Strength Calculation of Locally Loaded Orthotropic Shells

Directory of Open Access Journals (Sweden)

Yu. I. Vinogradov

2015-01-01

Full Text Available The article studies laminated orthotropic cylindrical, conic, spherical, and toroidal shells, which are often locally loaded in the aircraft designs over small areas of their surfaces.The aim of this work is to determine stress concentration in shells versus structure of orthotropic composite material, shell form and parameters, forms of loading areas, which borders do not coincide with lines of main curvatures of shells. For this purpose, an analytical computing algorithm to estimate strength of shells in terms of stress is developed. It enables us to have solution results of the boundary value problem with a controlled error. To solve differential equations an analytical method is used. An algorithm of the boundary value problem solution is multiplicative.The main results of researches are graphs of stress concentration in the orthotropic shells versus their parameters and areas of loading lineated by circles and ellipses.Among the other works aimed at determination of stress concentration in shells, the place of this one is defined by the analytical solution of applied problems for strength estimation in terms of shell stresses of classical forms.The developed effective analytical algorithm to solve the boundary value problem and received results are useful in research and development.

CONCERNING THE ELASTIC ORTHOTROPIC MODEL APPLIED TO WOOD ELASTIC PROPERTIES

OpenAIRE

Tadeu Mascia,Nilson

2003-01-01

Among the construction materials, wood reveals an orthotropic pattern, because of unique characteristics in its internal structure with three axes of wood biological directions (longitudinal, tangential and radial). elastic symmetry: longitudinal, tangential and radial, reveals an orthotropic pattern. The effect of grain angle orientation onin the elastic modulus constitutes the fundamental cause forof wood anisotropy. It is responsible for the greatest changes in the values of the constituti...

A 3D Orthotropic Elastic Continuum Damage Material Model

Energy Technology Data Exchange (ETDEWEB)

English, Shawn Allen [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Brown, Arthur A. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)

2013-08-01

A three dimensional orthotropic elastic constitutive model with continuum damage is implemented for polymer matrix composite lamina. Damage evolves based on a quadratic homogeneous function of thermodynamic forces in the orthotropic planes. A small strain formulation is used to assess damage. In order to account for large deformations, a Kirchhoff material formulation is implemented and coded for numerical simulation in Sandia’s Sierra Finite Element code suite. The theoretical formulation is described in detail. An example of material parameter determination is given and an example is presented.

Linear contextual modal type theory

DEFF Research Database (Denmark)

Schack-Nielsen, Anders; Schürmann, Carsten

Abstract. When one implements a logical framework based on linear type theory, for example the Celf system [?], one is immediately con- fronted with questions about their equational theory and how to deal with logic variables. In this paper, we propose linear contextual modal type theory that gives...... a mathematical account of the nature of logic variables. Our type theory is conservative over intuitionistic contextual modal type theory proposed by Nanevski, Pfenning, and Pientka. Our main contributions include a mechanically checked proof of soundness and a working implementation....

Elastic Constants of Plane Orthotropic Elasticity

DEFF Research Database (Denmark)

Krenk, Steen

1979-01-01

The four independent material parameters of plane orthotropic elasti city are introduced as the effective stiffness, the effective Poisson ratio, the stiffness ratio and the shear parameter. It is proved that stress boundary value problems with zero resulting force on internal contours lead...

Employing Theories Far beyond Their Limits - Linear Dichroism Theory.

Science.gov (United States)

Mayerhöfer, Thomas G

2018-05-15

Using linear polarized light, it is possible in case of ordered structures, such as stretched polymers or single crystals, to determine the orientation of the transition moments of electronic and vibrational transitions. This not only helps to resolve overlapping bands, but also assigning the symmetry species of the transitions and to elucidate the structure. To perform spectral evaluation quantitatively, a sometimes "Linear Dichroism Theory" called approach is very often used. This approach links the relative orientation of the transition moment and polarization direction to the quantity absorbance. This linkage is highly questionable for several reasons. First of all, absorbance is a quantity that is by its definition not compatible with Maxwell's equations. Furthermore, absorbance seems not to be the quantity which is generally compatible with linear dichroism theory. In addition, linear dichroism theory disregards that it is not only the angle between transition moment and polarization direction, but also the angle between sample surface and transition moment, that influences band shape and intensity. Accordingly, the often invoked "magic angle" has never existed and the orientation distribution influences spectra to a much higher degree than if linear dichroism theory would hold strictly. A last point that is completely ignored by linear dichroism theory is the fact that partially oriented or randomly-oriented samples usually consist of ordered domains. It is their size relative to the wavelength of light that can also greatly influence a spectrum. All these findings can help to elucidate orientation to a much higher degree by optical methods than currently thought possible by the users of linear dichroism theory. Hence, it is the goal of this contribution to point out these shortcomings of linear dichroism theory to its users to stimulate efforts to overcome the long-lasting stagnation of this important field. © 2018 Wiley-VCH Verlag GmbH & Co. KGa

Sensitivity analysis on the effective stiffness properties of 3-D orthotropic honeycomb cores

Science.gov (United States)

Karakoç, Alp

2018-01-01

The present study investigates the influences of representative volume element RVE mesh and material parameters, here cell wall elastic moduli, on the effective stiffness properties of three dimensional orthotropic honeycomb cores through strain driven computational homogenization in the finite element framework. For this purpose, case studies were carried out, for which hexagonal cellular RVEs were generated, meshed with eight node linear brick finite elements of varying numbers. Periodic boundary conditions were then implemented on the RVE boundaries by using one-to-one nodal match for the corresponding corners, edges and surfaces for the imposed macroscopic strains. As a novelty, orthotropic material properties were assigned for each cell wall by means of the transformation matrices following the cell wall orientations. Thereafter, simulations were conducted and volume averaged macroscopic stresses were obtained. Eventually, effective stiffness properties were obtained, through which RVE sensitivity analysis was carried out. The investigations indicate that there is a strong relation between number of finite elements and most of the effective stiffness parameters. In addition to this, cell wall elastic moduli also play critical role on the effective properties of the investigated materials.

Orthotropic conductivity reconstruction with virtual-resistive network and Faraday's law

KAUST Repository

Lee, Min-Gi

2015-06-01

We obtain the existence and the uniqueness at the same time in the reconstruction of orthotropic conductivity in two-space dimensions by using two sets of internal current densities and boundary conductivity. The curl-free equation of Faraday\\'s law is taken instead of the elliptic equation in a divergence form that is typically used in electrical impedance tomography. A reconstruction method based on layered bricks-type virtual-resistive network is developed to reconstruct orthotropic conductivity with up to 40% multiplicative noise.

Optimizing rib width to height and rib spacing to deck plate thickness ratios in orthotropic decks

Directory of Open Access Journals (Sweden)

Abdullah Fettahoglu

2016-12-01

Full Text Available Orthotropic decks are composed of deck plate, ribs, and cross-beams and are frequently used in industry to span long distances, due to their light structures and load carrying capacities. Trapezoidal ribs are broadly preferred as longitudinal stiffeners in design of orthotropic decks. They supply the required stiffness to the orthotropic deck in traffic direction. Trapezoidal ribs are chosen in industrial applications because of their high torsional and buckling rigidity, less material and welding needs. Rib width, height, spacing, thickness of deck plate are important parameters for designing of orthotropic decks. In the scope of this study, rib width to height and rib spacing to deck plate thickness ratios are assessed by means of the stresses developed under different ratios of these parameters. For this purpose a FE-model of orthotropic bridge is generated, which encompasses the entire bridge geometry and conforms to recommendations given in Eurocode 3 Part 2. Afterwards necessary FE-analyses are performed to reveal the stresses developed under different rib width to height and rib spacing to deck plate thickness ratios. Based on the results obtained in this study, recommendations regarding these ratios are provided for orthotropic steel decks occupying trapezoidal ribs.

Light radiation pressure upon a wrinkled membrane – parametrization of an optically orthotropic model

Science.gov (United States)

Nerovny, N. A.; Zimin, V. N.

2018-04-01

In this paper, the problem of representing the light pressure force upon the surface of a thin wrinkled film is discussed. The common source of wrinkles is the shear deformation of the membrane sample. The optical model of such a membrane is assumed to be optically orthotropic and an analytic equation for infinitesimal light pressure force is written. A linear regression model in the case of wrinkle geometry, where a surface element can have different optical parameters, is constructed and the Bayesian approach is used to calculate the parameters of this model.

On an orthotropic model for progressive degradation

DEFF Research Database (Denmark)

Hammer, Velaja B.; Pedersen, Pauli

1999-01-01

Progressive degradation in orthotropic materials is modelled from a smear-out point of view, and physical measurable quantities are used as the describing parameters. Evolution of stiffness and evolution of strength are kept uncoupled. For plane problems the stiffness evolution is modelled...

Linear system theory

Science.gov (United States)

Callier, Frank M.; Desoer, Charles A.

1991-01-01

The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

Using artificial neural networks in the design of orthotropic bridge decks

Directory of Open Access Journals (Sweden)

Ahmed Shamel Fahmy

2016-12-01

Full Text Available For orthotropic bridge decks a lot of progress has been made in the development of codes to aid in the design process, in addition to software tools for numerical analysis and design. However, professional software tools will not aid the designer in choosing a preliminary economic layout at the conceptual design stage. Designers would go through iterative, lengthy and expensive procedures to reach the best configuration. The present research provides a methodology to investigate the contingency of using artificial neural networks for conceptual design of orthotropic steel-deck bridge. A neural network model was trained with different combinations of dimensions, and eight types of safety checks were performed on all of them. The resulting network can predict whether the deck is safe or not. It is found that this approach for the selection of orthotropic deck dimensions is a better and cost-effective option compared with international codes or expert opinion.

Creep analysis of orthotropic shells

International Nuclear Information System (INIS)

Mehra, V.K.; Ghosh, A.

1975-01-01

A method of creep analysis of orthotropic cylindrical shells subjected to axisymmetric loads has been developed. A general study of creep behaviour of cylindrical shells subjected to a uniform internal pressure has been conducted for a wide range of values of anisotropy coefficients and creep law exponent. Analysis includes determination of stress re-distribution, strain rates, stationary state stresses. Application of reference stress technique has been extended to analysis of shells. (author)

Fatigue Properties of Orthotropic Decks on Railway Bridges

Czech Academy of Sciences Publication Activity Database

Frýba, Ladislav; Gajdoš, Lubomír

1999-01-01

Roč. 21, č. 7 (1999), s. 639-652 ISSN 0141-0296 Grant - others:XX(CZ) ERRI D 191 Keywords : railway bridges * orthotropic decks * fatigue Subject RIV: JM - Building Engineering Impact factor: 0.364, year: 1999

Far-Field Power Transmissions in Orthotropic Plates: A New Approach

Directory of Open Access Journals (Sweden)

Nirmal K. Mandal

2008-01-01

Full Text Available The structural intensity (SI technique is an essential tool for locating and ranking vibration sources and sinks on structures. It can quantify vibration fields by plotting a vector map of energy transmission on the structures. In this paper, a different strategy, changing coordinate systems of plate equations, is used to develop an intensity equation from shear force components in both x and y directions. The formulation is carried out in the frequency domain considering flexural waves. Orthotropic plate theory, far-field conditions, Fourier transform, and finite difference approximation are considered. The same intensity definition is obtained using this different strategy. A dual-channel FFT analyser is essential for data acquisition to get an intensity vector in a particular direction for far-field conditions.

Linear network theory

CERN Document Server

Sander, K F

1964-01-01

Linear Network Theory covers the significant algebraic aspect of network theory, with minimal reference to practical circuits. The book begins the presentation of network analysis with the exposition of networks containing resistances only, and follows it up with a discussion of networks involving inductance and capacity by way of the differential equations. Classification and description of certain networks, equivalent networks, filter circuits, and network functions are also covered. Electrical engineers, technicians, electronics engineers, electricians, and students learning the intricacies

Linear spaces: history and theory

OpenAIRE

Albrecht Beutelspracher

1990-01-01

Linear spaces belong to the most fundamental geometric and combinatorial structures. In this paper I would like to give an onerview about the theory of embedding finite linear spaces in finite projective planes.

Using Tabulated Experimental Data to Drive an Orthotropic Elasto-Plastic Three-Dimensional Model for Impact Analysis

Science.gov (United States)

Hoffarth, C.; Khaled, B.; Rajan, S. D.; Goldberg, R.; Carney, K.; DuBois, P.; Blankenhorn, Gunther

2016-01-01

An orthotropic elasto-plastic-damage three-dimensional model with tabulated input has been developed to analyze the impact response of composite materials. The theory has been implemented as MAT 213 into a tailored version of LS-DYNA being developed under a joint effort of the FAA and NASA and has the following features: (a) the theory addresses any composite architecture that can be experimentally characterized as an orthotropic material and includes rate and temperature sensitivities, (b) the formulation is applicable for solid as well as shell element implementations and utilizes input data in a tabulated form directly from processed experimental data, (c) deformation and damage mechanics are both accounted for within the material model, (d) failure criteria are established that are functions of strain and damage parameters, and mesh size dependence is included, and (e) the theory can be efficiently implemented into a commercial code for both sequential and parallel executions. The salient features of the theory as implemented in LS-DYNA are illustrated using a widely used composite - the T800S/3900-2B[P2352W-19] BMS8-276 Rev-H-Unitape fiber/resin unidirectional composite. First, the experimental tests to characterize the deformation, damage and failure parameters in the material behavior are discussed. Second, the MAT213 input model and implementation details are presented with particular attention given to procedures that have been incorporated to ensure that the yield surfaces in the rate and temperature dependent plasticity model are convex. Finally, the paper concludes with a validation test designed to test the stability, accuracy and efficiency of the implemented model.

Theory of linear operations

CERN Document Server

Banach, S

1987-01-01

This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'''') complements this important monograph.

Steel plate reinforcement of orthotropic bridge decks

NARCIS (Netherlands)

Teixeira de Freitas, S.

2012-01-01

The PhD research is focused on the reinforcement of fatigue cracked orthotropic steel bridge decks (OBD) by adding a second steel plate to the existing deck. The main idea is to stiffen the existing deck plate, which will reduce the stresses at the fatigue sensitive details and extend the fatigue

Thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion

International Nuclear Information System (INIS)

Sumi, N.

1981-01-01

On the basis of the complex variable method for determining the stationary two-dimensional thermal stresses, the thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion under a steady state temperature field is considered. The solution is found by the analytic continuation argument and the modified mapping-collocation technique. Numerical results indicate a dependence of the orthotropic stress intensity factors on the thermal, elastic and geometrical constants over a certain parameter range. (orig.)

Numerical linear algebra theory and applications

CERN Document Server

Beilina, Larisa; Karchevskii, Mikhail

2017-01-01

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

Science.gov (United States)

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

A local isotropic/global orthotropic finite element technique for modeling the crush of wood in impact limiters

International Nuclear Information System (INIS)

Attaway, S.W.; Yoshimura, H.R.

1989-01-01

Wood is often used as the energy absorbing material in impact limiters, because it begins to crush at low strains, then maintains a near constant crush stress up to nearly 60% volume reduction, and then locks up. Hill (Hill and Joseph, 1974) has performed tests that show that wood is an excellent absorber. However, wood's orthotropic behavior for large crush is difficult to model. In the past, analysts have used isotropic foam-like material models for modeling wood. A new finite element technique is presented in this paper that gives a better model of wood crush than the model currently in use. The orthotropic technique is based on locally isotropic, but globally orthotropic (LIGO) (Attaway, 1988) assumptions in which alternating layers of hard and soft crushable material are used. Each layer is isotropic; however, by alternating hard and soft thin layers, the resulting global behavior is orthotropic. In the remainder of this paper, the new technique for modeling orthotropic wood crush will be presented. The model is used to predict the crush behavior for different grain orientations of balsa wood. As an example problem, an impact limiter containing balsa wood as the crushable material is analyzed using both an isotropic model and the LIGO model

Improvement of fatigue properties of orthotropic decks

Czech Academy of Sciences Publication Activity Database

Frýba, Ladislav; Urushadze, Shota

2011-01-01

Roč. 33, č. 4 (2011), s. 1166-1169 ISSN 0141-0296 R&D Projects: GA ČR GA103/08/1340; GA MŠk(CZ) 7E08098 Grant - others:BRIFAG -Bridge Fatigue Guidance(XE) RFSR_CT-2008-00033 Institutional research plan: CEZ:AV0Z20710524 Keywords : orthotropic deck * fatigue * prolonged life Subject RIV: JM - Building Engineering Impact factor: 1.351, year: 2011

Rayleigh Waves in a Rotating Orthotropic Micropolar Elastic Solid Half-Space

Directory of Open Access Journals (Sweden)

Baljeet Singh

2013-01-01

Full Text Available A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numerical purpose, the frequency equation is approximated. The nondimensional speed of Rayleigh wave is computed and shown graphically versus nondimensional frequency and rotation-frequency ratio for both orthotropic micropolar elastic and isotropic micropolar elastic cases. The numerical results show the effects of rotation, orthotropy, and nondimensional frequency on the nondimensional speed of the Rayleigh wave.

Integral transform solution of bending problem of clamped orthotropic rectangular plates

International Nuclear Information System (INIS)

An, C.; Gu, J.-J.; Su, J.

2011-01-01

The generalized integral transform technique (GITT) is employed to obtain an exact solution for the bending problem of fully clamped orthotropic rectangular plates. The use of the GITT approach in the analysis of the transverse deflection equation leads to a coupled system of fourth order differential equations in the dimensionless longitudinal spatial variable. The resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from IMSL Library. Numerical results with automatic global accuracy control are produced for different values of aspect ratio. Critical comparisons with previously reported numerical results are performed with excellent agreement. Several sets of reference results for clamped orthotropic rectangular plates are also provided for future covalidation purposes. (author)

A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell

Science.gov (United States)

Kaplunov, J.; Nobili, A.

2017-08-01

Dispersion of elastic waves in a thin orthotropic cylindrical shell is considered, within the framework of classical 2D Kirchhoff-Love theory. In contrast to direct multi-parametric analysis of the lowest propagating modes, an alternative robust approach is proposed that simply requires evaluation of the evanescent modes (quasi-static edge effect), which, at leading order, do not depend on vibration frequency. A shortened dispersion relation for the propagating modes is then derived by polynomial division and its accuracy is numerically tested against the full Kirchhoff-Love dispersion relation. It is shown that the same shortened relation may be also obtained from a refined dynamic version of the semi-membrane theory for cylindrical shells. The presented results may be relevant for modelling various types of nanotubes which, according to the latest experimental findings, possess strong material anisotropy.

Algebraic Theory of Linear Viscoelastic Nematodynamics

International Nuclear Information System (INIS)

Leonov, Arkady I.

2008-01-01

This paper consists of two parts. The first one develops algebraic theory of linear anisotropic nematic 'N-operators' build up on the additive group of traceless second rank 3D tensors. These operators have been implicitly used in continual theories of nematic liquid crystals and weakly elastic nematic elastomers. It is shown that there exists a non-commutative, multiplicative group N 6 of N-operators build up on a manifold in 6D space of parameters. Positive N-operators, which in physical applications hold thermodynamic stability constraints, do not generally form a subgroup of group N 6 . A three-parametric, commutative transversal-isotropic subgroup S 3 subset of N 6 of positive symmetric nematic operators is also briefly discussed. The special case of singular, non-negative symmetric N-operators reveals the algebraic structure of nematic soft deformation modes. The second part of the paper develops a theory of linear viscoelastic nematodynamics applicable to liquid crystalline polymer. The viscous and elastic nematic components in theory are described by using the Leslie-Ericksen-Parodi (LEP) approach for viscous nematics and de Gennes free energy for weakly elastic nematic elastomers. The case of applied external magnetic field exemplifies the occurrence of non-symmetric stresses. In spite of multi-(10) parametric character of the theory, the use of nematic operators presents it in a transparent form. When the magnetic field is absent, the theory is simplified for symmetric case with six parameters, and takes an extremely simple, two-parametric form for viscoelastic nematodynamics with possible soft deformation modes. It is shown that the linear nematodynamics is always reducible to the LEP-like equations where the coefficients are changed for linear memory functionals whose parameters are calculated from original viscosities and moduli

Stresses and strains in thick perforated orthotropic plates

Science.gov (United States)

A. Alshaya; John Hunt; R. Rowlands

2016-01-01

Stress and strain concentrations and in-plane and out-of-plane stress constraint factors associated with a circular hole in thick, loaded orthotropic composite plates are determined by three-dimensional finite element method. The plate has essentially infinite in-plane geometry but finite thickness. Results for Sitka Spruce wood are emphasized, although some for carbon...

Renovation techniques for fatigue cracked orthotropic steel bridge decks

NARCIS (Netherlands)

de Jong, F.B.P.

2007-01-01

This dissertation presents the research into renovation techniques for orthotropic steel bridge decks. These techniques are needed to solve fatigue problems in the decks of these bridges, as several fatigue cracks have been detected in the deck structure of these bridges the last decade. A

A Generalized Orthotropic Elasto-Plastic Material Model for Impact Analysis

Science.gov (United States)

Hoffarth, Canio

Composite materials are now beginning to provide uses hitherto reserved for metals in structural systems such as airframes and engine containment systems, wraps for repair and rehabilitation, and ballistic/blast mitigation systems. These structural systems are often subjected to impact loads and there is a pressing need for accurate prediction of deformation, damage and failure. There are numerous material models that have been developed to analyze the dynamic impact response of polymer matrix composites. However, there are key features that are missing in those models that prevent them from providing accurate predictive capabilities. In this dissertation, a general purpose orthotropic elasto-plastic computational constitutive material model has been developed to predict the response of composites subjected to high velocity impacts. The constitutive model is divided into three components - deformation model, damage model and failure model, with failure to be added at a later date. The deformation model generalizes the Tsai-Wu failure criteria and extends it using a strain-hardening-based orthotropic yield function with a non-associative flow rule. A strain equivalent formulation is utilized in the damage model that permits plastic and damage calculations to be uncoupled and capture the nonlinear unloading and local softening of the stress-strain response. A diagonal damage tensor is defined to account for the directionally dependent variation of damage. However, in composites it has been found that loading in one direction can lead to damage in multiple coordinate directions. To account for this phenomena, the terms in the damage matrix are semi-coupled such that the damage in a particular coordinate direction is a function of the stresses and plastic strains in all of the coordinate directions. The overall framework is driven by experimental tabulated temperature and rate-dependent stress-strain data as well as data that characterizes the damage matrix and failure

Canonical perturbation theory in linearized general relativity theory

International Nuclear Information System (INIS)

Gonzales, R.; Pavlenko, Yu.G.

1986-01-01

Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field

Static elastic deformation in an orthotropic half-space with rigid ...

Indian Academy of Sciences (India)

Yogita Godara

2017-10-06

Oct 6, 2017 ... The solution of static elastic deformation of a homogeneous, orthotropic elastic uniform half-space with ... Faults are fractures in Earth's crust where rocks ...... Mavko G M 1981 Mechanics of motion on major faults; Ann. Rev.

Orthotropic conductivity reconstruction with virtual-resistive network and Faraday's law

KAUST Repository

Lee, Min-Gi; Ko, Min-Su; Kim, Yong-Jung

2015-01-01

We obtain the existence and the uniqueness at the same time in the reconstruction of orthotropic conductivity in two-space dimensions by using two sets of internal current densities and boundary conductivity. The curl-free equation of Faraday's law

Linear programming mathematics, theory and algorithms

CERN Document Server

1996-01-01

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

Fatigue Assessment of Full-Scale Retrofitted Orthotropic Bridge Decks

NARCIS (Netherlands)

Teixeira De Freitas, S.; Kolstein, M.H.; Bijlaard, F.S.K.

2017-01-01

Full-scale fatigue tests were performed on two retrofitted orthotropic bridge decks (OBDs). The retrofitting systems consist of adding a second steel plate on the top of the existing deck. The aim is to reduce the stresses at the fatigue-sensitive details and therefore extend the fatigue life of

Linear radial pulsation theory. Lecture 5

International Nuclear Information System (INIS)

Cox, A.N.

1983-01-01

We describe a method for getting an equilibrium stellar envelope model using as input the total mass, the envelope mass, the surface effective temperature, the total surface luminosity, and the composition of the envelope. Then wih the structure of the envelope model known, we present a method for obtaining the raidal pulsation periods and growth rates for low order modes. The large amplitude pulsations observed for the yellow and red giants and supergiants are always these radial models, but for the stars nearer the main sequence, as for all of our stars and for the white dwarfs, there frequently are nonradial modes occuring also. Application of linear theory radial pulsation theory is made to the giant star sigma Scuti variables, while the linear nonradial theory will be used for the B stars in later lectures

Problems of linear electron (polaron) transport theory in semiconductors

CERN Document Server

Klinger, M I

1979-01-01

Problems of Linear Electron (Polaron) Transport Theory in Semiconductors summarizes and discusses the development of areas in electron transport theory in semiconductors, with emphasis on the fundamental aspects of the theory and the essential physical nature of the transport processes. The book is organized into three parts. Part I focuses on some general topics in the theory of transport phenomena: the general dynamical theory of linear transport in dissipative systems (Kubo formulae) and the phenomenological theory. Part II deals with the theory of polaron transport in a crystalline semicon

Game Theory and its Relationship with Linear Programming Models ...

