationary horizons: a diagnostic for locating black holes.
Page, Don N; Shoom, Andrey A
2015-04-10
Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of n linearly independent gradients of scalar polynomial curvature invariants, where n is the local cohomogeneity of the spacetime.
Piecewise flat gravitational waves
Energy Technology Data Exchange (ETDEWEB)
Van de Meent, Maarten, E-mail: M.vandeMeent@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, PO Box 80.195, 3508 TD Utrecht (Netherlands)
2011-04-07
We examine the continuum limit of the piecewise flat locally finite gravity model introduced by 't Hooft. In the linear weak field limit, we find the energy-momentum tensor and metric perturbation of an arbitrary configuration of defects. The energy-momentum turns out to be restricted to satisfy certain conditions. The metric perturbation is mostly fixed by the energy-momentum except for its lightlike modes which reproduce linear gravitational waves, despite no such waves being present at the microscopic level.
Institute of Scientific and Technical Information of China (English)
WANG Renhong; ZHU Chungang
2004-01-01
The piecewise algebraic variety is a generalization of the classical algebraic variety. This paper discusses some properties of piecewise algebraic varieties and their coordinate rings based on the knowledge of algebraic geometry.
Local multifractal detrended fluctuation analysis for non-stationary image's texture segmentation
Wang, Fang; Li, Zong-shou; Li, Jin-wei
2014-12-01
Feature extraction plays a great important role in image processing and pattern recognition. As a power tool, multifractal theory is recently employed for this job. However, traditional multifractal methods are proposed to analyze the objects with stationary measure and cannot for non-stationary measure. The works of this paper is twofold. First, the definition of stationary image and 2D image feature detection methods are proposed. Second, a novel feature extraction scheme for non-stationary image is proposed by local multifractal detrended fluctuation analysis (Local MF-DFA), which is based on 2D MF-DFA. A set of new multifractal descriptors, called local generalized Hurst exponent (Lhq) is defined to characterize the local scaling properties of textures. To test the proposed method, both the novel texture descriptor and other two multifractal indicators, namely, local Hölder coefficients based on capacity measure and multifractal dimension Dq based on multifractal differential box-counting (MDBC) method, are compared in segmentation experiments. The first experiment indicates that the segmentation results obtained by the proposed Lhq are better than the MDBC-based Dq slightly and superior to the local Hölder coefficients significantly. The results in the second experiment demonstrate that the Lhq can distinguish the texture images more effectively and provide more robust segmentations than the MDBC-based Dq significantly.
Quantized, piecewise linear filter network
DEFF Research Database (Denmark)
Sørensen, John Aasted
1993-01-01
A quantization based piecewise linear filter network is defined. A method for the training of this network based on local approximation in the input space is devised. The training is carried out by repeatedly alternating between vector quantization of the training set into quantization classes an...
Österlind, Tomas; Kari, Leif; Nicolescu, Cornel Mihai
2017-02-01
Rotor vibration and stationary displacement patterns observed in rotating machineries subject to local harmonic excitation are analysed for improved understanding and dynamic characterization. The analysis stresses the importance of coordinate transformation between rotating and stationary frame of reference for accurate results and estimation of dynamic properties. A generic method which can be used for various rotor applications such as machine tool spindle and turbo machinery vibration is presented. The phenomenon shares similarities with stationary waves in rotating disks though focuses on vibration in shafts. The paper further proposes a graphical tool, the displacement map, which can be used for selection of stable rotational speed for rotating machinery. The results are validated through simulation of dynamic response of a milling cutter, which is a typical example of a variable speed rotor operating under different load conditions.
Stability of stationary states of non-local equations with singular interaction potentials
Fellner, Klemens
2011-04-01
We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin.For locally attractive singular interaction potentials we prove under a linear stability condition local non-linear stability of stationary states consisting of a finite sum of Dirac masses. For singular repulsive interaction potentials we show the stability of stationary states of uniformly bounded solutions under a convexity condition.Finally, we present numerical simulations to illustrate our results. © 2010 Elsevier Ltd.
Van der Veken, Frederik F
2014-01-01
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in calculations for constructing or modelling parton density functions. We develop an algorithm to express piecewise path ordered exponentials as path ordered integrals over the separate segments, and apply it on linear segments, reducing the number of diagrams needed to be calculated. We show how different linear path topologies can be related using their colour structure. This framework allows one to easily switch results between different Wilson line structures, which is especially useful when testing different structures against each other, e.g. when checking universality properties of non-perturbative objects.
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.
REAL PIECEWISE ALGEBRAIC VARIETY
Institute of Scientific and Technical Information of China (English)
Ren-hong Wang; Yi-sheng Lai
2003-01-01
We give definitions of real piecewise algebraic variety and its dimension. By using the techniques of real radical ideal, P-radical ideal, affine Hilbert polynomial, Bernstein-net form of polynomials on simplex, and decomposition of semi-algebraic set, etc., we deal with the dimension of the real piecewise algebraic variety and real Nullstellensatz in Cμ spline ring.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are,in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases. We give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A), and show an A∞-structure on E(A). Relations between Koszul algebras and piecewise-Koszul algebras are discussed. In particular, our results are related to the third question of Green-Marcos.
Maslova, N. S.; Mantsevich, V. N.; Arseyev, P. I.
2017-02-01
We perform theoretical investigation of the localized state dynamics in the presence of interaction with the reservoir and Coulomb correlations. We analyze kinetic equations for electron occupation numbers with different spins taking into account high order correlation functions for the localized electrons. We reveal that in the stationary state electron occupation numbers with the opposite spins always have the same value - the stationary state is a "paramagnetic" one. "Magnetic" properties can appear only in the non-stationary characteristics of the single-impurity Anderson model and in the dynamics of the localized electrons second order correlation functions. We found, that for deep energy levels and strong Coulomb correlations, relaxation time for initial "magnetic" state can be several orders larger than for "paramagnetic" one. So, long-living "magnetic" moment can exist in the system. We also found non-stationary spin polarized currents flowing in opposite directions for the different spins in the particular time interval.
Directory of Open Access Journals (Sweden)
Yu Jiang
2012-01-01
Full Text Available A new finite element variational multiscale (VMS method based on two local Gauss integrations is proposed and analyzed for the stationary conduction-convection problems. The valuable feature of our method is that the action of stabilization operators can be performed locally at the element level with minimal additional cost. The theory analysis shows that our method is stable and has a good precision. Finally, the numerical test agrees completely with the theoretical expectations and the “ exact solution,” which show that our method is highly efficient for the stationary conduction-convection problems.
Winey, Brian Andrew
Ultrasound-induced blood stasis has been observed for more than 30 years. The physical understanding of the phenomenon has not been fully explored. Analytical descriptions of the acoustic interaction with spheres in suspension have been derived but the physical implications and limitations have not been demonstrated. The analytical expressions will be tested against physical observations using numerical simulations. The simulations will begin with stationary spheres and continue with the inclusion of moving spheres and a moving suspending fluid. To date, experimental observations of acoustically induced blood stasis have been either in vitro or invasive. We demonstrate ultrasound-induced blood stasis in murine normal leg muscle versus tumor-bearing legs, observed through noninvasive measurements of optical spectroscopy, and discuss possible diagnostic uses for this effect of ultrasound. We derive the optimal optical wavelengths for measuring the effects of the ultrasound at small source detector separations. Using optical oximetry performed at the optimal wavelengths, we demonstrate that effects of ultrasound can be used to differentiate tumor from normal leg muscle tissue in mice. To provide a statistical analysis of the experiments, we propose a novel diagnostic algorithm that quantitatively differentiates tumor from nontumor with maximum specificity 0.83, maximum sensitivity 0.79, and area under receiver-operating-characteristics curve 0.90. Ultrasound has long been known to cause tissue heating when applied in high intensities. More recently, interest has arisen in the area of High Intensity Focused Ultrasound (HIFU) for localized tissue heating effects, specifically thermal ablation. All present techniques employ focused traveling high intensity acoustic waves to create a region of elevated temperature. Such high intensity traveling waves can be damaging to normal tissue in the vicinity of the focal region, and have demonstrated surface burns and caused
A family of quantization based piecewise linear filter networks
DEFF Research Database (Denmark)
Sørensen, John Aasted
1992-01-01
A family of quantization-based piecewise linear filter networks is proposed. For stationary signals, a filter network from this family is a generalization of the classical Wiener filter with an input signal and a desired response. The construction of the filter network is based on quantization of...
Institute of Scientific and Technical Information of China (English)
Changjiang Zhang; Xiaodong Wang; Haoran Zhang
2005-01-01
A new contrast enhancement algorithm for image is proposed employing wavelet neural network (WNN)and stationary wavelet transform (SWT). Incomplete Beta transform (IBT) is used to enhance the global contrast for image. In order to avoid the expensive time for traditional contrast enhancement algorithms,which search optimal gray transform parameters in the whole gray transform parameter space, a new criterion is proposed with gray level histogram. Contrast type for original image is determined employing the new criterion. Gray transform parameter space is given respectively according to different contrast types,which shrinks the parameter space greatly. Nonlinear transform parameters are searched by simulated annealing algorithm (SA) so as to obtain optimal gray transform parameters. Thus the searching direction and selection of initial values of simulated annealing is guided by the new parameter space. In order to calculate IBT in the whole image, a kind of WNN is proposed to approximate the IBT. Having enhanced the global contrast to input image, discrete SWT is done to the image which has been processed by previous global enhancement method, local contrast enhancement is implemented by a kind of nonlinear operator in the high frequency sub-band images of each decomposition level respectively. Experimental results show that the new algorithm is able to adaptively enhance the global contrast for the original image while it also extrudes the detail of the targets in the original image well. The computation complexity for the new algorithm is O(MN) log(MN), where M and N are width and height of the original image, respectively.
Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression
Bressloff, Paul C.
2011-01-01
We analyze radially symmetric bumps in a two-dimensional piecewise-smooth neural field model with synaptic depression. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Synaptic depression dynamically reduces the strength of synaptic weights in response to increases in activity. We show that in the case of a Mexican hat weight distribution, sufficiently strong synaptic depression can destabilize a stationary bump solution that would be stable in the absence of depression. Numerically it is found that the resulting instability leads to the formation of a traveling spot. The local stability of a bump is determined by solutions to a system of pseudolinear equations that take into account the sign of perturbations around the circular bump boundary. © 2011 Society for Industrial and Applied Mathematics.
Introduction to Piecewise Differentiable Equations
Scholtes, Stefan
2012-01-01
This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the non smooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop
Piecewise flat embeddings for hyperspectral image analysis
Hayes, Tyler L.; Meinhold, Renee T.; Hamilton, John F.; Cahill, Nathan D.
2017-05-01
Graph-based dimensionality reduction techniques such as Laplacian Eigenmaps (LE), Local Linear Embedding (LLE), Isometric Feature Mapping (ISOMAP), and Kernel Principal Components Analysis (KPCA) have been used in a variety of hyperspectral image analysis applications for generating smooth data embeddings. Recently, Piecewise Flat Embeddings (PFE) were introduced in the computer vision community as a technique for generating piecewise constant embeddings that make data clustering / image segmentation a straightforward process. In this paper, we show how PFE arises by modifying LE, yielding a constrained ℓ1-minimization problem that can be solved iteratively. Using publicly available data, we carry out experiments to illustrate the implications of applying PFE to pixel-based hyperspectral image clustering and classification.
Stationary and uniform entanglement distribution in qubit networks with quasi-local dissipation
Rafiee, Morteza; Mokhtari, Hossein; Mancini, Stefano
2012-01-01
We consider qubit networks where adjacent qubits besides interacting via XY-coupling, also dissipate into the same environment. The steady states are computed exactly for all network sizes and topologies, showing that they are always symmetric under permutation of network sites, leading to a uniform distribution of the stationary entanglement across the network. The maximum entanglement between two arbitrary qubits is shown to depend only on the total number of qubits in the network, and scales linearly with it. A possible physical realization by means of an array of doped cavities is discussed for the case of a linear chain.
MAP estimators for piecewise continuous inversion
Dunlop, M. M.; Stuart, A. M.
2016-10-01
We study the inverse problem of estimating a field u a from data comprising a finite set of nonlinear functionals of u a , subject to additive noise; we denote this observed data by y. Our interest is in the reconstruction of piecewise continuous fields u a in which the discontinuity set is described by a finite number of geometric parameters a. Natural applications include groundwater flow and electrical impedance tomography. We take a Bayesian approach, placing a prior distribution on u a and determining the conditional distribution on u a given the data y. It is then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP estimators can be characterised as minimisers of a generalised Onsager-Machlup functional, in the case where the prior measure is a Gaussian random field. We extend this theory to a more general class of prior distributions which allows for piecewise continuous fields. Specifically, the prior field is assumed to be piecewise Gaussian with random interfaces between the different Gaussians defined by a finite number of parameters. We also make connections with recent work on MAP estimators for linear problems and possibly non-Gaussian priors (Helin and Burger 2015 Inverse Problems 31 085009) which employs the notion of Fomin derivative. In showing applicability of our theory we focus on the groundwater flow and EIT models, though the theory holds more generally. Numerical experiments are implemented for the groundwater flow model, demonstrating the feasibility of determining MAP estimators for these piecewise continuous models, but also that the geometric formulation can lead to multiple nearby (local) MAP estimators. We relate these MAP estimators to the behaviour of output from MCMC samples of the posterior, obtained using a state-of-the-art function space Metropolis-Hastings method.
Piecewise nonlinear image registration using DCT basis functions
Gan, Lin; Agam, Gady
2015-03-01
The deformation field in nonlinear image registration is usually modeled by a global model. Such models are often faced with the problem that a locally complex deformation cannot be accurately modeled by simply increasing degrees of freedom (DOF). In addition, highly complex models require additional regularization which is usually ineffective when applied globally. Registering locally corresponding regions addresses this problem in a divide and conquer strategy. In this paper we propose a piecewise image registration approach using Discrete Cosine Transform (DCT) basis functions for a nonlinear model. The contributions of this paper are three-folds. First, we develop a multi-level piecewise registration framework that extends the concept of piecewise linear registration and works with any nonlinear deformation model. This framework is then applied to nonlinear DCT registration. Second, we show how adaptive model complexity and regularization could be applied for local piece registration, thus accounting for higher variability. Third, we show how the proposed piecewise DCT can overcome the fundamental problem of a large curvature matrix inversion in global DCT when using high degrees of freedoms. The proposed approach can be viewed as an extension of global DCT registration where the overall model complexity is increased while achieving effective local regularization. Experimental evaluation results provide comparison of the proposed approach to piecewise linear registration using an affine transformation model and a global nonlinear registration using DCT model. Preliminary results show that the proposed approach achieves improved performance.
Localization of non-stationary sources of electromagnetic radiation with the aid of phasometry
Mersov, G. A.
1978-01-01
The possibility of localizing sources of electromagnetic radiation by measurement of the time of passage of the radiation or the measurement of its phase at various points of cosmic space, at which are located satellite observatories is examined. Algorithms are proposed for localization using two, three, and four astronomical observatories. The precision of the localization and several partial results of practical significance are deduced.
Non-Zenoness of piecewise affine dynamical systems and affine complementarity systems with inputs
Institute of Scientific and Technical Information of China (English)
Le Quang THUAN
2014-01-01
In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs.
Non-stationary oscillations of sandwich plates under local dynamic loading
Skvortsov, Vitaly; Krakhmalev, Sergey; Koysin, V.; Shipsha, Andrey
2003-01-01
The paper addresses the elastic response of composite sandwich panels to local dynamic loading. The plane and axisymmetric formulations are considered; no overall bending is assumed. The governing equations are derived using the static Lamé equations for the core and the plate Kirchoff-Love dynamic
The Bezout Number of Piecewise Algebraic Curves
Institute of Scientific and Technical Information of China (English)
Dian Xuan GONG; Ren Hong WANG
2012-01-01
Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves,a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obtuse-angled triangulation is found.Bezout number of two piecewise algebraic curves on two different partitions is also discussed in this paper.
Continuous Approximations of a Class of Piecewise Continuous Systems
Danca, Marius-F.
In this paper, we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piecewise continuous functions. By using techniques from the theory of differential inclusions, the underlying piecewise functions can be locally or globally approximated. The approximation results can be used to model piecewise continuous-time dynamical systems of integer or fractional-order. In this way, by overcoming the lack of numerical methods for differential equations of fractional-order with discontinuous right-hand side, unattainable procedures for systems modeled by this kind of equations, such as chaos control, synchronization, anticontrol and many others, can be easily implemented. Several examples are presented and three comparative applications are studied.
Notes on Piecewise-Koszul Algebras
Institute of Scientific and Technical Information of China (English)
Jia Feng L(U); Xiao Lan YU
2011-01-01
The relationships between piecewise-Koszul algebras and other "Koszul-type" algebras are discussed.. The Yoneda-Ext algebra and the dual algebra of a piecewise-Koszul algebra are studied, and a sufficient condition for the dual algebra A to be piecewise-Koszul is given. Finally, by studying the trivial extension algebras of the path algebras of Dynkin quivers in bipartite orientation, we give explicit constructions for piecewise-Koszul algebras with arbitrary "period" and piecewise-Koszul algebras with arbitrary "jump-degree".
Bonetto, F.; Chernov, N. I.; Lebowitz, J. L.
1998-12-01
We studied numerically the validity of the fluctuation relation introduced in Evans et al. [Phys. Rev. Lett. 71, 2401-2404 (1993)] and proved under suitable conditions by Gallavotti and Cohen [J. Stat. Phys. 80, 931-970 (1995)] for a two-dimensional system of particles maintained in a steady shear flow by Maxwell demon boundary conditions [Chernov and Lebowitz, J. Stat. Phys. 86, 953-990 (1997)]. The theorem was found to hold if one considers the total phase space contraction sigma occurring at collisions with both walls: sigma=sigma( upward arrow )+sigma( downward arrow ). An attempt to extend it to more local quantities sigma( upward arrow ) and sigma( downward arrow ), corresponding to the collisions with the top or bottom wall only, gave negative results. The time decay of the correlations in sigma( upward arrow, downward arrow ) was very slow compared to that of sigma. (c) 1998 American Institute of Physics.
Piecewise power laws in individual learning curves.
Donner, Yoni; Hardy, Joseph L
2015-10-01
The notion that human learning follows a smooth power law (PL) of diminishing gains is well-established in psychology. This characteristic is observed when multiple curves are averaged, potentially masking more complex dynamics underpinning the curves of individual learners. Here, we analyzed 25,280 individual learning curves, each comprising 500 measurements of cognitive performance taken from four cognitive tasks. A piecewise PL (PPL) model explained the individual learning curves significantly better than a single PL, controlling for model complexity. The PPL model allows for multiple PLs connected at different points in the learning process. We also explored the transition dynamics between PL curve component pieces. Performance in later pieces typically surpassed that in earlier pieces, after a brief drop in performance at the transition point. The transition rate was negatively associated with age, even after controlling for overall performance. Our results suggest at least two processes at work in individual learning curves: locally, a gradual, smooth improvement, with diminishing gains within a specific strategy, which is modeled well as a PL; and globally, a discrete sequence of strategy shifts, in which each strategy is better in the long term than the ones preceding it. The piecewise extension of the classic PL of practice has implications for both individual skill acquisition and theories of learning.
Stable piecewise polynomial vector fields
Directory of Open Access Journals (Sweden)
Claudio Pessoa
2012-09-01
Full Text Available Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector field $Z=(X,Y$. This work pursues the stability and the transition analysis of solutions of $Z$ between $N$ and $S$, started by Filippov (1988 and Kozlova (1984 and reformulated by Sotomayor-Teixeira (1995 in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields $Z_{epsilon}$, defined by averaging $X$ and $Y$. This family approaches $Z$ when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002 providing conditions on $(X,Y$ for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on $mathbb{R}^2$. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.
Piecewise-adaptive decomposition methods
Energy Technology Data Exchange (ETDEWEB)
Ramos, J.I. [Room I-320-D, E.T.S. Ingenieros Industriales, Universidad de Malaga, Plaza El Ejido, s/n, 29013 Malaga (Spain)], E-mail: jirs@lcc.uma.es
2009-05-30
Piecewise-adaptive decomposition methods are developed for the solution of nonlinear ordinary differential equations. These methods are based on some theorems that show that Adomian's decomposition method is a homotopy perturbation technique and coincides with Taylor's series expansions for autonomous ordinary differential equations. Piecewise-decomposition methods provide series solutions in intervals which are subject to continuity conditions at the end points of each interval, and their adaption is based on the use of either a fixed number of approximants and a variable step size, a variable number of approximants and a fixed step size or a variable number of approximants and a variable step size. It is shown that the appearance of noise terms in the decomposition method is related to both the differential equation and the manner in which the homotopy parameter is introduced, especially for the Lane-Emden equation. It is also shown that, in order to avoid the use of numerical quadrature, there is a simple way of introducing the homotopy parameter in the two first-order ordinary differential equations that correspond to the second-order Thomas-Fermi equation. It is also shown that the piecewise homotopy perturbation methods presented here provide more accurate results than a modified Adomian decomposition technique which makes use of Pade approximants and the homotopy analysis method, for the Thomas-Fermi equation.
Mahmood, Toqeer; Irtaza, Aun; Mehmood, Zahid; Tariq Mahmood, Muhammad
2017-10-01
The most common image tampering often for malicious purposes is to copy a region of the same image and paste to hide some other region. As both regions usually have same texture properties, therefore, this artifact is invisible for the viewers, and credibility of the image becomes questionable in proof centered applications. Hence, means are required to validate the integrity of the image and identify the tampered regions. Therefore, this study presents an efficient way of copy-move forgery detection (CMFD) through local binary pattern variance (LBPV) over the low approximation components of the stationary wavelets. CMFD technique presented in this paper is applied over the circular regions to address the possible post processing operations in a better way. The proposed technique is evaluated on CoMoFoD and Kodak lossless true color image (KLTCI) datasets in the presence of translation, flipping, blurring, rotation, scaling, color reduction, brightness change and multiple forged regions in an image. The evaluation reveals the prominence of the proposed technique compared to state of the arts. Consequently, the proposed technique can reliably be applied to detect the modified regions and the benefits can be obtained in journalism, law enforcement, judiciary, and other proof critical domains. Copyright © 2017 Elsevier B.V. All rights reserved.
Incompressible flows with piecewise constant density
Danchin, Raphaël
2012-01-01
We investigate the incompressible Navier-Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous ini- tial density. In dimension n = 2, 3, assuming only that the initial density is bounded and bounded away from zero, and that the initial velocity is smooth enough, we get the local-in-time existence of unique solutions. Uniqueness holds in any dimension and for a wider class of velocity fields. Let us emphasize that all those results are true for piecewise constant densities with arbitrarily large jumps. Global results are established in dimension two if the density is close enough to a positive constant, and in n-dimension if, in addition, the initial velocity is small. The Lagrangian formula- tion for describing the flow plays a key role in the analysis that is proposed in the present paper.
Control and estimation of piecewise affine systems
Xu, Jun
2014-01-01
As a powerful tool to study nonlinear systems and hybrid systems, piecewise affine (PWA) systems have been widely applied to mechanical systems. Control and Estimation of Piecewise Affine Systems presents several research findings relating to the control and estimation of PWA systems in one unified view. Chapters in this title discuss stability results of PWA systems, using piecewise quadratic Lyapunov functions and piecewise homogeneous polynomial Lyapunov functions. Explicit necessary and sufficient conditions for the controllability and reachability of a class of PWA systems are
Smoothing of Piecewise Linear Paths
Directory of Open Access Journals (Sweden)
Michel Waringo
2008-11-01
Full Text Available We present an anytime-capable fast deterministic greedy algorithm for smoothing piecewise linear paths consisting of connected linear segments. With this method, path points with only a small influence on path geometry (i.e. aligned or nearly aligned points are successively removed. Due to the removal of less important path points, the computational and memory requirements of the paths are reduced and traversing the path is accelerated. Our algorithm can be used in many different applications, e.g. sweeping, path finding, programming-by-demonstration in a virtual environment, or 6D CNC milling. The algorithm handles points with positional and orientational coordinates of arbitrary dimension.
Stability of bumps in piecewise smooth neural fields with nonlinear adaptation
Kilpatrick, Zachary P.
2010-06-01
We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation variable associated with a bump solution means that bump stability cannot be analyzed by constructing the Evans function for a network with a sigmoidal gain function and then taking the high-gain limit. In the case of synaptic depression, we show that linear stability can be formulated in terms of solutions to a system of pseudo-linear equations. We thus establish that sufficiently strong synaptic depression can destabilize a bump that is stable in the absence of depression. These instabilities are dominated by shift perturbations that evolve into traveling pulses. In the case of spike frequency adaptation, we show that for a wide class of perturbations the activity and adaptation variables decouple in the linear regime, thus allowing us to explicitly determine stability in terms of the spectrum of a smooth linear operator. We find that bumps are always unstable with respect to this class of perturbations, and destabilization of a bump can result in either a traveling pulse or a spatially localized breather. © 2010 Elsevier B.V. All rights reserved.
Gray, Morgan; Rodionov, Sergey; Bocquet, Marc; Bertino, Laurent; Ferrari, Marc; Fusco, Thierry
2014-01-01
We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).
Algebra-Geometry of Piecewise Algebraic Varieties
Institute of Scientific and Technical Information of China (English)
Chun Gang ZHU; Ren Hong WANG
2012-01-01
Algebraic variety is the most important subject in classical algebraic geometry.As the zero set of multivariate splines,the piecewise algebraic variety is a kind generalization of the classical algebraic variety.This paper studies the correspondence between spline ideals and piecewise algebraic varieties based on the knowledge of algebraic geometry and multivariate splines.
DEFF Research Database (Denmark)
Gravesen, Jens
2005-01-01
t is shown that a closed polygon with an odd number of vertices is the median of exactly one piecewise planar cylinder and one piecewise planar Möbius band, intersecting each other orthogonally. A closed polygon with an even number of vertices is in the generic case neither the median of a piecew...
Enhanced piecewise regression based on deterministic annealing
Institute of Scientific and Technical Information of China (English)
ZHANG JiangShe; YANG YuQian; CHEN XiaoWen; ZHOU ChengHu
2008-01-01
Regression is one of the important problems in statistical learning theory. This paper proves the global convergence of the piecewise regression algorithm based on deterministic annealing and continuity of global minimum of free energy w.r.t temperature, and derives a new simplified formula to compute the initial critical temperature. A new enhanced piecewise regression algorithm by using "migration of prototypes" is proposed to eliminate "empty cell" in the annealing process. Numerical experiments on several benchmark datasets show that the new algo-rithm can remove redundancy and improve generalization of the piecewise regres-sion model.
Algebraic reconstruction of piecewise-smooth functions from integral measurements
Batenkov, Dmitry; Yomdin, Yosef
2011-01-01
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier coefficients, Radon transform, etc.). Our results concern reconstruction (from the moments or Fourier coefficients) of signals in two specific classes: linear combinations of shifts of a given function, and "piecewise $D$-finite functions" which satisfy on each continuity interval a linear differential equation with polynomial coefficients. In each case the problem is reduced to a solution of a certain type of non-linear algebraic system of equations ("Prony-type system"). We recall some known methods for explicitly solving such systems in one variable, and provide extensions to some multi-dimensional cases. Finally, we investigate the local stability of solving the Prony-type systems.
Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps
Zhang, Yiwei
2011-01-01
We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\\mathbb{R}^d$. This class of maps unifies piecewise isometries (PWIs) and piecewise hyperbolic maps where Lebesgue measure is locally preserved. In particular for PWIs, we use a functional approach to explore the relationship between topological transitivity and uniqueness of ACIPs, especially those measures with bounded variation densities. Our results "partially" answer one of the fundamental questions posed in \\cite{Goetz03} - determine all invariant non-atomic probability Borel measures in piecewise rotations. When reducing to interval exchange transformations (IETs), we demonstrate that for non-uniquely ergodic IETs with two or more ACIPs, these ACIPs have very irregular densities (namely of unbounded variation and discontinuous everywhere) and intermingle with each other.
Piecewise polynomial solutions to linear inverse problems
DEFF Research Database (Denmark)
Hansen, Per Christian; Mosegaard, K.
1996-01-01
We have presented a new algorithm PP-TSVD that computes piecewise polynomial solutions to ill-posed problems, without a priori knowledge about the positions of the break points. In particular, we can compute piecewise constant functions that describe layered models. Such solutions are useful, e.g.......g., in seismological problems, and the algorithm can also be used as a preprocessor for other methods where break points/discontinuities must be incorporated explicitly....
Piecewise polynomial representations of genomic tracks.
Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz
2012-01-01
Genomic data from micro-array and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewise-polynomial curves. We present a general framework for building piecewise polynomial representations of genome-scale signals and illustrate some of its applications via examples. We show that piecewise constant segmentation, a typical step in copy-number analyses, can be carried out within this framework for both array and (DNA) sequencing data offering advantages over existing methods in each case. Higher-order polynomial curves can be used, for example, to detect trends and/or discontinuities in transcription levels from RNA-seq data. We give a concrete application of piecewise linear functions to diagnose and quantify alignment quality at exon borders (splice sites). Our software (source and object code) for building piecewise polynomial models is available at http://sourceforge.net/projects/locsmoc/.
Global behaviour of a predator-prey like model with piecewise constant arguments.
Kartal, Senol; Gurcan, Fuat
2015-01-01
The present study deals with the analysis of a predator-prey like model consisting of system of differential equations with piecewise constant arguments. A solution of the system with piecewise constant arguments leads to a system of difference equations which is examined to study boundedness, local and global asymptotic behaviour of the positive solutions. Using Schur-Cohn criterion and a Lyapunov function, we derive sufficient conditions under which the positive equilibrium point is local and global asymptotically stable. Moreover, we show numerically that periodic solutions arise as a consequence of Neimark-Sacker bifurcation of a limit cycle.
Collisions in piecewise flat gravity in 3+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Van de Meent, Maarten, E-mail: M.vandeMeent@uu.n [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, PO Box 80.195, 3508 TD Utrecht (Netherlands)
2010-07-21
We consider the (3 + 1)-dimensional locally finite gravity model proposed by 't Hooft (2008 Found. Phys. 38 733-57). In particular we revisit the problem of resolving collisions of string defects. We provide a new geometric description of the configurations of strings using piecewise flat manifolds and use it to resolve a more general class of collisions. We argue that beyond certain bounds for the deficiency/surplus angles no resolutions may be found that satisfy the imposed causality conditions.
Piecewise deterministic Markov processes : an analytic approach
Alkurdi, Taleb Salameh Odeh
2013-01-01
The subject of this thesis, piecewise deterministic Markov processes, an analytic approach, is on the border between analysis and probability theory. Such processes can either be viewed as random perturbations of deterministic dynamical systems in an impulsive fashion, or as a particular kind of
N(o)ther-type theorem of piecewise algebraic curves
Institute of Scientific and Technical Information of China (English)
WANG Renhong; ZHU Chungang
2004-01-01
The piecewise algebraic curve is a generalization of the classical algebraic curve.This paper describes the improvement of the Nother-type theorem of piecewise algebraic curves on the star region.Moreover,the Nother-type theorem of piecewise algebraic curves on the cross-cut partition is discussed.
Budroni, M. A.; De Wit, A.
2016-06-01
When two solutions containing separate reactants A and B of an oscillating reaction are put in contact in a gel, localized spatiotemporal patterns can develop around the contact zone thanks to the interplay of reaction and diffusion processes. Using the Brusselator model, we explore analytically the deployment in space and time of the bifurcation diagram of such an A +B → oscillator system. We provide a parametric classification of possible instabilities as a function of the ratio of the initial reactant concentrations and of the reaction intermediate species diffusion coefficients. Related one-dimensional reaction-diffusion dynamics are studied numerically. We find that the system can spatially localize waves and Turing patterns as well as induce more complex dynamics such as zigzag spatiotemporal waves when Hopf and Turing modes interact.
Decomposed Implicit Models of Piecewise - Linear Networks
Directory of Open Access Journals (Sweden)
J. Brzobohaty
1992-05-01
Full Text Available The general matrix form of the implicit description of a piecewise-linear (PWL network and the symbolic block diagram of the corresponding circuit model are proposed. Their decomposed forms enable us to determine quite separately the existence of the individual breakpoints of the resultant PWL characteristic and their coordinates using independent network parameters. For the two-diode and three-diode cases all the attainable types of the PWL characteristic are introduced.
Embedding loop quantum cosmology without piecewise linearity
Engle, Jonathan
2013-01-01
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), {\\em directly at the quantum level}. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, as well as permitting lessons from the reduced theory to guide further development in the full theory. The present paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on \\textit{piecewise analytic paths}. The embedding is well-defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed, and at no point is the piecewise linear category used. This motivates for the first time a definition of operators in LQC corresponding to holonomies along non-piecewise-linear paths, without changing the usual kinematics of LQC in any way. The new embedding intertwines all operators corresponding to such hol...
Embedding loop quantum cosmology without piecewise linearity
Engle, Jonathan
2013-04-01
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, as well as permitting lessons from the reduced theory to guide further development in the full theory. This paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on piecewise analytic paths. The embedding is well defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed and at no point is the piecewise linear category used. This motivates for the first time a definition of operators in LQC corresponding to holonomies along non-piecewise linear paths, without changing the usual kinematics of LQC in any way. The new embedding intertwines all operators corresponding to such holonomies, and all elements in its image satisfy an operator equation which classically implies homogeneity and isotropy. The construction is made possible by a recent result proven by Fleischhack. Communicated by P Singh
H∞ controller synthesis of piecewise discrete time linear systems
Institute of Scientific and Technical Information of China (English)
Gang FENG
2003-01-01
This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomance and the controller can be obtained by solvng a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapnnov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.
Detecting ecological breakpoints: a new tool for piecewise regression
Directory of Open Access Journals (Sweden)
Alessandro Ferrarini
2011-06-01
Full Text Available Simple linear regression tries to determine a linear relationship between a given variable X (predictor and a dependent variable Y. Since most of the environmental problems involve complex relationships, X-Y relationship is often better modeled through a regression where, instead of fitting a single straight line to the data, the algorithm allows the fitting to bend. Piecewise regressions just do it, since they allow emphasize local, instead of global, rules connecting predictor and dependent variables. In this work, a tool called RolReg is proposed as an implementation of Krummel's method to detect breakpoints in regression models. RolReg, which is freely available upon request from the author, could useful to detect proper breakpoints in ecological laws.
A new approach to piecewise linear Wilson lines
Van der Veken, Frederik F
2014-01-01
Wilson lines are key objects in many QCD calculations. They are parallel transporters of the gauge field that can be used to render non-local operator products gauge invariant, which is especially useful for calculations concerning validation of factorization schemes and in calculations for constructing or modelling parton density functions. We develop an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their Wilson segments, reducing the number of diagrams needed to be calculated. We show how different linear path topologies can be related using their color structure. This framework allows one to easily switch results between different Wilson line structures, which is helpful when testing different structures against each other, e.g. when checking universality properties of non-perturbative objects.
[Optimizing algorithm design of piecewise linear classifier for spectra].
Lan, Tian-Ge; Fang, Yong-Hua; Xiong, Wei; Kong, Chao; Li, Da-Cheng; Dong, Da-Ming
2008-11-01
Being able to identify pollutant gases quickly and accurately is a basic request of spectroscopic technique for envirment monitoring for spectral classifier. Piecewise linear classifier is simple needs less computational time and approachs nonlinear boundary beautifully. Combining piecewise linear classifier and linear support vector machine which is based on the principle of maximizing margin, an optimizing algorithm for single side piecewise linear classifier was devised. Experimental results indicate that the piecewise linear classifier trained by the optimizing algorithm proposed in this paper can approach nonolinear boundary with fewer super_planes and has higher veracity for classification and recognition.
Piecewise Silence in Discrete Cosmological Models
Clifton, Timothy; Rosquist, Kjell
2014-01-01
We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon "piecewise silence".
Piecewise Linear Model-Based Image Enhancement
Directory of Open Access Journals (Sweden)
Fabrizio Russo
2004-09-01
Full Text Available A novel technique for the sharpening of noisy images is presented. The proposed enhancement system adopts a simple piecewise linear (PWL function in order to sharpen the image edges and to reduce the noise. Such effects can easily be controlled by varying two parameters only. The noise sensitivity of the operator is further decreased by means of an additional filtering step, which resorts to a nonlinear model too. Results of computer simulations show that the proposed sharpening system is simple and effective. The application of the method to contrast enhancement of color images is also discussed.
Bayesian regression of piecewise homogeneous Poisson processes
Directory of Open Access Journals (Sweden)
Diego Sevilla
2015-12-01
Full Text Available In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is valuable for detecting breaking points in the count rate of time series for Poisson processes. Received: 2 November 2015, Accepted: 27 November 2015; Edited by: R. Dickman; Reviewed by: M. Hutter, Australian National University, Canberra, Australia.; DOI: http://dx.doi.org/10.4279/PIP.070018 Cite as: D J R Sevilla, Papers in Physics 7, 070018 (2015
Renormalizable two-parameter piecewise isometries.
Lowenstein, J H; Vivaldi, F
2016-06-01
We exhibit two distinct renormalization scenarios for two-parameter piecewise isometries, based on 2π/5 rotations of a rhombus and parameter-dependent translations. Both scenarios rely on the recently established renormalizability of a one-parameter triangle map, which takes place if and only if the parameter belongs to the algebraic number field K=Q(5) associated with the rotation matrix. With two parameters, features emerge which have no counterpart in the single-parameter model. In the first scenario, we show that renormalizability is no longer rigid: whereas one of the two parameters is restricted to K, the second parameter can vary continuously over a real interval without destroying self-similarity. The mechanism involves neighbouring atoms which recombine after traversing distinct return paths. We show that this phenomenon also occurs in the simpler context of Rauzy-Veech renormalization of interval exchange transformations, here regarded as parametric piecewise isometries on a real interval. We explore this analogy in some detail. In the second scenario, which involves two-parameter deformations of a three-parameter rhombus map, we exhibit a weak form of rigidity. The phase space splits into several (non-convex) invariant components, on each of which the renormalization still has a free parameter. However, the foliations of the different components are transversal in parameter space; as a result, simultaneous self-similarity of the component maps requires that both of the original parameters belong to the field K.
Piecewise-Planar Parabolic Reflectarray Antenna
Hodges, Richard; Zawadzki, Mark
2009-01-01
The figure shows a dual-beam, dualpolarization Ku-band antenna, the reflector of which comprises an assembly of small reflectarrays arranged in a piecewise- planar approximation of a parabolic reflector surface. The specific antenna design is intended to satisfy requirements for a wide-swath spaceborne radar altimeter, but the general principle of piecewise-planar reflectarray approximation of a parabolic reflector also offers advantages for other applications in which there are requirements for wideswath antennas that can be stowed compactly and that perform equally in both horizontal and vertical polarizations. The main advantages of using flat (e.g., reflectarray) antenna surfaces instead of paraboloidal or parabolic surfaces is that the flat ones can be fabricated at lower cost and can be stowed and deployed more easily. Heretofore, reflectarray antennas have typically been designed to reside on single planar surfaces and to emulate the focusing properties of, variously, paraboloidal (dish) or parabolic antennas. In the present case, one approximates the nominal parabolic shape by concatenating several flat pieces, while still exploiting the principles of the planar reflectarray for each piece. Prior to the conception of the present design, the use of a single large reflectarray was considered, but then abandoned when it was found that the directional and gain properties of the antenna would be noticeably different for the horizontal and vertical polarizations.
Stationary Measure in the Multiverse
Linde, Andrei; Vanchurin, Vitaly; Winitzki, Sergei
2008-01-01
We study the recently proposed "stationary measure" in the context of the string landscape scenario. We show that it suffers neither from the "Boltzmann brain" problem nor from the "youngness" paradox that makes some other measures predict a high CMB temperature at present. We also demonstrate a satisfactory performance of this measure in predicting the results of local experiments, such as proton decay.
The piecewise constant method in gait design through optimization
Institute of Scientific and Technical Information of China (English)
Yizhen Wei
2014-01-01
The objective of this paper is to introduce the piecewise constant method in gait design of a planar, under actuated, five-link biped robot model and to discuss the advantages and disadvantages. The piecewise constant method transforms the dynamic optimal control problem into a static problem.
Using piecewise sinusoidal basis functions to blanket multiple wire segments
CSIR Research Space (South Africa)
Lysko, AA
2009-06-01
Full Text Available This paper discusses application of the piecewise sinusoidal (PWS) basis function (BF) over a chain of several wire segments, for example as a multiple domain basis function. The usage of PWS BF is compared to results based on the piecewise linear...
Dynamics of delayed piecewise linear systems
Directory of Open Access Journals (Sweden)
Laszlo E. Kollar
2003-02-01
Full Text Available In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by a piecewise constant control force which is the linear combination of the sampled values of the angle and the angular velocity of the pendulum. The control force is provided by a motor which drives one of the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid and the belt (elastic introduces a nonlinearity known as ``backlash" and causes the oscillation of the controlled pendulum around its upper equilibrium. The processing and sampling delays in the determination of the control force tend to destabilize the controlled system as well. We obtain conditions guaranteeing that the pendulum remains in the neighborhood of the upper equilibrium. Experimental findings obtained on a computer controlled inverted pendulum cart structure are also presented showing good agreement with the simulation results.
Piecewise deterministic processes in biological models
Rudnicki, Ryszard
2017-01-01
This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models. As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological processes into a unified mathematical theory, and...
Institute of Scientific and Technical Information of China (English)
Yanzhen Chang; Danping Yang
2008-01-01
In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Bénard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence analysis for the states and the co-states. Then we derive error estimates in L∞-norm and optimal error estimates in L2-norm.
Output feedback controller design for uncertain piecewise linear systems
Institute of Scientific and Technical Information of China (English)
Jianxiong ZHANG; Wansheng TANG
2007-01-01
This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities (BMIs). The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities (LMIs) which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.
Estimation of the Bezout number for piecewise algebraic curve
Institute of Scientific and Technical Information of China (English)
WANG; Renhong(王仁宏); XU; Zhiqiang(许志强)
2003-01-01
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function.In this paper, a conjecture on triangulation is confirmed. The relation between the piecewise linear algebraiccurve and four-color conjecture is also presented. By Morgan-Scott triangulation, we will show the instabilityof Bezout number of piecewise algebraic curves. By using the combinatorial optimization method, an upperbound of the Bezout number defined as the maximum finite number of intersection points of two piecewisealgebraic curves is presented.
