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
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.
Stenroos, Matti
2016-01-01
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from standard formulation. The approach and resulting solver are verified in three ways, including comparison to finite element method (FEM). In a two-compartment split-sphere model with two spaced monopoles, the results obtained with high-resolution FEM and the BEMs were almost identical (relative difference < 0.003).
Stenroos, Matti
2016-11-01
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.
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.
Graphene wire medium: Homogenization and application
DEFF Research Database (Denmark)
Andryieuski, Andrei; Chigrin, Dmitry N.; Lavrinenko, Andrei
2012-01-01
In this contribution we analyze numerically the optical properties of the graphene wire medium, which unit cell consists of a stripe of graphene embedded into dielectric. We propose a simple method for retrieval of the isofrequency contour and effective permittivity tensor. As an example...... of the graphene wire medium application we demonstrate a reconfigurable hyperlens for the terahertz subwavelength imaging capable of resolving two sources with separation λ0/5 in the far-field....
Electromagnetic Radiation in a Uniformly Moving, Homogeneous Medium
DEFF Research Database (Denmark)
Johannsen, Günther
1972-01-01
A new method of treating radiation problems in a uniformly moving, homogeneous medium is presented. A certain transformation technique in connection with the four-dimensional Green's function method makes it possible to elaborate the Green's functions of the governing differential equations in th...... in the rest system of the medium, whereas the final integrals determining the field may be calculated in the rest system of the source. ©1972 The American Institute of Physics...
Diffraction of a Shear Plane Wave in Elastic Medium with Piecewise Homogeneous Infinite Inclusion
Directory of Open Access Journals (Sweden)
Voskanyan A. R.
2007-06-01
Full Text Available Diffraction of shear plane wave incident from infinity at arbitrary angle on infinite inclusion is considered. The infinite inclusion consists of two semi-infinite parts made of different materials. The problem’s solution is presented in the form of sum of its even and odd problems. The case of long waves is considered and these problems (the even and odd ones are modelled in a corresponding way after which each of them is reduced to the solution of Wiener-Hopf functional equation. Asymptotic formulas are obtained for displacement’s amplitude and contacts stresses in the far field. The behaviors of contact stresses in the neighborhood of the bonding line of the semi-infinite parts of the inclusion are also obtained.
Dynamical friction for supersonic motion in a homogeneous gaseous medium
Thun, Daniel; Schmidt, Franziska; Kley, Wilhelm
2016-01-01
The supersonic motion of gravitating objects through a gaseous medium constitutes a classical problem in theoretical astrophysics. Its application covers a broad range of objects and scales from planets up to galaxies. Especially the dynamical friction, caused by the forming wake behind the object, plays an important role for the dynamics of the system. To calculate the dynamical friction, standard formulae, based on linear theory are often used. It is our goal to check the general validity of these formulae and provide suitable expressions for the dynamical friction acting on the moving object, based on the basic physical parameters of the problem. We perform sequences of high resolution numerical studies of rigid bodies moving supersonically through a homogeneous medium, and calculate the total drag acting on the object, which is the sum of gravitational and hydro drag. We study cases without gravity with purely hydrodynamical drag, as well as gravitating objects. From the final equilibrium state of the sim...
Dynamical friction for supersonic motion in a homogeneous gaseous medium
Thun, Daniel; Kuiper, Rolf; Schmidt, Franziska; Kley, Wilhelm
2016-05-01
Context. The supersonic motion of gravitating objects through a gaseous ambient medium constitutes a classical problem in theoretical astrophysics. Its application covers a broad range of objects and scales from planetesimals, planets, and all kind of stars up to galaxies and black holes. In particular, the dynamical friction caused by the wake that forms behind the object plays an important role for the dynamics of the system. To calculate the dynamical friction for a particular system, standard formulae based on linear theory are often used. Aims: It is our goal to check the general validity of these formulae and provide suitable expressions for the dynamical friction acting on the moving object, based on the basic physical parameters of the problem: first, the mass, radius, and velocity of the perturber; second, the gas mass density, soundspeed, and adiabatic index of the gaseous medium; and finally, the size of the forming wake. Methods: We perform dedicated sequences of high-resolution numerical studies of rigid bodies moving supersonically through a homogeneous ambient medium and calculate the total drag acting on the object, which is the sum of gravitational and hydrodynamical drag. We study cases without gravity with purely hydrodynamical drag, as well as gravitating objects. In various numerical experiments, we determine the drag force acting on the moving body and its dependence on the basic physical parameters of the problem, as given above. From the final equilibrium state of the simulations, for gravitating objects we compute the dynamical friction by direct numerical integration of the gravitational pull acting on the embedded object. Results: The numerical experiments confirm the known scaling laws for the dependence of the dynamical friction on the basic physical parameters as derived in earlier semi-analytical studies. As a new important result we find that the shock's stand-off distance is revealed as the minimum spatial interaction scale of
Rohan, Eduard; Naili, Salah; Nguyen, Vu-Hieu
2016-08-01
We study wave propagation in an elastic porous medium saturated with a compressible Newtonian fluid. The porous network is interconnected whereby the pores are characterized by two very different characteristic sizes. At the mesoscopic scale, the medium is described using the Biot model, characterized by a high contrast in the hydraulic permeability and anisotropic elasticity, whereas the contrast in the Biot coupling coefficient is only moderate. Fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. The homogenization method based on the asymptotic analysis is used to obtain a macroscopic model. To respect the high contrast in the material properties, they are scaled by the small parameter, which is involved in the asymptotic analysis and characterized by the size of the heterogeneities. Using the estimates of wavelengths in the double-porosity networks, it is shown that the macroscopic descriptions depend on the contrast in the static permeability associated with pores and micropores and on the frequency. Moreover, the microflow in the double porosity is responsible for fading memory effects via the macroscopic poroviscoelastic constitutive law. xml:lang="fr"
Anisotropic enhancement of group velocity in a homogenized dielectric composite medium
Mackay, Tom G.; Lakhtakia, Akhlesh
2005-01-01
Under certain circumstances, the group velocity in a homogenized composite medium (HCM) can exceed the group velocity in its component material phases. We explore this phenomenon for a uniaxial dielectric HCM comprising isotropic component material phases distributed as oriented spheroidal particles. The theoretical approach is based upon the Bruggeman homogenization formalism. Enhancement in group velocity in the HCM with respect to the component material phases is shown to be sensitively de...
Directory of Open Access Journals (Sweden)
Sethi M.
2016-05-01
Full Text Available The present paper discusses the dispersion equation for SH waves in a non-homogeneous monoclinic layer over a semi infinite isotropic medium. The wave velocity equation has been obtained. In the isotropic case, when non-homogeneity is absent, the dispersion equation reduces to the standard SH wave equation. The dispersion curves are depicted by means of graphs for different values of non-homogeneity parameters for the layer and semi-infinite medium.
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
HOMOGENIZATION OF A STATIONARY NAVIER-STOKES FLOW IN POROUS MEDIUM WITH THIN FILM
Institute of Scientific and Technical Information of China (English)
Yao Zhengan; Zhao Hongxing
2008-01-01
The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition. At the end of the article, "Darcy's law" is rigorously derived from this model as the parameter e tends to zero, which is independent of the coordinates towards the thickness.
Li, Jia; Chen, Feinan; Chang, Liping
2016-10-17
Within the validity of the first-order Born approximation, expressions are derived for the correlation between intensity fluctuations (CIF) of an electromagnetic plane wave scattered from a spatially quasi-homogeneous (QH), anisotropic medium. Upon establishing the correlation matrix of the scattering potential of the medium, we show that the CIF is the summation of Fourier transforms of the strengths and normalized correlation coefficients (NCCs) of the scattering potential matrix. Numerical results reveal that the CIF is susceptible to the effective width and correlation length of the medium, and degree of polarization of the incident electromagnetic wave. Our study not only extends the current knowledge of the CIF of a scattered field but also provides an important reference to the study of high-order intensity correlations of light scattered from a spatially anisotropic medium.
Propagation of seismic waves through a spatio-temporally fluctuating medium: Homogenization
Hanasoge, Shravan; Bal, Guillaume
2013-01-01
Measurements of seismic wave travel times at the photosphere of the Sun have enabled inferences of its interior structure and dynamics. In interpreting these measurements, the simplifying assumption that waves propagate through a temporally stationary medium is almost universally invoked. However, the Sun is in a constant state of evolution, on a broad range of spatio-temporal scales. At the zero wavelength limit, i.e., when the wavelength is much shorter than the scale over which the medium varies, the WKBJ (ray) approximation may be applied. Here, we address the other asymptotic end of the spectrum, the infinite wavelength limit, using the technique of homogenization. We apply homogenization to scenarios where waves are propagating through rapidly varying media (spatially and temporally), and derive effective models for the media. One consequence is that a scalar sound speed becomes a tensorial wavespeed in the effective model and anisotropies can be induced depending on the nature of the perturbation. The ...
Radiation pattern of plasmonic nano-antennas in a homogeneous medium.
Sugita, Takafumi; Yanazawa, Kaori; Maeda, Satoshi; Hofmann, Holger F; Kadoya, Yutaka
2014-06-02
Radiation patterns from plasmonic nano-antennas formed on a glass substrate were investigated using index-matching oils. It was confirmed that the pattern from single nano-antennas for various cases of index-mismatching between the substrate and the oil is explained well by the patterns of infinitesimal electric dipoles. We found that for an angular resolution of 2°, the index mismatch must be smaller than 0.001 to realize isotropic radiation. By using the appropriate condition, the radiation patterns of nano Yagi-Uda antennas in a quasi-homogeneous medium were obtained experimentally.
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.
Directory of Open Access Journals (Sweden)
Wang Lihong V
2004-05-01
Full Text Available Abstract Background The bioluminescent enzyme firefly luciferase (Luc or variants of green fluorescent protein (GFP in transformed cells can be effectively used to reveal molecular and cellular features of neoplasia in vivo. Tumor cell growth and regression in response to various therapies can be evaluated by using bioluminescent imaging. In bioluminescent imaging, light propagates in highly scattering tissue, and the diffusion approximation is sufficiently accurate to predict the imaging signal around the biological tissue. The numerical solutions to the diffusion equation take large amounts of computational time, and the studies for its analytic solutions have attracted more attention in biomedical engineering applications. Methods Biological tissue is a turbid medium that both scatters and absorbs photons. An accurate model for the propagation of photons through tissue can be adopted from transport theory, and its diffusion approximation is applied to predict the imaging signal around the biological tissue. The solution to the diffusion equation is formulated by the convolution between its Green's function and source term. The formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium can be obtained to accelerate the forward simulation of bioluminescent phenomena. Results The closed form solutions have been derived for the time-dependent diffusion equation and the steady-state diffusion equation with solid and hollow spherical sources in a homogeneous medium, respectively. Meanwhile, the relationship between solutions with a solid sphere source and ones with a surface sphere source is obtained. Conclusion We have formulated solutions for the diffusion equation with solid and hollow spherical sources in an infinite homogeneous medium. These solutions have been verified by Monte Carlo simulation for use in biomedical optical imaging studies. The closed form solution is highly accurate and more
Homogenization of a locally-periodic medium with areas of low and high diffusivity
van Noorden, T
2010-01-01
We aim at understanding transport in porous materials including regions with both high and low diffusivities. For such scenarios, the transport becomes structured (here: {\\em micro-macro}). The geometry we have in mind includes regions of low diffusivity arranged in a locally-periodic fashion. We choose a prototypical advection-diffusion system (of minimal size), discuss its formal homogenization (the heterogenous medium being now assumed to be made of zones with circular areas of low diffusivity of $x$-varying sizes), and prove the weak solvability of the limit two-scale reaction-diffusion model. A special feature of our analysis is that most of the basic estimates (positivity, $L^\\infty$-bounds, uniqueness, energy inequality) are obtained in $x$-dependent Bochner spaces.
Application of linear-extended neutron diffusion equation in a semi-infinite homogeneous medium
Energy Technology Data Exchange (ETDEWEB)
Espinosa-Paredes, Gilberto, E-mail: gepe@xanum.uam.mx [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, Mexico 09340, D.F. (Mexico); Vazquez-Rodriguez, Rodolfo [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, Mexico 09340, D.F. (Mexico)
2011-02-15
The linear-extended neutron diffusion equation (LENDE) is the volume-averaged neutron diffusion equation (VANDE) which includes two correction terms: the first correction is related with the absorption process of the neutron and the second is a contribution to the neutron diffusion, both parameters are related to neutron effects on the interface of a heterogeneous configuration. In this work an analysis of a plane source in a semi-infinite homogeneous medium was considered to study the effects of the correction terms and the results obtained with the linear-extended neutron diffusion equation were compared against a semi-analytical benchmark for the same case. The comparison of the results demonstrate the excellent approach between the linear-extended diffusion theory and the selected benchmark, which means that the correction terms of the VANDE are physically acceptable.
Markel, Vadim A
2013-01-01
Reflection and refraction of electromagnetic waves by artificial periodic composites (metamaterials) can be accurately modeled by an effective medium theory only if the boundary of the medium is explicitly taken into account and the two effective parameters of the medium -- the index of refraction and the impedance -- are correctly determined. Theories that consider infinite periodic composites do not satisfy the above condition. As a result, they cannot model reflection and transmission by finite samples with the desired accuracy and are not useful for design of metamaterial-based devices. As an instructive case in point, we consider the "current-driven" homogenization theory, which has recently gained popularity. We apply this theory to the case of one-dimensional periodic medium wherein both exact and homogenization results can be obtained analytically in closed form. We show that, beyond the well-understood zero-cell limit, the current-driven homogenization result is inconsistent with the exact reflection...
Sun, Fei; He, Sailing
2015-10-01
A new theory on designing electromagnetic/optical devices is proposed, namely, an optical surface transformation (OST). One arbitrary surface can establish the corresponding relationship with another surface entirely optically with an optic-null medium (ONM), (i.e. the electromagnetic wave propagates from one surface to its equivalent surface without any phase delay). Many novel optical devices can be designed by an OST with the help of an ONM. Compared with traditional devices designed by Transformation Optics, our optical surface-reshaping devices have two main advantages. Firstly, the design process is very simple (i.e. we do not need to consider any mathematics on how to make a coordinate transformation, and what we need to do is simply to design the shapes of the input and the output surfaces of the devices). Secondly, we only need one homogeneous anisotropic medium to realize all devices designed by this method. Our method will explore a new way to design novel optical devices without considering any coordinate transformations.
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.
Xin, Z. D.; Xu, Y. Y.; Ji, Y.; Jin, W. F.; Zheng, H. R.; Zhang, L.; Wang, Y. W.
2016-10-01
In the paper, a decoupling method for homogeneous and dual-medium cells' refractive index, and the entropy tomographic phase imaging method are proposed. Based on the decoupling method, the 3D morphology of sample can be obtained by the imaging method, which only needs two phase images of the cell. Thus the information about 3D refractive index distribution is given, and the 3D structure image of the model is reconstructed as well based on the relationship between the refractive index and thickness. In order to verify these methods, we set up the typical models after analysing the characteristic of blood cells, and the related orthogonal phase images are obtained by simulation experiment. Thus the 3D reconstructed structure images of the models are presented in this paper. Finally, the feasibility of this method is verified by simulating on a red blood cell and a monocyte model. The results show that subsurface imaging of samples can be achieved based on this method with a good accuracy.
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.
Li, Jia; Chang, Liping; Chen, Feinan
2016-12-01
Based on the first-order Born approximation, the correlation between intensity fluctuations is derived for a partially coherent, electromagnetic plane wave scattering from a spatially quasi-homogeneous medium. Young's pinholes are utilized to control the degree of coherence of the incident field. For the electromagnetic scattering case, it is shown that the CIF of the scattered field strongly depends on the degree of polarization of the incident wave, Young's pinhole parameter, effective radius and correlation length of the medium. The influences of these parameters on the CIF distributions are revealed by numerical calculations.
Bruining, H.; Darwish, M.; Rijnks, A.
2011-01-01
This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that the longitudinal dispersion coefficient can be
Bruining, J.; Darwish, M.; Rijnks, A.
2011-01-01
This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that the longitudinal dispersion coefficient can be
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.
Marciniak-Czochra, Anna
2012-01-01
We present modeling of the incompressible viscous flows in the domain containing an unconfined fluid and a porous medium. For such setting a rigorous derivation of the Beavers-Joseph-Saffman interface condition was undertaken by J\\"ager and Mikeli\\'c [SIAM J. Appl. Math. \\rm 60 (2000), p. 1111-1127] using the homogenization method. So far the interface law for the pressure was conceived and confirmed only numerically. In this article we justify rigorously the pressure jump condition using the corresponding boundary layer.
Azimuthally dependent radiative transfer in a non-homogeneous cylindrical medium
Hsu, S C; Ou, N R
1998-01-01
This work applies the discrete-ordinate method (DOM) to study azimuthally dependent radiative transfer in a two-dimensional cylindrical medium with spatially varying properties. Product angular quadratures are selected to generate discrete-ordinate approximations. The validity of the present DOM scheme is examined by comparing the present results with the results available in the literature. The effects of the optical thickness and the spatially varying extinction coefficient, scattering albedo and coefficients of the phase function are investigated.