African Journals Online (AJOL)

Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.

An enstrophy-based linear and nonlinear receptivity theory

Science.gov (United States)

Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata

2018-05-01

In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

EXACT SOLUTION OF HEAT CONDUCTION IN A TWO-DOMAIN COMPOSITE CYLINDER WITH AN ORTHOTROPIC OUTER LAYER

International Nuclear Information System (INIS)

AVILES-RAMOS, C.; RUDY, C.

2000-01-01

The transient exact solution of heat conduction in a two-domain composite cylinder is developed using the separation of variables technique. The inner cylinder is isotropic and the outer cylindrical layer is orthotropic. Temperature solutions are obtained for boundary conditions of the first and second kinds at the outer surface of the orthotropic layer. These solutions are applied to heat flow calorimeters modeling assuming that there is heat generation due to nuclear reactions in the inner cylinder. Heat flow calorimeter simulations are carried out assuming that the inner cylinder is filled with plutonium oxide powder. The first objective in these simulations is to predict the onset of thermal equilibrium of the calorimeter with its environment. Two types of boundary conditions at the outer surface of the orthotropic layer are used to predict thermal equilibrium. The procedure developed to carry out these simulations can be used as a guideline for the design of calorimeters. Another important application of these solutions is on the estimation of thermophysical properties of orthotropic cylinders. The thermal conductivities in the vertical, radial and circumferential directions of the orthotropic outer layer can be estimated using this exact solution and experimental data. Simultaneous estimation of the volumetric heat capacity and thermal conductivities is also possible. Furthermore, this solution has potential applications to the solution of the inverse heat conduction problem in this cylindrical geometry. An interesting feature of the construction of this solution is that two different sets of eigenfunctions need to be considered in the eigenfunction expansion. These eigenfunctions sets depend on the relative values of the thermal diffusivity of the inner cylinder and the thermal diffusivity in the vertical direction of the outer cylindrical layer

Research on construction technology for orthotropic steel deck pavement of Haihe River Chunyi Bridge

Science.gov (United States)

Xue, Y. C.; Qian, Z. D.; Zhang, M.

2017-01-01

In order to ensure the good service quality of orthotropic steel deck pavement of Haihe River Chunyi Bridge in Tianjin, and to reduce the occurrence of pavement diseases like lateral and longitudinal cracks, the key working procedures such as steel deck cleaning, anticorrosive coating, bonding layer spraying, seam cutting, epoxy asphalt concrete’s mixing, transportation, paving and compaction were studied. The study was based on the main features of epoxy asphalt concrete which is the pavement materials of Haihe River Chunyi Bridge, and combined with the basic characteristics and construction conditions of Haihe River Chunyi Bridge. Furthermore, some processing measures like controlling time and temperature, continuous paving with two pavers, lateral feeding, and improving the compaction method were proposed. The project example shows that the processing measures can effectively solve the technical difficulties in the construction of orthotropic steel deck pavement of Haihe River Chunyi Bridge, can greatly improve the construction speed and quality, and can provide reference for the same kinds of orthotropic steel deck pavement construction.

Wave propagation in isotropic- or composite-material piping conveying swirling liquid

International Nuclear Information System (INIS)

Chen, T.L.C.; Bert, C.W.

1977-01-01

An analysis is presented for the propagation of free harmonic waves in a thin-walled, circular cylindrical shell of orthotropic or isotropic material conveying a swirling flow. The shell motion is modeled by using the dynamic orthotropic version of the Sanders improved first-approximation linear shell theory and the fluid forces are described by using inviscid incompressible flow theory. Frequency spectra are presented for pipes made of isotropic material and composite materials of current engineering interest. (Auth.)

Scattering theory of the linear Boltzmann operator

International Nuclear Information System (INIS)

Hejtmanek, J.

1975-01-01

In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.) [de

A nonlocal strain gradient model for dynamic deformation of orthotropic viscoelastic graphene sheets under time harmonic thermal load

Science.gov (United States)

Radwan, Ahmed F.; Sobhy, Mohammed

2018-06-01

This work presents a nonlocal strain gradient theory for the dynamic deformation response of a single-layered graphene sheet (SLGS) on a viscoelastic foundation and subjected to a time harmonic thermal load for various boundary conditions. Material of graphene sheets is presumed to be orthotropic and viscoelastic. The viscoelastic foundation is modeled as Kelvin-Voigt's pattern. Based on the two-unknown plate theory, the motion equations are obtained from the dynamic version of the virtual work principle. The nonlocal strain gradient theory is established from Eringen nonlocal and strain gradient theories, therefore, it contains two material scale parameters, which are nonlocal parameter and gradient coefficient. These scale parameters have two different effects on the graphene sheets. The obtained deflection is compared with that predicted in the literature. Additional numerical examples are introduced to illustrate the influences of the two length scale coefficients and other parameters on the dynamic deformation of the viscoelastic graphene sheets.

Linear response theory for quantum open systems

OpenAIRE

Wei, J. H.; Yan, YiJing

2011-01-01

Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.

Spectral theories for linear differential equations

International Nuclear Information System (INIS)

Sell, G.R.

1976-01-01

The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

Strain rate dependent orthotropic properties of pristine and impulsively loaded porcine temporomandibular joint disk.

Science.gov (United States)

Beatty, M W; Bruno, M J; Iwasaki, L R; Nickel, J C

2001-10-01

The purpose of this study was to characterize the tensile stress-strain behavior of the porcine temporomandibular joint (TMJ) disk with respect to collagen orientation and strain rate dependency. The apparent elastic modulus, ultimate tensile strength, and strain at maximum stress were measured at three elongation rates (0.5, 50, and 500 mm/min) for dumbbell-shaped samples oriented along either anteroposterior or mediolateral axes of the disks. In order to study the effects of impact-induced fissuring on the mechanical behavior, the same properties were measured along each orientation at an elongation rate of 500 mm/min for disks subjected to impulsive loads of 0.5 N. s. The results suggested a strongly orthotropic nature to the healthy pristine disk. The values for the apparent modulus and ultimate strength were 10-fold higher along the anteroposterior axis (p disks for either orientation (p > 0.05). The results demonstrated the importance of choosing an orthotropic model for the TMJ disk to conduct finite element modeling, to develop failure criteria, and to construct tissue-engineered replacements. Impact-induced fissuring requires further study to determine if the TMJ disk is orthotropic with respect to fatigue.

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

Solvability of Static Contact Problems with Coulomb Friction for Orthotropic Material

Czech Academy of Sciences Publication Activity Database

Eck, C.; Jarušek, Jiří

2008-01-01

Roč. 93, č. 1 (2008), s. 93-104 ISSN 0374-3535 R&D Projects: GA AV ČR IAA1075402 Institutional research plan: CEZ:AV0Z10190503 Keywords : contact problem * Coulomb friction * orthotropic elasticity Subject RIV: BA - General Mathematics Impact factor: 1.277, year: 2008

Methods in half-linear asymptotic theory

Directory of Open Access Journals (Sweden)

Pavel Rehak

2016-10-01

Full Text Available We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t|y'|^{\\alpha-1}\\hbox{sgn} y''=p(t|y|^{\\alpha-1}\\hbox{sgn} y, $$ where r(t and p(t are positive continuous functions on $[a,\\infty$, $\\alpha\\in(1,\\infty$. The aim of this article is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. Most of our observations are new also in the linear case.

Linear {GLP}-algebras and their elementary theories

Science.gov (United States)

Pakhomov, F. N.

2016-12-01

The polymodal provability logic {GLP} was introduced by Japaridze in 1986. It is the provability logic of certain chains of provability predicates of increasing strength. Every polymodal logic corresponds to a variety of polymodal algebras. Beklemishev and Visser asked whether the elementary theory of the free {GLP}-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable [1]. For every positive integer n we solve the corresponding question for the logics {GLP}_n that are the fragments of {GLP} with n modalities. We prove that the elementary theory of the free {GLP}_n-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable for all n. We introduce the notion of a linear {GLP}_n-algebra and prove that all free {GLP}_n-algebras generated by the constants \\mathbf{0}, \\mathbf{1} are linear. We also consider the more general case of the logics {GLP}_α whose modalities are indexed by the elements of a linearly ordered set α: we define the notion of a linear algebra and prove the latter result in this case.

Alternative theories of the non-linear negative mass instability

International Nuclear Information System (INIS)

Channell, P.J.

1974-01-01

A theory non-linear negative mass instability is extended to include resistance. The basic assumption is explained physically and an alternative theory is offered. The two theories are compared computationally. 7 refs., 8 figs

Bayes linear statistics, theory & methods

CERN Document Server

Goldstein, Michael

2007-01-01

Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field. The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples. The book covers:The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification...

Graph-based linear scaling electronic structure theory

Energy Technology Data Exchange (ETDEWEB)

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.; Swart, Pieter J.; Germann, Timothy C.; Bock, Nicolas [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Mniszewski, Susan M.; Mohd-Yusof, Jamal; Wall, Michael E.; Djidjev, Hristo [Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Rubensson, Emanuel H. [Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala (Sweden)

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Linear circuits, systems and signal processing: theory and application

International Nuclear Information System (INIS)

Byrnes, C.I.; Saeks, R.E.; Martin, C.F.

1988-01-01

In part because of its universal role as a first approximation of more complicated behaviour and in part because of the depth and breadth of its principle paradigms, the study of linear systems continues to play a central role in control theory and its applications. Enhancing more traditional applications to aerospace and electronics, application areas such as econometrics, finance, and speech and signal processing have contributed to a renaissance in areas such as realization theory and classical automatic feedback control. Thus, the last few years have witnessed a remarkable research effort expended in understanding both new algorithms and new paradigms for modeling and realization of linear processes and in the analysis and design of robust control strategies. The papers in this volume reflect these trends in both the theory and applications of linear systems and were selected from the invited and contributed papers presented at the 8th International Symposium on the Mathematical Theory of Networks and Systems held in Phoenix on June 15-19, 1987

Linear algebra and group theory for physicists

CERN Document Server

Rao, K N Srinivasa

2006-01-01

Professor Srinivasa Rao's text on Linear Algebra and Group Theory is directed to undergraduate and graduate students who wish to acquire a solid theoretical foundation in these mathematical topics which find extensive use in physics. Based on courses delivered during Professor Srinivasa Rao's long career at the University of Mysore, this text is remarkable for its clear exposition of the subject. Advanced students will find a range of topics such as the Representation theory of Linear Associative Algebras, a complete analysis of Dirac and Kemmer algebras, Representations of the Symmetric group via Young Tableaux, a systematic derivation of the Crystallographic point groups, a comprehensive and unified discussion of the Rotation and Lorentz groups and their representations, and an introduction to Dynkin diagrams in the classification of Lie groups. In addition, the first few chapters on Elementary Group Theory and Vector Spaces also provide useful instructional material even at an introductory level. An author...

A local homology theory for linearly compact modules

International Nuclear Information System (INIS)

Nguyen Tu Cuong; Tran Tuan Nam

2004-11-01

We introduce a local homology theory for linearly modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties of local homology modules are shown such as: the vanishing and non-vanishing, the noetherianness of local homology modules. By using duality, we extend some well-known results in theory of local cohomology of A. Grothendieck. (author)

On the determination of general plane stress states in orthotropic materials from ultrasonic velocity data in non symmetry planes

International Nuclear Information System (INIS)

Goncalves Filho, Orlando J.A.

2015-01-01

This work reports the progress in the development of a new experimental protocol for plane stress determination in orthotropic materials based on the ultrasonic velocity of bulk waves propagating in non symmetry planes with oblique incidence. The presence of stress-induced deformation introduces an acoustic anisotropy in the material in addition to that defined by its texture. Orthotropic materials under general plane stress states become acoustically monoclic and its orthotropic planes orthogonal to the stress plane become non symmetry planes. The inverse solution of the generalized Christoffel equation for ultrasonic bulk waves propagating in non symmetry planes of anisotropic bodies is known to be numerically unstable. The suggested protocol deals with this numerical instability without recourse to bulk wave propagation in the stress plane as proposed in the literature. Hence, it should be useful for plane stress analysis of thin wall pressure vessels where ultrasonic measurements in the direction of the wall plane are not possible. For the initial validation of the suggested protocol and verification of the stability of the inversion algorithm, computer simulation of stress determination have been performed from synthetic sets of velocity data obtained by the forward solution of the generalized Christoffel equation. Preliminary results for slightly orthotropic aluminium highlight the potential of the suggested protocol. (author)

Pore-fluid effects on seismic waves in vertically fractured earth with orthotropic symmetry

Energy Technology Data Exchange (ETDEWEB)

Berryman, J.G.

2010-05-15

For elastically noninteracting vertical-fracture sets at arbitrary orientation angles to each other, a detailed model is presented in which the resulting anisotropic fractured medium generally has orthorhombic symmetry overall. Some of the analysis methods and ideas of Schoenberg are emphasized, together with their connections to other similarly motivated and conceptually related methods by Sayers and Kachanov, among others. Examples show how parallel vertical-fracture sets having HTI (horizontal transversely isotropic) symmetry transform into orthotropic fractured media if some subsets of the vertical fractures are misaligned with the others, and then the fractured system can have VTI (vertical transversely isotropic) symmetry if all of the fractures are aligned randomly or half parallel and half perpendicular to a given vertical plane. An orthotropic example having vertical fractures in an otherwise VTI earth system (studied previously by Schoenberg and Helbig) is compared with the other examples treated and it is finally shown how fluids in the fractures affect the orthotropic poroelastic system response to seismic waves. The key result is that fracture-influence parameters are multiplied by a factor of (1-B), where 0 {le} B < 1 is Skempton's second coefficient for poroelastic media. Skempton's B coefficient is itself a measurable characteristic of fluid-saturated porous rocks, depending on porosity, solid moduli, and the pore-fluid bulk modulus. For heterogeneous porous media, connections between the present work and earlier related results of Brown and Korringa are also established.

Case Criterion of Crack Onset in Orthotropic Bi-material Notches

Czech Academy of Sciences Publication Activity Database

Profant, T.; Klusák, Jan; Kotoul, M.

2011-01-01

Roč. 465, - (2011), s. 157-160 ISSN 1013-9826. [Materials Structure and Micromechanics of Fracture. Brno, 28.06.2010-30.06.2010] R&D Projects: GA ČR GA101/08/0994; GA ČR GAP108/10/2049 Institutional research plan: CEZ:AV0Z20410507 Keywords : orthotropic bi-material notch * crack initiation * matched asymptotic procedure Subject RIV: JL - Materials Fatigue, Friction Mechanics

Determination of the threshold values of orthotropic bi-material notches

Czech Academy of Sciences Publication Activity Database

Klusák, Jan; Profant, T.; Kotoul, M.

2010-01-01

Roč. 2, č. 1 (2010), s. 1635-1642 E-ISSN 1877-7058. [Fatigue 2010. Praha, 06.06.2010-11.06.2010] R&D Projects: GA ČR GA101/08/0994; GA ČR GAP108/10/2049 Institutional research plan: CEZ:AV0Z20410507 Keywords : Bi-material notch es * Generalized singular stress concentrators * Stability criterion * Orthotropic materials Subject RIV: JL - Materials Fatigue, Friction Mechanics

Coarse-graining free theories with gauge symmetries: the linearized case

International Nuclear Information System (INIS)

Bahr, Benjamin; Dittrich, Bianca; He Song

2011-01-01

Discretizations of continuum theories often do not preserve the gauge symmetry content. This occurs in particular for diffeomorphism symmetry in general relativity, which leads to severe difficulties in both canonical and covariant quantization approaches. We discuss here the method of perfect actions, which attempts to restore gauge symmetries by mirroring exactly continuum physics on a lattice via a coarse graining process. Analytical results can only be obtained via a perturbative approach, for which we consider the first step, namely the coarse graining of the linearized theory. The linearized gauge symmetries are exact also in the discretized theory; hence, we develop a formalism to deal with gauge systems. Finally, we provide a discretization of linearized gravity as well as a coarse graining map and show that with this choice the three-dimensional (3D) linearized gravity action is invariant under coarse graining.

Three caveats for linear stability theory: Rayleigh-Benard convection

International Nuclear Information System (INIS)

Greenside, H.S.

1984-06-01

Recent theories and experiments challenge the applicability of linear stability theory near the onset of buoyancy-driven (Rayleigh-Benard) convection. This stability theory, based on small perturbations of infinite parallel rolls, is found to miss several important features of the convective flow. The reason is that the lateral boundaries have a profound influence on the possible wave numbers and flow patterns even for the largest cells studied. Also, the nonlinear growth of incoherent unstable modes distorts the rolls, leading to a spatially disordered and sometimes temporally nonperiodic flow. Finally, the relation of the skewed varicose instability to the onset of turbulence (nonperiodic time dependence) is examined. Linear stability theory may not suffice to predict the onset of time dependence in large cells close to threshold

Formulated linear programming problems from game theory and its ...

African Journals Online (AJOL)

Formulated linear programming problems from game theory and its computer implementation using Tora package. ... Game theory, a branch of operations research examines the various concepts of decision ... AJOL African Journals Online.

The dynamic response and perturbation of magnetic field vector of orthotropic cylinders under various shock loads

International Nuclear Information System (INIS)

Dai, H.L.; Wang, X.

2006-01-01

In this paper, an analytical method is introduced to solve the problem for the dynamic stress-focusing and centred-effect of perturbation of the magnetic field vector in orthotropic cylinders under thermal and mechanical shock loads. Analytical expressions for the dynamic stresses and the perturbation of the magnetic field vector are obtained by means of finite Hankel transforms and Laplace transforms. The response histories of dynamic stresses and the perturbation of the field vector are also obtained. In practical examples, the dynamic focusing effect on both magnetoelastic stress and perturbation of the axial magnetic field vector in an orthotropic cylinder subjected to various shock loads is presented and discussed

VARIATIONAL PRINCIPLES FOR NONLOCAL CONTINUUM MODEL OF ORTHOTROPIC GRAPHENE SHEETS EMBEDDED IN AN ELASTIC MEDIUM

Institute of Scientific and Technical Information of China (English)

Sarp Adali

2012-01-01

Equations governing the vibrations and buckling of multilayered orthotropic graphene sheets can be expressed as a system of n partial differential equations where n refers to the number of sheets.This description is based on the continuum model of the graphene sheets which can also take the small scale effects into account by employing a nonlocal theory.In the present article a variational principle is derived for the nonlocal elastic theory of rectangular graphene sheets embedded in an elastic medium and undergoing transverse vibrations.Moreover the graphene sheets are subject to biaxial compression.Rayleigh quotients are obtained for the frequencies of freely vibrating graphene sheets and for the buckling load. The influence of small scale effects on the frequencies and the buckling load can be observed qualiatively from the expressions of the Rayleigh quotients.Elastic medium is modeled as a combination of Winkler and Pasternak foundations acting on the top and bottom layers of the mutilayered nano-structure.Natural boundary conditions of the problem are derived using the variational principle formulated in the study.It is observed that free boundaries lead to coupled boundary conditions due to nonlocal theory used in the continuum formulation while the local (classical) elasticity theory leads to uncoupled boundary conditions.The mathematical methods used in the study involve calculus of variations and the semi-inverse method for deriving the variational integrals.

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

International Nuclear Information System (INIS)

Hack, Thomas-Paul; Schenkel, Alexander

2012-05-01

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

Energy Technology Data Exchange (ETDEWEB)

Hack, Thomas-Paul [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Schenkel, Alexander [Bergische Univ., Wuppertal (Germany). Fachgruppe Physik

2012-05-15

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

The linearization method in hydrodynamical stability theory

CERN Document Server

Yudovich, V I

1989-01-01

This book presents the theory of the linearization method as applied to the problem of steady-state and periodic motions of continuous media. The author proves infinite-dimensional analogues of Lyapunov's theorems on stability, instability, and conditional stability for a large class of continuous media. In addition, semigroup properties for the linearized Navier-Stokes equations in the case of an incompressible fluid are studied, and coercivity inequalities and completeness of a system of small oscillations are proved.

Natural Vibration Analysis of Clamped Rectangular Orthotropic Plates

Science.gov (United States)

dalaei, m.; kerr, a. d.

The natural vibrations of clamped rectangular orthotropic plates are analyzed using the extended Kantorovich method. The developed iterative scheme converges very rapidly to the final result. The obtained natural frequencies are evaluated for a square plate made of Kevlar 49 Epoxy and the obtained results are compared with those published by Kanazawa and Kawai, and by Leissa. The agreement was found to be very close. As there are no exact analytical solutions for clamped rectangular plates, the generated closed form expression for the natural modes, and the corresponding natural frequencies, are very suitable for use in engineering analyses.

Concept and development of an orthotropic FE model of the proximal femur.

Science.gov (United States)

Wirtz, Dieter Christian; Pandorf, Thomas; Portheine, Frank; Radermacher, Klaus; Schiffers, Norbert; Prescher, Andreas; Weichert, Dieter; Niethard, Fritz Uwe

2003-02-01

In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE "model femur" to realistically simulate three-dimensional bone remodelling. The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known "density-determined" bony material properties (Young's modulus; Poisson's ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same "CT-density-characterized" volumetric group. In order to fix the principal directions of stiffness in FE areas with the same "density characterization", the cadaveric femurs were cut in 2mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the "CT-density characterized" three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter's criterion. In the constructed "model femur", each FE is characterized by the principal directions of the stiffness and the "CT-density-determined" material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. With the orthotropic "model femur", the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

Science.gov (United States)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Orthotropic Piezoelectricity in 2D Nanocellulose.

Science.gov (United States)

García, Y; Ruiz-Blanco, Yasser B; Marrero-Ponce, Yovani; Sotomayor-Torres, C M

2016-10-06

The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V -1 , ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies.

Orthotropic Piezoelectricity in 2D Nanocellulose

Science.gov (United States)

García, Y.; Ruiz-Blanco, Yasser B.; Marrero-Ponce, Yovani; Sotomayor-Torres, C. M.

2016-10-01

The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V-1, ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies.

Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients

KAUST Repository

Gao, Longfei; Calo, Victor M.

2015-01-01

In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved.

Effect of Rotation in an Orthotropic Elastic Slab

Directory of Open Access Journals (Sweden)

Santra S.

2017-02-01

Full Text Available The fundamental equations of the two dimensional generalized thermoelasticity (L-S model with one relaxation time parameter in orthotropic elastic slab has been considered under effect of rotation. The normal mode analysis is used to the basic equations of motion and heat conduction equation. Finally, the resulting equations are written in the form of a vector-matrix differential equation which is then solved by the eigenvalue approach. The field variables in the space time domain are obtained numerically. The results corresponding to the cases of conventional thermoelasticity CTE, extended thermoelasticity (ETE and temperature rate dependent thermoelasticity (TRDTE are compared by means of graphs.

Azerbaijan Technical University’s Experience in Teaching Linear Electrical Circuit Theory

Directory of Open Access Journals (Sweden)

G. A. Mamedov

2006-01-01

Full Text Available An experience in teaching linear electrical circuit theory at the Azerbaijan Technical University is presented in the paper. The paper describes structure of the Linear Electrical Circuit Theory course worked out by the authors that contains a section on electrical calculation of track circuits, information on electro-magnetic compatibility and typical tests for better understanding of the studied subject.

Modelling and fatigue life assessment of orthotropic bridge deck details using FEM

Czech Academy of Sciences Publication Activity Database

Aygül, M.; AL-Emrani, M.; Urushadze, Shota

2012-01-01

Roč. 40, July (2012), s. 129-142 ISSN 0142-1123 R&D Projects: GA MŠk(CZ) 7E08098 Grant - others:evropská komise(XE) RFSR-CT-2008-00033 (BRIFAG) Institutional support: RVO:68378297 Keywords : orthotropic bridge deck * open ribs * structural hot spot stress * effective notch stress Subject RIV: JM - Building Engineering Impact factor: 1.976, year: 2012

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

Science.gov (United States)

Freed, Alan D.; Leonov, Arkady I.

2002-01-01

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

International Nuclear Information System (INIS)

Marcos, B.

2008-01-01

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called ''particle linear theory''(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects--in the linear regime--of N-body simulations for which initial conditions have been set up using these different lattices.

Feasibility of combining linear theory and impact theory methods for the analysis and design of high speed configurations

Science.gov (United States)

Brooke, D.; Vondrasek, D. V.