Harnessing piecewise-linear systems to construct dynamic logic architecture.
Peng, Haipeng; Yang, Yixian; Li, Lixiang; Luo, Hong
2008-09-01
This paper explores piecewise-linear systems to construct dynamic logic architecture. We present three schemes to obtain various basic logic gates, adders, and memory by using piecewise-linear systems. These schemes can switch easily among different operational roles by changing parameters. The proposed schemes are computationally efficient and easy to use. It is convenient for us to study and analyze them with the theory of linear systems.
A prototype piecewise-linear dynamic attenuator
Hsieh, Scott S.; Peng, Mark V.; May, Christopher A.; Shunhavanich, Picha; Fleischmann, Dominik; Pelc, Norbert J.
2016-07-01
The piecewise-linear dynamic attenuator has been proposed as a mechanism in CT scanning for personalizing the x-ray illumination on a patient- and application-specific basis. Previous simulations have shown benefits in image quality, scatter, and dose objectives. We report on the first prototype implementation. This prototype is reduced in scale and speed and is integrated into a tabletop CT system with a smaller field of view (25 cm) and longer scan time (42 s) compared to a clinical system. Stainless steel wedges were machined and affixed to linear actuators, which were in turn held secure by a frame built using rapid prototyping technologies. The actuators were computer-controlled, with characteristic noise of about 100 microns. Simulations suggest that in a clinical setting, the impact of actuator noise could lead to artifacts of only 1 HU. Ring artifacts were minimized by careful design of the wedges. A water beam hardening correction was applied and the scan was collimated to reduce scatter. We scanned a 16 cm water cylinder phantom as well as an anthropomorphic pediatric phantom. The artifacts present in reconstructed images are comparable to artifacts normally seen with this tabletop system. Compared to a flat-field reference scan, increased detectability at reduced dose is shown and streaking is reduced. Artifacts are modest in our images and further refinement is possible. Issues of mechanical speed and stability in the challenging clinical CT environment will be addressed in a future design.
Stationary measure in the multiverse
Energy Technology Data Exchange (ETDEWEB)
Linde, Andrei [Department of Physics, Stanford University, Stanford, CA 94305 (United States); Vanchurin, Vitaly; Winitzki, Sergei, E-mail: alinde@stanford.edu, E-mail: vitaly@cosmos2.phy.tufts.edu, E-mail: winitzki@physik.uni-muenchen.de [Department of Physics, Ludwig-Maximilians University, Munich (Germany)
2009-01-15
We study the recently proposed ''stationary measure'' in the context of the string landscape scenario. We show that it suffers neither from the ''Boltzmann brain'' problem nor from the ''youngness'' paradox that makes some other measures predict a high CMB temperature at present. We also demonstrate a good performance of this measure in predicting the results of local experiments, such as proton decay.
Piecewise linear hypersurfaces using the marching cubes algorithm
Roberts, Jonathan C.; Hill, Steve
1999-03-01
Surface visualization is very important within scientific visualization. The surfaces depict a value of equal density (an isosurface) or display the surrounds of specified objects within the data. Likewise, in two dimensions contour plots may be used to display the information. Thus similarly, in four dimensions hypersurfaces may be formed around hyperobjects. These surfaces (or contours) are often formed from a set of connected triangles (or lines). These piecewise segments represent the simplest non-degenerate object of that dimension and are named simplices. In four dimensions a simplex is represented by a tetrahedron, which is also known as a 3- simplex. Thus, a continuous n dimensional surface may be represented by a lattice of connected n-1 dimensional simplices. This lattice of connected simplices may be calculated over a set of adjacent n dimensional cubes, via for example the Marching Cubes Algorithm. We propose that the methods of this local-cell tiling method may be usefully- applied to four dimensions and potentially to N-dimensions. Thus, we organize the large number of traversal cases and major cases; introduce the notion of a sub-case (that enables the large number of cases to be further reduced); and describe three methods for implementing the Marching Cubes lookup table in four-dimensions.
Piecewise Filter of Infrared Image Based on Moment Theory
Institute of Scientific and Technical Information of China (English)
GAO Yang; LI Yan-jun; ZHANG Ke
2007-01-01
The disadvantages of IR images mostly include high noise, blurry edge and so on. The characteristics make the existent smoothing methods ineffective in preserving edge. To solve this problem, a piecewise moment filter (PMF) is put forward. By using moment and piecewise linear theory, the filter can preserve edge. Based on the statistical model of random noise, a related-coefficient method is presented to estimate the variance of noise. The edge region and model are then detected by the estimated variance. The expectation of first-order derivatives is used in getting the reliable offset of edge.At last, a fast moment filter of double-stair edge model is used to gain the piecewise smoothing results and reduce the calculation. The experimental result shows that the new method has a better capability than other methods in suppressing noise and preserving edge.
RESERVOIR DESCRIPTION BY USING A PIECEWISE CONSTANT LEVEL SET METHOD
Institute of Scientific and Technical Information of China (English)
Hongwei Li; Xuecheng Tai; Sigurd Ivar Aanonsen
2008-01-01
We consider the permeability estimation problem in two-phase porous media flow. We try to identify the permeability field by utilizing both the production data from wells as well as inverted seismic data. The permeability field is assumed to be piecewise constant, or can be approximated well by a piecewise constant function. A variant of the level set method, called Piecewise Constant Level Set Method is used to represent the interfaces between the regions with different permeability levels. The inverse problem is solved by minimizing a functional, and TV norm regularization is used to deal with the ill-posedness. We also use the operator-splitting technique to decompose the constraint term from the fidelity term. This gives us more flexibility to deal with the constraint and helps to stabilize the algorithm.
Piecewise-linearized methods for oscillators with limit cycles
Energy Technology Data Exchange (ETDEWEB)
Ramos, J.I. [Room I-320-D, E.T.S. Ingenieros Industriales, Universidad de Malaga, Plaza El Ejido, s/n 29013 Malaga (Spain)] e-mail: jirs@lcc.uma.es
2006-03-01
A piecewise linearization method based on the linearization of nonlinear ordinary differential equations in small intervals, that provides piecewise analytical solutions in each interval and smooth solutions everywhere, is developed for the study of the limit cycles of smooth and non-smooth, conservative and non-conservative, nonlinear oscillators. It is shown that this method provides nonlinear maps for the displacement and velocity which depend on the previous values through the nonlinearity and its partial derivatives with respect to time, displacement and velocity, and yields non-standard finite difference formulae. It is also shown by means of five examples that the piecewise linearization method presented here is more robust and yields more accurate (in terms of displacement, energy and frequency) solutions than the harmonic balance procedure, the method of slowly varying amplitude and phase, and other non-standard finite difference equations.
Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension
Institute of Scientific and Technical Information of China (English)
Shun ZHONG; Yu-shu CHEN
2009-01-01
A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established.Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory.Transition sets of the system and 40 groups of bifurcation diagrams are obtained.The local bifurcation is found,and shows the overall characteristics of bifurcation.Based on the relationship between parameters and the topological bifurcation solutions,motion characteristics with different parameters are obtained.The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.
Furstenberg, Hillel
2009-01-01
Following works of Furstenberg and Nevo and Zimmer we present an outline of a theory of stationary (or m-stationary) dynamical systems for a general acting group G equipped with a probability measure m. Our purpose is two-fold: First to suggest a more abstract line of development, including a simple structure theory. Second, to point out some interesting applications; one of these is a Szemeredi type theorem for SL(2,R).
Existence of homoclinic connections in continuous piecewise linear systems.
Carmona, Victoriano; Fernández-Sánchez, Fernando; García-Medina, Elisabeth; Teruel, Antonio E
2010-03-01
Numerical methods are often used to put in evidence the existence of global connections in differential systems. The principal reason is that the corresponding analytical proofs are usually very complicated. In this work we give an analytical proof of the existence of a pair of homoclinic connections in a continuous piecewise linear system, which can be considered to be a version of the widely studied Michelson system. Although the computations developed in this proof are specific to the system, the techniques can be extended to other piecewise linear systems.
Virtual estimator for piecewise linear systems based on observability analysis.
Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés, Luis G; Beltrán, Carlos Daniel García
2013-02-27
This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results.
Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis
Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel
2013-01-01
This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007
An analogue of Polya's theorem for piecewise holomorphic functions
Buslaev, V. I.
2015-12-01
A well-known result due to Polya for a function given by its holomorphic germ at z=∞ is extended to the case of a piecewise holomorphic function on an arbitrary compact set in \\overline{ C}. This result is applied to the problem of the existence of compact sets that have the minimum transfinite diameter in the external field of the logarithmic potential of a negative unit charge among all compact sets such that a certain multivalued analytic function is single-valued and piecewise holomorphic on their complement. Bibliography: 13 titles.
DEFF Research Database (Denmark)
Lauritzen, Hans P M M; Galbo, Henrik; Brandauer, Josef
2007-01-01
OBJECTIVE: Insulin stimulates glucose transport in skeletal muscle by GLUT4 translocation from intracellular compartments to sarcolemma and t-tubules. We studied in living animals the recruitment of GLUT4 vesicles in more detail than previously done and, for the first time, analyzed the steady......-state recycling and subsequent re-internalization of GLUT4 on an insulin bolus. RESEARCH DESIGN AND METHODS: A confocal imaging technique was used in GLUT4-enhanced green fluorescent protein-transfected superficial muscle fibers in living mice. RESULTS: During the first 30 min of insulin stimulation, very few...... superficially or deeply located GLUT4 storage vesicles (>1 microm) moved in toto. Rather, big vesicles were stationary in their original position at sarcolemma or t-tubules and were locally depleted of GLUT4 by budding off of smaller vesicles. Photobleaching experiments revealed that during initial...
Limit Cycles and Bifurcation in Piecewise-Analytic Systems: 1. General Theory
Banks, S.P.; Khathur, Saadi. A.
1989-01-01
The existence of limit cycles and periodic doubling bifurcations in piecewise-linear and piecewise-analytic systems is studied. Some theoretical sufficient conditions are obtained directly in terms of the right hand sided of the system.
Characterization of well-posedness of piecewise linear systems
Imura, J.-I.; Schaft, van der A.J.
1998-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carath\\'eodory
Characterization of well-posedness of piecewise linear systems
Imura, Jun-ichi; Schaft, van der Arjan
2000-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Caratheodory. T
Characterization of Well-Posedness of Piecewise-Linear Systems
Imura, Jun-ichi; Schaft, Arjan van der
2000-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carathéodory. T
On the dynamic analysis of piecewise-linear networks
Heemels, WPMH; Camlibel, MK; Schumacher, JM
2002-01-01
Piecewise-linear (PL) modeling is often used to approximate the behavior of nonlinear circuits. One of the possible PL modeling methodologies is based on the linear complementarity problem, and this approach has already been used extensively in the circuits and systems community for static networks.
On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Directory of Open Access Journals (Sweden)
Ciepliński Krzysztof
2009-01-01
Full Text Available We investigate the existence and uniqueness of solutions of the functional equation , , where are closed intervals, and , are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.
Combinatorial Vector Fields for Piecewise Affine Control Systems
DEFF Research Database (Denmark)
Wisniewski, Rafal; Larsen, Jesper Abildgaard
2008-01-01
This paper is intended to be a continuation of Habets and van Schuppen (2004) and Habets, Collins and van Schuppen (2006), which address the control problem for piecewise-affine systems on an arbitrary polytope or a family of these. Our work deals with the underlying combinatorics of the underlyi...
Safety Verification of Piecewise-Deterministic Markov Processes
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer; Bujorianu, Manuela
2016-01-01
We consider the safety problem of piecewise-deterministic Markov processes (PDMP). These are systems that have deterministic dynamics and stochastic jumps, where both the time and the destination of the jumps are stochastic. Specifically, we solve a p-safety problem, where we identify the set...
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Hogan, S. J.
2015-01-01
In this paper we use the blowup method of Dumortier and Roussarie, in the formulation due to Krupa and Szmolyan, to study the regularization of singularities of piecewise smooth dynamical systems in R3. Using the regularization method of Sotomayor and Teixeira, we first demonstrate the power of our...... approach by considering the case of a fold line. We quickly extend a main result of Reves and Seara in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when...... the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided...
Stationary Double Layers in a Collisionless Magnetoplasma
DEFF Research Database (Denmark)
Noriyoshi, Sato; Mieno, Tetsu; Hatakeyama, Rikizo;
1983-01-01
Stationary double layers are generated in a magnetoplasma by applying potential differences between two heated plates on which the plasma is produced by surface ionization. By measuring the double-layer formation process, a localized potential drop is found to be formed initially in front of the ...
L0 Regularized Stationary-time Estimation for Crowd Analysis.
Yi, Shuai; Wang, Xiaogang; Lu, Cewu; Jia, Jiaya; Li, Hongsheng
2016-04-29
In this paper, we tackle the problem of stationary crowd analysis which is as important as modeling mobile groups in crowd scenes and finds many important applications in crowd surveillance. Our key contribution is to propose a robust algorithm for estimating how long a foreground pixel becomes stationary. It is much more challenging than only subtracting background because failure at a single frame due to local movement of objects, lighting variation, and occlusion could lead to large errors on stationary-time estimation. To achieve robust and accurate estimation, sparse constraints along spatial and temporal dimensions are jointly added by mixed partials (which are second-order gradients) to shape a 3D stationary-time map. It is formulated as an L0 optimization problem. Besides background subtraction, it distinguishes among different foreground objects, which are close or overlapped in the spatio-temporal space by using a locally shared foreground codebook. The proposed technologies are further demonstrated through three applications. 1) Based on the results of stationary-time estimation, twelve descriptors are proposed to detect four types of stationary crowd activities. 2) The averaged stationary-time map is estimated to analyze crowd scene structures. 3) The result of stationary-time estimation is also used to study the influence of stationary crowd groups to traffic patterns.
Nie, Xiaobing; Zheng, Wei Xing
2015-11-01
In this paper, we discuss the coexistence and dynamical behaviors of multiple equilibrium points for recurrent neural networks with a class of discontinuous nonmonotonic piecewise linear activation functions. It is proved that under some conditions, such n -neuron neural networks can have at least 5(n) equilibrium points, 3(n) of which are locally stable and the others are unstable, based on the contraction mapping theorem and the theory of strict diagonal dominance matrix. The investigation shows that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibrium points and more locally stable equilibrium points than the ones with continuous Mexican-hat-type activation function or discontinuous two-level activation functions. An illustrative example with computer simulations is presented to verify the theoretical analysis.
Piecewise linear and Boolean models of chemical reaction networks
Veliz-Cuba, Alan; Kumar, Ajit; Josić, Krešimir
2014-01-01
Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions (xn/(Jn + xn)). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent n is large. However, while the case of small constant J appears in practice, it is not well understood. We provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator. PMID:25412739
Discretization of Fractional Differential Equations by a Piecewise Constant Approximation
Angstmann, Christopher N; McGann, Anna V
2016-01-01
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a dynamical systems analysis. Unfortunately, due to mistakes in the fundamental papers, the difference equations formulated through this process do not capture the dynamics of the fractional order equations. We show that the correct application of this nonstandard piecewise approximation leads to a one parameter family of fractional order differential equations that converges to the original equation as the parameter tends to zero. A closed formed solution exists for each member of this family and leads to the formulation of a difference equation that is of increasing order as time steps are taken. Whilst this does not lead to a simplified dynamical analysis it does lead to a numerical method for solving the fractional order differential equation. The method is shown to be eq...
A 3D Facial Expression Tracking Method Using Piecewise Deformations
Directory of Open Access Journals (Sweden)
Jing Chi
2013-02-01
Full Text Available We present a new fast method for 3D facial expression tracking based on piecewise non-rigid deformations. Our method takes as input a video-rate sequence of face meshes that record the shape and time-varying expressions of a human face, and deforms a source mesh to match each input mesh to output a new mesh sequence with the same connectivity that reflects the facial shape and expressional variations. In mesh matching, we automatically segment the source mesh and estimate a non-rigid transformation for each segment to approximate the input mesh closely. Piecewise non-rigid transformation significantly reduces computational complexity and improves tracking speed because it greatly decreases the unknowns to be estimated. Our method can also achieve desired tracking accuracy because segmentation can be adjusted automatically and flexibly to approximate arbitrary deformations on the input mesh. Experiments demonstrate the efficiency of our method.
Piecewise linear and Boolean models of chemical reaction networks.
Veliz-Cuba, Alan; Kumar, Ajit; Josić, Krešimir
2014-12-01
Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions ([Formula: see text]). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent [Formula: see text] is large. However, while the case of small constant [Formula: see text] appears in practice, it is not well understood. We provide a mathematical analysis of this limit and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed-form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator.
Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis
Directory of Open Access Journals (Sweden)
Ilse Cervantes
2013-02-01
Full Text Available This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system’s outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results.
Border Collision Bifurcations in Two Dimensional Piecewise Smooth Maps
Banerjee, S; Banerjee, Soumitro; Grebogi, Celso
1999-01-01
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like saddle-node, pitchfork or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the theoretical problem: the development of a theory and classification of the new type of bifurcations resulting from border collision. We then present a systematic analysis of such bifurcations by deriving a normal form --- the piecewise linear approximation in the neighborhood of the border. We show that there can be eleven qualitatively different types of border collision bifurcations depending on the parameters of the normal form, and these are classified under six cases. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. This theoretical framework will help in explaining bifurcations in all syst...
Convergence of the natural approximations of piecewise monotone interval maps.
Haydn, Nicolai
2004-06-01
We consider piecewise monotone interval mappings which are topologically mixing and satisfy the Markov property. It has previously been shown that the invariant densities of the natural approximations converge exponentially fast in uniform pointwise topology to the invariant density of the given map provided its derivative is piecewise Lipshitz continuous. We provide an example of a map which is Lipshitz continuous and for which the densities converge in the bounded variation norm at a logarithmic rate. This shows that in general one cannot expect exponential convergence in the bounded variation norm. Here we prove that if the derivative of the interval map is Holder continuous and its variation is well approximable (gamma-uniform variation for gamma>0), then the densities converge exponentially fast in the norm.
Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers
Goulden, I. P.; Guay-Paquet, Mathieu; Novak, Jonathan
2016-04-01
This article introduces mixed double Hurwitz numbers, which interpolate combinatorially between the classical double Hurwitz numbers studied by Okounkov and the monotone double Hurwitz numbers introduced recently by Goulden, Guay-Paquet and Novak. Generalizing a result of Okounkov, we prove that a certain generating series for the mixed double Hurwitz numbers solves the 2-Toda hierarchy of partial differential equations. We also prove that the mixed double Hurwitz numbers are piecewise polynomial, thereby generalizing a result of Goulden, Jackson and Vakil.
On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Directory of Open Access Journals (Sweden)
Krzysztof Ciepliński
2009-01-01
Full Text Available We investigate the existence and uniqueness of solutions φ:I→J of the functional equation φ(f(x=F(φ(x, x∈I, where I,J are closed intervals, and f:I→I, F:J→J are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.
Rectification of aerial images using piecewise linear transformation
Liew, L. H.; Lee, B. Y.; Wang, Y. C.; Cheah, W. S.
2014-02-01
Aerial images are widely used in various activities by providing visual records. This type of remotely sensed image is helpful in generating digital maps, managing ecology, monitoring crop growth and region surveying. Such images could provide insight into areas of interest that have lower altitude, particularly in regions where optical satellite imaging is prevented due to cloudiness. Aerial images captured using a non-metric cameras contain real details of the images as well as unexpected distortions. Distortions would affect the actual length, direction and shape of objects in the images. There are many sources that could cause distortions such as lens, earth curvature, topographic relief and the attitude of the aircraft that is used to carry the camera. These distortions occur differently, collectively and irregularly in the entire image. Image rectification is an essential image pre-processing step to eliminate or at least reduce the effect of distortions. In this paper, a non-parametric approach with piecewise linear transformation is investigated in rectifying distorted aerial images. The non-parametric approach requires a set of corresponding control points obtained from a reference image and a distorted image. The corresponding control points are then applied with piecewise linear transformation as geometric transformation. Piecewise linear transformation divides the image into regions by triangulation. Different linear transformations are employed separately to triangular regions instead of using a single transformation as the rectification model for the entire image. The result of rectification is evaluated using total root mean square error (RMSE). Experiments show that piecewise linear transformation could assist in improving the limitation of using global transformation to rectify images.
A spectral gap for transer operators of piecewise expanding maps
Thomine, Damien
2010-01-01
We provide a simplified proof of the existence, under some assumptions, of a spectral gap for the Perron-Frobenius operator of piecewise uniformly expanding maps on Riemannian manifolds when acting on some Sobolev spaces. Its consequences include, among others, the existence of invariant physical measures, and an exponential decay of correlations for suitable observables. These features are then adapted to different function spaces (functions with bounded variation or bounded oscillation), so as to give a new insight of - and generalize - earlier results.
Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems
Senthilkumar, D. V.; Lakshmanan, M.
2004-01-01
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two parameter space of time delay and strength of nonlinearity. Significant role played by transients in attain...
Considerations Related to Interpolation of Experimental Data Using Piecewise Functions
Directory of Open Access Journals (Sweden)
Stelian Alaci
2016-12-01
Full Text Available The paper presents a method for experimental data interpolation by means of a piecewise function, the points where the form of the function changes being found simultaneously with the other parameters utilized in an optimization criterion. The optimization process is based on defining the interpolation function using a single expression founded on the Heaviside function and regarding the optimization function as a generalised infinitely derivable function. The exemplification of the methodology is made via a tangible example.
Mohanty, B. P.; Bowman, R. S.; Hendrickx, J. M. H.; van Genuchten, M. T.
Modeling water flow in macroporous field soils near saturation has been a major challenge in vadose zone hydrology. Using in situ and laboratory measurements, we developed new piecewise-continuous soil water retention and hydraulic conductivity functions to describe preferential flow in tile drains under a flood-irrigated agricultural field in Las Nutrias, New Mexico. After incorporation into a two-dimensional numerical flow code, CHAIN_2D, the performance of the new piecewise-continuous hydraulic functions was compared with that of the unimodal van Genuchten-Mualem model and with measured tile-flow data at the field site during a number of irrigation events. Model parameters were collected/estimated by site characterization (e.g., soil texture, surface/subsurface saturated/unsaturated soil hydraulic property measurements), as well as by local and regional-scale hydrologic monitoring (including the use of groundwater monitoring wells, piezometers, and different surface-irrigation and subsurface-drainage measurement systems). Comparison of numerical simulation results with the observed tile flow indicated that the new piecewise-continuous hydraulic functions generally predicted preferential flow in the tile drain reasonably well following all irrigation events at the field site. Also, the new bimodal soil water retention and hydraulic conductivity functions performed better than the unimodal van Genuchten-Mualem functions in terms of describing the observed flow regime at the field site.
Institute of Scientific and Technical Information of China (English)
常晓蓉; 冯民富
2011-01-01
本文将近年来基于协调有限元逼近提出的涡旋粘性法推广应用到非协调有限元逼近,对非定常的对流占优扩散问题,空间采用非协调Crouzeix-Raviart元逼近,时间用Crank-Nicolson差分离散格式,提出了Crank-Nicolson差分-局部投影法稳定化有限元格式,我们对稳定性和误差估计给出了详细的分析,得出了最优的估计.%This paper is concerned with the extension of the conforming element approximations based on eddy viscosity to the nonconforming element approximation. For the non-stationary convection diffusion problem, where the Crouzeix-Raviart element is employed. A fully discretized formulation with a Crank-Nicholson scheme for the time variable, and a Crank-Nicholson difference - local projection method finite element scheme is prensented.We prove stability and convergence, then an optimal error estimate is obtained.
Yao, Weigang; Liou, Meng-Sing
2016-08-01
To preserve nonlinearity of a full-order system over a range of parameters of interest, we propose an accurate and robust nonlinear modeling approach by assembling a set of piecewise linear local solutions expanded about some sampling states. The work by Rewienski and White [1] on micromachined devices inspired our use of piecewise linear local solutions to study nonlinear unsteady aerodynamics. These local approximations are assembled via nonlinear weights of radial basis functions. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving with different pitching motions, specifically AGARD's CT2 and CT5 problems [27], in which the flows exhibit different nonlinear behaviors. Furthermore, application of the developed aerodynamic model to a two-dimensional aero-elastic system proves the approach is capable of predicting limit cycle oscillations (LCOs) by using AGARD's CT6 [28] as a benchmark test. All results, based on inviscid solutions, confirm that our nonlinear model is stable and accurate, against the full model solutions and measurements, and for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robust for inputs that considerably depart from the base trajectory in form and magnitude. This modeling provides a very efficient way for predicting unsteady flowfields with varying parameters because it needs only a tiny fraction of the cost of a full-order modeling for each new condition-the more cases studied, the more savings rendered. Hence, the present approach is especially useful for parametric studies, such as in the case of design optimization and exploration of flow phenomena.
Geophysics-based method of locating a stationary earth object
Daily, Michael R.; Rohde, Steven B.; Novak, James L.
2008-05-20
A geophysics-based method for determining the position of a stationary earth object uses the periodic changes in the gravity vector of the earth caused by the sun- and moon-orbits. Because the local gravity field is highly irregular over a global scale, a model of local tidal accelerations can be compared to actual accelerometer measurements to determine the latitude and longitude of the stationary object.
Approximating Stationary Statistical Properties
Institute of Scientific and Technical Information of China (English)
Xiaoming WANG
2009-01-01
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
Nther-type theorem of piecewise algebraic curves on triangulation
Institute of Scientific and Technical Information of China (English)
2007-01-01
The piecewise algebraic curve is a kind generalization of the classical algebraic curve. Nther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space.In this paper,using the properties of bivariate splines,the Nther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.
Stability Analysis of Uncertain Discrete-Time Piecewise Linear Systems with Time Delays
Institute of Scientific and Technical Information of China (English)
Ou Ou; Hong-Bin Zhang; Jue-Bang Yu
2009-01-01
This paper considers the stability analysis of uncertain discrete-time piecewise linear systems with time delays based on piecewise Lyapunov-Krasovskii functionals. It is shown that the stability can be established for the control systems if there is a piecewise Lyapunov-Krasovskii functional, and moreover, the functional can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example is given to demonstrate the efficiency and advantage of the proposed method.
N(o)ther-type theorem of piecewise algebraic curves on triangulation
Institute of Scientific and Technical Information of China (English)
Chun-gang ZHU; Ren-hong WANG
2007-01-01
The piecewise algebraic curve is a kind generalization of the classical algebraic curve.N(o)ther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space. In this paper, using the properties of bivariate splines, the N(o)ther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.
Mixed-Mode Oscillations in a piecewise linear system with multiple time scale coupling
Fernández-García, S.; Krupa, M.; Clément, F.
2016-10-01
In this work, we analyze a four dimensional slow-fast piecewise linear system with three time scales presenting Mixed-Mode Oscillations. The system possesses an attractive limit cycle along which oscillations of three different amplitudes and frequencies can appear, namely, small oscillations, pulses (medium amplitude) and one surge (largest amplitude). In addition to proving the existence and attractiveness of the limit cycle, we focus our attention on the canard phenomena underlying the changes in the number of small oscillations and pulses. We analyze locally the existence of secondary canards leading to the addition or subtraction of one small oscillation and describe how this change is globally compensated for or not with the addition or subtraction of one pulse.
Video Enhancement Using Adaptive Spatio-Temporal Connective Filter and Piecewise Mapping
Directory of Open Access Journals (Sweden)
Wang Chao
2008-01-01
Full Text Available This paper presents a novel video enhancement system based on an adaptive spatio-temporal connective (ASTC noise filter and an adaptive piecewise mapping function (APMF. For ill-exposed videos or those with much noise, we first introduce a novel local image statistic to identify impulse noise pixels, and then incorporate it into the classical bilateral filter to form ASTC, aiming to reduce the mixture of the most two common types of noises—Gaussian and impulse noises in spatial and temporal directions. After noise removal, we enhance the video contrast with APMF based on the statistical information of frame segmentation results. The experiment results demonstrate that, for diverse low-quality videos corrupted by mixed noise, underexposure, overexposure, or any mixture of the above, the proposed system can automatically produce satisfactory results.
Video Enhancement Using Adaptive Spatio-Temporal Connective Filter and Piecewise Mapping
Directory of Open Access Journals (Sweden)
Shi-Qiang Yang
2008-06-01
Full Text Available This paper presents a novel video enhancement system based on an adaptive spatio-temporal connective (ASTC noise filter and an adaptive piecewise mapping function (APMF. For ill-exposed videos or those with much noise, we first introduce a novel local image statistic to identify impulse noise pixels, and then incorporate it into the classical bilateral filter to form ASTC, aiming to reduce the mixture of the most two common types of noisesÃ¢Â€Â”Gaussian and impulse noises in spatial and temporal directions. After noise removal, we enhance the video contrast with APMF based on the statistical information of frame segmentation results. The experiment results demonstrate that, for diverse low-quality videos corrupted by mixed noise, underexposure, overexposure, or any mixture of the above, the proposed system can automatically produce satisfactory results.
Data-based identification and control of nonlinear systems via piecewise affine approximation.
Lai, Chow Yin; Xiang, Cheng; Lee, Tong Heng
2011-12-01
The piecewise affine (PWA) model represents an attractive model structure for approximating nonlinear systems. In this paper, a procedure for obtaining the PWA autoregressive exogenous (ARX) (autoregressive systems with exogenous inputs) models of nonlinear systems is proposed. Two key parameters defining a PWARX model, namely, the parameters of locally affine subsystems and the partition of the regressor space, are estimated, the former through a least-squares-based identification method using multiple models, and the latter using standard procedures such as neural network classifier or support vector machine classifier. Having obtained the PWARX model of the nonlinear system, a controller is then derived to control the system for reference tracking. Both simulation and experimental studies show that the proposed algorithm can indeed provide accurate PWA approximation of nonlinear systems, and the designed controller provides good tracking performance.
Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Soukhoterin, E.A.; Mosekilde, Erik
2002-01-01
Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject...... of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border...
The Cayley-Bacharach Theorem for Continuous Piecewise Algebraic Curves over Cross-cut Triangulations
Institute of Scientific and Technical Information of China (English)
Renhong WANG; Shaofan WANG
2011-01-01
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function.In this paper,we propose the Cayley-Bacharach theorem for continuous piecewise algebraic curves over cross-cut triangulations.We show that,if two continuous piecewise algebraic curves of degrees m and n respectively meet at mnT distinct points over a cross-cut triangulation,where T denotes the number of cells of the triangulation,then any continuous piecewise algebraic curve of degree m + n - 2 containing all but one point of them also contains the last point.
Ceramic stationary gas turbine
Energy Technology Data Exchange (ETDEWEB)
Roode, M. van [Solar Turbines Inc., San Diego, CA (United States)
1995-10-01
The performance of current industrial gas turbines is limited by the temperature and strength capabilities of the metallic structural materials in the engine hot section. Because of their superior high-temperature strength and durability, ceramics can be used as structural materials for hot section components (blades, nozzles, combustor liners) in innovative designs at increased turbine firing temperatures. The benefits include the ability to increase the turbine inlet temperature (TIT) to about 1200{degrees}C ({approx}2200{degrees}F) or more with uncooled ceramics. It has been projected that fully optimized stationary gas turbines would have a {approx}20 percent gain in thermal efficiency and {approx}40 percent gain in output power in simple cycle compared to all metal-engines with air-cooled components. Annual fuel savings in cogeneration in the U.S. would be on the order of 0.2 Quad by 2010. Emissions reductions to under 10 ppmv NO{sub x} are also forecast. This paper describes the progress on a three-phase, 6-year program sponsored by the U.S. Department of Energy, Office of Industrial Technologies, to achieve significant performance improvements and emissions reductions in stationary gas turbines by replacing metallic hot section components with ceramic parts. Progress is being reported for the period September 1, 1994, through September 30, 1995.
Ceramic stationary gas turbine
Energy Technology Data Exchange (ETDEWEB)
Roode, M. van
1995-12-31
The performance of current industrial gas turbines is limited by the temperature and strength capabilities of the metallic structural materials in the engine hot section. Because of their superior high-temperature strength and durability, ceramics can be used as structural materials for hot section components (blades, nozzles, combustor liners) in innovative designs at increased turbine firing temperatures. The benefits include the ability to increase the turbine inlet temperature (TIT) to about 1200{degrees}C ({approx}2200{degrees}F) or more with uncooled ceramics. It has been projected that fully optimized stationary gas turbines would have a {approx}20 percent gain in thermal efficiency and {approx}40 percent gain in output power in simple cycle compared to all metal-engines with air-cooled components. Annual fuel savings in cogeneration in the U.S. would be on the order of 0.2 Quad by 2010. Emissions reductions to under 10 ppmv NO{sub x} are also forecast. This paper describes the progress on a three-phase, 6-year program sponsored by the U.S. Department of Energy, Office of Industrial Technologies, to achieve significant performance improvements and emissions reductions in stationary gas turbines by replacing metallic hot section components with ceramic parts. Progress is being reported for the period September 1, 1994, through September 30, 1995.
Feedback control design for discrete-time piecewise affine systems
Institute of Scientific and Technical Information of China (English)
XU Jun; XIE Li-hua
2007-01-01
This paper investigates the design of state feedback and dynamic output feedback stabilizing controllers for discrete-time piecewise affine (PWA) systems. The main objective is to derive design methods that will incorporate the partition information of the PWA systems so as to reduce the design conservatism embedded in existing design methods. We first introduce a transformation that converts the feedback control design problem into a bilinear matrix inequality (BMI) problem. Then, two iterative algorithms are proposed to compute the feedback controllers characterized by the BMI. Several simulation examples are given to demonstrate the advantages of the proposed design.
Guidance law based on piecewise constant control for hypersonic gliders
Hull, David G.; Seguin, Jean-Marie
A midcourse guidance law is developed for the descent of a hypersonic glider to a fixed target on the ground. It is based on an optimal piecewise constant control (N intervals) obtained from an approximate physical model (flat earth, exponential atmosphere, parabolic drag polar, etc). The resulting optimal control equations can be integrated either analytically or by quadrature, and the guidance algorithm requires the solution of 2N+1 nonlinear algebraic equations. The guidance law is implemented in a realistic glider simulation, the intercept is achieved, and final velocities within 14 percent of the true values are obtained for the downrange and crossranges considered.
Mixing with piecewise isometries on a hemispherical shell
Park, Paul P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.
2016-07-01
We introduce mixing with piecewise isometries (PWIs) on a hemispherical shell, which mimics features of mixing by cutting and shuffling in spherical shells half-filled with granular media. For each PWI, there is an inherent structure on the hemispherical shell known as the exceptional set E, and a particular subset of E, E+, provides insight into how the structure affects mixing. Computer simulations of PWIs are used to visualize mixing and approximations of E+ to demonstrate their connection. While initial conditions of unmixed materials add a layer of complexity, the inherent structure of E+ defines fundamental aspects of mixing by cutting and shuffling.
Piecewise-linear maps and their application to financial markets
Directory of Open Access Journals (Sweden)
Fabio Tramontana
2016-08-01
Full Text Available The goal of this paper is to review some work on agent-based financial market models in which the dynamics is driven by piecewise-linear maps. As we will see, such models allow deep analytical insights into the functioning of financial markets, may give rise to unexpected dynamics effects, allow explaining a number of important stylized facts of financial markets, and offer novel policy recommendations. However, much remains to be done in this rather new research field. We hope that our paper attracts more scientists to this area.
A Parallel Encryption Algorithm Based on Piecewise Linear Chaotic Map
Directory of Open Access Journals (Sweden)
Xizhong Wang
2013-01-01
Full Text Available We introduce a parallel chaos-based encryption algorithm for taking advantage of multicore processors. The chaotic cryptosystem is generated by the piecewise linear chaotic map (PWLCM. The parallel algorithm is designed with a master/slave communication model with the Message Passing Interface (MPI. The algorithm is suitable not only for multicore processors but also for the single-processor architecture. The experimental results show that the chaos-based cryptosystem possesses good statistical properties. The parallel algorithm provides much better performance than the serial ones and would be useful to apply in encryption/decryption file with large size or multimedia.
Lower Bounds of the Discretization for Piecewise Polynomials
Lin, Qun; Xu, Jinchao
2011-01-01
Assume that $V_h$ is a space of piecewise polynomials of degree less than $r\\geq 1$ on a family of quasi-uniform triangulation of size $h$. Then the following well-known upper bound holds for a sufficiently smooth function $u$ and $p\\in [1, \\infty]$ $$ \\inf_{v_h\\in V_h}\\|u-v_h\\|_{j,p,\\Omega,h} \\le C h^{r-j} |u|_{r,p,\\Omega},\\quad 0\\le j\\le r. $$ In this paper, we prove that, roughly speaking, if $u\
Bifurcation Structures in a Bimodal Piecewise Linear Map
Directory of Open Access Journals (Sweden)
Anastasiia Panchuk
2017-05-01
Full Text Available In this paper we present an overview of the results concerning dynamics of a piecewise linear bimodal map. The organizing principles of the bifurcation structures in both regular and chaotic domains of the parameter space of the map are discussed. In addition to the previously reported structures, a family of regions closely related to the so-called U-sequence is described. The boundaries of distinct regions belonging to these structures are obtained analytically using the skew tent map and the map replacement technique.
Contribution to the ergodic theory of piecewise monotone continuous maps
Faller, Bastien
2008-01-01
This thesis is devoted to the ergodic theory of the piecewise monotone continuous maps of the interval. The coding is a classical approach for these maps. Thanks to the coding, we get a symbolic dynamical system which is almost isomorphic to the initial dynamical system. The principle of the coding is very similar to the one of expansion of real numbers. We first define the coding in a perspective similar to the one of the expansions of real numbers; this perspective was already adopted by Ré...
An I(2) cointegration model with piecewise linear trends
DEFF Research Database (Denmark)
Kurita, Takamitsu; Bohn Nielsen, Heino; Rahbæk, Anders
2011-01-01
This paper presents likelihood analysis of the I(2) cointegrated vector autoregression which allows for piecewise linear deterministic terms. Limiting behaviour of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio...... statistic for the cointegration ranks, extending Nielsen and Rahbek. The provided asymptotic theory extends also the results in Johansen et al. where asymptotic inference is discussed in detail for one of the cointegration parameters. An empirical analysis of US consumption, income and wealth, 1965...
Piecewise linear manifolds: Einstein metrics and Ricci flows
Schrader, Robert
2016-05-01
This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear (p.l.) spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field. On a given set of p.l. spaces we define and discuss (normalized) Einstein flows. p.l. Einstein metrics are defined and examples are provided. Criteria for flows to approach Einstein metrics are formulated. Second variations of the total scalar curvature at a specific Einstein space are calculated. Dedicated to Ludwig Faddeev on the occasion of his 80th birthday.
Nonlinear optics with stationary pulses of light
Andre, A.; Bajcsy, M.; Zibrov, A. S.; Lukin, M. D.
2004-01-01
We show that the recently demonstrated technique for generating stationary pulses of light [Nature {\\bf 426}, 638 (2003)] can be extended to localize optical pulses in all three spatial dimensions in a resonant atomic medium. This method can be used to dramatically enhance the nonlinear interaction between weak optical pulses. In particular, we show that an efficient Kerr-like interaction between two pulses can be implemented as a sequence of several purely linear optical processes. The resul...
A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Shi Dongyang; Ren Jincheng; Gong Wei
2011-01-01
In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.
Chaotic dynamics and diffusion in a piecewise linear equation.
Shahrear, Pabel; Glass, Leon; Edwards, Rod
2015-03-01
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.
Chaotic dynamics and diffusion in a piecewise linear equation
Energy Technology Data Exchange (ETDEWEB)
Shahrear, Pabel, E-mail: pabelshahrear@yahoo.com [Department of Mathematics, Shah Jalal University of Science and Technology, Sylhet–3114 (Bangladesh); Glass, Leon, E-mail: glass@cnd.mcgill.ca [Department of Physiology, 3655 Promenade Sir William Osler, McGill University, Montreal, Quebec H3G 1Y6 (Canada); Edwards, Rod, E-mail: edwards@uvic.ca [Department of Mathematics and Statistics, University of Victoria, P.O. Box 1700 STN CSC, Victoria, British Columbia V8W 2Y2 (Canada)
2015-03-15
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.
Model Based Adaptive Piecewise Linear Controller for Complicated Control Systems
Directory of Open Access Journals (Sweden)
Tain-Sou Tsay
2014-01-01
Full Text Available A model based adaptive piecewise linear control scheme for industry processes with specifications on peak overshoots and rise times is proposed. It is a gain stabilized control technique. Large gain is used for large tracking error to get fast response. Small gain is used between large and small tracking error for good performance. Large gain is used again for small tracking error to cope with large disturbance. Parameters of the three-segment piecewise linear controller are found by an automatic regulating time series which is function of output characteristics of the plant and reference model. The time series will be converged to steady values after the time response of the considered system matching that of the reference model. The proposed control scheme is applied to four numerical examples which have been compensated by PID controllers. Parameters of PID controllers are found by optimization method. It gives an almost command independent response and gives significant improvements for response time and performance.
Regular and chaotic dynamics of a piecewise smooth bouncer
Energy Technology Data Exchange (ETDEWEB)
Langer, Cameron K., E-mail: c.k.langer@tcu.edu; Miller, Bruce N., E-mail: b.miller@tcu.edu [Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76129 (United States)
2015-07-15
The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is possible for the system's sinusoidal counterpart. We consider three distinct approaches to modeling collisions: (i) elastic, (ii) inelastic with constant restitution coefficient, and (iii) inelastic with a velocity-dependent restitution function. We confirm the existence of distinct unbounded orbits (Fermi acceleration) in the elastic model, and investigate regular and chaotic behavior in the inelastic cases. We also examine in the constant restitution model trajectories wherein the particle experiences an infinite number of collisions in a finite time, i.e., the phenomenon of inelastic collapse. We address these so-called “sticking solutions” and their relation to both the overall dynamics and the phenomenon of self-reanimating chaos. Additionally, we investigate the long-term behavior of the system as a function of both initial conditions and parameter values. We find the non-smooth nature of the system produces novel bifurcation phenomena not seen in the sinusoidal model, including border-collision bifurcations. The analytical and numerical investigations reveal that although our piecewise linear bouncer is a simplified version of the sinusoidal model, the former not only captures essential features of the latter but also exhibits behavior unique to the discontinuous dynamics.