Lechleiter, Armin; Nguyen, Dinh Liem
2010-01-01
Scattering of acoustic waves from an inhomogeneous medium can be described by the Lippmann-Schwinger integral equation. For scattering problems in free space, Vainikko proposed a fast spectral solution method that exploits the convolution structure of this equation's integral operator by using the fast Fourier transform. In a planar 3--dimensional waveguide, the integral operator of the Lippmann-Schwinger integral equation fails to be a convolution. In this paper, we show that the separable s...
Piao, Daqing; Barbour, Randall L; Graber, Harry L; Lee, Daniel C
2015-10-01
This work analytically examines some dependences of the differential pathlength factor (DPF) for steady-state photon diffusion in a homogeneous medium on the shape, dimension, and absorption and reduced scattering coefficients of the medium. The medium geometries considered include a semi-infinite geometry, an infinite-length cylinder evaluated along the azimuthal direction, and a sphere. Steady-state photon fluence rate in the cylinder and sphere geometries is represented by a form involving the physical source, its image with respect to the associated extrapolated half-plane, and a radius-dependent term, leading to simplified formula for estimating the DPFs. With the source-detector distance and medium optical properties held fixed across all three geometries, and equal radii for the cylinder and sphere, the DPF is the greatest in the semi-infinite and the smallest in the sphere geometry. When compared to the results from finite-element method, the DPFs analytically estimated for 10 to 25 mm source–detector separations on a sphere of 50 mm radius with μa=0.01 mm(−1) and μ′s=1.0 mm(−1) are on average less than 5% different. The approximation for sphere, generally valid for a diameter≥20 times of the effective attenuation pathlength, may be useful for rapid estimation of DPFs in near-infrared spectroscopy of an infant head and for short source–detector separation.
Piao, Daqing; Barbour, Randall L.; Graber, Harry L.; Lee, Daniel C.
2015-01-01
Abstract. This work analytically examines some dependences of the differential pathlength factor (DPF) for steady-state photon diffusion in a homogeneous medium on the shape, dimension, and absorption and reduced scattering coefficients of the medium. The medium geometries considered include a semi-infinite geometry, an infinite-length cylinder evaluated along the azimuthal direction, and a sphere. Steady-state photon fluence rate in the cylinder and sphere geometries is represented by a form involving the physical source, its image with respect to the associated extrapolated half-plane, and a radius-dependent term, leading to simplified formula for estimating the DPFs. With the source-detector distance and medium optical properties held fixed across all three geometries, and equal radii for the cylinder and sphere, the DPF is the greatest in the semi-infinite and the smallest in the sphere geometry. When compared to the results from finite-element method, the DPFs analytically estimated for 10 to 25 mm source–detector separations on a sphere of 50 mm radius with μa=0.01 mm−1 and μs′=1.0 mm−1 are on average less than 5% different. The approximation for sphere, generally valid for a diameter ≥20 times of the effective attenuation pathlength, may be useful for rapid estimation of DPFs in near-infrared spectroscopy of an infant head and for short source–detector separation. PMID:26465613
Source-like solution for radial imbibition into a homogeneous semi-infinite porous medium
Xiao, Junfeng; Attinger, Daniel
2012-01-01
We describe the imbibition process from a point source into a homogeneous semi-infinite porous material. When body forces are negligible, the advance of the wetting front is driven by capillary pressure and resisted by viscous forces. With the assumption that the wetting front assumes a hemispherical shape, our analytical results show that the absorbed volume flow rate is approximately constant with respect to time, and that the radius of the wetting evolves in time as r \\approx t^(1/3). This cube-root law for the long-time dynamics is confirmed by experiments using a packed cell of glass microspheres with average diameter of 42 {\\mu}m. This result complements the classical one-dimensional imbibition result where the imbibition length l \\approx t^(1/2), and studies in axisymmetric porous cones with small opening angles where l \\approx t^(1/4) at long times.
Kostinski, Alexander B.
2002-12-01
In response to comments by Borovoi [J. Opt. Soc. Am. A 19, 2517 (2002)] on my earlier work [J. Opt. Soc. Am. A 18, 1929 (2001)], the kinetic approach to extinction is compared with the traditional radiative transfer formalism and advantages of the former are illustrated with concrete examples. It is pointed out that the basic differential equation dI(l)=- cσI(l)dl already implies perfect randomness (absence of correlations) on small scales. One of the consequences is that the extinction of radiation in a negatively correlated random medium cannot be treated within the traditional framework. This limits the usefulness of the Jensen inequality. Also, simple counterexamples to theorems given in the first reference above and in Dokl. Akad. Nauk SSSR, 276, 1374 (1984) are presented.
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.
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
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.
Directory of Open Access Journals (Sweden)
Vladimir Jurak
2006-12-01
Full Text Available A great deal of data which determine the characteristics of engineering soils was collected in the course of geotechnical explorations conducted for the purpose of building two industrial objects near Kutina (Tvornica umjetnih gnojiva / Artificial fertilizer factory II and Soot Factory II/ Čađara II. Wishing to familiarize ourselves with the condition of homogeneity/heterogeneity underneath the object, we decided to check the hypothesis regarding the homogeneity of the a priori acquired geotechnical mediums and their geotechnical similarity. The relationship of the two mediums under observation is superpositional, they are lithologically similar but genetically different. They are represented through an engineering geological model reaching the depth of forty meters. Following the basic statistical data analysis for identification, geotechnical parameters and the use of several statistical tests, we were able to reach an engineering judgment on the basis of statistical conclusions. We realized that, from a statistical point of view, both geotechnical mediums are mostly homogenous or, speaking from the engineering point of view, ''quasi-homogenous''. The comparison of these two mediums showed that there is no statistically significant difference according to certain geotechnical parameters of geotechnical parameters. It follows, therefore, that the unification of the superpositioned mediums in a physically united halfspace located under the object is acceptable (the paper is published in Croatian.
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
Rahmati, A. H.; Mohammadimehr, M.
2014-05-01
Electro-thermo-mechanical vibration analysis of non-uniform and non-homogeneous boron nitride nanorod (BNNR) embedded in elastic medium is presented. The steady state heat transfer equation without external heat source for non-homogeneous rod is developed and temperature distribution is derived. Using Maxwell's equation and nonlocal elasticity theory the coupled displacement and electrical potential equations are presented. Differential quadrature method (DQM) is implemented to evaluate the natural frequencies. The effects of attached mass, lower and higher vibrational mode, elastic medium, piezoelectric coefficient, dielectric coefficient, cross section coefficient, non-homogeneity parameter and small scale parameter on the natural frequency are investigated. The appropriate values for Winkler and Pasternak modulus in axial vibration of boron nitride nanorod are reported. The mass sensitivity limit of 10-1 (zg) is derived for BNNR-based nano-electro-mechanical sensors. The results show that the C-F boundary condition of BNNRs are more sensitive to attached mass than the C-C boundary condition and also the sensitivity range for BNNRs. It is concluded that frequency ratio decreases considering electro-thermal loadings and electrical loadings are more effective in non-uniform nanorods, in comparison with uniform nanorod. The natural frequency of BNNRs can be varied using different cross section coefficient and non-homogeneity parameter. This fact can be employed for practical tools to design and control nano-devices and nano-electro-mechanical systems (NEMS) to prevent resonance phenomenon.
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...
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.
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".
Piao, Daqing; Zhang, Anqi; Xu, Guan
2013-04-01
As Part V in our series, this paper examines steady-state fluorescence photon diffusion in a homogenous medium that contains a homogenous distribution of fluorophores, and is enclosed by a "concave" circular cylindrical applicator or is enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to predict by analytics and examine with the finite-element method the changing characteristics of the fluorescence-wavelength photon-fluence rate and the ratio (sometimes called the Born ratio) of it versus the excitation-wavelength photon-fluence rate, with respect to the source-detector distance. The analysis is performed for a source and a detector located on the medium-applicator interface and aligned either azimuthally or longitudinally in both concave and convex geometries. When compared to its steady-state counterparts on a semi-infinite medium-applicator interface with the same line-of-sight source-detector distance, the fluorescence-wavelength photon-fluence rate reduces faster along the longitudinal direction and slower along the azimuthal direction in the concave geometry, and conversely in the convex geometry. However, the Born ratio increases slower in both azimuthal and longitudinal directions in the concave geometry and faster in both directions in the convex geometry, respectively, when compared to that in the semi-infinite geometry.
Li, Jia; Chen, Feinan
2016-11-01
Based on the first-order Born approximation, formulas are derived for the correlation between intensity fluctuations (CIF) of light generated by a Young’s diffractive electromagnetic wave scattered by a spatially quasi-homogeneous (QH), anisotropic medium. It is shown that the CIF of the scattered field can be written as the summation of the Fourier transforms of the strengths and normalized correlation coefficients (NCCs) of the scattering potentials. The differences between our results and those obtained in the previous literature are discussed. Our results might be important in investigating the high-order intensity correlation of an electromagnetic wave scattered from a 3D anisotropic object.
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.
Directory of Open Access Journals (Sweden)
N.V. Chernysheva
2016-08-01
Full Text Available The application of algorithms of the finite element method (FEM or the boundary element method (BEM reveals some peculiar properties for a numerical solution of the three-dimensional analysis in infinite domains. Various algorithms offer to avoid such problems at the expense of combining different methods and equations. The algorithm of the 3d analysis developed to solve an external boundary problem by applying the combined method based on incorporating the FEM and Somigliana’s integral formula is considered. The algorithm is modified for the case of the interaction of a structure with an inhomogeneous medium. The efficiency of software implementation of both algorithms has been tested. A stress-strain analysis of an inhomogeneous medium with a cavity has been carried out to illustrate the given approach.
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...
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.
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.
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/.
Surface instability of a homogeneous half-space coupled with finite number of laminas
Energy Technology Data Exchange (ETDEWEB)
Chekhov, V.N.; Stukotilov, V.S.
1995-09-10
In the context of the model of a piecewise-homogeneous medium in three-dimensional formulation we study the problem of the surface loss of stability in laminated semi-bounded media with a finite number of laminas. For the study we invoke a version of three-dimensional stability theory constructed for small pre-critical deformations when the pre-critical state is determined from the geometrically linear theory. To construct the resolvent characteristic equations we use the matrix representation of the basic relations. Using a computer we carry out a numerical study of the stability of a homogeneous half-space coupled to various numbers of laminas, and we conduct a comparative analysis of the results.
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.
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.
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.
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.
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...
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.
[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.
Institute of Scientific and Technical Information of China (English)
张华荣; 蒋月; 李成; 余向阳
2009-01-01
用数值计算方法研究了均匀展宽二能级体系在激光超短脉冲作用下介质参量、入射脉冲面积、弛豫时间和频率失谐量对光脉冲面积演化的影响.计算结果表明,脉冲面积会在最接近输入脉冲面积2π偶数倍的值上振荡,并经过一定的传播距离后,台阶式跳跃到下一个偶数倍2π的值上振荡.%The evolution rule of the ultra-short laser pulse area which propagate through a homogeneously broadened two level system was studied.The numerical result shows that the pulse area will oscillate near the even times of 2π,and then change jumpily into the next even times of 2π after a propagation distance.The mechanism of these phenomena was analyzed particularly.In addition,by considering the medium parameter,the input pulse area,relaxation time,detune respectively,we also investigate the evolution rule of ultar-short pulse′s propagation in a homogeneously broadened two-level atomic medium.
Chadwick, John C; Freixa, Zoraida; van Leeuwen, Piet W N M
2011-01-01
This first book to illuminate this important aspect of chemical synthesis improves the lifetime of catalysts, thus reducing material and saving energy, costs and waste.The international panel of expert authors describes the studies that have been conducted concerning the way homogeneous catalysts decompose, and the differences between homogeneous and heterogeneous catalysts. The result is a ready reference for organic, catalytic, polymer and complex chemists, as well as those working in industry and with/on organometallics.
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.
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.
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...
Chen, J.-S.; Lai, G.-X.
2009-04-01
The morphological evolution of a chemical dissolution front is an important topic in geological processes and engineering practices. Although previous studies have extensively presented a number of numerical models which couples a system of nonlinear governing equations of porosity change due to mineral dissolution, the conservations of groundwater flow and transport of chemical species to investigate the morphological pattern of a chemical dissolution front within a fluid-saturated porous medium, whereas the mechanical dispersion effect has generally been neglected in the model development. This study addresses the effects of mechanical dispersion on the morphological evolution of a chemical dissolution front for a variety of cases. Mechanical dispersion processes is incorporated with the coupled nonlinear governing equation system so as to rebuild a newly numerical model. The results of numerical simulations demonstrate that mechanical dispersion has pronounced impacts on the morphological pattern of the chemical dissolution front. For single local non-uniformity case, mechanical dispersion reduces the finger length of an unstable single-fingering front or retains the shape of a stable planar front while speeding up the front advancement. In the case of two local non-uniformities, adding mechanical dispersion with different flow conditions can yield one of the following results: (1) the shape of the stable planar front is maintained but its advancement is accelerated; (2) the shape of the unstable single-fingering front is maintained but its length is reduced; (3) the unstable double-fingering front is merged into an unstable single-fingering front; and (4) the shape of the unstable double-fingering front is preserved but its fingering length is reduced.. A comparison between the behavior diagrams of dissolution front morphology (with and without considering mechanical dispersion) shows that the double-fingering front occurs under condition where the upstream
Akhundov, V. M.
2017-01-01
Results of an analysis of form changes of a toroidal body highly filled with fibers at large torsional deformations and rotational motions are presented. The body is reinforced in the meridional direction. The investigation was carried out by using the two-level carcass theory of fibrous media at large deformations, according to which the macroscopic fields of a reinforced body are determined by its internal fields. These fields are represented by the material configurations of nodal material blocks of the body, for which, on the basis of the model of a piecewise homogeneous medium, boundary-values problems of the micromechanical level of the theory are solved. The results obtained are compared with those for a homogeneous body. The congruent deformation of the homogeneous body at which its initial form and dimensions are practically restored upon superposition of torsion and rotation is determined.
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...
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.
Energy Technology Data Exchange (ETDEWEB)
Tran Ngoc, T.D
2008-07-15
This Ph.D thesis presents the development of the solute transport models in unsaturated double-porosity medium, by using the asymptotic homogenization method. The obtained macroscopic models concern diffusion, diffusion-convection and dispersion-convection, according to the transport regime which is characterized by the non-dimensional numbers. The models consist of two coupled equations that show the local non-equilibrium of concentrations. The double-porosity transport models were numerically implemented using the code COMSOL Multiphysics (finite elements method), and compared with the solution of the same problem at the fine scale. The implementation allows solving the coupled equations in the macro- and micro-porosity domains (two-scale computations). The calculations of the dispersion tensor as a solution of the local boundary value problems, were also conducted. It was shown that the dispersivity depends on the saturation, the physical properties of the macro-porosity domain and the internal structure of the double-porosity medium. Finally, two series of experiments were performed on a physical model of double-porosity that is composed of a periodic assemblage of sintered clay spheres in Hostun sand HN38. The first experiment was a drainage experiment, which was conducted in order to validate the unsaturated flow model. The second series was a dispersion experiment in permanent unsaturated water flow condition (water content measured by gamma ray attenuation technique). A good agreement between the numerical simulations and the experimental observations allows the validation of the developed models. (author)
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.
Energy Technology Data Exchange (ETDEWEB)
Sanchez, R.; Ragusa, J.; Santandrea, S. [Commissariat a l' Energie Atomique, Direction de l' Energie Nucleaire, Service d' Etudes de Reacteurs et de Modelisation Avancee, CEA de Saclay, DM2S/SERMA 91 191 Gif-sur-Yvette cedex (France)]. e-mail: richard.sanchez@cea.fr
2004-07-01
The problem of the determination of a homogeneous reflector that preserves a set of prescribed albedo is considered. Duality is used for a direct estimation of the derivatives needed in the iterative calculation of the optimal homogeneous cross sections. The calculation is based on the preservation of collapsed multigroup albedo obtained from detailed reference calculations and depends on the low-order operator used for core calculations. In this work we analyze diffusion and transport as low-order operators and argue that the P{sub 0} transfers are the best choice for the unknown cross sections to be adjusted. Numerical results illustrate the new approach for SP{sub N} core calculations. (Author)
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.
Energy Technology Data Exchange (ETDEWEB)
Ramirez Ros, J. C.; Jerez Sainz, M. I.; Lobato Munoz, M.; Jodar Lopez, C. A.; Ruiz Lopez, M. A.; Carrasco rodriguez, J. L.; Pamos Urena, M.
2013-07-01
We evaluated the Monte Carlo Monaco Planner v2.0.3 for calculation between non-homogeneous low density (equivalent to lung), as a complement to the verification of modeling in homogeneous medium and prior to the introduction of the SBRT technique. We performed the same tests on Pinnacle v8.0m, with the same purpose. We compare the results obtained with the algorithm Monte Carlo of Monaco and the Collapsed Cone of Pinnacle. (Author)
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.
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.
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.
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.
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.
Schulreich, M. M.; Breitschwerdt, D.; Feige, J.; Dettbarn, C.