1978-01-01

The aerodynamic influence coefficients calculated using an existing linear theory program were used to modify the pressures calculated using impact theory. Application of the combined approach to several wing-alone configurations shows that the combined approach gives improved predictions of the local pressure and loadings over either linear theory alone or impact theory alone. The approach not only removes most of the short-comings of the individual methods, as applied in the Mach 4 to 8 range, but also provides the basis for an inverse design procedure applicable to high speed configurations.

A 3D Orthotropic Strain-Rate Dependent Elastic Damage Material Model.

Energy Technology Data Exchange (ETDEWEB)

English, Shawn Allen

2014-09-01

A three dimensional orthotropic elastic constitutive model with continuum damage and cohesive based fracture is implemented for a general polymer matrix composite lamina. The formulation assumes the possibility of distributed (continuum) damage followed b y localized damage. The current damage activation functions are simply partially interactive quadratic strain criteria . However, the code structure allows for changes in the functions without extraordinary effort. The material model formulation, implementation, characterization and use cases are presented.

Effect of a growth hormone treatment on bone orthotropic elasticity in dwarf rats

Science.gov (United States)

Kohles, S. S.; Martinez, D. A.; Bowers, J. R.; Vailas, A. C.; Vanderby, R. Jr

1997-01-01

A refinement of the current ultrasonic elasticity technique was used to measure the orthotropic elastic properties of rat cortical bone as well as to quantify changes in elastic properties, density, and porosity of the dwarf rat cortex after a treatment with recombinant human growth hormone (rhGH). The ultrasonic elasticity technique was refined via optimized signal management of high-frequency wave propagation through cubic cortical specimens. Twenty dwarf rats (37 days old) were randomly assigned to two groups (10 rats each). The dwarf rat model (5-10% of normal GH) was given subcutaneous injections of either rhGH or saline over a 14-day treatment period. Density was measured using Archimedes technique. Porosity and other microstructural characteristics were also explored via scanning electron microscopy and image analysis. Statistical tests verified significant decreases in cortical orthotropic Young's (-26.7%) and shear (-16.7%) moduli and density (-2.42%) concomitant with an increase in porosity (+125%) after rhGH treatments to the dwarf model (p bone properties at this time interval. Structural implications of these changes throughout physiological loading regimens should be explored.

When is quasi-linear theory exact. [particle acceleration

Science.gov (United States)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

Wigner's little group as a gauge generator in linearized gravity theories

International Nuclear Information System (INIS)

Scaria, Tomy; Chakraborty, Biswajit

2002-01-01

We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the one-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the Einstein-Pauli-Fierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for the Einstein-Pauli-Fierz theory

A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories

Directory of Open Access Journals (Sweden)

V. V. Zozulya

2013-01-01

Full Text Available A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.

Study of the stress distribution around an orthotropic bi-material notch tip

Czech Academy of Sciences Publication Activity Database

Klusák, Jan; Profant, T.; Kotoul, M.

417-418, - (2010), s. 385-388 ISSN 1013-9826. [International Conference on Fracture and Damage Mechanics /8./. Malta, 08.09.2009-10.09.2009] R&D Projects: GA ČR GA101/08/0994; GA AV ČR 1QS200410502 Institutional research plan: CEZ:AV0Z20410507 Keywords : Generalized fracture mechanics * Singular stress distribution * Orthotropic bimaterial notch Subject RIV: JL - Materials Fatigue, Friction Mechanics www.scientific.net

Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control

CERN Document Server

Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

2016-01-01

This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...

Linear control theory for gene network modeling.

Science.gov (United States)

Shin, Yong-Jun; Bleris, Leonidas

2010-09-16

Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

An experimental test of the linear no-threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1990-01-01

There is a substantial body of quantitative information on radiation-induced cancer at high dose, but there are no data at low dose. The usual method for estimating effects of low-level radiation is to assume a linear no-threshold dependence. if this linear no-threshold assumption were not used, essentially all fears about radiation would disappear. Since these fears are costing tens of billions of dollars, it is most important that the linear no-threshold theory be tested at low dose. An opportunity for possibly testing the linear no-threshold concept is now available at low dose due to radon in homes. The purpose of this paper is to attempt to use this data to test the linear no-threshold theory

Experimental Investigation of Membrane Materials used in Multilayer Surfacing Systems for Orthotropic Steel Deck Bridges

NARCIS (Netherlands)

Tzimiris, G.

2017-01-01

In the Netherlands asphaltic surfacings on orthotropic steel deck bridges (OSDB) mostly consist of two structural layers. The upper layer consists of what is known as very open porous asphalt (ZOAB) for noise reduction. For the lower layer Guss Asphalt (GA) is used. Earlier investigations have shown

Hydrodynamic theory for quantum plasmonics: Linear-response dynamics of the inhomogeneous electron gas

DEFF Research Database (Denmark)

Yan, Wei

2015-01-01

We investigate the hydrodynamic theory of metals, offering systematic studies of the linear-response dynamics for an inhomogeneous electron gas. We include the quantum functional terms of the Thomas-Fermi kinetic energy, the von Weizsa¨cker kinetic energy, and the exchange-correlation Coulomb...... energies under the local density approximation. The advantages, limitations, and possible improvements of the hydrodynamic theory are transparently demonstrated. The roles of various parameters in the theory are identified. We anticipate that the hydrodynamic theory can be applied to investigate the linear...... response of complex metallic nanostructures, including quantum effects, by adjusting theory parameters appropriately....

Clifford Algebras and Spinorial Representation of Linear Canonical Transformations in Quantum Theory

International Nuclear Information System (INIS)

Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.

2017-11-01

This work is a continuation of previous works that we have done concerning linear canonical transformations and a phase space representation of quantum theory. It is mainly focused on the description of an approach which permits to establish spinorial representation of linear canonical transformations. It begins with an introduction section in which the reason and context of the content are discussed. The introduction section is followed by a brief recall about Clifford algebra and spin group. The description of the approach is started with the presentation of an adequate parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operators space. The establishment of the spinorial representation is deduced using relation between special pseudo-orthogonal groups and spin groups. The cases of one dimension quantum mechanics and general multidimensional theory are both studied. The case of linear canonical transformation related to Minkowski space is particularly studied and it is shown that Lorentz transformation may be considered as particular case of linear canonical transformation. Some results from the spinorial representation are also exploited to define operators which may be used to establish equations for fields if one considers the possibility of envisaging a field theory which admits as main symmetry group the group constituted by linear canonical transformations.

Linear control theory for gene network modeling.

Directory of Open Access Journals (Sweden)

Yong-Jun Shin

Full Text Available Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain and linear state-space (time domain can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

Plane answers to complex questions the theory of linear models

CERN Document Server

Christensen, Ronald

1987-01-01

This book was written to rigorously illustrate the practical application of the projective approach to linear models. To some, this may seem contradictory. I contend that it is possible to be both rigorous and illustrative and that it is possible to use the projective approach in practical applications. Therefore, unlike many other books on linear models, the use of projections and sub­ spaces does not stop after the general theory. They are used wherever I could figure out how to do it. Solving normal equations and using calculus (outside of maximum likelihood theory) are anathema to me. This is because I do not believe that they contribute to the understanding of linear models. I have similar feelings about the use of side conditions. Such topics are mentioned when appropriate and thenceforward avoided like the plague. On the other side of the coin, I just as strenuously reject teaching linear models with a coordinate free approach. Although Joe Eaton assures me that the issues in complicated problems freq...

A simple theory of linear mode conversion

International Nuclear Information System (INIS)

Cairns, R.A.; Lashmore-Davies, C.N.; Woods, A.M.

1984-01-01

A summary is given of the basic theory of linear mode conversion involving the construction of differential equations for the mode amplitudes based on the properties of the dispersion relation in the neighbourhood of the mode conversion point. As an example the transmission coefficient for tunneling from the upper hybrid resonance through the evanescent region to the adjacent cut-off is treated. 7 refs, 3 figs

The Influence of Material Properties on the Behaviour of Rayleigh Edge Waves in Thin Orthotropic Media

Czech Academy of Sciences Publication Activity Database

Červ, Jan

2008-01-01

Roč. 2, č. 5 (2008), s. 762-772 ISSN 1970-8734 R&D Projects: GA AV ČR(CZ) IAA200760611 Institutional research plan: CEZ:AV0Z20760514 Keywords : rayleigh edge waves * elastic orthotropic material * plane state of stress Subject RIV: BI - Acoustics

A quantum-mechanical perspective on linear response theory within polarizable embedding

DEFF Research Database (Denmark)

List, Nanna Holmgaard; Norman, Patrick; Kongsted, Jacob

2017-01-01

We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole...

Optimization of orthotropic distributed-mode loudspeaker using attached masses and multi-exciters.

Science.gov (United States)

Lu, Guochao; Shen, Yong; Liu, Ziyun

2012-02-01

Based on the orthotropic model of the plate, the method to optimize the sound response of the distributed-mode loudspeaker (DML) using the attached masses and the multi-exciters has been investigated. The attached masses method will rebuild the modes distribution of the plate, based on which multi-exciter method will smooth the sound response. The results indicate that the method can be used to optimize the sound response of the DML. © 2012 Acoustical Society of America

A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs

OpenAIRE

Giang, Phan H.; Shenoy, Prakash P.

2013-01-01

In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should behave so as to maximize "qualitative expected utility." Our axiomatization of the qualitative utility is similar to the axiomatization developed by von Neumann and Morgenstern for probabilistic l...

Energy-Based Yield Criteria for Orthotropic Materials, Exhibiting Strength-Differential Effect. Specification for Sheets under Plane Stress State

Directory of Open Access Journals (Sweden)

Szeptyński P.

2017-06-01

Full Text Available A general proposition of an energy-based limit condition for anisotropic materials exhibiting strength-differential effect (SDE based on spectral decomposition of elasticity tensors and the use of scaling pressure-dependent functions is specified for the case of orthotropic materials. A detailed algorithm (based on classical solutions of cubic equations for the determination of elastic eigenstates and eigenvalues of the orthotropic stiffness tensor is presented. A yield condition is formulated for both two-dimensional and three-dimensional cases. Explicit formulas based on simple strength tests are derived for parameters of criterion in the plane case. The application of both criteria for the description of yielding and plastic deformation of metal sheets is discussed in detail. The plane case criterion is verified with experimental results from the literature.

Primer on theory and operation of linear accelerators in radiation therapy

International Nuclear Information System (INIS)

Karzmark, C.J.; Morton, R.J.

1981-12-01

This primer is part of an educational package that also includes a series of 3 videotapes entitled Theory and Operation of Linear Accelerators in Radiation Therapy, Parts I, II, and III. This publication provides an overview of the components of the linear accelerator and how they function and interrelate. The auxiliary systems necessary to maintain the operation of the linear accelerator are also described

Linearized analysis of (2+1)-dimensional Einstein-Maxwell theory

International Nuclear Information System (INIS)

Soda, Jiro.

1989-08-01

On the basis of previous result by Hosoya and Nakao that (2+1)-dimensional gravity reduces the geodesic motion in moduli space, we investigate the effects of matter fields on the geodesic motion using the linearized theory. It is shown that the transverse-traceless parts of energy-momentum tensor make the deviation from the geodesic motion. This result is important for the Einstein-Maxwell theory due to the existence of global modes of Maxwell fields on torus. (author)

A non-linear theory of strong interactions

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs

An anisotropic linear thermo-viscoelastic constitutive law - Elastic relaxation and thermal expansion creep in the time domain

Science.gov (United States)

Pettermann, Heinz E.; DeSimone, Antonio

2017-09-01

A constitutive material law for linear thermo-viscoelasticity in the time domain is presented. The time-dependent relaxation formulation is given for full anisotropy, i.e., both the elastic and the viscous properties are anisotropic. Thereby, each element of the relaxation tensor is described by its own and independent Prony series expansion. Exceeding common viscoelasticity, time-dependent thermal expansion relaxation/creep is treated as inherent material behavior. The pertinent equations are derived and an incremental, implicit time integration scheme is presented. The developments are implemented into an implicit FEM software for orthotropic material symmetry under plane stress assumption. Even if this is a reduced problem, all essential features are present and allow for the entire verification and validation of the approach. Various simulations on isotropic and orthotropic problems are carried out to demonstrate the material behavior under investigation.

Comparison of Linear Induction Motor Theories for the LIMRV and TLRV Motors

Science.gov (United States)

1978-01-01

The Oberretl, Yamamura, and Mosebach theories of the linear induction motor are described and also applied to predict performance characteristics of the TLRV & LIMRV linear induction motors. The effect of finite motor width and length on performance ...

Asymptotic solutions and spectral theory of linear wave equations

International Nuclear Information System (INIS)

Adam, J.A.

1982-01-01

This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

Nonlinear static analysis of single layer annular/circular graphene sheets embedded in Winkler–Pasternak elastic matrix based on non-local theory of Eringen

Directory of Open Access Journals (Sweden)

Shahriar Dastjerdi

2016-06-01

Full Text Available Nonlinear bending analysis of orthotropic annular/circular graphene sheets has been studied based on the non-local elasticity theory. The first order shear deformation theory (FSDT is applied in combination with the nonlinear Von-Karman strain field. The obtained differential equations are solved by using two methods, first the differential quadrature method (DQM and a new semi-analytical polynomial method (SAPM which is innovated by the authors. Applying the DQM or SAPM, the differential equations are transformed to nonlinear algebraic equations system. Then the Newton–Raphson iterative scheme is used. First, the obtained results from DQM and SAPM are compared and it is concluded that although the SAPM’s formulation is considerably simpler than DQM, however, the SAPM’s results are so close to DQM. The results are validated with available papers. Finally, the effects of small scale parameter on the results, the comparison between local and non-local theories, and linear to nonlinear analyses are investigated.

Linear and nonlinear instability theory of a noble gas MHD generator

International Nuclear Information System (INIS)

Mesland, A.J.

1982-01-01

This thesis deals with the stability of the working medium of a seeded noble gas magnetohydrodynamic generator. The aim of the study is to determine the instability mechanism which is most likely to occur in experimental MHD generators and to describe its behaviour with linear and nonlinear theories. In chapter I a general introduction is given. The pertinent macroscopic basic equations are derived in chapter II, viz. the continuity, the momentum and the energy equation for the electrons and the heavy gas particles, consisting of the seed particles and the noble gas atoms. Chapter III deals with the linear plane wave analysis of small disturbances of a homogeneous steady state. The steady state is discussed in chapter IV. The values for the steady state parameters used for the calculations both for the linear analysis as for the nonlinear analysis are made plausible with the experimental values. Based on the results of the linear plane wave theory a nonlinear plane wave model of the electrothermal instability is introduced in chapter V. (Auth.)

The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

International Nuclear Information System (INIS)

Pfirsch, D.; Morrison, P.J.; Texas Univ., Austin

1990-02-01

A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any kind of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated - which need not be the same for all particle species in a plasma - are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. (orig.)

The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

International Nuclear Information System (INIS)

Pfirsch, D.; Morrison, P.J.

1990-02-01

A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any king of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated --- which need not be the same for all particle species in a plasma --- are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. 11 refs

Linear kinetic theory and particle transport in stochastic mixtures

Energy Technology Data Exchange (ETDEWEB)

Pomraning, G.C. [Univ. of California, Los Angeles, CA (United States)

1995-12-31

We consider the formulation of linear transport and kinetic theory describing energy and particle flow in a random mixture of two or more immiscible materials. Following an introduction, we summarize early and fundamental work in this area, and we conclude with a brief discussion of recent results.

Modification of linear response theory for mean-field approximations

NARCIS (Netherlands)

Hütter, M.; Öttinger, H.C.

1996-01-01

In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the

Linear response theory an analytic-algebraic approach

CERN Document Server

De Nittis, Giuseppe

2017-01-01

This book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3–5: the relevant von Neumann algebras, noncommutative $L^p$- and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and Kubo-Streda formulas. The book closes with a chapter about...

Stoneley waves in a non-homogeneous orthotropic granular medium under the influence of gravity

Directory of Open Access Journals (Sweden)

S. M. Ahmed

2005-01-01

Full Text Available The aim of this paper is to investigate the Stoneley waves in a non-homogeneous orthotropic granular medium under the influence of a gravity field. The frequency equation obtained, in the form of a sixth-order determinantal expression, is in agreement with the corresponding result when both media are elastic. The frequency equation when the gravity field is neglected has been deduced as a particular case.

Spectral theory of linear operators and spectral systems in Banach algebras

CERN Document Server

Müller, Vladimir

2003-01-01

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...

Theory of linear operators in Hilbert space

CERN Document Server

Akhiezer, N I

1993-01-01

This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

Turnpike theory of continuous-time linear optimal control problems

CERN Document Server

Zaslavski, Alexander J

2015-01-01

Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems.  The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands.  Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...

Linear conversion theory on the second harmonic emission from a plasma filament

International Nuclear Information System (INIS)

Tan Weihan; Gu Min

1989-01-01

The linear conversion theory of laser produced plasma filaments is studied. By calculations for the energy flux of the second harmonic emission on the basis of the planar wave-plasma interaction model, it has been found that there exists no 2ω 0 harmonic emission in the direction perpendicular to the incident laser, in contradiction with the experiments. A linear conversion theory is proposed on the second harmonic emission from a plasma filament and discovered the intense 2ω 0 harmonic emission in the direction perpendicular to the incident laser, which is in agreement with the experiments. (author)

Janus field theories from non-linear BF theories for multiple M2-branes

International Nuclear Information System (INIS)

Ryang, Shijong

2009-01-01

We integrate the nonpropagating B μ gauge field for the non-linear BF Lagrangian describing N M2-branes which includes terms with even number of the totally antisymmetric tensor M IJK in arXiv:0808.2473 and for the two-types of non-linear BF Lagrangians which include terms with odd number of M IJK as well in arXiv:0809:0985. For the former Lagrangian we derive directly the DBI-type Lagrangian expressed by the SU(N) dynamical A μ gauge field with a spacetime dependent coupling constant, while for the low-energy expansions of the latter Lagrangians the B μ integration is iteratively performed. The derived Janus field theory Lagrangians are compared.

Linearized propulsion theory of flapping airfoils revisited

Science.gov (United States)

Fernandez-Feria, Ramon

2016-11-01

A vortical impulse theory is used to compute the thrust of a plunging and pitching airfoil in forward flight within the framework of linear potential flow theory. The result is significantly different from the classical one of Garrick that considered the leading-edge suction and the projection in the flight direction of the pressure force. By taking into account the complete vorticity distribution on the airfoil and the wake the mean thrust coefficient contains a new term that generalizes the leading-edge suction term and depends on Theodorsen function C (k) and on a new complex function C1 (k) of the reduced frequency k. The main qualitative difference with Garrick's theory is that the propulsive efficiency tends to zero as the reduced frequency increases to infinity (as 1 / k), in contrast to Garrick's efficiency that tends to a constant (1 / 2). Consequently, for pure pitching and combined pitching and plunging motions, the maximum of the propulsive efficiency is not reached as k -> ∞ like in Garrick's theory, but at a finite value of the reduced frequency that depends on the remaining non-dimensional parameters. The present analytical results are in good agreement with experimental data and numerical results for small amplitude oscillations. Supported by the Ministerio de Economia y Competitividad of Spain Grant No. DPI2013-40479-P.

Symmetric linear systems - An application of algebraic systems theory

Science.gov (United States)

Hazewinkel, M.; Martin, C.

1983-01-01

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

Linear response theory of activated surface diffusion with interacting adsorbates

Energy Technology Data Exchange (ETDEWEB)

Marti' nez-Casado, R. [Department of Chemistry, Imperial College London, South Kensington, London SW7 2AZ (United Kingdom); Sanz, A.S.; Vega, J.L. [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); Rojas-Lorenzo, G. [Instituto Superior de Tecnologi' as y Ciencias Aplicadas, Ave. Salvador Allende, esq. Luaces, 10400 La Habana (Cuba); Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain); Miret-Artes, S., E-mail: s.miret@imaff.cfmac.csic.es [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain)

2010-05-12

Graphical abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed. - Abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed.

Linear-response theory of Coulomb drag in coupled electron systems

DEFF Research Database (Denmark)

Flensberg, Karsten; Hu, Ben Yu-Kuang; Jauho, Antti-Pekka

1995-01-01

We report a fully microscopic theory for the transconductivity, or, equivalently, the momentum transfer rate, of Coulomb coupled electron systems. We use the Kubo linear-response formalism and our main formal result expresses the transconductivity in terms of two fluctuation diagrams, which...

An energetic criterion for a micro-crack of finite length initiated in orthotropic bi-material notches

Czech Academy of Sciences Publication Activity Database

Profant, T.; Klusák, Jan; Ševeček, O.; Hrstka, M.; Kotoul, M.

2013-01-01

Roč. 110, SEP (2013), s. 396-409 ISSN 0013-7944 R&D Projects: GA ČR(CZ) GAP108/10/2049; GA ČR(CZ) GA101/09/1821 Institutional support: RVO:68081723 Keywords : crack initiation * bi-material notch * orthotropic bi-material notch * singular stress concentrator Subject RIV: JL - Materials Fatigue, Friction Mechanics Impact factor: 1.662, year: 2013

Linear theory of equatorial spread F

International Nuclear Information System (INIS)

Hudson, M.K.; Kennel, C.F.

1975-01-01

A fluid dispersion relation for the drift and interchange (Rayleigh-Taylor) modes in a collisional plasma forms the basis for a linear theory of equatorial spread F. The collisional drift mode growth rate will exceed the growth rate of the Rayleigh-Taylor mode at short perpendicular wavelengths and density gradient scale lengths, and the drift mode can grow on top side as well as on bottom side density gradients. However, below the F peak, where spread F predominates, it is concluded that both the drift and the Rayleigh-Taylor modes contribute to the total spread F spectrum, the Rayleigh-Taylor mode dominating at long and the drift mode at short perpendicular wavelengths above the ion Larmor radius

Stochastic linear programming models, theory, and computation

CERN Document Server

Kall, Peter

2011-01-01

This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...

Linearly Polarized IR Spectroscopy Theory and Applications for Structural Analysis

CERN Document Server

Kolev, Tsonko

2011-01-01

A technique that is useful in the study of pharmaceutical products and biological molecules, polarization IR spectroscopy has undergone continuous development since it first emerged almost 100 years ago. Capturing the state of the science as it exists today, "Linearly Polarized IR Spectroscopy: Theory and Applications for Structural Analysis" demonstrates how the technique can be properly utilized to obtain important information about the structure and spectral properties of oriented compounds. The book starts with the theoretical basis of linear-dichroic infrared (IR-LD) spectroscop

Transient thermal stresses in an orthotropic rectangular plate with convective heat transfer at upper and lower surfaces

International Nuclear Information System (INIS)

Sugano, Yoshihiro; Nakanishi, Takanori; Ito, Masahiko; Saito, Koichi.

1982-01-01

Recently, anisotropic materials have been used widely for reactor core elements and fast flying objects, therefore, the problem of thermal stress in anisotropic bodies has been studied actively. In this study, the unsteady plane thermal stress in an orthotropic rectangular thin plate heated by the temperature of ambient medium was analyzed, taking the heat transfer on both surfaces into account. The influence that the anisotropy of material constants and the heat transfer on both surfaces exert on the temperature and thermal stress of the plate was examined. Moreover, in order to investigate into the effect of the aspect ratio of the plate on the temperature and thermal stress, the unsteady distributions of temperature and thermal stress in an orthotropic semi-infinite band, of which the end surfaces are heated by ambient medium, were analyzed. The numerical calculation was carried out, and the results are shown. Before, it was difficult to satisfy the boundary condition related to shearing stress, accordingly, the analysis has not been performed, but in this study, it was shown that the analysis is possible. (Kako, I.)

MODELING OF RAILWAY TRACK OPERATION AS A SYSTEM OF QUASI-ELASTIC ORTHOTROPIC LAYERS

Directory of Open Access Journals (Sweden)

Sychev Vyacheslav Petrovich

2016-03-01

Full Text Available In this paper the authors give a solution to the problem of the impact of a rolling stock on the rail track on the basis of modeling a railway track as a multi-layered space, introducing each of the layers is a quasi-elastic orthotropic layer with cylindrical anisotropy in the polar coordinate system. The article describes wave equations, taking into account the rotational inertia of cross sectional and transverse shear strains. From the point of view of classical structural mechanics train path can be represented as a multilayer system comprising separate layers with different stiffness, lying on the foundation being the elastic-isotropic space. Winkler model provides that the basis is linearly deformable space, there are loads influencing its surface. These loads are transferred through a layered deformable half-space. This representation is used in this study as an initial approximation. For more accurate results of the deformation of a railway track because of rolling dynamic loads it is proposed to present a railway track in the form of a layered structure, where each element (assembled rails and sleepers, ballast section, the soil in the embankment, basement soils is modeled as a planar quasi-elastic orthotropic layer with cylindrical anisotropy. The equations describing the dynamic behaviour of flat element in a polar coordinate system are hyperbolic in nature and take into account the rotational inertia of the cross sectional and the transverse shear strains. This allows identifying the impact on the final characteristics of the blade wave effects, and oscillatory processes. In order to determine the unknown functions included in the constitutive equations it is proposed to use decomposition in power series in spatial coordinate and time. In order to determine the coefficients of ray series for the required functions, it is necessary to differentiate the defining wave equations k times on time, to take their difference on the different

Application of linear programming and perturbation theory in optimization of fuel utilization in a nuclear reactor

International Nuclear Information System (INIS)

Zavaljevski, N.