Piecewise multivariate modelling of sequential metabolic profiling data
Directory of Open Access Journals (Sweden)
Nicholson Jeremy K
2008-02-01
Full Text Available Abstract Background Modelling the time-related behaviour of biological systems is essential for understanding their dynamic responses to perturbations. In metabolic profiling studies, the sampling rate and number of sampling points are often restricted due to experimental and biological constraints. Results A supervised multivariate modelling approach with the objective to model the time-related variation in the data for short and sparsely sampled time-series is described. A set of piecewise Orthogonal Projections to Latent Structures (OPLS models are estimated, describing changes between successive time points. The individual OPLS models are linear, but the piecewise combination of several models accommodates modelling and prediction of changes which are non-linear with respect to the time course. We demonstrate the method on both simulated and metabolic profiling data, illustrating how time related changes are successfully modelled and predicted. Conclusion The proposed method is effective for modelling and prediction of short and multivariate time series data. A key advantage of the method is model transparency, allowing easy interpretation of time-related variation in the data. The method provides a competitive complement to commonly applied multivariate methods such as OPLS and Principal Component Analysis (PCA for modelling and analysis of short time-series data.
Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes
Faggionato, A.; Gabrielli, D.; Ribezzi Crivellari, M.
2009-10-01
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states ( x, σ)∈Ω×Γ, Ω being a region in ℝ d or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601, 2001; J. Stat. Phys. 107(3-4):635-675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at http://www.arxiv.org/abs/0807.4457, 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti-Cohen-type symmetry relation with involution map different from time-reversal.
Smoothing a Piecewise-Smooth: An Example from Plankton Population Dynamics
DEFF Research Database (Denmark)
Piltz, Sofia Helena
2016-01-01
In this work we discuss a piecewise-smooth dynamical system inspired by plankton observations and constructed for one predator switching its diet between two different types of prey. We then discuss two smooth formulations of the piecewise-smooth model obtained by using a hyperbolic tangent...
High resolution A/D conversion based on piecewise conversion at lower resolution
Terwilliger, Steve
2012-06-05
Piecewise conversion of an analog input signal is performed utilizing a plurality of relatively lower bit resolution A/D conversions. The results of this piecewise conversion are interpreted to achieve a relatively higher bit resolution A/D conversion without sampling frequency penalty.
Piecewise Linear-Linear Latent Growth Mixture Models with Unknown Knots
Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.
2013-01-01
Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…
Bifurcation in a Class of Planar Piecewise Smo oth Systems with 3-parameters
Institute of Scientific and Technical Information of China (English)
Liu Yuan-yuan; Chai Zhen-hua; Ma Fu-ming(Communicated)
2014-01-01
This paper is concerned with the bifurcation properties on the line of discontinuity of planar piecewise smooth systems. The existence of equilibria and periodic solutions with sliding motion in a class of planar piecewise smooth systems with 3-parameters is investigated in this paper using the theory of differential inclu-sion and tools of Poincar´e maps.
Stationary and Transient Response Statistics
DEFF Research Database (Denmark)
Madsen, Peter Hauge; Krenk, Steen
1982-01-01
The covariance functions for the transient response of a linear MDOF-system due to stationary time limited excitation with an arbitrary frequency content are related directly to the covariance functions of the stationary response. For rational spectral density functions closed form expressions...
Digital architecture for a piecewise-linear arbitrary-waveform generator
Indian Academy of Sciences (India)
VICTOR M JIMENEZ-FERNANDEZ; HECTOR VAZQUEZ-LEAL; PABLO S LUNA-LOZANO; J L VAZQUEZ-BELTRAN; G GARCIA-SANTIAGO; E VALDES-ORTEGA
2016-08-01
In this paper a digital architecture for generating piecewise-linear arbitrary waveforms is presented. The proposed design is able to generate a piecewise-linear periodic signal by only using a minimum number of input data (breakpoints). The generator circuit implements a hybrid scheme which takes advantage of two methods: the purely piecewise-linear interpolation and the lookup-table structure. From the piecewise-linear method exploits the characteristic of a reduced memory requirement as well as the capability of automatically construct a waveform by repetitive (iterative) function evaluations. From lookup-table makes use of the simplicity in hardware implementation and the higher processing speed. In order to verify the performance of thisproposal, three piecewise-linear waveforms have been successfully implemented in a ATMEGA32 microcontroller. Experimental results show a fast execution speed and a reduced memory demand in the proposed circuit realization.
Some Researches on Real Piecewise Algebraic Curves%实分片代数曲线的某些研究
Institute of Scientific and Technical Information of China (English)
朱春钢; 王仁宏
2008-01-01
The piecewise algebraic curve,defined by a bivariate spline,is a generalization of the classical algebraic curve.In this palper,we present some researches on real piecewise algebraic curves using elementary algebra.A real piecewise algebraic curve is studied according to the fact that a real spline for the curve is indefinite,definite or semidefinite(nondefinite).Moreover,the isolated points of a real piecewise algebraic curve is also discussed.
Relativistic elasticity of stationary fluid branes
DEFF Research Database (Denmark)
Armas, J.; Obers, N.A.
2013-01-01
Fluid mechanics can be formulated on dynamical surfaces of arbitrary codimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show...... under certain conditions that a given stationary fluid configuration living on a dynamical surface of vanishing thickness and satisfying locally the first law of thermodynamics will behave like an elastic brane when the surface is subject to small deformations. These results, which are independent...... of the number of space-time dimensions and of the fluid arising from a gravitational dual, reveal the (electro)elastic character of (charged) black branes when considering extrinsic perturbations....
Relativistic Elasticity of Stationary Fluid Branes
Armas, Jay
2012-01-01
Fluid mechanics can be formulated on dynamical surfaces of arbitrary co-dimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show under certain conditions that a given stationary fluid configuration living on a dynamical surface of vanishing thickness and satisfying locally the first law of thermodynamics will behave like an elastic brane when the surface is subject to small deformations. These results, which are independent of the number of space-time dimensions and of the fluid arising from a gravitational dual, reveal the (electro)elastic character of (charged) black branes when considering extrinsic perturbations.
Nie, Xiaobing; Zheng, Wei Xing
2016-03-01
This paper addresses the problem of coexistence and dynamical behaviors of multiple equilibria for competitive neural networks. First, a general class of discontinuous nonmonotonic piecewise linear activation functions is introduced for competitive neural networks. Then based on the fixed point theorem and theory of strict diagonal dominance matrix, it is shown that under some conditions, such n -neuron competitive neural networks can have 5(n) equilibria, among which 3(n) equilibria are locally stable and the others are unstable. More importantly, it is revealed that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibria and locally stable equilibria than the ones with other activation functions, such as the continuous Mexican-hat-type activation function and discontinuous two-level activation function. Furthermore, the 3(n) locally stable equilibria given in this paper are located in not only saturated regions, but also unsaturated regions, which is different from the existing results on multistability of neural networks with multiple level activation functions. A simulation example is provided to illustrate and validate the theoretical findings.
An Improved Piecewise Linear Chaotic Map Based Image Encryption Algorithm
Directory of Open Access Journals (Sweden)
Yuping Hu
2014-01-01
Full Text Available An image encryption algorithm based on improved piecewise linear chaotic map (MPWLCM model was proposed. The algorithm uses the MPWLCM to permute and diffuse plain image simultaneously. Due to the sensitivity to initial key values, system parameters, and ergodicity in chaotic system, two pseudorandom sequences are designed and used in the processes of permutation and diffusion. The order of processing pixels is not in accordance with the index of pixels, but it is from beginning or end alternately. The cipher feedback was introduced in diffusion process. Test results and security analysis show that not only the scheme can achieve good encryption results but also its key space is large enough to resist against brute attack.
Complete parameterization of piecewise-polynomial interpolation kernels.
Blu, Thierry; Thévenaz, Philippe; Unser, Michael
2003-01-01
Every now and then, a new design of an interpolation kernel appears in the literature. While interesting results have emerged, the traditional design methodology proves laborious and is riddled with very large systems of linear equations that must be solved analytically. We propose to ease this burden by providing an explicit formula that can generate every possible piecewise-polynomial kernel given its degree, its support, its regularity, and its order of approximation. This formula contains a set of coefficients that can be chosen freely and do not interfere with the four main design parameters; it is thus easy to tune the design to achieve any additional constraints that the designer may care for.
Piecewise Sliding Mode Decoupling Fault Tolerant Control System
Directory of Open Access Journals (Sweden)
Rafi Youssef
2010-01-01
Full Text Available Problem statement: Proposed method in the present study could deal with fault tolerant control system by using the so called decentralized control theory with decoupling fashion sliding mode control, dealing with subsystems instead of whole system and to the knowledge of the author there is no known computational algorithm for decentralized case, Approach: In this study we present a decoupling strategy based on the selection of sliding surface, which should be in piecewise sliding surface partition to apply the PwLTool which have as purpose in our case to delimit regions where sliding mode occur, after that as Results: We get a simple linearized model selected in those regions which could depict the complex system, Conclusion: With the 3 water tank level system as example we implement this new design scenario and since we are interested in networked control system we believe that this kind of controller implementation will not be affected by network delays.
The Piecewise Cubic Method (PCM) for computational fluid dynamics
Lee, Dongwook; Faller, Hugues; Reyes, Adam
2017-07-01
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed solutions are evolved in time with a fourth-order accuracy by tracing the characteristics of the cubic polynomials. As a result, our temporal update scheme provides a significantly simpler and computationally more efficient approach in achieving fourth order accuracy in time, relative to the comparable fourth-order Runge-Kutta method. We demonstrate that the solutions of PCM converges at fifth-order in solving 1D smooth flows described by hyperbolic conservation laws. We test the new scheme on a range of numerical experiments, including both gas dynamics and magnetohydrodynamics applications in multiple spatial dimensions.
The Piecewise Cubic Method (PCM) for Computational Fluid Dynamics
Lee, Dongwook; Reyes, Adam
2016-01-01
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed solutions are evolved in time with a fourth-order accuracy by tracing the characteristics of the cubic polynomials. As a result, our temporal update scheme provides a significantly simpler and computationally more efficient approach in achieving fourth order accuracy in time, relative to the comparable fourth-order Runge-Kutta method. We demonstrate that the solutions of PCM converges in fifth-order in solving 1D smooth flows described by hyperbolic conservation laws. We test the new scheme in a range of numerical experiments, including both gas dynamics and magnetohydrodynamics applications in multiple spatial dimensions.
An Improved Piecewise Linear Chaotic Map Based Image Encryption Algorithm
Hu, Yuping; Wang, Zhijian
2014-01-01
An image encryption algorithm based on improved piecewise linear chaotic map (MPWLCM) model was proposed. The algorithm uses the MPWLCM to permute and diffuse plain image simultaneously. Due to the sensitivity to initial key values, system parameters, and ergodicity in chaotic system, two pseudorandom sequences are designed and used in the processes of permutation and diffusion. The order of processing pixels is not in accordance with the index of pixels, but it is from beginning or end alternately. The cipher feedback was introduced in diffusion process. Test results and security analysis show that not only the scheme can achieve good encryption results but also its key space is large enough to resist against brute attack. PMID:24592159
Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems
Directory of Open Access Journals (Sweden)
Hong Shi
2012-01-01
Full Text Available Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper studies the controllability and observability of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.
Gravitational backreaction on piecewise linear cosmic string loops
Wachter, Jeremy M.; Olum, Ken D.
2017-01-01
We calculate the metric and affine connection due to a piecewise linear cosmic string loop, and the effect of gravitational backreaction for the Garfinkle-Vachaspati loop with four straight segments. As expected, backreaction reduces the size of the loop, in accord with the energy going into gravitational waves. The "square" (maximally symmetric) loop evaporates without changing shape, but for all other loops in this class, the kinks become less sharp and segments between kinks become curved. If the loop is close to the square case, it will evaporate before its kinks are significantly changed; if it is far from square, the opening out of the kinks is much faster than evaporation of the loop.
Gravitational back reaction on piecewise linear cosmic string loops
Wachter, Jeremy M
2016-01-01
We calculate the metric and affine connection due to a piecewise linear cosmic string loop, and the effect of gravitational back reaction for the Garfinkle-Vachaspati loop with four straight segments. As expected, back reaction reduces the size of the loop, in accord with the energy going into gravitational waves. The "square" loop whose generators lie at right angles evaporates without changing shape, but in all other cases, the kinks become less sharp and segments between kinks become curved. If the loop is close to the square case, the loop will evaporate before its kinks are significantly changed; if it is far from square, the opening out of the kinks is much faster than evaporation of the loop. In more realistic loops, the curvature of the straight segments due to gravitational back reaction may lead to cusps which did not exist in the original shape with the bending of the string concentrated at kinks.
Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics
Directory of Open Access Journals (Sweden)
J. Petrzela
2012-04-01
Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided
Elasticity in Amorphous Solids: Nonlinear or Piecewise Linear?
Dubey, Awadhesh K; Procaccia, Itamar; Shor, Carmel A B Z; Singh, Murari
2016-02-26
Quasistatic strain-controlled measurements of stress versus strain curves in macroscopic amorphous solids result in a nonlinear-looking curve that ends up either in mechanical collapse or in a steady state with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress versus strain curves and propose that a useful description of the mechanical response is given by a stress (or strain) -dependent shear modulus for which a theoretical evaluation exists. The elastic response is piecewise linear rather than nonlinear.
Autocalibrating Tiled Projectors on Piecewise Smooth Vertically Extruded Surfaces.
Sajadi, Behzad; Majumder, Aditi
2011-09-01
In this paper, we present a novel technique to calibrate multiple casually aligned projectors on fiducial-free piecewise smooth vertically extruded surfaces using a single camera. Such surfaces include cylindrical displays and CAVEs, common in immersive virtual reality systems. We impose two priors to the display surface. We assume the surface is a piecewise smooth vertically extruded surface for which the aspect ratio of the rectangle formed by the four corners of the surface is known and the boundary is visible and segmentable. Using these priors, we can estimate the display's 3D geometry and camera extrinsic parameters using a nonlinear optimization technique from a single image without any explicit display to camera correspondences. Using the estimated camera and display properties, the intrinsic and extrinsic parameters of each projector are recovered using a single projected pattern seen by the camera. This in turn is used to register the images on the display from any arbitrary viewpoint making it appropriate for virtual reality systems. The fast convergence and robustness of this method is achieved via a novel dimension reduction technique for camera parameter estimation and a novel deterministic technique for projector property estimation. This simplicity, efficiency, and robustness of our method enable several coveted features for nonplanar projection-based displays. First, it allows fast recalibration in the face of projector, display or camera movements and even change in display shape. Second, this opens up, for the first time, the possibility of allowing multiple projectors to overlap on the corners of the CAVE-a popular immersive VR display system. Finally, this opens up the possibility of easily deploying multiprojector displays on aesthetic novel shapes for edutainment and digital signage applications.
Piecewise Mapping in HEVC Lossless Intra-prediction Coding.
Sanchez, Victor; Auli-Llinas, Francesc; Serra-Sagrista, Joan
2016-05-19
The lossless intra-prediction coding modality of the High Efficiency Video Coding (HEVC) standard provides high coding performance while allowing frame-by-frame basis access to the coded data. This is of interest in many professional applications such as medical imaging, automotive vision and digital preservation in libraries and archives. Various improvements to lossless intra-prediction coding have been proposed recently, most of them based on sample-wise prediction using Differential Pulse Code Modulation (DPCM). Other recent proposals aim at further reducing the energy of intra-predicted residual blocks. However, the energy reduction achieved is frequently minimal due to the difficulty of correctly predicting the sign and magnitude of residual values. In this paper, we pursue a novel approach to this energy-reduction problem using piecewise mapping (pwm) functions. Specifically, we analyze the range of values in residual blocks and apply accordingly a pwm function to map specific residual values to unique lower values. We encode appropriate parameters associated with the pwm functions at the encoder, so that the corresponding inverse pwm functions at the decoder can map values back to the same residual values. These residual values are then used to reconstruct the original signal. This mapping is, therefore, reversible and introduces no losses. We evaluate the pwm functions on 4×4 residual blocks computed after DPCM-based prediction for lossless coding of a variety of camera-captured and screen content sequences. Evaluation results show that the pwm functions can attain maximum bit-rate reductions of 5.54% and 28.33% for screen content material compared to DPCM-based and block-wise intra-prediction, respectively. Compared to Intra- Block Copy, piecewise mapping can attain maximum bit-rate reductions of 11.48% for camera-captured material.
Quasi-stationary Stefan problem as limit case of Mullins-Sekerka problem
Institute of Scientific and Technical Information of China (English)
易法槐; 陶有山; 刘祖汉
1997-01-01
The existence of a local classical solution to the Mullins-Sekerka problem and the convergence to the two-phase quasi-stationary Stefan problem are proved when surface tension approaches zero. This convergence gives a proof of the existence of a local classical solution of quasi-stationary Stefan problem. The methods work in all dimensions.
Analysis and control for a new chaotic system via piecewise linear feedback
Energy Technology Data Exchange (ETDEWEB)
Zhang Jianxiong [Institute of Systems Engineering, Tianjin University, Tianjin 300072 (China)], E-mail: jxzhang@tju.edu.cn; Tang Wansheng [Institute of Systems Engineering, Tianjin University, Tianjin 300072 (China)
2009-11-30
This paper presents a new three-dimensional chaotic system containing two system parameters and a nonlinear term in the form of arc-hyperbolic sine function. The complicated dynamics are studied by virtue of theoretical analysis, numerical simulation and Lyapunov exponents spectrum. The system proposed is converted to an uncertain piecewise linear system. Then, based on piecewise quadratic Lyapunov function technique, the global control of the new chaotic system with {alpha}-stability constraint via piecewise linear state feedback is studied, where the optimal controller maximizing the decay rate {alpha} can be obtained by solving an optimization problem under bilinear matrix inequalities (BMIs) constraints.
Nther-type theorem of piecewise algebraic curves on quasi-cross-cut partition
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Nther’s theorem of algebraic curves plays an important role in classical algebraic geometry. As the zero set of a bivariate spline, the piecewise algebraic curve is a generalization of the classical algebraic curve. Nther-type theorem of piecewise algebraic curves is very important to construct the Lagrange interpolation sets for bivariate spline spaces. In this paper, using the characteristics of quasi-cross-cut partition, properties of bivariate splines and results in algebraic geometry, the Nther-type theorem of piecewise algebraic curves on the quasi-cross-cut is presented.
N(o)ther-type theorem of piecewise algebraic curves on quasi-cross-cut partition
Institute of Scientific and Technical Information of China (English)
ZHU ChunGang; WANG RenHong
2009-01-01
Nother's theorem of algebraic curves plays an important role in classical algebraic geome-try. As the zero set of a bivariate spline, the piecewise algebraic curve is a generalization of the classical algebraic curve. Nother-type theorem of piecewise algebraic curves is very important to construct the Lagrange interpolation sets for bivariate spline spaces. In this paper, using the characteristics of quasi-cross-cut partition, properties of bivariate splines and results in algebraic geometry, the Nother-type theorem of piecewise algebraic curves on the quasi-cross-cut is presented.
Piecewise Linear Analysis for Pseudo-elasticity of Shape Memory Alloy (SMA)
Institute of Scientific and Technical Information of China (English)
WANG Xiao-dong; DU Xiao-wei; SUN Guo-jun
2005-01-01
Based on the Brinson constitutive model of SMA, a piecewise linear model for the hysteresis loop of pseudo-elasticity is proposed and applied in the analysis of responses of an SMA-spring-mass system under initial velocity activation. The histories of displacement and velocity of the mass, and the response of stress of SMA are calculated with Brinson's model and the piecewise linear model. The difference of results of the two models is not significant. The calculation with piecewise-linear model needs no iteration and is highly efficient.
Gyrokinetic modelling of stationary electron and impurity profiles in tokamaks
Skyman, Andreas; Tegnered, Daniel
2014-01-01
Particle transport due to Ion Temperature Gradient/Trapped Electron (ITG/TE) mode turbulence is investigated using the gyrokinetic code GENE. Both a reduced quasilinear (QL) treatment and nonlinear (NL) simulations are performed for typical tokamak parameters corresponding to ITG dominated turbulence. A selfconsistent treatment is used, where the stationary local profiles are calculated corresponding to zero particle flux simultaneously for electrons and trace impurities. The scaling of the stationary profiles with magnetic shear, safety factor, electron-to-ion temperature ratio, collisionality, toroidal sheared rotation, triangularity, and elongation is investigated. In addition, the effect of different main ion mass on the zero flux condition is discussed. The electron density gradient can significantly affect the stationary impurity profile scaling. It is therefore expected, that a selfconsistent treatment will yield results more comparable to experimental results for parameter scans where the stationary b...
Breaking the continuity of a piecewise linear map
Directory of Open Access Journals (Sweden)
Schenke Björn
2012-08-01
Full Text Available Knowledge about the behavior of discontinuous piecewise-linear maps is important for a wide range of applications. An efficient way to investigate the bifurcation structure in 2D parameter spaces of such maps is to detect specific codimension-2 bifurcation points, called organizing centers, and to describe the bifurcation structure in their neighborhood. In this work, we present the organizing centers in the 1D discontinuous piecewise-linear map in the generic form, which can be used as a normal form for these bifurcations in other 1D discontinuous maps with one discontinuity. These organizing centers appear when the continuity of the system function is broken in a fixed point. The type of an organizing center depends on the slopes of the piecewise-linear map. The organizing centers that occur if the slopes have an absolute value smaller than one were already described in previous works, so we concentrate on presenting the organizing centers that occur if one or both slopes have absolute values larger than one. By doing this, we also show that the behavior for each organizing center can be explained using four basic bifurcation scenarios: the period incrementing and the period adding scenarios in the periodic domain, as well as the bandcount incrementing and the bandcount adding scenarios in the chaotic domain. Les connaissances sur le comportement d’applications linéaires par morceaux discontinues sont importantes pour de nombreuses applications. Une méthode puissante pour étudier la structure de bifurcation dans les espaces de paramètre 2D de telles applications est de détecter des points de bifurcation spécifiques de codimension 2, appelés centres organisateurs, et de décrire la structure de bifurcation dans leur voisinage. Dans ce travail, nous présentons les centres organisateurs pour une application linéaire par morceaux discontinue 1D sous forme générique, ce qui peut être utilisé comme une forme normale pour ces
Stationary one-dimensional dispersive shock waves
Kartashov, Yaroslav V
2011-01-01
We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defect in defocusing media with linear gain and two-photon absorption. We found that in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from defect or generating beam, the competition between gain and two-photon absorption in dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed certain critical value.
Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Soukhoterin, E.A.; Mosekilde, Erik
2002-01-01
Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject...... of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border......-collision bifurcations. The paper contains a detailed analysis of this type of bifurcational transition in the dynamics of the voltage converter, in particular, the merging and subsequent disappearance of cycles of different types, change of solution type, and period-doubling, -tripling, -quadrupling and -quintupling...
Construction of a Class of Four-Dimensional Piecewise Affine Systems with Homoclinic Orbits
Wu, Tiantian; Yang, Xiao-Song
2016-06-01
Based on mathematical analysis, this paper provides a methodology to ensure the existence of homoclinic orbits in a class of four-dimensional piecewise affine systems. In addition, an example is provided to illustrate the effectiveness of the method.
Real zeros of the zero-dimensional parametric piecewise algebraic variety
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems containing strict inequalities. With the regular decomposition of semi- algebraic systems and the partial cylindrical algebraic decomposition method, we give a method to compute the supremum of the number of torsion-free real zeros of a given zero-dimensional parametric piecewise algebraic variety, and to get distributions of the number of real zeros in every n-dimensional cell when the number reaches the supremum. This method also produces corresponding necessary and suffcient conditions for reaching the supremum and its distributions. We also present an algorithm to produce a necessary and suffcient condition for a given zero-dimensional parametric piecewise algebraic variety to have a given number of distinct torsion-free real zeros in every n-cell in the n-complex.
Vision servoing of robot systems using piecewise continuous controllers and observers
Wang, H. P.; Vasseur, C.; Christov, N.; Koncar, V.
2012-11-01
This paper deals with the visual servoing of X-Y robot systems using low cost CCD camera. The proposed approach is based on the theory of piecewise continuous systems which are a particular class of hybrid systems with autonomous switching and controlled impulses. Visual trajectory tracking systems comprising piecewise continuous controllers and observers, are developed. Real-time results are given to illustrate the effectiveness of the proposed visual control system.
Caneco, Acilina; Rocha, Jose; Gracio, Clara
2009-01-01
In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupl...
Hirata, Yoshito; Aihara, Kazuyuki
2012-06-01
We introduce a low-dimensional description for a high-dimensional system, which is a piecewise affine model whose state space is divided by permutations. We show that the proposed model tends to predict wind speeds and photovoltaic outputs for the time scales from seconds to 100 s better than by global affine models. In addition, computations using the piecewise affine model are much faster than those of usual nonlinear models such as radial basis function models.
Decomposition of piecewise-polynomial model of a predistorter for power amplifier
2015-01-01
Decomposition of piecewise-polynomial model of a predistorter has been performed taking into account the alteration dynamics of the complex envelope’s magnitude for the signal, which is converted by an amplifier. Decomposition model provides higher accuracy of nonlinear distortions compensation for signals in the amplifier compared with piecewise-polynomial model of a predistorter. Comparative analysis of predistorters’ models has been carried out for the linearization of the Wiener–Hammerste...
A Piecewise Linear Fitting Technique for Multivalued Two-dimensional Paths
Directory of Open Access Journals (Sweden)
V.M. Jimenez-Fernandez
2013-10-01
Full Text Available This paper presents a curve-fitting technique for multivalued two-dimensional piecewise-linear paths. The proposed method is based on a decomposed formulation of the canonical piecewise linear model description of Chua and Kang. The path is treated as a parametric system of two position equations (x(k, y(k, where k is an artificial parameter to map each variable (x and y into an independent k-domain.
Wavelets centered on a knot sequence: piecewise polynomial wavelets on a quasi-crystal lattice
Atkinson, Bruce W; Geronimo, Jeffrey S; Hardin, Douglas P
2011-01-01
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. As an application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the $\\tau$-integers where $\\tau$ is the golden-mean. The resulting spaces then generate a multiresolution analysis of $L^2(\\mathbf{R})$ with scaling factor $\\tau$.
Optimal Piecewise Linear Basis Functions in Two Dimensions
Energy Technology Data Exchange (ETDEWEB)
Brooks III, E D; Szoke, A
2009-01-26
We use a variational approach to optimize the center point coefficients associated with the piecewise linear basis functions introduced by Stone and Adams [1], for polygonal zones in two Cartesian dimensions. Our strategy provides optimal center point coefficients, as a function of the location of the center point, by minimizing the error induced when the basis function interpolation is used for the solution of the time independent diffusion equation within the polygonal zone. By using optimal center point coefficients, one expects to minimize the errors that occur when these basis functions are used to discretize diffusion equations, or transport equations in optically thick zones (where they approach the solution of the diffusion equation). Our optimal center point coefficients satisfy the requirements placed upon the basis functions for any location of the center point. We also find that the location of the center point can be optimized, but this requires numerical calculations. Curiously, the optimum center point location is independent of the values of the dependent variable on the corners only for quadrilaterals.
Dynamical zeta functions for piecewise monotone maps of the interval
Ruelle, David
2004-01-01
Consider a space M, a map f:M\\to M, and a function g:M \\to {\\mathbb C}. The formal power series \\zeta (z) = \\exp \\sum ^\\infty _{m=1} \\frac {z^m}{m} \\sum _{x \\in \\mathrm {Fix}\\,f^m} \\prod ^{m-1}_{k=0} g (f^kx) yields an example of a dynamical zeta function. Such functions have unexpected analytic properties and interesting relations to the theory of dynamical systems, statistical mechanics, and the spectral theory of certain operators (transfer operators). The first part of this monograph presents a general introduction to this subject. The second part is a detailed study of the zeta functions associated with piecewise monotone maps of the interval [0,1]. In particular, Ruelle gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of \\zeta (z) and the eigenvalues of the transfer operator. He also proves a theorem expressing the largest eigenvalue of the transfer operator in terms of the ergodic properties of (M,f,g).
Piecewise linear models for the quasiperiodic transition to chaos
Campbell, D K; Tresser, C; Uherka, D J; Campbell, David K; Galeeva, Roza; Tresser, Charles; Uherka, David J
1995-01-01
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on mode...
Piecewise linear mapping algorithm for SAR raw data compression
Institute of Scientific and Technical Information of China (English)
QI HaiMing; YU WeiDong; CHEN Xi
2008-01-01
When the saturation degree (SD) of space-borne SAR raw data is high, the performance of conventional block adaptive quantization (BAQ) deteriorates obviously. In order to overcome the drawback, this paper studies the mapping between the average signal magnitude (ASM) and the standard deviation of the input signal (SDIS) to the A/D from the original reference. Then, it points out the mistake of the mapping and introduces the concept of the standard deviation of the output signal (SDOS) from the A/D. After that, this paper educes the mapping between the ASM and SDOS from the A/D. Monte-Carlo experiment shows that none of the above two mappings is the optimal in the whole set of SD. Thus, this paper proposes the concept of piecewise linear mapping and the searching algorithm in the whole set of SD. According to the linear part, this paper gives the certification and analytical value of k and for nonlinear part, and utilizes the searching algorithm mentioned above to search the corresponding value of k. Experimental results based on simulated data and real data show that the performance of new algorithm is better than conventional BAQ when raw data is in heavy SD.
One Line or Two? Perspectives on Piecewise Regression
Energy Technology Data Exchange (ETDEWEB)
R.P. Ewing; D.W. Meek
2006-10-12
Sometimes we are faced with data that could reasonably be represented either as a single line, or as two or more line segments. How do we identify the best breakpoint(s), and decide how many segments are ''really'' present? Most of us are taught to distrust piecewise regression, because it can be easily abused. The best method for identifying the breakpoint varies according to specifics of the data; for example, the minimum sum of squares method excels for ''well-behaved'' data. In some cases, hidden Markov methods are more likely to succeed than are more ''obvious'' methods. Likewise, the most appropriate method for deciding between one or two lines depends on your expectations and understanding of the data: an unexpected break requires more justification than an expected one, and some decision criteria (e.g., the Akaike Information Criterion) are less strict than others (e.g., the Bayesian Information Criterion). This presentation will review some options and make specific, practical recommendations.
Interactive seismic interpretation with piecewise global energy minimization
Hollt, Thomas
2011-03-01
Increasing demands in world-wide energy consumption and oil depletion of large reservoirs have resulted in the need for exploring smaller and more complex oil reservoirs. Planning of the reservoir valorization usually starts with creating a model of the subsurface structures, including seismic faults and horizons. However, seismic interpretation and horizon tracing is a difficult and error-prone task, often resulting in hours of work needing to be manually repeated. In this paper, we propose a novel, interactive workflow for horizon interpretation based on well positions, which include additional geological and geophysical data captured by actual drillings. Instead of interpreting the volume slice-by-slice in 2D, we propose 3D seismic interpretation based on well positions. We introduce a combination of 2D and 3D minimal cost path and minimal cost surface tracing for extracting horizons with very little user input. By processing the volume based on well positions rather than slice-based, we are able to create a piecewise optimal horizon surface at interactive rates. We have integrated our system into a visual analysis platform which supports multiple linked views for fast verification, exploration and analysis of the extracted horizons. The system is currently being evaluated by our collaborating domain experts. © 2011 IEEE.
A Piecewise Hysteresis Model for a Damper of HIS System
Directory of Open Access Journals (Sweden)
Kaidong Tian
2016-01-01
Full Text Available A damper of the hydraulically interconnected suspension (HIS system, as a quarter HIS, is prototyped and its damping characteristic is tested to characterize the damping property. The force-velocity characteristic of the prototype is analyzed based on a set of testing results and accordingly a piecewise hysteresis model for the damper is proposed. The proposed equivalent parametric model consists of two parts: hysteresis model in low speed region and saturation model in high speed region which are used to describe the hysteresis phenomenon in low speed and nonhysteresis phenomenon in high speed, respectively. The parameters of the model are identified based on genetic algorithm by setting the constraints of parameters according to their physical significances and the corresponding testing results. The advantages of the model are highlighted by comparing to the nonhysteresis model and the permanent hysteresis model. The numerical simulation results are compared with the testing results to validate the accuracy and effectiveness of the proposed model. Finally, to further verify the proposed model’s wide applicability under different excitation conditions, its results are compared to the testing results in three-dimensional space. The research in this paper is significant for the dynamic analysis of the HIS vehicle.
The N(o)ther and Riemann-Roch type theorems for piecewise algebraic curve
Institute of Scientific and Technical Information of China (English)
Yi-sheng LAI; Ren-hong WANG
2007-01-01
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, the N(o)ther type theorems for Cμ piecewise algebraic curves are obtained.The theory of the linear series of sets of places on the piecewise algebraic curve is also established.In this theory, singular cycles are put into the linear series, and a complete series of the piecewise algebraic curves consists of all effective ordinary cycles in an equivalence class and all effective singular cycles which are equivalent specifically to any effective ordinary cycle in the equivalence class. This theory is a generalization of that of linear series of the algebraic curve. With this theory and the fundamental theory of multivariate splines on smoothing cofactors and global conformality conditions,and the results on the general expression of multivariate splines, we get a formula on the index, the order and the dimension of a complete series of the irreducible Cμ piecewise algebraic curves and the degree, the genus and the smoothness of the curves, hence the Riemann-Roch type theorem of the Cμpiecewise algebraic curve is established.
The Nother and Riemann-Roch type theorems for piecewise algebraic curve
Institute of Scientific and Technical Information of China (English)
2007-01-01
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, the Nother type theorems for Cμpiecewise algebraic curves are obtained. The theory of the linear series of sets of places on the piecewise algebraic curve is also established. In this theory, singular cycles are put into the linear series, and a complete series of the piecewise algebraic curves consists of all effective ordinary cycles in an equivalence class and all effective singular cycles which are equivalent specifically to any effective ordinary cycle in the equivalence class. This theory is a generalization of that of linear series of the algebraic curve. With this theory and the fundamental theory of multivariate splines on smoothing cofactors and global conformality conditions, and the results on the general expression of multivariate splines, we get a formula on the index, the order and the dimension of a complete series of the irreducible Cμpiecewise algebraic curves and the degree, the genus and the smoothness of the curves, hence the Riemann-Roch type theorem of the Cμpiecewise algebraic curve is established.
Gorban, A N; Mirkes, E M; Zinovyev, A
2016-12-01
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0basic universal data approximation algorithms (k-means, principal components, principal manifolds and graphs, regularized and sparse regression), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize arbitrary sub-quadratic error potentials using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.
Nonequilibrium stationary states and entropy.
Gallavotti, G; Cohen, E G D
2004-03-01
In transformations between nonequilibrium stationary states, entropy might not be a well defined concept. It might be analogous to the "heat content" in transformations in equilibrium which is not well defined either, if they are not isochoric (i.e., do involve mechanical work). Hence we conjecture that in a nonequilibrium stationary state the entropy is just a quantity that can be transferred or created, such as heat in equilibrium, but has no physical meaning as "entropy content" as a property of the system.
Stationary Stability for Evolutionary Dynamics in Finite Populations
Directory of Open Access Journals (Sweden)
Marc Harper
2016-08-01
Full Text Available We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We define the notion of stationary stability for the Moran process with mutation and generalizations, as well as a generalized notion of evolutionary stability that includes mutation called an incentive stable state (ISS candidate. For sufficiently large populations, extrema of the stationary distribution are ISS candidates and we give a family of Lyapunov quantities that are locally minimized at the stationary extrema and at ISS candidates. In various examples, including for the Moran and Wright–Fisher processes, we show that the local maxima of the stationary distribution capture the traditionally-defined evolutionarily stable states. The classical stability theory of the replicator dynamic is recovered in the large population limit. Finally we include descriptions of possible extensions to populations of variable size and populations evolving on graphs.
Condensational theory of stationary tornadoes
Makarieva, Anastassia M; Nefiodov, Andrei V; 10.1016/j.physleta.2011.04.023
2012-01-01
Using the Bernoulli integral for air streamline with condensing water vapor a stationary axisymmetric tornado circulation is described. The obtained profiles of vertical, radial and tangential velocities are in agreement with observations for the Mulhall tornado, world's largest on record and longest-lived among the three tornadoes for which 3D velocity data are available. Maximum possible vortex velocities are estimated.
Directory of Open Access Journals (Sweden)
Abílio Amiguinho
2005-01-01
Full Text Available The process of socio-educational territorialisation in rural contexts is the topic of this text. The theme corresponds to a challenge to address it having as main axis of discussion either the problem of social exclusion or that of local development. The reasons to locate the discussion in this last field of analysis are discussed in the first part of the text. Theoretical and political reasons are there articulated because the question is about projects whose intentions and practices call for the political both in the theoretical debate and in the choices that anticipate intervention. From research conducted for several years, I use contributions that aim at discuss and enlighten how school can be a potential locus of local development. Its identification and recognition as local institution (either because of those that work and live in it or because of those that act in the surrounding context are crucial steps to progressively constitute school as a partner for development. The promotion of the local values and roots, the reconstruction of socio-personal and local identities, the production of sociabilities and the equation and solution of shared problems were the dimensions of a socio-educative intervention, markedly globalising. This scenario, as it is argued, was also, intentionally, one of transformation and of deliberate change of school and of the administration of the educative territoires.
Slow Sphering to Suppress Non-Stationaries in the EEG
Reuderink, Boris; Farquhar, Jason; Poel, Mannes
2011-01-01
Non-stationary signals are ubiquitous in electroencephalogram (EEG) signals and pose a problem for robust application of brain-computer interfaces (BCIs). These non-stationarities can be caused by changes in neural background activity. We present a dynamic spatial filter based on time local whitenin
Robust Forecasting of Non-Stationary Time Series
Croux, C.; Fried, R.; Gijbels, I.; Mahieu, K.
2010-01-01
This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable foreca
Perfect Sampling of Markov Chains with Piecewise Homogeneous Events
Bušić, Ana; Pin, Furcy
2010-01-01
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events in the system have monotonicity property. However, in the general (non-monotone) case, this technique needs to consider the whole state space, which limits its application only to chains with a state space of small cardinality. We propose here a new approach for the general case that only needs to consider two trajectories. Instead of the original chain, we use two bounding processes (envelopes) and we show that, whenever they couple, one obtains a sample under the stationary distribution of the original chain. We show that this new approach is particularly effective when the state space can be partitioned into pieces where envelopes can be easily computed. We further show that most Markovian queueing networks have this property and we propose efficient algorithms for some...
Dose reduction using a dynamic, piecewise-linear attenuator
Energy Technology Data Exchange (ETDEWEB)
Hsieh, Scott S., E-mail: sshsieh@stanford.edu [Department of Radiology, Stanford University, Stanford, California 94305 and Department of Electrical Engineering, Stanford University, Stanford, California 94305 (United States); Fleischmann, Dominik [Department of Radiology, Stanford University, Stanford, California 94305 (United States); Pelc, Norbert J. [Department of Radiology, Stanford University, Stanford, California 94305 and Department of Bioengineering, Stanford University, Stanford, California 94305 (United States)
2014-02-15
Purpose: The authors recently proposed a dynamic, prepatient x-ray attenuator capable of producing a piecewise-linear attenuation profile customized to each patient and viewing angle. This attenuator was intended to reduce scatter-to-primary ratio (SPR), dynamic range, and dose by redistributing flux. In this work the authors tested the ability of the attenuator to reduce dose and SPR in simulations. Methods: The authors selected four clinical applications, including routine full field-of-view scans of the thorax and abdomen, and targeted reconstruction tasks for an abdominal aortic aneurysm and the pancreas. Raw data were estimated by forward projection of the image volume datasets. The dynamic attenuator was controlled to reduce dose while maintaining peak variance by solving a convex optimization problem, assuminga priori knowledge of the patient anatomy. In targeted reconstruction tasks, the noise in specific regions was given increased weighting. A system with a standard attenuator (or “bowtie filter”) was used as a reference, and used either convex optimized tube current modulation (TCM) or a standard TCM heuristic. The noise of the scan was determined analytically while the dose was estimated using Monte Carlo simulations. Scatter was also estimated using Monte Carlo simulations. The sensitivity of the dynamic attenuator to patient centering was also examined by shifting the abdomen in 2 cm intervals. Results: Compared to a reference system with optimized TCM, use of the dynamic attenuator reduced dose by about 30% in routine scans and 50% in targeted scans. Compared to the TCM heuristics which are typically used withouta priori knowledge, the dose reduction is about 50% for routine scans. The dynamic attenuator gives the ability to redistribute noise and variance and produces more uniform noise profiles than systems with a conventional bowtie filter. The SPR was also modestly reduced by 10% in the thorax and 24% in the abdomen. Imaging with the dynamic
Detection of Multiple Stationary Humans Using UWB MIMO Radar
Directory of Open Access Journals (Sweden)
Fulai Liang
2016-11-01
Full Text Available Remarkable progress has been achieved in the detection of single stationary human. However, restricted by the mutual interference of multiple humans (e.g., strong sidelobes of the torsos and the shadow effect, detection and localization of the multiple stationary humans remains a huge challenge. In this paper, ultra-wideband (UWB multiple-input and multiple-output (MIMO radar is exploited to improve the detection performance of multiple stationary humans for its multiple sight angles and high-resolution two-dimensional imaging capacity. A signal model of the vital sign considering both bi-static angles and attitude angle of the human body is firstly developed, and then a novel detection method is proposed to detect and localize multiple stationary humans. In this method, preprocessing is firstly implemented to improve the signal-to-noise ratio (SNR of the vital signs, and then a vital-sign-enhanced imaging algorithm is presented to suppress the environmental clutters and mutual affection of multiple humans. Finally, an automatic detection algorithm including constant false alarm rate (CFAR, morphological filtering and clustering is implemented to improve the detection performance of weak human targets affected by heavy clutters and shadow effect. The simulation and experimental results show that the proposed method can get a high-quality image of multiple humans and we can use it to discriminate and localize multiple adjacent human targets behind brick walls.