2017-08-01
Context. The discovery of radionuclides like 60Fe with half-lives of million years in deep-sea crusts and sediments offers the unique possibility to date and locate nearby supernovae. Aims: We want to quantitatively establish that the 60Fe enhancement is the result of several supernovae which are also responsible for the formation of the Local Bubble, our Galactic habitat. Methods: We performed three-dimensional hydrodynamic adaptive mesh refinement simulations (with resolutions down to subparsec scale) of the Local Bubble and the neighbouring Loop I superbubble in different homogeneous, self-gravitating environments. For setting up the Local and Loop I superbubble, we took into account the time sequence and locations of the generating core-collapse supernova explosions, which were derived from the mass spectrum of the perished members of certain stellar moving groups. The release of 60Fe and its subsequent turbulent mixing process inside the superbubble cavities was followed via passive scalars, where the yields of the decaying radioisotope were adjusted according to recent stellar evolution calculations. Results: The models are able to reproduce both the timing and the intensity of the 60Fe excess observed with rather high precision, provided that the external density does not exceed 0.3 cm-3 on average. Thus the two best-fit models presented here were obtained with background media mimicking the classical warm ionised and warm neutral medium. We also found that 60Fe (which is condensed onto dust grains) can be delivered to Earth via two physical mechanisms: either through individual fast-paced supernova blast waves, which cross the Earth's orbit sometimes even twice as a result of reflection from the Local Bubble's outer shell, or, alternatively, through the supershell of the Local Bubble itself, injecting the 60Fe content of all previous supernovae at once, but over a longer time range.
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.
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...
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...
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.
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...
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.
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.
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.
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.
Cherenkov radiation in moving medium
2010-01-01
Cherenkov radiation in uniformly moving homogenous isotropic medium without dispersion is studied. Formula for the spectrum of Cherenkov radiation of fermion was derived for the case when the speed of the medium is less than the speed of light in this medium at rest. The properties of Cherenkov spectrum are investigated.
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.
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.
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.
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.
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.
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.
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.
Homogeneous models for bianisotropic crystals
Ponti, S; Oldano, C
2002-01-01
We extend to bianisotropic structures a formalism already developed, based on the Bloch method for defining the effective dielectric tensor of anisotropic crystals in the long-wavelength approximation. More precisely, we provide a homogenization scheme which yields a wavevector-dependent effective medium for any 3D, 2D, or 1D bianisotropic crystal. We illustrate our procedure by applying this to a 1D magneto-electric smectic C*-type structure. The resulting equations confirm that the presence of dielectric and magnetic susceptibilities in the periodic structures generates magneto-electric pseudo-tensors for the effective medium. Their contribution to the optical activity of structurally chiral media can be of the same order of magnitude as the one present in dielectric helix-shaped crystals. Simple analytical expressions are found for the most important optical properties of smectic C*-type structures which are simultaneously dielectric and magnetic.
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.
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.
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.
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.
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.
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.
Inverse acoustic problem of N homogeneous scatterers
DEFF Research Database (Denmark)
Berntsen, Svend
2002-01-01
The three-dimensional inverse acoustic medium problem of N homogeneous objects with known geometry and location is considered. It is proven that one scattering experiment is sufficient for the unique determination of the complex wavenumbers of the objects. The mapping from the scattered fields...
Inverse acoustic problem of N homogeneous scatterers
DEFF Research Database (Denmark)
Berntsen, Svend
2002-01-01
The three-dimensional inverse acoustic medium problem of N homogeneous objects with known geometry and location is considered. It is proven that one scattering experiment is sufficient for the unique determination of the complex wavenumbers of the objects. The mapping from the scattered fields...
Lifting locally homogeneous geometric structures
McKay, Benjamin
2011-01-01
We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.
Functionality and homogeneity.
2011-01-01
Functionality and homogeneity are two of the five Sustainable Safety principles. The functionality principle aims for roads to have but one exclusive function and distinguishes between traffic function (flow) and access function (residence). The homogeneity principle aims at differences in mass, spe
Functionality and homogeneity.
2011-01-01
Functionality and homogeneity are two of the five Sustainable Safety principles. The functionality principle aims for roads to have but one exclusive function and distinguishes between traffic function (flow) and access function (residence). The homogeneity principle aims at differences in mass, spe
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.
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
Homogeneity of Inorganic Glasses
DEFF Research Database (Denmark)
Jensen, Martin; Zhang, L.; Keding, Ralf;
2011-01-01
Homogeneity of glasses is a key factor determining their physical and chemical properties and overall quality. However, quantification of the homogeneity of a variety of glasses is still a challenge for glass scientists and technologists. Here, we show a simple approach by which the homogeneity...... of different glass products can be quantified and ranked. This approach is based on determination of both the optical intensity and dimension of the striations in glasses. These two characteristic values areobtained using the image processing method established recently. The logarithmic ratio between...... the dimension and the intensity is used to quantify and rank the homogeneity of glass products. Compared with the refractive index method, the image processing method has a wider detection range and a lower statistical uncertainty....
Homogeneity of Inorganic Glasses
DEFF Research Database (Denmark)
Jensen, Martin; Zhang, L.; Keding, Ralf
2011-01-01
Homogeneity of glasses is a key factor determining their physical and chemical properties and overall quality. However, quantification of the homogeneity of a variety of glasses is still a challenge for glass scientists and technologists. Here, we show a simple approach by which the homogeneity...... of different glass products can be quantified and ranked. This approach is based on determination of both the optical intensity and dimension of the striations in glasses. These two characteristic values areobtained using the image processing method established recently. The logarithmic ratio between...... the dimension and the intensity is used to quantify and rank the homogeneity of glass products. Compared with the refractive index method, the image processing method has a wider detection range and a lower statistical uncertainty....
Benchmarking monthly homogenization algorithms
Directory of Open Access Journals (Sweden)
V. K. C. Venema
2011-08-01
Full Text Available The COST (European Cooperation in Science and Technology Action ES0601: Advances in homogenization methods of climate series: an integrated approach (HOME has executed a blind intercomparison and validation study for monthly homogenization algorithms. Time series of monthly temperature and precipitation were evaluated because of their importance for climate studies and because they represent two important types of statistics (additive and multiplicative. The algorithms were validated against a realistic benchmark dataset. The benchmark contains real inhomogeneous data as well as simulated data with inserted inhomogeneities. Random break-type inhomogeneities were added to the simulated datasets modeled as a Poisson process with normally distributed breakpoint sizes. To approximate real world conditions, breaks were introduced that occur simultaneously in multiple station series within a simulated network of station data. The simulated time series also contained outliers, missing data periods and local station trends. Further, a stochastic nonlinear global (network-wide trend was added.
Participants provided 25 separate homogenized contributions as part of the blind study as well as 22 additional solutions submitted after the details of the imposed inhomogeneities were revealed. These homogenized datasets were assessed by a number of performance metrics including (i the centered root mean square error relative to the true homogeneous value at various averaging scales, (ii the error in linear trend estimates and (iii traditional contingency skill scores. The metrics were computed both using the individual station series as well as the network average regional series. The performance of the contributions depends significantly on the error metric considered. Contingency scores by themselves are not very informative. Although relative homogenization algorithms typically improve the homogeneity of temperature data, only the best ones improve
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.
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.
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.
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.
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.
Homogenization scheme for acoustic metamaterials
Yang, Min
2014-02-26
We present a homogenization scheme for acoustic metamaterials that is based on reproducing the lowest orders of scattering amplitudes from a finite volume of metamaterials. This approach is noted to differ significantly from that of coherent potential approximation, which is based on adjusting the effective-medium parameters to minimize scatterings in the long-wavelength limit. With the aid of metamaterials’ eigenstates, the effective parameters, such as mass density and elastic modulus can be obtained by matching the surface responses of a metamaterial\\'s structural unit cell with a piece of homogenized material. From the Green\\'s theorem applied to the exterior domain problem, matching the surface responses is noted to be the same as reproducing the scattering amplitudes. We verify our scheme by applying it to three different examples: a layered lattice, a two-dimensional hexagonal lattice, and a decorated-membrane system. It is shown that the predicted characteristics and wave fields agree almost exactly with numerical simulations and experiments and the scheme\\'s validity is constrained by the number of dominant surface multipoles instead of the usual long-wavelength assumption. In particular, the validity extends to the full band in one dimension and to regimes near the boundaries of the Brillouin zone in two dimensions.
Dynamics of homogeneous nucleation
DEFF Research Database (Denmark)
Toxværd, Søren
2015-01-01
The classical nucleation theory for homogeneous nucleation is formulated as a theory for a density fluctuation in a supersaturated gas at a given temperature. But molecular dynamics simulations reveal that it is small cold clusters which initiates the nucleation. The temperature in the nucleating...
Tignanelli, H. L.; Vazquez, R. A.; Mostaccio, C.; Gordillo, S.; Plastino, A.
1990-11-01
RESUMEN. Presentamos una metodologia de analisis de la homogeneidad a partir de la Teoria de la Informaci6n, aplicable a muestras de datos observacionales. ABSTRACT:Standard concepts that underlie Information Theory are employed in order design a methodology that enables one to analyze the homogeneity of a given data sample. Key : DATA ANALYSIS
Electro-Thermo-Mechanical Homogenization of Ferroelectric Atomistic Medium
2011-03-23
changing their properties (behavior) depending on the environment. These are so-called “smart structures” where feedback loop comprises of sensors ...response of so-called smart structures to various excitations. Electroactive materials are used for actuators, sensors and smart structures...resonators and filters for frequency control and selection for telecommunication, precise timing and synchronization[14], MEM and NEM devices
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
Dynamics of homogeneous nucleation
DEFF Research Database (Denmark)
Toxværd, Søren
2015-01-01
The classical nucleation theory for homogeneous nucleation is formulated as a theory for a density fluctuation in a supersaturated gas at a given temperature. But molecular dynamics simulations reveal that it is small cold clusters which initiates the nucleation. The temperature in the nucleating...... clusters fluctuates, but the mean temperature remains below the temperature in the supersaturated gas until they reach the critical nucleation size. The critical nuclei have, however, a temperature equal to the supersaturated gas. The kinetics of homogeneous nucleation is not only caused by a grow...... or shrink by accretion or evaporation of monomers only but also by an exponentially declining change in cluster size per time step equal to the cluster distribution in the supersaturated gas....
Homogeneous group, research, institution
Directory of Open Access Journals (Sweden)
Francesca Natascia Vasta
2014-09-01
Full Text Available The work outlines the complex connection among empiric research, therapeutic programs and host institution. It is considered the current research state in Italy. Italian research field is analyzed and critic data are outlined: lack of results regarding both the therapeutic processes and the effectiveness of eating disorders group analytic treatment. The work investigates on an eating disorders homogeneous group, led into an eating disorder outpatient service. First we present the methodological steps the research is based on including the strong connection among theory and clinical tools. Secondly clinical tools are described and the results commented. Finally, our results suggest the necessity of validating some more specifical hypothesis: verifying the relationship between clinical improvement (sense of exclusion and painful emotions reduction and specific group therapeutic processes; verifying the relationship between depressive feelings, relapses and transition trough a more differentiated groupal field.Keywords: Homogeneous group; Eating disorders; Institutional field; Therapeutic outcome
Homogenous finitary symmetric groups
Directory of Open Access Journals (Sweden)
Otto. H. Kegel
2015-03-01
Full Text Available We characterize strictly diagonal type of embeddings of finitary symmetric groups in terms of cardinality and the characteristic. Namely, we prove the following. Let kappa be an infinite cardinal. If G=underseti=1stackrelinftybigcupG i , where G i =FSym(kappan i , (H=underseti=1stackrelinftybigcupH i , where H i =Alt(kappan i , is a group of strictly diagonal type and xi=(p 1 ,p 2 ,ldots is an infinite sequence of primes, then G is isomorphic to the homogenous finitary symmetric group FSym(kappa(xi (H is isomorphic to the homogenous alternating group Alt(kappa(xi , where n 0 =1,n i =p 1 p 2 ldotsp i .
Homogenization of resonant chiral metamaterials
DEFF Research Database (Denmark)
Andryieuski, Andrei; Menzel, C.; Rockstuhl, Carsten
2010-01-01
Homogenization of metamaterials is a crucial issue as it allows to describe their optical response in terms of effective wave parameters as, e.g., propagation constants. In this paper we consider the possible homogenization of chiral metamaterials. We show that for meta-atoms of a certain size...... an analytical criterion for performing the homogenization and a tool to predict the homogenization limit. We show that strong coupling between meta-atoms of chiral metamaterials may prevent their homogenization at all....
Homogenization of resonant chiral metamaterials
DEFF Research Database (Denmark)
Andryieuski, Andrei; Menzel, C.; Rockstuhl, Carsten
2010-01-01
Homogenization of metamaterials is a crucial issue as it allows to describe their optical response in terms of effective wave parameters as, e.g., propagation constants. In this paper we consider the possible homogenization of chiral metamaterials. We show that for meta-atoms of a certain size...... an analytical criterion for performing the homogenization and a tool to predict the homogenization limit. We show that strong coupling between meta-atoms of chiral metamaterials may prevent their homogenization at all....
Homogeneous Clifford structures
Moroianu, Andrei; Pilca, Mihaela
2012-01-01
We give an upper bound for the rank r of homogeneous (even) Clifford structures on compact manifolds of non-vanishing Euler characteristic. More precisely, we show that if r = 2a � b with b odd, then r � 9 for a = 0, r � 10 for a = 1, r � 12 for a = 2 and r � 16 for a � 3. Moreover, we describe the four limiting cases and show that there is exactly one solution in each case.
Figueroa-O'Farrill, José
2015-01-01
Motivated by the search for new gravity duals to M2 branes with $N>4$ supersymmetry --- equivalently, M-theory backgrounds with Killing superalgebra $\\mathfrak{osp}(N|4)$ for $N>4$ --- we classify (except for a small gap) homogeneous M-theory backgrounds with symmetry Lie algebra $\\mathfrak{so}(n) \\oplus \\mathfrak{so}(3,2)$ for $n=5,6,7$. We find that there are no new backgrounds with $n=6,7$ but we do find a number of new (to us) backgrounds with $n=5$. All backgrounds are metrically products of the form $\\operatorname{AdS}_4 \\times P^7$, with $P$ riemannian and homogeneous under the action of $\\operatorname{SO}(5)$, or $S^4 \\times Q^7$ with $Q$ lorentzian and homogeneous under the action of $\\operatorname{SO}(3,2)$. At least one of the new backgrounds is supersymmetric (albeit with only $N=2$) and we show that it can be constructed from a supersymmetric Freund--Rubin background via a Wick rotation. Two of the new backgrounds have only been approximated numerically.
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.
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....
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.
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.
Deng, Shaoqiang
2012-01-01
"Homogeneous Finsler Spaces" is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems. This book contains a series of new results obtained by the author and collaborators during the last decade. The topic of Finsler geometry has developed rapidly in recent years. One of the main reasons for its surge in development is its use in many scientific fields, such as general relativity, mathematical biology, and phycology (study of algae). This monograph introduc
Energy Technology Data Exchange (ETDEWEB)
Bershadskii, A.G.
1985-06-01
An exact solution for the nonlinear problem of the spectral energy function of a homogeneous turbulence is derived under the assumption that energy transfer under the effect of inertial forces is determined mainly by the interactions among vortices whose wavenumbers are only slightly different from each other. The results are experimentally verified for turbulence behind grids. Similar problems are solved for MHD turbulence and for a nonstationary spectral energy function. It is shown that at the initial stage of degeneration, the spectral energy function is little influenced by the Stewart number; this agrees with experimental data for the damping of longitudinal velocity pulsations behind a grid in a longitudinal magnetic field. 15 references.
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.
Symmetries of homogeneous cosmologies
Cotsakis, S; Pantazi, H; Cotsakis, Spiros; Leach, Peter; Pantazi, Hara
1998-01-01
We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self-interaction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi-scalar field equations become subsets of the second Bianchi jet bundle, $J^2$, and every Bianchi cosmology is naturally extended to live on a variety of $J^2$. We are interested in the existence and behaviour of extensions of arbitrary Bianchi-Lie and variational vector fields acting on the Bianchi variety and accordingly we classify all such vector fields corresponding to both Bianchi classes $A$ and $B$. We give examples of functions defined on Bianchi jet bundles which are constant along some Bianchi models (first integrals) and use these to find particular solutions in the Bianchi total space. We discuss how our approach could be used to shed new light to questions like isotropization and the nature of singularities of homogeneous cosmologies by examining the behaviour of the vari...
On acoustic band gaps in homogenized piezoelectric phononic materials
Directory of Open Access Journals (Sweden)
Rohan E.
2010-07-01
Full Text Available We consider a composite medium made of weakly piezoelectric inclusions periodically distributed in the matrix which ismade of a different piezoelectricmaterial. Themediumis subject to a periodic excitation with an incidence wave frequency independent of scale ε of the microscopic heterogeneities. Two-scale method of homogenization is applied to obtain the limit homogenized model which describes acoustic wave propagation in the piezoelectric medium when ε → 0. In analogy with the purely elastic composite, the resulting model allows existence of the acoustic band gaps. These are identified for certain frequency ranges whenever the so-called homogenized mass becomes negative. The homogenized model can be used for band gap prediction and for dispersion analysis for low wave numbers. Modeling such composite materials seems to be perspective in the context of Smart Materials design.
Electromagnetic Sources in a Moving Conducting Medium
DEFF Research Database (Denmark)
Johannsen, Günther
1971-01-01
The problem of an arbitrary source distribution in a uniformly moving, homogeneous, isotropic, nondispersive, conducting medium is solved. The technique used is to solve the problem in the rest system of the medium and then write the result in an appropriate four-dimensional, covariant form which...
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).
Homogenization of High-Contrast Brinkman Flows
Brown, Donald L.