1985-01-01

Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time

A dynamical theory for linearized massive superspin 3/2

International Nuclear Information System (INIS)

Gates, James S. Jr.; Koutrolikos, Konstantinos

2014-01-01

We present a new theory of free massive superspin Y=3/2 irreducible representation of the 4D, N=1 Super-Poincaré group, which has linearized non-minimal supergravity (superhelicity Y=3/2) as it’s massless limit. The new results will illuminate the underlying structure of auxiliary superfields required for the description of higher massive superspin systems

System theory as applied differential geometry. [linear system

Science.gov (United States)

Hermann, R.

1979-01-01

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

Non-cooperative stochastic differential game theory of generalized Markov jump linear systems

CERN Document Server

Zhang, Cheng-ke; Zhou, Hai-ying; Bin, Ning

2017-01-01

This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the...

Non-linear electrodynamics in Kaluza-Klein theory

International Nuclear Information System (INIS)

Kerner, R.

1987-01-01

The most general variational principle based on the invariants of the Riemann tensor and leading to the second order differential equations should contain, in dimensions higher than four, the invariants of the Gauss-Bonnet type. In five dimensions the lagrangian should be a linear combination of the scalar curvature and the second-order invariant. The equations of the electromagnetic field are derived in the absence of scalar and gravitational fields of the Kaluza-Klein model. They yield the unique extension of Maxwell's system in the Kaluza-Klein theory. Some properties of eventual solutions are discussed [fr

Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...

Calculation of the interfacial tension of the methane-water system with the linear gradient theory

DEFF Research Database (Denmark)

Schmidt, Kurt A. G.; Folas, Georgios; Kvamme, Bjørn

2007-01-01

The linear gradient theory (LGT) combined with the Soave-Redlich-Kwong (SRK EoS) and the Peng-Robinson (PR EoS) equations of state has been used to correlate the interfacial tension data of the methane-water system. The pure component influence parameters and the binary interaction coefficient...... for the mixture influence parameter have been obtained for this system. The model was successfully applied to correlate the interfacial tension data set to within 2.3% for the linear gradient theory and the SRK EoS (LGT-SRK) and 2.5% for the linear gradient theory and PE EoS (LGT-PR). A posteriori comparison...... of data not used in the parameterisation were to within 3.2% for the LGT-SRK model and 2.7% for the LGT-PR model. An exhaustive literature review resulted in a large database for the investigation which covers a wide range of temperature and pressures. The results support the success of the linear...

The spin polarized linear response from density functional theory: Theory and application to atoms

Energy Technology Data Exchange (ETDEWEB)

Fias, Stijn, E-mail: sfias@vub.ac.be; Boisdenghien, Zino; De Proft, Frank; Geerlings, Paul [General Chemistry (ALGC), Vrije Universiteit Brussel (Free University Brussels – VUB), Pleinlaan 2, 1050 Brussels (Belgium)

2014-11-14

Within the context of spin polarized conceptual density functional theory, the spin polarized linear response functions are introduced both in the [N, N{sub s}] and [N{sub α}, N{sub β}] representations. The mathematical relations between the spin polarized linear response functions in both representations are examined and an analytical expression for the spin polarized linear response functions in the [N{sub α}, N{sub β}] representation is derived. The spin polarized linear response functions were calculated for all atoms up to and including argon. To simplify the plotting of our results, we integrated χ(r, r′) to a quantity χ(r, r{sup ′}), circumventing the θ and ϕ dependence. This allows us to plot and to investigate the periodicity throughout the first three rows in the periodic table within the two different representations. For the first time, χ{sub αβ}(r, r{sup ′}), χ{sub βα}(r, r{sup ′}), and χ{sub SS}(r, r{sup ′}) plots have been calculated and discussed. By integration of the spin polarized linear response functions, different components to the polarisability, α{sub αα}, α{sub αβ}, α{sub βα}, and α{sub ββ} have been calculated.

Quantum optimal control theory in the linear response formalism

International Nuclear Information System (INIS)

Castro, Alberto; Tokatly, I. V.

2011-01-01

Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice, this normally means optimizing the value of some observable, a so-called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization: the unperturbed Hamiltonian is allowed to be time dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in terms of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for nonequilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems.

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

Science.gov (United States)

Taousser, Fatima; Defoort, Michael; Djemai, Mohamed

2016-01-01

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.

Generation companies decision-making modeling by linear control theory

International Nuclear Information System (INIS)

Gutierrez-Alcaraz, G.; Sheble, Gerald B.

2010-01-01

This paper proposes four decision-making procedures to be employed by electric generating companies as part of their bidding strategies when competing in an oligopolistic market: naive, forward, adaptive, and moving average expectations. Decision-making is formulated in a dynamic framework by using linear control theory. The results reveal that interactions among all GENCOs affect market dynamics. Several numerical examples are reported, and conclusions are presented. (author)

Moving Griffith crack in an orthotropic strip with punches at boundary faces

Directory of Open Access Journals (Sweden)

S. Mukherjee

2005-01-01

Full Text Available Integral transform technique is employed to solve the elastodynamic problem of steady-state propagation of a Griffith crack centrally situated along the midplane of orthotropic strip of finite thickness 2h and subjected to point loading with centrally situated moving punches under constant pressure along the boundaries of the layer. The problem is reduced to the solution of a pair of simultaneous singular integral equations with Cauchy-type singularities which have finally been solved through the finite Hilbert transform technique. For large h, analytical expression for the stress intensity factor at the crack tip is obtained. Graphical plots of the numerical results are also presented.

Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

Science.gov (United States)

Gasbarro, Andrew

2018-03-01

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ2/d.o.f. = 0.5 compared to Χ2/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ2/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.

Analytical solution for static and dynamic analysis of magnetically affected viscoelastic orthotropic double-layered graphene sheets resting on viscoelastic foundation

Science.gov (United States)

Jalaei, M. H.; Arani, A. Ghorbanpour

2018-02-01

By considering the small scale effect based on the nonlocal Eringen's theory, the static and dynamic analysis of viscoelastic orthotropic double-layered graphene sheets subjected to longitudinal magnetic field and mechanical load is investigated analytically. For this objective, first order shear deformation theory (FSDT) is proposed. The surrounding medium is simulated by visco-Pasternak foundation model in which damping, normal and transverse shear loads are taken into account. The governing equations of motion are obtained via energy method and Hamilton's principle which are then solved analytically by means of Navier's approach and Laplace inversion technique in the space and time domains, respectively. Through various parametric studies, the influences of the nonlocal parameter, structural damping, van der Waals (vdW) interaction, stiffness and damping coefficient of the foundation, magnetic parameter, aspect ratio and length to thickness ratio on the static and dynamic response of the nanoplates are examined. The results depict that when the vdW interaction is considered to be zero, the upper layer deflection reaches a maximum point whereas the lower layer deflection becomes zero. In addition, it is observed that with growing the vdW interaction, the effect of magnetic field on the deflection of the lower layer increases while this effect reduces for the upper layer deflection.

Development of test method for assessing the bonding characteristics of membrane layers in wearing course laid on orthotropic steel bridge decks

NARCIS (Netherlands)

Liu, X.; Scarpas, A.; Li, J.; Tzimiris, G.; Hofman, R.; Voskuilen, J.

2013-01-01

In order to adequately characterize the adhesive bonding strength of the various membranes with surrounding materials on orthotropic steel decks and collect the necessary parameters for FE modeling, details of the Membrane Adhesion Test (MAT) are introduced. Analytical constitutive relations of the

Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

International Nuclear Information System (INIS)

Sugahara, Y.; Toki, H.

1994-01-01

We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

Linear spin-wave theory of incommensurably modulated magnets

DEFF Research Database (Denmark)

Ziman, Timothy; Lindgård, Per-Anker

1986-01-01

Calculations of linearized theories of spin dynamics encounter difficulties when applied to incommensurable magnetic phases: lack of translational invariance leads to an infinite coupled system of equations. The authors resolve this for the case of a `single-Q' structure by mapping onto the problem......: at higher frequency there appear bands of response sharply defined in frequency, but broad in momentum transfer; at low frequencies there is a response maximum at the q vector corresponding to the modulation vector. They discuss generalizations necessary for application to rare-earth magnets...

Checking the foundation: recent radiobiology and the linear no-threshold theory.

Science.gov (United States)

Ulsh, Brant A

2010-12-01

The linear no-threshold (LNT) theory has been adopted as the foundation of radiation protection standards and risk estimation for several decades. The "microdosimetric argument" has been offered in support of the LNT theory. This argument postulates that energy is deposited in critical cellular targets by radiation in a linear fashion across all doses down to zero, and that this in turn implies a linear relationship between dose and biological effect across all doses. This paper examines whether the microdosimetric argument holds at the lowest levels of biological organization following low dose, low dose-rate exposures to ionizing radiation. The assumptions of the microdosimetric argument are evaluated in light of recent radiobiological studies on radiation damage in biological molecules and cellular and tissue level responses to radiation damage. There is strong evidence that radiation initially deposits energy in biological molecules (e.g., DNA) in a linear fashion, and that this energy deposition results in various forms of prompt DNA damage that may be produced in a pattern that is distinct from endogenous (e.g., oxidative) damage. However, a large and rapidly growing body of radiobiological evidence indicates that cell and tissue level responses to this damage, particularly at low doses and/or dose-rates, are nonlinear and may exhibit thresholds. To the extent that responses observed at lower levels of biological organization in vitro are predictive of carcinogenesis observed in vivo, this evidence directly contradicts the assumptions upon which the microdosimetric argument is based.

Thermal flexural analysis of cross-ply laminated plates using trigonometric shear deformation theory

Directory of Open Access Journals (Sweden)

Yuwaraj Marotrao Ghugal

Full Text Available Thermal stresses and displacements for orthotropic, two-layer antisymmetric, and three-layer symmetric square cross-ply laminated plates subjected to nonlinear thermal load through the thickness of laminated plates are presented by using trigonometric shear deformation theory. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The validity of present theory is verified by comparing the results with those of classical plate theory and first order shear deformation theory and higher order shear deformation theory.

Linear canonical transforms theory and applications

CERN Document Server

Kutay, M; Ozaktas, Haldun; Sheridan, John

2016-01-01

This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.

Background field method in gauge theories and on linear sigma models

International Nuclear Information System (INIS)

van de Ven, A.E.M.

1986-01-01

This dissertation constitutes a study of the ultraviolet behavior of gauge theories and two-dimensional nonlinear sigma-models by means of the background field method. After a general introduction in chapter 1, chapter 2 presents algorithms which generate the divergent terms in the effective action at one-loop for arbitrary quantum field theories in flat spacetime of dimension d ≤ 11. It is demonstrated that global N = 1 supersymmetric Yang-Mills theory in six dimensions in one-loop UV-finite. Chapter 3 presents an algorithm which produces the divergent terms in the effective action at two-loops for renormalizable quantum field theories in a curved four-dimensional background spacetime. Chapter 4 presents a study of the two-loop UV-behavior of two-dimensional bosonic and supersymmetric non-linear sigma-models which include a Wess-Zumino-Witten term. It is found that, to this order, supersymmetric models on quasi-Ricci flat spaces are UV-finite and the β-functions for the bosonic model depend only on torsionful curvatures. Chapter 5 summarizes a superspace calculation of the four-loop β-function for two-dimensional N = 1 and N = 2 supersymmetric non-linear sigma-models. It is found that besides the one-loop contribution which vanishes on Ricci-flat spaces, the β-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for superstrings are discussed. Chapters 6 and 7 treat the details of these calculations

Non-linear theory of elasticity and optimal design

CERN Document Server

Ratner, LW

2003-01-01

In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it

On the Influence of Clearance in Orthotropic Disc-Pin Contacts

DEFF Research Database (Denmark)

Pedersen, Pauli

2007-01-01

, an orthotropic disc-pin contact problem. The most simple solutions are named Hertz solutions (from 1882), and we use one of these solutions for comparison with finite element results. As a function of the total contact force we find (inversely) the size of the contact area, the distribution of the contact......Solutions to contact problems are important in mechanical as well as in civil engineering, and even for the most simple problems there is still a need for research results. In the present paper we use an alternative super element procedure to solve directly, without iteration and incrementation...... pressure, and the contact compliance. In models of finite size the compliance depends on the flexibility of the total model, including the boundary condition of the model, and therefore disagreement with the locally based analytical models is expected. The examples of an earlier paper were restricted...

Linear extended neutron diffusion theory for semi-in finites homogeneous means

International Nuclear Information System (INIS)

Vazquez R, R.; Vazquez R, A.; Espinosa P, G.

2009-10-01

Originally developed for heterogeneous means, the linear extended neutron diffusion theory is applied to the limit case of monoenergetic neutron diffusion in a semi-infinite homogeneous mean with a neutron source, located in the coordinate origin situated in the frontier of dispersive material. The monoenergetic neutron diffusion is studied taking into account the spatial deviations in the neutron flux to the interfacial current caused by the neutron source, as well as the influence of the spatial deviations in the absorption rate. The developed pattern is an unidimensional model for an energy group obtained of application of volumetric average diffusion equation in the moderator. The obtained results are compared against the classic diffusion theory and qualitatively against the neutron transport theory. (Author)

ONETEP: linear-scaling density-functional theory with plane-waves

International Nuclear Information System (INIS)

Haynes, P D; Mostof, A A; Skylaris, C-K; Payne, M C

2006-01-01

This paper provides a general overview of the methodology implemented in onetep (Order-N Electronic Total Energy Package), a parallel density-functional theory code for largescale first-principles quantum-mechanical calculations. The distinctive features of onetep are linear-scaling in both computational effort and resources, obtained by making well-controlled approximations which enable simulations to be performed with plane-wave accuracy. Titanium dioxide clusters of increasing size designed to mimic surfaces are studied to demonstrate the accuracy and scaling of onetep

Linear kinetic theory and particle transport in stochastic mixtures

International Nuclear Information System (INIS)

Pomraning, G.C.

1994-03-01

The primary goal in this research is to develop a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. The statistics considered correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components of the mixture. The mixing statistics studied are Markovian as well as more general statistics, such as renewal processes. A further goal of this work is to demonstrate the applicability of the formalism to real world engineering problems. This three year program was initiated June 15, 1993 and has been underway nine months. Many significant results have been obtained, both in the formalism development and in representative applications. These results are summarized by listing the archival publications resulting from this grant, including the abstracts taken directly from the papers

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles.

Science.gov (United States)

Navarrete-Benlloch, Carlos; Weiss, Talitha; Walter, Stefan; de Valcárcel, Germán J

2017-09-29

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.

Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

Directory of Open Access Journals (Sweden)

2007-01-01

Full Text Available Hysteresis is a rate-independent non-linearity that is expressed through thresholds, switches, and branches. Exceedance of a threshold, or the occurrence of a turning point in the input, switches the output onto a particular output branch. Rate-independent branching on a very large set of switches with non-local memory is the central concept in the new definition of hysteresis. Hysteretic loops are a special case. A self-consistent mathematical description of hydrological systems with hysteresis demands a new non-linear systems theory of adequate generality. The goal of this paper is to establish this and to show how this may be done. Two results are presented: a conceptual model for the hysteretic soil-moisture characteristic at the pedon scale and a hysteretic linear reservoir at the catchment scale. Both are based on the Preisach model. A result of particular significance is the demonstration that the independent domain model of the soil moisture characteristic due to Childs, Poulavassilis, Mualem and others, is equivalent to the Preisach hysteresis model of non-linear systems theory, a result reminiscent of the reduction of the theory of the unit hydrograph to linear systems theory in the 1950s. A significant reduction in the number of model parameters is also achieved. The new theory implies a change in modelling paradigm.

A test of the linear-no threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1990-01-01

It has been pointed out that, while an ecological study cannot determine whether radon causes lung cancer, it can test the validity of a linear-no threshold relationship between them. The linear-no threshold theory predicts a substantial positive correlation between the average radon exposure in various counties and their lung cancer mortality rates. Data on living areas of houses in 411 counties from all parts of the United States exhibit, rather, a substantial negative correlation with the slopes of the lines of regression differing from zero by 10 and 7 standard deviations for males and females, respectively, and from the positive slope predicted by the theory by at least 16 and 12 standard deviations. When the data are segmented into 23 groups of states or into 7 regions of the country, the predominantly negative slopes and correlations persist, applying to 18 of the 23 state groups and 6 of the 7 regions. Five state-sponsored studies are analyzed, and four of these give a strong negative slope (the other gives a weak positive slope, in agreement with our data for that state). A strong negative slope is also obtained in our data on basements in 253 counties. A random selection-no charge study of 39 high and low lung cancer counties (+4 low population states) gives a much stronger negative correlation. When nine potential confounding factors are included in a multiple linear regression analysis, the discrepancy with theory is reduced only to 12 and 8.5 standard deviations for males and females, respectively. When the data are segmented into four groups by population, the multiple regression vs radon level gives a strong negative slope for each of the four groups. Other considerations are introduced to reduce the discrepancy, but it remains very substantial

On the non-linear scale of cosmological perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-04-15

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

International Nuclear Information System (INIS)

Blas, Diego; Garny, Mathias; Konstandin, Thomas

2013-04-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

CERN Document Server

Blas, Diego; Konstandin, Thomas

2013-01-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

A simplified density matrix minimization for linear scaling self-consistent field theory

International Nuclear Information System (INIS)

Challacombe, M.

1999-01-01

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics

Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

Energy Technology Data Exchange (ETDEWEB)

Shalchi, A. [Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2 (Canada); Negrea, M.; Petrisor, I. [Department of Physics, University of Craiova, Association Euratom-MEdC, 13A.I.Cuza Str, 200585 Craiova (Romania)

2016-07-15

We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficients and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.

Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

International Nuclear Information System (INIS)

Shalchi, A.; Negrea, M.; Petrisor, I.

2016-01-01

We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficients and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.

Natural excitation orbitals from linear response theories : Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory

NARCIS (Netherlands)

Van Meer, R.; Gritsenko, O. V.; Baerends, E. J.

2017-01-01

Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In

Analysis of B-WIM Signals acquired in Millau Orthotropic Viaduct Using Statistical Classification

OpenAIRE

IENG, Sio Song; ZERMANE, Abderraouf; SCHMIDT, Franziska; JACOB, Bernard

2012-01-01

Les systèmes B-WIM classiques sont généralement fondés sur les travaux de Moses utilisant la notion de la ligne d'influence. Ces systèmes ont été testés avec succès sur les ponts en béton à travers le monde. Ce papier s'intéresse aux travaux de recherche concernant l'utilisation d'un système B-WIM sur le viaduc de Millau qui est un pont à haubans avec une à dalle orthotrope. Nous montrons d'abord qu'un système de B-WIM ne peut pas être utilisé directement sur ce type de pont sans adaptation d...

Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory

DEFF Research Database (Denmark)

Frier, Christian; Sørensen, John Dalsgaard

2003-01-01

A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

Science.gov (United States)

Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.

2018-06-01

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

Linear theory of density perturbations in a neutrino+baryon universe

International Nuclear Information System (INIS)

Wasserman, I.

1981-01-01

Various aspects of the linear theory of density perturbations in a universe containing a significant population of massive neutrinos are calculated. Because linear perturbations in the neutrino density are subject to nonviscous damping on length scales smaller than the effective neutrino Jeans length, the fluctuation spectrum of the neutrino density perturbations just after photon decoupling is expected to peak near the maximum neutrino Jeans mass. The gravitational effects of nonneutrino species are included in calculating the maximum neutrino Jeans mass, which is found to be [M/sub J/(t)]/sub max/approx.10 17 M/sub sun//[m/sub ν/(eV)] 2 , about an order of magnitude smaller than is obtained when nonneutrino species are ignored. An explicit expression for the nonviscous damping of neutrino density perturbations less massive than the maximum neutrino Jeans mass is derived. The linear evolution of density perturbations after photon decoupling is discussed. Of particular interest is the possibility that fluctuations in the neutrino density induce baryon density perturbations after photon decoupling and that the maximum neutrino Jeans determines the characteristic bound mass of galaxy clusters

Classes and Theories of Trees Associated with a Class Of Linear Orders

DEFF Research Database (Denmark)

Goranko, Valentin; Kellerman, Ruaan

2011-01-01

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between...... these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of the first-order theory of the generating class C, and indicate the problems obstructing such general...... results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees....

Linear theory on temporal instability of megahertz faraday waves for monodisperse microdroplet ejection.

Science.gov (United States)

Tsai, Shirley C; Tsai, Chen S

2013-08-01

A linear theory on temporal instability of megahertz Faraday waves for monodisperse microdroplet ejection based on mass conservation and linearized Navier-Stokes equations is presented using the most recently observed micrometer- sized droplet ejection from a millimeter-sized spherical water ball as a specific example. The theory is verified in the experiments utilizing silicon-based multiple-Fourier horn ultrasonic nozzles at megahertz frequency to facilitate temporal instability of the Faraday waves. Specifically, the linear theory not only correctly predicted the Faraday wave frequency and onset threshold of Faraday instability, the effect of viscosity, the dynamics of droplet ejection, but also established the first theoretical formula for the size of the ejected droplets, namely, the droplet diameter equals four-tenths of the Faraday wavelength involved. The high rate of increase in Faraday wave amplitude at megahertz drive frequency subsequent to onset threshold, together with enhanced excitation displacement on the nozzle end face, facilitated by the megahertz multiple Fourier horns in resonance, led to high-rate ejection of micrometer- sized monodisperse droplets (>10(7) droplets/s) at low electrical drive power (<;1 W) with short initiation time (<;0.05 s). This is in stark contrast to the Rayleigh-Plateau instability of a liquid jet, which ejects one droplet at a time. The measured diameters of the droplets ranging from 2.2 to 4.6 μm at 2 to 1 MHz drive frequency fall within the optimum particle size range for pulmonary drug delivery.

Effect of elliptic or circular holes on the stress distribution in plates of wood or plywood considered as orthotropic materials

Science.gov (United States)

C. B. Smith

1944-01-01

This is a mathematical analysis of the stress distribution existing near a hole in a wood or plywood plate subjected to tension, as, for example, near holes in the tension flanges of wood box beams. It is assumed that the strains are small and remain within the proportional limit. In this analysis a large, rectangular, orthotropic plate with a small elliptic hole at...

Linear response theory for magnetic Schrodinger operators in disordered media

CERN Document Server

Bouclet, J M; Klein, A; Schenker, J

2004-01-01

We justify the linear response theory for an ergodic Schrodinger operator with magnetic field within the non-interacting particle approximation, and derive a Kubo formula for the electric conductivity tensor. To achieve that, we construct suitable normed spaces of measurable covariant operators where the Liouville equation can be solved uniquely. If the Fermi level falls into a region of localization, we recover the well-known Kubo-Streda formula for the quantum Hall conductivity at zero temperature.

Solar Wind Proton Temperature Anisotropy: Linear Theory and WIND/SWE Observations

Science.gov (United States)

Hellinger, P.; Travnicek, P.; Kasper, J. C.; Lazarus, A. J.

2006-01-01

We present a comparison between WIND/SWE observations (Kasper et al., 2006) of beta parallel to p and T perpendicular to p/T parallel to p (where beta parallel to p is the proton parallel beta and T perpendicular to p and T parallel to p are the perpendicular and parallel proton are the perpendicular and parallel proton temperatures, respectively; here parallel and perpendicular indicate directions with respect to the ambient magnetic field) and predictions of the Vlasov linear theory. In the slow solar wind, the observed proton temperature anisotropy seems to be constrained by oblique instabilities, by the mirror one and the oblique fire hose, contrary to the results of the linear theory which predicts a dominance of the proton cyclotron instability and the parallel fire hose. The fast solar wind core protons exhibit an anticorrelation between beta parallel to c and T perpendicular to c/T parallel to c (where beta parallel to c is the core proton parallel beta and T perpendicular to c and T parallel to c are the perpendicular and parallel core proton temperatures, respectively) similar to that observed in the HELIOS data (Marsch et al., 2004).