Non-Stationary Dependence Structures for Spatial Extremes
Huser, Raphaël
2016-03-03
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. In this paper, we develop non-stationary max-stable dependence structures in which covariates can be easily incorporated. Inference is performed using pairwise likelihoods, and its performance is assessed by an extensive simulation study based on a non-stationary locally isotropic extremal t model. Evidence that unknown parameters are well estimated is provided, and estimation of spatial return level curves is discussed. The methodology is demonstrated with temperature maxima recorded over a complex topography. Models are shown to satisfactorily capture extremal dependence.
Time scale of stationary decoherence
Polonyi, Janos
2017-07-01
The decoherence of a test particle interacting with an ideal gas is studied by the help of the effective Lagrangian, derived in the leading order of the perturbation expansion and in order O (∂t2) . The stationary decoherence time is found to be comparable to or longer than the diffusion time. The decoherence time reaches its minimal value for classical, completely decohered environment, suggesting that physical decoherence is slowed down as compared with diffusion by the quantum coherence of the environment.
Toktarbay, Saken
2015-01-01
We present a stationary generalization of the static $q-$metric, the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. It possesses three independent parameters that are related to the mass, quadrupole moment and angular momentum. We investigate the geometric and physical properties of this exact solution of Einstein's vacuum equations, and show that it can be used to describe the exterior gravitational field of rotating, axially symmetric, compact objects.
Toktarbay, S.; Quevedo, H.
2014-10-01
We present a stationary generalization of the static $q-$metric, the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. It possesses three independent parameters that are related to the mass, quadrupole moment and angular momentum. We investigate the geometric and physical properties of this exact solution of Einstein's vacuum equations, and show that it can be used to describe the exterior gravitational field of rotating, axially symmetric, compact objects.
An intelligent approach for variable size segmentation of non-stationary signals.
Azami, Hamed; Hassanpour, Hamid; Escudero, Javier; Sanei, Saeid
2015-09-01
In numerous signal processing applications, non-stationary signals should be segmented to piece-wise stationary epochs before being further analyzed. In this article, an enhanced segmentation method based on fractal dimension (FD) and evolutionary algorithms (EAs) for non-stationary signals, such as electroencephalogram (EEG), magnetoencephalogram (MEG) and electromyogram (EMG), is proposed. In the proposed approach, discrete wavelet transform (DWT) decomposes the signal into orthonormal time series with different frequency bands. Then, the FD of the decomposed signal is calculated within two sliding windows. The accuracy of the segmentation method depends on these parameters of FD. In this study, four EAs are used to increase the accuracy of segmentation method and choose acceptable parameters of the FD. These include particle swarm optimization (PSO), new PSO (NPSO), PSO with mutation, and bee colony optimization (BCO). The suggested methods are compared with other most popular approaches (improved nonlinear energy operator (INLEO), wavelet generalized likelihood ratio (WGLR), and Varri's method) using synthetic signals, real EEG data, and the difference in the received photons of galactic objects. The results demonstrate the absolute superiority of the suggested approach.
An intelligent approach for variable size segmentation of non-stationary signals
Directory of Open Access Journals (Sweden)
Hamed Azami
2015-09-01
Full Text Available In numerous signal processing applications, non-stationary signals should be segmented to piece-wise stationary epochs before being further analyzed. In this article, an enhanced segmentation method based on fractal dimension (FD and evolutionary algorithms (EAs for non-stationary signals, such as electroencephalogram (EEG, magnetoencephalogram (MEG and electromyogram (EMG, is proposed. In the proposed approach, discrete wavelet transform (DWT decomposes the signal into orthonormal time series with different frequency bands. Then, the FD of the decomposed signal is calculated within two sliding windows. The accuracy of the segmentation method depends on these parameters of FD. In this study, four EAs are used to increase the accuracy of segmentation method and choose acceptable parameters of the FD. These include particle swarm optimization (PSO, new PSO (NPSO, PSO with mutation, and bee colony optimization (BCO. The suggested methods are compared with other most popular approaches (improved nonlinear energy operator (INLEO, wavelet generalized likelihood ratio (WGLR, and Varri’s method using synthetic signals, real EEG data, and the difference in the received photons of galactic objects. The results demonstrate the absolute superiority of the suggested approach.
Piecewise-homogeneous model for electron side injection into linear plasma waves
Energy Technology Data Exchange (ETDEWEB)
Golovanov, A.A., E-mail: agolovanov256@gmail.com; Kostyukov, I.Yu., E-mail: kost@appl.sci-nnov.ru
2016-09-01
An analytical piecewise-homogeneous model for electron side injection into linear plasma waves is developed. The dynamics of transverse betatron oscillations are studied. Based on the characteristics of the transversal motion the longitudinal motion of electrons is described. The electron parameters for which the electron trapping and subsequent acceleration are possible are estimated. The analytical results are verified by numerical simulations in the scope of the piecewise-homogeneous model. The results predicted by this model are also compared to the results given by a more realistic inhomogeneous model. - Highlights: • A piecewise-homogeneous model of side injection into a linear wakefield is developed. • The dynamics of betatron oscillations in the focusing phase is analytically studied. • The area of parameters for electron trapping is determined. • The model is compared to a more realistic inhomogeneous model.
Multi-Dimensional Piece-Wise Self-Affine Fractal Interpolation Model
Institute of Scientific and Technical Information of China (English)
ZHANG Tong; ZHUANG Zhuo
2007-01-01
Iterated function system (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R2 or R3 (R is the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended from R3 to Rn (n is an integer greater than 3), which is called the multi-dimensional piece-wise self-affine fractal interpolation model. This model uses a "mapping partial derivative", and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine in Rn. Therefore, the result is very general. The class of functions obtained is much more diverse because their values depend continuously on all of the variables, with all the coefficients of the possible multi-dimensional affine maps determining the functions.
High efficiency stationary hydrogen storage
Energy Technology Data Exchange (ETDEWEB)
Hynek, S.; Fuller, W.; Truslow, S. [Arthur D. Little, Inc., Cambridge, MA (United States)
1995-09-01
Stationary storage of hydrogen permits one to make hydrogen now and use it later. With stationary hydrogen storage, one can use excess electrical generation capacity to power an electrolyzer, and store the resultant hydrogen for later use or transshipment. One can also use stationary hydrogen as a buffer at fueling stations to accommodate non-steady fueling demand, thus permitting the hydrogen supply system (e.g., methane reformer or electrolyzer) to be sized to meet the average, rather than the peak, demand. We at ADL designed, built, and tested a stationary hydrogen storage device that thermally couples a high-temperature metal hydride to a phase change material (PCM). The PCM captures and stores the heat of the hydriding reaction as its own heat of fusion (that is, it melts), and subsequently returns that heat of fusion (by freezing) to facilitate the dehydriding reaction. A key component of this stationary hydrogen storage device is the metal hydride itself. We used nickel-coated magnesium powder (NCMP) - magnesium particles coated with a thin layer of nickel by means of chemical vapor deposition (CVD). Magnesium hydride can store a higher weight fraction of hydrogen than any other practical metal hydride, and it is less expensive than any other metal hydride. We designed and constructed an experimental NCM/PCM reactor out of 310 stainless steel in the form of a shell-and-tube heat exchanger, with the tube side packed with NCMP and the shell side filled with a eutectic mixture of NaCL, KCl, and MgCl{sub 2}. Our experimental results indicate that with proper attention to limiting thermal losses, our overall efficiency will exceed 90% (DOE goal: >75%) and our overall system cost will be only 33% (DOE goal: <50%) of the value of the delivered hydrogen. It appears that NCMP can be used to purify hydrogen streams and store hydrogen at the same time. These prospects make the NCMP/PCM reactor an attractive component in a reformer-based hydrogen fueling station.
Separable geodesic action slicing in stationary spacetimes
Bini, Donato; Jantzen, Robert T
2014-01-01
A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent freely falling observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function. This explains some of the properties of the original Painlev\\'e-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the G\\"odel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.
Meneses, Domingos De Sousa; Rousseau, Benoit; Echegut, Patrick; Matzen, Guy
2007-06-01
A new expression of dielectric function model based on piecewise polynomials is introduced. Its association with spline and more recent shape preserving interpolation algorithms allows easy reproduction of every kind of experimental spectra and thus retrieval of all the linear optical functions of a material. Based on a pure mathematical framework, the expression of the model is always applicable and does not necessitate any knowledge of the microscopic mechanisms of absorption responsible for the optical response. The potential of piecewise polynomial dielectric functions is shown through synthetic examples and the analysis of experimental spectra.
A Piecewise Affine Hybrid Systems Approach to Fault Tolerant Satellite Formation Control
DEFF Research Database (Denmark)
Grunnet, Jacob Deleuran; Larsen, Jesper Abildgaard; Bak, Thomas
2008-01-01
In this paper a procedure for modelling satellite formations including failure dynamics as a piecewise-affine hybrid system is shown. The formulation enables recently developed methods and tools for control and analysis of piecewise-affine systems to be applied leading to synthesis of fault...... tolerant controllers and analysis of the system behaviour given possible faults. The method is illustrated using a simple example involving two satellites trying to reach a specific formation despite of actuator faults occurring....
Passive Fault-tolerant Control of Discrete-time Piecewise Affine Systems against Actuator Faults
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Izadi-Zamanabadi, Roozbeh; Bak, Thomas
2012-01-01
In this paper, we propose a new method for passive fault-tolerant control of discrete time piecewise affine systems. Actuator faults are considered. A reliable piecewise linear quadratic regulator (LQR) state feedback is designed such that it can tolerate actuator faults. A sufficient condition...... for the exis- tence of a passive fault-tolerant controller is derived and formulated as the feasibility of a set of linear matrix inequalities (LMIs). The upper bound on the performance cost can be minimized using a convex optimization problem with LMI constraints which can be solved efficiently. The approach...
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathe ́odory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in finite...... time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix...
A Piecewise Affine Hybrid Systems Approach to Fault Tolerant Satellite Formation Control
DEFF Research Database (Denmark)
Grunnet, Jacob Deleuran; Larsen, Jesper Abildgaard; Bak, Thomas
2008-01-01
In this paper a procedure for modelling satellite formations including failure dynamics as a piecewise-affine hybrid system is shown. The formulation enables recently developed methods and tools for control and analysis of piecewise-affine systems to be applied leading to synthesis of fault...... tolerant controllers and analysis of the system behaviour given possible faults. The method is illustrated using a simple example involving two satellites trying to reach a specific formation despite of actuator faults occurring....
The Cauchy Boundary Value Problems on Closed Piecewise Smooth Manifolds in Cn
Institute of Scientific and Technical Information of China (English)
Liang Yu LIN; Chun Hui QIU
2004-01-01
Suppose that D is a bounded domain with a piecewise C1 smooth boundary in Cn. Let ψ∈ C1+α((б)D). By using the Hadamard principal value of the higher order singular integral and solid angle coefficient method of points on the boundary, we give the Plemelj formula of the higher order singular integral with the Bochner-Martinelli kernel, which has integral density ψ. Moreover,by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauchy boundary value problem with the Bochner-Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution.
On the Kamke-Muller conditions, monotonicity and continuity for bi-modal piecewise-smooth systems
O'Donoghue, Yoann; Mason, Oliver; Middleton, Rick
2012-01-01
We show that the Kamke-Muller conditions for bimodal piecewise-smooth systems are equivalent to simple conditions on the vector elds dening the system. As a consequence, we show that for a specic class of such systems, monotonicity is equivalent to continuity. Furthermore, we apply our results to derive a stability condition for piecewise positive linear systems.
Stationary bubbles: information loss paradox?
Domènech, Guillem
2016-01-01
The main purpose of this work is to build classically stationary bubbles, within the thin-shell formalism, which are unstable under quantum effects; they either collapse into a black hole or expand. Thus, the final state can be thought of a superposition of geometries. We point out that, from a quantum mechanical point of view, there is no issue with a loss of information in such configuration. A classical observer sees a definite geometry and, hence, finds an effective loss of information. Although it does not cover all possible cases, we emphasise the role of semi-classical gravitational effects, mediated by instatons, in alleviating/solving the information loss paradox.
Directory of Open Access Journals (Sweden)
Zhinan Xia
2015-07-01
Full Text Available In this article, we show sufficient conditions for the existence, uniqueness and attractivity of piecewise weighted pseudo almost periodic classical solution of nonlinear impulsive integro-differential equations. The working tools are based on the fixed point theorem and fractional powers of operators. An application to impulsive integro-differential equations is presented.
Computation of the Metric Average of 2D Sets with Piecewise Linear Boundaries
Directory of Open Access Journals (Sweden)
Shay Kels
2010-07-01
Full Text Available The metric average is a binary operation between sets in Rn which is used in the approximation of set-valued functions. We introduce an algorithm that applies tools of computational geometry to the computation of the metric average of 2D sets with piecewise linear boundaries.
Model predictive control for Max-Plus-Linear and piecewise affine systems
Necoara, I.
2006-01-01
This Ph.D. thesis considers the development of new analysis and control techniques for special classes of hybrid systems and discrete event systems. Two particular classes of hybrid systems (piecewise affine systems and max-min-plus-scaling systems), and two particular classes of discrete event
Moses, Tim
2013-01-01
The purpose of this study was to evaluate the use of adjoined and piecewise linear approximations (APLAs) of raw equipercentile equating functions as a postsmoothing equating method. APLAs are less familiar than other postsmoothing equating methods (i.e., cubic splines), but their use has been described in historical equating practices of…
Directory of Open Access Journals (Sweden)
Pradeep Kumar
2013-10-01
Full Text Available The objective of this article is to prove the existence of piecewise continuous mild solutions to impulsive functional differential equation with iterated deviating arguments in a Banach space. The results are obtained by using the theory of analytic semigroups and fixed point theorems.
Robust Stabilization for Uncertain Control Systems Using Piecewise Quadratic Lyapunov Functions
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The sufficient condition based on piecewise quadratic simultaneous Lyapunov functions for robust stabilizationof uncertain control systems via a constant linear state feedback control law is obtained. The objective is to use a robuststability criterion that is less conservative than the usual quadratic stability criterion. Numerical example is given, show-ing the advanteges of the proposed method.
Institute of Scientific and Technical Information of China (English)
冯月才
2004-01-01
The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.
Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Bak, Thomas
2013-01-01
In this paper a new integrated observer-based fault estimation and accommodation strategy for discrete-time piecewise linear (PWL) systems subject to actuator faults is proposed. A robust estimator is designed to simultaneously estimate the state of the system and the actuator fault. Then, the es...
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Bak, Thomas
2012-01-01
In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H∞ performance of the fault estimation is minimized. Then...
Transitions from phase-locked dynamics to chaos in a piecewise-linear map
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Mosekilde, Erik; De, S.
2008-01-01
place via border-collision fold bifurcations. We examine the transition to chaos through torus destruction in such maps. Considering a piecewise-linear normal-form map we show that this transition, by virtue of the interplay of border-collision bifurcations with period-doubling and homoclinic...
Model predictive control for Max-Plus-Linear and piecewise affine systems
Necoara, I.
2006-01-01
This Ph.D. thesis considers the development of new analysis and control techniques for special classes of hybrid systems and discrete event systems. Two particular classes of hybrid systems (piecewise affine systems and max-min-plus-scaling systems), and two particular classes of discrete event s
Method of folding a piecewise polynomial function in the delta function integral representation
Energy Technology Data Exchange (ETDEWEB)
Lee, D.K.
1978-12-01
A simple procedure is presented for determining the folded form of a piecewise polynomial function in the delta function integral representation. The procedure is useful in evaluating the autocorrelation function by means of the algebraic convolution technique developed by Polge and Hasy (IEEE Trans. Comput. pp. 970-975, Nov 1973).
Franco, Glaura C.; Reisen, Valderio A.
2007-03-01
This paper deals with different bootstrap approaches and bootstrap confidence intervals in the fractionally autoregressive moving average (ARFIMA(p,d,q)) process [J. Hosking, Fractional differencing, Biometrika 68(1) (1981) 165-175] using parametric and semi-parametric estimation techniques for the memory parameter d. The bootstrap procedures considered are: the classical bootstrap in the residuals of the fitted model [B. Efron, R. Tibshirani, An Introduction to the Bootstrap, Chapman and Hall, New York, 1993], the bootstrap in the spectral density function [E. Paparoditis, D.N Politis, The local bootstrap for periodogram statistics. J. Time Ser. Anal. 20(2) (1999) 193-222], the bootstrap in the residuals resulting from the regression equation of the semi-parametric estimators [G.C Franco, V.A Reisen, Bootstrap techniques in semiparametric estimation methods for ARFIMA models: a comparison study, Comput. Statist. 19 (2004) 243-259] and the Sieve bootstrap [P. Bühlmann, Sieve bootstrap for time series, Bernoulli 3 (1997) 123-148]. The performance of these procedures and confidence intervals for d in the stationary and non-stationary ranges are empirically obtained through Monte Carlo experiments. The bootstrap confidence intervals here proposed are alternative procedures with some accuracy to obtain confidence intervals for d.
Nie, Xiaobing; Zheng, Wei Xing
2015-05-01
This paper is concerned with the problem of coexistence and dynamical behaviors of multiple equilibrium points for neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays. The fixed point theorem and other analytical tools are used to develop certain sufficient conditions that ensure that the n-dimensional discontinuous neural networks with time-varying delays can have at least 5(n) equilibrium points, 3(n) of which are locally stable and the others are unstable. The importance of the derived results is that it reveals that the discontinuous neural networks can have greater storage capacity than the continuous ones. Moreover, different from the existing results on multistability of neural networks with discontinuous activation functions, the 3(n) locally stable equilibrium points obtained in this paper are located in not only saturated regions, but also unsaturated regions, due to the non-monotonic structure of discontinuous activation functions. A numerical simulation study is conducted to illustrate and support the derived theoretical results.
Extracting stationary segments from non-stationary synthetic and cardiac signals
Rodríguez, María. G.; Ledezma, Carlos A.; Perpiñán, Gilberto; Wong, Sara; Altuve, Miguel
2015-01-01
Physiological signals are commonly the result of complex interactions between systems and organs, these interactions lead to signals that exhibit a non-stationary behaviour. For cardiac signals, non-stationary heart rate variability (HRV) may produce misinterpretations. A previous work proposed to divide a non-stationary signal into stationary segments by looking for changes in the signal's properties related to changes in the mean of the signal. In this paper, we extract stationary segments from non-stationary synthetic and cardiac signals. For synthetic signals with different signal-to-noise ratio levels, we detect the beginning and end of the stationary segments and the result is compared to the known values of the occurrence of these events. For cardiac signals, RR interval (cardiac cycle length) time series, obtained from electrocardiographic records during stress tests for two populations (diabetic patients with cardiovascular autonomic neuropathy and control subjects), were divided into stationary segments. Results on synthetic signals reveal that the non-stationary sequence is divided into more stationary segments than needed. Additionally, due to HRV reduction and exercise intolerance reported on diabetic cardiovascular autonomic neuropathy patients, non-stationary RR interval sequences from these subjects can be divided into longer stationary segments compared to the control group.
The cost of using stationary inventory policies when demand is non-stationary
Tunc, Huseyin; Kilic, Onur A.; Tarim, S. Armagan; Eksioglu, Burak
Non-stationary stochastic demands are very common in industrial settings with seasonal patterns, trends, business cycles, and limited-life items. In such cases, the optimal inventory control policies are also non-stationary. However, due to high computational complexity, non-stationary inventory
Space plasma physics: I - Stationary processes
Hasegawa, Akira; Sato, Tetsuya
1989-01-01
The physics of stationary processes in space plasmas is examined theoretically in an introduction intended for graduate students. The approach involves the extensive use of numerical simulations. Chapters are devoted to fundamental principles, small-amplitude waves, and the stationary solar plasma system; typical measurement data and simulation results are presented graphically.
Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions
Energy Technology Data Exchange (ETDEWEB)
Batt, J.; Rein, G. (Muenchen Univ. (Germany). Mathematisches Inst.); Morrison, P.J. (Texas Univ., Austin, TX (United States))
1993-03-01
Rigorous results on the stability of stationary solutions of the Vlasov-Poisson system are obtained in both the plasma physics and stellar dynamics contexts. It is proven that stationary solutions in the plasma physics (stellar dynamics) case are linearly stable if they are decreasing (increasing) functions of the local, i.e. particle, energy. The main tool in the analysis is the free energy of the system, a conserved quantity. In addition, an appropriate global existence result is proven for the linearized Vlasov-Poisson system and the existence of stationary solutions that satisfy the above stability condition is established.
Stationary Black Holes in a Generalized Three-Dimensional Theory of Gravity
Sá, P M
1998-01-01
We consider a generalized three-dimensional theory of gravity which is specified by two fields, the graviton and the dilaton, and one parameter. This theory contains, as particular cases, three-dimensional General Relativity and three-dimensional String Theory. Stationary black hole solutions are generated from the static ones using a simple coordinate transformation. The stationary black holes solutions thus obtained are locally equivalent to the corresponding static ones, but globally distinct. The mass and angular momentum of the stationary black hole solutions are computed using an extension of the Regge and Teitelboim formalism. The causal structure of the black holes is described.
Cappell, M S; Spray, D C; Bennett, M V
1988-06-28
Protractor muscles in the gastropod mollusc Navanax inermis exhibit typical spontaneous miniature end plate potentials with mean amplitude 1.71 +/- 1.19 (standard deviation) mV. The evoked end plate potential is quantized, with a quantum equal to the miniature end plate potential amplitude. When their rate is stationary, occurrence of miniature end plate potentials is a random, Poisson process. When non-stationary, spontaneous miniature end plate potential occurrence is a non-stationary Poisson process, a Poisson process with the mean frequency changing with time. This extends the random Poisson model for miniature end plate potentials to the frequently observed non-stationary occurrence. Reported deviations from a Poisson process can sometimes be accounted for by the non-stationary Poisson process and more complex models, such as clustered release, are not always needed.
Perceptually Relevant and Piecewise Linear Matching of Silhouettes
DEFF Research Database (Denmark)
Zabulis, Xenophon; Sporring, Jon; Orphanoudakis, Xenophon
2005-01-01
correct correspondences than conventional methods that scale the arc-length descriptions of silhouettes to align them. The selection of landmarks is investigated as to the robustness of their localization and their perceptual relevance. Matching of silhouettes is then achieved by quantifying...... the dissimilarity of a pair of silhouette boundaries, based on a novel dissimilarity metric. The matching procedure is evaluated, based on retrieval experiments, and it is concluded that the precision of the results is higher than that obtained by conventional pointwise comparison methods....
Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde
2015-11-01
The problem of coexistence and dynamical behaviors of multiple equilibrium points is addressed for a class of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. By virtue of the fixed point theorem, nonsmooth analysis theory and other analytical tools, some sufficient conditions are established to guarantee that such n-dimensional memristive Cohen-Grossberg neural networks can have 5(n) equilibrium points, among which 3(n) equilibrium points are locally exponentially stable. It is shown that greater storage capacity can be achieved by neural networks with the non-monotonic activation functions introduced herein than the ones with Mexican-hat-type activation function. In addition, unlike most existing multistability results of neural networks with monotonic activation functions, those obtained 3(n) locally stable equilibrium points are located both in saturated regions and unsaturated regions. The theoretical findings are verified by an illustrative example with computer simulations.
Simpson, D. J. W.
2017-01-01
The mode-locking regions of a dynamical system are subsets of parameter space within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a distinctive chain structure with points of zero width called shrinking points. In this paper a local analysis about an arbitrary shrinking point is performed. This is achieved by studying the symbolic itineraries of periodic solutions in nearby mode-locking regions and performing an asymptotic analysis on one-dimensional centre manifolds in order to build a comprehensive theoretical framework for the local dynamics. The main results are universal quantitative descriptions for the shape of nearby mode-locking regions, the location of nearby shrinking points, and the key properties of these shrinking points. The results are applied to the three-dimensional border-collision normal form, a model of an oscillator subject to dry friction, and a model of a DC/DC power converter.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Automated Controller Synthesis for non-Deterministic Piecewise-Affine Hybrid Systems
DEFF Research Database (Denmark)
Grunnet, Jacob Deleuran
a computational tree logic formula and refining the resulting solution to a catalogue of piecewise-affine controllers. The method has been implemented as aMatlab toolbox, PAHSCTRL , using linear matrix inequality feasibility computations for finding the discrete abstraction, UppAal Tiga for solving the discrete...... formations. This thesis uses a hybrid systems model of a satellite formation with possible actuator faults as a motivating example for developing an automated control synthesis method for non-deterministic piecewise-affine hybrid systems (PAHS). The method does not only open an avenue for further research...... in fault tolerant satellite formation control, but can be used to synthesise controllers for a wide range of systems where external events can alter the system dynamics. The synthesis method relies on abstracting the hybrid system into a discrete game, finding a winning strategy for the game meeting...
Energy Technology Data Exchange (ETDEWEB)
Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)
2005-07-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Yang, B; Zika, M R
2005-07-15
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Bak, Thomas
2012-01-01
In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H∞ performance of the fault estimation is minimized. Then......, the estimate of fault is used to compensate for the effect of the fault. Hence, using the estimate of fault, a fault tolerant controller using a piecewise linear static output feedback is designed such that it stabilizes the system and provides an upper bound on the H∞ performance of the faulty system....... Sufficient conditions for the existence of robust fault estimator and fault tolerant controller are derived in terms of linear matrix inequalities. Upper bounds on the H∞ performance can be minimized by solving convex optimization problems with linear matrix inequality constraints. The efficiency...
Resonance near Border-Collision Bifurcations in Piecewise-Smooth, Continuous Maps
Simpson, D J W
2010-01-01
Mode-locking regions (resonance tongues) formed by border-collision bifurcations of piecewise-smooth, continuous maps commonly exhibit a distinctive sausage-like geometry with pinch points called "shrinking points". In this paper we extend our unfolding of the piecewise-linear case [{\\em Nonlinearity}, 22(5):1123-1144, 2009] to show how shrinking points are destroyed by nonlinearity. We obtain a codimension-three unfolding of this shrinking point bifurcation for $N$-dimensional maps. We show that the destruction of the shrinking points generically occurs by the creation of a curve of saddle-node bifurcations that smooth one boundary of the sausage, leaving a kink in the other boundary.
Identification of Wiener systems with nonlinearity being piecewise-linear function
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Identification of the Wiener system with the nonlinear block being a piecewise-linear function is considered in the paper, generalizing the results given by H. E. Chen to the case of noisy observation. Recursive algorithms are given for estimating all unknown parameters contained in the system, and their strong consistency is proved. The estimation method is similar to that used by H. E. Chen for Hammerstein systems with the same nonlinearity. However, the assumption imposed by H. E. Chen on the availability of an upper bound for the nonsmooth points of the piecewise-linear function has been removed in this paper with the help of designing an additional algorithm for estimating the upper bound.
Directory of Open Access Journals (Sweden)
H. Vazquez-Leal
2014-01-01
Full Text Available We present a homotopy continuation method (HCM for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation.
Normal form and limit cycle bifurcation of piecewise smooth differential systems with a center
Wei, Lijun; Zhang, Xiang
2016-07-01
In this paper we prove that any Σ-center (either nondegenerate or degenerate) of a planar piecewise Cr smooth vector field Z is topologically equivalent to that of Z0: (x ˙ , y ˙) = (- 1 , 2 x) for y ≥ 0, (x ˙ , y ˙) = (1 , 2 x) for y ≤ 0, and that the homeomorphism between Z and Z0 is Cr smoothness when restricted to each side of the switching line except at the center p. We illustrate by examples that there are degenerate Σ-centers whose flows are conjugate to that of Z0, and also there exist nondegenerate Σ-centers whose flows cannot be conjugate to that of Z0. Finally applying the normal form Z0 together with the piecewise smooth equivalence, we study the number of limit cycles which can be bifurcated from the Σ-center of Z.
Jump bifurcations in some degenerate planar piecewise linear differential systems with three zones
Euzébio, Rodrigo; Pazim, Rubens; Ponce, Enrique
2016-06-01
We consider continuous piecewise-linear differential systems with three zones where the central one is degenerate, that is, the determinant of its linear part vanishes. By moving one parameter which is associated to the equilibrium position, we detect some new bifurcations exhibiting jump transitions both in the equilibrium location and in the appearance of limit cycles. In particular, we introduce the scabbard bifurcation, characterized by the birth of a limit cycle from a continuum of equilibrium points. Some of the studied bifurcations are detected, after an appropriate choice of parameters, in a piecewise linear Morris-Lecar model for the activity of a single neuron activity, which is usually considered as a reduction of the celebrated Hodgkin-Huxley equations.
Directory of Open Access Journals (Sweden)
Essam R. El-Zahar
2016-01-01
Full Text Available A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM. First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term.
On piecewise interpolation techniques for estimating solar radiation missing values in Kedah
Energy Technology Data Exchange (ETDEWEB)
Saaban, Azizan; Zainudin, Lutfi [School of Science Quantitative, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Bakar, Mohd Nazari Abu [Faculty of Applied Science, Universiti Teknologi MARA, 02600 Arau, Perlis (Malaysia)
2014-12-04
This paper discusses the use of piecewise interpolation method based on cubic Ball and Bézier curves representation to estimate the missing value of solar radiation in Kedah. An hourly solar radiation dataset is collected at Alor Setar Meteorology Station that is taken from Malaysian Meteorology Deparment. The piecewise cubic Ball and Bézier functions that interpolate the data points are defined on each hourly intervals of solar radiation measurement and is obtained by prescribing first order derivatives at the starts and ends of the intervals. We compare the performance of our proposed method with existing methods using Root Mean Squared Error (RMSE) and Coefficient of Detemination (CoD) which is based on missing values simulation datasets. The results show that our method is outperformed the other previous methods.
Set-membership state estimation for discrete time piecewise affine systems using zonotopes
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Stoustrup, Jakob
2013-01-01
This paper presents a method for guaranteed state estimation of discrete time piecewise affine systems with unknown but bounded noise and disturbance. Using zonotopic set representations, the proposed method computes the set of states that are consistent with the model, observation, and bounds...... on the noise and disturbance such that the real state of the system is guaranteed to lie in this set. Because in piecewise affine systems, the state space is partitioned into a number of polyhedral sets, at each iteration the intersection of the zonotopes containing a set-valued estimation of the states...... with each of the polyhedral partitions must be computed. We use an analytic method to compute the intersection as a zonotope and minimize the size of the intersection. A numerical example is provided to illuminate the algorithm....
A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains
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.
Wu, Tiantian; Yang, Xiao-Song
2016-05-01
Based on mathematical analysis, this paper provides a methodology to ensure the existence of heteroclinic cycles in a class of four-dimensional piecewise affine systems. In addition, examples are provided to illustrate the effectiveness of the method.
A New 3-D Piecewise-Linear System for Chaos Generation
Directory of Open Access Journals (Sweden)
Z. Elhadj
2007-06-01
Full Text Available We propose in this paper a new simple continuous-time piecewise-linear three dimensional system for chaos generation. Nonlinearity in this model is introduced by the characteristic function of the Chua's circuit given in [1]. Simulated results of some chaotic attractors are shown and justified numerically via computing the largest Lyapunov exponent. The possibility and the robustness of the circuitry realization is also given and discussed.
Su, Yan; Jun, Xie Cheng
2006-08-01
An algorithm of combining LZC and arithmetic coding algorithm for image compression is presented and both theory deduction and simulation result prove the correctness and feasibility of the algorithm. According to the characteristic of context-based adaptive binary arithmetic coding and entropy, LZC was modified to cooperate the optimized piecewise arithmetic coding, this algorithm improved the compression ratio without any additional time consumption compared to traditional method.
Cao, YY; Lam, J.
2001-01-01
This paper is concerned with simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems via piecewise constant output feedback. First, the discrete-time simultaneous LQ optimal control design problem is reduced to solving a set of coupled matrix inequalities and an iterative LMI algorithm is presented to compute the feedback gain. Then, simultaneous stabilization and simultaneous LQ optimal control design of a set of LTI continuous-time systems are considered via perio...
Numerical Stability of Differential Equations with Piecewise Constant Arguments of Mixed Type
Institute of Scientific and Technical Information of China (English)
Qi WANG
2013-01-01
This paper deals with the stability analysis of the Euler-Maclaurin method for differential equations with piecewise constant arguments of mixed type.The expression of analytical solution is derived and the stability regions of the analytical solution are given.The necessary and sufficient conditions under which the numerical solution is asymptotically stable are discussed.The conditions under which the analytical stability region is contained in the numerical stability region are obtained and some numerical examples are given.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2012-01-01
Full Text Available This paper centres on the application of the new piecewise successive linearization method (PSLM in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including those that are chaotic in nature.
Piecewise-polynomial and cascade models of predistorter for linearization of power amplifier
2012-01-01
To combat non-linear signal distortions in a power amplifier we suggest using predistorter with cascade structure in which first and second nodes have piecewise-polynomial and polynomial models. On example of linearizing the Winner–Hammerstein amplifier model we demonstrate that cascade structure of predistorter improves precision of amplifier’s linearization. To simplify predistorter’s synthesis the degree of polynomial model used in first node should be moderate, while precision should be i...
Passive Fault Tolerant Control of Piecewise Affine Systems Based on H Infinity Synthesis
DEFF Research Database (Denmark)
Gholami, Mehdi; Cocquempot, vincent; Schiøler, Henrik
2011-01-01
In this paper we design a passive fault tolerant controller against actuator faults for discretetime piecewise affine (PWA) systems. By using dissipativity theory and H analysis, fault tolerant state feedback controller design is expressed as a set of Linear Matrix Inequalities (LMIs). In the cur......). In the current paper, the PWA system switches not only due to the state but also due to the control input. The method is applied on a large scale livestock ventilation model....
Stability Analysis of Periodic Orbits in a Class of Duffing-Like Piecewise Linear Vibrators
El Aroudi, A.
2014-09-01
In this paper, we study the dynamical behavior of a Duffing-like piecewise linear (PWL) springmass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. From this PWL model, numerical simulations are carried out by computing frequency response and bifurcation diagram under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Fillipov method.
The Diffusion Coefficient For Piecewise Expanding Maps Of The Interval With Metastable States
Dolgopyat, Dmitry
2010-01-01
Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs). After this system is perturbed to make the subintervals lose their invariance in such a way that there is a unique ACIM, we show how to approximate the diffusion coefficient for an observable of bounded variation by the diffusion coefficient of a related continuous time Markov chain.
Institute of Scientific and Technical Information of China (English)
2008-01-01
In general normed spaces,we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior.We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function.Moreover,we provide necessary and suffcient conditions about the existence of weak(sharp) Pareto solutions.
Oscillation region of a piecewise-smooth model of the vocal folds
Lucero, Jorge C.; Gajo, Cristiane A.
2006-01-01
The two-mass model of the vocal folds is a popular representation of their dynamical structure used in phonation studies. This paper presents an analysis of a recent piecewise-smooth version of the model. This version has two equilibrium positions, and in one of them (the initial prephonatory position) the system is nondifferentiable. Standard methods of stability analysis do not apply for that position, because they require smoothness of the system. A geometrical approac...
Quantization of a class of piecewise affine transformations on the torus
De Bièvre, S; De Bievre, S; Giachetti, R
1995-01-01
We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of ``chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the automorphisms, translations and skew translations. We then treat some discontinuous transformations such as the Baker map and the sawtooth-like maps. Our approach extends some ideas from geometric quantization and it is both conceptually and calculationally simple.
Dynamical ensembles in stationary states
Energy Technology Data Exchange (ETDEWEB)
Gallavotti, G. [Universita di Roma la Sapienza, Rome (Italy); Cohen, E.G.D. [Rockefeller Univ., New York, NY (United States)
1995-09-01
We propose, as a generalization of an idea of Ruelle`s to describe turbulent fluid flow, a chaotic hypothesis for reversible dissipative many-particle systems in nonequilibrium stationary states in general. This implies an extension of the zeroth law of thermodynamics to nonequilibrium states and it leads to the identification of a unique distribution {mu} describing the asymptotic properties of the time evolution of the system for initial data randomly chosen with respect to a uniform distribution on phase space. For conservative systems in thermal equilibrium the chaotic hypothesis implies the ergodic hypothesis. We outline a procedure to obtain the distribution {mu}: it leads to a new unifying point of view for the phase space behavior of dissipative and conservative systems. The chaotic hypothesis is confirmed in a nontrivial, parameter-free, way by a recent computer experiment on the entropy production fluctuations in a shearing fluid far from equilibrium. Similar applications to other models are proposed, in particular to a model for the Kolmogorov-Obuchov theory for turbulent flow.
Model of non-stationary, inhomogeneous turbulence
Bragg, Andrew D.; Kurien, Susan; Clark, Timothy T.
2017-02-01
We compare results from a spectral model for non-stationary, inhomogeneous turbulence (Besnard et al. in Theor Comp Fluid Dyn 8:1-35, 1996) with direct numerical simulation (DNS) data of a shear-free mixing layer (SFML) (Tordella et al. in Phys Rev E 77:016309, 2008). The SFML is used as a test case in which the efficacy of the model closure for the physical-space transport of the fluid velocity field can be tested in a flow with inhomogeneity, without the additional complexity of mean-flow coupling. The model is able to capture certain features of the SFML quite well for intermediate to long times, including the evolution of the mixing-layer width and turbulent kinetic energy. At short-times, and for more sensitive statistics such as the generation of the velocity field anisotropy, the model is less accurate. We propose two possible causes for the discrepancies. The first is the local approximation to the pressure-transport and the second is the a priori spherical averaging used to reduce the dimensionality of the solution space of the model, from wavevector to wavenumber space. DNS data are then used to gauge the relative importance of both possible deficiencies in the model.
Zimmermann, Karl-Heinz; Achtziger, Wolfgang
2001-09-01
The size of a systolic array synthesized from a uniform recurrence equation, whose computations are mapped by a linear function to the processors, matches the problem size. In practice, however, there exist several limiting factors on the array size. There are two dual schemes available to derive arrays of smaller size from large-size systolic arrays based on the partitioning of the large-size arrays into subarrays. In LSGP, the subarrays are clustered one-to-one into the processors of a small-size array, while in LPGS, the subarrays are serially assigned to a reduced-size array. In this paper, we propose a common methodology for both LSGP and LPGS based on polyhedral partitionings of large-size k-dimensional systolic arrays which are synthesized from n-dimensional uniform recurrences by linear mappings for allocation and timing. In particular, we address the optimization problem of finding optimal piecewise linear timing functions for small-size arrays. These are mappings composed of linear timing functions for the computations of the subarrays. We study a continuous approximation of this problem by passing from piecewise linear to piecewise quasi-linear timing functions. The resultant problem formulation is then a quadratic programming problem which can be solved by standard algorithms for nonlinear optimization problems.
Dolgin, Madlena; Einziger, Pinchas D
2010-05-01
Image reconstruction in electrical impedance tomography is, generally, an ill-posed nonlinear inverse problem. Regularization methods are widely used to ensure a stable solution. Herein, we present a case study, which uses a novel electrical impedance tomography method for reconstruction of layered biological tissues with piecewise continuous plane-stratified profiles. The algorithm implements the recently proposed reconstruction scheme for piecewise constant conductivity profiles, utilizing Legendre expansion in conjunction with improved Prony method. It is shown that the proposed algorithm is capable of successfully reconstructing piecewise continuous conductivity profiles with moderate slop. This reconstruction procedure, which calculates both the locations and the conductivities, repetitively provides inhomogeneous depth discretization, i.e., the depths grid is not equispaced. Incorporation of this specific inhomogeneous grid in the widely used mean least square reconstruction procedure results in a stable and accurate reconstruction, whereas, the commonly selected equispaced depth grid leads to unstable reconstruction. This observation establishes the main result of our investigation, highlighting the impact of physical phenomenon (the image series expansion) on electrical impedance tomography, leading to a physically motivated stabilization of the inverse problem, i.e., an inhomogeneous depth discretization renders an inherent regularization of the mean least square algorithm. The effectiveness and the significance of inhomogeneous discretization in electrical impedance tomography reconstruction procedure is further demonstrated and verified via numerical simulations.
A WENO-type slope-limiter for a family of piecewise polynomial methods
Engwirda, Darren
2016-01-01
A new, high-order slope-limiting procedure for the Piecewise Parabolic Method (PPM) and the Piecewise Quartic Method (PQM) is described. Following a Weighted Essentially Non-Oscillatory (WENO)-type paradigm, the proposed slope-limiter seeks to reconstruct smooth, non-oscillatory piecewise polynomial profiles as a non-linear combination of the natural and monotone-limited PPM and PQM interpolants. Compared to existing monotone slope-limiting techniques, this new strategy is designed to improve accuracy at smooth extrema, while controlling spurious oscillations in the neighbourhood of sharp features. Using the new slope-limited PPM and PQM interpolants, a high-order accurate Arbitrary-Lagrangian-Eulerian framework for advection-dominated flows is constructed, and its effectiveness is examined using a series of one- and two-dimensional benchmark cases. It is shown that the new WENO-type slope-limiting techniques offer a significant improvement in accuracy compared to existing strategies, allowing the PPM- and PQ...
Davies, David L.; Smith, Peter H.; Liutermoza, John F.
1980-06-01
Profile analysis and piecewise correlation techniques for measuring internal machine part clearances by digital processing of industrial radiographs are described in this paper. These methods were developed at the Image and Pattern Analysis Laboratory of Pratt & Whitney Aircraft Group. Profile analysis requires mathematical modeling of the expected optical density of a radiograph as a function of machine part position. Part separations are estimated on the basis of individual image scan lines. A final part separation estimate is produced by fitting a polynominal to the individual estimates and correcting for imaging and processing degradations which are simulated using a mathematical model. Piecewise correlation involves an application of image registration where radiographs are correlated in a piecewise fashion to allow inference of the relative motion of machine parts in a time varying series of images. Each image is divided into segments which are dominated by a small number of features. Segments from one image are cross-correlated with subsequent images to identify machine part motion in image space. Correlation peak magnitude is used in assessing the confidence that a particular motion has occurred between images. The rigid feature motion of machine parts requires image registration by discon-tinuous parts. This method differs from the continuous deformations one encounters in perspective projective transformations characteristic of remote sensing applications.
Weak-noise limit of a piecewise-smooth stochastic differential equation.
Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram
2013-11-01
We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.