2015-04-16
Modeling porous flow in complex media is a challenging problem. Not only is the problem inherently multiscale but, due to high contrast in permeability values, flow velocities may differ greatly throughout the medium. To avoid complicated interface conditions, the Brinkman model is often used for such flows [O. Iliev, R. Lazarov, and J. Willems, Multiscale Model. Simul., 9 (2011), pp. 1350--1372]. Instead of permeability variations and contrast being contained in the geometric media structure, this information is contained in a highly varying and high-contrast coefficient. In this work, we present two main contributions. First, we develop a novel homogenization procedure for the high-contrast Brinkman equations by constructing correctors and carefully estimating the residuals. Understanding the relationship between scales and contrast values is critical to obtaining useful estimates. Therefore, standard convergence-based homogenization techniques [G. A. Chechkin, A. L. Piatniski, and A. S. Shamev, Homogenization: Methods and Applications, Transl. Math. Monogr. 234, American Mathematical Society, Providence, RI, 2007, G. Allaire, SIAM J. Math. Anal., 23 (1992), pp. 1482--1518], although a powerful tool, are not applicable here. Our second point is that the Brinkman equations, in certain scaling regimes, are invariant under homogenization. Unlike in the case of Stokes-to-Darcy homogenization [D. Brown, P. Popov, and Y. Efendiev, GEM Int. J. Geomath., 2 (2011), pp. 281--305, E. Marusic-Paloka and A. Mikelic, Boll. Un. Mat. Ital. A (7), 10 (1996), pp. 661--671], the results presented here under certain velocity regimes yield a Brinkman-to-Brinkman upscaling that allows using a single software platform to compute on both microscales and macroscales. In this paper, we discuss the homogenized Brinkman equations. We derive auxiliary cell problems to build correctors and calculate effective coefficients for certain velocity regimes. Due to the boundary effects, we construct
Universum Inference and Corpus Homogeneity
Vogel, Carl; Lynch, Gerard; Janssen, Jerom
Universum Inference is re-interpreted for assessment of corpus homogeneity in computational stylometry. Recent stylometric research quantifies strength of characterization within dramatic works by assessing the homogeneity of corpora associated with dramatic personas. A methodological advance is suggested to mitigate the potential for the assessment of homogeneity to be achieved by chance. Baseline comparison analysis is constructed for contributions to debates by nonfictional participants: the corpus analyzed consists of transcripts of US Presidential and Vice-Presidential debates from the 2000 election cycle. The corpus is also analyzed in translation to Italian, Spanish and Portuguese. Adding randomized categories makes assessments of homogeneity more conservative.
Homogenization of geological fissured systems with curved non-periodic cracks
Directory of Open Access Journals (Sweden)
Fernando A. Morales
2014-09-01
Full Text Available We analyze the steady fluid flow in a porous medium containing a network of thin fissures of width $\\mathcal{O}(\\epsilon$, generated by the rigid translation of continuous piecewise $C^{1}$ functions in a fixed direction. The phenomenon is modeled in mixed variational formulation, using the stationary Darcy's law and coefficients of low resistance $\\mathcal{O}(\\epsilon$ on the network. The singularities are removed by asymptotic analysis as $\\epsilon \\to 0$ which yields an analogous system hosting only tangential flow in the fissures. Finally the fissures are collapsed into two dimensional manifolds.
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.
Homogeneous crystal nucleation in polymers.
Schick, Christoph; Androsch, R; Schmelzer, Juern W P
2017-07-14
The pathway of crystal nucleation significantly influences the structure and properties of semi-crystalline polymers. Crystal nucleation is normally heterogeneous at low supercooling, and homogeneous at high supercooling, of the polymer melt. Homogeneous nucleation in bulk polymers has been, so far, hardly accessible experimentally, and was even doubted to occur at all. This topical review summarizes experimental findings on homogeneous crystal nucleation in polymers. Recently developed fast scanning calorimetry, with cooling and heating rates up to 106 K s-1, allows for detailed investigations of nucleation near and even below the glass transition temperature, including analysis of nuclei stability. As for other materials, the maximum homogeneous nucleation rate for polymers is located close to the glass transition temperature. In the experiments discussed here, it is shown that polymer nucleation is homogeneous at such temperatures. Homogeneous nucleation in polymers is discussed in the framework of classical nucleation theory. The majority of our observations are consistent with the theory. The discrepancies may guide further research, particularly experiments to progress theoretical development. Progress in the understanding of homogeneous nucleation is much needed, since most of the modelling approaches dealing with polymer crystallization exclusively consider homogeneous nucleation. This is also the basis for advancing theoretical approaches to the much more complex phenomena governing heterogeneous nucleation. © 2017 IOP Publishing Ltd.
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.
Homogeneous Spaces and Equivariant Embeddings
Timashev, DA
2011-01-01
Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standard reasons of algebraic geometry, in order to solve various problems on a homogeneous space it is natural and helpful to compactify it keeping track of the group action, i.e. to consider equivariant completions or, more generally, open embeddings of a given homogeneous space. Such equivariant embeddings are the subject of this book. We focus on classification of equivariant em
Peripheral nerve magnetic stimulation: influence of tissue non-homogeneity
Directory of Open Access Journals (Sweden)
Papazov Sava P
2003-12-01
Full Text Available Abstract Background Peripheral nerves are situated in a highly non-homogeneous environment, including muscles, bones, blood vessels, etc. Time-varying magnetic field stimulation of the median and ulnar nerves in the carpal region is studied, with special consideration of the influence of non-homogeneities. Methods A detailed three-dimensional finite element model (FEM of the anatomy of the wrist region was built to assess the induced currents distribution by external magnetic stimulation. The electromagnetic field distribution in the non-homogeneous domain was defined as an internal Dirichlet problem using the finite element method. The boundary conditions were obtained by analysis of the vector potential field excited by external current-driven coils. Results The results include evaluation and graphical representation of the induced current field distribution at various stimulation coil positions. Comparative study for the real non-homogeneous structure with anisotropic conductivities of the tissues and a mock homogeneous media is also presented. The possibility of achieving selective stimulation of either of the two nerves is assessed. Conclusion The model developed could be useful in theoretical prediction of the current distribution in the nerves during diagnostic stimulation and therapeutic procedures involving electromagnetic excitation. The errors in applying homogeneous domain modeling rather than real non-homogeneous biological structures are demonstrated. The practical implications of the applied approach are valid for any arbitrary weakly conductive medium.
Homogenization of Partial Differential Equations
Kaiser, Gerald
2005-01-01
A comprehensive study of homogenized problems, focusing on the construction of nonstandard models: non-local models, multicomponent models, and models with memory. This work is intended for graduate students, applied mathematicians, physicists, and engineers.
Operator estimates in homogenization theory
Zhikov, V. V.; Pastukhova, S. E.
2016-06-01
This paper gives a systematic treatment of two methods for obtaining operator estimates: the shift method and the spectral method. Though substantially different in mathematical technique and physical motivation, these methods produce basically the same results. Besides the classical formulation of the homogenization problem, other formulations of the problem are also considered: homogenization in perforated domains, the case of an unbounded diffusion matrix, non-self-adjoint evolution equations, and higher-order elliptic operators. Bibliography: 62 titles.
Simulation and experimental results of kaleidoscope homogenizers for longitudinal diode pumping.
Bartnicki, Eric; Bourdet, Gilbert L
2010-03-20
With the goal to set a homogenizer to allow coupling of a stack of diodes with a disk amplifier medium for a longitudinally pumped laser or amplifier, we report simulation and experimental results on homogenization of the light supplied by a large stack of diodes. We investigate various kaleidoscope cross-section shapes and various optical coupling configurations.
On the Mechanical Interaction of Light With Homogeneous Liquids
de Reus, Michiel
2013-01-01
We investigate one of the consequences of the three competing models describing the mechanical interaction of light with a dielectric medium. According to both the Abraham and Minkowski models the time-averaged force density is zero inside a homogeneous dielectric, whereas the induced-current Lorentz force model predicts a non-zero force density. We argue that the latter force, if exists, could drive a hydrodynamic flow inside a homogeneous fluid. Our numerical experiments show that such flows have distinct spatial patterns and may influence the dynamics of particles in a water-based single-beam optical trap.
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.
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.
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.
Genetic Homogenization of Composite Materials
Directory of Open Access Journals (Sweden)
P. Tobola
2009-04-01
Full Text Available The paper is focused on numerical studies of electromagnetic properties of composite materials used for the construction of small airplanes. Discussions concentrate on the genetic homogenization of composite layers and composite layers with a slot. The homogenization is aimed to reduce CPU-time demands of EMC computational models of electrically large airplanes. First, a methodology of creating a 3-dimensional numerical model of a composite material in CST Microwave Studio is proposed focusing on a sufficient accuracy of the model. Second, a proper implementation of a genetic optimization in Matlab is discussed. Third, an association of the optimization script and a simplified 2-dimensional model of the homogeneous equivalent model in Comsol Multiphysics is proposed considering EMC issues. Results of computations are experimentally verified.
Remote measurements of electro-physical parameters of layer mediums
Lobach, Vladimir T.; Dmitriev, Vladimir A.; Lobatch, Yaroslav V.
1999-07-01
The paper deals with the problem of measuring electrical and geometrical parameters of the layer medium. The measurements are based on the control of radio wave reflection coefficient as a function of frequency. Based on solution of the system of transcendental equations for reflection coefficient such parameters of the homogeneous layer medium as complex dielectric permeability, depth of the layer and complex dielectric permeability of the lower homogeneous hemispace.
Ultrasound fields in an attenuating medium
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Gandhi,, D; O'Brien,, W.D., Jr.
1993-01-01
Ultrasound fields propagating in tissue will undergo changes in shape not only due to diffraction, but also due to the frequency dependent attenuation. Linear fields can be fairly well predicted for a non-attenuating medium like water by using the Tupholme-Stepanishen method for calculating...... the spatial impulse response, whereas the field cannot readily be found for an attenuating medium. In this paper we present a simulation program capable of calculating the field in a homogeneous attenuating medium. The program splits the aperture into rectangles and uses a far-field approximation for each...
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.
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.
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.
Soliton-Complex Dynamics in Strongly Dispersive Medium
Bogdan, M M; Maugin, G A; Bogdan, Mikhail M.; Kosevich, Arnold M.; Maugin, Gerard A.
1999-01-01
The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon is considered to be universal and applicable to various physical systems. The soliton complex and its "excited" states are described analytically and numerically as solutions of nonlinear dispersive equations with the fourth and higher spatial or mixed derivatives. The dispersive sine-Gordon, double and triple sine-Gordon, and piecewise-linear models are studied in detail. Mechanisms and conditions of the formation of soliton complexes, and peculiarities of their stationary dynamics are investigated. A phenomenological approach to the description of the complexes and the classification of all the possible complex states are proposed. Some examples of physical systems, where the phenomenon can be experimentally observed, are briefly discussed.
Uniqueness of the differential Mueller matrix of uniform homogeneous media.
Devlaminck, Vincent; Ossikovski, Razvigor
2014-06-01
We show that the differential matrix of a uniform homogeneous medium containing birefringence may not be uniquely determined from its Mueller matrix, resulting in the potential existence of an infinite set of elementary polarization properties parameterized by an integer parameter. The uniqueness depends on the symmetry properties of a special differential matrix derived from the eigenvalue decomposition of the Mueller matrix. The conditions for the uniqueness of the differential matrix are identified, physically discussed, and illustrated in examples from the literature.
A Simple First-Principles Homogenization Theory for Chiral Metamaterials
Directory of Open Access Journals (Sweden)
Carlo Rizza
2015-04-01
Full Text Available We discuss a simple first-principles homogenization theory for describing, in the long-wavelength limit, the effective bianisotropic response of a periodic metamaterial composite without intrinsic chiral and magnetic inclusions. In the case where the dielectric contrast is low, we obtain a full analytical description which can be considered the extension of Landau-Lifshitz-Looyenga effective-medium formulation in the context of periodic metamaterials.
Eigenview on Jones matrix models of homogeneous anisotropic media
Directory of Open Access Journals (Sweden)
Savenkov S.
2010-06-01
Full Text Available The polarization of light when it passes through optical medium can change as a result of change in the amplitude (dichroism or phase shift (birefringence of the electric vector. The anisotropic properties of media can be determined from these two optical effects. Our main concern here is to revisit the factor of eigenpolarizations and eigenvalues in modeling of polarization properties of homogeneous media and elucidate certain new features in polarization behavior of birefringent and dichroic media.
Residual homogenization for seismic forward and inverse problems in layered media
Capdeville, Yann; Stutzmann, Éléonore; Wang, Nian; Montagner, Jean-Paul
2013-07-01
An elastic wavefield propagating in an inhomogeneous elastic medium is only sensitive in an effective way to inhomogeneities much smaller than its minimum wavelength. The corresponding effective medium, or homogenized medium, can be computed thanks to the non-periodic homogenization technique. In the seismic imaging context, limiting ourselves to layered media, we numerically show that a tomographic elastic model which results of the inversion of limited frequency band seismic data is an homogenized model. Moreover, we show that this homogenized model is the same as the model that can be computed with the non-periodic homogenization technique. We first introduce the notion of residual homogenization, which is computing the effective properties of the difference between a reference model and a `real' model. This is necessary because most imaging technique parametrizations use a reference model that often contains small scales, such as elastic discontinuities. We then use a full-waveform inversion method to numerically show that the result of the inversion is indeed the homogenized residual model. The full-waveform inversion method used here has been specifically developed for that purpose. It is based on the iterative Gauss-Newton least-square non-linear optimization technique, using full normal mode coupling to compute the partial Hessian and gradient. The parametrization has been designed according to the residual homogenized parameters allowing to build a real multiscale inversion with progressive frequency band enrichment along the Gauss-Newton iterations.
Statistical Testing of Segment Homogeneity in Classification of Piecewise–Regular Objects
Directory of Open Access Journals (Sweden)
Savchenko Andrey V.
2015-12-01
Full Text Available The paper is focused on the problem of multi-class classification of composite (piecewise-regular objects (e.g., speech signals, complex images, etc.. We propose a mathematical model of composite object representation as a sequence of independent segments. Each segment is represented as a random sample of independent identically distributed feature vectors. Based on this model and a statistical approach, we reduce the task to a problem of composite hypothesis testing of segment homogeneity. Several nearest-neighbor criteria are implemented, and for some of them the well-known special cases (e.g., the Kullback–Leibler minimum information discrimination principle, the probabilistic neural network are highlighted. It is experimentally shown that the proposed approach improves the accuracy when compared with contemporary classifiers.
The influence of non-homogenous dielectric material in the waveguide propagation modes
Directory of Open Access Journals (Sweden)
Ion VONCILA
2006-12-01
Full Text Available The aim of this paper is to indicate the equations of electromagnetic wave in homogenous and non-homogenous dielectric material, estabilising the bundary conditions and solves by FEM the equations of the electromagnetic wave in the rectangular cavity. By numeric simulation of the waveguide in the cavity there have been studied the modifications of both the ways of propagation and the field’s distribution. The non-homogenous mediums afectes the field’s amplitude, obtaining a non-homogenous distribution. Poyting vector of the wave’s transmision, indicates the energetic flux’s concentration in the air besides the dielectric material.
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.
Homogeneity and plane-wave limits
Figueroa-O'Farrill, J M; Philip, S; Farrill, Jos\\'e Figueroa-O'; Meessen, Patrick; Philip, Simon
2005-01-01
We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the behaviour of (reductive) homogeneous structures under the plane-wave limit.
Homogenization method for elastic materials
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Seifrt F.
2007-11-01
Full Text Available In the paper we study the homogenization method and its potential for research of some phenomenons connected with periodic elastic materials. This method will be applied on partial differential equations that describe the deformation of a periodic composite material. The next part of the paper will deal with applications of the homogenization method. The importance of the method will be discussed more detailed for the exploration of the so called bandgaps. Bandgap is a phenomenon which may appear during vibrations of some periodically heterogeneous materials. This phenomenon is not only observable during vibrations for the aforementioned materials, but we may also observe similar effects by propagation of electromagnetic waves of heterogeneous dielectric medias.
Giant dielectric anisotropy via homogenization
Mackay, Tom G
2014-01-01
A random mixture of two isotropic dielectric materials, one composed of oriented spheroidal particles of relative permittivity $\\epsilon_a$ and the other composed of oriented spheroidal particles of relative permittivity $\\epsilon_b$, was considered in the long wavelength regime. The permittivity dyadic of the resulting homogenized composite material (HCM) was estimated using the Bruggeman homogenization formalism. The HCM was an orthorhombic biaxial material if the symmetry axes of the two populations of spheroids were mutually perpendicular and a uniaxial material if these two axes were mutually aligned. The degree of anisotropy of the HCM, as gauged by the ratio of the eigenvalues of the HCM's permittivity dyadic, increased as the shape of the constituent particles became more eccentric. The greatest degrees of HCM anisotropy were achieved for the limiting cases wherein the constituent particles were shaped as needles or discs. In these instances explicit formulas for the HCM anisotropy were derived from t...
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...