Theory of linear physical systems theory of physical systems from the viewpoint of classical dynamics, including Fourier methods

CERN Document Server

Guillemin, Ernst A

2013-01-01

An eminent electrical engineer and authority on linear system theory presents this advanced treatise, which approaches the subject from the viewpoint of classical dynamics and covers Fourier methods. This volume will assist upper-level undergraduates and graduate students in moving from introductory courses toward an understanding of advanced network synthesis. 1963 edition.

Test of the linear-no threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1994-01-01

We recently completed a compilation of radon measurements from available sources which gives the average radon level, in homes for 1730 counties, well over half of all U.S. counties and comprising about 90% of the total U.S. population. Epidemiologists normally study the relationship between mortality risks to individuals, m, vs their personal exposure, r, whereas an ecological study like ours deals with the relationship between the average risk to groups of individuals (population of counties) and their average exposure. It is well known to epidemiologists that, in general, the average dose does not determine the average risk, and to assume otherwise is called 'the ecological fallacy'. However, it is easy to show that, in testing a linear-no threshold theory, 'the ecological fallacy' does not apply; in that theory, the average dose does determine the average risk. This is widely recognized from the fact that 'person-rem' determines the number of deaths. Dividing person-rem by population gives average dose, and dividing number of deaths by population gives mortality rate. Because of the 'ecological fallacy', epidemiology textbooks often state that an ecological study cannot determine a causal relationship between risk and exposure. That may be true, but it is irrelevant here because the purpose of our study is not to determine a causal relationship; it is rather to test the linear-no threshold dependence of m on r. (author)

A statistical theory of cell killing by radiation of varying linear energy transfer

International Nuclear Information System (INIS)

Hawkins, R.B.

1994-01-01

A theory is presented that provides an explanation for the observed features of the survival of cultured cells after exposure to densely ionizing high-linear energy transfer (LET) radiation. It starts from a phenomenological postulate based on the linear-quadratic form of cell survival observed for low-LET radiation and uses principles of statistics and fluctuation theory to demonstrate that the effect of varying LET on cell survival can be attributed to random variation of dose to small volumes contained within the nucleus. A simple relation is presented for surviving fraction of cells after exposure to radiation of varying LET that depends on the α and β parameters for the same cells in the limit of low-LET radiation. This relation implies that the value of β is independent of LET. Agreement of the theory with selected observations of cell survival from the literature is demonstrated. A relation is presented that gives relative biological effectiveness (RBE) as a function of the α and β parameters for low-LET radiation. Measurements from microdosimetry are used to estimate the size of the subnuclear volume to which the fluctuation pertains. 11 refs., 4 figs., 2 tabs

Digital linear control theory applied to automatic stepsize control in electrical circuit simulation

NARCIS (Netherlands)

Verhoeven, A.; Beelen, T.G.J.; Hautus, M.L.J.; Maten, ter E.J.W.; Di Bucchianico, A.; Mattheij, R.M.M.; Peletier, M.A.

2006-01-01

Adaptive stepsize control is used to control the local errors of the numerical solution. For optimization purposes smoother stepsize controllers are wanted, such that the errors and stepsizes also behave smoothly. We consider approaches from digital linear control theory applied to multistep

Digital linear control theory applied to automatic stepsize control in electrical circuit simulation

NARCIS (Netherlands)

Verhoeven, A.; Beelen, T.G.J.; Hautus, M.L.J.; Maten, ter E.J.W.

2005-01-01

Adaptive stepsize control is used to control the local errors of the numerical solution. For optimization purposes smoother stepsize controllers are wanted, such that the errors and stepsizes also behave smoothly. We consider approaches from digital linear control theory applied to multistep

Synthetic Domain Theory and Models of Linear Abadi & Plotkin Logic

DEFF Research Database (Denmark)

Møgelberg, Rasmus Ejlers; Birkedal, Lars; Rosolini, Guiseppe

2008-01-01

Plotkin suggested using a polymorphic dual intuitionistic/linear type theory (PILLY) as a metalanguage for parametric polymorphism and recursion. In recent work the first two authors and R.L. Petersen have defined a notion of parametric LAPL-structure, which are models of PILLY, in which one can...... reason using parametricity and, for example, solve a large class of domain equations, as suggested by Plotkin.In this paper, we show how an interpretation of a strict version of Bierman, Pitts and Russo's language Lily into synthetic domain theory presented by Simpson and Rosolini gives rise...... to a parametric LAPL-structure. This adds to the evidence that the notion of LAPL-structure is a general notion, suitable for treating many different parametric models, and it provides formal proofs of consequences of parametricity expected to hold for the interpretation. Finally, we show how these results...

Non-linear wave loads and ship responses by a time-domain strip theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...

Application of linear and higher perturbation theory in reactor physics

International Nuclear Information System (INIS)

Woerner, D.

1978-01-01

For small perturbations in the material composition of a reactor according to the first approximation of perturbation theory the eigenvalue perturbation is proportional to the perturbation of the system. This assumption is true for the neutron flux not influenced by the perturbance. The two-dimensional code LINESTO developed for such problems in this paper on the basis of diffusion theory determines the relative change of the multiplication constant. For perturbations varying the neutron flux in the space of energy and position the eigenvalue perturbation is also influenced by this changed neutron flux. In such cases linear perturbation theory yields larger errors. Starting from the methods of calculus of variations there is additionally developed in this paper a perturbation method of calculation permitting in a quick and simple manner to assess the influence of flux perturbation on the eigenvalue perturbation. While the source of perturbations is evaluated in isotropic approximation of diffusion theory the associated inhomogeneous equation may be used to determine the flux perturbation by means of diffusion or transport theory. Possibilities of application and limitations of this method are studied in further systematic investigations on local perturbations. It is shown that with the integrated code system developed in this paper a number of local perturbations may be checked requiring little computing time. With it flux perturbations in first approximation and perturbations of the multiplication constant in second approximation can be evaluated. (orig./RW) [de

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

Science.gov (United States)

Özer, Hatice; Delice, Özgür

2018-03-01

Two different ways of generalizing Einstein’s general theory of relativity with a cosmological constant to Brans–Dicke type scalar–tensor theories are investigated in the linearized field approximation. In the first case a cosmological constant term is coupled to a scalar field linearly whereas in the second case an arbitrary potential plays the role of a variable cosmological term. We see that the former configuration leads to a massless scalar field whereas the latter leads to a massive scalar field. General solutions of these linearized field equations for both cases are obtained corresponding to a static point mass. Geodesics of these solutions are also presented and solar system effects such as the advance of the perihelion, deflection of light rays and gravitational redshift were discussed. In general relativity a cosmological constant has no role in these phenomena. We see that for the Brans–Dicke theory, the cosmological constant also has no effect on these phenomena. This is because solar system observations require very large values of the Brans–Dicke parameter and the correction terms to these phenomena becomes identical to GR for these large values of this parameter. This result is also observed for the theory with arbitrary potential if the mass of the scalar field is very light. For a very heavy scalar field, however, there is no such limit on the value of this parameter and there are ranges of this parameter where these contributions may become relevant in these scales. Galactic and intergalactic dynamics is also discussed for these theories at the latter part of the paper with similar conclusions.

A Linear Gradient Theory Model for Calculating Interfacial Tensions of Mixtures

DEFF Research Database (Denmark)

Zou, You-Xiang; Stenby, Erling Halfdan

1996-01-01

excellent agreement between the predicted and experimental IFTs at high and moderate levels of IFTs, while the agreement is reasonably accurate in the near-critical region as the used equations of state reveal classical scaling behavior. To predict accurately low IFTs (sigma ... with proper scaling behavior at the critical point is at least required.Key words: linear gradient theory; interfacial tension; equation of state; influence parameter; density profile....

Analysis and Characterization of Damage Utilizing an Orthotropic Generalized Composite Material Model Suitable for Use in Impact Problems

Science.gov (United States)

Goldberg, Robert K.; Carney, Kelly S.; DuBois, Paul; Hoffarth, Canio; Rajan, Subramaniam; Blankenhorn, Gunther

2016-01-01

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive communities. In order to address a series of issues identified by the aerospace community as being desirable to include in a next generation composite impact model, an orthotropic, macroscopic constitutive model incorporating both plasticity and damage suitable for implementation within the commercial LS-DYNA computer code is being developed. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain hardening-based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used in which a load in one direction results in a stiffness reduction in multiple material coordinate directions. A detailed analysis is carried out to ensure that the strain equivalence assumption is appropriate for the derived plasticity and damage formulations that are employed in the current model. Procedures to develop the appropriate input curves for the damage model are presented and the process required to develop an appropriate characterization test matrix is discussed

Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence.

Science.gov (United States)

Ozaktas, Haldun M; Yüksel, Serdar; Kutay, M Alper

2002-08-01

A linear algebraic theory of partial coherence is presented that allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights but also allows us to employ the conceptual and algebraic tools of linear algebra in applications. We define several scalar measures of the degree of partial coherence of an optical field that are zero for full incoherence and unity for full coherence. The mathematical definitions are related to our physical understanding of the corresponding concepts by considering them in the context of Young's experiment.

Shear-transformation-zone theory of linear glassy dynamics.

Science.gov (United States)

Bouchbinder, Eran; Langer, J S

2011-06-01

We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main features of the barrier-height distribution are determined by the effective temperature and other near-equilibrium properties of the configurational degrees of freedom. Our theory accounts for the wide range of relaxation rates observed in both metallic glasses and soft glassy materials such as colloidal suspensions. We find that the frequency-dependent loss modulus is not just a superposition of Maxwell modes. Rather, it exhibits an α peak that rises near the viscous relaxation rate and, for nearly jammed, glassy systems, extends to much higher frequencies in accord with experimental observations. We also use this theory to compute strain recovery following a period of large, persistent deformation and then abrupt unloading. We find that strain recovery is determined in part by the initial barrier-height distribution, but that true structural aging also occurs during this process and determines the system's response to subsequent perturbations. In particular, we find by comparison with experimental data that the initial deformation produces a highly disordered state with a large population of low activation barriers, and that this state relaxes quickly toward one in which the distribution is dominated by the high barriers predicted by the near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height distribution is the most important of the issues raised and left unresolved in this paper.

Using system theory and energy methods to prove existence of non-linear PDE's

NARCIS (Netherlands)

Zwart, H.J.

2015-01-01

In this discussion paper we present an idea of combining techniques known from systems theory with energy estimates to show existence for a class of non-linear partial differential equations (PDE's). At the end of the paper a list of research questions with possible approaches is given.

Using a quasi-heat-pulse method to determine heat and moisture transfer properties for porous orthotropic wood products or cellular solid materials

Science.gov (United States)

M. A. Dietenberger

2006-01-01

Understanding heat and moisture transfer in a wood specimen as used in the K-tester has led to an unconventional numerical solution arid intriguing protocol to deriving the transfer properties. Laplace transform solutions of Luikov’s differential equations are derived for one-dimensional heat and moisture transfer in porous hygroscopic orthotropic materials and for a...

Verification and Validation of a Three-Dimensional Orthotropic Plasticity Constitutive Model Using a Unidirectional Composite

Directory of Open Access Journals (Sweden)

Canio Hoffarth

2017-03-01

Full Text Available A three-dimensional constitutive model has been developed for modeling orthotropic composites subject to impact loads. It has three distinct components—a deformation model involving elastic and plastic deformations; a damage model; and a failure model. The model is driven by tabular data that is generated either using laboratory tests or via virtual testing. A unidirectional composite—T800/F3900, commonly used in the aerospace industry, is used in the verification and validation tests. While the failure model is under development, these tests indicate that the implementation of the deformation and damage models in a commercial finite element program, LS-DYNA, is efficient, robust and accurate.

Transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations

International Nuclear Information System (INIS)

Sugano, Y.

1980-01-01

The transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations on two edges are studied by means of the Airy stress function. The purposes of this paper are to present a method of determing the transient thermal stresses in an orthographic rectangular plate with four edges of distinct thermal boundary condition of the third kind which exactly satisfy the traction-free conditions of shear stress over all boundaries including four corners of the plate, and to consider the effects of the anisotropies of material properties and the convective heat transfer on the upper and lower surfaces on the thermal stress distribution. (orig.)

Two-fluid static spherical configurations with linear mass function in the Einstein-Cartan theory

International Nuclear Information System (INIS)

Gallakhmetov, A.M.

2002-01-01

In the framework of the Einstein-Cartan theory, two-fluid static spherical configurations with linear mass function are considered. One of these modelling anisotropic matter distributions within star and the other fluid is a perfect fluid representing a source of torsion. It is shown that the solutions of the Einstein equations for anisotropic relativistic spheres in General Relativity may generate the solutions in the Einstein-Cartan theory. Some exact solutions are obtained

Microscopic theory of ultrafast spin linear reversal

Energy Technology Data Exchange (ETDEWEB)

Zhang, G P, E-mail: gpzhang@indstate.edu [Department of Physics, Indiana State University, Terre Haute, IN 47809 (United States)

2011-05-25

A recent experiment (Vahaplar et al 2009 Phys. Rev. Lett. 103 117201) showed that a single femtosecond laser can reverse the spin direction without spin precession, or spin linear reversal (SLR), but its microscopic theory has been missing. Here we show that SLR does not occur naturally. Two generic spin models, the Heisenberg and Hubbard models, are employed to describe magnetic insulators and metals, respectively. We find analytically that the spin change is always accompanied by a simultaneous excitation of at least two spin components. The only model that has prospects for SLR is the Stoner single-electron band model. However, under the influence of the laser field, the orbital angular momenta are excited and are coupled to each other. If a circularly polarized light is used, then all three components of the orbital angular momenta are excited, and so are their spins. The generic spin commutation relation further reveals that if SLR exists, it must involve a complicated multiple state excitation.

Homogenized approach for the non linear dynamic analysis of entire masonry buildings by means of rigid plate elements and damaging interfaces

Science.gov (United States)

Bertolesi, Elisa; Milani, Gabriele

2017-07-01

The present paper is devoted to the analysis of entire 3D masonry structures adopting a Rigid Body and Spring-Mass (HRBSM) model. A series of non linear static and dynamic analyses are conducted with respect to two structures with technical relevance. The elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. At a structural level, the non-linear analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM) by means of which both in and out of plane mechanisms are allowed. In order to validate the proposed model for the analyses of full scale structures subjected to seismic actions, two different examples are critically discussed, namely a church façade and an in-scale masonry building, both subjected to dynamic excitation. The results obtained are compared with experimental or numerical results available in literature.

Conformal field theory with two kinds of Bosonic fields and two linear dilatons

International Nuclear Information System (INIS)

Kamani, Davoud

2010-01-01

We consider a two-dimensional conformal field theory which contains two kinds of the bosonic degrees of freedom. Two linear dilaton fields enable to study a more general case. Various properties of the model such as OPEs, central charge, conformal properties of the fields and associated algebras will be studied. (author)

Non-linearities in Theory-of-Mind Development.

Science.gov (United States)

Blijd-Hoogewys, Els M A; van Geert, Paul L C

2016-01-01

Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72-78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths.

Linear methods in band theory

DEFF Research Database (Denmark)

Andersen, O. Krogh

1975-01-01

of Korringa-Kohn-Rostoker, linear-combination-of-atomic-orbitals, and cellular methods; the secular matrix is linear in energy, the overlap integrals factorize as potential parameters and structure constants, the latter are canonical in the sense that they neither depend on the energy nor the cell volume...

On the direction of a crack initiated from an orthotropic bi-material notch composed of materials with non-uniform fracture mechanics properties

Czech Academy of Sciences Publication Activity Database

Profant, T.; Klusák, Jan; Ševeček, O.; Kotoul, M.

525-526, č. 1 (2013), s. 545-548 ISSN 1013-9826. [Fracture and Damage Mechanics /11./. Xi'an, 18.09.2012-21.09.2012] R&D Projects: GA ČR GA101/09/1821; GA ČR GAP108/10/2049 Institutional support: RVO:68081723 Keywords : Orthotropic bi-material notch * generalized stress intensity factor * complex potentials Subject RIV: JL - Materials Fatigue, Friction Mechanics

Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity

International Nuclear Information System (INIS)

Kao, B.G.

1979-11-01

Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials

Three-dimensional linear peeling-ballooning theory in magnetic fusion devices

Energy Technology Data Exchange (ETDEWEB)

Weyens, T., E-mail: tweyens@fis.uc3m.es; Sánchez, R.; García, L. [Departamento de Física, Universidad Carlos III de Madrid, Madrid 28911 (Spain); Loarte, A.; Huijsmans, G. [ITER Organization, Route de Vinon sur Verdon, 13067 Saint Paul Lez Durance (France)

2014-04-15

Ideal magnetohydrodynamics theory is extended to fully 3D magnetic configurations to investigate the linear stability of intermediate to high n peeling-ballooning modes, with n the toroidal mode number. These are thought to be important for the behavior of edge localized modes and for the limit of the size of the pedestal that governs the high confinement H-mode. The end point of the derivation is a set of coupled second order ordinary differential equations with appropriate boundary conditions that minimize the perturbed energy and that can be solved to find the growth rate of the perturbations. This theory allows of the evaluation of 3D effects on edge plasma stability in tokamaks such as those associated with the toroidal ripple due to the finite number of toroidal field coils, the application of external 3D fields for elm control, local modification of the magnetic field in the vicinity of ferromagnetic components such as the test blanket modules in ITER, etc.

Recent development of linear scaling quantum theories in GAMESS

Energy Technology Data Exchange (ETDEWEB)

Choi, Cheol Ho [Kyungpook National Univ., Daegu (Korea, Republic of)

2003-06-01

Linear scaling quantum theories are reviewed especially focusing on the method adopted in GAMESS. The three key translation equations of the fast multipole method (FMM) are deduced from the general polypolar expansions given earlier by Steinborn and Rudenberg. Simplifications are introduced for the rotation-based FMM that lead to a very compact FMM formalism. The OPS (optimum parameter searching) procedure, a stable and efficient way of obtaining the optimum set of FMM parameters, is established with complete control over the tolerable error {epsilon}. In addition, a new parallel FMM algorithm requiring virtually no inter-node communication, is suggested which is suitable for the parallel construction of Fock matrices in electronic structure calculations.

Classical Noether theory with application to the linearly damped particle

International Nuclear Information System (INIS)

Leone, Raphaël; Gourieux, Thierry

2015-01-01

This paper provides a modern presentation of Noether’s theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close relationships between Noether symmetries and first integrals, we investigate the variational point symmetries of the Lagrangian introduced by Bateman, Caldirola and Kanai. This analysis leads to the determination of all the time-independent potentials allowing such symmetries, in the one-dimensional and the radial cases. Then we develop a symmetry-based transformation of Lagrangians into autonomous others, and apply it to our problem. To be complete, we enlarge the study to Lie point symmetries which we associate logically to the Noether ones. Finally, we succinctly address the issue of a ‘weakened’ Noether’s theory, in connection with ‘on-flows’ symmetries and non-local constant of motions, because it has a direct physical interpretation in our specific problem. Since the Lagrangian we use gives rise to simple calculations, we hope that this work will be of didactic interest to graduate students, and give teaching material as well as food for thought for physicists regarding Noether’s theory and the recent developments around the idea of symmetry in classical mechanics. (paper)

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

Science.gov (United States)

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

2018-05-01

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

Linear theory period ratios for surface helium enhanced double-mode Cepheids

International Nuclear Information System (INIS)

Cox, A.N.; Hodson, S.W.; King, D.S.

1979-01-01

Linear nonadiabatic theory period ratios for models of double-mode Cepheids with their two periods between 1 and 7 days have been computed, assuming differing amounts and depths of surface helium enhancement. Evolution theory masses and luminosities are found to be consistent with the observed periods. All models give Pi 1 /Pi 0 approx. =0.70 as observed for the 11 known variables, contrary to previous theoretical conclusions. The composition structure that best fits the period ratios has the helium mass fraction in the outer 10 -3 of the stellar mass (T< or =250,000 K) as 0.65, similar to a previous model for the triple-mode pulsator AC And. This enrichment can be established by a Cepheid wind and downward inverted μ gradient instability mixing in the lifetime of these low-mass classical Cepheids

A non-linear field theory

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjecture necessarily to have the value (h/2π)c, or perhaps 1/2(h/2π)c, in the quantized theory. (author). 5 refs

Linear algebra and group theory

CERN Document Server

Smirnov, VI

2011-01-01

This accessible text by a Soviet mathematician features material not otherwise available to English-language readers. Its three-part treatment covers determinants and systems of equations, matrix theory, and group theory. 1961 edition.

Development of an Input Suite for an Orthotropic Composite Material Model

Science.gov (United States)

Hoffarth, Canio; Shyamsunder, Loukham; Khaled, Bilal; Rajan, Subramaniam; Goldberg, Robert K.; Carney, Kelly S.; Dubois, Paul; Blankenhorn, Gunther

2017-01-01

An orthotropic three-dimensional material model suitable for use in modeling impact tests has been developed that has three major components elastic and inelastic deformations, damage and failure. The material model has been implemented as MAT213 into a special version of LS-DYNA and uses tabulated data obtained from experiments. The prominent features of the constitutive model are illustrated using a widely-used aerospace composite the T800S3900-2B[P2352W-19] BMS8-276 Rev-H-Unitape fiber resin unidirectional composite. The input for the deformation model consists of experimental data from 12 distinct experiments at a known temperature and strain rate: tension and compression along all three principal directions, shear in all three principal planes, and off axis tension or compression tests in all three principal planes, along with other material constants. There are additional input associated with the damage and failure models. The steps in using this model are illustrated composite characterization tests, verification tests and a validation test. The results show that the developed and implemented model is stable and yields acceptably accurate results.

Sequential double excitations from linear-response time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Mosquera, Martín A.; Ratner, Mark A.; Schatz, George C., E-mail: g-schatz@northwestern.edu [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States); Chen, Lin X. [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States); Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 South Cass Ave., Lemont, Illinois 60439 (United States)

2016-05-28

Traditional UV/vis and X-ray spectroscopies focus mainly on the study of excitations starting exclusively from electronic ground states. However there are many experiments where transitions from excited states, both absorption and emission, are probed. In this work we develop a formalism based on linear-response time-dependent density functional theory to investigate spectroscopic properties of excited states. We apply our model to study the excited-state absorption of a diplatinum(II) complex under X-rays, and transient vis/UV absorption of pyrene and azobenzene.

The flow analysis of supercavitating cascade by linear theory

Energy Technology Data Exchange (ETDEWEB)

Park, E.T. [Sung Kyun Kwan Univ., Seoul (Korea, Republic of); Hwang, Y. [Seoul National Univ., Seoul (Korea, Republic of)

1996-06-01

In order to reduce damages due to cavitation effects and to improve performance of fluid machinery, supercavitation around the cascade and the hydraulic characteristics of supercavitating cascade must be analyzed accurately. And the study on the effects of cavitation on fluid machinery and analysis on the performances of supercavitating hydrofoil through various elements governing flow field are critically important. In this study comparison of experiment results with the computed results of linear theory using singularity method was obtainable. Specially singularity points like sources and vortexes on hydrofoil and freestreamline were distributed to analyze two dimensional flow field of supercavitating cascade, and governing equations of flow field were derived and hydraulic characteristics of cascade were calculated by numerical analysis of the governing equations. 7 refs., 6 figs.

A density distribution algorithm for bone incorporating local orthotropy, modal analysis and theories of cellular solids.

Science.gov (United States)

Impelluso, Thomas J

2003-06-01

An algorithm for bone remodeling is presented which allows for both a redistribution of density and a continuous change of principal material directions for the orthotropic material properties of bone. It employs a modal analysis to add density for growth and a local effective strain based analysis to redistribute density. General re-distribution functions are presented. The model utilizes theories of cellular solids to relate density and strength. The code predicts the same general density distributions and local orthotropy as observed in reality.

Linear systems formulation of scattering theory for rough surfaces with arbitrary incident and scattering angles.

Science.gov (United States)

Krywonos, Andrey; Harvey, James E; Choi, Narak

2011-06-01

Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. A recent linear systems formulation of nonparaxial scalar diffraction theory applied to surface scatter phenomena resulted first in an empirically modified Beckmann-Kirchhoff surface scatter model, then a generalized Harvey-Shack theory that produces accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff and the original Harvey-Shack theories. These new developments simplify the analysis and understanding of nonintuitive scattering behavior from rough surfaces illuminated at arbitrary incident angles.

Guided ultrasonic waves for determining effective orthotropic material parameters of continuous-fiber reinforced thermoplastic plates.

Science.gov (United States)

Webersen, Manuel; Johannesmann, Sarah; Düchting, Julia; Claes, Leander; Henning, Bernd

2018-03-01

Ultrasonic methods are widely established in the NDE/NDT community, where they are mostly used for the detection of flaws and structural damage in various components. A different goal, despite the similar technological approach, is non-destructive material characterization, i.e. the determination of parameters like Young's modulus. Only few works on this topic have considered materials with high damping and strong anisotropy, such as continuous-fiber reinforced plastics, but due to the increasing demand in the industry, appropriate methods are needed. In this contribution, we demonstrate the application of laser-induced ultrasonic Lamb waves for the characterization of fiber-reinforced plastic plates, providing effective parameters for a homogeneous, orthotropic material model. Copyright © 2017 Elsevier B.V. All rights reserved.