A HYBRID TECHNIQUE FOR PAPR REDUCTION OF OFDM USING DHT PRECODING WITH PIECEWISE LINEAR COMPANDING
Directory of Open Access Journals (Sweden)
Thammana Ajay
2016-06-01
Full Text Available Orthogonal Frequency Division Multiplexing (OFDM is a fascinating approach for wireless communication applications which require huge amount of data rates. However, OFDM signal suffers from its large Peak-to-Average Power Ratio (PAPR, which results in significant distortion while passing through a nonlinear device, such as a transmitter high power amplifier (HPA. Due to this high PAPR, the complexity of HPA as well as DAC also increases. For the reduction of PAPR in OFDM many techniques are available. Among them companding is an attractive low complexity technique for the OFDM signal’s PAPR reduction. Recently, a piecewise linear companding technique is recommended aiming at minimizing companding distortion. In this paper, a collective piecewise linear companding approach with Discrete Hartley Transform (DHT method is expected to reduce peak-to-average of OFDM to a great extent. Simulation results shows that this new proposed method obtains significant PAPR reduction while maintaining improved performance in the Bit Error Rate (BER and Power Spectral Density (PSD compared to piecewise linear companding method.
New contractivity condition in a population model with piecewise constant arguments
Muroya, Yoshiaki
2008-10-01
In this paper, we improve contractivity conditions of solutions for the positive equilibrium of the following differential equation with piecewise constant arguments: where r(t) is a nonnegative continuous function on [0,+[infinity]), r(t)[not identical with]0, , bi[greater-or-equal, slanted]0, i=0,1,2,...,m, and . In particular, for the case a=0 and m[greater-or-equal, slanted]1, we really improve the known three type conditions of the contractivity for solutions of this model (see for example, [Y. Muroya, A sufficient condition on global stability in a logistic equation with piecewise constant arguments, Hokkaido Math. J. 32 (2003) 75-83]). For the other case a[not equal to]0 and m[greater-or-equal, slanted]1, under the condition , the obtained result partially improves the known results on the contractivity of solutions for the positive equilibrium of this model given by the author [Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002) 602-635] and others.
Directory of Open Access Journals (Sweden)
Miguel Angel Luque-Fernandez
2016-10-01
Full Text Available Abstract Background In population-based cancer research, piecewise exponential regression models are used to derive adjusted estimates of excess mortality due to cancer using the Poisson generalized linear modelling framework. However, the assumption that the conditional mean and variance of the rate parameter given the set of covariates x i are equal is strong and may fail to account for overdispersion given the variability of the rate parameter (the variance exceeds the mean. Using an empirical example, we aimed to describe simple methods to test and correct for overdispersion. Methods We used a regression-based score test for overdispersion under the relative survival framework and proposed different approaches to correct for overdispersion including a quasi-likelihood, robust standard errors estimation, negative binomial regression and flexible piecewise modelling. Results All piecewise exponential regression models showed the presence of significant inherent overdispersion (p-value <0.001. However, the flexible piecewise exponential model showed the smallest overdispersion parameter (3.2 versus 21.3 for non-flexible piecewise exponential models. Conclusion We showed that there were no major differences between methods. However, using a flexible piecewise regression modelling, with either a quasi-likelihood or robust standard errors, was the best approach as it deals with both, overdispersion due to model misspecification and true or inherent overdispersion.
Dynamical response to a stationary tidal field
Landry, Philippe
2015-01-01
We demonstrate that a slowly rotating compact body subjected to a stationary tidal field undergoes a dynamical response, in which the fluid variables and the interior metric vary on the time scale of the rotation period. This dynamical response requires the tidal field to have a gravitomagnetic component generated by external mass currents; the response to a gravitoelectric tidal field is stationary. We confirm that in a calculation carried out to first order in the body's rotation, the exterior geometry bears no trace of this internal dynamics; it remains stationary in spite of the time-dependent interior.
Métris, Aline; George, Susie M; Ropers, Delphine
2017-01-02
Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available
On the existence of stationary Ricci solitons
Figueras, Pau
2016-01-01
Previously the DeTurck 'trick' has been used to render the stationary Einstein's equation a well posed elliptic system that may be solved numerically by geometric flow or directly. Whilst in the static case for pure gravity with zero or negative cosmological constant there is a simple proof that solving the modified "harmonic" Einstein's equation leads to a solution of the original Einstein system - i.e. not a Ricci soliton - in the stationary case this argument no longer works. Here we provide a new argument that extends the static result to the case of stationary spacetimes that possess a "$t$-$\\phi$" reflection symmetry. Defining a "soliton charge" from the asymptotic behaviour of the solution, we show that this quantity is always non-positive. Provided asymptotic conditions are chosen such that this charge vanishes, then stationary solitons cannot exist.
Self-Organized Stationary States of Tokamaks.
Jardin, S C; Ferraro, N; Krebs, I
2015-11-20
We demonstrate that in a 3D resistive magnetohydrodynamic simulation, for some parameters it is possible to form a stationary state in a tokamak where a saturated interchange mode in the center of the discharge drives a near helical flow pattern that acts to nonlinearly sustain the configuration by adjusting the central loop voltage through a dynamo action. This could explain the physical mechanism for maintaining stationary nonsawtoothing "hybrid" discharges, often referred to as "flux pumping."
Stable Stationary Harmonic Maps to Spheres
Institute of Scientific and Technical Information of China (English)
Fang Hua LIN; Chang You WANG
2006-01-01
For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere Sk. We show that the singular set of stable-stationary harmonic maps from B5 to S3 is the union of finitely many isolated singular points and finitely many Holder continuous curves. We also discuss the minimization problem among continuous maps from Bn to S2.
Stationary inﬁnitely divisible processes
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.
Several recent strands of work has led to the consideration of various types of continuous time stationary and infinitely divisible processes. A review of these types, with some new results, is presented.......Several recent strands of work has led to the consideration of various types of continuous time stationary and infinitely divisible processes. A review of these types, with some new results, is presented....
Stationary phase deposition based on onium salts
Wheeler, David R.; Lewis, Patrick R.; Dirk, Shawn M.; Trudell, Daniel E.
2008-01-01
Onium salt chemistry can be used to deposit very uniform thickness stationary phases on the wall of a gas chromatography column. In particular, the stationary phase can be bonded to non-silicon based columns, especially microfabricated metal columns. Non-silicon microfabricated columns may be manufactured and processed at a fraction of the cost of silicon-based columns. In addition, the method can be used to phase-coat conventional capillary columns or silicon-based microfabricated columns.
The existence of Hamiltonian stationary Lagrangian tori in Kahler manifolds of any dimension
Lee, Yng-Ing
2010-01-01
Hamiltonian stationary Lagrangians are Lagrangian submanifolds that are critical points of the volume functional under Hamiltonian deformations. They can be considered as a generalization of special Lagrangians or Lagrangian and minimal submanifolds. Joyce, Schoen and the author show that given any compact rigid Hamiltonian stationary Lagrangian in $\\C^n$, one can always find a family of Hamiltonian stationary Lagrangians of the same type in any compact symplectic manifolds with a compatible metric. The advantage of this result is that it holds in very general classes. But the disadvantage is that we do not know where these examples locate and examples in this family might be far apart. In this paper, we derive a local condition on Kahler manifolds which ensures the existence of one family of Hamiltonian stationary Lagrangian tori near a point with given frame satisfying the criterion. Butscher and Corvino ever proposed a condition in n=2. But our condition appears to be different from theirs. The condition d...
Shift ergodicity for stationary Markov processes
Institute of Scientific and Technical Information of China (English)
东金文
2001-01-01
In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our results provide partial answers to certain interesting problems in spin systems.
Stationary states in quantum walk search
PrÅ«sis, Krišjānis; Vihrovs, Jevgěnijs; Wong, Thomas G.
2016-09-01
When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, additional marked vertices can make the search harder by causing the system to approximately begin in a stationary state, so the system fails to evolve. In this paper, we completely characterize the stationary states, or 1-eigenvectors, of the quantum walk search operator for general graphs and configurations of marked vertices by decomposing their amplitudes into uniform and flip states. This infinitely expands the number of known stationary states and gives an optimization procedure to find the stationary state closest to the initial uniform state of the walk. We further prove theorems on the existence of stationary states, with them conditionally existing if the marked vertices form a bipartite connected component and always existing if nonbipartite. These results utilize the standard oracle in Grover's algorithm, but we show that a different type of oracle prevents stationary states from interfering with the search algorithm.
Stationary Liquid Fuel Fast Reactor
Energy Technology Data Exchange (ETDEWEB)
Yang, Won Sik [Purdue Univ., West Lafayette, IN (United States); Grandy, Andrew [Argonne National Lab. (ANL), Argonne, IL (United States); Boroski, Andrew [Argonne National Lab. (ANL), Argonne, IL (United States); Krajtl, Lubomir [Argonne National Lab. (ANL), Argonne, IL (United States); Johnson, Terry [Argonne National Lab. (ANL), Argonne, IL (United States)
2015-09-30
For effective burning of hazardous transuranic (TRU) elements of used nuclear fuel, a transformational advanced reactor concept named SLFFR (Stationary Liquid Fuel Fast Reactor) was proposed based on stationary molten metallic fuel. The fuel enters the reactor vessel in a solid form, and then it is heated to molten temperature in a small melting heater. The fuel is contained within a closed, thick container with penetrating coolant channels, and thus it is not mixed with coolant nor flow through the primary heat transfer circuit. The makeup fuel is semi- continuously added to the system, and thus a very small excess reactivity is required. Gaseous fission products are also removed continuously, and a fraction of the fuel is periodically drawn off from the fuel container to a processing facility where non-gaseous mixed fission products and other impurities are removed and then the cleaned fuel is recycled into the fuel container. A reference core design and a preliminary plant system design of a 1000 MWt TRU- burning SLFFR concept were developed using TRU-Ce-Co fuel, Ta-10W fuel container, and sodium coolant. Conservative design approaches were adopted to stay within the current material performance database. Detailed neutronics and thermal-fluidic analyses were performed to develop a reference core design. Region-dependent 33-group cross sections were generated based on the ENDF/B-VII.0 data using the MC2-3 code. Core and fuel cycle analyses were performed in theta-r-z geometries using the DIF3D and REBUS-3 codes. Reactivity coefficients and kinetics parameters were calculated using the VARI3D perturbation theory code. Thermo-fluidic analyses were performed using the ANSYS FLUENT computational fluid dynamics (CFD) code. Figure 0.1 shows a schematic radial layout of the reference 1000 MWt SLFFR core, and Table 0.1 summarizes the main design parameters of SLFFR-1000 loop plant. The fuel container is a 2.5 cm thick cylinder with an inner radius of 87.5 cm. The fuel
Nonequilibrium stationary states and phase transitions in directed Ising models
Godrèche, Claude; Bray, Alan J.
2009-12-01
We study the nonequilibrium properties of directed Ising models with non-conserved dynamics, in which each spin is influenced by only a subset of its nearest neighbours. We treat the following models: (i) the one-dimensional chain; (ii) the two-dimensional square lattice; (iii) the two-dimensional triangular lattice and (iv) the three-dimensional cubic lattice. We raise and answer the question: (a) under what conditions is the stationary state described by the equilibrium Boltzmann-Gibbs distribution? We show that, for models (i), (ii) and (iii), in which each spin 'sees' only half of its neighbours, there is a unique set of transition rates, namely with exponential dependence in the local field, for which this is the case. For model (iv), we find that any rates satisfying the constraints required for the stationary measure to be Gibbsian should satisfy detailed balance, ruling out the possibility of directed dynamics. We finally show that directed models on lattices of coordination number z>=8 with exponential rates cannot accommodate a Gibbsian stationary state. We conjecture that this property extends to any form of the rates. We are thus led to the conclusion that directed models with Gibbsian stationary states only exist in dimensions one and two. We then raise the question: (b) do directed Ising models, augmented by Glauber dynamics, exhibit a phase transition to a ferromagnetic state? For the models considered above, the answers are open problems, with the exception of the simple cases (i) and (ii). For Cayley trees, where each spin sees only the spins further from the root, we show that there is a phase transition provided the branching ratio, q, satisfies q>=3.
CLASSICAL SOLUTION OF QUASI-STATIONARY STEFAN PROBLEM
Institute of Scientific and Technical Information of China (English)
YIFAHUAI
1996-01-01
This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv+δu/δv=0 on the free boundary. under the natural conditions the existence of classical solution locally in time is proved by making use of the property of Frechet derivative operator and fixed point theorem. For the sake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can be dealt with in a similar way with more complicated calculation.
Mesoscopic thermodynamics of stationary non-equilibrium states
Energy Technology Data Exchange (ETDEWEB)
SantamarIa-Holek, I [Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Circuito exterior de Ciudad Universitaria, 04510 DF (Mexico); RubI, J M [Facultad de FIsica, Universitat de Barcelona, Av. Diagonal 647, 08028, Barcelona (Spain); Perez-Madrid, A [Facultad de FIsica, Universitat de Barcelona, Av. Diagonal 647, 08028, Barcelona (Spain)
2005-01-01
Thermodynamics for systems at non-equilibrium stationary states have been formulated, based on the assumption of the existence of a local equilibrium in phase space which enables one to interpret the probability density and its conjugated non-equilibrium chemical potential as mesoscopic thermodynamic variables. The probability current is obtained from the entropy production related to the probability diffusion process and leads to the formulation of the Fokker-Planck equation. For the case of a gas of Brownian particles under steady flow in the dilute and concentrated regimes, we derive non-equilibrium equations of state.
Goreac, D
2010-01-01
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general On/Off systems, Cook's model for haploinssuficiency, and a stochastic model for bacteriophage lambda.
A three-layer preon star model from exact piecewise-continuous solutions of Einstein's equations
Pazameta, Zoran
2012-01-01
A metric of Birkhoffian form is employed to model a hybrid astrophysical compact object consisting of a preon gas core, a mantle of electrically charged hot quark-gluon plasma, and an outer envelope of charged hadronic matter which is matched to an exterior Reissner-Nordstr\\"om vacuum. The piecewise-continuous metric and the pressure and density functions consist of polynomials that are everywhere well-behaved. Boundary conditions at each interface yield estimates for physical parameters applicable to each layer, and to the star as a whole.
Analytic, piecewise solution to the Lane-Emden equation for stars with complex density profiles
Miller, Jeff; Bogdanovic, Tamara
2017-01-01
The polytropic models of stars are used for a variety of applications in computational astrophysics. These are typically obtained by numerically solving the Lane-Emden equation for a star in hydrostatic equilibrium under assumption that the pressure and density within the star obey the polytropic equation of state. We present an efficient analytic, piecewise differentiable solution to the Lane-Emden equation which allows “stitching” of different polytropes to represent complex pressure and density profiles. This approach can be used to model stars with distinct properties in their cores and envelopes, such as the evolved red giant and horizontal branch stars.
On the Convergence of Piecewise Linear Strategic Interaction Dynamics on Networks
Gharesifard, Bahman
2015-09-11
We prove that the piecewise linear best-response dynamical systems of strategic interactions are asymptotically convergent to their set of equilibria on any weighted undirected graph. We study various features of these dynamical systems, including the uniqueness and abundance properties of the set of equilibria and the emergence of unstable equilibria. We also introduce the novel notions of social equivalence and social dominance on directed graphs, and demonstrate some of their interesting implications, including their correspondence to consensus and chromatic number of partite graphs. Examples illustrate our results.
Topological invariants in forced piecewise-linear FitzHugh-Nagumo-like systems
Energy Technology Data Exchange (ETDEWEB)
Duarte, Jorge E-mail: jduarte@deq.isel.pt; Ramos, J. Sousa. E-mail: sramos@math.ist.utl.pt
2005-03-01
Mathematical models for periodically-forced excitable systems arise in many biological and physiological contexts. Chaotic dynamics of a forced piecewise-linear Fitzhugh-Nagumo-like system under large-amplitude forcing was identified by Othmer and Xie in their work [J. Math. Biol. 39 (1999) 139]. Using kneading theory we study the topological entropy of some chaotic return maps associated with a singular system. Finally we introduce a new topological invariant to distinguish isentropic dynamics and we exhibit numerical results about maps with the same topological entropy, that suggest the existence of a relation between the parameters A and {theta}, when T is fixed.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In the paper,we investigate the problem of finding a piecewise output feedback control law for an uncertain affine system such that the resulting closed-loop output satisfies a desired linear temporal logic (LTL) specification.A two-level hierarchical approach is proposed to solve the problem in a triangularized output space.In the lower level,we explore whether there exists a robust output feedback control law to make the output starting in a simplex either remains in it or leaves via a specific facet.In t...
Regularity of absolutely continuous invariant measures for piecewise expanding unimodal maps
Contreras, Fabián; Dolgopyat, Dmitry
2016-09-01
Let f:[0,1]\\to [0,1] be a piecewise expanding unimodal map of class C k+1, with k≥slant 1 , and μ =ρ \\text{d}x the (unique) SRB measure associated to it. We study the regularity of ρ. In particular, points N where ρ is not differentiable has zero Hausdorff dimension, but is uncountable if the critical orbit of f is dense. This improves on a work of Szewc (1984). We also obtain results about higher orders of differentiability of ρ in the sense of Whitney.
Piecewise oblique boundary treatment for the elastic-plastic wave equation on a cartesian grid
Giese, Guido
2009-11-01
Numerical schemes for hyperbolic conservation laws in 2-D on a Cartesian grid usually have the advantage of being easy to implement and showing good computational performances, without allowing the simulation of “real-world” problems on arbitrarily shaped domains. In this paper a numerical treatment of boundary conditions for the elastic-plastic wave equation is developed, which allows the simulation of problems on an arbitrarily shaped physical domain surrounded by a piece-wise smooth boundary curve, but using a PDE solver on a rectangular Cartesian grid with the afore-mentioned advantages.
Explicit Piecewise Smooth Solutions of Landau-Lifshitz Equation with Discontinuous External Field
Institute of Scientific and Technical Information of China (English)
Gan-shan Yang; Yun-zhang Zhang; Li-min Liu
2009-01-01
In this paper,we shall construct some explicit piecewise smooth(global continuous)solutions as well as blow up solutions to the multidimensional Landau-Lifshitz equation,subject to the external magnetic fields being both discontinuous and unbounded.When the external magnetic field is continuous,some explicit exact smooth solutions and blow up solution are also constructed.We also establish some necessary and sufficient conditions to ensure that the solution of multidimensional Landau-Lifshitz equation with external magnetic field converges to the solution of equation without external magnetic field when the external magnetic field tends to zero.
Traveling waves in a nonlocal, piecewise linear reaction-diffusion population model
Autry, E. A.; Bayliss, A.; Volpert, V. A.
2017-08-01
We consider an analytically tractable switching model that is a simplification of a nonlocal, nonlinear reaction-diffusion model of population growth where we take the source term to be piecewise linear. The form of this source term allows us to consider both the monostable and bistable versions of the problem. By transforming to a traveling frame and choosing specific kernel functions, we are able to reduce the problem to a system of algebraic equations. We construct solutions and examine the propagation speed and monotonicity of the resulting waves.
Phase patterns in finite oscillator networks with insights from the piecewise linear approximation
Goldstein, Daniel
2015-03-01
Recent experiments on spatially extend arrays of droplets containing Belousov-Zhabotinsky reactants have shown a rich variety of spatio-temporal patterns. Motivated by this experimental set up, we study a simple model of chemical oscillators in the highly nonlinear excitable regime in order to gain insight into the mechanism giving rise to the observed multistable attractors. When coupled, these two attractors have different preferred phase synchronizations, leading to complex behavior. We study rings of coupled oscillators and observe a rich array of oscillating patterns. We combine Turing analysis and a piecewise linear approximation to better understand the observed patterns.
Energy Technology Data Exchange (ETDEWEB)
Vereshchagin, D.A. [Theoretical Physics Department, Kaliningrad State University, A. Nevsky st. 14, Kaliningrad (Russian Federation); Leble, S.B. [Theoretical Physics Department, Kaliningrad State University, A. Nevsky st. 14, Kaliningrad (Russian Federation) and Theoretical Physics and Mathematical Methods Department, Gdansk University of Technology, ul. Narutowicza 11/12, Gdansk (Poland)]. E-mail: leble@mifgate.pg.gda.pl; Solovchuk, M.A. [Theoretical Physics Department, Kaliningrad State University, A. Nevsky st. 14, Kaliningrad (Russian Federation)]. E-mail: solovchuk@yandex.ru
2006-01-02
The system of hydrodynamic-type equations for a stratified gas in gravity field is derived from BGK equation by method of piecewise continuous distribution function. The obtained system of the equations generalizes the Navier-Stokes one at arbitrary Knudsen numbers. The problem of a wave disturbance propagation in a rarefied gas is explored. The verification of the model is made for a limiting case of a homogeneous medium. The phase velocity and attenuation coefficient values are in an agreement with former fluid mechanics theories; the attenuation behavior reproduces experiment and kinetics-based results at more wide range of the Knudsen numbers.
An I(2) Cointegration Model with Piecewise Linear Trends: Likelihood Analysis and Application
DEFF Research Database (Denmark)
Kurita, Takamitsu; Nielsen, Heino Bohn; Rahbæk, Anders
for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where...... asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980....
A low-power piecewise linear analog to digital converter for use in particle tracking
Energy Technology Data Exchange (ETDEWEB)
Valencic, V.; Deval, P. [MEAD Microelectronics S.A., St. Sulpice (Switzerland)]|[EPFL, Lausanne (Switzerland). Electronics Labs.; Anghinolfi, F. [CERN, Geneva (Switzerland); Bonino, R.; Marra, D. La; Kambara, Hisanori [Univ. of Geneva (Switzerland)
1995-08-01
This paper describes a low-power piecewise linear A/D converter. A 5MHz {at} 5V with 25mW power consumption prototype has been implemented in a 1.5{micro}m CMOS process. The die area excluding pads is 5mm{sup 2}. 11-bit absolute accuracy is obtained with a new DC offset plus charge injection compensation technique used in the comparators scheme. This ADC with large dynamic range and high resolution is developed for the readout of a tracker and/or preshower in the future LHC experiments.
2016-01-01
response variable taking on ordinal values 1 to C and a 1x vector of explanatory variables , , the proportional odds model is given by...I N S T I T U T E F O R D E F E N S E A N A L Y S E S Regularization for Continuously Observed Ordinal Response Variables with Piecewise...response variable , quality of video provided by the Shadow to friendly ground units, was measured on an ordinal scale continuously over time. Functional
An Approach to Formulation of FNLP with Complex Piecewise Linear Membership Functions
Institute of Scientific and Technical Information of China (English)
闻博; 李宏光
2014-01-01
Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming (FNLP) problem with piecewise linear membership functions (PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.
Agilan, V.; Umamahesh, N. V.
2017-03-01
Present infrastructure design is primarily based on rainfall Intensity-Duration-Frequency (IDF) curves with so-called stationary assumption. However, in recent years, the extreme precipitation events are increasing due to global climate change and creating non-stationarity in the series. Based on recent theoretical developments in the Extreme Value Theory (EVT), recent studies proposed a methodology for developing non-stationary rainfall IDF curve by incorporating trend in the parameters of the Generalized Extreme Value (GEV) distribution using Time covariate. But, the covariate Time may not be the best covariate and it is important to analyze all possible covariates and find the best covariate to model non-stationarity. In this study, five physical processes, namely, urbanization, local temperature changes, global warming, El Niño-Southern Oscillation (ENSO) cycle and Indian Ocean Dipole (IOD) are used as covariates. Based on these five covariates and their possible combinations, sixty-two non-stationary GEV models are constructed. In addition, two non-stationary GEV models based on Time covariate and one stationary GEV model are also constructed. The best model for each duration rainfall series is chosen based on the corrected Akaike Information Criterion (AICc). From the findings of this study, it is observed that the local processes (i.e., Urbanization, local temperature changes) are the best covariate for short duration rainfall and global processes (i.e., Global warming, ENSO cycle and IOD) are the best covariate for the long duration rainfall of the Hyderabad city, India. Furthermore, the covariate Time is never qualified as the best covariate. In addition, the identified best covariates are further used to develop non-stationary rainfall IDF curves of the Hyderabad city. The proposed methodology can be applied to other situations to develop the non-stationary IDF curves based on the best covariate.
Non-stationary (13)C-metabolic flux ratio analysis.
Hörl, Manuel; Schnidder, Julian; Sauer, Uwe; Zamboni, Nicola
2013-12-01
(13)C-metabolic flux analysis ((13)C-MFA) has become a key method for metabolic engineering and systems biology. In the most common methodology, fluxes are calculated by global isotopomer balancing and iterative fitting to stationary (13)C-labeling data. This approach requires a closed carbon balance, long-lasting metabolic steady state, and the detection of (13)C-patterns in a large number of metabolites. These restrictions mostly reduced the application of (13)C-MFA to the central carbon metabolism of well-studied model organisms grown in minimal media with a single carbon source. Here we introduce non-stationary (13)C-metabolic flux ratio analysis as a novel method for (13)C-MFA to allow estimating local, relative fluxes from ultra-short (13)C-labeling experiments and without the need for global isotopomer balancing. The approach relies on the acquisition of non-stationary (13)C-labeling data exclusively for metabolites in the proximity of a node of converging fluxes and a local parameter estimation with a system of ordinary differential equations. We developed a generalized workflow that takes into account reaction types and the availability of mass spectrometric data on molecular ions or fragments for data processing, modeling, parameter and error estimation. We demonstrated the approach by analyzing three key nodes of converging fluxes in central metabolism of Bacillus subtilis. We obtained flux estimates that are in agreement with published results obtained from steady state experiments, but reduced the duration of the necessary (13)C-labeling experiment to less than a minute. These results show that our strategy enables to formally estimate relative pathway fluxes on extremely short time scale, neglecting cellular carbon balancing. Hence this approach paves the road to targeted (13)C-MFA in dynamic systems with multiple carbon sources and towards rich media.
STATIONARY CONNECTED CURVES IN HILBERT SPACES
Directory of Open Access Journals (Sweden)
Raed Hatamleh
2014-01-01
Full Text Available In this article the structure of non-stationary curves which are stationary connected in Hilbert space is studied using triangular models of non-self-adjoint operator. The concept of evolutionary representability plays here an important role. It is proved that if one of two curves in Hilbert space is evolutionary representable and the curves are stationary connected, then another curve is evolutionary representable too. These curves are studied firstly. The structure of a cross-correlation function in the case when operator, defining the evolutionary representation, has one-dimensional non-Hermitian subspace (the spectrum is discreet and situated in the upper complex half-plane or has infinite multiplicity at zero (Volterra operator is studied.
Piecewise Function Hysteretic Model for Cold-Formed Steel Shear Walls with Reinforced End Studs
Directory of Open Access Journals (Sweden)
Jihong Ye
2017-01-01
Full Text Available Cold-formed steel (CFS shear walls with concrete-filled rectangular steel tube (CFRST columns as end studs can upgrade the performance of mid-rise CFS structures, such as the vertical bearing capacity, anti-overturning ability, shear strength, and fire resistance properties, thereby enhancing the safety of structures. A theoretical hysteretic model is established according to a previous experimental study. This model is described in a simple mathematical form and takes nonlinearity, pinching, strength, and stiffness deterioration into consideration. It was established in two steps: (1 a discrete coordinate method was proposed to determine the load-displacement skeleton curve of the wall, by which governing deformations and their corresponding loads of the hysteretic loops under different loading cases can be obtained; afterwards; (2 a piecewise function was adopted to capture the hysteretic loop relative to each governing deformation, the hysteretic model of the wall was further established, and additional criteria for the dominant parameters of the model were stated. Finally, the hysteretic model was validated by experimental results from other studies. The results show that elastic lateral stiffness Ke and shear capacity Fp are key factors determining the load-displacement skeleton curve of the wall; hysteretic characteristics of the wall with reinforced end studs can be fully reflected by piecewise function hysteretic model, moreover, the model has intuitional expressions with clear physical interpretations for each parameter, paving the way for predicting the nonlinear dynamic responses of mid-rise CFS structures.
DEFF Research Database (Denmark)
Gholami, M.; Cocquempot, V.; Schiøler, H.
2014-01-01
An active fault tolerant control (AFTC) method is proposed for discrete-time piecewise affine (PWA) systems. Only actuator faults are considered. The AFTC framework contains a supervisory scheme, which selects a suitable controller in a set of controllers such that the stability and an acceptable...... the reference signal while the control inputs are bounded. The PFTC problem is transformed into a feasibility problem of a set of LMIs. The method is applied on a large-scale live-stock ventilation model.......An active fault tolerant control (AFTC) method is proposed for discrete-time piecewise affine (PWA) systems. Only actuator faults are considered. The AFTC framework contains a supervisory scheme, which selects a suitable controller in a set of controllers such that the stability and an acceptable...... performance of the faulty system are held. The design of the supervisory scheme is not considered here. The set of controllers is composed of a normal controller for the fault-free case, an active fault detection and isolation controller for isolation and identification of the faults, and a set of passive...
A Neurodynamic Approach for Real-Time Scheduling via Maximizing Piecewise Linear Utility.
Guo, Zhishan; Baruah, Sanjoy K
2016-02-01
In this paper, we study a set of real-time scheduling problems whose objectives can be expressed as piecewise linear utility functions. This model has very wide applications in scheduling-related problems, such as mixed criticality, response time minimization, and tardiness analysis. Approximation schemes and matrix vectorization techniques are applied to transform scheduling problems into linear constraint optimization with a piecewise linear and concave objective; thus, a neural network-based optimization method can be adopted to solve such scheduling problems efficiently. This neural network model has a parallel structure, and can also be implemented on circuits, on which the converging time can be significantly limited to meet real-time requirements. Examples are provided to illustrate how to solve the optimization problem and to form a schedule. An approximation ratio bound of 0.5 is further provided. Experimental studies on a large number of randomly generated sets suggest that our algorithm is optimal when the set is nonoverloaded, and outperforms existing typical scheduling strategies when there is overload. Moreover, the number of steps for finding an approximate solution remains at the same level when the size of the problem (number of jobs within a set) increases.
Tatsii, R. M.; Pazen, O. Yu.
2016-03-01
A constructive scheme for the construction of a solution of a mixed problem for the heat conduction equation with piecewise-continuous coefficients coordinate-dependent in the final interval is suggested and validated in the present work. The boundary conditions are assumed to be most general. The scheme is based on: the reduction method, the concept of quasi-derivatives, the currently accepted theory of the systems of linear differential equations, the Fourier method, and the modified method of eigenfunctions. The method based on this scheme should be related to direct exact methods of solving mixed problems that do not employ the procedures of constructing Green's functions or integral transformations. Here the theorem of eigenfunction expansion is adapted for the case of coefficients that have discontinuity points of the 1st kind. The results obtained can be used, for example, in investigating the process of heat transfer in a multilayer slab under conditions of ideal thermal contact between the layers. A particular case of piecewise-continuous coefficients is considered. A numerical example of calculation of a temperature field in a real four-layer building slab under boundary conditions of the 3rd kind (conditions of convective heat transfer) that model the phenomenon of fire near one of the external surfaces is given.
GRMHD Simulations of Binary Neutron Star Mergers with Piecewise Polytropic Equations of State
Giacomazzo, Bruno
2015-04-01
We present new results of fully general relativistic magnetohydrodynamic (GRMHD) simulations of binary neutron star (BNS) mergers performed with the Whisky code. Our new simulations consider both equal and unequal-mass systems and describe the NS matter via piecewise polytropic equations of state (EOSs). BNS mergers are powerful sources of gravitational waves (GWs) that can be detected by ground based detectors, such as advanced Virgo and LIGO, and they are also thought to be behind the central engine powering short gamma-ray bursts. In our simulations we therefore focus both on the GW emission and on the dynamics of matter and magnetic fields, both in the case a black hole is promptly formed and in the case of the formation of a long-lived magnetized NS. Since the EOS has an important role in both GW emission and matter dynamics, our simulations employ piecewise polytropic EOSs composed by seven pieces, four for the low-density regions (including the crust) and three for the core, in order to more accurately match physically motivated EOSs. Thermal effects are also included in order to more properly describe the post-merger dynamics.
The stiffness variation of a micro-ring driven by a traveling piecewise-electrode.
Li, Yingjie; Yu, Tao; Hu, Yuh-Chung
2014-09-16
In the practice of electrostatically actuated micro devices; the electrostatic force is implemented by sequentially actuated piecewise-electrodes which result in a traveling distributed electrostatic force. However; such force was modeled as a traveling concentrated electrostatic force in literatures. This article; for the first time; presents an analytical study on the stiffness variation of microstructures driven by a traveling piecewise electrode. The analytical model is based on the theory of shallow shell and uniform electrical field. The traveling electrode not only applies electrostatic force on the circular-ring but also alters its dynamical characteristics via the negative electrostatic stiffness. It is known that; when a structure is subjected to a traveling constant force; its natural mode will be resonated as the traveling speed approaches certain critical speeds; and each natural mode refers to exactly one critical speed. However; for the case of a traveling electrostatic force; the number of critical speeds is more than that of the natural modes. This is due to the fact that the traveling electrostatic force makes the resonant frequencies of the forward and backward traveling waves of the circular-ring different. Furthermore; the resonance and stability can be independently controlled by the length of the traveling electrode; though the driving voltage and traveling speed of the electrostatic force alter the dynamics and stabilities of microstructures. This paper extends the fundamental insights into the electromechanical behavior of microstructures driven by electrostatic forces as well as the future development of MEMS/NEMS devices with electrostatic actuation and sensing.
Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics.
Cao, Qingjie; Wiercigroch, Marian; Pavlovskaia, Ekaterina E; Thompson, J Michael T; Grebogi, Celso
2008-02-28
In a recent paper we examined a model of an arch bridge with viscous damping subjected to a sinusoidally varying central load. We showed how this yields a useful archetypal oscillator which can be used to study the transition from smooth to discontinuous dynamics as a parameter, alpha, tends to zero. Decreasing this smoothness parameter (a non-dimensional measure of the span of the arch) changes the smooth load-deflection curve associated with snap-buckling into a discontinuous sawtooth. The smooth snap-buckling curve is not amenable to closed-form theoretical analysis, so we here introduce a piecewise linearization that correctly fits the sawtooth in the limit at alpha=0. Using a Hamiltonian formulation of this linearization, we derive an analytical expression for the unperturbed homoclinic orbit, and make a Melnikov analysis to detect the homoclinic tangling under the perturbation of damping and driving. Finally, a semi-analytical method is used to examine the full nonlinear dynamics of the perturbed piecewise linear system. A chaotic attractor located at alpha=0.2 compares extremely well with that exhibited by the original arch model: the topological structures are the same, and Lyapunov exponents (and dimensions) are in good agreement.
Implementation of nonlinear registration of brain atlas based on piecewise grid system
Liu, Rong; Gu, Lixu; Xu, Jianrong
2007-12-01
In this paper, a multi-step registration method of brain atlas and clinical Magnetic Resonance Imaging (MRI) data based on Thin-Plate Splines (TPS) and Piecewise Grid System (PGS) is presented. The method can help doctors to determine the corresponding anatomical structure between patient image and the brain atlas by piecewise nonlinear registration. Since doctors mostly pay attention to particular Region of Interest (ROI), and a global nonlinear registration is quite time-consuming which is not suitable for real-time clinical application, we propose a novel method to conduct linear registration in global area before nonlinear registration is performed in selected ROI. The homogenous feature points are defined to calculate the transform matrix between patient data and the brain atlas to conclude the mapping function. Finally, we integrate the proposed approach into an application of neurosurgical planning and guidance system which lends great efficiency in both neuro-anatomical education and guiding of neurosurgical operations. The experimental results reveal that the proposed approach can keep an average registration error of 0.25mm in near real-time manner.
Gardini, Laura; Fournier-Prunaret, Danièle; Chargé, Pascal
2011-06-01
In recent years, the study of chaotic and complex phenomena in electronic circuits has been widely developed due to the increasing number of applications. In these studies, associated with the use of chaotic sequences, chaos is required to be robust (not occurring only in a set of zero measure and persistent to perturbations of the system). These properties are not easy to be proved, and numerical simulations are often used. In this work, we consider a simple electronic switching circuit, proposed as chaos generator. The object of our study is to determine the ranges of the parameters at which the dynamics are chaotic, rigorously proving that chaos is robust. This is obtained showing that the model can be studied via a two-dimensional piecewise smooth map in triangular form and associated with a one-dimensional piecewise linear map. The bifurcations in the parameter space are determined analytically. These are the border collision bifurcation curves, the degenerate flip bifurcations, which only are allowed to occur to destabilize the stable cycles, and the homoclinic bifurcations occurring in cyclical chaotic regions leading to chaos in 1-piece.
The Melnikov method and subharmonic orbits in a piecewise smooth system
Granados, A; Seara, T M
2012-01-01
In this work we consider a two-dimensional piecewise smooth system, defined in two domains separated by the switching manifold $x=0$. We assume that there exists a piecewise-defined continuous Hamiltonian that is a first integral of the system. We also suppose that the system possesses an invisible fold-fold at the origin and two heteroclinic orbits connecting two hyperbolic critical points on either side of $x=0$. Finally, we assume that the region closed by these heteroclinic connections is fully covered by periodic orbits surrounding the origin, whose periods monotonically increase as they approach the heteroclinic connection. When considering a non-autonomous ($T$-periodic) Hamiltonian perturbation of amplitude $\\varepsilon$, using an impact map, we rigorously prove that, for every $n$ and $m$ relatively prime and $\\varepsilon>0$ small enough, there exists a $nT$-periodic orbit impacting $2m$ times with the switching manifold at every period if a modified subharmonic Melnikov function possesses a simple z...
Group lassoing change-points in piecewise-constant AR processes
Angelosante, Daniele; Giannakis, Georgios B.
2012-12-01
Regularizing the least-squares criterion with the total number of coefficient changes, it is possible to estimate time-varying (TV) autoregressive (AR) models with piecewise-constant coefficients. Such models emerge in various applications including speech segmentation, biomedical signal processing, and geophysics. To cope with the inherent lack of continuity and the high computational burden when dealing with high-dimensional data sets, this article introduces a convex regularization approach enabling efficient and continuous estimation of TV-AR models. To this end, the problem is cast as a sparse regression one with grouped variables, and is solved by resorting to the group least-absolute shrinkage and selection operator (Lasso). The fresh look advocated here permeates benefits from advances in variable selection and compressive sampling to signal segmentation. An efficient block-coordinate descent algorithm is developed to implement the novel segmentation method. Issues regarding regularization and uniqueness of the solution are also discussed. Finally, an alternative segmentation technique is introduced to improve the detection of change instants. Numerical tests using synthetic and real data corroborate the merits of the developed segmentation techniques in identifying piecewise-constant TV-AR models.
Shen, Ji Yao; Abu-Saba, Elias G.; Mcginley, William M.; Sharpe, Lonnie, Jr.; Taylor, Lawrence W., Jr.
1992-01-01
Distributed parameter modeling offers a viable alternative to the finite element approach for modeling large flexible space structures. The introduction of the transfer matrix method into the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to some more complex configurations. A uniform Timoshenko beam model for the estimation of the dynamic properties of beam-like structures has given comparable results. But many aeronautical and aerospace structures are comprised of non-uniform sections or sectional properties, such as aircraft wings and satellite antennas. This paper proposes a piecewise continuous Timoshenko beam model which is used for the dynamic analysis of tapered beam-like structures. A tapered beam is divided into several segments of uniform beam elements. Instead of arbitrarily assumed shape functions used in finite element analysis, the closed-form solution of the Timoshenko beam equation is used. Application of the transfer matrix method relates all the elements as a whole. By corresponding boundary conditions and compatible conditions a characteristic equation for the global tapered beam has been developed, from which natural frequencies can be derived. A computer simulation is shown in this paper, and compared with the results obtained from the finite element analysis. While piecewise continuous Timoshenko beam model decreases the number of elements significantly; comparable results to the finite element method are obtained.
Saito, Asaki; Yasutomi, Shin-ichi; Tamura, Jun-ichi; Ito, Shunji
2015-06-01
We introduce a true orbit generation method enabling exact simulations of dynamical systems defined by arbitrary-dimensional piecewise linear fractional maps, including piecewise linear maps, with rational coefficients. This method can generate sufficiently long true orbits which reproduce typical behaviors (inherent behaviors) of these systems, by properly selecting algebraic numbers in accordance with the dimension of the target system, and involving only integer arithmetic. By applying our method to three dynamical systems—that is, the baker's transformation, the map associated with a modified Jacobi-Perron algorithm, and an open flow system—we demonstrate that it can reproduce their typical behaviors that have been very difficult to reproduce with conventional simulation methods. In particular, for the first two maps, we show that we can generate true orbits displaying the same statistical properties as typical orbits, by estimating the marginal densities of their invariant measures. For the open flow system, we show that an obtained true orbit correctly converges to the stable period-1 orbit, which is inherently possessed by the system.
Spectral analysis and an area-preserving extension of a piecewise linear intermittent map
Miyaguchi, Tomoshige; Aizawa, Yoji
2007-06-01
We investigate the spectral properties of a one-dimensional piecewise linear intermittent map, which has not only a marginal fixed point but also a singular structure suppressing injections of the orbits into neighborhoods of the marginal fixed point. We explicitly derive generalized eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map for classes of observables and piecewise constant initial densities, and it is found that the Frobenius-Perron operator has two simple real eigenvalues 1 and λdɛ(-1,0) and a continuous spectrum on the real line [0,1]. From these spectral properties, we also found that this system exhibits a power law decay of correlations. This analytical result is found to be in a good agreement with numerical simulations. Moreover, the system can be extended to an area-preserving invertible map defined on the unit square. This extended system is similar to the baker transformation, but does not satisfy hyperbolicity. A relation between this area-preserving map and a billiard system is also discussed.
Energy Technology Data Exchange (ETDEWEB)
Ramos, J.I. [Universidad de Malaga, E.T.S. Ingenieros Industriales, Room I-320-D, Plaza El Ejido, s/n, 29013 Malaga (Spain)]. E-mail: jirs@lcc.uma.es
2006-06-15
An approximate method based on piecewise linearization is developed for the determination of periodic orbits of nonlinear oscillators. The method is based on Taylor series expansions, provides piecewise analytical solutions in three-point intervals which are continuous everywhere and explicit three-point difference equations which are P-stable and have an infinite interval of periodicity. It is shown that the method presented here reduces to the well-known Stoermer technique, is second-order accurate, and yields, upon applying Taylor series expansion and a Pade approximation, another P-stable technique whenever the Jacobian is different from zero. The method is generalized for single degree-of-freedom problems that contain the velocity, and (approximate) analytical solutions are presented. Finally, by introducing the inverse of a vector and the vector product and quotient, and using Taylor series expansions and a Pade approximation, the method has been generalized to multiple degree-of-freedom problems and results in explicit three-point finite difference equations which only involve vector multiplications.