Mouche, Emmanuel; Hayek, Mohamed; Mügler, Claude
2010-09-01
We present an upscaled model for the vertical migration of a CO 2 plume through a vertical column filled with a periodic layered porous medium. This model may describe the vertical migration of a CO 2 plume in a perfectly layered horizontal aquifer. Capillarity and buoyancy are taken into account and semi-explicit upscaled flux functions are proposed in the two following cases: (i) capillarity is the main driving force and (ii) buoyancy is the only driving force. In both cases, we show that the upscaled buoyant flux is a bell-shaped function of the saturation, as in the case of a homogeneous porous medium. In the capillary-dominant case, we show that the upscaled buoyant flux is the harmonic mean of the buoyant fluxes in each layer. The upscaled saturation is governed by the continuity of the capillary pressure at the interface between layers. In the capillary-free case, the upscaled buoyant flux and upscaled saturation are determined by the flux continuity condition at the interface. As the flux is not continuous over the entire range of saturation, the upscaled saturation is only defined where continuity is verified, i.e. in two saturation domains. As a consequence, the upscaled buoyant flux is described by a piecewise continuous function. Two analytical approximations of this flux are proposed and this capillary-free upscaled model is validated for two cases of heterogeneity. Upscaled and cell averaged saturations are in good agreement. Furthermore, the proposed analytical upscaled fluxes provide satisfactory approximations as long as the saturation set at the inlet of the column is in a range where analytical and numerical upscaled fluxes are close.
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...
Video Enhancement Using Adaptive Spatio-Temporal Connective Filter and Piecewise Mapping
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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
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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.
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).
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.
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.
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
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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.
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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.
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.
Quantization of the radiation field in an anisotropic dielectric medium
Institute of Scientific and Technical Information of China (English)
Li Wei; Liu Shi-Bing; Yang Wei
2009-01-01
There are both loss and dispersion characteristics for most dielectric media. In quantum theory the loss in medium is generally described by Langevin force in the Langevin noise (LN) scheme by which the quantization of the radiation field in various homogeneous absorbing dielectrics can be successfully actualized. However, it is invalid for the anisotropic dispersion medium. This paper extends the LN theory to an anisotropic dispersion medium and presented the quantization of the radiation field as well as the transformation relation between the homogeneous and anisotropic dispersion media.
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
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.
The Stiffness Variation of a Micro-Ring Driven by a Traveling Piecewise-Electrode
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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.
Heterotic strings on homogeneous spaces
Israel, D; Orlando, D; Petropoulos, P M; Israel, Dan; Kounnas, Costas; Orlando, Domenico
2004-01-01
We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS-NS 2-forms and gauge field fluxes. We give the general formalism and modular-invariant partition functions, then we consider some examples such as SU(2)/U(1) ~ S^2 (already described in a previous paper) and the SU(3)/U(1)^2 flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.
Homogeneous orbit closures and applications
Lindenstrauss, Elon
2011-01-01
We give new classes of examples of orbits of the diagonal group in the space of unit volume lattices in R^d for d > 2 with nice (homogeneous) orbit closures, as well as examples of orbits with explicitly computable but irregular orbit closures. We give Diophantine applications to the former, for instance we show that if x is the cubic root of 2 then for any y,z in R liminf |n|=0 (as |n| goes to infinity), where denotes the distance of a real number c to the integers.
ISOTOPE METHODS IN HOMOGENEOUS CATALYSIS.
Energy Technology Data Exchange (ETDEWEB)
BULLOCK,R.M.; BENDER,B.R.
2000-12-01
The use of isotope labels has had a fundamentally important role in the determination of mechanisms of homogeneously catalyzed reactions. Mechanistic data is valuable since it can assist in the design and rational improvement of homogeneous catalysts. There are several ways to use isotopes in mechanistic chemistry. Isotopes can be introduced into controlled experiments and followed where they go or don't go; in this way, Libby, Calvin, Taube and others used isotopes to elucidate mechanistic pathways for very different, yet important chemistries. Another important isotope method is the study of kinetic isotope effects (KIEs) and equilibrium isotope effect (EIEs). Here the mere observation of where a label winds up is no longer enough - what matters is how much slower (or faster) a labeled molecule reacts than the unlabeled material. The most careti studies essentially involve the measurement of isotope fractionation between a reference ground state and the transition state. Thus kinetic isotope effects provide unique data unavailable from other methods, since information about the transition state of a reaction is obtained. Because getting an experimental glimpse of transition states is really tantamount to understanding catalysis, kinetic isotope effects are very powerful.
Homogenization of a nonlinear degenerate parabolic equation
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The homogenization of one kind of nonlinear parabolic equation is studied. The weak convergence and corrector results are obtained by combining carefully the compactness method and two-scale convergence method in the homogenization theory.
The Calkin algebra is not countably homogeneous
Farah, Ilijas; Hirshberg, Ilan
2015-01-01
We show that the Calkin algebra is not countably homogeneous, in the sense of continuous model theory. We furthermore show that the connected component of the unitary group of the Calkin algebra is not countably homogeneous.
Numerical computing of elastic homogenized coefficients for periodic fibrous tissue
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Roman S.
2009-06-01
Full Text Available The homogenization theory in linear elasticity is applied to a periodic array of cylindrical inclusions in rectangular pattern extending to infinity in the inclusions axial direction, such that the deformation of tissue along this last direction is negligible. In the plane of deformation, the homogenization scheme is based on the average strain energy whereas in the third direction it is based on the average normal stress along this direction. Namely, these average quantities have to be the same on a Repeating Unit Cell (RUC of heterogeneous and homogenized media when using a special form of boundary conditions forming by a periodic part and an affine part of displacement. It exists an infinity of RUCs generating the considered array. The computing procedure is tested with different choices of RUC to control that the results of the homogenization process are independent of the kind of RUC we employ. Then, the dependence of the homogenized coefficients on the microstructure can be studied. For instance, a special anisotropy and the role of the inclusion volume are investigated. In the second part of this work, mechanical traction tests are simulated. We consider two kinds of loading, applying a density of force or imposing a displacement. We test five samples of periodic array containing one, four, sixteen, sixty-four and one hundred of RUCs. The evolution of mean stresses, strains and energy with the numbers of inclusions is studied. Evolutions depend on the kind of loading, but not their limits, which could be predicted by simulating traction test of the homogenized medium.
Stochastic model of milk homogenization process using Markov's chain
Directory of Open Access Journals (Sweden)
A. A. Khvostov
2016-01-01
Full Text Available The process of development of a mathematical model of the process of homogenization of dairy products is considered in the work. The theory of Markov's chains was used in the development of the mathematical model, Markov's chain with discrete states and continuous parameter for which the homogenisation pressure is taken, being the basis for the model structure. Machine realization of the model is implemented in the medium of structural modeling MathWorks Simulink™. Identification of the model parameters was carried out by minimizing the standard deviation calculated from the experimental data for each fraction of dairy products fat phase. As the set of experimental data processing results of the micrographic images of fat globules of whole milk samples distribution which were subjected to homogenization at different pressures were used. Pattern Search method was used as optimization method with the Latin Hypercube search algorithm from Global Optimization Тoolbox library. The accuracy of calculations averaged over all fractions of 0.88% (the relative share of units, the maximum relative error was 3.7% with the homogenization pressure of 30 MPa, which may be due to the very abrupt change in properties from the original milk in the particle size distribution at the beginning of the homogenization process and the lack of experimental data at homogenization pressures of below the specified value. The mathematical model proposed allows to calculate the profile of volume and mass distribution of the fat phase (fat globules in the product, depending on the homogenization pressure and can be used in the laboratory and research of dairy products composition, as well as in the calculation, design and modeling of the process equipment of the dairy industry enterprises.
Coherence delay augmented laser beam homogenizer
Rasmussen, P.; Bernhardt, A.
1993-06-29
The geometrical restrictions on a laser beam homogenizer are relaxed by ug a coherence delay line to separate a coherent input beam into several components each having a path length difference equal to a multiple of the coherence length with respect to the other components. The components recombine incoherently at the output of the homogenizer, and the resultant beam has a more uniform spatial intensity suitable for microlithography and laser pantogography. Also disclosed is a variable aperture homogenizer, and a liquid filled homogenizer.
Orthogonality Measurement for Homogenous Projects-Bases
Ivan, Ion; Sandu, Andrei; Popa, Marius
2009-01-01
The homogenous projects-base concept is defined. Next, the necessary steps to create a homogenous projects-base are presented. A metric system is built, which then will be used for analyzing projects. The indicators which are meaningful for analyzing a homogenous projects-base are selected. The given hypothesis is experimentally verified. The…
Improving homogeneity by dynamic speed limit systems.
Nes, N. van Brandenberg, S. & Twisk, D.A.M.
2010-01-01
Homogeneity of driving speeds is an important variable in determining road safety; more homogeneous driving speeds increase road safety. This study investigates the effect of introducing dynamic speed limit systems on homogeneity of driving speeds. A total of 46 subjects twice drove a route along 12
Agarwal, Naman; Yoon, Jiho; Garcia-Caurel, Enric; Novikova, Tatiana; Vanel, Jean-Charles; Pierangelo, Angelo; Bykov, Alexander; Popov, Alexey; Meglinski, Igor; Ossikovski, Razvigor
2015-12-01
We show, through visible-range Mueller polarimetry, as well as numerical simulations, that the depolarization in a homogeneous turbid medium consisting of submicron spherical particles follows a parabolic law with the path-length traveled by light through the medium. This result is in full agreement with the phenomenological theory of the fluctuating medium within the framework of the differential Mueller matrix formalism. We further found that the standard deviations of the fluctuating elementary polarization properties of the medium depend linearly on the concentration of particles. These findings are believed to be useful for the phenomenological interpretation of polarimetric experiments, with special emphasis on biomedical applications.
Numerical Homogenization of Jointed Rock Masses Using Wave Propagation Simulation
Gasmi, Hatem; Hamdi, Essaïeb; Bouden Romdhane, Nejla
2014-07-01
Homogenization in fractured rock analyses is essentially based on the calculation of equivalent elastic parameters. In this paper, a new numerical homogenization method that was programmed by means of a MATLAB code, called HLA-Dissim, is presented. The developed approach simulates a discontinuity network of real rock masses based on the International Society of Rock Mechanics (ISRM) scanline field mapping methodology. Then, it evaluates a series of classic joint parameters to characterize density (RQD, specific length of discontinuities). A pulse wave, characterized by its amplitude, central frequency, and duration, is propagated from a source point to a receiver point of the simulated jointed rock mass using a complex recursive method for evaluating the transmission and reflection coefficient for each simulated discontinuity. The seismic parameters, such as delay, velocity, and attenuation, are then calculated. Finally, the equivalent medium model parameters of the rock mass are computed numerically while taking into account the natural discontinuity distribution. This methodology was applied to 17 bench fronts from six aggregate quarries located in Tunisia, Spain, Austria, and Sweden. It allowed characterizing the rock mass discontinuity network, the resulting seismic performance, and the equivalent medium stiffness. The relationship between the equivalent Young's modulus and rock discontinuity parameters was also analyzed. For these different bench fronts, the proposed numerical approach was also compared to several empirical formulas, based on RQD and fracture density values, published in previous research studies, showing its usefulness and efficiency in estimating rapidly the Young's modulus of equivalent medium for wave propagation analysis.
Effective Gravity and Homogenous Solutions
Müller, Daniel
2013-01-01
Near the singularity, gravity should be modified to an effective theory, in the same sense as with the Euler-Heisenberg electrodynamics. This effective gravity surmounts to higher derivative theory, and as is well known, a much more reacher theory concerning the solution space. On the other hand, as a highly non linear theory, the understanding of this solution space must go beyond the linearized approach. In this talk we will present some results previously published by collaborators and myself, concerning solutions for vacuum spatially homogenous cases of Bianchi types $I$ and $VII_A$. These are the anisotropic generalizations of the cosmological spatially "flat", and "open" models respectively. The solutions present isotropisation in a weak sense depending on the initial condition. Also, depending on the initial condition, singular solutions are obtained.
Effective Gravity and Homogenous Solutions
Müller, Daniel
2015-01-01
Near the singularity, gravity should be modified to an effective theory, in the same sense as with the Euler-Heisenberg electrodynamics. This effective gravity surmounts to higher derivative theory, and as is well known, a much more reacher theory concerning the solution space. On the other hand, as a highly non linear theory, the understanding of this solution space must go beyond the linearized approach. In this talk we will present some results previously published by collaborators and myself, concerning solutions for vacuum spatially homogenous cases of Bianchi types I and VIIA. These are the anisotropic generalizations of the cosmological spatially "flat", and "open" models respectively. The solutions present isotropisation in a weak sense depending on the initial condition. Also, depending on the initial condition, singular solutions are obtained.
Projective duality and homogeneous spaces
Tevelev, E A
2006-01-01
Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry. This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.
Some variance reduction methods for numerical stochastic homogenization.
Blanc, X; Le Bris, C; Legoll, F
2016-04-28
We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here.
Suhir, E.
2009-02-01
We consider a bi-material assembly with a 'piecewise-continuous' bonding layer. The layer is characterized by different elastic constants of its 'pieces' (segments) and is assumed to be thin. Young's moduli of all the 'pieces' of the bonding layer are significantly lower than the moduli of the adherend materials. In such a situation the coefficient of thermal expansion (CTE) of the bonding material need not be accounted for. Only the interfacial compliance of the bonding layer is important. This is indeed the case for the majority of electronic, opto-electronic or photonic assemblies. We consider the situation when the assembly is manufactured at an elevated temperature and is subsequently cooled down to a low (say, room) temperature. The objective of the analysis is to develop a simple, easy-to-use and physically meaningful analytical ('mathematical') predictive model for the evaluation of the interfacial shearing stresses that arise at the boundaries of the 'pieces' (segments) of the bonding layer and at the assembly edge. The basic equation is obtained for the thermally induced forces acting in the adherends' cross-sections that correspond to the boundaries between the dissimilar portions of the bonding layer. This equation has the form of the theorem of three (bending) moments in the theory of multi-span beams lying on separate simple supports and could therefore be called the 'theorem of three axial forces'. We show, as an illustration, how this equation could be employed to design a bi-material assembly with an inhomogeneous bonding layer and with low interfacial shearing stresses. Low shearing stresses will certainly result in lower peeling stresses as well. The numerical example is carried out for an assembly with a relatively high-modulus bonding material in its mid-portion (aimed primarily at providing good adhesion and, if necessary, good heat transfer as well) and a low-modulus material in its peripheral portions (aimed primarily at bringing down the
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...
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.
Ait Kaci Azzou, S; Larribe, F; Froda, S
2016-10-01
In Ait Kaci Azzou et al. (2015) we introduced an Importance Sampling (IS) approach for estimating the demographic history of a sample of DNA sequences, the skywis plot. More precisely, we proposed a new nonparametric estimate of a population size that changes over time. We showed on simulated data that the skywis plot can work well in typical situations where the effective population size does not undergo very steep changes. In this paper, we introduce an iterative procedure which extends the previous method and gives good estimates under such rapid variations. In the iterative calibrated skywis plot we approximate the effective population size by a piecewise constant function, whose values are re-estimated at each step. These piecewise constant functions are used to generate the waiting times of non homogeneous Poisson processes related to a coalescent process with mutation under a variable population size model. Moreover, the present IS procedure is based on a modified version of the Stephens and Donnelly (2000) proposal distribution. Finally, we apply the iterative calibrated skywis plot method to a simulated data set from a rapidly expanding exponential model, and we show that the method based on this new IS strategy correctly reconstructs the demographic history.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Stochastic model of milk homogenization process using Markov's chain
A. A. Khvostov; R. S. Sumina; G. I. Kotov; Ivanov, A. V.
2016-01-01
The process of development of a mathematical model of the process of homogenization of dairy products is considered in the work. The theory of Markov's chains was used in the development of the mathematical model, Markov's chain with discrete states and continuous parameter for which the homogenisation pressure is taken, being the basis for the model structure. Machine realization of the model is implemented in the medium of structural modeling MathWorks Simulink™. Identification of the model...
Institute of Scientific and Technical Information of China (English)
Houde Han; Zhongyi Huang
2008-01-01
In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in L2-norm.
Reciprocity theory of homogeneous reactions
Agbormbai, Adolf A.
1990-03-01
The reciprocity formalism is applied to the homogeneous gaseous reactions in which the structure of the participating molecules changes upon collision with one another, resulting in a change in the composition of the gas. The approach is applied to various classes of dissociation, recombination, rearrangement, ionizing, and photochemical reactions. It is shown that for the principle of reciprocity to be satisfied it is necessary that all chemical reactions exist in complementary pairs which consist of the forward and backward reactions. The backward reaction may be described by either the reverse or inverse process. The forward and backward processes must satisfy the same reciprocity equation. Because the number of dynamical variables is usually unbalanced on both sides of a chemical equation, it is necessary that this balance be established by including as many of the dynamical variables as needed before the reciprocity equation can be formulated. Statistical transformation models of the reactions are formulated. The models are classified under the titles free exchange, restricted exchange and simplified restricted exchange. The special equations for the forward and backward processes are obtained. The models are consistent with the H theorem and Le Chatelier's principle. The models are also formulated in the context of the direct simulation Monte Carlo method.