Linear theory of the tearing instability in axisymmetric toroidal devices

International Nuclear Information System (INIS)

Rogister, A.; Singh, R.

1988-08-01

We derive a very general kinetic equation describing the linear evolution of low m/l modes in axisymmetric toroidal plasmas with arbitrary cross sections. Included are: Ion sound, inertia, diamagnetic drifts, finite poloidal beta, and finite ion Larmor radius effects. Assuming the magnetic surfaces to form a set of nested tori with circular cross sections of shifted centers, and introducing adequate simplifications justified by our knowledge of experimental tokamak plasmas, we then obtain explicitely the sets of equations describing the coupling of the quasimodes 0/1, 1/1, 2/1, and, for m≥2, m/1, (m+1)/1. By keeping finite aspect ratio effects into account when calculating the jump of the derivative of the eigenfunction, it is shown that the theory can explain the rapid evolution, within one sawtooth period, of the growth rate of the sawteeth precursors from resistive values to magnetohydrodynamic ones. The characteristics thus theoretically required from current profiles in sawtoothing discharges have clearly been observed. Other aspects of the full theory could be relevant to the phenomenon of major disruptions. (orig.)

Test of the linear-no threshold theory of radiation carcinogenesis for inhaled radon decay products

International Nuclear Information System (INIS)

Cohen, B.L.

1995-01-01

Data on lung cancer mortality rates vs. average radon concentration in homes for 1,601 U.S. counties are used to test the linear-no threshold theory. The widely recognized problems with ecological studies, as applied to this work, are addressed extensively. With or without corrections for variations in smoking prevalence, there is a strong tendency for lung cancer rates to decrease with increasing radon exposure, in sharp contrast to the increase expected from the theory. The discrepancy in slope is about 20 standard deviations. It is shown that uncertainties in lung cancer rates, radon exposures, and smoking prevalence are not important and that confounding by 54 socioeconomic factors, by geography, and by altitude and climate can explain only a small fraction of the discrepancy. Effects of known radon-smoking prevalence correlations - rural people have higher radon levels and smoke less than urban people, and smokers are exposed to less radon than non-smokers - are calculated and found to be trivial. In spite of extensive efforts, no potential explanation for the discrepancy other than failure of the linear-no threshold theory for carcinogenesis from inhaled radon decay products could be found. (author)

Selected topics in the quantum theory of solids: collective excitations and linear response

International Nuclear Information System (INIS)

Balakrishnan, V.

1977-08-01

This report is based on the lecture notes of a course given at the Department of Physics, Indian Institute of Technology, Madras, during the period January-April 1976 for M.Sc. students. The emphasis is on the concept of elementary excitations in many-body systems, and on the technique of linear response theory. Various topics are covered in 7 sections. The second section following the introductory section is on 'second quantization' and includes discussion on creation and destruction operators, multiparticle states, time-dependent operators etc. Section 3 deals with the 'electron gas' and includes discussion on non-interacting Fermi gas, Coulomb interaction and exchange energy, the two-electron correlation function etc. Section 4 deals with the dielectric response analysis of the electron gas and includes discussion on Coulomb interaction in terms of density fluctuations, self-consistent field dielectric function etc. In section 5 the 'linear response theory' is explained. The Liouville operator, Boltzmann's superposition integral, dispersion relations etc. are explained. Quasiparticles and plasmous are discussed in the Section 6. Section 7 deals with 'lattice dynamics and phonons'. In the last section 8, spin waves are explained. The Heisenberg exchange hamiltonian, Green Function for noninteracting magnons etc. are discussed. (author)

From 6D superconformal field theories to dynamic gauged linear sigma models

Science.gov (United States)

Apruzzi, Fabio; Hassler, Falk; Heckman, Jonathan J.; Melnikov, Ilarion V.

2017-09-01

Compactifications of six-dimensional (6D) superconformal field theories (SCFTs) on four- manifolds generate a large class of novel two-dimensional (2D) quantum field theories. We consider in detail the case of the rank-one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kähler surfaces, we present evidence that this provides a method to realize 2D SCFTs with N =(0 ,2 ) supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2D fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a "dynamic GLSM" (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the antichiral two-form of the 6D theory. These extra sectors include both chiral and antichiral currents, as well as spacetime filling noncritical strings of the 6D theory. For each candidate 2D SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold.

Hadronic equation of state in the statistical bootstrap model and linear graph theory

International Nuclear Information System (INIS)

Fre, P.; Page, R.

1976-01-01

Taking a statistical mechanical point og view, the statistical bootstrap model is discussed and, from a critical analysis of the bootstrap volume comcept, it is reached a physical ipothesis, which leads immediately to the hadronic equation of state provided by the bootstrap integral equation. In this context also the connection between the statistical bootstrap and the linear graph theory approach to interacting gases is analyzed

An algorithm for full parametric solution of problems on the statics of orthotropic plates by the method of boundary states with perturbations

Science.gov (United States)

Penkov, V. B.; Ivanychev, D. A.; Novikova, O. S.; Levina, L. V.

2018-03-01

The article substantiates the possibility of building full parametric analytical solutions of mathematical physics problems in arbitrary regions by means of computer systems. The suggested effective means for such solutions is the method of boundary states with perturbations, which aptly incorporates all parameters of an orthotropic medium in a general solution. We performed check calculations of elastic fields of an anisotropic rectangular region (test and calculation problems) for a generalized plane stress state.

Linear Programming (LP)

International Nuclear Information System (INIS)

Rogner, H.H.

1989-01-01

The submitted sections on linear programming are extracted from 'Theorie und Technik der Planung' (1978) by W. Blaas and P. Henseler and reformulated for presentation at the Workshop. They consider a brief introduction to the theory of linear programming and to some essential aspects of the SIMPLEX solution algorithm for the purposes of economic planning processes. 1 fig

An analogue of Morse theory for planar linear networks and the generalized Steiner problem

International Nuclear Information System (INIS)

Karpunin, G A

2000-01-01

A study is made of the generalized Steiner problem: the problem of finding all the locally minimal networks spanning a given boundary set (terminal set). It is proposed to solve this problem by using an analogue of Morse theory developed here for planar linear networks. The space K of all planar linear networks spanning a given boundary set is constructed. The concept of a critical point and its index is defined for the length function l of a planar linear network. It is shown that locally minimal networks are local minima of l on K and are critical points of index 1. The theorem is proved that the sum of the indices of all the critical points is equal to χ(K)=1. This theorem is used to find estimates for the number of locally minimal networks spanning a given boundary set

Linear optical response of finite systems using multishift linear system solvers

Energy Technology Data Exchange (ETDEWEB)

Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)

2014-07-28

We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.

Airfoil wake and linear theory gust response including sub and superresonant flow conditions

Science.gov (United States)

Henderson, Gregory H.; Fleeter, Sanford

1992-01-01

The unsteady aerodynamic gust response of a high solidity stator vane row is examined in terms of the fundamental gust modeling assumptions with particular attention given to the effects near an acoustic resonance. A series of experiments was performed with gusts generated by rotors comprised of perforated plates and airfoils. It is concluded that, for both the perforated plate and airfoil wake generated gusts, the unsteady pressure responses do not agree with the linear-theory gust predictions near an acoustic resonance. The effects of the acoustic resonance phenomena are clearly evident on the airfoil surface unsteady pressure responses. The transition of the measured lift coefficients across the acoustic resonance from the subresonant regime to the superresonant regime occurs in a simple linear fashion.

Coupling of a structural analysis and flow simulation for short-fiber-reinforced polymers: property prediction and transfer of results

Science.gov (United States)

Kröner, C.; Altenbach, H.; Naumenko, K.

2009-05-01

The aim of this paper is to discuss the basic theories of interfaces able to transfer the results of an injection molding analyis of fiber-reinforced polymers, performed by using the commercial computer code Moldflow, to the structural analysis program ABAQUS. The elastic constants of the materials, such as Young's modulus, shear modulus, and Poisson's ratio, which depend on both the fiber content and the degree of fiber orientation, were calculated not by the usual method of "orientation averaging," but with the help of linear functions fitted to experimental data. The calculation and transfer of all needed data, such as material properties, geometry, directions of anisotropy, and so on, is performed by an interface developed. The interface is suit able for midplane elements in Moldflow. It calculates and transfers to ABAQUS all data necessary for the use of shell elements. In addition, a method is described how a nonlinear orthotropic behavior can be modeled starting from the generalized Hooke's law. It is also shown how such a model can be implemented in ABAQUS by means of a material subroutine. The results obtained according to this subroutine are compared with those based on an orthotropic, linear, elastic simulation.

Non-linear σ-models and string theories

International Nuclear Information System (INIS)

Sen, A.

1986-10-01

The connection between σ-models and string theories is discussed, as well as how the σ-models can be used as tools to prove various results in string theories. Closed bosonic string theory in the light cone gauge is very briefly introduced. Then, closed bosonic string theory in the presence of massless background fields is discussed. The light cone gauge is used, and it is shown that in order to obtain a Lorentz invariant theory, the string theory in the presence of background fields must be described by a two-dimensional conformally invariant theory. The resulting constraints on the background fields are found to be the equations of motion of the string theory. The analysis is extended to the case of the heterotic string theory and the superstring theory in the presence of the massless background fields. It is then shown how to use these results to obtain nontrivial solutions to the string field equations. Another application of these results is shown, namely to prove that the effective cosmological constant after compactification vanishes as a consequence of the classical equations of motion of the string theory. 34 refs

Relevance of sampling schemes in light of Ruelle's linear response theory

International Nuclear Information System (INIS)

Lucarini, Valerio; Wouters, Jeroen; Faranda, Davide; Kuna, Tobias

2012-01-01

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We first show that using a general functional decomposition for space–time dependent forcings, we can define elementary susceptibilities that allow us to construct the linear response of the system to general perturbations. Starting from the definition of SRB measure, we then study the consequence of taking different sampling schemes for analysing the response of the system. We show that only a specific choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows us to obtain the formula first presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be fine-tuned to make the definition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analysing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick

Foundations of linear and generalized linear models

CERN Document Server

Agresti, Alan

2015-01-01

A valuable overview of the most important ideas and results in statistical analysis Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical model building. The book begins by illustrating the fundamentals of linear models,

Non-linear gauge transformations in D=10 SYM theory and the BCJ duality

Energy Technology Data Exchange (ETDEWEB)

Lee, Seungjin [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany); Mafra, Carlos R. [Institute for Advanced Study, School of Natural Sciences,Einstein Drive, Princeton, NJ 08540 (United States); DAMTP, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany)

2016-03-14

Recent progress on scattering amplitudes in super Yang-Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang-Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. Moreover, we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.

Scalar-tensor linear inflation

Energy Technology Data Exchange (ETDEWEB)

Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)

2017-04-01

We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.

Simplified non-linear time-history analysis based on the Theory of Plasticity

DEFF Research Database (Denmark)

Costa, Joao Domingues

2005-01-01

This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...... is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation...

A modification to linearized theory for prediction of pressure loadings on lifting surfaces at high supersonic Mach numbers and large angles of attack

Science.gov (United States)

Carlson, H. W.

1979-01-01

A new linearized-theory pressure-coefficient formulation was studied. The new formulation is intended to provide more accurate estimates of detailed pressure loadings for improved stability analysis and for analysis of critical structural design conditions. The approach is based on the use of oblique-shock and Prandtl-Meyer expansion relationships for accurate representation of the variation of pressures with surface slopes in two-dimensional flow and linearized-theory perturbation velocities for evaluation of local three-dimensional aerodynamic interference effects. The applicability and limitations of the modification to linearized theory are illustrated through comparisons with experimental pressure distributions for delta wings covering a Mach number range from 1.45 to 4.60 and angles of attack from 0 to 25 degrees.

The fully relativistic foundation of linear transfer theory in electron optics based on the Dirac equation

NARCIS (Netherlands)

Ferwerda, H.A.; Hoenders, B.J.; Slump, C.H.

The fully relativistic quantum mechanical treatment of paraxial electron-optical image formation initiated in the previous paper (this issue) is worked out and leads to a rigorous foundation of the linear transfer theory. Moreover, the status of the relativistic scaling laws for mass and wavelength,

Application of supersonic linear theory and hypersonic impact methods to three nonslender hypersonic airplane concepts at Mach numbers from 1.10 to 2.86

Science.gov (United States)

Pittman, J. L.

1979-01-01

Aerodynamic predictions from supersonic linear theory and hypersonic impact theory were compared with experimental data for three hypersonic research airplane concepts over a Mach number range from 1.10 to 2.86. The linear theory gave good lift prediction and fair to good pitching-moment prediction over the Mach number (M) range. The tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone/tangent-wedge method gave the least accurate prediction of lift and pitching moment. The zero-lift drag was overestimated, especially for M less than 2.0. The linear theory drag prediction was generally poor, with areas of good agreement only for M less than or equal to 1.2. For M more than or equal to 2.), the tangent-cone method predicted the zero-lift drag most accurately.

Connection between perturbation theory, projection-operator techniques, and statistical linearization for nonlinear systems

International Nuclear Information System (INIS)

Budgor, A.B.; West, B.J.

1978-01-01

We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation

Absorption line profiles in a moving atmosphere - A single scattering linear perturbation theory

Science.gov (United States)

Hays, P. B.; Abreu, V. J.

1989-01-01

An integral equation is derived which linearly relates Doppler perturbations in the spectrum of atmospheric absorption features to the wind system which creates them. The perturbation theory is developed using a single scattering model, which is validated against a multiple scattering calculation. The nature and basic properties of the kernels in the integral equation are examined. It is concluded that the kernels are well behaved and that wind velocity profiles can be recovered using standard inversion techniques.

A Stream Function Theory Based Calculation of Wave Kinematics for Very Steep Waves Using a Novel Non-linear Stretching Technique

DEFF Research Database (Denmark)

Stroescu, Ionut Emanuel; Sørensen, Lasse; Frigaard, Peter Bak

2016-01-01

A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good...

Non-Markovian linear response theory for quantum open systems and its applications.

Science.gov (United States)

Shen, H Z; Li, D X; Yi, X X

2017-01-01

The Kubo formula is an equation that expresses the linear response of an observable due to a time-dependent perturbation. It has been extended from closed systems to open systems in recent years under the Markovian approximation, but is barely explored for open systems in non-Markovian regimes. In this paper, we derive a formula for the linear response of an open system to a time-independent external field. This response formula is available for both Markovian and non-Markovian dynamics depending on parameters in the spectral density of the environment. As an illustration of the theory, the Hall conductance of a two-band system subjected to environments is derived and discussed. With the tight-binding model, we point out the Hall conductance changes from Markovian to non-Markovian dynamics by modulating the spectral density of the environment. Our results suggest a way to the controlling of the system response, which has potential applications for quantum statistical mechanics and condensed matter physics.

Canonical-ensemble extended Lagrangian Born-Oppenheimer molecular dynamics for the linear scaling density functional theory.

Science.gov (United States)

Hirakawa, Teruo; Suzuki, Teppei; Bowler, David R; Miyazaki, Tsuyoshi

2017-10-11

We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nosé-Hoover chain thermostat with the extended Lagrangian Born-Oppenheimer molecular dynamics (BOMD) scheme, using a linear scaling density functional theory (DFT) approach. An integration scheme for this canonical-ensemble extended Lagrangian BOMD is developed and discussed in the context of the Liouville operator formulation. Linear scaling DFT canonical-ensemble extended Lagrangian BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration scheme. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.

Sparse linear systems: Theory of decomposition, methods, technology, applications and implementation in Wolfram Mathematica

Energy Technology Data Exchange (ETDEWEB)

Pilipchuk, L. A., E-mail: pilipchik@bsu.by [Belarussian State University, 220030 Minsk, 4, Nezavisimosti avenue, Republic of Belarus (Belarus); Pilipchuk, A. S., E-mail: an.pilipchuk@gmail.com [The Natural Resources and Environmental Protestion Ministry of the Republic of Belarus, 220004 Minsk, 10 Kollektornaya Street, Republic of Belarus (Belarus)

2015-11-30

In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure.

Sparse linear systems: Theory of decomposition, methods, technology, applications and implementation in Wolfram Mathematica

International Nuclear Information System (INIS)

Pilipchuk, L. A.; Pilipchuk, A. S.

2015-01-01

In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure

Generalized multivariate Fokker-Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

International Nuclear Information System (INIS)

Frank, T.D.

2002-01-01

We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions

Wavelet-based linear-response time-dependent density-functional theory

Science.gov (United States)

Natarajan, Bhaarathi; Genovese, Luigi; Casida, Mark E.; Deutsch, Thierry; Burchak, Olga N.; Philouze, Christian; Balakirev, Maxim Y.

2012-06-01

Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BIGDFT and results are compared against those obtained with the all-electron Gaussian-type orbital program DEMON2K for the calculation of electronic absorption spectra of N2 using the TD local density approximation (LDA). The two programs give comparable excitation energies and absorption spectra once suitably extensive basis sets are used. Convergence of LDA density orbitals and orbital energies to the basis-set limit is significantly faster for BIGDFT than for DEMON2K. However the number of virtual orbitals used in TD-DFT calculations is a parameter in BIGDFT, while all virtual orbitals are included in TD-DFT calculations in DEMON2K. As a reality check, we report the X-ray crystal structure and the measured and calculated absorption spectrum (excitation energies and oscillator strengths) of the small organic molecule N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1, 2-a]pyridin-3-amine.

Poroelastic Response of Orthotropic Fractured Porous Media

Energy Technology Data Exchange (ETDEWEB)

Berryman, James G. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Earth Sciences Division

2011-12-16

In this paper, an algorithm is presented for inverting either laboratory or field poroelastic data for all the drained constants of an anisotropic (specifically orthotropic) fractured poroelastic system. While fractures normally weaken the system by increasing the mechanical compliance, any liquids present in these fractures are expected to increase the stiffness somewhat, thus negating to some extent the mechanical weakening influence of the fractures themselves. The analysis presented in this article quantifies these effects and shows that the key physical variable needed to account for the pore-fluid effects is a factor of (1 - B), where B is Skempton’s second coefficient and satisfies 0 ≤ B < 1. This scalar factor uniformly reduces the increase in compliance due to the presence of communicating fractures, thereby stiffening the fractured composite medium by a predictable amount. One further aim of the discussion is to determine the number of the poroelastic constants that needs to be known by other means to determine the rest from remote measurements, such as seismic wave propagation data in the field. Quantitative examples arising in the analysis show that, if the fracture aspect ratio a_f ≃ 0.1 and the pore fluid is liquid water, then for several cases considered, Skempton’s B ≃ 0.9, and so the stiffening effect of the pore-liquid reduces the change in compliance due to the fractures by a factor 1-B ≃ 0.1, in these examples. The results do, however, depend on the actual moduli of the unfractured elastic material, as well as on the pore-liquid bulk modulus, so these quantitative predictions are just examples, and should not be treated as universal results. Attention is also given to two previously unremarked poroelastic identities, both being useful variants of Gassmann’s equations for homogeneous—but anisotropic—poroelasticity. Relationships to Skempton’s analysis of saturated soils are also noted. Finally, the article concludes

New composites graphite/salt for high temperature thermal energy storage: From elaboration to development of thermal characterization methods for orthotropic conductive materials

International Nuclear Information System (INIS)

Acem, Zoubir

2007-01-01

This PhD is carried out within the framework of DISTOR (European) and HTPSTOCK (French) projects, which have for objective to conceive and study new graphite/salt composites dedicated to high temperature energy storage (>200 deg. C). She is split into two distinct part. The first one focused mainly on works linked with elaboration and thermal characterisation of these new composites. The different composites ways of elaboration (Dispersion, uniaxial compression, isostatic) associated to the different kind of graphite (Natural expanded graphite (ENG), synthetic graphite) investigated during the PhD are presented. The results of the thermal characterization campaign of these composites are also presented and permit to highlight the impact of graphite in the thermal behaviour of studied materials. Based on these results, modelling studies of the evolution of the thermal conductivity have been undertaken to deepen the understanding of the effect of graphite (quantity, size of particles) on the effective conductivity composites. The second one describes the thermal characterization devices and associated thermo-kinetics models which had to be developed and adapted to the specificities of newly developed materials. This concerns mainly the materials prepared by compression, which present orthotropic properties and are difficult to reproduce. So, the characterization of this kind of material is very difficult and tedious. That is why we are committed to develop and adapt existing methods of characterization to allow the complete thermal characterisation of an orthotropic conductive material from a single experimentation on a single sample. (author) [fr

Linearization instability for generic gravity in AdS spacetime

Science.gov (United States)

Altas, Emel; Tekin, Bayram

2018-01-01

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

Topological characterizations of S-Linearity

Directory of Open Access Journals (Sweden)

Carfi', David

2007-10-01

Full Text Available We give several characterizations of basic concepts of S-linear algebra in terms of weak duality on topological vector spaces. On the way, some classic results of Functional Analysis are reinterpreted in terms of S-linear algebra, by an application-oriented fashion. The results are required in the S-linear algebra formulation of infinite dimensional Decision Theory and in the study of abstract evolution equations in economical and physical Theories.

Linear and non-linear optics of condensed matter

International Nuclear Information System (INIS)

McLean, T.P.

1977-01-01

Part I - Linear optics: 1. General introduction. 2. Frequency dependence of epsilon(ω, k vector). 3. Wave-vector dependence of epsilon(ω, k vector). 4. Tensor character of epsilon(ω, k vector). Part II - Non-linear optics: 5. Introduction. 6. A classical theory of non-linear response in one dimension. 7. The generalization to three dimensions. 8. General properties of the polarizability tensors. 9. The phase-matching condition. 10. Propagation in a non-linear dielectric. 11. Second harmonic generation. 12. Coupling of three waves. 13. Materials and their non-linearities. 14. Processes involving energy exchange with the medium. 15. Two-photon absorption. 16. Stimulated Raman effect. 17. Electro-optic effects. 18. Limitations of the approach presented here. (author)

A Bivariate Generalized Linear Item Response Theory Modeling Framework to the Analysis of Responses and Response Times.

Science.gov (United States)

Molenaar, Dylan; Tuerlinckx, Francis; van der Maas, Han L J

2015-01-01

A generalized linear modeling framework to the analysis of responses and response times is outlined. In this framework, referred to as bivariate generalized linear item response theory (B-GLIRT), separate generalized linear measurement models are specified for the responses and the response times that are subsequently linked by cross-relations. The cross-relations can take various forms. Here, we focus on cross-relations with a linear or interaction term for ability tests, and cross-relations with a curvilinear term for personality tests. In addition, we discuss how popular existing models from the psychometric literature are special cases in the B-GLIRT framework depending on restrictions in the cross-relation. This allows us to compare existing models conceptually and empirically. We discuss various extensions of the traditional models motivated by practical problems. We also illustrate the applicability of our approach using various real data examples, including data on personality and cognitive ability.

A primer on Hilbert space theory linear spaces, topological spaces, metric spaces, normed spaces, and topological groups

CERN Document Server

Alabiso, Carlo

2015-01-01

This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all sub...

Cosmological large-scale structures beyond linear theory in modified gravity

Energy Technology Data Exchange (ETDEWEB)

Bernardeau, Francis; Brax, Philippe, E-mail: francis.bernardeau@cea.fr, E-mail: philippe.brax@cea.fr [CEA, Institut de Physique Théorique, 91191 Gif-sur-Yvette Cédex (France)

2011-06-01

We consider the effect of modified gravity on the growth of large-scale structures at second order in perturbation theory. We show that modified gravity models changing the linear growth rate of fluctuations are also bound to change, although mildly, the mode coupling amplitude in the density and reduced velocity fields. We present explicit formulae which describe this effect. We then focus on models of modified gravity involving a scalar field coupled to matter, in particular chameleons and dilatons, where it is shown that there exists a transition scale around which the existence of an extra scalar degree of freedom induces significant changes in the coupling properties of the cosmic fields. We obtain the amplitude of this effect for realistic dilaton models at the tree-order level for the bispectrum, finding them to be comparable in amplitude to those obtained in the DGP and f(R) models.

Non linear system become linear system

Directory of Open Access Journals (Sweden)

Petre Bucur

2007-01-01

Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.