A piecewise-integration method for simulating the influence of external forcing on climate
Institute of Scientific and Technical Information of China (English)
Zhifu Zhang; Chongjian Qiu; Chenghai Wang
2008-01-01
Climate drift occurs in most general circulation models (GCMs) as a result of incomplete physical and numerical representation of the complex climate system,which may cause large uncertainty in sensitivity experiments evaluating climate response to changes in external forcing.To solve this problem,we propose a piecewise-integration method to reduce the systematic error in climate sensitivity studies.The observations are firstly assimilated into a numerical model by using the dynamic relaxation technique to relax to the current state of atmosphere,and then the assimilated fields are continuously used to reinitialize the simulation to reduce the error of climate simulation.When the numerical model is integrated with changed external forcing,the results can be split into two parts,background and perturbation fields,and the background is the state before the external forcing is changed.The piecewise-integration method is used to continuously reinitialize the model with the assimilated field,instead of the background.Therefore,the simulation error of the model with the external forcing can be reduced.In this way,the accuracy of climate sensitivity experiments is greatly improved.Tests with a simple low-order spectral model show that this approach can significantly reduce the uncertainty of climate sensitivity experiments.
Hasegawa, Hideo
2007-02-01
We have studied the finite N-unit Langevin model subjected to multiplicative noises, by using the augmented moment method (AMM), as a continuation of our previous paper [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. Effects of couplings on stationary and dynamical properties of the model have been investigated. The difference and similarity between the results of diffusive and sigmoid couplings are studied in details. Time dependences of average and fluctuations in local and global variables calculated by the AMM are in good agreement with those of direct simulations (DSs). We also discuss stationary distributions of local and global variables with the use of the Fokker-Planck equation (FPE) method and DSs. It is demonstrated that stationary distributions show much variety when multiplicative noise and external inputs are taken into account.
A voxelation-corrected non-stationary 3D cluster-size test based on random field theory.
Li, Huanjie; Nickerson, Lisa D; Zhao, Xuna; Nichols, Thomas E; Gao, Jia-Hong
2015-09-01
Cluster-size tests (CSTs) based on random field theory (RFT) are commonly adopted to identify significant differences in brain images. However, the use of RFT in CSTs rests on the assumption of uniform smoothness (stationarity). When images are non-stationary, CSTs based on RFT will likely lead to increased false positives in smooth regions and reduced power in rough regions. An adjustment to the cluster size according to the local smoothness at each voxel has been proposed for the standard test based on RFT to address non-stationarity, however, this technique requires images with a large degree of spatial smoothing, large degrees of freedom and high intensity thresholding. Recently, we proposed a voxelation-corrected 3D CST based on Gaussian random field theory that does not place constraints on the degree of spatial smoothness. However, this approach is only applicable to stationary images, requiring further modification to enable use for non-stationary images. In this study, we present modifications of this method to develop a voxelation-corrected non-stationary 3D CST based on RFT. Both simulated and real data were used to compare the voxelation-corrected non-stationary CST to the standard cluster-size adjusted non-stationary CST based on RFT and the voxelation-corrected stationary CST. We found that voxelation-corrected stationary CST is liberal for non-stationary images and the voxelation-corrected non-stationary CST performs better than cluster-size adjusted non-stationary CST based on RFT under low smoothness, low intensity threshold and low degrees of freedom. Published by Elsevier Inc.
Stationary Light Pulses in Cold Atomic Media
Liao, Wen-Te; Peters, Thorsten; Chou, Hung-Chih; Wang, Jian-Siung; Kuan, Pei-Chen; Yu, Ite A
2008-01-01
Stationary light pulses (SLPs), i.e., light pulses without motion, are formed via the retrieval of stored probe pulses with two counter-propagating coupling fields. We show that there exist non-negligible hybrid Raman excitations in media of cold atoms that prohibit the SLP formation. We experimentally demonstrate a method to suppress these Raman excitations and realize SLPs in laser-cooled atoms. Our work opens the way to SLP studies in cold as well as in stationary atoms and provides a new avenue to low-light-level nonlinear optics.
Stationary axisymmetric black holes with matter
Chodosh, Otis
2015-01-01
We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and analyze the compatibility of the resulting equations. This framework will be fundamental to our forthcoming construction of metric-stationary axisymmetric bifurcations of Kerr solving the Einstein--Klein--Gordon system, and as such, we include specializations of all of our formulas to the case of a time-periodic massive scalar field.
Facial Expression Recognition Using Stationary Wavelet Transform Features
Directory of Open Access Journals (Sweden)
Huma Qayyum
2017-01-01
Full Text Available Humans use facial expressions to convey personal feelings. Facial expressions need to be automatically recognized to design control and interactive applications. Feature extraction in an accurate manner is one of the key steps in automatic facial expression recognition system. Current frequency domain facial expression recognition systems have not fully utilized the facial elements and muscle movements for recognition. In this paper, stationary wavelet transform is used to extract features for facial expression recognition due to its good localization characteristics, in both spectral and spatial domains. More specifically a combination of horizontal and vertical subbands of stationary wavelet transform is used as these subbands contain muscle movement information for majority of the facial expressions. Feature dimensionality is further reduced by applying discrete cosine transform on these subbands. The selected features are then passed into feed forward neural network that is trained through back propagation algorithm. An average recognition rate of 98.83% and 96.61% is achieved for JAFFE and CK+ dataset, respectively. An accuracy of 94.28% is achieved for MS-Kinect dataset that is locally recorded. It has been observed that the proposed technique is very promising for facial expression recognition when compared to other state-of-the-art techniques.
Yang, Xitao; Yuan, Rong
2006-10-01
In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established.
Tripathi, B. B.; Espíndola, D.; Pinton, G. F.
2017-06-01
The recent discovery of shear shock wave generation and propagation in the porcine brain suggests that this new shock phenomenology may be responsible for a broad range of traumatic injuries. Blast-induced head movement can indirectly lead to shear wave generation in the brain, which could be a primary mechanism for injury. Shear shock waves amplify the local acceleration deep in the brain by up to a factor of 8.5, which may tear and damage neurons. Currently, there are numerical methods that can model compressional shock waves, such as comparatively well-studied blast waves, but there are no numerical full-wave solvers that can simulate nonlinear shear shock waves in soft solids. Unlike simplified representations, e.g., retarded time, full-wave representations describe fundamental physical behavior such as reflection and heterogeneities. Here we present a piecewise parabolic method-based solver for one-dimensional linearly polarized nonlinear shear wave in a homogeneous medium and with empirical frequency-dependent attenuation. This method has the advantage of being higher order and more directly extendable to multiple dimensions and heterogeneous media. The proposed numerical scheme is validated analytically and experimentally and compared to other shock capturing methods. A Riemann step-shock problem is used to characterize the numerical dissipation. This dissipation is then tuned to be negligible with respect to the physical attenuation by choosing an appropriate grid spacing. The numerical results are compared to ultrasound-based experiments that measure planar polarized shear shock wave propagation in a tissue-mimicking gelatin phantom. Good agreement is found between numerical results and experiment across a 40 mm propagation distance. We anticipate that the proposed method will be a starting point for the development of a two- and three-dimensional full-wave code for the propagation of nonlinear shear waves in heterogeneous media.
Energy and angular momentum densities of stationary gravity fields
Lynden-Bell, D; Bicak, Jiri; 10.1103/PhysRevD.75.024040
2009-01-01
We give physical explanations of explicit invariant expressions for the energy and angular momentum densities of gravitational fields in stationary space-times. These expressions involve non-locally defined conformal factors. In certain coordinates these become locally defined in terms of the metric. These results are derived via expressions for total gravitational potential energy from the difference between the total energy and the mechanical energy. The latter involves kinetic energy seen in the frame of static observers. When in the axially symmetric case we consider zero angular momentum observers (who move orthogonally to surfaces of constant time), we find that the angular momentum they attribute to the gravitational field is solely due to their motion.
Rafferty, Jake L; Siepmann, J Ilja; Schure, Mark R
2011-12-23
Reversed-phase liquid chromatography (RPLC) is the foremost technique for the separation of analytes that have very similar chemical functionalities, but differ only in their molecular shape. This ability is crucial in the analysis of various mixtures with environmental and biological importance including polycyclic aromatic hydrocarbons (PAHs) and steroids. A large amount of effort has been devoted to studying this phenomenon experimentally, but a detailed molecular-level description remains lacking. To provide some insight on the mechanism of shape selectivity in RPLC, particle-based simulations were carried out for stationary phases and chromatographic parameters that closely mimic those in an experimental study by Sentell and Dorsey [J. Chromatogr. 461 (1989) 193]. The retention of aromatic hydrocarbons ranging in size from benzene to the isomeric PAHs of the formula C(18)H(12) was examined for model RPLC systems consisting of monomeric dimethyl octadecylsilane (ODS) stationary phases with surface coverages ranging from 1.6 to 4.2 μmol/m(2) (i.e., stationary phases yielding low to intermediate shape selectivity) in contact with a 67/33 mol% acetonitrile/water mobile phase. The simulations show that the stationary phase acts as a very heterogeneous environment where analytes with different shapes prefer different spatial regions with specific local bonding environments of the ODS chains. However, these favorable retentive regions cannot be described as pre-existing cavities because the chain conformation in these local stationary phase regions adapts to accommodate the analytes.
Zhang, Hongbin; Feng, Gang
2008-10-01
This paper is concerned with stability analysis and H(infinity) decentralized control of discrete-time fuzzy large-scale systems based on piecewise Lyapunov functions. The fuzzy large-scale systems consist of J interconnected discrete-time Takagi-Sugeno (T-S) fuzzy subsystems, and the stability analysis is based on Lyapunov functions that are piecewise quadratic. It is shown that the stability of the discrete-time fuzzy large-scale systems can be established if a piecewise quadratic Lyapunov function can be constructed, and moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. The H(infinity) controllers are also designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions. It is demonstrated via numerical examples that the stability and controller synthesis results based on the piecewise quadratic Lyapunov functions are less conservative than those based on the common quadratic Lyapunov functions.
Model of strong stationary vortex turbulence in space plasmas
Directory of Open Access Journals (Sweden)
G. D. Aburjania
2009-01-01
Full Text Available This paper investigates the macroscopic consequences of nonlinear solitary vortex structures in magnetized space plasmas by developing theoretical model of plasma turbulence. Strongly localized vortex patterns contain trapped particles and, propagating in a medium, excite substantial density fluctuations and thus, intensify the energy, heat and mass transport processes, i.e., such vortices can form strong vortex turbulence. Turbulence is represented as an ensemble of strongly localized (and therefore weakly interacting vortices. Vortices with various amplitudes are randomly distributed in space (due to collisions. For their description, a statistical approach is applied. It is supposed that a stationary turbulent state is formed by balancing competing effects: spontaneous development of vortices due to nonlinear twisting of the perturbations' fronts, cascading of perturbations into short scales (direct spectral cascade and collisional or collisionless damping of the perturbations in the short-wave domain. In the inertial range, direct spectral cascade occurs through merging structures via collisions. It is shown that in the magneto-active plasmas, strong turbulence is generally anisotropic Turbulent modes mainly develop in the direction perpendicular to the local magnetic field. It is found that it is the compressibility of the local medium which primarily determines the character of the turbulent spectra: the strong vortex turbulence forms a power spectrum in wave number space. For example, a new spectrum of turbulent fluctuations in k^{−8/3} is derived which agrees with available experimental data. Within the framework of the developed model particle diffusion processes are also investigated. It is found that the interaction of structures with each other and particles causes anomalous diffusion in the medium. The effective coefficient of diffusion has a square root dependence on the stationary level of noise.
Stationary axion/dilaton solutions and supersymmetry
Bergshoeff, E. A.; Kallosh, R.; Ortín, Tomas
1996-01-01
We present a new set of supersymmetric stationary solutions of pure N = 4, d = 4 supergravity (and, hence, of low-energy effective string theory) that generalize (and include) the Israel-Wilson-Pejes solutions of Einstein-Maxwell theory. All solutions have 1/4 of the supersymmetries unbroken and som
On non-stationary threshold autoregressive models
Liu, Weidong; Shao, Qi-Man; 10.3150/10-BEJ306
2011-01-01
In this paper we study the limiting distributions of the least-squares estimators for the non-stationary first-order threshold autoregressive (TAR(1)) model. It is proved that the limiting behaviors of the TAR(1) process are very different from those of the classical unit root model and the explosive AR(1).
SS 433: Stationary lines and primary eclipses
Bowler, M G
2015-01-01
Some stationary lines in the emission spectra of SS 433 are eclipsed, but most are not. Lines attributed to a circumbinary disk are not eclipsed, but double in relative intensity during primary eclipse. A C II doublet is eclipsed and Doppler shifts over two periods yield an orbital speed of 176 +/- 13 km/s.
Realizability of stationary spherically symmetric transonic accretion
Ray, A K; Ray, Arnab K.
2002-01-01
The spherically symmetric stationary transonic (Bondi) flow is considered a classic example of an accretion flow. This flow, however, is along a separatrix, which is usually not physically realizable. We demonstrate, using a pedagogical example, that it is the dynamics which selects the transonic flow.
The stationary states of interacting fields
Frazer, W.R.; Hove, Léon van
1958-01-01
As an application of a time-independent perturbation formalism developed earlier for systems with many degrees of freedom, we give in terms of diagrams the general perturbation expressions for the exact stationary states of interacting fields. The physical vacuum is obtained by applying to the bare
Calendar Year 2016 Stationary Source Emissions Inventory
Energy Technology Data Exchange (ETDEWEB)
Evelo, Stacie [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-01-01
The City of Albuquerque (COA) Environmental Health Department Air Quality Program has issued stationary source permits and registrations the Department of Energy/Sandia Field Office for operations at the Sandia National Laboratories/New Mexico. This emission inventory report meets the annual reporting compliance requirements for calendar year (CY) 2016 as required by the COA.
Robust Nonlinear Causality Analysis of Non-Stationary Multivariate Physiological Time Series.
Schaeck, Tim; Muma, Michael; Feng, Mengling; Guan, Cuntai; Zoubir, Abdelhak
2017-05-26
An important research area in biomedical signal processing is that of quantifying the relationship between simultaneously observed time series and to reveal interactions between the signals. Since biomedical signals are potentially non-stationary and the measurements may contain outliers and artifacts, we introduce a robust time-varying generalized partial directed coherence (rTV-gPDC) function. The proposed method, which is based on a robust estimator of the timevarying autoregressive (TVAR) parameters, is capable of revealing directed interactions between signals. By definition, the rTV-gPDC only displays the linear relationships between the signals. We therefore suggest to approximate the residuals of the TVAR process, which potentially carry information about the nonlinear causality by a piece-wise linear time-varying moving-average (TVMA) model. The performance of the proposed method is assessed via extensive simulations. To illustrate the method's applicability to real-world problems, it is applied to a neurophysiological study that involves intracranial pressure (ICP), arterial blood pressure (ABP), and brain tissue oxygenation level (PtiO2) measurements. The rTV-gPDC reveals causal patterns that are in accordance with expected cardiosudoral meachanisms and potentially provides new insights regarding traumatic brain injuries (TBI). The rTV-gPDC is not restricted to the above problem but can be useful in revealing interactions in a broad range of applications.
Institute of Scientific and Technical Information of China (English)
DU XiuLi; WANG FengQuan
2009-01-01
A new time-domain modal identification method of linear time-lnvariant system driven by the non-stationary Gaussian random excitation is introduced based on the continuous time AR model.The method can identify physical parameters of the system from response data.In order to identify the parameters of the system, the structural dynamic equation is first transformed into the continuous time AR model, and subsequently written into the forms of observation equation and state equation which is just a stochastic differential equation.Secondly, under the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short time period, the uniformly modulated func-tion is identified piecewise.Then, we present the exact maximum likelihood estimators of parameters by virtue of the Girsanov theorem.Finally, the modal parameters are identified by eigenanalysis.Nu-merical results show that the method we introduce here not only has high precision and robustness, but also has very high computing efficiency.Therefore, it is suitable for real-time modal identification.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A new time-domain modal identification method of linear time-invariant system driven by the non-stationary Gaussian random excitation is introduced based on the continuous time AR model. The method can identify physical parameters of the system from response data. In order to identify the parameters of the system, the structural dynamic equation is first transformed into the continuous time AR model, and subsequently written into the forms of observation equation and state equation which is just a stochastic differential equation. Secondly, under the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short time period, the uniformly modulated function is identified piecewise. Then, we present the exact maximum likelihood estimators of parameters by virtue of the Girsanov theorem. Finally, the modal parameters are identified by eigenanalysis. Numerical results show that the method we introduce here not only has high precision and robustness, but also has very high computing efficiency. Therefore, it is suitable for real-time modal identification.
Assessment of the environmental benefits of transport and stationary fuel
Energy Technology Data Exchange (ETDEWEB)
Bauen, A.; Hart, D. [Energy-Environment Policy Group, TH Huxley School, Imperial College, London (United Kingdom)
2000-03-01
Fuel cells (FCs) offer significant environmental benefits over competing technologies and hence the environment is a strong driving force behind the development of FC systems for transport and stationary applications. This paper provides a comprehensive comparison of FC and competing systems, and points out strengths and weaknesses of the different FC systems, suggesting areas for improvement. The results presented build on earlier work [D. Hart, G. Hoermandinger, Initial assessment of the environmental characteristics of fuel cells and competing technologies, ETSU F/02/00111/REP/1, ETSU, Harwell, UK, 1997.] and provide a detailed analysis of a wider range of systems, The analysis takes the form of a model, which compares system emissions (global, regional and local pollutants) and energy consumption on a full fuel cycle basis. It considers a variety of primary energy sources, intermediate fuel supply steps and FC systems for transport and stationary end-uses. These are compared with alternative systems for transport and stationary applications. Energy and pollutant emission reductions of FC systems compared to alternative vehicle technology vary considerably, though all FC technologies show reduction in energy use and CO{sub 2} emissions of at least 20%; as well as reductions of several orders of magnitude in regulated pollutants compared to the base-case vehicle. The location of emissions is also of importance, with most emissions in the case of FC vehicles occurring in the fuel supply stage. The energy, CO{sub 2} and regulated emissions advantages of FC systems for distributed and baseload electricity are more consistent than for transport applications, with reductions in regulated pollutants generally larger than one order of magnitude compared to competing technologies. For CHP applications, the advantages of FC systems with regard to regulated pollutants remain large. However, energy and CO{sub 2} emission advantages are reduced, depending largely on the
Exact Stationary and Non-stationary Solutions to Inelastic Maxwell Model with Infinite Energy
Ilyin, Oleg
2016-11-01
The one-dimensional inelastic Boltzmann equation with a constant collision rate (the Maxwell model) is considered. It is shown that for special values of restitution parameter there exists a stationary solution with the characteristic function in the form e^{-P(log (z))z}, where P is a periodic function. The corresponding distribution function belongs to a one special class of stochastic processes termed as a generalized stable in the probability theory. The Fourier transform of the non-stationary equation has the solution bigl (1+P(log (z))zbigr )e^{-Q(log (z))z}. It is proved that this solution is a characteristic function if periodic functions P, Q satisfy some not very restrictive conditions. The stationary and non-stationary solutions correspond to a gas with infinite temperature.
Le Quang, Thuan; Camlibel, M. K.
2014-01-01
In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the conditions guaranteeing uniqueness of Filippov solutions in t
DEFF Research Database (Denmark)
Wolf, Paul A.; Jørgensen, Jakob Sauer; Schmidt, Taly G.
2013-01-01
A sparsity-exploiting algorithm intended for few-view Single Photon Emission Computed Tomography (SPECT) reconstruction is proposed and characterized. The algorithm models the object as piecewise constant subject to a blurring operation. To validate that the algorithm closely approximates the true...
Automated Controller Synthesis for non-Deterministic Piecewise-Affine Hybrid Systems
DEFF Research Database (Denmark)
Grunnet, Jacob Deleuran
formations. This thesis uses a hybrid systems model of a satellite formation with possible actuator faults as a motivating example for developing an automated control synthesis method for non-deterministic piecewise-affine hybrid systems (PAHS). The method does not only open an avenue for further research......To further advance space based science the need for ever more precise measurement techniques increases. One of the most promising new ideas are satellite formations where accurate spatial control of multiple spacecraft can be used to create very large virtual apertures or very sensitive...... interferometric measurements. Control of satellite formations presents a whole new set of challenges for spacecraft control systems requiring advances in actuation, sensing, communication, and control algorithms. Specifically having the control system duplicated onto multiple satellites increases the possibility...
Piecewise Smooth Dynamical Systems Theory: The Case of the Missing Boundary Equilibrium Bifurcations
Hogan, S. J.; Homer, M. E.; Jeffrey, M. R.; Szalai, R.
2016-10-01
We present two codimension-one bifurcations that occur when an equilibrium collides with a discontinuity in a piecewise smooth dynamical system. These simple cases appear to have escaped recent classifications. We present them here to highlight some of the powerful results from Filippov's book Differential Equations with Discontinuous Righthand Sides (Kluwer, 1988). Filippov classified the so-called boundary equilibrium collisions without providing their unfolding. We show the complete unfolding here, for the first time, in the particularly interesting case of a node changing its stability as it collides with a discontinuity. We provide a prototypical model that can be used to generate all codimension-one boundary equilibrium collisions, and summarize the elements of Filippov's work that are important in achieving a full classification.
Directory of Open Access Journals (Sweden)
Hwanyub Joo
2015-01-01
Full Text Available This paper addresses the output regulation problem of synchronous buck converters with piecewise-constant load fluctuations via linear parameter varying (LPV control scheme. To this end, an output-error state-space model is first derived in the form of LPV systems so that it can involve a mismatch error that temporally arises from the process of generating a feedforward control. Then, to attenuate the mismatch error in parallel with improving the transient behavior of the converter, this paper proposes an LMI-based stabilization condition capable of achieving both H∞ and pole-placement objectives. Finally, the simulation and experimental results are provided to show the validity of our approach.
Ultra-high-frequency piecewise-linear chaos using delayed feedback loops
Cohen, Seth D.; Rontani, Damien; Gauthier, Daniel J.
2012-12-01
We report on an ultra-high-frequency (>1 GHz), piecewise-linear chaotic system designed from low-cost, commercially available electronic components. The system is composed of two electronic time-delayed feedback loops: A primary analog loop with a variable gain that produces multi-mode oscillations centered around 2 GHz and a secondary loop that switches the variable gain between two different values by means of a digital-like signal. We demonstrate experimentally and numerically that such an approach allows for the simultaneous generation of analog and digital chaos, where the digital chaos can be used to partition the system's attractor, forming the foundation for a symbolic dynamics with potential applications in noise-resilient communications and radar.
Generalized Methods and Solvers for Noise Removal from Piecewise Constant Signals
Little, Max A
2010-01-01
Removing noise from piecewise constant (PWC) signals, is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need separating into stratigraphic zones, and in biophysics, jumps between molecular dwell states need extracting from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited however. This paper shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following, and coordinate descent. We intr...
Mandrekar, Pratik
2011-01-01
We study the properties of least time trajectories for particles moving on a two dimensional surface which consists of piecewise homogeneous regions. The particles are assumed to move with different constant speeds on different regions and on the boundary between regions. The speed of the particle is assumed to be highest when it moves along the edges formed by the boundary of two regions. We get an analogous behavior to Snell's Law of light refraction, but in a more generalized form. The model could be used for studying properties of animal and insect trails which tend to form predominantly along edges. The model predicts three types of behavior for the trajectories near a corner forming edge: fully edge following, partial edge following and complete avoidance of the edge, which are indeed observed in natural ant trails.
Synchronization regions of two pulse-coupled electronic piecewise linear oscillators
Rubido, N.; Cabeza, C.; Kahan, S.; Ramírez Ávila, G. M.; Marti, Arturo C.
2011-03-01
Stable synchronous states of different order were analytically, numerically and experimentally characterized in pulse-coupled light-controlled oscillators (LCOs). The Master-Slave (MS) configuration was studied in conditions where different time-scale parameters were tuned under varying coupling strength. Arnold tongues calculated analytically - based on the piecewise two-time-scale model for LCOs - and obtained numerically were consistent with experimental results. The analysis of the stability pattern and tongue shape for (1 : n) synchronization was based on the construction of return maps representing the Slave LCO evolution induced by the action of the Master LCO. The analysis of these maps showed that both tongue shape and stability pattern remained invariant. Considering the wide variation range of LCO parameters, the obtained results could have further applications on ethological models.
Generic fractal structure of finite parts of trajectories of piecewise smooth Hamiltonian systems
Hildebrand, R.; Lokutsievskiy, L. V.; Zelikin, M. I.
2013-03-01
Piecewise smooth Hamiltonian systems with tangent discontinuity are studied. A new phenomenon is discovered, namely, the generic chaotic behavior of finite parts of trajectories. The approach is to consider the evolution of Poisson brackets for smooth parts of the initial Hamiltonian system. It turns out that, near second-order singular points lying on a discontinuity stratum of codimension two, the system of Poisson brackets is reduced to the Hamiltonian system of the Pontryagin Maximum Principle. The corresponding optimization problem is studied and the topological structure of its optimal trajectories is constructed (optimal synthesis). The synthesis contains countably many periodic solutions on the quotient space by the scale group and a Cantor-like set of nonwandering points (NW) having fractal Hausdorff dimension. The dynamics of the system is described by a topological Markov chain. The entropy is evaluated, together with bounds for the Hausdorff and box dimension of (NW).
Yuan, Xiao-Tong; Yan, Shuicheng
2012-04-01
We investigate Newton-type optimization methods for solving piecewise linear systems (PLSs) with nondegenerate coefficient matrix. Such systems arise, for example, from the numerical solution of linear complementarity problem, which is useful to model several learning and optimization problems. In this letter, we propose an effective damped Newton method, PLS-DN, to find the exact (up to machine precision) solution of nondegenerate PLSs. PLS-DN exhibits provable semiiterative property, that is, the algorithm converges globally to the exact solution in a finite number of iterations. The rate of convergence is shown to be at least linear before termination. We emphasize the applications of our method in modeling, from a novel perspective of PLSs, some statistical learning problems such as box-constrained least squares, elitist Lasso (Kowalski & Torreesani, 2008), and support vector machines (Cortes & Vapnik, 1995). Numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of PLS-DN on these problems.
Energy Technology Data Exchange (ETDEWEB)
Budantsev, M. V., E-mail: budants@isp.nsc.ru; Lavrov, R. A.; Pogosov, A. G.; Zhdanov, E. Yu.; Pokhabov, D. A. [Russian Academy of Sciences, Rzhanov Institute of Semiconductor Physics, Siberian Branch (Russian Federation)
2011-02-15
Extraordinary piecewise parabolic behavior of the magnetoresistance has been experimentally detected in the two-dimensional electron gas with a dense triangular lattice of antidots, where commensurability magnetoresistance oscillations are suppressed. The magnetic field range of 0-0.6 T can be divided into three wide regions, in each of which the magnetoresistance is described by parabolic dependences with high accuracy (comparable to the experimental accuracy) and the transition regions between adjacent regions are much narrower than the regions themselves. In the region corresponding to the weakest magnetic fields, the parabolic behavior becomes almost linear. The observed behavior is reproducible as the electron gas density changes, which results in a change in the resistance by more than an order of magnitude. Possible physical mechanisms responsible for the observed behavior, including so-called 'memory effects,' are discussed.
An Adaptive Piecewise Curve-Fitting Package Using a Look-Ahead Strategy.
1981-01-01
LOOK-AHEAD STRATEGY# ,PI -lNGC- ;EI AqF AUTHO~fqj T-8 CC’NTPA:T DFZ -CNALN NJIMiiEP BlD C.Platt G. D. /aylor ’_,_.____--_-__ T-EPiRORMINGO CRAWANIH 44VN...8. SMTH= 6. TOL= . 100 . KNOTS ARE INDICATED BY 0. .700E-01 .600E-01 .500E-01 .400E-01 .300E-01 .2OCE-01 * IOCE-01 0 . . I I I I I I l I I I I I I I I...SMTH= 1, TOL= . 100 . KNOTS ARE INDICATED BY 0. * IOOE-01 X a. .. I0E+01 .200E+01 .300E-C PIECEWISE POLYNOMIAL APPROX. USING (DISCRETE) L2 APPROX
Directory of Open Access Journals (Sweden)
Dufan Wu
2013-01-01
Full Text Available Dual energy CT has the ability to give more information about the test object by reconstructing the attenuation factors under different energies. These images under different energies share identical structures but different attenuation factors. By referring to the fully sampled low-energy image, we show that it is possible to greatly reduce the sampling rate of the high-energy image in order to lower dose. To compensate the attenuation factor difference between the two modalities, we use piecewise polynomial fitting to fit the low-energy image to the high-energy image. During the reconstruction, the result is constrained by its distance to the fitted image, and the structural information thus can be preserved. An ASD-POCS-based optimization schedule is proposed to solve the problem, and numerical simulations are taken to verify the algorithm.
Development of New Loan Payment Models with Piecewise Geometric Gradient Series
Directory of Open Access Journals (Sweden)
Erdal Aydemir
2014-12-01
Full Text Available Engineering economics plays an important role in decision making. Also, the cash flows, time value of money and interest rates are the most important research fields in mathematical finance. Generalized formulae obtained from a variety of models with the time value of money and cash flows are inadequate to solve some problems. In this study, a new generalized formulae is considered for the first time and derived from a loan payment model which is a certain number of payment amount determined by customer at the beginning of payment period and the other repayments with piecewise linear gradient series. As a result, some numerical examples with solutions are given for the developed models.
Liu, Xuele
2016-01-01
Finding new phase is a fundamental task in physics. Landau's theory explained the deep connection between symmetry breaking and phase transition commonly occurring in magnetic, superconducting and super uid systems. The discovery of the quantum Hall effect led to Z topological phases which could be different for same symmetry and are characterized by the discrete values of the Berry phases. By studying 1D trimer lattices we report new phases characterized by Berry phases which are piecewise continuous rather than discrete numbers. The phase transition occurs at the discontinuity point. With time-dependent changes, trimer lattices also give a 2D phases characterized by very specific 2D Berry phases of half period. These Berry phases change smoothly within a phase while change discontinuously at the transition point. We further demonstrate the existence of adiabatic pumping for each phase and gain assisted enhanced pumping. The non-reciprocity of the pumping process makes the system a good optical diode.
Averaging for a Fully-Coupled Piecewise Deterministic Markov Process in Infinite Dimension
Genadot, Alexandre
2011-01-01
In this paper, we consider the generalized Hodgkin-Huxley model introduced by Austin in \\cite{Austin}. This model describes the propagation of an action potential along the axon of a neuron at the scale of ion channels. Mathematically, this model is a fully-coupled Piecewise Deterministic Markov Process (PDMP) in infinite dimension. We introduce two time scales in this model in considering that some ion channels open and close at faster jump rates than others. We perform a slow-fast analysis of this model and prove that asymptotically this two time scales model reduces to the so called averaged model which is still a PDMP in infinite dimension for which we provide effective evolution equations and jump rates.
Locomotion of C. elegans: a piecewise-harmonic curvature representation of nematode behavior.
Directory of Open Access Journals (Sweden)
Venkat Padmanabhan
Full Text Available Caenorhabditis elegans, a free-living soil nematode, displays a rich variety of body shapes and trajectories during its undulatory locomotion in complex environments. Here we show that the individual body postures and entire trails of C. elegans have a simple analytical description in curvature representation. Our model is based on the assumption that the curvature wave is generated in the head segment of the worm body and propagates backwards. We have found that a simple harmonic function for the curvature can capture multiple worm shapes during the undulatory movement. The worm body trajectories can be well represented in terms of piecewise sinusoidal curvature with abrupt changes in amplitude, wavevector, and phase.
Stationary discrete solitons in a driven dissipative Bose-Hubbard chain
Naether, Uta; Quijandría, Fernando; García-Ripoll, Juan José; Zueco, David
2015-03-01
We demonstrate that stationary localized solutions (discrete solitons) exist in one-dimensional Bose-Hubbard lattices with gain and loss in a semiclassical regime. Stationary solutions, by definition, are robust and do not demand state preparation. Losses, unavoidable in experiments, are not a drawback, but a necessary ingredient for these modes to exist. The semiclassical calculations are complemented with their classical limit and dynamics based on a Gutzwiller ansatz. We argue that circuit quantum electrodynamic architectures are ideal platforms for realizing the physics developed here. Finally, within the input-output formalism, we explain how to experimentally access the different phases, including the solitons, of the chain.
3D Aware Correction and Completion of Depth Maps in Piecewise Planar Scenes
Thabet, Ali Kassem
2015-04-16
RGB-D sensors are popular in the computer vision community, especially for problems of scene understanding, semantic scene labeling, and segmentation. However, most of these methods depend on reliable input depth measurements, while discarding unreliable ones. This paper studies how reliable depth values can be used to correct the unreliable ones, and how to complete (or extend) the available depth data beyond the raw measurements of the sensor (i.e. infer depth at pixels with unknown depth values), given a prior model on the 3D scene. We consider piecewise planar environments in this paper, since many indoor scenes with man-made objects can be modeled as such. We propose a framework that uses the RGB-D sensor’s noise profile to adaptively and robustly fit plane segments (e.g. floor and ceiling) and iteratively complete the depth map, when possible. Depth completion is formulated as a discrete labeling problem (MRF) with hard constraints and solved efficiently using graph cuts. To regularize this problem, we exploit 3D and appearance cues that encourage pixels to take on depth values that will be compatible in 3D to the piecewise planar assumption. Extensive experiments, on a new large-scale and challenging dataset, show that our approach results in more accurate depth maps (with 20 % more depth values) than those recorded by the RGB-D sensor. Additional experiments on the NYUv2 dataset show that our method generates more 3D aware depth. These generated depth maps can also be used to improve the performance of a state-of-the-art RGB-D SLAM method.
Interior region-of-interest reconstruction using a small, nearly piecewise constant subregion.
Taguchi, Katsuyuki; Xu, Jingyan; Srivastava, Somesh; Tsui, Benjamin M W; Cammin, Jochen; Tang, Qiulin
2011-03-01
To develop a method to reconstruct an interior region-of-interest (ROI) image with sufficient accuracy that uses differentiated backprojection (DBP) projection onto convex sets (POCS) [H. Kudo et al., "Tiny a priori knowledge solves the interior problem in computed tomography," Phys. Med. Biol. 53, 2207-2231 (2008)] and a tiny knowledge that there exists a nearly piecewise constant subregion. The proposed method first employs filtered backprojection to reconstruct an image on which a tiny region P with a small variation in the pixel values is identified inside the ROI. Total variation minimization [H. Yu and G. Wang, "Compressed sensing based interior tomography," Phys. Med. Biol. 54, 2791-2805 (2009); W. Han et al., "A general total variation minimization theorem for compressed sensing based interior tomography," Int. J. Biomed. Imaging 2009, Article 125871 (2009)] is then employed to obtain pixel values in the subregion P, which serve as a priori knowledge in the next step. Finally, DBP-POCS is performed to reconstruct f(x,y) inside the ROI. Clinical data and the reconstructed image obtained by an x-ray computed tomography system (SOMATOM Definition; Siemens Healthcare) were used to validate the proposed method. The detector covers an object with a diameter of approximately 500 mm. The projection data were truncated either moderately to limit the detector coverage to Ø 350 mm of the object or severely to cover Ø199 mm. Images were reconstructed using the proposed method. The proposed method provided ROI images with correct pixel values in all areas except near the edge of the ROI. The coefficient of variation, i.e., the root mean square error divided by the mean pixel values, was less than 2.0% or 4.5% with the moderate or severe truncation cases, respectively, except near the boundary of the ROI. The proposed method allows for reconstructing interior ROI images with sufficient accuracy with a tiny knowledge that there exists a nearly piecewise constant
The Stiffness Variation of a Micro-Ring Driven by a Traveling Piecewise-Electrode
Directory of Open Access Journals (Sweden)
Yingjie Li
2014-09-01
Full Text Available In the practice of electrostatically actuated micro devices; the electrostatic force is implemented by sequentially actuated piecewise-electrodes which result in a traveling distributed electrostatic force. However; such force was modeled as a traveling concentrated electrostatic force in literatures. This article; for the first time; presents an analytical study on the stiffness variation of microstructures driven by a traveling piecewise electrode. The analytical model is based on the theory of shallow shell and uniform electrical field. The traveling electrode not only applies electrostatic force on the circular-ring but also alters its dynamical characteristics via the negative electrostatic stiffness. It is known that; when a structure is subjected to a traveling constant force; its natural mode will be resonated as the traveling speed approaches certain critical speeds; and each natural mode refers to exactly one critical speed. However; for the case of a traveling electrostatic force; the number of critical speeds is more than that of the natural modes. This is due to the fact that the traveling electrostatic force makes the resonant frequencies of the forward and backward traveling waves of the circular-ring different. Furthermore; the resonance and stability can be independently controlled by the length of the traveling electrode; though the driving voltage and traveling speed of the electrostatic force alter the dynamics and stabilities of microstructures. This paper extends the fundamental insights into the electromechanical behavior of microstructures driven by electrostatic forces as well as the future development of MEMS/NEMS devices with electrostatic actuation and sensing.
The Northern Hemisphere winter stationary wave response to global warming in CMIP5
Simpson, Isla; Seager, Richard; Ting, Mingfang; Shaw, Tiffany
2015-04-01
During the Northern Hemisphere winter, models tend to predict a poleward shifting of the zonal mean mid-latitude westerlies under anthropogenic greenhouse gas emissions. Locally, however, changes in the stationary waves tend to dominate, resulting in considerable deviation from this around the longitude circle, with important implications for regional climate change. Past studies have demonstrated diversity in the stationary wave response to global warming and differ in their views of the mechanisms involved in producing it. Here we will explore the stationary wave response to global warming in the CMIP5 dataset and demonstrate a strong consensus on a wavenumber 5 stationary wave response with a particular phasing that contributes to hydroclimate change across North America and Europe, such as wetting on the west coast of the USA, drying in the south west USA and drying in the eastern Mediterranean. The mechanisms responsible for producing this multi-model mean response are explored using a stationary wave model. It is demonstrated that, to first order, it is produced by changes in the zonal mean basic state, in agreement with the majority of previous stationary wave modelling studies. The relative importance of different features of this basic state change such as Arctic amplification, enhanced tropical upper tropospheric warming, stratospheric cooling and their associated zonal mean zonal wind responses will be explored. Through an understanding of the mechanisms involved in this stationary wave response we can begin to assess our confidence in whether the real world will behave as the models do and understand any diversity among the modelled responses.
Convergence Rate to Stationary Solutions for Boltzmann Equation with External Force
Institute of Scientific and Technical Information of China (English)
Seiji UKAI; Tong YANG; Huijiang ZHAO
2006-01-01
For the Boltzmann equation with an external force in the form of the gradient of a potential function in space variable, the stability of its stationary solutions as local Maxwellians was studied by S. Ukai et al. (2005) through the energy method. Based on this stability analysis and some techniques on analyzing the convergence rates to stationary solutions for the compressible Navier-Stokes equations, in this paper, we study the convergence rate to the above stationary solutions for the Boltzmann equation which is a fundamental equation in statistical physics for non-equilibrium rarefied gas. By combining the dissipation from the viscosity and heat conductivity on the fluid components and the dissipation on the non-fluid component through the celebrated H-theorem, a convergence rate of the same order as the one for the compressible Navier-Stokes is obtained by constructing some energy functionals.
Compounding approach for univariate time series with non-stationary variances
Schäfer, Rudi; Guhr, Thomas; Stöckmann, Hans-Jürgen; Kuhl, Ulrich
2015-01-01
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent parameters. To model the long-term statistical behavior, we compound the local distribution with the distribution of its parameters. Here we consider two concrete, but diverse examples of such non-stationary systems, the turbulent air flow of a fan and a time series of foreign exchange rates. Our main focus is to empirically determine the appropriate parameter distribution for the compounding approach. To this end we have to estimate the parameter distribution for univariate time series in a highly non-stationary situation.
Universal portfolios generated by weakly stationary processes
Tan, Choon Peng; Pang, Sook Theng
2014-12-01
Recently, a universal portfolio generated by a set of independent Brownian motions where a finite number of past stock prices are weighted by the moments of the multivariate normal distribution is introduced and studied. The multivariate normal moments as polynomials in time consequently lead to a constant rebalanced portfolio depending on the drift coefficients of the Brownian motions. For a weakly stationary process, a different type of universal portfolio is proposed where the weights on the stock prices depend only on the time differences of the stock prices. An empirical study is conducted on the returns achieved by the universal portfolios generated by the Ornstein-Uhlenbeck process on selected stock-price data sets. Promising results are demonstrated for increasing the wealth of the investor by using the weakly-stationary-process-generated universal portfolios.
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, M.; Illerup, J. B.
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are SO2, NOX, NMVOC, CH4, CO, CO2, N2O, particulate matter, heavy metals, dioxins and PAH. Since 1990 the fuel consumption...... in stationary combustion has increased by 14% - the fossil fuel consumption however only by 8%. Despite the increased fuel consumption the emission of several pollutants has decreased due to the improved flue gas cleaning technology, improved burner technology and the change of fuel type used. A considerable...... decrease of the SO2, NOX and heavy metal emissions is mainly a result of decreased emissions from large power plants and waste incineration plants. The greenhouse gas emission has decreased 1,3% since 1990. The emission of CH4, however, has increased due to increased use of lean-burn gas engines in CHP...
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, M.; Illerup, J. B.
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are: SO2, NOx, NMVOC, CH4, CO, CO2, N2O, particulate matter, heavy metals, dioxins and PAH. Since 1990 the fuel consumption...... in stationary combustion has increased by 12% - the fossil fuel consumption however only by 6%. Despite the increased fuel consumption the emission of several pollutants have decreased due to the improved flue gas cleaning technology, improved burner technology and the change of fuel type used. A considerable...... decrease of the SO2, NOx and heavy metal emissions is mainly a result of decreased emissions from large power plants and waste incineration plants. The greenhouse gas emission has decreased 1,5% since 1990. The emission of CH4, however, has increased due to increased use of lean-burn gas engines in CHP...