Pharmaceutical Industry Oriented Homogeneous Catalysis
Institute of Scientific and Technical Information of China (English)
Zhang Xumu
2004-01-01
Chiral therapeutics already makes up over one-third of pharmaceutical drugs currently sold worldwide. This is a growing industry with global chiral drug sales for 2002 increasing by 12%to $160 billion (Technology Catalysts International) of a total drug market of $410bn. The increasing demand to produce enantiomerically pure pharmaceuticals, agrochemicals, flavors, and other fine chemicals has advanced the field of asymmetric catalytic technologies.We aim to become a high value technology provider and partner in the chiral therapeutics industry by offering proprietary catalysts, novel building blocks, and collaborative synthetic solutions. In decade, we have developed a set of novel chiral homogeneous phosphorus ligands such as Binaphane, Me-KetalPhos, TangPhos, f-Binaphane, Me-f-KetalPhos, C4TunePhos and Binapine,which we called Chiral Ligand ToolKit. Complementing the ToolKit, (R, S, S, R)-DIOP*, T-Phos,o-BIPHEP, o-BINAPO and FAP were added recently[1].These ligands can be applied to a broad variety of drug structural features by asymmetric hydrogenation of dehydroamino acid derivatives, enamides, unsatisfied acids and esters, ketones,beta ketoesters, imines and cyclic imines. And ligand FAP had been apllied succefully in allylic alkylation and [3+2] cycloaddition.
Effect of Fresnel Reflectivity in a Spherical Turbid Medium
Elghazaly, A
2003-01-01
Radiative transfer problem for anisotropic scattering in a spherical homogeneous, turbid medium with angular dependent (specular) reflecting boundary is solved using the pomraning-Eddington approximation method. The angular dependent reflectivity of the boundary is considered as Fresnel's reflection probability function. The partial heat flux is calculated with anisotropic scattering through a homogeneous solid sphere. our results are compared with the available data and give an excellent agreement.
Derivation of the state matrix for dynamic analysis of linear homogeneous media.
Parra Martinez, Juan Pablo; Dazel, Olivier; Göransson, Peter; Cuenca, Jacques
2016-08-01
A method to obtain the state matrix of an arbitrary linear homogeneous medium excited by a plane wave is proposed. The approach is based on projections on the eigenspace of the governing equations matrix. It is an alternative to manually obtaining a linearly independent set of equations by combining the governing equations. The resulting matrix has been validated against previously published derivations for an anisotropic poroelastic medium.
Analysis of ray stability and caustic formation in a layered moving fluid medium
Bergman, David R
2015-01-01
Caustic formation occurs within a ray skeleton as optical or acoustic fields propagate in a medium with variable refractive properties and are unphysical, their presence being an artifact of the ray approximation of the field, and methods of correcting the field near a caustic are well known. Differential geometry provides a novel approach to calculating acoustic intensity, assessing ray stability and locating caustics in acoustic ray traces when the properties of medium are completely arbitrary by identifying points on the caustic with conjugate points along various rays. The method of geodesic deviation is applied to the problem of determining ray stability and locating caustics in 2-dimensional acoustic ray traces in a layered moving medium. Specifically, a general treatment of caustic formation in sound ducts and in piecewise continuous media is presented and applied to various idealized and realistic scenarios.
A Class of Homogeneous Einstein Manifolds
Institute of Scientific and Technical Information of China (English)
Yifang KANG; Ke LIANG
2006-01-01
A Riemannian manifold (M,g) is called Einstein manifold if its Ricci tensor satisfies r=c·g for some constant c. General existence results are hard to obtain,e.g., it is as yet unknown whether every compact manifold admits an Einstein metric. A natural approach is to impose additional homogeneous assumptions. M. Y. Wang and W. Ziller have got some results on compact homogeneous space G/H. They investigate standard homogeneous metrics, the metric induced by Killing form on G/H, and get some classification results. In this paper some more general homogeneous metrics on some homogeneous space G/H are studies, and a necessary and sufficient condition for this metric to be Einstein is given. The authors also give some examples of Einstein manifolds with non-standard homogeneous metrics.
AQUEOUS HOMOGENEOUS REACTORTECHNICAL PANEL REPORT
Energy Technology Data Exchange (ETDEWEB)
Diamond, D.J.; Bajorek, S.; Bakel, A.; Flanagan, G.; Mubayi, V.; Skarda, R.; Staudenmeier, J.; Taiwo, T.; Tonoike, K.; Tripp, C.; Wei, T.; Yarsky, P.
2010-12-03
Considerable interest has been expressed for developing a stable U.S. production capacity for medical isotopes and particularly for molybdenum- 99 (99Mo). This is motivated by recent re-ductions in production and supply worldwide. Consistent with U.S. nonproliferation objectives, any new production capability should not use highly enriched uranium fuel or targets. Conse-quently, Aqueous Homogeneous Reactors (AHRs) are under consideration for potential 99Mo production using low-enriched uranium. Although the Nuclear Regulatory Commission (NRC) has guidance to facilitate the licensing process for non-power reactors, that guidance is focused on reactors with fixed, solid fuel and hence, not applicable to an AHR. A panel was convened to study the technical issues associated with normal operation and potential transients and accidents of an AHR that might be designed for isotope production. The panel has produced the requisite AHR licensing guidance for three chapters that exist now for non-power reactor licensing: Reac-tor Description, Reactor Coolant Systems, and Accident Analysis. The guidance is in two parts for each chapter: 1) standard format and content a licensee would use and 2) the standard review plan the NRC staff would use. This guidance takes into account the unique features of an AHR such as the fuel being in solution; the fission product barriers being the vessel and attached systems; the production and release of radiolytic and fission product gases and their impact on operations and their control by a gas management system; and the movement of fuel into and out of the reactor vessel.
Homogeneity and thermodynamic identities in geometrothermodynamics
Quevedo, Hernando; Quevedo, María N.; Sánchez, Alberto
2017-03-01
We propose a classification of thermodynamic systems in terms of the homogeneity properties of their fundamental equations. Ordinary systems correspond to homogeneous functions and non-ordinary systems are given by generalized homogeneous functions. This affects the explicit form of the Gibbs-Duhem relation and Euler's identity. We show that these generalized relations can be implemented in the formalism of black hole geometrothermodynamics in order to completely fix the arbitrariness present in Legendre invariant metrics.
Homogeneity and thermodynamic identities in geometrothermodynamics
Energy Technology Data Exchange (ETDEWEB)
Quevedo, Hernando [Universidad Nacional Autonoma de Mexico, Instituto de Ciencias Nucleares (Mexico); Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); ICRANet, Rome (Italy); Quevedo, Maria N. [Universidad Militar Nueva Granada, Departamento de Matematicas, Facultad de Ciencias Basicas, Bogota (Colombia); Sanchez, Alberto [CIIDET, Departamento de Posgrado, Queretaro (Mexico)
2017-03-15
We propose a classification of thermodynamic systems in terms of the homogeneity properties of their fundamental equations. Ordinary systems correspond to homogeneous functions and non-ordinary systems are given by generalized homogeneous functions. This affects the explicit form of the Gibbs-Duhem relation and Euler's identity. We show that these generalized relations can be implemented in the formalism of black hole geometrothermodynamics in order to completely fix the arbitrariness present in Legendre invariant metrics. (orig.)
Gravitational lensing in plasmic medium
Energy Technology Data Exchange (ETDEWEB)
Bisnovatyi-Kogan, G. S., E-mail: gkogan@iki.rssi.ru; Tsupko, O. Yu., E-mail: tsupko@iki.rssi.ru [Russian Academy of Sciences, Space Research Institute (Russian Federation)
2015-07-15
The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhomogeneous medium are well known, the new effect is that, in the case of a homogeneous plasma, in the absence of refractive deflection, the gravitational deflection differs from the vacuum deflection and depends on the photon frequency. In the presence of a plasma nonhomogeneity, the chromatic refractive deflection also occurs, so the presence of plasma always makes gravitational lensing chromatic. In particular, the presence of plasma leads to different angular positions of the same image if it is observed at different wavelengths. It is discussed in detail how to apply the presented formulas for the calculation of the deflection angle in different situations. Gravitational lensing in plasma beyond the weak deflection approximation is also considered.
The Homogeneity Scale of the universe
Ntelis, Pierros
2016-01-01
In this study, we probe the cosmic homogeneity with the BOSS CMASS galaxy sample in the redshift region of $0.43 < z < 0.7$. We use the normalised counts-in-spheres estimator $\\mathcal{N}(
DYNAMIC DEFORMATION THE VISCOELASTIC TWOCOMPONENT MEDIUM
Directory of Open Access Journals (Sweden)
V. S. Polenov
2015-01-01
Full Text Available Summary. In the article are scope harmonious warping of the two-component medium, one component which are represent viscoelastic medium, hereditary properties which are described by the kernel aftereffect Abel integral-differential ratio BoltzmannVolterr, while second – compressible liquid. Do a study one-dimensional case. Use motion equation of two-component medium at movement. Look determination system these equalization in the form of damped wave. Introduce dimensionless coefficient. Combined equations happen to homogeneous system with complex factor relatively waves amplitude in viscoelastic component and in fluid. As a result opening system determinant receive biquadratic equation. Elastic operator express through kernel aftereffect Abel for space Fourier. With the help transformation and symbol series biquadratic equation reduce to quadratic equation. Come to the conclusion that in two-component viscoelastic medium exist two mode sonic waves. As a result solution of quadratic equation be found description advance of waves sonic in viscoelastic two-component medium, which physical-mechanical properties represent complex parameter. Velocity determination advance of sonic waves, attenuation coefficient, mechanical loss tangent, depending on characteristic porous medium and circular frequency formulas receive. Graph dependences of description advance of waves sonic from the temperature logarithm and with the fractional parameter γ are constructed.
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.
Self-consolidating concrete homogeneity
Directory of Open Access Journals (Sweden)
Jarque, J. C.
2007-08-01
Full Text Available Concrete instability may lead to the non-uniform distribution of its properties. The homogeneity of self-consolidating concrete in vertically cast members was therefore explored in this study, analyzing both resistance to segregation and pore structure uniformity. To this end, two series of concretes were prepared, self-consolidating and traditional vibrated materials, with different w/c ratios and types of cement. The results showed that selfconsolidating concretes exhibit high resistance to segregation, albeit slightly lower than found in the traditional mixtures. The pore structure in the former, however, tended to be slightly more uniform, probably as a result of less intense bleeding. Such concretes are also characterized by greater bulk density, lower porosity and smaller mean pore size, which translates into a higher resistance to pressurized water. For pore diameters of over about 0.5 Î¼m, however, the pore size distribution was found to be similar to the distribution in traditional concretes, with similar absorption rates.En este trabajo se estudia la homogeneidad de los hormigones autocompactantes en piezas hormigonadas verticalmente, determinando su resistencia a la segregación y la uniformidad de su estructura porosa, dado que la pérdida de estabilidad de una mezcla puede conducir a una distribución no uniforme de sus propiedades. Para ello se han fabricado dos tipos de hormigones, uno autocompactante y otro tradicional vibrado, con diferentes relaciones a/c y distintos tipos de cemento. Los resultados ponen de manifiesto que los hormigones autocompactantes presentan una buena resistencia a la segregación, aunque algo menor que la registrada en los hormigones tradicionales. A pesar de ello, su estructura porosa tiende a ser ligeramente más uniforme, debido probablemente a un menor sangrado. Asimismo, presentan una mayor densidad aparente, una menor porosidad y un menor tamaño medio de poro, lo que les confiere mejores
Waché, Y; Bergmark, K; Courthaudon, J L; Aguedo, M; Nicaud, J M; Belin, J M
2000-03-01
Size of methyl ricinoleate droplets during biotransformation into gamma-decalactone by Yarrowia lipolytica was measured in both homogenized and non-homogenized media. In non-homogenized but shaken medium, droplets had an average volume surface diameter d32 of 2.5 microm whereas it was 0.7 microm in homogenized and shaken medium. But as soon as yeast cells were inoculated, both diameters became similar at about 0.7 microm and did not vary significantly until the end of the culture. The growth of Y. lipolytica in both media was very similar except for the lag phase which was lowered in homogenized medium conditions.
Indian Academy of Sciences (India)
U Mosel
2006-04-01
In these lectures I first give the motivation for investigations of in-medium properties of hadrons. I discuss the relevant symmetries of QCD and how they might affect the observed hadron properties. I then discuss at length the observable consequences of in-medium changes of hadronic properties in reactions with elementary probes, and in particular photons, on nuclei. Here I put an emphasis on new experiments on changes of the - and -mesons in medium.
A new homogenizer for the isolation of nuclei in concentrated glycerine
Poort, C.
1957-01-01
A homogenizer has been designed, which, while being of a simple construction, is capable of liberating nuclei from animal tissues in a continuous and reproducible way. The apparatus may be used with viscous media. The isolation procedure of nuclei from beef pancreas in a 70 % glycerine medium is d
A new homogenizer for the isolation of nuclei in concentrated glycerine
Poort, C.
1957-01-01
A homogenizer has been designed, which, while being of a simple construction, is capable of liberating nuclei from animal tissues in a continuous and reproducible way. The apparatus may be used with viscous media. The isolation procedure of nuclei from beef pancreas in a 70 % glycerine medium is d
A new homogenizer for the isolation of nuclei in concentrated glycerine
Poort, C.
1957-01-01
A homogenizer has been designed, which, while being of a simple construction, is capable of liberating nuclei from animal tissues in a continuous and reproducible way. The apparatus may be used with viscous media. The isolation procedure of nuclei from beef pancreas in a 70 % glycerine medium
CLASSIFICATION OF CUBIC PARAMETERIZED HOMOGENEOUS VECTOR FIELDS
Institute of Scientific and Technical Information of China (English)
Karnal H.Yasir; TANG Yun
2002-01-01
In this paper the cubic homogeneous parameterized vector fields are studied.The classification of the phase portrait near the critical point is presented. This classification is an extension of the result given by Takens to the cubic homogeneous parameterized vector fields with six parameters.
CLASSIFICATION OF CUBIC PARAMETERIZED HOMOGENEOUS VECTOR FIELDS
Institute of Scientific and Technical Information of China (English)
KamalH.Yasir; TNAGYun
2002-01-01
In this paper the cubic homogeneous parameterized vector fields are studied.The classification of the phase portrait near the critical point is presented.This classification is an extension of the result given by takens to the cubic homogeneous parameterized vector fields with six parameters.
Investigations into homogenization of electromagnetic metamaterials
DEFF Research Database (Denmark)
Clausen, Niels Christian Jerichau
This dissertation encompasses homogenization methods, with a special interest into their applications to metamaterial homogenization. The first method studied is the Floquet-Bloch method, that is based on the assumption of a material being infinite periodic. Its field can then be expanded in term...
The Case Against Homogeneous Sets in Mathematics
Jackman, M. K.
1973-01-01
A point-by-point criticism is made of F. H. Flynn's article, The Case for Homogeneous Sets in Mathematics'' (Mathematics in School, Volume 1 Number 2, 1972) in an attempt to show that the arguments used in trying to justify homogeneous grouping in mathematics are invalid. (Editor/DT)
The homogeneous geometries of real hyperbolic space
DEFF Research Database (Denmark)
Castrillón López, Marco; Gadea, Pedro Martínez; Swann, Andrew Francis
We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use ...
DETERMINISTIC HOMOGENIZATION OF QUASILINEAR DAMPED HYPERBOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Gabriel Nguetseng; Hubert Nnang; Nils Svanstedt
2011-01-01
Deterministic homogenization is studied for quasilinear monotone hyperbolic problems with a linear damping term.It is shown by the sigma-convergence method that the sequence of solutions to a class of multi-scale highly oscillatory hyperbolic problems converges to the solution to a homogenized quasilinear hyperbolic problem.
Finalization report: homogeneous PVM/PARIX
B.J. Overeinder; P.M.A. Sloot; J. Petersen
1994-01-01
This document reports on the design and implementation considerations of PVM/PARIX, homogeneous version 1.0. This version is for use with PARIX 1.2 only. Further, it contains information how to use Homogeneous PVM/PARIX and the appendix contains the installation notes.
Shape optimization of phononic band gap structures using the homogenization approach
Vondřejc, Jaroslav; Heczko, Jan
2016-01-01
The paper deals with optimization of the acoustic band gaps computed using the homogenized model of strongly heterogeneous elastic composite which is constituted by soft inclusions periodically distributed in stiff elastic matrix. We employ the homogenized model of such medium to compute intervals - band gaps - of the incident wave frequencies for which acoustic waves cannot propagate. It was demonstrated that the band gaps distribution can be influenced by changing the shape of inclusions. Therefore, we deal with the shape optimization problem to maximize low-frequency band gaps; their bounds are determined by analyzing the effective mass tensor of the homogenized medium. Analytic transformation formulas are derived which describe dispersion effects of resizing the inclusions. The core of the problem lies in sensitivity of the eigenvalue problem associated with the microstructure. Computational sensitivity analysis is developed, which allows for efficient using of the gradient based optimization methods. Num...
Homogeneity of Prototypical Attributes in Soccer Teams
Directory of Open Access Journals (Sweden)
Christian Zepp
2015-09-01
Full Text Available Research indicates that the homogeneous perception of prototypical attributes influences several intragroup processes. The aim of the present study was to describe the homogeneous perception of the prototype and to identify specific prototypical subcategories, which are perceived as homogeneous within sport teams. The sample consists of N = 20 soccer teams with a total of N = 278 athletes (age M = 23.5 years, SD = 5.0 years. The results reveal that subcategories describing the cohesiveness of the team and motivational attributes are mentioned homogeneously within sport teams. In addition, gender, identification, team size, and the championship ranking significantly correlate with the homogeneous perception of prototypical attributes. The results are discussed on the basis of theoretical and practical implications.