Applicability of linear and non-linear potential flow models on a Wavestar float

DEFF Research Database (Denmark)

Bozonnet, Pauline; Dupin, Victor; Tona, Paolino

2017-01-01

as a model based on non-linear potential flow theory and weakscatterer hypothesis are successively considered. Simple tests, such as dip tests, decay tests and captive tests enable to highlight the improvements obtained with the introduction of nonlinearities. Float motion under wave actions and without...... control action, limited to small amplitude motion with a single float, is well predicted by the numerical models, including the linear one. Still, float velocity is better predicted by accounting for non-linear hydrostatic and Froude-Krylov forces.......Numerical models based on potential flow theory, including different types of nonlinearities are compared and validated against experimental data for the Wavestar wave energy converter technology. Exact resolution of the rotational motion, non-linear hydrostatic and Froude-Krylov forces as well...

Discovery of the Linear Region of Near Infrared Diffuse Reflectance Spectra Using the Kubelka-Munk Theory

Directory of Open Access Journals (Sweden)

Shengyun Dai

2018-05-01

Full Text Available Particle size is of great importance for the quantitative model of the NIR diffuse reflectance. In this paper, the effect of sample particle size on the measurement of harpagoside in Radix Scrophulariae powder by near infrared diffuse (NIR reflectance spectroscopy was explored. High-performance liquid chromatography (HPLC was employed as a reference method to construct the quantitative particle size model. Several spectral preprocessing methods were compared, and particle size models obtained by different preprocessing methods for establishing the partial least-squares (PLS models of harpagoside. Data showed that the particle size distribution of 125–150 μm for Radix Scrophulariae exhibited the best prediction ability with Rpre2 = 0.9513, RMSEP = 0.1029 mg·g−1, and RPD = 4.78. For the hybrid granularity calibration model, the particle size distribution of 90–180 μm exhibited the best prediction ability with Rpre2 = 0.8919, RMSEP = 0.1632 mg·g−1, and RPD = 3.09. Furthermore, the Kubelka-Munk theory was used to relate the absorption coefficient k (concentration-dependent and scatter coefficient s (particle size-dependent. The scatter coefficient s was calculated based on the Kubelka-Munk theory to study the changes of s after being mathematically preprocessed. A linear relationship was observed between k/s and absorption A within a certain range and the value for k/s was >4. According to this relationship, the model was more accurately constructed with the particle size distribution of 90–180 μm when s was kept constant or in a small linear region. This region provided a good reference for the linear modeling of diffuse reflectance spectroscopy. To establish a diffuse reflectance NIR model, further accurate assessment should be obtained in advance for a precise linear model.

Linear theory for filtering nonlinear multiscale systems with model error.

Science.gov (United States)

Berry, Tyrus; Harlim, John

2014-07-08

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering

Test of the linear-no threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1998-01-01

It is shown that testing the linear-no threshold theory (L-NT) of radiation carcinogenesis is extremely important and that lung cancer resulting from exposure to radon in homes is the best tool for doing this. A study of lung cancer rates vs radon exposure in U.S. Counties, reported in 1975, is reviewed. It shows, with extremely powerful statistics, that lung cancer rates decrease with increasing radon exposure, in sharp contrast to the prediction of L-NT, with a discrepancy of over 20 standard deviations. Very extensive efforts were made to explain an appreciable part of this discrepancy consistently with L-NT, with no success; it was concluded that L-NT fails, grossly exaggerating the cancer risk of low level radiation. Two updating studies reported in 1996 are also reviewed. New updating studies utilizing more recent lung cancer statistics and considering 450 new potential confounding factors are reported. All updates reinforce the previous conclusion, and the discrepancy with L-NT is increased. (author)

Microscopic theory of linear and nonlinear terahertz spectroscopy of semiconductors

Energy Technology Data Exchange (ETDEWEB)

Steiner, Johannes

2008-12-09

This Thesis presents a fully microscopic theory to describe terahertz (THz)-induced processes in optically-excited semiconductors. The formation process of excitons and other quasi-particles after optical excitation has been studied in great detail for a variety of conditions. Here, the formation process is not modelled but a realistic initial many-body state is assumed. In particular, the linear THz response is reviewed and it is demonstrated that correlated quasi-particles such as excitons and plasmons can be unambiguously detected via THz spectroscopy. The focus of the investigations, however, is on situations where the optically-excited many-body state is excited by intense THz fields. While weak pulses detect the many-body state, strong THz pulses control and manipulate the quasi-particles in a way that is not accessible via conventional techniques. The nonlinear THz dynamics of exciton populations is especially interesting because similarities and differences to optics with atomic systems can be studied. (orig.)

Classifying Linear Canonical Relations

OpenAIRE

Lorand, Jonathan

2015-01-01

In this Master's thesis, we consider the problem of classifying, up to conjugation by linear symplectomorphisms, linear canonical relations (lagrangian correspondences) from a finite-dimensional symplectic vector space to itself. We give an elementary introduction to the theory of linear canonical relations and present partial results toward the classification problem. This exposition should be accessible to undergraduate students with a basic familiarity with linear algebra.

Lie algebras and linear differential equations.

Science.gov (United States)

Brockett, R. W.; Rahimi, A.

1972-01-01

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

Optimal control linear quadratic methods

CERN Document Server

Anderson, Brian D O

2007-01-01

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the

Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude.

Science.gov (United States)

McDowell, J J; Wood, H M

1984-03-01

Eight human subjects pressed a lever on a range of variable-interval schedules for 0.25 cent to 35.0 cent per reinforcement. Herrnstein's hyperbola described seven of the eight subjects' response-rate data well. For all subjects, the y-asymptote of the hyperbola increased with increasing reinforcer magnitude and its reciprocal was a linear function of the reciprocal of reinforcer magnitude. These results confirm predictions made by linear system theory; they contradict formal properties of Herrnstein's account and of six other mathematical accounts of single-alternative responding.

On the Generalization of the Timoshenko Beam Model Based on the Micropolar Linear Theory: Static Case

Directory of Open Access Journals (Sweden)

Andrea Nobili

2015-01-01

Full Text Available Three generalizations of the Timoshenko beam model according to the linear theory of micropolar elasticity or its special cases, that is, the couple stress theory or the modified couple stress theory, recently developed in the literature, are investigated and compared. The analysis is carried out in a variational setting, making use of Hamilton’s principle. It is shown that both the Timoshenko and the (possibly modified couple stress models are based on a microstructural kinematics which is governed by kinosthenic (ignorable terms in the Lagrangian. Despite their difference, all models bring in a beam-plane theory only one microstructural material parameter. Besides, the micropolar model formally reduces to the couple stress model upon introducing the proper constraint on the microstructure kinematics, although the material parameter is generally different. Line loading on the microstructure results in a nonconservative force potential. Finally, the Hamiltonian form of the micropolar beam model is derived and the canonical equations are presented along with their general solution. The latter exhibits a general oscillatory pattern for the microstructure rotation and stress, whose behavior matches the numerical findings.

A generic double-curvature piezoelectric shell energy harvester: Linear/nonlinear theory and applications

Science.gov (United States)

Zhang, X. F.; Hu, S. D.; Tzou, H. S.

2014-12-01

Converting vibration energy to useful electric energy has attracted much attention in recent years. Based on the electromechanical coupling of piezoelectricity, distributed piezoelectric zero-curvature type (e.g., beams and plates) energy harvesters have been proposed and evaluated. The objective of this study is to develop a generic linear and nonlinear piezoelectric shell energy harvesting theory based on a double-curvature shell. The generic piezoelectric shell energy harvester consists of an elastic double-curvature shell and piezoelectric patches laminated on its surface(s). With a current model in the closed-circuit condition, output voltages and energies across a resistive load are evaluated when the shell is subjected to harmonic excitations. Steady-state voltage and power outputs across the resistive load are calculated at resonance for each shell mode. The piezoelectric shell energy harvesting mechanism can be simplified to shell (e.g., cylindrical, conical, spherical, paraboloidal, etc.) and non-shell (beam, plate, ring, arch, etc.) distributed harvesters using two Lamé parameters and two curvature radii of the selected harvester geometry. To demonstrate the utility and simplification procedures, the generic linear/nonlinear shell energy harvester mechanism is simplified to three specific structures, i.e., a cantilever beam case, a circular ring case and a conical shell case. Results show the versatility of the generic linear/nonlinear shell energy harvesting mechanism and the validity of the simplification procedures.

Time-dependent density functional theory of open quantum systems in the linear-response regime.

Science.gov (United States)

Tempel, David G; Watson, Mark A; Olivares-Amaya, Roberto; Aspuru-Guzik, Alán

2011-02-21

Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Görling-Levy perturbation theory is calculated.

Linear algebra

CERN Document Server

Stoll, R R

1968-01-01

Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

Linear and Generalized Linear Mixed Models and Their Applications

CERN Document Server

Jiang, Jiming

2007-01-01

This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models, and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it has included recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested

Linear algebra

CERN Document Server

Berberian, Sterling K

2014-01-01

Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.

Orthotropic creep in polyethylene glycol impregnated archaeological oak from the Vasa ship - Results of creep experiments in a museum-like climate

Science.gov (United States)

Vorobyev, Alexey; van Dijk, Nico P.; Kristofer Gamstedt, E.

2018-02-01

Creep in archaeological oak samples and planks from the Vasa ship impregnated with polyethylene glycol (PEG) has been studied in museum-like climate. Creep studies of duration up to three years have been performed in nearly constant relative humidity and temperature of the controlled museum climate. Cubic samples were subjected to compressive creep tests in all orthotropic directions. Additionally, the creep behaviour of planks with and without PEG and of recent oak was tested in four-point bending. The experimental results have been summarised and also compared with reference results from recent oak wood. The effect of variable ambient conditions on creep and mass changes is discussed. The experimental results of creep in the longitudinal direction showed deformations even for the low stresses. There is relatively much more scatter in creep behaviour, and not all samples showed linear viscoelastic response. The creep in radial and tangential directions of the cubes and the plank samples showed a strong dependency on the ambient conditions. Some samples showed expansion for decreasing moisture content, possibly caused by the thermal expansion of the PEG component. For the planks, increasing creep deformation was observed induced by changing ambient conditions. Such behaviour may be related to e.g. oscillations in ambient conditions and presence of PEG in the wood cell wall and cell lumen. The behaviour of PEG archaeological wood depends on the level of deterioration that occurred over centuries. However, although the findings presented here apply to this specific case, they provide a unique view on such wood.

Theoretical Development of an Orthotropic Elasto-Plastic Generalized Composite Material Model

Science.gov (United States)

Goldberg, Robert; Carney, Kelly; DuBois, Paul; Hoffarth, Canio; Harrington, Joseph; Rajan, Subramaniam; Blankenhorn, Gunther

2014-01-01

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within LSDYNA (Livermore Software Technology Corporation), there are several features that have been identified that could improve the predictive capability of a composite model. To address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed and is being implemented into LS-DYNA as MAT_213. A key feature of the improved material model is the use of tabulated stress-strain data in a variety of coordinate directions to fully define the stress-strain response of the material. To date, the model development efforts have focused on creating the plasticity portion of the model. The Tsai-Wu composite failure model has been generalized and extended to a strain-hardening based orthotropic yield function with a nonassociative flow rule. The coefficients of the yield function, and the stresses to be used in both the yield function and the flow rule, are computed based on the input stress-strain curves using the effective plastic strain as the tracking variable. The coefficients in the flow rule are computed based on the obtained stress-strain data. The developed material model is suitable for implementation within LS-DYNA for use in analyzing the nonlinear response of polymer composites.

Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains.

Science.gov (United States)

Dudowicz, Jacek; Freed, Karl F

2012-02-14

The lattice cluster theory (LCT) for the thermodynamics of a wide array of polymer systems has been developed by using an analogy to Mayer's virial expansions for non-ideal gases. However, the high-temperature expansion inherent to the LCT has heretofore precluded its application to systems exhibiting strong, specific "sticky" interactions. The present paper describes a reformulation of the LCT necessary to treat systems with both weak and strong, "sticky" interactions. This initial study concerns solutions of linear telechelic chains (with stickers at the chain ends) as the self-assembling system. The main idea behind this extension of the LCT lies in the extraction of terms associated with the strong interactions from the cluster expansion. The generalized LCT for sticky systems reduces to the quasi-chemical theory of hydrogen bonding of Panyioutou and Sanchez when correlation corrections are neglected in the LCT. A diagrammatic representation is employed to facilitate the evaluation of the corrections to the zeroth-order approximation from short range correlations. © 2012 American Institute of Physics

Applicability of linearized-theory attached-flow methods to design and analysis of flap systems at low speeds for thin swept wings with sharp leading edges

Science.gov (United States)

Carlson, Harry W.; Darden, Christine M.

1987-01-01

Low-speed experimental force and data on a series of thin swept wings with sharp leading edges and leading and trailing-edge flaps are compared with predictions made using a linearized-theory method which includes estimates of vortex forces. These comparisons were made to assess the effectiveness of linearized-theory methods for use in the design and analysis of flap systems in subsonic flow. Results demonstrate that linearized-theory, attached-flow methods (with approximate representation of vortex forces) can form the basis of a rational system for flap design and analysis. Even attached-flow methods that do not take vortex forces into account can be used for the selection of optimized flap-system geometry, but design-point performance levels tend to be underestimated unless vortex forces are included. Illustrative examples of the use of these methods in the design of efficient low-speed flap systems are included.

State space and input-output linear systems

CERN Document Server

Delchamps, David F

1988-01-01

It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year gradu­ ate level linear system theory course i...

Thermal stress state of laminated shells of revolution made of isotropic and linearly orthotropic materials

International Nuclear Information System (INIS)

Savchenko, V.G.

1995-01-01

In this investigation, we will use a cylindrical coordinate system to study the stress state of laminated shells of revolution made of inelastically deforming isotropic materials and elastic materials with linear orthotropy. One of the principal directions of anisotropy coincides with the axis of revolution of the body. The shells will be subjected to nonaxisymmetric loading by body bar K (K Z , K r , K var-phi ) and surface bar t n (t nz , t nr , t nvar-phi ) forces and heating. The level of loading is such that the rheological properties of the materials of the layers are not a factor, although their thermomechanical characteristics depend on temperature. In addition, the loading and heating of the body occur in such a way that simple (or close to simple) deformation processes take place in its isotropic elements. These processes are accompanied by inelastic strains and the formation of unloading regions in which plastic strains having the sign opposite the initial strains develop. It is assumed that the layers of the body are secured to one another without interference and that conditions corresponding to ideal contact prevail at their interfaces

Linear programming

CERN Document Server

Solow, Daniel

2014-01-01

This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.

Linear and Nonlinear Theories of Cosmic Ray Transport

International Nuclear Information System (INIS)

Shalchi, A.

2005-01-01

The transport of charged cosmic rays in plasmawave turbulence is a modern and interesting field of research. We are mainly interested in spatial diffusion parallel and perpendicular to a large scale magnetic field. During the last decades quasilinear theory was the standard tool for the calculation of diffusion coefficients. Through comparison with numerical simulations we found several cases where quasilinear theory is invalid. On could define three major problems of transport theory. I will demonstrate that new nonlinear theories which were proposed recently can solve at least some to these problems

Multi-stratified multiple regression tests of the linear/no-threshold theory of radon-induced lung cancer

International Nuclear Information System (INIS)

Cohen, B.L.

1992-01-01

A plot of lung-cancer rates versus radon exposures in 965 US counties, or in all US states, has a strong negative slope, b, in sharp contrast to the strong positive slope predicted by linear/no-threshold theory. The discrepancy between these slopes exceeds 20 standard deviations (SD). Including smoking frequency in the analysis substantially improves fits to a linear relationship but has little effect on the discrepancy in b, because correlations between smoking frequency and radon levels are quite weak. Including 17 socioeconomic variables (SEV) in multiple regression analysis reduces the discrepancy to 15 SD. Data were divided into segments by stratifying on each SEV in turn, and on geography, and on both simultaneously, giving over 300 data sets to be analyzed individually, but negative slopes predominated. The slope is negative whether one considers only the most urban counties or only the most rural; only the richest or only the poorest; only the richest in the South Atlantic region or only the poorest in that region, etc., etc.,; and for all the strata in between. Since this is an ecological study, the well-known problems with ecological studies were investigated and found not to be applicable here. The open-quotes ecological fallacyclose quotes was shown not to apply in testing a linear/no-threshold theory, and the vulnerability to confounding is greatly reduced when confounding factors are only weakly correlated with radon levels, as is generally the case here. All confounding factors known to correlate with radon and with lung cancer were investigated quantitatively and found to have little effect on the discrepancy

Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

Science.gov (United States)

Neitzel, G. P.; Chang, K.-T.; Jankowski, D. F.; Mittelmann, H. D.

1992-01-01

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.

Basic operator theory

CERN Document Server

Gohberg, Israel

2001-01-01

rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat­ ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz­ Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems, except for the last chapter which is an introduction to the theory of nonlinear operators. In addition to the standard topics in functional anal­ ysis, we have presented relatively recent results which appear, for example, in Chapter VII. In general, in writ­ ing this book, the authors were strongly influenced by re­ cent developments in operator theory which affected the choice of topics, proofs and exercises. One ...

Linear analysis near a steady-state of biochemical networks: control analysis, correlation metrics and circuit theory

Directory of Open Access Journals (Sweden)

Qian Hong

2008-05-01

Full Text Available Abstract Background: Several approaches, including metabolic control analysis (MCA, flux balance analysis (FBA, correlation metric construction (CMC, and biochemical circuit theory (BCT, have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. Results: In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RT BS and ST BS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC. Conclusion: One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA.

Confirmation of linear system theory prediction: Rate of change of Herrnstein's κ as a function of response-force requirement

Science.gov (United States)

McDowell, J. J; Wood, Helena M.

1985-01-01

Four human subjects worked on all combinations of five variable-interval schedules and five reinforcer magnitudes (¢/reinforcer) in each of two phases of the experiment. In one phase the force requirement on the operandum was low (1 or 11 N) and in the other it was high (25 or 146 N). Estimates of Herrnstein's κ were obtained at each reinforcer magnitude. The results were: (1) response rate was more sensitive to changes in reinforcement rate at the high than at the low force requirement, (2) κ increased from the beginning to the end of the magnitude range for all subjects at both force requirements, (3) the reciprocal of κ was a linear function of the reciprocal of reinforcer magnitude for seven of the eight data sets, and (4) the rate of change of κ was greater at the high than at the low force requirement by an order of magnitude or more. The second and third findings confirm predictions made by linear system theory, and replicate the results of an earlier experiment (McDowell & Wood, 1984). The fourth finding confirms a further prediction of the theory and supports the theory's interpretation of conflicting data on the constancy of Herrnstein's κ. PMID:16812408

Confirmation of linear system theory prediction: Rate of change of Herrnstein's kappa as a function of response-force requirement.

Science.gov (United States)

McDowell, J J; Wood, H M

1985-01-01

Four human subjects worked on all combinations of five variable-interval schedules and five reinforcer magnitudes ( cent/reinforcer) in each of two phases of the experiment. In one phase the force requirement on the operandum was low (1 or 11 N) and in the other it was high (25 or 146 N). Estimates of Herrnstein's kappa were obtained at each reinforcer magnitude. The results were: (1) response rate was more sensitive to changes in reinforcement rate at the high than at the low force requirement, (2) kappa increased from the beginning to the end of the magnitude range for all subjects at both force requirements, (3) the reciprocal of kappa was a linear function of the reciprocal of reinforcer magnitude for seven of the eight data sets, and (4) the rate of change of kappa was greater at the high than at the low force requirement by an order of magnitude or more. The second and third findings confirm predictions made by linear system theory, and replicate the results of an earlier experiment (McDowell & Wood, 1984). The fourth finding confirms a further prediction of the theory and supports the theory's interpretation of conflicting data on the constancy of Herrnstein's kappa.

Methods in half-linear asymptotic theory

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel

2016-01-01

Roč. 2016, Č. 267 (2016), s. 1-27 ISSN 1072-6691 Institutional support: RVO:67985840 Keywords : half-linear differential equation * nonoscillatory solution * regular variation Subject RIV: BA - General Mathematics Impact factor: 0.954, year: 2016 http://ejde.math.txstate.edu/Volumes/2016/267/abstr.html

Linear algebraic groups

CERN Document Server

Springer, T A

1998-01-01

"[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of t...

Spectral analysis of linear relations and degenerate operator semigroups

International Nuclear Information System (INIS)

Baskakov, A G; Chernyshov, K I

2002-01-01

Several problems of the spectral theory of linear relations in Banach spaces are considered. Linear differential inclusions in a Banach space are studied. The construction of the phase space and solutions is carried out with the help of the spectral theory of linear relations, ergodic theorems, and degenerate operator semigroups

Linear theory of the Rayleigh-Taylor instability in the equatorial ionsophere

International Nuclear Information System (INIS)

Russel, D.A.; Ott, E.

1979-01-01

We present a liner theory of the Rayleigh-Taylor instability in the equatorial ionosphere. For a purely exponential density profile, we find that no unstable eigenmode solutions exist. For a particular model ionosphere with an F peak, unstable eigenmode solutions exist only for sufficiently small horizontal wave numbers. In the later case, purely exponential growth at a rate identical to that for the sharp boundary instability is found. To clarify the situation in the case that eigenmodes do not exist, we solve the initial value problem for the linearized ion equation of motion in the long time asymptotic limit. Ion inertia and ion-neutral collisions are included. Assuming straight magnetic field lines, we find that when eigenmodes do not exist the growth of the response to an impulse is slower than exponential viz, t=/sup -1/2/ exp (γ/sup t/) below the F peak and t/sup -3/2/ exp(γ/sup t/) above the peak; and we determine γ

Basic concepts of control theory

International Nuclear Information System (INIS)

Markus, L.

1976-01-01

After a philosophical introduction on control theory and its position among various branches of science, mathematical control theory and its connection with functional analysis are discussed. A chapter on system theory concepts follows. After a summary of results and notations in the general theory of ordinary differential equations, a qualitative theory of control dynamical systems and chapters on the topological dynamics, and the controllability of linear systems are presented. As examples of autonomous linear systems, the switching locus for the synthesis of optimal controllers and linear dynamics with quadratic cost optimization are considered. (author)

Scalable algorithms for contact problems

CERN Document Server

Dostál, Zdeněk; Sadowská, Marie; Vondrák, Vít

2016-01-01

This book presents a comprehensive and self-contained treatment of the authors’ newly developed scalable algorithms for the solutions of multibody contact problems of linear elasticity. The brand new feature of these algorithms is theoretically supported numerical scalability and parallel scalability demonstrated on problems discretized by billions of degrees of freedom. The theory supports solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca’s friction, and transient contact problems. It covers BEM discretization, jumping coefficients, floating bodies, mortar non-penetration conditions, etc. The exposition is divided into four parts, the first of which reviews appropriate facets of linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third part of the volume. The presentation is complete, including continuous formulation, discretization, decomposition, optimality results, and numerical experimen...

Enriching an effect calculus with linear types

DEFF Research Database (Denmark)

Egger, Jeff; Møgelberg, Rasmus Ejlers; Simpson, Alex

2009-01-01

We define an ``enriched effect calculus'' by conservatively extending  a type theory for computational effects with primitives from linear logic. By doing so, we obtain a generalisation of linear type theory, intended as a formalism for expressing linear aspects of effects. As a worked example, we...... formulate  linearly-used continuations in the enriched effect calculus. These are captured by a fundamental translation of the enriched effect calculus into itself, which extends existing call-by-value and call-by-name linearly-used CPS translations. We show that our translation is involutive. Full...... completeness results for the various linearly-used CPS translations  follow. Our main results, the conservativity of enriching the effect calculus with linear primitives, and the involution property of the fundamental translation, are proved using a category-theoretic semantics for the enriched effect calculus...

Applied linear regression

CERN Document Server

Weisberg, Sanford

2013-01-01

Praise for the Third Edition ""...this is an excellent book which could easily be used as a course text...""-International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illus

Linearizing W-algebras

International Nuclear Information System (INIS)

Krivonos, S.O.; Sorin, A.S.

1994-06-01

We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras W 3 and W (2) 3 can be embedded as subalgebras into some linear algebras with finite set of currents. Using these linear algebras we find new field realizations of W (2) 3 and W 3 which could be a starting point for constructing new versions of W-string theories. We also reveal a number of hidden relationships between W 3 and W (2) 3 . We conjecture that similar linear algebras can exist for other W-algebra as well. (author). 10 refs

Oscillation theory of linear differential equations

Czech Academy of Sciences Publication Activity Database

Došlý, Ondřej

2000-01-01

Roč. 36, č. 5 (2000), s. 329-343 ISSN 0044-8753 R&D Projects: GA ČR GA201/98/0677 Keywords : discrete oscillation theory %Sturm-Liouville equation%Riccati equation Subject RIV: BA - General Mathematics

Linear theory of a cold relativistic beam in a strongly magnetized finite-geometry plasma

International Nuclear Information System (INIS)

Gagne, R.R.J.; Shoucri, M.M.