Stationary populations with below-replacement fertility
Directory of Open Access Journals (Sweden)
Carl Schmertmann
2012-04-01
Full Text Available BACKGROUND A population with sustained below-replacement fertility and constant immigration eventually becomes stationary. Stationary-through-immigration (SI populations have unusual age structures that depend on the distribution of immigrants' arrival ages. OBJECTIVE I summarize known formal relationships between the distribution of immigrants' entry ages and the long-run size and structure of SI populations. I clarify a previously published result about SI dependency ratios. RESULTS The long-run size and age structure of an SI population depend on the remaining life expectancies of arriving immigrants, but are also sensitive to the expected numbers of native children born after arrival. Numerical calculations with contemporary Austrian data show (1 contrary to previously published results, immigration flows need not be concentrated in early working ages in order to ensure low overall dependency, and (2 the SI dependency ratio is minimized when all immigrants are in their mid-30s.
Stationary SMS lenses for concentrating photovoltaics
Kotsidas, Panagiotis; Chatzi, Eleni; Modi, Vijay
2010-08-01
This paper presents a novel approach regarding the design of stationary, non imaging, refractive lenses with high acceptance angles. A lens lies on a stationary aperture and as the sun moves throughout the day, the concentrated focal spot is tracked by a moving solar cell. The purpose of this work is to replace the 2-axis tracking of the sun with internal motion of the miniaturized solar cell inside the module. We show families of linear lenses with wide acceptance angles 60. and 30. achieving moderate concentrations of 10 - 30 suns. The lens is designed with a variation of the simultaneous multiple surface (SMS) technique which is combined with a genetic algorithm to optimize the free variables of the problem.
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, M.; Illerup, J. B.
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are SO2, NOX, NMVOC, CH4, CO, CO2, N2O, particulate matter, heavy metals, dioxins and PAH. Since 1990 the fuel consumption...... in stationary combustion has increased by 14% - the fossil fuel consumption however only by 8%. Despite the increased fuel consumption the emission of several pollutants has decreased due to the improved flue gas cleaning technology, improved burner technology and the change of fuel type used. A considerable...... plants. The emission of PAH increased as a result of the increased combustion of wood in residential boilers and stoves. Uncertainties for the emissions and trends have been estimated...
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, M.; Illerup, J. B.
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are: SO2, NOx, NMVOC, CH4, CO, CO2, N2O, particulate matter, heavy metals, dioxins and PAH. Since 1990 the fuel consumption...... in stationary combustion has increased by 12% - the fossil fuel consumption however only by 6%. Despite the increased fuel consumption the emission of several pollutants have decreased due to the improved flue gas cleaning technology, improved burner technology and the change of fuel type used. A considerable...... plants. The emission of PAH increased as a result of the increased combustion of wood in residential boilers and stoves. Uncertainties for the emissions and trends have been estimated....
EDITORIAL: CAMOP: Quantum Non-Stationary Systems CAMOP: Quantum Non-Stationary Systems
Dodonov, Victor V.; Man'ko, Margarita A.
2010-09-01
QED. Another rapidly growing research field (although its origin can be traced to the beginning of the 1980s) is the quantum control of evolution at the microscopic level. These examples show that quantum non-stationary systems continue to be a living and very interesting part of quantum physics, uniting researchers from many different areas. Thus it is no mere chance that several special scientific meetings devoted to these topics have been organized recently. One was the international seminar 'Time-Dependent Phenomena in Quantum Mechanics' organized by Manfred Kleber and Tobias Kramer in 2007 at Blaubeuren, Germany. The proceedings of that event were published in 2008 as volume 99 of Journal of Physics: Conference Series. Another recent meeting was the International Workshop on Quantum Non-Stationary Systems, held on 19-23 October 2009 at the International Center for Condensed Matter Physics (ICCMP) in Brasilia, Brazil. It was organized and directed by Victor Dodonov (Institute of Physics, University of Brasilia, Brazil), Vladimir Man'ko (P N Lebedev Physical Institute, Moscow, Russia) and Salomon Mizrahi (Physics Department, Federal University of Sao Carlos, Brazil). This event was accompanied by a satellite workshop 'Quantum Dynamics in Optics and Matter', organized by Salomon Mizrahi and Victor Dodonov on 25-26 October 2009 at the Physics Department of the Federal University of Sao Carlos, Brazil. These two workshops, supported by the Brazilian federal agencies CAPES and CNPq and the local agencies FAP-DF and FAPESP, were attended by more than 120 participants from 16 countries. Almost 50 invited talks and 20 poster presentations covered a wide area of research in quantum mechanics, quantum optics and quantum information. This special issue of CAMOP/Physica Scripta contains contributions presented by some invited speakers and participants of the workshop in Brasilia. Although they do not cover all of the wide spectrum of problems related to quantum non-stationary
Superheater Tube Flat Wall Stationary Temperature Field
Directory of Open Access Journals (Sweden)
Parpiev A.T.
2016-01-01
Full Text Available The BKZ-220-100-9 steam generator platen superheater tube flat wall stationary temperature fields analysis have been made. The six steel grades, using in boiler fabrication, namely, St. 10, St. 20, 12H1MF, 15HM, 1H18N9T and 12H18N12T, have been used. The temperature curves calculation has been made by using outer and inner surface heat-transfer coefficients nine different combinations.
Canceling Stationary Interference Signals Exploiting Secondary Data
Swärd, Johan; Jakobsson, Andreas
2014-01-01
In this paper, we propose a novel interference cancellation method that exploits secondary data to estimate stationary interference components present in both the primary and the secondary data sets, thereby allowing for the removal of such interference from the data sets, even when these components share frequencies with the signal of interest. The algorithm estimates the present interference components one frequency at a time, thus enabling for a computationally efficient algorithm, that re...
Capacity of the Stationary Gaussian Channel
1988-03-01
defined by a covariance function rW - 1 - corresponding to a rational spectral density function 4w. Hw will denote the REHS of rw with parameter set tO,m...wide sense (w.s.) stationary processes X with a SDF ( spectral density function ), denoted by tx, such that I/Ow is bounded and f A -{X)d& 2rP. The
Variance of partial sums of stationary sequences
Deligiannidis, George
2012-01-01
Let $X_1, X_2,...$ be a centred sequence of weakly stationary random variables with spectral measure $F$ and partial sums $S_n = X_1 +...+ X_n$, and let $G(x) = \\int_{-x}^x F(\\rd x)$. We show that $\\var(S_n)$ is regularly varying of index $\\gamma$ at infinity, if and only if $G(x)$ is regularly varying of index $2-\\gamma$ at the origin ($0<\\gamma<2$).
Generalization error bounds for stationary autoregressive models
McDonald, Daniel J; Schervish, Mark
2011-01-01
We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that the stationarity assumption alone lets us treat the estimation of AR models as a regularized kernel regression without the need to further regularize the model arbitrarily. We thereby bound the Rademacher complexity of AR models and apply existing Rademacher complexity results to characterize the predictive risk of AR models. We demonstrate our methods by predicting interest rate movements.
49 CFR 325.55 - Ambient conditions; stationary test.
2010-10-01
... 49 Transportation 5 2010-10-01 2010-10-01 false Ambient conditions; stationary test. 325.55... MOTOR CARRIER NOISE EMISSION STANDARDS Measurement of Noise Emissions; Stationary Test § 325.55 Ambient conditions; stationary test. (a)(1) Sound. The ambient A-weighted sound level at the microphone...
Towards Fluid Instabilities of Stationary Non-Killing Horizons
Fischetti, Sebastian
2016-01-01
Flowing black holes are asymptotically locally AdS spacetimes that are stationary but have non-Killing horizons. Holographically, they are dual to a steady-state heat flow in the boundary field theory. We investigate the stability of these black holes in the limit in which they are well-described by the relativistic conformal Navier-Stokes equations. More precisely, we study the quasi-normal modes of the linearized ideal fluid equations. Though we find no unstable modes, there are an infinite number at finite transverse momentum which are arbitrarily long-lived. This suggests the possibility that either non-modal effects or nonlinear interactions between these modes can give rise to new types of gravitational instabilities.
Towards fluid instabilities of stationary non-Killing horizons
Fischetti, Sebastian; Way, Benson
2016-12-01
Flowing black holes are asymptotically locally AdS spacetimes that are stationary but have non-Killing horizons. Holographically, they are dual to a steady-state heat flow in the boundary field theory. We investigate the stability of these black holes in the limit in which they are well-described by the relativistic conformal Navier-Stokes equation. More precisely, we study the quasi-normal modes of the linearized ideal fluid equations. Though we find no unstable modes, there are an infinite number of modes at finite transverse momentum which are arbitrarily long-lived. This suggests the possibility that either non-modal effects or nonlinear interactions between these modes can give rise to new types of gravitational instabilities.
DEFF Research Database (Denmark)
Hovmøller, M.S.; Munk, L.; Østergård, Hanne
1995-01-01
Gene frequencies in samples of aerial populations of barley powdery mildew (Erysiphe graminis f.sp. hordei), which were collected in adjacent barley areas and in successive periods of time, were compared using mobile and stationary sampling techniques. Stationary samples were collected from trap...... by the stationary technique will mainly reflect the source varieties present in the local area, whereas samples collected by the mobile spore trap will mainly reflect sources close to the sampling route. Therefore, sampling sites as well as sampling routes should be defined such that source varieties...... plants in three periods within 1 week at a distance of more than 1000 m from the nearest barley field. At four dates within the same 8-day period, other samples were collected by a mobile spore trap along four sampling routes of a total distance of 130 km around the stationary stand of exposure...
Sandhu, Ali Imran
2016-04-10
A sparsity-regularized Born iterative method (BIM) is proposed for efficiently reconstructing two-dimensional piecewise-continuous inhomogeneous dielectric profiles. Such profiles are typically not spatially sparse, which reduces the efficiency of the sparsity-promoting regularization. To overcome this problem, scattered fields are represented in terms of the spatial derivative of the dielectric profile and reconstruction is carried out over samples of the dielectric profile\\'s derivative. Then, like the conventional BIM, the nonlinear problem is iteratively converted into a sequence of linear problems (in derivative samples) and sparsity constraint is enforced on each linear problem using the thresholded Landweber iterations. Numerical results, which demonstrate the efficiency and accuracy of the proposed method in reconstructing piecewise-continuous dielectric profiles, are presented.
Ibáñez, Javier; Hernández, Vicente
2011-03-01
Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied physics and engineering. For example, these equations play a fundamental role in control theory, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a new method based on a theorem proved in this paper is described for solving DMREs by a piecewise-linearized approach. This method is applied for developing two block-oriented algorithms based on diagonal Padé approximants. MATLAB versions of the above algorithms are developed, comparing, under equal conditions, accuracy and computational costs with other piecewise-linearized algorithms implemented by the authors. Experimental results show the advantages of solving stiff or non-stiff DMREs by the implemented algorithms.
Hernández-Lloreda, María Victoria; Colmenares, Fernando; Martínez-Arias, Rosario
2004-09-01
In behavioral science, developmental discontinuities are thought to arise when the association between an outcome measure and the underlying process changes over time. Sudden changes in behavior across time are often taken to indicate that a reorganization in the outcome-process relationship may have occurred. The authors proposed in this article the use of piecewise hierarchical linear growth modeling as a statistical methodology to search for discontinuities in behavioral development and illustrated its possibilities by applying 2-piece hierarchical linear models to the study of developmental trajectories of baboon (Papio hamadryas) mothers' behavior during their infants' 1st year of life. The authors provided empirical evidence that piecewise growth modeling can be used to determine whether abrupt changes in development trajectories are tied to changes in the underlying process. ((c) 2004 APA, all rights reserved).
Venkatesh, P. R.; Venkatesan, A.
2016-10-01
We report the occurrence of vibrational resonance in piecewise-linear non-autonomous system. Especially, we show that an optimal amplitude of the high frequency second harmonic driving enhances the response of a piece-wise linear non-autonomous Murali-Lakshmanan-Chua (MLC) system to a low frequency first harmonic signal. This phenomenon is illustrated with the analytical solutions of circuit equations characterising the system and finally compared with the numerical method. Further, it has been enunciated explicitly, the implementation of the fundamental NOR/NAND gate via vibrational resonance, both by numerical and analytical solutions. In addition, these logical behaviours (AND/NAND/OR/NOR) can be decided by the amplitude of the input square waves without altering the system parameters.
Institute of Scientific and Technical Information of China (English)
康宝生; 贺文杰
2002-01-01
An interpolation scheme constructing shape preserving piecewise de-gree 2k parametric polynomial curves is presented. For the given data set {Qi＝(x1,yi) }n i-0, the shape preserving interpolation curve is Gk continuous.
Stationary Black Holes: Uniqueness and Beyond
Directory of Open Access Journals (Sweden)
Piotr T. Chruściel
2012-05-01
Full Text Available The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.
Stationary Black Holes: Uniqueness and Beyond
Directory of Open Access Journals (Sweden)
Heusler Markus
1998-01-01
Full Text Available The spectrum of known black hole solutions to the stationary Einstein equations has increased in an unexpected way during the last decade. In particular, it has turned out that not all black hole equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black hole space-times ceases to exist in self-gravitating non-linear field theories. This text aims to review some of the recent developments and to discuss them in the light of the uniqueness theorem for the Einstein-Maxwell system.
Stationary stochastic processes for scientists and engineers
Lindgren, Georg; Sandsten, Maria
2013-01-01
""This book is designed for a first course in stationary stochastic processes in science and engineering and does a very good job in introducing many concepts and ideas to students in these fields. … the book has probably been tested in the classroom many times, which also manifests itself in its virtual lack of typos. … Another great feature of the book is that it contains a wealth of worked example from many different fields. These help clarify concepts and theorems and I believe students will appreciate them-I certainly did. … The book is well suited for a one-semester course as it contains
Carbon nanotube stationary phases for microchip electrochromatography
DEFF Research Database (Denmark)
Mogensen, Klaus Bo; Bøggild, Peter; Kutter, Jörg Peter
nanotubes are very interesting for integration in especially microfluidic devices, because they can readily be grown on planar substrates by means of chemical vapour deposition. In this way the cumbersome process of packing of the stationary phase in the finished microfluidic channels is avoided and the CNT......, microfluidic devices with microfabricated carbon nanotube columns for electrochromatographic separations will be presented. The electrically conductive carbon nanotube layer has been patterned into hexoganol micropillars in order to support electroosmotic flow without forming gas bubbles from electrolysis...
Numerical Methods for Finding Stationary Gravitational Solutions
Dias, Oscar J C; Way, Benson
2015-01-01
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly-spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory-Laflamme zero modes of small rotating black holes in AdS$_5\\times S^5$. We also include several tools and tricks that have been useful throughout the literature.
Energy Technology Data Exchange (ETDEWEB)
Rajpathak, Bhooshan, E-mail: bhooshan@ee.iitb.ac.in; Pillai, Harish K., E-mail: hp@ee.iitb.ac.in [Department of Electrical Engineering, IIT Bombay, Mumbai 400076 (India); Bandyopadhyay, Santanu, E-mail: santanu@me.iitb.ac.in [Department of Energy Science and Engineering, IIT Bombay, Mumbai 400076 (India)
2015-10-15
In this paper, we analytically examine the unstable periodic orbits and chaotic orbits of the 1-D linear piecewise-smooth discontinuous map. We explore the existence of unstable orbits and the effect of variation in parameters on the coexistence of unstable orbits. Further, we show that this structuring is different from the well known period adding cascade structure associated with the stable periodic orbits of the same map. Further, we analytically prove the existence of chaotic orbit for this map.
Xia, Youshen; Feng, Gang; Wang, Jun
2004-09-01
This paper presents a recurrent neural network for solving strict convex quadratic programming problems and related linear piecewise equations. Compared with the existing neural networks for quadratic program, the proposed neural network has a one-layer structure with a low model complexity. Moreover, the proposed neural network is shown to have a finite-time convergence and exponential convergence. Illustrative examples further show the good performance of the proposed neural network in real-time applications.
Development and evaluation of the piecewise Prony method for evoked potential analysis.
Garoosi, V; Jansen, B H
2000-12-01
A new method is presented to decompose nonstationary signals into a summation of oscillatory components with time varying frequency, amplitude, and phase characteristics. This method, referred to as piecewise Prony method (PPM), is an improvement over the classical Prony method, which can only deal with signals containing components with fixed frequency, amplitude and phase, and monotonically increasing or decreasing rate of change. PPM allows the study of the temporal profile of post-stimulus signal changes in single-trial evoked potentials (EPs), which can lead to new insights in EP generation. We have evaluated this method on simulated data to test its limitations and capabilities, and also on single-trial EPs. The simulation experiments showed that the PPM can detect amplitude changes as small as 10%, rate changes as small as 10%, and 0.15 Hz of frequency changes. The capabilities of the PPM were demonstrated using single electroencephalogram/EP trials of flash visual EPs recorded from one normal subject. The trial-by-trial results confirmed that the stimulation drastically attenuates the alpha activity shortly after stimulus presentation, with the alpha activity returning about 0.5 s later. The PPM results also provided evidence that delta activity undergoes phase alignment following stimulus presentation.
A few remarks on recurrence relations for geometrically continuous piecewise Chebyshevian B-splines
Mazure, Marie-Laurence
2009-08-01
This works complements a recent article (Mazure, J. Comp. Appl. Math. 219(2):457-470, 2008) in which we showed that T. Lyche's recurrence relations for Chebyshevian B-splines (Lyche, Constr. Approx. 1:155-178, 1985) naturally emerged from blossoms and their properties via de Boor type algorithms. Based on Chebyshevian divided differences, T. Lyche's approach concerned splines with all sections in the same Chebyshev space and with ordinary connections at the knots. Here, we consider geometrically continuous piecewise Chebyshevian splines, namely, splines with sections in different Chebyshev spaces, and with geometric connections at the knots. In this general framework, we proved in (Mazure, Constr. Approx. 20:603-624, 2004) that existence of B-spline bases could not be separated from existence of blossoms. Actually, the present paper enhances the powerfulness of blossoms in which not only B-splines are inherent, but also their recurrence relations. We compare this fact with the work by G. Mühlbach and Y. Tang (Mühlbach and Tang, Num. Alg. 41:35-78, 2006) who obtained the same recurrence relations via generalised Chebyshevian divided differences, but only under some total positivity assumption on the connexion matrices. We illustrate this comparison with splines with four-dimensional sections. The general situation addressed here also enhances the differences of behaviour between B-splines and the functions of smaller and smaller supports involved in the recurrence relations.
Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes
Herencia-Zapana, Heber; Gonzalez, Oscar R.; Gray, W. Steven
2006-01-01
The analysis and design of practical control systems requires that stochastic models be employed. Analysis and design tools have been developed, for example, for Markovian jump linear continuous and discrete-time systems, piecewise-deterministic processes (PDP's), and general stochastic hybrid systems (GSHS's). These model classes have been used in many applications, including fault tolerant control and networked control systems. This paper presents initial results on the analysis of a sampled-data PDP representation of a nonlinear sampled-data system with a jump linear controller. In particular, it is shown that the state of the sampled-data PDP satisfies the strong Markov property. In addition, a relation between the invariant measures of a sampled-data system driven by a stochastic process and its associated discrete-time representation are presented. As an application, when the plant is linear with no external input, a sufficient testable condition for the convergence in distribution to the invariant delta Dirac measure is given.
Effect of stochastically moving border on basins of attraction in a class of piecewise smooth maps
Mandal, Dhrubajyoti; Banerjee, Soumitro
2017-07-01
Determination of the basin of attraction of an attractor plays an important role in understanding the dynamics of a system. In all the existing literature, the basin of attraction of any attractor has been described to be deterministic. In this paper we show the existence of a non-deterministic basin of attraction of an attractor. We have considered a piecewise smooth (PWS) one-dimensional map, having stochastically varying border, which is allowed to move in a small bounded region of the phase space while retaining the deterministic dynamics on each compartment of the phase space. In case of this type of systems there exists a region in the phase space with the property that orbits starting from a single point lying inside this region do not display the same property of convergence or divergence, i.e., one may converge while another may diverge. In other words, the convergence or divergence of an orbit starting from a point inside this region is a probabilistic event, and the probabilities of convergence and divergence are both non-zero. We also derive the upper and lower bounds of the corresponding probability curves. Since all physical systems contain noise, the occurrence of such non-deterministic basin of attraction is a definite possibility, if the noise affects the position of the border. This may lead to dangerous consequences, as a region of the basin of attraction of an attractor may become non-deterministic, with a non-zero probability of divergence of orbits starting inside it.
Linear vs. piecewise Weibull model for genetic evaluation of sires for longevity in Simmental cattle
Directory of Open Access Journals (Sweden)
Nikola Raguž
2014-09-01
Full Text Available This study was focused on genetic evaluation of longevity in Croatian Simmental cattle using linear and survival models. The main objective was to create a genetic model that is most appropriate to describe the longevity data. Survival analysis, using piecewise Weibull proportional hazards model, used all information on the length of productive life including censored as well as uncensored observations. Linear models considered culled animals only. The relative milk production within herd had a highest impact on cows’ longevity. In comparison of estimated genetic parameters among methods, survival analysis yielded higher heritability value (0.075 than linear sire (0.037 and linear animal model (0.056. When linear models were used, genetic trend of Simmental bulls for longevity was slightly increasing over the years, unlike a decreasing trend in case of survival analysis methodology. Average reliability of bulls’ breeding values was higher in case of survival analysis. The rank correlations between survival analysis and linear models bulls’ breeding values for longevity were ranged between 0.44 and 0.46 implying huge differences in ranking of sires.
Piecewise compensation for the nonlinear error of fiber-optic gyroscope scale factor
Zhang, Yonggang; Wu, Xunfeng; Yuan, Shun; Wu, Lei
2013-08-01
Fiber-Optic Gyroscope (FOG) scale factor nonlinear error will result in errors in Strapdown Inertial Navigation System (SINS). In order to reduce nonlinear error of FOG scale factor in SINS, a compensation method is proposed in this paper based on curve piecewise fitting of FOG output. Firstly, reasons which can result in FOG scale factor error are introduced and the definition of nonlinear degree is provided. Then we introduce the method to divide the output range of FOG into several small pieces, and curve fitting is performed in each output range of FOG to obtain scale factor parameter. Different scale factor parameters of FOG are used in different pieces to improve FOG output precision. These parameters are identified by using three-axis turntable, and nonlinear error of FOG scale factor can be reduced. Finally, three-axis swing experiment of SINS verifies that the proposed method can reduce attitude output errors of SINS by compensating the nonlinear error of FOG scale factor and improve the precision of navigation. The results of experiments also demonstrate that the compensation scheme is easy to implement. It can effectively compensate the nonlinear error of FOG scale factor with slightly increased computation complexity. This method can be used in inertial technology based on FOG to improve precision.
Piecewise log-normal approximation of size distributions for aerosol modelling
Directory of Open Access Journals (Sweden)
K. von Salzen
2006-01-01
Full Text Available An efficient and accurate method for the representation of particle size distributions in atmospheric models is proposed. The method can be applied, but is not necessarily restricted, to aerosol mass and number size distributions. A piecewise log-normal approximation of the number size distribution within sections of the particle size spectrum is used. Two of the free parameters of the log-normal approximation are obtained from the integrated number and mass concentration in each section. The remaining free parameter is prescribed. The method is efficient in a sense that only relatively few calculations are required for applications of the method in atmospheric models. Applications of the method in simulations of particle growth by condensation and simulations with a single column model for nucleation, condensation, gravitational settling, wet deposition, and mixing are described. The results are compared to results from simulations employing single- and double-moment bin methods that are frequently used in aerosol modelling. According to these comparisons, the accuracy of the method is noticeably higher than the accuracy of the other methods.
Directory of Open Access Journals (Sweden)
Yanan Liu
2016-10-01
Full Text Available There are many uncertainties and risks in residential electricity consumption associated with economic development. Knowledge of the relationship between residential electricity consumption and its key determinant—income—is important to the sustainable development of the electric power industry. Using panel data from 30 provinces for the 1995–2012 period, this study investigates how residential electricity consumption changes as incomes increase in China. Previous studies typically used linear or quadratic double-logarithmic models imposing ex ante restrictions on the indistinct relationship between residential electricity consumption and income. Contrary to those models, we employed a reduced piecewise linear model that is self-adaptive and highly flexible and circumvents the problem of “prior restrictions”. Robust tests of different segment specifications and regression methods are performed to ensure the validity of the research. The results provide strong evidence that the income elasticity was approximately one, and it remained stable throughout the estimation period. The income threshold at which residential electricity consumption automatically remains stable or slows has not been reached. To ensure the sustainable development of the electric power industry, introducing higher energy efficiency standards for electrical appliances and improving income levels are vital. Government should also emphasize electricity conservation in the industrial sector rather than in residential sector.
Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system
Sarrouy, E.; Dessombz, O.; Sinou, J.-J.
2013-02-01
This paper proposes numerical developments based on polynomial chaos (PC) expansions to process stochastic eigenvalue problems efficiently. These developments are applied to the problem of linear stability calculations for a simplified brake system: the stability of a finite element model of a brake is investigated when its friction coefficient or the contact stiffness are modeled as random parameters. Getting rid of the statistical point of view of the PC method but keeping the principle of a polynomial decomposition of eigenvalues and eigenvectors, the stochastic space is decomposed into several elements to realize a low degree piecewise polynomial approximation of these quantities. An approach relying on continuation principles is compared to the classical dichotomy method to build the partition. Moreover, a criterion for testing accuracy of the decomposition over each cell of the partition without requiring evaluation of exact eigenmodes is proposed and implemented. Several random distributions are tested, including a uniform-like law for description of friction coefficient variation. Results are compared to Monte Carlo simulations so as to determine the method accuracy and efficiency. Some general rules relative to the influence of the friction coefficient or the contact stiffness are also inferred from these calculations.
Institute of Scientific and Technical Information of China (English)
Lu Kun; Liu Xingzhao
2005-01-01
Recognition and correction of ionospheric phase path contamination is a vital part of the global radar signal processing sequence. A number of model-based correction algorithms have been developed to deal with the radar performance degradation due to the ionospheric distortion and contamination. This paper addresses a novel parametric estimation and compensation method based on High-order Ambiguity Function (HAF) to solve the problem of phase path contamination of HF skywave radar signals. When signal-to-noise ratio and data sequence available satisfy the predefined conditions, the ionospheric phase path contamination may be modeled by a polynomial phase signal (PPS). As a new parametric tool for analyzing the PPS, HAF is introduced to estimate parameters of the polynomial-phase model and reconstruct the correction signal. Using the reconstructed correction signal, compensation can be performed before coherent integration so that the original echo spectrum can be restored. A piecewise scheme is proposed to track rapid variation of the phase contamination based on HAF method, and it can remove the Doppler spread effect caused by the ionos phere nonstationarity. Simulation and experimental results are given to demonstrate the efficiency of the proposed algorithm.
Directory of Open Access Journals (Sweden)
Veronica Chan
2017-03-01
Full Text Available This paper presents the application of a neural network rule extraction algorithm, called the piece-wise linear artificial neural network or PWL-ANN algorithm, on a carbon capture process system dataset. The objective of the application is to enhance understanding of the intricate relationships among the key process parameters. The algorithm extracts rules in the form of multiple linear regression equations by approximating the sigmoid activation functions of the hidden neurons in an artificial neural network (ANN. The PWL-ANN algorithm overcomes the weaknesses of the statistical regression approach, in which accuracies of the generated predictive models are often not satisfactory, and the opaqueness of the ANN models. The results show that the generated PWL-ANN models have accuracies that are as high as the originally trained ANN models of the four datasets of the carbon capture process system. An analysis of the extracted rules and the magnitude of the coefficients in the equations revealed that the three most significant parameters of the CO2 production rate are the steam flow rate through reboiler, reboiler pressure, and the CO2 concentration in the flue gas.
Directory of Open Access Journals (Sweden)
Shujin Qin
2016-01-01
Full Text Available Workforce scheduling is an important and common task for projects with high labour intensities. It becomes particularly complex when employees have multiple skills and the employees’ productivity changes along with their learning of knowledge according to the tasks they are assigned to. Till now, in this context, only little work has considered the minimum quality limit of tasks and the quality learning effect. In this research, the workforce scheduling model is developed for assigning tasks to multiskilled workforce by considering learning of knowledge and requirements of project quality. By using piecewise linearization to learning curve, the mixed 0-1 nonlinear programming model (MNLP is transformed into a mixed 0-1 linear programming model (MLP. After that, the MLP model is further improved by taking account of the upper bound of employees’ experiences accumulation, and the stable performance of mature employees. Computational experiments are provided using randomly generated instances based on the investigation of a software company. The results demonstrate that the proposed MLPs can precisely approach the original MNLP model but can be calculated in much less time.
Directory of Open Access Journals (Sweden)
Dongmei Huang
2017-01-01
Full Text Available The principal resonance of a delayed piecewise-smooth (DPWS system with negative stiffness under narrow-band random excitation is investigated in aspects of multiscale analysis, design methodology of the controller, and response properties. The amplitude-frequency response and steady-state moments together with the corresponding stability conditions of the controlled stochastic system are derived, in which the degradation case is also under consideration. Then, from the perspective of the equivalent damping, the comparisons of the response characteristics of the controlled system to the uncontrolled system, such as the phenomenon of frequency island, are fulfilled. Furthermore, sensitivity of the system response to feedback gain and time delay is studied and interesting dynamic properties are found. Meanwhile, the classification of the steady-state solution is also discussed. To control the maximum amplitude, the feedback parameters are determined by the frequency response together with stability boundaries which must be utilized to exclude the combinations of the unstable parameters. For the case with small noise intensity, mean-square responses present the similar characteristics to what is discussed in the deterministic case.
El Aroudi, Abdelali
2014-05-01
Recently, nonlinearities have been shown to play an important role in increasing the extracted energy of vibration-based energy harvesting systems. In this paper, we study the dynamical behavior of a piecewise linear (PWL) spring-mass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. Different configurations of the PWL model and their corresponding state-space regions are derived. Then, from this PWL model, extensive numerical simulations are carried out by computing time-domain waveforms, state-space trajectories and frequency responses under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Filippov method, Poincaré map modeling and finite difference method (FDM). The Floquet multipliers are calculated using these three approaches and a good concordance is obtained among them. The performance of the system in terms of the harvested energy is studied by considering both purely harmonic excitation and a noisy vibrational source. A frequency-domain analysis shows that the harvested energy could be larger at low frequencies as compared to an equivalent linear system, in particular, for relatively low excitation intensities. This could be an advantage for potential use of this system in low frequency ambient vibrational-based energy harvesting applications. © 2014 World Scientific Publishing Company.
Werner, Rolf; Valev, Dimitar; Danov, Dimitar; Guineva, Veneta
2015-12-01
The study of climate trends taking into consideration possible structural changes is important for understanding climate development characterized by a stochastic trend or by a determined one. In the paper global and hemisphere temperature anomalies are modeled by piecewise linear regression and break points in the temperature evolution are found. It was demonstrated that the used method allowed finding of breaks characterized by long time trends (low frequency processes) as well as abrupt changes (fast frequency processes). The obtained break points for slow temperature change are close to the ones found by other authors however additional conditions (as segment length, gradient and others) are not used here. The results for higher break point numbers are like the ones of step slope models. It was demonstrated that the successive phases of warming and cooling and most of the break points subdividing these periods in the Northern Hemisphere are introduced by the Atlantic multidecadal oscillation. Because the strong quasi periodicity of the Atlantic multidecadal oscillation the authors recommend the removal of its influence on the temperature from the temperature series before studies of trends or structural changes. The Northern Hemisphere temperature data after the removal of the Atlantic multidecadal oscillation influence show structures like the Southern Hemisphere temperatures. Model selection by the Schwarz-Bayesian Information Criterion developed by Liu, Wu and Zidek (LWZ criterion) shows that models with only one break point are to be preferred.
Piecewise-Constant-Model-Based Interior Tomography Applied to Dentin Tubules
Directory of Open Access Journals (Sweden)
Peng He
2013-01-01
Full Text Available Dentin is a hierarchically structured biomineralized composite material, and dentin’s tubules are difficult to study in situ. Nano-CT provides the requisite resolution, but the field of view typically contains only a few tubules. Using a plate-like specimen allows reconstruction of a volume containing specific tubules from a number of truncated projections typically collected over an angular range of about 140°, which is practically accessible. Classical computed tomography (CT theory cannot exactly reconstruct an object only from truncated projections, needless to say a limited angular range. Recently, interior tomography was developed to reconstruct a region-of-interest (ROI from truncated data in a theoretically exact fashion via the total variation (TV minimization under the condition that the ROI is piecewise constant. In this paper, we employ a TV minimization interior tomography algorithm to reconstruct interior microstructures in dentin from truncated projections over a limited angular range. Compared to the filtered backprojection (FBP reconstruction, our reconstruction method reduces noise and suppresses artifacts. Volume rendering confirms the merits of our method in terms of preserving the interior microstructure of the dentin specimen.
Akaishi, A.; Shudo, A.
2009-12-01
We investigate the stickiness of the two-dimensional piecewise linear map with a family of marginal unstable periodic orbits (FMUPOs), and show that a series of unstable periodic orbits accumulating to FMUPOs plays a significant role to give rise to the power law correlation of trajectories. We can explicitly specify the sticky zone in which unstable periodic orbits whose stability increases algebraically exist, and find that there exists a hierarchy in accumulating periodic orbits. In particular, the periodic orbits with linearly increasing stability play the role of fundamental cycles as in the hyperbolic systems, which allows us to apply the method of cycle expansion. We also study the recurrence time distribution, especially discussing the position and size of the recurrence region. Following the definition adopted in one-dimensional maps, we show that the recurrence time distribution has an exponential part in the short time regime and an asymptotic power law part. The analysis on the crossover time Tc∗ between these two regimes implies Tc∗˜-log[μ(R)] where μ(R) denotes the area of the recurrence region.
Canards in a minimal piecewise-linear square-wave burster
Desroches, M.; Fernández-García, S.; Krupa, M.
2016-07-01
We construct a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model that is minimal, in the sense that the vector field has the least number of linearity zones, in order to reproduce all the dynamics present in the original HR model with classical parameter values. This includes square-wave bursting and also special trajectories called canards, which possess long repelling segments and organise the transitions between stable bursting patterns with n and n + 1 spikes, also referred to as spike-adding canard explosions. We propose a first approximation of the smooth HR model, using a continuous PWL system, and show that its fast subsystem cannot possess a homoclinic bifurcation, which is necessary to obtain proper square-wave bursting. We then relax the assumption of continuity of the vector field across all zones, and we show that we can obtain a homoclinic bifurcation in the fast subsystem. We use the recently developed canard theory for PWL systems in order to reproduce the spike-adding canard explosion feature of the HR model as studied, e.g., in Desroches et al., Chaos 23(4), 046106 (2013).
Noise destroys the coexistence of periodic orbits of a piecewise linear map
Institute of Scientific and Technical Information of China (English)
Wang Can-Jun; Yang Ke-Li; Qu Shi-Xian
2013-01-01
The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5 (P-5) and period-6 (P-6) in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D =0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc ＜ τ ＜ τe',only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ ＞ τ'c(τc and τ'c are critical values),only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ ＜ τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.
Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.
Petrinović, Davor; Brezović, Marko
2011-04-01
We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device.
Weighted piecewise LDA for solving the small sample size problem in face verification.
Kyperountas, Marios; Tefas, Anastasios; Pitas, Ioannis
2007-03-01
A novel algorithm that can be used to boost the performance of face-verification methods that utilize Fisher's criterion is presented and evaluated. The algorithm is applied to similarity, or matching error, data and provides a general solution for overcoming the "small sample size" (SSS) problem, where the lack of sufficient training samples causes improper estimation of a linear separation hyperplane between the classes. Two independent phases constitute the proposed method. Initially, a set of weighted piecewise discriminant hyperplanes are used in order to provide a more accurate discriminant decision than the one produced by the traditional linear discriminant analysis (LDA) methodology. The expected classification ability of this method is investigated throughout a series of simulations. The second phase defines proper combinations for person-specific similarity scores and describes an outlier removal process that further enhances the classification ability. The proposed technique has been tested on the M2VTS and XM2VTS frontal face databases. Experimental results indicate that the proposed framework greatly improves the face-verification performance.
A micro-power LDO with piecewise voltage foldback current limit protection
Institute of Scientific and Technical Information of China (English)
Wei Hailong; Liu Youbao; Guo Zhongjie; Liao Xue
2012-01-01
To achieve a constant current limit,low power consumption and high driving capability,a micro-power LDO with a piecewise voltage-foldback current-limit circuit is presented.The current-limit threshold is dynamically adjusted to achieve a maximum driving capability and lower quiescent current of only 300 nA.To increase the loop stability of the proposed LDO,a high impedance transconductance buffer under a micro quiescent current is designed for splitting the pole that exists at the gate of the pass transistor to the dominant pole,and a zero is designed for the purpose of the second pole phase compensation.The proposed LDO is fabricated in a BiCMOS process.The measurement results show that the short-circuit current of the LDO is 190 mA,the constant limit current under a high drop-out voltage is 440 mA,and the maximum load current under a low drop-out voltage is up to 800 mA.In addition,the quiescent current of the LDO is only 7 μA,the load regulation is about 0.56％ on full scale,the line regulation is about 0.012％/V,the PSRR at 120 Hz is 58 dB and the drop-out voltage is only 70 mV when the load current is 250 mA.
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-01
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-28
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
Farag, Mohammed; Fleckenstein, Matthias; Habibi, Saeid
2017-02-01
Model-order reduction and minimization of the CPU run-time while maintaining the model accuracy are critical requirements for real-time implementation of lithium-ion electrochemical battery models. In this paper, an isothermal, continuous, piecewise-linear, electrode-average model is developed by using an optimal knot placement technique. The proposed model reduces the univariate nonlinear function of the electrode's open circuit potential dependence on the state of charge to continuous piecewise regions. The parameterization experiments were chosen to provide a trade-off between extensive experimental characterization techniques and purely identifying all parameters using optimization techniques. The model is then parameterized in each continuous, piecewise-linear, region. Applying the proposed technique cuts down the CPU run-time by around 20%, compared to the reduced-order, electrode-average model. Finally, the model validation against real-time driving profiles (FTP-72, WLTP) demonstrates the ability of the model to predict the cell voltage accurately with less than 2% error.
Feasibility of a stationary micro-SQUID
Berger, Jorge
2016-01-01
The standard operation of a dc SQUID leads to oscillatory electric fields that emit electromagnetic radiation and can change the state of the measured sample. A stationary SQUID could be advantageous when back action on the measured sample has to be avoided. We study a superconducting loop that encloses a magnetic flux, connected to a superconducting and to a normal electrode, when a fixed electric current between the electrodes flows through the loop. The considered circuit does not contain Josephson junctions. We find that in a very broad range of parameters the current flow converges to a stationary regime. The potential difference between the electrodes depends on the magnetic flux, so that measuring this voltage would provide information on the enclosed flux. The influence of thermal noise was estimated. The sizes of the voltage and of the power dissipation could be appropriate for the design of a practical fluxmeter. We found narrow ranges of flux at which the voltage varies sharply with the flux.
Information Spreading in Stationary Markovian Evolving Graphs
Clementi, Andrea; Pasquale, Francesco; Silvestri, Riccardo
2011-01-01
Markovian evolving graphs are dynamic-graph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamic-network scenarios. We study the speed of information spreading in the "stationary phase" by analyzing the completion time of the "flooding mechanism". We prove a general theorem that establishes an upper bound on flooding time in any stationary Markovian evolving graph in terms of its node-expansion properties. We apply our theorem in two natural and relevant cases of such dynamic graphs. "Geometric Markovian evolving graphs" where the Markovian behaviour is yielded by "n" mobile radio stations, with fixed transmission radius, that perform independent random walks over a square region of the plane. "Edge-Markovian evolving graphs" where the probability of existence of any edge at time "t" depends on the existence (or not) of the same edge at time "t-1". In both cases, the obtained upper...
Stationary versus non-stationary (13)C-MFA: a comparison using a consistent dataset.
Noack, Stephan; Nöh, Katharina; Moch, Matthias; Oldiges, Marco; Wiechert, Wolfgang
2011-07-10
Besides the well-established (13)C-metabolic flux analysis ((13)C-MFA) which characterizes a cell's fluxome in a metabolic and isotopic stationary state a current area of research is isotopically non-stationary MFA. Non-stationary (13)C-MFA uses short-time isotopic transient data instead of long-time isotopic equilibrium data and thus is capable to resolve fluxes within much shorter labeling experiments. However, a comparison of both methods with data from one single experiment has not been made so far. In order to create a consistent database for directly comparing both methods a (13)C-labeling experiment in a fed-batch cultivation with a Corynebacterium glutamicum lysine producer was carried out. During the experiment the substrate glucose was switched from unlabeled to a specifically labeled glucose mixture which was immediately traced by fast sampling and metabolite quenching. The time course of labeling enrichments in intracellular metabolites until isotopic stationarity was monitored by LC-MS/MS. The resulting dataset was evaluated using the classical as well as the isotopic non-stationary MFA approach. The results show that not only the obtained relative data, i.e. intracellular flux distributions, but also the more informative quantitative fluxome data significantly depend on the combination of the measurements and the underlying modeling approach used for data integration. Taking further criteria on the experimental and computational part into consideration, the current limitations of both methods are demonstrated and possible pitfalls are concluded.
Non-stationary blind deconvolution of medical ultrasound scans
Michailovich, Oleg V.
2017-03-01
In linear approximation, the formation of a radio-frequency (RF) ultrasound image can be described based on a standard convolution model in which the image is obtained as a result of convolution of the point spread function (PSF) of the ultrasound scanner in use with a tissue reflectivity function (TRF). Due to the band-limited nature of the PSF, the RF images can only be acquired at a finite spatial resolution, which is often insufficient for proper representation of the diagnostic information contained in the TRF. One particular way to alleviate this problem is by means of image deconvolution, which is usually performed in a "blind" mode, when both PSF and TRF are estimated at the same time. Despite its proven effectiveness, blind deconvolution (BD) still suffers from a number of drawbacks, chief among which stems from its dependence on a stationary convolution model, which is incapable of accounting for the spatial variability of the PSF. As a result, virtually all existing BD algorithms are applied to localized segments of RF images. In this work, we introduce a novel method for non-stationary BD, which is capable of recovering the TRF concurrently with the spatially variable PSF. Particularly, our approach is based on semigroup theory which allows one to describe the effect of such a PSF in terms of the action of a properly defined linear semigroup. The approach leads to a tractable optimization problem, which can be solved using standard numerical methods. The effectiveness of the proposed solution is supported by experiments with in vivo ultrasound data.