Multilevel Monte Carlo Approaches for Numerical Homogenization
Efendiev, Yalchin R.
2015-10-01
In this article, we study the application of multilevel Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the homogenized solutions. This is accomplished within MLMC by considering different sizes of representative volumes (RVEs). Many inexpensive computations with the smallest RVE size are combined with fewer expensive computations performed on larger RVEs. Likewise, when it comes to homogenized solutions, different levels of coarse-grid meshes are used to solve the homogenized equation. We show that, by carefully selecting the number of realizations at each level, we can achieve a speed-up in the computations in comparison to a standard Monte Carlo method. Numerical results are presented for both one-dimensional and two-dimensional test-cases that illustrate the efficiency of the approach.
Dispersion of a solute in peristaltic motion of a couple stress fluid through a porous medium
National Research Council Canada - National Science Library
G. Radhakrishnamacharya; Habtu Alemayehu
2012-01-01
The paper presents an analytical solution for dispersion of a solute in the peristaltic motion of a couple stress fluid through a porous medium in the presence of both homogeneous and heterogeneous chemical reactions...
Energy Technology Data Exchange (ETDEWEB)
Capdebosq, Y
1999-09-01
In order to study and simulate nuclear reactor cores, one needs to access the neutron distribution in the core. In practice, the description of this density of neutrons is given by a system of diffusion equations, coupled by non differential exchange terms. The strong heterogeneity of the medium constitutes a major obstacle to the numerical computation of this models at reasonable cost. Homogenization appears as compulsory. Heuristic methods have been developed since the origin by nuclear physicists, under a periodicity assumption on the coefficients. They consist in doing a fine computation one a single periodicity cell, to solve the system on the whole domain with homogeneous coefficients, and to reconstruct the neutron density by multiplying the solutions of the two computations. The objectives of this work are to provide mathematically rigorous basis to this factorization method, to obtain the exact formulas of the homogenized coefficients, and to start on geometries where two periodical medium are placed side by side. The first result of this thesis concerns eigenvalue problem models which are used to characterize the state of criticality of the reactor, under a symmetry assumption on the coefficients. The convergence of the homogenization process is proved, and formulas of the homogenized coefficients are given. We then show that without symmetry assumptions, a drift phenomenon appears. It is characterized by the mean of a real Bloch wave method, which gives the homogenized limit in the general case. These results for the critical problem are then adapted to the evolution model. Finally, the homogenization of the critical problem in the case of two side by side periodic medium is studied on a one dimensional on equation model. (authors)
Edwards, D. Gareth
1984-01-01
Examines the effect in the primary and secondary school levels of teaching through the medium of Welsh and the response of the University of Wales. The media and the educational system are two formal social organizations which help the threatened Welsh language to survive. Another would be the establishment of a Welsh-medium university. (SED)
Kuipers, G.; Ritzer, G.
2012-01-01
"The medium is the message" is a phrase coined by Canadian media theorist Marshall McLuhan (1911-1980), in his book Understanding Media: The Extensions of Man (1964). In this book, McLuhan examines the impact of media on societies and human relations, arguing for the primacy of the medium -
Kuipers, G.; Ritzer, G.
2012-01-01
"The medium is the message" is a phrase coined by Canadian media theorist Marshall McLuhan (1911-1980), in his book Understanding Media: The Extensions of Man (1964). In this book, McLuhan examines the impact of media on societies and human relations, arguing for the primacy of the medium - understo
Stokowski, Stanley E.
1989-01-01
A laser medium is particularly useful in high average power solid state lasers. The laser medium includes a chormium dopant and preferably neodymium ions as codopant, and is primarily a gadolinium scandium gallium garnet, or an analog thereof. Divalent cations inhibit spiral morphology as large boules from which the laser medium is derived are grown, and a source of ions convertible between a trivalent state and a tetravalent state at a low ionization energy are in the laser medium to reduce an absorption coefficient at about one micron wavelength otherwise caused by the divalent cations. These divalent cations and convertible ions are dispersed in the laser medium. Preferred convertible ions are provided from titanium or cerium sources.
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.
Effects of Homogeneous Plasma on Strong Gravitational Lensing of Kerr Black Hole
Liu, Changqing; Jing, Jiliang
2016-01-01
Considering a Kerr black hole surrounded by the homogenous unmagnetised plasma medium, we study the strong gravitational lensing on the equatorial plane of the Kerr black hole. We find that the presence of the uniform plasma increases the photon-sphere radius $r_{ps}$, the coefficient $\\bar{a},\\bar{b}$, the angular position of the relativistic images $\\theta_{\\infty}$, the deflection angle $\\alpha(\\theta)$ and the angular separation $s$. However the relative magnitudes $r_m$ decrease in presence of the uniform plasma medium. It is also shown that the impact of the uniform plasma on the effect of strong gravitational become smaller as the spin of the Kerr black increace in prograde orbit($a>0$). Especially, for the extreme black hole(a=0.5), the effect of strong gravitational lensing in homogenous plasma medium is the same as the case in vacuum for the prograde orbit.
Mattiucci, Nadia; Akozbek, Neset; Scalora, Michael; Bloemer, Mark J
2008-01-01
Classical theory of crystals states that a medium to be considered homogeneous must satisfy the following requirements: a) the dimension of the elementary cell must be much smaller than the incident wavelength; b) the sample must contain a large number of elementary cells, i.e. it must be macroscopic with respect to wavelength. Under these conditions, macroscopic quantities can be introduced in order to describe the optical response of the medium. We analytically demonstrate that for a symmetric elementary cell those requirements can be relaxed, and it is possible to assign a permittivity and a permeability to a composite structure, even if the metamaterial cannot be considered homogeneous under the requirements stated above. However, the effective permittivity and permeability in some cases may give rise to unphysical, effective behaviors inside the medium, notwithstanding the fact that they satisfy requirements like being Kramers-Kronig pairs, for example, and are consistent with all the linear properties o...
Deforestation homogenizes tropical parasitoid-host networks.
Laliberté, Etienne; Tylianakis, Jason M
2010-06-01
Human activities drive biotic homogenization (loss of regional diversity) of many taxa. However, whether species interaction networks (e.g., food webs) can also become homogenized remains largely unexplored. Using 48 quantitative parasitoid-host networks replicated through space and time across five tropical habitats, we show that deforestation greatly homogenized network structure at a regional level, such that interaction composition became more similar across rice and pasture sites compared with forested habitats. This was not simply caused by altered consumer and resource community composition, but was associated with altered consumer foraging success, such that parasitoids were more likely to locate their hosts in deforested habitats. Furthermore, deforestation indirectly homogenized networks in time through altered mean consumer and prey body size, which decreased in deforested habitats. Similar patterns were obtained with binary networks, suggesting that interaction (link) presence-absence data may be sufficient to detect network homogenization effects. Our results show that tropical agroforestry systems can support regionally diverse parasitoid-host networks, but that removal of canopy cover greatly homogenizes the structure of these networks in space, and to a lesser degree in time. Spatiotemporal homogenization of interaction networks may alter coevolutionary outcomes and reduce ecological resilience at regional scales, but may not necessarily be predictable from community changes observed within individual trophic levels.
String pair production in non homogeneous backgrounds
Energy Technology Data Exchange (ETDEWEB)
Bolognesi, S. [Department of Physics “E. Fermi” University of Pisa, and INFN - Sezione di Pisa,Largo Pontecorvo, 3, Ed. C, 56127 Pisa (Italy); Rabinovici, E. [Racah Institute of Physics, The Hebrew University of Jerusalem,91904 Jerusalem (Israel); Tallarita, G. [Departamento de Ciencias, Facultad de Artes Liberales,Universidad Adolfo Ibáñez, Santiago 7941169 (Chile)
2016-04-28
We consider string pair production in non homogeneous electric backgrounds. We study several particular configurations which can be addressed with the Euclidean world-sheet instanton technique, the analogue of the world-line instanton for particles. In the first case the string is suspended between two D-branes in flat space-time, in the second case the string lives in AdS and terminates on one D-brane (this realizes the holographic Schwinger effect). In some regions of parameter space the result is well approximated by the known analytical formulas, either the particle pair production in non-homogeneous background or the string pair production in homogeneous background. In other cases we see effects which are intrinsically stringy and related to the non-homogeneity of the background. The pair production is enhanced already for particles in time dependent electric field backgrounds. The string nature enhances this even further. For spacial varying electrical background fields the string pair production is less suppressed than the rate of particle pair production. We discuss in some detail how the critical field is affected by the non-homogeneity, for both time and space dependent electric field backgrouds. We also comment on what could be an interesting new prediction for the small field limit. The third case we consider is pair production in holographic confining backgrounds with homogeneous and non-homogeneous fields.
Benchmarking homogenization algorithms for monthly data
Directory of Open Access Journals (Sweden)
V. K. C. Venema
2012-01-01
Full Text Available The COST (European Cooperation in Science and Technology Action ES0601: advances in homogenization methods of climate series: an integrated approach (HOME has executed a blind intercomparison and validation study for monthly homogenization algorithms. Time series of monthly temperature and precipitation were evaluated because of their importance for climate studies and because they represent two important types of statistics (additive and multiplicative. The algorithms were validated against a realistic benchmark dataset. The benchmark contains real inhomogeneous data as well as simulated data with inserted inhomogeneities. Random independent break-type inhomogeneities with normally distributed breakpoint sizes were added to the simulated datasets. To approximate real world conditions, breaks were introduced that occur simultaneously in multiple station series within a simulated network of station data. The simulated time series also contained outliers, missing data periods and local station trends. Further, a stochastic nonlinear global (network-wide trend was added.
Participants provided 25 separate homogenized contributions as part of the blind study. After the deadline at which details of the imposed inhomogeneities were revealed, 22 additional solutions were submitted. These homogenized datasets were assessed by a number of performance metrics including (i the centered root mean square error relative to the true homogeneous value at various averaging scales, (ii the error in linear trend estimates and (iii traditional contingency skill scores. The metrics were computed both using the individual station series as well as the network average regional series. The performance of the contributions depends significantly on the error metric considered. Contingency scores by themselves are not very informative. Although relative homogenization algorithms typically improve the homogeneity of temperature data, only the best ones improve
Higher Order Macro Coefficients in Periodic Homogenization
Energy Technology Data Exchange (ETDEWEB)
Conca, Carlos; San Martin, Jorge [Departamento de IngenierIa Matematica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile and Centro de Modelamiento Matematico, UMR 2071 CNRS-UChile, Casilla 170/3 - Correo 3, Santiago (Chile); Smaranda, Loredana [Department of Mathematics, Faculty of Mathematics and Computer Science, University of Pitesti, 110040 Pitesti, Str. Targu din Vale Nr.1, Arges (Romania); Vanninathan, Muthusamy, E-mail: cconca@dim.uchile.cl, E-mail: jorge@dim.uchile.cl, E-mail: smaranda@dim.uchile.cl, E-mail: vanni@math.tifrbng.res.in [TIFR-CAM, Post Bag 6503, GKVK Post, Bangalore - 560065 (India)
2011-09-15
A first set of macro coefficients known as the homogenized coefficients appear in the homogenization of PDE on periodic structures. If energy is increased or scale is decreased, these coefficients do not provide adequate approximation. Using Bloch decomposition, it is first realized that the above coefficients correspond to the lowest energy and the largest scale. This naturally paves the way to introduce other sets of macro coefficients corresponding to higher energies and lower scales which yield better approximation. The next task is to compare their properties with those of the homogenized coefficients. This article reviews these developments along with some new results yet to be published.
Effect of non-homogenous thermal stress during sub-lethal photodynamic antimicrobial chemotherapy
Gadura, N.; Kokkinos, D.; Dehipawala, S.; Cheung, E.; Sullivan, R.; Subramaniam, R.; Schneider, P.; Tremberger, G., Jr.; Holden, T.; Lieberman, D.; Cheung, T.
2012-03-01
Pathogens could be inactivated via a light source coupled with a photosensitizing agent in photodynamic antimicrobial chemotherapy (PACT). This project studied the effect of non-homogenous substrate on cell colony. The non-homogeneity could be controlled by iron oxide nano-particles doping in porous glassy substrates such that each cell would experience tens of hot spots when illuminated with additional light source. The substrate non-homogeneity was characterized by Atomic Force Microscopy, Transmission Electron Microscopy and Extended X-Ray Absorption Fine Structure at Brookhaven Synchrotron Light Source. Microscopy images of cell motion were used to study the motility. Laboratory cell colonies on non-homogenous substrates exhibit reduced motility similar to those observed with sub-lethal PCAT treatment. Such motility reduction on non-homogenous substrate is interpreted as the presence of thermal stress. The studied pathogens included E. coli and Pseudomonas aeruginosa. Non-pathogenic microbes Bacillus subtilis was also studied for comparison. The results show that sub-lethal PACT could be effective with additional non-homogenous thermal stress. The use of non-uniform illumination on a homogeneous substrate to create thermal stress in sub-micron length scale is discussed via light correlation in propagation through random medium. Extension to sub-lethal PACT application complemented with thermal stress would be an appropriate application.
具有分片线性NCP函数的QP-Free可行域方法%Piecewise Linear NCP Function for QP-Free Feasible Method
Institute of Scientific and Technical Information of China (English)
濮定国; 周岩
2006-01-01
In this paper, a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems. The new NCP functions are piecewise linear-rational, regular pseudo-smooth and have nice properties. This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions, by using the piecewise NCP functions. This method is implementable and globally convergent without assuming the strict complementarity condition, the isolatedness of accumulation points. Furthermore, the gradients of active constraints are not requested to be linearly independent. The submatrix which may be obtained by quasi-Newton methods, is not requested to be uniformly positive definite. Preliminary numerical results indicate that this new QP-free method is quite promising.
Directory of Open Access Journals (Sweden)
Supavadee TAWARO
2008-06-01
Full Text Available Seeds of Cymbidium findlaysonianum Lindl. were germinated and regenerated on media supplemented with various additives. After germination for 3 months, solidified Vacin and Went (VW medium supplemented with, 15 % coconut water, 5 % banana homogenate, 5 % potato homogenate, 0.2 % activated charcoal and 20 g/l sucrose promoted higher seedling germination than the control medium. The number of protocorm cultured in a modified liquid VW medium with Murashige and Skoog (MS vitamin (VWM increased 4 times for every month of culture, a significant difference from the VW medium, MS medium and half strength MS medium (½ MS. Moreover, the activated charcoal added to the medium stimulated seedlings growth significantly more than when coconut water, banana homogenate and/or potato homogenate were added to the medium. Healthy plants transferred to a plastic tray containing coconut peat successfully acclimatized (70 % in the greenhouse. More than 100,000 plantlets may be obtained from a capsule after being cultured for a year. Thus, organic additives and medium components had an effect on the growth and development of asymbiotic seeds in C. findlaysonianum.
On the Cancellation Rule in the Homogenization
2008-01-01
We consider the possible ways of the homogenization of non-graded non-commutative algebra and show that it should be combined with the cancellation rule to get the mathematically adequate correspondence between graded and non-graded algebras.
Non-homogeneous fractal hierarchical weighted networks.
Dong, Yujuan; Dai, Meifeng; Ye, Dandan
2015-01-01
A model of fractal hierarchical structures that share the property of non-homogeneous weighted networks is introduced. These networks can be completely and analytically characterized in terms of the involved parameters, i.e., the size of the original graph Nk and the non-homogeneous weight scaling factors r1, r2, · · · rM. We also study the average weighted shortest path (AWSP), the average degree and the average node strength, taking place on the non-homogeneous hierarchical weighted networks. Moreover the AWSP is scrupulously calculated. We show that the AWSP depends on the number of copies and the sum of all non-homogeneous weight scaling factors in the infinite network order limit.
Magnifying absolute instruments for optically homogeneous regions
Tyc, Tomas
2011-01-01
We propose a class of magnifying absolute optical instruments with a positive isotropic refractive index. They create magnified stigmatic images, either virtual or real, of optically homogeneous three-dimensional spatial regions within geometrical optics.
Homogeneous Dielectric Equivalents of Composite Material Shields
Directory of Open Access Journals (Sweden)
P. Tobola
2009-04-01
Full Text Available The paper deals with the methodology of replacing complicated parts of an airplane skin by simple homogeneous equivalents, which can exhibit similar shielding efficiency. On one hand, the airplane built from the virtual homogeneous equivalents can be analyzed with significantly reduced CPU-time demands and memory requirements. On the other hand, the equivalent model can estimate the internal fields satisfactory enough to evaluate the electromagnetic immunity of the airplane.
Commensurability effects in holographic homogeneous lattices
Andrade, Tomas; Krikun, Alexander
2016-01-01
An interesting application of the gauge/gravity duality to condensed matter physics is the description of a lattice via breaking translational invariance on the gravity side. By making use of global symmetries, it is possible to do so without scarifying homogeneity of the pertinent bulk solutions, which we thus term as "homogeneous holographic lattices." Due to their technical simplicity, these configurations have received a great deal of attention in the last few years and have been shown to...
Homogeneous cosmological models and new inflation
Turner, Michael S.; Widrow, Lawrence M.
1986-01-01
The promise of the inflationary-universe scenario is to free the present state of the universe from extreme dependence upon initial data. Paradoxically, inflation is usually analyzed in the context of the homogeneous and isotropic Robertson-Walker cosmological models. It is shown that all but a small subset of the homogeneous models undergo inflation. Any initial anisotropy is so strongly damped that if sufficient inflation occurs to solve the flatness and horizon problems, the universe today would still be very isotropic.