Kulyanitsa, A. L.; Rukhovich, A. D.; Rukhovich, D. D.; Koroleva, P. V.; Rukhovich, D. I.; Simakova, M. S.
2017-04-01
The concept of soil line can be to describe the temporal distribution of spectral characteristics of the bare soil surface. In this case, the soil line can be referred to as the multi-temporal soil line, or simply temporal soil line (TSL). In order to create TSL for 8000 regular lattice points for the territory of three regions of Tula oblast, we used 34 Landsat images obtained in the period from 1985 to 2014 after their certain transformation. As Landsat images are the matrices of the values of spectral brightness, this transformation is the normalization of matrices. There are several methods of normalization that move, rotate, and scale the spectral plane. In our study, we applied the method of piecewise linear approximation to the spectral neighborhood of soil line in order to assess the quality of normalization mathematically. This approach allowed us to range normalization methods according to their quality as follows: classic normalization > successive application of the turn and shift > successive application of the atmospheric correction and shift > atmospheric correction > shift > turn > raw data. The normalized data allowed us to create the maps of the distribution of a and b coefficients of the TSL. The map of b coefficient is characterized by the high correlation with the ground-truth data obtained from 1899 soil pits described during the soil surveys performed by the local institute for land management (GIPROZEM).
On the Local Equilibrium Principle
Hessling, H
2001-01-01
A physical system should be in a local equilibrium if it cannot be distinguished from a global equilibrium by ``infinitesimally localized measurements''. This seems to be a natural characterization of local equilibrium, however the problem is to give a precise meaning to the qualitative phrase ``infinitesimally localized measurements''. A solution is suggested in form of a {\\em Local Equilibrium Condition} (LEC) which can be applied to non-interacting quanta. The Unruh temperature of massless quanta is derived by applying LEC to an arbitrary point inside the Rindler Wedge. Massless quanta outside a hot sphere are analyzed. A stationary spherically symmetric local equilibrium does only exist according to LEC if the temperature is globally constant. Using LEC a non-trivial stationary local equilibrium is found for rotating massless quanta between two concentric cylinders of different temperatures. This shows that quanta may behave like a fluid with a B\\'enard instability.
Static- and Stationary-complete Spacetimes: Algebraic and Causal Structures
Harris, Steven G
2014-01-01
This is intended as an analysis of the global properties of static and stationary spacetimes with complete (timelike) Killing field, with particular attention to quotients by group actions. This is presented in terms of algebraic structures which are fairly simple for the static case and more involved for the stationary case; the most important tool, the fundamental cocycle, is a cohomological class for static spacetimes but of somewhat looser structure in the stationary case. In particular: (1) A new measurement, similar to the spacetime interval in Minkowski space, is devised for detecting whether two points are causally related in a stationary spacetime; this proves very useful for analysis. (2) All stationary spacetimes are categorized by how they behave with respect to the fundamental cocycle; this enables a complete characterization of global causality properties. (3) It is shown how these tools determine whether global hyperbolicity of a stationary spacetime is inherited by its quotients. (4) Examples ...
On general filtering problem of stationary processes with fixed transformation
Directory of Open Access Journals (Sweden)
Li Long
2011-01-01
Full Text Available Abstract A fixed transformation are given for one-dimensional stationary processes in this paper. Based on this, we propose a general filtering problem of stationary processes with fixed transformation. Finally, on a stationary processes with no any additional conditions, we get the spectral characteristics of P H η ( t ξ in the space L2(FX(dλ, and then we calculate the value of the best predict quantity Q of the general filtering problem.
Stationary phase optimized selectivity supercritical fluid chromatography (SOS-SFC)
Delahaye, Sander; Lynen, Frederic
2013-01-01
In stationary phase optimized selectivity liquid chromatography (SOS-LC) the stationary phase becomes a tunable parameter by connecting column segments with variable lengths of different stationary phases. An optimization procedure and algorithm based on the PRISMA model for optimization of the mobile phase in LC was developed to apply this strategy for isocratic and gradient separations. An optimized column segment combination, giving the highest separation selectivity for all compounds in a...
An Entropy Measure of Non-Stationary Processes
Directory of Open Access Journals (Sweden)
Ling Feng Liu
2014-03-01
Full Text Available Shannon’s source entropy formula is not appropriate to measure the uncertainty of non-stationary processes. In this paper, we propose a new entropy measure for non-stationary processes, which is greater than or equal to Shannon’s source entropy. The maximum entropy of the non-stationary process has been considered, and it can be used as a design guideline in cryptography.
Gaussian semiparametric estimation of non-stationary time series
Velasco, Carlos
1998-01-01
Generalizing the definition of the memory parameter d in terms of the differentiated series, we showed in Velasco (Non-stationary log-periodogram regression, Forthcoming J. Economet., 1997) that it is possible to estimate consistently the memory of non-stationary processes using methods designed for stationary long-range-dependent time series. In this paper we consider the Gaussian semiparametric estimate analysed by Robinson (Gaussian semiparametric estimation of long range dependence. Ann. ...
Numerical Modeling of Unsteady Cavitating Flows around a Stationary Hydrofoil
Directory of Open Access Journals (Sweden)
Antoine Ducoin
2012-01-01
Full Text Available The objective of this paper is to evaluate the predictive capability of three popular transport equation-based cavitation models for the simulations of partial sheet cavitation and unsteady sheet/cloud cavitating flows around a stationary NACA66 hydrofoil. The 2D calculations are performed by solving the Reynolds-averaged Navier-Stokes equation using the CFD solver CFX with the k-ω SST turbulence model. The local compressibility effect is considered using a local density correction for the turbulent eddy viscosity. The calculations are validated with experiments conducted in a cavitation tunnel at the French Naval Academy. The hydrofoil has a fixed angle of attack of α=6° with a Reynolds number of Re = 750,000 at different cavitation numbers σ. Without the density modification, over-prediction of the turbulent viscosity near the cavity closure reduces the cavity length and modifies the cavity shedding characteristics. The results show that it is important to capture both the mean and fluctuating values of the hydrodynamic coefficients because (1 the high amplitude of the fluctuations is critical to capturing the extremes of the loads to ensure structural safety and (2 the need to capture the frequency of the fluctuations, to avoid unwanted noise, vibrations, and accelerated fatigue issues.
Numerical Investigation of a Statistically Stationary Turbulent Reacting Flow
Overholt, Matthew R.; Pope, Stephen B.
1997-11-01
Direct numerical simulation (DNS) has been very useful in the study of inert scalar mixing in turbulent flows, and has recently become feasible for studies of reacting scalars. We have formulated an accessible inhomogeneous nonpremixed turbulent reactive flow for investigating the effects of mixing on reaction and testing mixing models. The mixture fraction-progress variable approach is used with a model single-step reversible finite-rate thermochemistry, yielding non-trivial stationary solutions corresponding to stable reaction and allowing local extinction to occur. A mean gradient in the mixture fraction gives rise to stationarity without forcing, as well as a flame brush. A range of reaction zone thicknesses and Damkohler numbers are examined, yielding a broad spectrum of behavior, ranging from thick to thin flames, and from local extinction to near equilibrium. Based on this study results from full probability density function (PDF) simulations using the IEM and EMST mixing models are evaluated. Conditional moment closure (CMC) results are evaluated as well.
Spectral Model of Non-Stationary, Inhomogeneous Turbulence
Bragg, Andrew D; Clark, Timothy T
2015-01-01
We compare results from a spectral model for non-stationary, inhomogeneous turbulence (Besnard et al., Theor. Comp. Fluid. Dyn., vol. 8, pp 1-35, 1996) with Direct Numerical Simulation (DNS) data of a shear-free mixing layer (SFML) (Tordella et al., Phys. Rev. E, vol. 77, 016309, 2008). The SFML is used as a test case in which the efficacy of the model closure for the physical-space transport of the fluid velocity field can be tested in a flow with inhomogeneity, without the additional complexity of mean-flow coupling. The model is able to capture certain features of the SFML quite well for intermediate to long-times, including the evolution of the mixing-layer width and turbulent kinetic energy. At short-times, and for more sensitive statistics such as the generation of the velocity field anisotropy, the model is less accurate. We present arguments, supported by the DNS data, that a significant cause of the discrepancies is the local approximation to the intrinsically non-local pressure-transport in physical...
Stationary Charged Scalar Clouds around Black Holes in String Theory
Bernard, Canisius
2016-01-01
It was reported that Kerr-Newman black holes can support linear charged scalar field in their exterior regions. This stationary massive charged scalar field can form a bound-state and these bound-states are called stationary scalar clouds. In this paper, we study that Kerr-Sen black holes can also support stationary massive charged scalar clouds by matching the near and far region solutions of the radial part of Klein-Gordon wave equation. We also review stationary scalar clouds within the background of static electrically charged black hole solution in the low energy limit of heterotic string field theory namely the GMGHS black holes.
Stationary charged scalar clouds around black holes in string theory
Bernard, Canisius
2016-10-01
It was reported that Kerr-Newman black holes can support linear charged scalar fields in their exterior regions. These stationary massive charged scalar fields can form bound states, which are called stationary scalar clouds. In this paper, we show that Kerr-Sen black holes can also support stationary massive charged scalar clouds by matching the near- and far-region solutions of the radial part of the Klein-Gordon wave equation. We also review stationary scalar clouds within the background of static electrically charged black hole solutions in the low-energy limit of heterotic string field theory, namely, the Gibbons-Maeda-Garfinkle-Horowitz-Strominger black holes.
Effect of non-stationary climate on infectious gastroenteritis transmission in Japan
Onozuka, Daisuke
2014-06-01
Local weather factors are widely considered to influence the transmission of infectious gastroenteritis. Few studies, however, have examined the non-stationary relationships between global climatic factors and transmission of infectious gastroenteritis. We analyzed monthly data for cases of infectious gastroenteritis in Fukuoka, Japan from 2000 to 2012 using cross-wavelet coherency analysis to assess the pattern of associations between indices for the Indian Ocean Dipole (IOD) and El Niño Southern Oscillation (ENSO). Infectious gastroenteritis cases were non-stationary and significantly associated with the IOD and ENSO (Multivariate ENSO Index [MEI], Niño 1 + 2, Niño 3, Niño 4, and Niño 3.4) for a period of approximately 1 to 2 years. This association was non-stationary and appeared to have a major influence on the synchrony of infectious gastroenteritis transmission. Our results suggest that non-stationary patterns of association between global climate factors and incidence of infectious gastroenteritis should be considered when developing early warning systems for epidemics of infectious gastroenteritis.
Effect of non-stationary climate on infectious gastroenteritis transmission in Japan.
Onozuka, Daisuke
2014-06-03
Local weather factors are widely considered to influence the transmission of infectious gastroenteritis. Few studies, however, have examined the non-stationary relationships between global climatic factors and transmission of infectious gastroenteritis. We analyzed monthly data for cases of infectious gastroenteritis in Fukuoka, Japan from 2000 to 2012 using cross-wavelet coherency analysis to assess the pattern of associations between indices for the Indian Ocean Dipole (IOD) and El Niño Southern Oscillation (ENSO). Infectious gastroenteritis cases were non-stationary and significantly associated with the IOD and ENSO (Multivariate ENSO Index [MEI], Niño 1 + 2, Niño 3, Niño 4, and Niño 3.4) for a period of approximately 1 to 2 years. This association was non-stationary and appeared to have a major influence on the synchrony of infectious gastroenteritis transmission. Our results suggest that non-stationary patterns of association between global climate factors and incidence of infectious gastroenteritis should be considered when developing early warning systems for epidemics of infectious gastroenteritis.
Studying the Dynamics of Non-stationary Jet Streams Formation in the Northern Hemisphere Troposphere
Emtsev, Sergey; Krasouski, Aliaksandr; Svetashev, Alexander; Turishev, Leonid; Barodka, Siarhei
2015-04-01
In the present study, we investigate dynamics of non-stationary jets formation in troposphere by means of mesoscale simulations in the Weather Research & Forecasting (WRF) modeling system, analyzing jet streams that affected the territory of Belarus over the time period of 2010-2012. For that purpose, we perform modeling on domains with 5 km, 3 km and 1 km grid steps and 35 vertical coordinate levels with an upper boundary of 10 hPa. We focus our attention to identification of basic regularities in formation, movements and transformations of jet streams, as well as to analysis of their characteristic features, geographical position and underlying atmospheric processes and their classification. On the basis of these regularities, we define basic meteorological parameters that can be used to directly or indirectly (as well as qualitatively and quantitatively) identify the presence of jet streams in the specific region of troposphere, and also to determine their localization, stage of development and other characteristics. Furthermore, we estimate energetic parameters of the identified jet streams and their impact on synoptic situation in the surrounding region. Analyzing meteorological fields obtained from satellite observations, we elaborate a methodology of operational detection and localization of non-stationary jet streams from satellite data. Validation of WRF modeling results with these data proves that mesoscale simulations with WRF are able to provide quite successful forecasts of non-stationary tropospheric jet streams occurrence and also determination of their localization and main characteristics up to 3 days in advance.
Stationary Light Pulses without Bragg Gratings
Lin, Yen-Wei; Peters, Thorsten; Liao, Wen-Te; Cho, Hung-Wen; Guan, Pei-Chen; Yu, Ite A
2008-01-01
The underlying mechanism of the stationary light pulse (SLP) was identified as a band gap being created by a Bragg grating formed by two counter-propagating coupling fields of similar wavelength. Here we present a more general view of the formation of SLPs, namely several balanced four-wave mixing processes sharing the same ground-state coherence. Utilizing this new concept we report the first experimental observation of a bichromatic SLP at wavelengths for which no Bragg grating can be established. We also demonstrate the production of a SLP directly from a propagating light pulse without prior storage. Being easily controlled externally makes SLPs a very versatile tool for low-light-level nonlinear optics and quantum information manipulation.
Stationary phases for superheated water chromatography
Saha, S
2002-01-01
This project focused on the comparison of conventional liquid chromatography and superheated water chromatography. It examined the differences in efficiency and retention of a range of different stationary phases. Alkyl aryl ketones and eight aromatic compounds were separated on PBD-zirconia, Xterra RP 18, Luna C sub 1 sub 8 (2) and Oasis HLB columns using conventional LC and superheated water chromatography system. The retention indices were determined in the different eluents. On changing the organic component of the eluent from methanol to acetonitrile to superheated water considerable improvements were found in the peak shapes and column efficiencies on the PBD-zirconia and Oasis HLB columns. PS-DVB, PBD-zirconia and Xterra RP 18 columns have been used in efficiency studies. It was found that simply elevating the column temperature did not increase the efficiency of a separation in superheated water chromatography. The efficiency depended on flow rate, injection volume and also mobile phase preheating sys...
Learning Markov models for stationary system behaviors
DEFF Research Database (Denmark)
Chen, Yingke; Mao, Hua; Jaeger, Manfred
2012-01-01
Establishing an accurate model for formal verification of an existing hardware or software system is often a manual process that is both time consuming and resource demanding. In order to ease the model construction phase, methods have recently been proposed for automatically learning accurate...... system models from data in the form of observations of the target system. Common for these approaches is that they assume the data to consist of multiple independent observation sequences. However, for certain types of systems, in particular many running embedded systems, one would only have access...... the learned model. Experiments demonstrate that system properties (formulated as stationary probabilities of LTL formulas) can be reliably identified using the learned model....
Effective complexity of stationary process realizations
Ay, Nihat; Szkola, Arleta
2010-01-01
The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. Based on their work we gave a precise definition of effective complexity of finite binary strings in terms of algorithmic information theory in our previous paper. Here we study the effective complexity of strings generated by stationary processes. Sufficiently long typical process realizations turn out to be effectively simple under any linear scaling with the string's length of the parameter $\\Delta$ which determines the minimization domain. For a class of computable ergodic processes including i.i.d. and ergodic Markovian processes a stronger result can be shown: There exist sublinear scalings of $\\Delta$ for which typical realizations turn out to be effectively simple. Our results become most transparent in the context of coarse effective complexity --a modification of plain effective complexity, where $\\Delta$ appears as a minimization argument. A similar modif...
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, Malene; Nielsen, Ole-Kenneth; Plejdrup, Marlene Schmidt
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are SO2, NOx, NMVOC, CH4, CO, CO2, N2O, particulate matter, heavy metals, dioxins, HCB and PAH. The CO2 emission in 2007 was 10......% lower than in 1990. However fluctuations in the emission level are large as a result of electricity import/export. The emission of CH4 has increased due to increased use of lean-burn gas engines in combined heating and power (CHP) plants. However the emission has decreased in recent years due...... to structural changes in the Danish electricity market. The N2O emission was higher in 2007 than in 1990 but the fluctuations in the time-series are significant. A considerable decrease of the SO2, NOx and heavy metal emissions is mainly a result of decreased emissions from large power plants and waste...
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, Malene; Nielsen, Ole-Kenneth; Plejdrup, Marlene Schmidt
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are SO2, NOx, NMVOC, CH4, CO, CO2, N2O, NH3, particulate matter, heavy metals, PCDD/F, HCB and PAH. The CO2 emission in 2011...... of decreased emissions from large power plants and waste incineration plants. The combustion of wood in residential plants has increased considerably until 2007 resulting in increased emission of PAH and particulate matter. The emission of NMVOC has increased since 1990 as a result of both the increased...... was 30 % lower than in 1990. However, fluctuations in the emission level are large as a result of electricity import/export. The emission of CH4 has increased due to increased use of lean-burn gas engines in combined heating and power (CHP) plants. In recent years, the emission has declined. This is due...
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, Malene; Nielsen, Ole-Kenneth; Plejdrup, Marlene Schmidt
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are SO2, NOx, NMVOC, CH4, CO, CO2, N2O, NH3, particulate matter, heavy metals, dioxins, HCB and PAH. The CO2 emission in 2008...... incineration plants. The combustion of wood in residential plants has increased considerably in recent years resulting in increased emission of PAH, particulate matter and CO. The emission of NMVOC has increased since 1990 as a result of both the increased combustion of wood in residential plants...... was 16 % lower than in 1990. However, fluctuations in the emission level are large as a result of electricity import/export. The emission of CH4 has increased due to increased use of lean-burn gas engines in combined heating and power (CHP) plants. However, the emission has decreased in recent years due...
Stationary Traffic In The Urban Planning System
Directory of Open Access Journals (Sweden)
Ivica Martinić
2005-03-01
Full Text Available Since ancient times human lives pulsed between two poles- moving and stationmy. Moving as element of functioning issupplemented by standing. Today, when modem life in cities isbased on using passenger cars as the dominant means of mobility,the explosion of their number is the generator of the growingproblems both of the moving and of the stationary traffic. Consideringparking as direct product of the moving traffic, usuallyits negative characteristics are mentioned such as greater volumeof parking, fines, legal-regulative and safety aspects, degradationof other swfaces by the parked vehicles, etc. Never oralmostnever does one speak about the origin of the problem, andthis would be the only way to find its solution.
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, Malene; Nielsen, Ole-Kenneth; Plejdrup, Marlene Schmidt
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are SO2, NOx, NMVOC, CH4, CO, CO2, N2O, particulate matter, heavy metals, dioxins, HCB and PAH. The CO2 emission in 2007 was 10...... incineration plants. The combustion of wood in residential plants has increased considerably in recent years resulting in increased emission of PAH, particulate matter and CO. The emission of NMVOC has increased since 1990 as a result of both the increased combustion of wood in residential plants...... and the increased emission from lean-burn gas engines. The dioxin emission decreased since 1990 due to flue gas cleaning on waste incineration plants. However in recent years the emission has increased as a result of the increased combustion of wood in residential plants....
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, Malene; Nielsen, Ole-Kenneth; Plejdrup, Marlene Schmidt
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are SO2, NOx, NMVOC, CH4, CO, CO2, N2O, NH3, particulate matter, heavy metals, PCDD/F, HCB and PAH. The CO2 emission in 2011...... of decreased emissions from large power plants and waste incineration plants. The combustion of wood in residential plants has increased considerably until 2007 resulting in increased emission of PAH and particulate matter. The emission of NMVOC has increased since 1990 as a result of both the increased...... combustion of wood in residential plants and the increased emission from lean-burn gas engines. The PCDD/F emission decreased since 1990 due to flue gas cleaning on waste incineration plants....
Danish emission inventories for stationary combustion plants
DEFF Research Database (Denmark)
Nielsen, Malene; Nielsen, Ole-Kenneth; Plejdrup, Marlene Schmidt
Emission inventories for stationary combustion plants are presented and the methodologies and assumptions used for the inventories are described. The pollutants considered are SO2, NOx, NMVOC, CH4, CO, CO2, N2O, NH3, particulate matter, heavy metals, dioxins, HCB and PAH. The CO2 emission in 2008...... incineration plants. The combustion of wood in residential plants has increased considerably in recent years resulting in increased emission of PAH, particulate matter and CO. The emission of NMVOC has increased since 1990 as a result of both the increased combustion of wood in residential plants...... and the increased emission from lean-burn gas engines. The dioxin emission decreased since 1990 due to flue gas cleaning on waste incineration plants. However in recent years the emission has increased as a result of the increased combustion of wood in residential plants....
Baroclinic stationary waves in aquaplanet models
Lucarini, V.; Zappa, G.
2012-04-01
An aquaplanet model is used to study the nature of the highly persistent low frequency waves that have been observed in models forced by zonally symmetric boundary conditions. Using the Hayashi spectral analysis of the extratropical waves, we find that a quasi-stationary (QS) wave five belongs to a wave packet obeying a well defined dispersion relation with eastward group velocity. The components of the dispersion relation with k>5 baroclinically convert eddy available potential energy into eddy kinetic energy, while those with kinverse energy cascade, which had been previously proposed as a main forcing for this type of waves, only acts as a positive feedback on its predominantly baroclinic energetics. The QS wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. We also find that the Pedlosky bounds on the phase speed of unstable waves provide guidance in explaining the latitudinal structure of the energy conversion, which is shown to be more enhanced where the zonal westerly surface wind is weaker. The wave energy is then trapped in the wave guide created by the upper tropospheric jet stream. In agreement with Green's theory, as the equator to pole SST difference is reduced the stationary marginally stable component shifts toward higher wavenumbers, while the wave five becomes neutral and westward propagating. Some properties of the aquaplanet QS waves are found in interesting agreement with a low frequency wave observed by Salby (1982) in the southern hemisphere DJF, so that this perspective on low frequency variability might be, apart from its value in terms of basic geophysical fluid dynamics, of specific interest for studying the Earth's atmosphere.
Graph-Based Transform for 2D Piecewise Smooth Signals With Random Discontinuity Locations.
Zhang, Dong; Liang, Jie
2017-04-01
The graph-based block transform recently emerged as an effective tool for compressing some special signals such as depth images in 3D videos. However, in existing methods, overheads are required to describe the graph of the block, from which the decoder has to calculate the transform via time-consuming eigendecomposition. To address these problems, in this paper, we aim to develop a single graph-based transform for a class of 2D piecewise smooth signals with similar discontinuity patterns. We first consider the deterministic case with a known discontinuity location in each row. We propose a 2D first-order autoregression (2D AR1) model and a 2D graph for this type of signals. We show that the closed-form expression of the inverse of a biased Laplacian matrix of the proposed 2D graph is exactly the covariance matrix of the proposed 2D AR1 model. Therefore, the optimal transform for the signal are the eigenvectors of the proposed graph Laplacian. Next, we show that similar results hold in the random case, where the locations of the discontinuities in different rows are randomly distributed within a confined region, and we derive the closed-form expression of the corresponding optimal 2D graph Laplacian. The theory developed in this paper can be used to design both pre-computed transforms and signal-dependent transforms with low complexities. Finally, depth image coding experiments demonstrate that our methods can achieve similar performance to the state-of-the-art method, but our complexity is much lower.
Maximum error-bounded Piecewise Linear Representation for online stream approximation
Xie, Qing
2014-04-04
Given a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.
Merge Frame Design for Video Stream Switching Using Piecewise Constant Functions
Dai, Wei; Cheung, Gene; Cheung, Ngai-Man; Ortega, Antonio; Au, Oscar C.
2016-08-01
The ability to efficiently switch from one pre-encoded video stream to another (e.g., for bitrate adaptation or view switching) is important for many interactive streaming applications. Recently, stream-switching mechanisms based on distributed source coding (DSC) have been proposed. In order to reduce the overall transmission rate, these approaches provide a "merge" mechanism, where information is sent to the decoder such that the exact same frame can be reconstructed given that any one of a known set of side information (SI) frames is available at the decoder (e.g., each SI frame may correspond to a different stream from which we are switching). However, the use of bit-plane coding and channel coding in many DSC approaches leads to complex coding and decoding. In this paper, we propose an alternative approach for merging multiple SI frames, using a piecewise constant (PWC) function as the merge operator. In our approach, for each block to be reconstructed, a series of parameters of these PWC merge functions are transmitted in order to guarantee identical reconstruction given the known side information blocks. We consider two different scenarios. In the first case, a target frame is first given, and then merge parameters are chosen so that this frame can be reconstructed exactly at the decoder. In contrast, in the second scenario, the reconstructed frame and merge parameters are jointly optimized to meet a rate-distortion criteria. Experiments show that for both scenarios, our proposed merge techniques can outperform both a recent approach based on DSC and the SP-frame approach in H.264, in terms of compression efficiency and decoder complexity.
The quartic piecewise-linear criterion for the multiaxial yield behavior of human trabecular bone.
Sanyal, Arnav; Scheffelin, Joanna; Keaveny, Tony M
2015-01-01
Prior multiaxial strength studies on trabecular bone have either not addressed large variations in bone volume fraction and microarchitecture, or have not addressed the full range of multiaxial stress states. Addressing these limitations, we utilized micro-computed tomography (lCT) based nonlinear finite element analysis to investigate the complete 3D multiaxial failure behavior of ten specimens (5mm cube) of human trabecular bone, taken from three anatomic sites and spanning a wide range of bone volume fraction (0.09–0.36),mechanical anisotropy (range of E3/E1¼3.0–12.0), and microarchitecture. We found that most of the observed variation in multiaxial strength behavior could be accounted for by normalizing the multiaxial strength by specimen-specific values of uniaxial strength (tension,compression in the longitudinal and transverse directions). Scatter between specimens was reduced further when the normalized multiaxial strength was described in strain space.The resulting multiaxial failure envelope in this normalized-strain space had a rectangular boxlike shape for normal–normal loading and either a rhomboidal box like shape or a triangular shape for normal-shear loading, depending on the loading direction. The finite element data were well described by a single quartic yield criterion in the 6D normalized strain space combined with a piecewise linear yield criterion in two planes for normalshear loading (mean error SD: 4.660.8% for the finite element data versus the criterion).This multiaxial yield criterion in normalized-strain space can be used to describe the complete 3D multiaxial failure behavior of human trabecular bone across a wide range of bone volume fraction, mechanical anisotropy, and microarchitecture.
Scale parameters in stationary and non-stationary GEV modeling of extreme precipitation
Panagoulia, Dionysia; Economou, Polychronis; Caroni, Chrys
2013-04-01
The generalized extreme value (GEV) distribution is often fitted to environmental time series of extreme values such as annual maxima of daily precipitation. We study two methodological issues here. First we compare methods of selecting the best model among a set of 16 GEV models that allow non-stationary scale and location parameters. Results of simulation studies showed that both the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) correctly detected non-stationarity but the BIC was superior in selecting the correct model more often. The second issue is how best to produce confidence intervals (CIs) for the parameters of the model and other quantities such as the return levels that are usually required for hydrological and climatological time series. Four bootstrap CIs - normal, percentile, basic, and bias corrected and accelerated (BCa) - constructed by random-t resampling, fixed-t resampling and the parametric bootstrap methods were compared. CIs for parameters of the stationary model do not present major differences. CIs for the more extreme quantiles tend to become very wide for all bootstrap methods. For non-stationary GEV models with linear time dependence of location or log-linear time dependence of scale, coverage probabilities of the CIs are reasonably accurate for the parameters. For the extreme percentiles, the BCa method is best overall and the fixed-t method also gives good average coverage probabilities.
Energy Technology Data Exchange (ETDEWEB)
Steinhorst, F. [Hamburger Hochbahn AG, Hamburg (Germany). Abt. Energieanlagen; Jonassen, I.; Peters, A. [Hamburger Hochbahn AG, Hamburg (Germany). Fachbereich Energieversorgung
2008-07-01
A stationary energy storage is to be used as a model in a substation of the Hamburg subway network with a view to the environmentally compatible and technically proper use of the brake energy available in electrified local public transport systems. A further question to be reviewed is whether the use of other energy storages in the subway network is a reasonable solution. (orig.)
Institute of Scientific and Technical Information of China (English)
陈刚; 冯民富; 何银年
2013-01-01
A unified analysis is presented for the stabilized methods including the pres-sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa-tions. The existence and uniqueness of the solution and the optimal error estimates are proved.
Stationary MHD equilibria describing azimuthal rotations in symmetric plasmas
da Silva, Sidney T.; Viana, Ricardo L.
2016-12-01
We consider the stationary magnetohydrodynamical (MHD) equilibrium equation for an axisymmetric plasma undergoing azimuthal rotations. The case of cylindrical symmetry is treated, and we present two semi-analytical solutions for the stationary MHD equilibrium equations, from which a number of physical properties of the magnetically confined plasma are derived.
Stationary solutions of equations of incompressible viscoelastic polymer liquid
Bambaeva, N. V.; Blokhin, A. M.
2014-05-01
The equations describing flows of an incompressible viscoelastic polymer liquid are studied. Stationary solutions similar to the Poiseuille and Couette solutions for the system of the Navier-Stokes equations are constructed. Stationary discontinuous solutions of the polymer liquid equation are also considered.
30 CFR 57.4561 - Stationary diesel equipment underground.
2010-07-01
... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Stationary diesel equipment underground. 57... AND NONMETAL MINE SAFETY AND HEALTH SAFETY AND HEALTH STANDARDS-UNDERGROUND METAL AND NONMETAL MINES... underground. Stationary diesel equipment underground shall be— (a) Supported on a noncombustible base; and (b...
Weighted least squares stationary approximations to linear systems.
Bierman, G. J.
1972-01-01
Investigation of the problem of replacing a certain time-varying linear system by a stationary one. Several quadratic criteria are proposed to aid in determining suitable candidate systems. One criterion for choosing the matrix B (in the stationary system) is initial-condition dependent, and another bounds the 'worst case' homogeneous system performance. Both of these criteria produce weighted least square fits.
Time reversibility from visibility graphs of non-stationary processes
Lacasa, Lucas
2015-01-01
Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of both natural and horizontal visibility graphs associated to several non-stationary processes, and we pay particular attention to their capacity to assess time irreversibility. Non-stationary signals are (infinitely) irreversible by definition (independently of whether the process is Markovian or producing entropy at a positive rate), and thus the link between entropy production and time series irreversibility has only been explored in non-equilibrium stationary states. Here we show that the visibility formalism naturally induces a new working definition of time irreversibility, which allows to quantify several degrees of irreversibility for stationary and non-stationary series, yielding finite values that can be used to efficiently assess the presence of memory and off-equ...
Diagnostics of many-particle electronic states: non-stationary currents and residual charge dynamics
Maslova, N. S.; Mantsevich, V. N.; Arseyev, P. I.
2017-01-01
We propose the method for identifying many particle electronic states in the system of coupled quantum dots (impurities) with Coulomb correlations. We demonstrate that different electronic states can be distinguished by the complex analysis of localized charge dynamics and non-stationary characteristics. We show that localized charge time evolution strongly depends on the properties of initial state and analyze different time scales in charge kinetics for initially prepared singlet and triplet states. We reveal the conditions for existence of charge trapping effects governed by the selection rules for electron transitions between the states with different occupation numbers.
Localization Algorithms of Underwater Wireless Sensor Networks: A Survey
Han, Guangjie; Jiang, Jinfang; Shu, Lei; Xu, Yongjun; Wang, Feng
2012-01-01
In Underwater Wireless Sensor Networks (UWSNs), localization is one of most important technologies since it plays a critical role in many applications. Motivated by widespread adoption of localization, in this paper, we present a comprehensive survey of localization algorithms. First, we classify localization algorithms into three categories based on sensor nodes’ mobility: stationary localization algorithms, mobile localization algorithms and hybrid localization algorithms. Moreover, we compare the localization algorithms in detail and analyze future research directions of localization algorithms in UWSNs. PMID:22438752
Energy Technology Data Exchange (ETDEWEB)
Woodward, P. R.
2003-03-26
This report summarizes the results of the project entitled, ''Piecewise-Parabolic Methods for Parallel Computation with Applications to Unstable Fluid Flow in 2 and 3 Dimensions'' This project covers a span of many years, beginning in early 1987. It has provided over that considerable period the core funding to my research activities in scientific computation at the University of Minnesota. It has supported numerical algorithm development, application of those algorithms to fundamental fluid dynamics problems in order to demonstrate their effectiveness, and the development of scientific visualization software and systems to extract scientific understanding from those applications.
Energy Technology Data Exchange (ETDEWEB)
Woodward, P. R.
2003-03-26
This report summarizes the results of the project entitled, ''Piecewise-Parabolic Methods for Parallel Computation with Applications to Unstable Fluid Flow in 2 and 3 Dimensions'' This project covers a span of many years, beginning in early 1987. It has provided over that considerable period the core funding to my research activities in scientific computation at the University of Minnesota. It has supported numerical algorithm development, application of those algorithms to fundamental fluid dynamics problems in order to demonstrate their effectiveness, and the development of scientific visualization software and systems to extract scientific understanding from those applications.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Chang, J H
2008-10-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.
Watts, Benjamin
2014-09-22
An algorithm is presented for the calculation of the Kramers-Kronig transform of a spectrum via a piecewise Laurent polynomial method. This algorithm is demonstrated to be highly accurate, while also being computationally efficient. The algorithm places no requirements on data point spacing and is capable of integrating across the full spectrum (i.e. from zero to infinity). Further, we present a computer application designed to aid in calculating the Kramers-Kronig transform on near-edge experimental X-ray absorption spectra (extended with atomic scattering factor data) in order to produce the dispersive part of the X-ray refractive index, including near-edge features.
Self-organising mixture autoregressive model for non-stationary time series modelling.
Ni, He; Yin, Hujun
2008-12-01
Modelling non-stationary time series has been a difficult task for both parametric and nonparametric methods. One promising solution is to combine the flexibility of nonparametric models with the simplicity of parametric models. In this paper, the self-organising mixture autoregressive (SOMAR) network is adopted as a such mixture model. It breaks time series into underlying segments and at the same time fits local linear regressive models to the clusters of segments. In such a way, a global non-stationary time series is represented by a dynamic set of local linear regressive models. Neural gas is used for a more flexible structure of the mixture model. Furthermore, a new similarity measure has been introduced in the self-organising network to better quantify the similarity of time series segments. The network can be used naturally in modelling and forecasting non-stationary time series. Experiments on artificial, benchmark time series (e.g. Mackey-Glass) and real-world data (e.g. numbers of sunspots and Forex rates) are presented and the results show that the proposed SOMAR network is effective and superior to other similar approaches.
Stationary flow conditions in pulsed supersonic beams.
Christen, Wolfgang
2013-10-21
We describe a generally applicable method for the experimental determination of stationary flow conditions in pulsed supersonic beams, utilizing time-resolved electron induced fluorescence measurements of high pressure jet expansions of helium. The detection of ultraviolet photons from electronically excited helium emitted very close to the nozzle exit images the valve opening behavior-with the decided advantage that a photon signal is not affected by beam-skimmer and beam-residual gas interactions; it thus allows to conclusively determine those operation parameters of a pulsed valve that yield complete opening. The studies reveal that a "flat-top" signal, indicating constant density and commonly considered as experimental criterion for continuous flow, is insufficient. Moreover, translational temperature and mean terminal flow velocity turn out to be significantly more sensitive in testing for the equivalent behavior of a continuous nozzle source. Based on the widely distributed Even-Lavie valve we demonstrate that, in principle, it is possible to achieve quasi-continuous flow conditions even with fast-acting valves; however, the two prerequisites are a minimum pulse duration that is much longer than standard practice and previous estimates, and a suitable tagging of the appropriate beam segment.
Growth of microalgae in autotrophic stationary systems
Directory of Open Access Journals (Sweden)
Paulo Cunha
2008-06-01
Full Text Available In this paper we evaluate the growth of nine marine microalgae species (Nannochloropsis oculata, Thalassiosira pseudonana, Phaeodactylum tricornutum, Isochrysis galbana, Tetraselmis suecica, Tetraselmis chuii, Chaetoceros muelleri, Thalassiosira fluviatilis and Isochrysis sp. and one freshwater species (Chlorella vulgaris under stationary autotrophy conditions, using erlenmeyers fl asks with 800mL of culture medium exposed to constant light intensities providing a photon flux density of about 150μmol.m-2.s-1 and 25±2oC temperature and constant air flow. The experiment was carried out in a controlled environment considering a block delineating randomized over time with three replicates. The Nannochloropsis oculata showed the highest value of maximum cellular density, but with a longer period of time and a lower growth rate. This was probably due to its tiny cell size, demanding a large number of cells per volume to attain its optimum conditions for light, nutrients, water and atmospheric carbon dioxide. In addition, in spite of showing one of the lowest values of maximum cellular density, Thalassiosira fluviatilis was the species that reached its maximum in a short period of time at the highest growth rate. Chlorella vulgaris was the only freshwater species tested and it showed the poorest performance for all the variables analyzed in the current study.
Baroclinic stationary waves in aquaplanet models
Zappa, Giuseppe; Navarra, Antonio; 10.1175/2011JAS3573.1
2011-01-01
An aquaplanet model is used to study the nature of the highly persistent low frequency waves that have been observed in models forced by zonally symmetric boundary conditions. Using the Hayashi spectral analysis of the extratropical waves, we find that a quasi-stationary (QS) wave five belongs to a wave packet obeying a well defined dispersion relation with eastward group velocity. The components of the dispersion relation with k>5 baroclinically convert eddy available potential energy into eddy kinetic energy, while those with k<5 are baroclinically neutral. In agreement with the Green's model of baroclinic instability, the wave five is weakly unstable, and the inverse energy cascade, which had been previously proposed as a main forcing for this type of waves, only acts as a positive feedback on its predominantly baroclinic energetics. The QS wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. We also find that the Pedlos...
Quasi-stationary distributions and population processes
Méléard, Sylvie
2011-01-01
This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes when 0 is an absorbing point almost surely attained by the process. The hitting time of this point, namely the extinction time, can be large compared to the physical time and the population size can fluctuate for large amount of time before extinction actually occurs. This phenomenon can be understood by the study of quasi-limiting distributions. In this paper, general results on quasi-stationarity are given and examples developed in detail. One shows in particular how this notion is related to the spectral properties of the semi-group of the process killed at 0. Then we study different stochastic population models including nonlinear terms modeling the regulation of the population. These models will take values in countable sets (as birth and death processes) or in continuou...
Stationary intraoral tomosynthesis for dental imaging
Inscoe, Christina R.; Wu, Gongting; Soulioti, Danai E.; Platin, Enrique; Mol, Andre; Gaalaas, Laurence R.; Anderson, Michael R.; Tucker, Andrew W.; Boyce, Sarah; Shan, Jing; Gonzales, Brian; Lu, Jianping; Zhou, Otto
2017-03-01
Despite recent advances in dental radiography, the diagnostic accuracies for some of the most common dental diseases have not improved significantly, and in some cases remain low. Intraoral x-ray is the most commonly used x-ray diagnostic tool in dental clinics. It however suffers from the typical limitations of a 2D imaging modality including structure overlap. Cone-beam computed tomography (CBCT) uses high radiation dose and suffers from image artifacts and relatively low resolution. The purpose of this study is to investigate the feasibility of developing a stationary intraoral tomosynthesis (s-IOT) using spatially distributed carbon nanotube (CNT) x-ray array technology, and to evaluate its diagnostic accuracy compared to conventional 2D intraoral x-ray. A bench-top s-IOT device was constructed using a linear CNT based X-ray source array and a digital intraoral detector. Image reconstruction was performed using an iterative reconstruction algorithm. Studies were performed to optimize the imaging configuration. For evaluation of s-IOT's diagnostic accuracy, images of a dental quality assurance phantom, and extracted human tooth specimens were acquired. Results show s-IOT increases the diagnostic sensitivity for caries compared to intraoral x-ray at a comparable dose level.
Stationary radiation cataracts: an animal model
Energy Technology Data Exchange (ETDEWEB)
Holsclaw, D.S.; Merriam, G.R. Jr; Medvedovsky, C.; Worgul, B.V. (Columbia Univ., New York, NY (USA)); Rothstein, H. (Fordham Univ., New York, NY (USA))
1989-03-01
This report describes the induction of stationary radiation cataracts in postmetamorphic bullfrogs following ocular irradiation with a 10 Gy dose of X-rays. The eyes of non-irradiated animals and animals irradiated with 25 Gy served as controls. The 25 Gy irradiated lenses rapidly progressed to complete opacification (4+) by 26 weeks, while lenses exposed to 10 Gy advanced to the 2.5+ stage by 35 weeks and progressed no further. In the lower dose lenses, transparent cortex began to appear anteriorly and posteriorly between the capsule and opaque fibers at 45 weeks. As the clear fibers accumulated, the disrupted region came to occupy increasingly deeper cortex. Histologically, opacities in both groups were preceded by disorganization of the bow cytoarchitecture, meridional row disorganization, and the appearance in the lens epithelium of nuclear polymorphism, fragmented nuclei, micronuclei, clusters of nuclei, and abnormal mitotic figures. In the lenses exposed to the 25 Gy dose, this damage continued to worsen, so that the 4+ stage was characterized by extensive epithelial cell death, absence of the lens bow, degenerated fiber masses, and liquefied substrata. In contrast, prior to the appearance of transparent cortex in the 10 Gy group, the lens epithelial aberrations, arc of the bow, and meridional row disorganization were all observed to improve. Further, by 69 weeks, the lens epithelium appeared as a largely homogeneous population, and the meridional rows and the arc of the bow had become reestablished. (author).