Wu, Ailong; Liu, Ling; Huang, Tingwen; Zeng, Zhigang
2017-01-01
Neurodynamic system is an emerging research field. To understand the essential motivational representations of neural activity, neurodynamics is an important question in cognitive system research. This paper is to investigate Mittag-Leffler stability of a class of fractional-order neural networks in the presence of generalized piecewise constant arguments. To identify neural types of computational principles in mathematical and computational analysis, the existence and uniqueness of the solution of neurodynamic system is the first prerequisite. We prove that the existence and uniqueness of the solution of the network holds when some conditions are satisfied. In addition, self-active neurodynamic system demands stable internal dynamical states (equilibria). The main emphasis will be then on several sufficient conditions to guarantee a unique equilibrium point. Furthermore, to provide deeper explanations of neurodynamic process, Mittag-Leffler stability is studied in detail. The established results are based on the theories of fractional differential equation and differential equation with generalized piecewise constant arguments. The derived criteria improve and extend the existing related results.
Energy Technology Data Exchange (ETDEWEB)
Boys, Craig A.; Robinson, Wayne; Miller, Brett; Pflugrath, Brett D.; Baumgartner, Lee J.; Navarro, Anna; Brown, Richard S.; Deng, Zhiqun
2016-05-13
Barotrauma injury can occur when fish are exposed to rapid decompression during downstream passage through river infrastructure. A piecewise regression approach was used to objectively quantify barotrauma injury thresholds in two physoclistous species (Murray cod Maccullochella peelii and silver perch Bidyanus bidyanus) following simulated infrastructure passage in barometric chambers. The probability of injuries such as swim bladder rupture; exophthalmia; and haemorrhage and emphysema in various organs increased as the ratio between the lowest exposure pressure and the acclimation pressure (ratio of pressure change RPCE/A) fell. The relationship was typically non-linear and piecewise regression was able to quantify thresholds in RPCE/A that once exceeded resulted in a substantial increase in barotrauma injury. Thresholds differed among injury types and between species but by applying a multi-species precautionary principle, the maintenance of exposure pressures at river infrastructure above 70% of acclimation pressure (RPCE/A of 0.7) should sufficiently protect downstream migrating juveniles of these two physoclistous species. These findings have important implications for determining the risk posed by current infrastructures and informing the design and operation of new ones.
Directory of Open Access Journals (Sweden)
Zhenhua Zhou
2015-01-01
Full Text Available This paper is concerned with the problem of designing robust H-infinity output feedback controller and resilient filtering for a class of discrete-time singular piecewise-affine systems with input saturation and state constraints. Based on a singular piecewise Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, the H-infinity stabilization condition is established and the resilient H-infinity filtering error dynamic system is investigated, and, meanwhile, the domain of attraction is well estimated. Under energy bounded disturbance, the input saturation disturbance tolerance condition is proposed; then, the resilient H-infinity filter is designed in some restricted region. It is shown that the controller gains and filter design parameters can be obtained by solving a family of LMIs parameterized by one or two scalar variables. Meanwhile, by using the corresponding optimization methods, the domain of attraction and the disturbance tolerance level is maximized, and the H-infinity performance γ is minimized. Numerical examples are given to illustrate the effectiveness of the proposed design methods.
Directory of Open Access Journals (Sweden)
John Alexander Taborda
2014-04-01
Full Text Available In this paper, we propose a novel strategy for the synthesis and the classification of nonsmooth limit cycles and its bifurcations (named Non-Standard Bifurcations or Discontinuity Induced Bifurcations or DIBs in n-dimensional piecewise-smooth dynamical systems, particularly Continuous PWS and Discontinuous PWS (or Filippov-type PWS systems. The proposed qualitative approach explicitly includes two main aspects: multiple discontinuity boundaries (DBs in the phase space and multiple intersections between DBs (or corner manifolds—CMs. Previous classifications of DIBs of limit cycles have been restricted to generic cases with a single DB or a single CM. We use the definition of piecewise topological equivalence in order to synthesize all possibilities of nonsmooth limit cycles. Families, groups and subgroups of cycles are defined depending on smoothness zones and discontinuity boundaries (DB involved. The synthesized cycles are used to define bifurcation patterns when the system is perturbed with parametric changes. Four families of DIBs of limit cycles are defined depending on the properties of the cycles involved. Well-known and novel bifurcations can be classified using this approach.
Abou-Jaoudé, Wassim; Chaves, Madalena; Gouzé, Jean-Luc
2014-12-01
A class of piecewise affine differential (PWA) models, initially proposed by Glass and Kauffman (in J Theor Biol 39:103-129, 1973), has been widely used for the modelling and the analysis of biological switch-like systems, such as genetic or neural networks. Its mathematical tractability facilitates the qualitative analysis of dynamical behaviors, in particular periodic phenomena which are of prime importance in biology. Notably, a discrete qualitative description of the dynamics, called the transition graph, can be directly associated to this class of PWA systems. Here we present a study of periodic behaviours (i.e. limit cycles) in a class of two-dimensional piecewise affine biological models. Using concavity and continuity properties of Poincaré maps, we derive structural principles linking the topology of the transition graph to the existence, number and stability of limit cycles. These results notably extend previous works on the investigation of structural principles to the case of unequal and regulated decay rates for the 2-dimensional case. Some numerical examples corresponding to minimal models of biological oscillators are treated to illustrate the use of these structural principles.
Energy Technology Data Exchange (ETDEWEB)
Zainudin, Mohd Lutfi, E-mail: mdlutfi07@gmail.com [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Institut Matematik Kejuruteraan (IMK), Universiti Malaysia Perlis, 02600 Arau, Perlis (Malaysia); Saaban, Azizan, E-mail: azizan.s@uum.edu.my [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Bakar, Mohd Nazari Abu, E-mail: mohdnazari@perlis.uitm.edu.my [Faculty of Applied Science, Universiti Teknologi Mara, 02600 Arau, Perlis (Malaysia)
2015-12-11
The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.
Zainudin, Mohd Lutfi; Saaban, Azizan; Bakar, Mohd Nazari Abu
2015-12-01
The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device's development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.
Mamey, Mary Rose; Barbosa-Leiker, Celestina; McPherson, Sterling; Burns, G. Leonard; Parks, Craig; Roll, John
2015-01-01
Researchers often want to examine two comorbid conditions simultaneously. One strategy to do so is through the use of parallel latent growth curve modeling (LGCM). This statistical technique allows for the simultaneous evaluation of two disorders to determine the explanations and predictors of change over time. Additionally, a piecewise model can help identify whether there are more than two growth processes within each disorder (e.g., during a clinical trial). A parallel piecewise LGCM was applied to self-reported attention deficit/hyperactivity disorder (ADHD) and self-reported substance use symptoms in 303 adolescents enrolled in cognitive behavioral therapy treatment for a substance use disorder (SUD) and receiving either oral-methylphenidate or placebo for ADHD across 16 weeks. Assessing these two disorders concurrently allowed us to determine whether elevated levels of one disorder predicted elevated levels or increased risk of the other disorder. First, a piecewise growth model measured ADHD and SU separately. Next, a parallel piecewise LGCM was used to estimate the regressions across disorders to determine whether higher scores at baseline of the disorders (i.e., ADHD or SUD) predicted rates of change in the related disorder. Finally, treatment was added to the model to predict change. While the analyses revealed no significant relationships across disorders, this study explains and applies a parallel piecewise growth model to examine the developmental processes of comorbid conditions over the course of a clinical trial. Strengths of piecewise and parallel LGCMs for other addictions researchers interested in examining dual processes over time are discussed. PMID:26389639
Significance tests and sample homogeneity loophole
Kupczynski, Marian
2015-01-01
In their recent comment, published in Nature, Jeffrey T.Leek and Roger D.Peng discuss how P-values are widely abused in null hypothesis significance testing . We agree completely with them and in this short comment we discuss the importance of sample homogeneity tests. No matter with how much scrutiny data are gathered if homogeneity tests are not performed the significance tests suffer from sample homogeneity loophole and the results may not be trusted. For example sample homogeneity loophole was not closed in the experiment testing local realism in which a significant violation of Eberhard inequality was found. We are not surprised that Bell type inequalities are violated since if the contextual character of quantum observables is properly taken into account these inequalities cannot be proven. However in order to trust the significance of the violation sample homogeneity loophole must be closed. Therefore we repeat after Jeffrey T.Leek and Roger D.Peng that sample homogeneity loophole is probably just the ...
有理三角曲面的分片线性逼近%Piecewise Linear Approximation of Rational Triangular Surfaces
Institute of Scientific and Technical Information of China (English)
周联; 王国瑾
2012-01-01
Piecewise linear approximation of rational triangular surfaces is useful in surfaces intersection, surfaces rendering and mesh generation. The approximation error bound is usually estimated based on the information about second-order derivative bounds of the rational triangular surfaces. But the derivative bounds of rational triangular surfaces are difficult and less effective to be estimated. To solve this problem, using homogeneous coordinates and inequality method, we present an algorithm to estimate subdivision depths for rational triangular surfaces which are defined in any arbitrary triangle. The estimation is performed on the polynomial surfaces, of which the given rational surfaces are the images under the standard perspective projection. It is more efficient than evaluating the derivative bounds of the given surfaces directly. The subdivison depth is obtained in advance, however, it guarantees the required flatness of the given surface after the subdivision. Moreover, using Mobius reparameterization technique, the variance of the log weights of rational triangular Bezier surfaces is minimized, which can obviously improve the efficiency of the algorithm. In particular, the optimal reparameterization is solved explicitly, so reparameterization hardly increases operating times. Numerical examples suggest that this algorithm not only possesses more powerful properties, but also is more effective compared with any other old methods.%有理三角曲面的分片线性逼近在参数曲面的求交、绘制等方面有着重要应用.已有研究主要采用曲面的二阶导矢界来估计逼近误差,而有理曲面的导矢界估计是一项困难的工作.为解决上述问题,利用齐次坐标,给出了一种定义域为任意三角形的有理三角曲面的分片线性逼近算法.该算法有效地避免了有理三角曲面的导矢界估计,并且离散段数可先验地给出.此外,通过重新参数化技术来缩小有理三角Bézier曲面的权
DEFF Research Database (Denmark)
Bjerrum, Peter
2005-01-01
The present essay is an attempt to determine the architectural project of the 21st century in relation to a modern conception of space as the medium of architecture, and of sociality as its program......The present essay is an attempt to determine the architectural project of the 21st century in relation to a modern conception of space as the medium of architecture, and of sociality as its program...
Institute of Scientific and Technical Information of China (English)
Xin Wen
2009-01-01
In this paper we give proof of three binomial coefficient inequalities. These inequalities are key ingredients in [Wen and Jin, J. Comput. Math. 26, (2008), 1-22] to establish the L1-error estimates for the upwind difference scheme to the linear advection equations with a piecewise constant wave speed and a general interface condition, which were further used to establish the L1-error estimates for a Hamiltonian-preserving scheme developed in [Jin and Wen, Commun. Math. Sci. 3, (2005), 285-315] to the Liouville equation with piecewise constant potentials [Wen and Jin, SIAM J. Numer. Anal. 46, (2008), 2688-2714].
Valdés, Felipe
2013-03-01
Single-source time-domain electric-and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia alongside the high-order divergence-and quasi curl-conforming (DQCC) basis functions of Valdés The combination of these two sets allows for a well-conditioned mapping from div-to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme. © 2012 IEEE.
Gao, Kai
2015-06-05
The development of reliable methods for upscaling fine-scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. Therefore, we have proposed a numerical homogenization algorithm based on multiscale finite-element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that was similar to the rotated staggered-grid finite-difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity in which the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.
Butet, Jérémy; Duboisset, Julien; Bachelier, Guillaume; Russier-Antoine, Isabelle; Benichou, Emmanuel; Jonin, Christian; Brevet, Pierre-François
2010-05-12
We report the optical second harmonic generation from individual 150 nm diameter gold nanoparticles dispersed in gelatin. The quadratic hyperpolarizability of the particles is determined and the input polarization dependence of the second harmonic intensity obtained. These results are found in excellent agreement with ensemble measurements and finite element simulations. These results open up new perspectives for the investigation of the nonlinear optical properties of noble metal nanoparticles.
Defined medium for Moraxella bovis.
Juni, E; Heym, G A
1986-01-01
A defined medium (medium MB) for Moraxella bovis was formulated. Nineteen strains grew well on medium MB. One strain was auxotrophic for asparagine, and another was auxotrophic for methionine. Strains of M. equi and M. lacunata also grew on medium MB. All strains had an absolute requirement for thiamine and were stimulated by or actually required the other growth factors in the medium.
Defined medium for Moraxella bovis.
Juni, E; Heym, G A
1986-10-01
A defined medium (medium MB) for Moraxella bovis was formulated. Nineteen strains grew well on medium MB. One strain was auxotrophic for asparagine, and another was auxotrophic for methionine. Strains of M. equi and M. lacunata also grew on medium MB. All strains had an absolute requirement for thiamine and were stimulated by or actually required the other growth factors in the medium.
Defined medium for Moraxella bovis.
1986-01-01
A defined medium (medium MB) for Moraxella bovis was formulated. Nineteen strains grew well on medium MB. One strain was auxotrophic for asparagine, and another was auxotrophic for methionine. Strains of M. equi and M. lacunata also grew on medium MB. All strains had an absolute requirement for thiamine and were stimulated by or actually required the other growth factors in the medium.
AN INTRODUCTION TO A HOMOGENEOUS CHARGE COMPRESSION IGNITION ENGINE
Directory of Open Access Journals (Sweden)
A.A. Hairuddin
2014-12-01
Full Text Available Homogeneous charge compression ignition (HCCI engine technology is relatively new and has not matured sufficiently to be commercialised compared with conventional engines. It can use spark ignition or compression ignition engine configurations, capitalizing on the advantages of both: high engine efficiency with low emissions levels. HCCI engines can use a wide range of fuels with low emissions levels. Due to these advantages, HCCI engines are suitable for use in a hybrid engine configuration, where they can reduce the fuel consumption even further. However, HCCI engines have some disadvantages, such as knocking and a low to medium operating load range, which need to be resolved before the engine can be commercialised. Therefore, a comprehensive study has to be performed to understand the behaviour of HCCI engines.
AUTOMATION OF QUALITY CONTROL OF MILK HOMOGENIZATION BY ULTRASONIC SPECTROSCOPY METHODS
Directory of Open Access Journals (Sweden)
V. K. Bityukov
2015-01-01
Full Text Available The paper deals with the possibility of determining homogenization degree of milk and dairy products using ultrasonic vibrations absorption spectra. Advantages of this method application in automated manufacturing systems were examined. Theoretical background of the method, as well as the possibility of determining the distribution of the fat globules in milk, depending on their sizes were substantiated. We derived mathematical equations, showing the relationship between the homogenization degree of dairy products and the acoustic properties of the medium, such as the propagation velocity of ultrasonic vibrations in the medium tested and the absorption coefficient in the medium at a specific frequency of the ultrasonic impact and medium temperature. It was shown that the measurement of the propagation of the milk acoustic properties in frequency, evaluation of their density function of the relaxation times spectrum, and then from the relaxation times to the particles masses allow operational control of the fat globules masses distribution in fractions. Theoretical studies were confirmed by experimental research carrying out whose results demonstrate clearly the dependence of absorption degree of ultrasonic vibrations on the degree of milk homogenization. The dependence between the estimates of the relaxation spectra and the first two moments of the statistical distribution of milk fat globules, which demonstrated their relationship was studied. Possible improvements the method under consideration to increase the reliability of the results obtained were proposed.
Fisanov, V. V.
2017-09-01
Analytical expressions for complex values of the wave number, refractive index, and the characteristic wave impedance of homogeneous electromagnetic plane waves propagating in a linear, homogeneous, isotropic medium with losses and gain are derived. Formulas for determining the type of normal wave as a function of the values of the real and imaginary parts of the permittivity and permeability are obtained, and conditions for the appearance of positive and negative refraction at the interface of two isotropic media are indicated. In the approach applied here, the concept of a negative refractive index is not used.
Arteaga, Oriol
2013-04-01
In general the transmission of polarized light through a homogeneous depolarizing sample has motion-reversal symmetry because the response remains the same for light traveling in the opposite direction. As a consequence, the optical properties of a sample, characterized by the differential Mueller matrix, must be invariant upon motion reversal. This Letter shows that the 16 parameters of the differential Mueller matrix must therefore obey six conditions to satisfy this symmetry. This limits the number of independent parameters to 10. The 10 elementary optical properties of a depolarizing homogeneous medium are defined and discussed.
Scattering of light by Gaussian-correlated quasi-homogeneous anisotropic media.
Du, Xinyue; Zhao, Daomu
2010-02-01
We investigate the case when light is scattered by Gaussian-correlated, quasi-homogeneous, anisotropic media. The analytical expression for the cross-spectral density function of the scattered field that is produced by scattering of a polychromatic plane wave incident upon a Gaussian-correlated, quasi-homogeneous, anisotropic medium is derived by use of a tensor method. Numerical examples are given to illustrate the normalized spectral density and the spectral degree of coherence of the field scattered by the anisotropic scatterer in contrast with that scattered by the isotropic scatterer.