1976-01-01

The linear theory of a finite-geometry cold relativistic beam propagating in a cold homogeneous finite-geometry plasma, is investigated in the case of a strongly magnetized plasma. The beam is assumed to propagate parallel to the external magnetic field. It is shown that the instability which takes place at the Cherenkov resonance ωapprox. =k/subz/v/subb/ is of the convective type. The effect of the finite geometry on the instability growth rate is studied and is shown to decrease the growth rate, with respect to the infinite geometry, by a factor depending on the ratio of the beam-to-plasma radius

Simulation of electron energy loss spectra of nanomaterials with linear-scaling density functional theory

International Nuclear Information System (INIS)

Tait, E W; Payne, M C; Ratcliff, L E; Haynes, P D; Hine, N D M

2016-01-01

Experimental techniques for electron energy loss spectroscopy (EELS) combine high energy resolution with high spatial resolution. They are therefore powerful tools for investigating the local electronic structure of complex systems such as nanostructures, interfaces and even individual defects. Interpretation of experimental electron energy loss spectra is often challenging and can require theoretical modelling of candidate structures, which themselves may be large and complex, beyond the capabilities of traditional cubic-scaling density functional theory. In this work, we present functionality to compute electron energy loss spectra within the onetep linear-scaling density functional theory code. We first demonstrate that simulated spectra agree with those computed using conventional plane wave pseudopotential methods to a high degree of precision. The ability of onetep to tackle large problems is then exploited to investigate convergence of spectra with respect to supercell size. Finally, we apply the novel functionality to a study of the electron energy loss spectra of defects on the (1 0 1) surface of an anatase slab and determine concentrations of defects which might be experimentally detectable. (paper)

Molecular and vibrational structure of diphenylether and its 4,4' -dibromo derivative. Infrared linear dichroism spectroscopy and density functional theory calculations

DEFF Research Database (Denmark)

Eriksen, Troels K; Karlsen, Eva; Spanget-Larsen, Jens

2015-01-01

The title compounds were investigated by means of Linear Dichroism (LD) IR spectroscopy on samples partially aligned in uniaxially stretched low-density polyethylene and by density functional theory calculations. Satisfactory overall agreement between observed and calculated vibrational wavenumbers...

Extending the precision and efficiency of the all-electron full-potential linearized augmented plane-wave density-functional theory method

International Nuclear Information System (INIS)

Michalicek, Gregor

2015-01-01

Density functional theory (DFT) is the most widely-used first-principles theory for analyzing, describing and predicting the properties of solids based on the fundamental laws of quantum mechanics. The success of the theory is a consequence of powerful approximations to the unknown exchange and correlation energy of the interacting electrons and of sophisticated electronic structure methods that enable the computation of the density functional equations on a computer. A widely used electronic structure method is the full-potential linearized augmented plane-wave (FLAPW) method, that is considered to be one of the most precise methods of its kind and often referred to as a standard. Challenged by the demand of treating chemically and structurally increasingly more complex solids, in this thesis this method is revisited and extended along two different directions: (i) precision and (ii) efficiency. In the full-potential linearized augmented plane-wave method the space of a solid is partitioned into nearly touching spheres, centered at each atom, and the remaining interstitial region between the spheres. The Kohn-Sham orbitals, which are used to construct the electron density, the essential quantity in DFT, are expanded into a linearized augmented plane-wave basis, which consists of plane waves in the interstitial region and angular momentum dependent radial functions in the spheres. In this thesis it is shown that for certain types of materials, e.g., materials with very broad electron bands or large band gaps, or materials that allow the usage of large space-filling spheres, the variational freedom of the basis in the spheres has to be extended in order to represent the Kohn-Sham orbitals with high precision over a large energy spread. Two kinds of additional radial functions confined to the spheres, so-called local orbitals, are evaluated and found to successfully eliminate this error. A new efficient basis set is developed, named linearized augmented lattice

Evaluation of Wall Interference Effects in a Two-Dimensional Transonic Wind Tunnel by Subsonic Linear Theory,

Science.gov (United States)

1979-02-01

tests were conducted on two geometrica lly similar models of each of two aerofoil sections -—t he NA CA 00/ 2 and the BGK- 1 sections -and covered a...and slotted-wall tes t sections are corrected for wind tunnel wall interference efJ~cts by the application of classical linearized theory. For the...solid wall results , these corrections appear to produce data which are very close to being free of the effects of interference. In the case of

3D-Printing of Meso-structurally Ordered Carbon Fiber/Polymer Composites with Unprecedented Orthotropic Physical Properties

Science.gov (United States)

Lewicki, James P.; Rodriguez, Jennifer N.; Zhu, Cheng; Worsley, Marcus A.; Wu, Amanda S.; Kanarska, Yuliya; Horn, John D.; Duoss, Eric B.; Ortega, Jason M.; Elmer, William; Hensleigh, Ryan; Fellini, Ryan A.; King, Michael J.

2017-03-01

Here we report the first example of a class of additively manufactured carbon fiber reinforced composite (AMCFRC) materials which have been achieved through the use of a latent thermal cured aromatic thermoset resin system, through an adaptation of direct ink writing (DIW) 3D-printing technology. We have developed a means of printing high performance thermoset carbon fiber composites, which allow the fiber component of a resin and carbon fiber fluid to be aligned in three dimensions via controlled micro-extrusion and subsequently cured into complex geometries. Characterization of our composite systems clearly show that we achieved a high order of fiber alignment within the composite microstructure, which in turn allows these materials to outperform equivalently filled randomly oriented carbon fiber and polymer composites. Furthermore, our AM carbon fiber composite systems exhibit highly orthotropic mechanical and electrical responses as a direct result of the alignment of carbon fiber bundles in the microscale which we predict will ultimately lead to the design of truly tailorable carbon fiber/polymer hybrid materials having locally programmable complex electrical, thermal and mechanical response.

An asymptotic homogenization model for smart 3D grid-reinforced composite structures with generally orthotropic constituents

International Nuclear Information System (INIS)

Hassan, E M; Kalamkarov, A L; Georgiades, A V; Challagulla, K S

2009-01-01

A comprehensive micromechanical model for smart 3D composite structures reinforced with a periodic grid of generally orthotropic cylindrical reinforcements that also exhibit piezoelectric behavior is developed. The original boundary value problem characterizing the piezothermoelastic behavior of these structures is decoupled into a set of three simpler unit cell problems dealing, separately, with the elastic, piezoelectric and thermal expansion characteristics of the smart composite. The technique used is that of asymptotic homogenization and the solution of the unit cell problems permits determination of the effective elastic, piezoelectric and thermal expansion coefficients. The general orthotropy of the constituent materials is very important from the practical viewpoint and makes the analysis much more complicated. Several examples of practical interest are used to illustrate the work including smart 3D composites with cubic and conical embedded grids as well as diagonally reinforced smart structures. It is also shown in this work that in the limiting particular case of 2D grid-reinforced structures with isotropic reinforcements our results converge to earlier published results

Is the local linearity of space-time inherited from the linearity of probabilities?

Science.gov (United States)

Müller, Markus P.; Carrozza, Sylvain; Höhn, Philipp A.

2017-02-01

The appearance of linear spaces, describing physical quantities by vectors and tensors, is ubiquitous in all of physics, from classical mechanics to the modern notion of local Lorentz invariance. However, as natural as this seems to the physicist, most computer scientists would argue that something like a ‘local linear tangent space’ is not very typical and in fact a quite surprising property of any conceivable world or algorithm. In this paper, we take the perspective of the computer scientist seriously, and ask whether there could be any inherently information-theoretic reason to expect this notion of linearity to appear in physics. We give a series of simple arguments, spanning quantum information theory, group representation theory, and renormalization in quantum gravity, that supports a surprising thesis: namely, that the local linearity of space-time might ultimately be a consequence of the linearity of probabilities. While our arguments involve a fair amount of speculation, they have the virtue of being independent of any detailed assumptions on quantum gravity, and they are in harmony with several independent recent ideas on emergent space-time in high-energy physics.

Is the local linearity of space-time inherited from the linearity of probabilities?

International Nuclear Information System (INIS)

Müller, Markus P; Carrozza, Sylvain; Höhn, Philipp A

2017-01-01

The appearance of linear spaces, describing physical quantities by vectors and tensors, is ubiquitous in all of physics, from classical mechanics to the modern notion of local Lorentz invariance. However, as natural as this seems to the physicist, most computer scientists would argue that something like a ‘local linear tangent space’ is not very typical and in fact a quite surprising property of any conceivable world or algorithm. In this paper, we take the perspective of the computer scientist seriously, and ask whether there could be any inherently information-theoretic reason to expect this notion of linearity to appear in physics. We give a series of simple arguments, spanning quantum information theory, group representation theory, and renormalization in quantum gravity, that supports a surprising thesis: namely, that the local linearity of space-time might ultimately be a consequence of the linearity of probabilities. While our arguments involve a fair amount of speculation, they have the virtue of being independent of any detailed assumptions on quantum gravity, and they are in harmony with several independent recent ideas on emergent space-time in high-energy physics. (paper)

Strings and superstrings. Electron linear colliders

International Nuclear Information System (INIS)

Alessandrini, V.; Bambade, P.; Binetruy, P.; Kounnas, C.; Le Duff, J.; Schwimmer, A.

1989-01-01

Basic string theory; strings in interaction; construction of strings and superstrings in arbitrary space-time dimensions; compactification and phenomenology; linear e+e- colliders; and the Stanford linear collider were discussed [fr

The Schrödinger representation and its relation to the holomorphic representation in linear and affine field theory

International Nuclear Information System (INIS)

Oeckl, Robert

2012-01-01

We establish a precise isomorphism between the Schrödinger representation and the holomorphic representation in linear and affine field theory. In the linear case, this isomorphism is induced by a one-to-one correspondence between complex structures and Schrödinger vacua. In the affine case we obtain similar results, with the role of the vacuum now taken by a whole family of coherent states. In order to establish these results we exhibit a rigorous construction of the Schrödinger representation and use a suitable generalization of the Segal-Bargmann transform. Our construction is based on geometric quantization and applies to any real polarization and its pairing with any Kähler polarization.

Linear positivity and virtual probability

International Nuclear Information System (INIS)

Hartle, James B.

2004-01-01

We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. The objective of any quantum theory of a closed system, most generally the universe, is the prediction of probabilities for the individual members of sets of alternative coarse-grained histories of the system. Quantum interference between members of a set of alternative histories is an obstacle to assigning probabilities that are consistent with the rules of probability theory. A quantum theory of closed systems therefore requires two elements: (1) a condition specifying which sets of histories may be assigned probabilities and (2) a rule for those probabilities. The linear positivity condition of Goldstein and Page is the weakest of the general conditions proposed so far. Its general properties relating to exact probability sum rules, time neutrality, and conservation laws are explored. Its inconsistency with the usual notion of independent subsystems in quantum mechanics is reviewed. Its relation to the stronger condition of medium decoherence necessary for classicality is discussed. The linear positivity of histories in a number of simple model systems is investigated with the aim of exhibiting linearly positive sets of histories that are not decoherent. The utility of extending the notion of probability to include values outside the range of 0-1 is described. Alternatives with such virtual probabilities cannot be measured or recorded, but can be used in the intermediate steps of calculations of real probabilities. Extended probabilities give a simple and general way of formulating quantum theory. The various decoherence conditions are compared in terms of their utility for characterizing classicality and the role they might play in further generalizations of quantum mechanics

Linear algebra

CERN Document Server

Said-Houari, Belkacem

2017-01-01

This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

Science.gov (United States)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to

Matrices and linear transformations

CERN Document Server

Cullen, Charles G

1990-01-01

""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first

Periodic feedback stabilization for linear periodic evolution equations

CERN Document Server

Wang, Gengsheng

2016-01-01

This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.

Applied linear algebra and matrix analysis

CERN Document Server

Shores, Thomas S

2018-01-01

In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...

Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum

Science.gov (United States)

Rips, Ilya

2017-01-01

Decay of the metastable state is analyzed within the quantum Kramers model in the weak-to-intermediate dissipation regime. The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. In our previous paper [Phys. Rev. A 42, 4427 (1990), 10.1103/PhysRevA.42.4427], Grabert's perturbative approach to well dynamics in the case of the discrete bath [Phys. Rev. Lett. 61, 1683 (1988), 10.1103/PhysRevLett.61.1683] has been extended to account for the second order terms in the classical equations of motion (EOM) for the stable modes. Account of the secular terms reduces EOM for the stable modes to those of the forced oscillator with the time-dependent frequency (TDF oscillator). Analytic expression for the characteristic function of energy loss of the unstable mode has been derived in terms of the generating function of the transition probabilities for the quantum forced TDF oscillator. In this paper, the approach is further developed and applied to the case of the continuous frequency spectrum of the bath. The spectral density functions of the bath of stable modes are expressed in terms of the dissipative properties (the friction function) of the original bath. They simplify considerably for the one-dimensional systems, when the density of phonon states is constant. Explicit expressions for the fourth order corrections to the linear response theory result for the characteristic function of the energy loss and its cumulants are obtained for the particular case of the cubic potential with Ohmic (Markovian) dissipation. The range of validity of the perturbative approach in this case is determined (γ /ωbrate for the quantum and for the classical Kramers models. Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers. The results can serve as an additional proof of the robustness and accuracy of the linear response theory.

Uncertainties Concerning the Free Vibration of Inhomogeneous Orthotropic Reinforced Concrete Plates

Science.gov (United States)

Shahsavar, Vahid Lal; Tofighi, Samira

2014-09-01

Analyzing nearly collapsed and broken structures gives good insights into possible architectural and engineering design mistakes and faults in the detailing and mismanagement of a construction by building contractors. Harmful vibration effects of construction operations occur frequently. The background reviews have demonstrated that the problem of the vibration serviceability of long-span concrete floors in buildings is complex and interdisciplinary in nature. In public buildings, floor vibration control is required in order to meet Serviceability Limit States that ensure the comfort of the users of a building. In industrial buildings, machines are often placed on floors. Machines generate vibrations of various frequencies, which are transferred to supporting constructions. Precision machines require a stable floor with defined and known dynamic characteristics. In recent years there has been increasing interest in the motion of elastic bodies whose material properties (density, elastic moduli, etc.) are not constant, but vary with their position, perhaps in a random manner. Concrete is a non-homogeneous and anisotropic material. Modeling the mechanical behavior of reinforced concrete (RC) is still one of the most difficult challenges in the field of structural engineering. One of several methods for determining the dynamic modulus of the elasticity of engineering materials is the vibration frequency procedure. In this method, the required variables except for the modulus of elasticity are accurately and certainly determined. In this research, the uncertainly analysis of the free vibration of inhomogeneous orthotropic reinforced concrete plates has been investigated. Due to the numerous outputs obtained, the software package has been written in Matlab, and an analysis of the data and drawing related charts has been done.

Using linear time-invariant system theory to estimate kinetic parameters directly from projection measurements

International Nuclear Information System (INIS)

Zeng, G.L.; Gullberg, G.T.

1995-01-01

It is common practice to estimate kinetic parameters from dynamically acquired tomographic data by first reconstructing a dynamic sequence of three-dimensional reconstructions and then fitting the parameters to time activity curves generated from the time-varying reconstructed images. However, in SPECT, the pharmaceutical distribution can change during the acquisition of a complete tomographic data set, which can bias the estimated kinetic parameters. It is hypothesized that more accurate estimates of the kinetic parameters can be obtained by fitting to the projection measurements instead of the reconstructed time sequence. Estimation from projections requires the knowledge of their relationship between the tissue regions of interest or voxels with particular kinetic parameters and the project measurements, which results in a complicated nonlinear estimation problem with a series of exponential factors with multiplicative coefficients. A technique is presented in this paper where the exponential decay parameters are estimated separately using linear time-invariant system theory. Once the exponential factors are known, the coefficients of the exponentials can be estimated using linear estimation techniques. Computer simulations demonstrate that estimation of the kinetic parameters directly from the projections is more accurate than the estimation from the reconstructed images

Non-linear theory of elasticity

CERN Document Server

Lurie, AI

2012-01-01

This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.

Signals and transforms in linear systems analysis

CERN Document Server

Wasylkiwskyj, Wasyl

2013-01-01

Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7.  The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to...

Linear algebra

CERN Document Server

Liesen, Jörg

2015-01-01

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

On the stimulated Raman sidescattering in inhomogeneous plasmas: revisit of linear theory and three-dimensional particle-in-cell simulations

Science.gov (United States)

Xiao, C. Z.; Zhuo, H. B.; Yin, Y.; Liu, Z. J.; Zheng, C. Y.; Zhao, Y.; He, X. T.

2018-02-01

Stimulated Raman sidescattering (SRSS) in inhomogeneous plasma is comprehensively revisited on both theoretical and numerical aspects due to the increasing concern of its detriments to inertial confinement fusion. Firstly, two linear mechanisms of finite beam width and collisional effects that could suppress SRSS are investigated theoretically. Thresholds for the eigenmode and wave packet in a finite-width beam are derived as a supplement to the theory proposed by Mostrom and Kaufman (1979 Phys. Rev. Lett. 42 644). Collisional absorption of SRSS is efficient at high-density plasma and high-Z material, otherwise, it allows emission of sidescattering. Secondly, we have performed the first three-dimensional particle-in-cell simulations in the context of SRSS to investigate its linear and nonlinear effects. Simulation results are qualitatively agreed with the linear theory. SRSS with the maximum growth gain is excited at various densities, grows to an amplitude that is comparable with the pump laser, and evolutes to lower densities with a large angle of emergence. Competitions between SRSS and other parametric instabilities such as stimulated Raman backscattering, two-plasmon decay, and stimulated Brillouin scattering are discussed. These interaction processes are determined by gains, occurrence sites, scattering geometries of each instability, and will affect subsequent evolutions. Nonlinear effects of self-focusing and azimuthal magnetic field generation are observed to be accompanied with SRSS. In addition, it is found that SRSS is insensitive to ion motion, collision (low-Z material), and electron temperature.

Linear waves and instabilities

International Nuclear Information System (INIS)

Bers, A.

1975-01-01

The electrodynamic equations for small-amplitude waves and their dispersion relation in a homogeneous plasma are outlined. For such waves, energy and momentum, and their flow and transformation, are described. Perturbation theory of waves is treated and applied to linear coupling of waves, and the resulting instabilities from such interactions between active and passive waves. Linear stability analysis in time and space is described where the time-asymptotic, time-space Green's function for an arbitrary dispersion relation is developed. The perturbation theory of waves is applied to nonlinear coupling, with particular emphasis on pump-driven interactions of waves. Details of the time--space evolution of instabilities due to coupling are given. (U.S.)

Structure formation with massive neutrinos. Going beyond linear theory

International Nuclear Information System (INIS)

Blas, Diego; Garny, Mathias; Konstandin, Thomas; Lesgourgues, Julien; Institut de Theorie Phenomenes Physiques EPFL, Lausanne; Savoie Univ., CNRS, Annecy-le-Vieux

2014-08-01

We compute non-linear corrections to the matter power spectrum taking the time- and scale-dependent free-streaming length of neutrinos into account. We adopt a hybrid scheme that matches the full Boltzmann hierarchy to an effective two-fluid description at an intermediate redshift. The non-linearities in the neutrino component are taken into account by using an extension of the time-flow framework. We point out that this remedies a spurious behaviour that occurs when neglecting non-linear terms for neutrinos. This behaviour is related to how efficiently short modes decouple from long modes and can be traced back to the violation of momentum conservation if neutrinos are treated linearly. Furthermore, we compare our results at next to leading order to various other methods and quantify the accuracy of the fluid description. Due to the correct decoupling behaviour of short modes, the two-fluid scheme is a suitable starting point to compute higher orders in perturbations or for resummation methods.

Structure formation with massive neutrinos: going beyond linear theory

CERN Document Server

Blas, Diego; Konstandin, Thomas; Lesgourgues, Julien

2014-01-01

We compute non-linear corrections to the matter power spectrum taking the time- and scale-dependent free-streaming length of neutrinos into account. We adopt a hybrid scheme that matches the full Boltzmann hierarchy to an effective two-fluid description at an intermediate redshift. The non-linearities in the neutrino component are taken into account by using an extension of the time-flow framework. We point out that this remedies a spurious behaviour that occurs when neglecting non-linear terms for neutrinos. This behaviour is related to how efficiently short modes decouple from long modes and can be traced back to the violation of momentum conservation if neutrinos are treated linearly. Furthermore, we compare our results at next to leading order to various other methods and quantify the accuracy of the fluid description. Due to the correct decoupling behaviour of short modes, the two-fluid scheme is a suitable starting point to compute higher orders in perturbations or for resummation methods.

Combining linear polarization spectroscopy and the Representative Layer Theory to measure the Beer-Lambert law absorbance of highly scattering materials.

Science.gov (United States)

Gobrecht, Alexia; Bendoula, Ryad; Roger, Jean-Michel; Bellon-Maurel, Véronique

2015-01-01

Visible and Near Infrared (Vis-NIR) Spectroscopy is a powerful non destructive analytical method used to analyze major compounds in bulk materials and products and requiring no sample preparation. It is widely used in routine analysis and also in-line in industries, in-vivo with biomedical applications or in-field for agricultural and environmental applications. However, highly scattering samples subvert Beer-Lambert law's linear relationship between spectral absorbance and the concentrations. Instead of spectral pre-processing, which is commonly used by Vis-NIR spectroscopists to mitigate the scattering effect, we put forward an optical method, based on Polarized Light Spectroscopy to improve the absorbance signal measurement on highly scattering samples. This method selects part of the signal which is less impacted by scattering. The resulted signal is combined in the Absorption/Remission function defined in Dahm's Representative Layer Theory to compute an absorbance signal fulfilling Beer-Lambert's law, i.e. being linearly related to concentration of the chemicals composing the sample. The underpinning theories have been experimentally evaluated on scattering samples in liquid form and in powdered form. The method produced more accurate spectra and the Pearson's coefficient assessing the linearity between the absorbance spectra and the concentration of the added dye improved from 0.94 to 0.99 for liquid samples and 0.84-0.97 for powdered samples. Copyright © 2014 Elsevier B.V. All rights reserved.

Anomalous electron transport in Hall-effect thrusters: Comparison between quasi-linear kinetic theory and particle-in-cell simulations

Science.gov (United States)

Lafleur, T.; Martorelli, R.; Chabert, P.; Bourdon, A.

2018-06-01

Kinetic drift instabilities have been implicated as a possible mechanism leading to anomalous electron cross-field transport in E × B discharges, such as Hall-effect thrusters. Such instabilities, which are driven by the large disparity in electron and ion drift velocities, present a significant challenge to modelling efforts without resorting to time-consuming particle-in-cell (PIC) simulations. Here, we test aspects of quasi-linear kinetic theory with 2D PIC simulations with the aim of developing a self-consistent treatment of these instabilities. The specific quantities of interest are the instability growth rate (which determines the spatial and temporal evolution of the instability amplitude), and the instability-enhanced electron-ion friction force (which leads to "anomalous" electron transport). By using the self-consistently obtained electron distribution functions from the PIC simulations (which are in general non-Maxwellian), we find that the predictions of the quasi-linear kinetic theory are in good agreement with the simulation results. By contrast, the use of Maxwellian distributions leads to a growth rate and electron-ion friction force that is around 2-4 times higher, and consequently significantly overestimates the electron transport. A possible method for self-consistently modelling the distribution functions without requiring PIC simulations is discussed.

Quasi-linear theory and transport theory. [particle acceleration in interplanetary medium

Science.gov (United States)

Smith, Charles W.

1992-01-01

The theory of energetic particle scattering by magnetostatic fluctuations is reviewed in so far as it fails to produce the rigidity-independent mean-free-paths observed. Basic aspects of interplanetary magnetic field fluctuations are reviewed with emphasis placed on the existence of dissipation range spectra at high wavenumbers. These spectra are then incorporated into existing theories for resonant magnetostatic scattering and are shown to yield infinite mean-free-paths. Nonresonant scattering in the form of magnetic mirroring is examined and offered as a partial solution to the magnetostatic problem. In the process, mean-free-paths are obtained in good agreement with observations in the interplanetary medium at 1 AU and upstream of planetary bow shocks.

Strain Rate Dependant Material Model for Orthotropic Metals

International Nuclear Information System (INIS)

Vignjevic, Rade

2016-01-01

deformation. In addition the constitutive model is coupled with a vector shock equation of state which allows for modelling of shock wave propagation in orthotropic the material. Parameters for the new constitutive model are typically derived on the basis of the tensile tests (performed over a range of temperatures and strain rates), plate impact tests and Taylor anvil tests. The model was applied to simulate explosively driven fragmentation, blast loading and cold spraying impacts. (paper)

Wavelet-based linear-response time-dependent density-functional theory

International Nuclear Information System (INIS)

Natarajan, Bhaarathi; Genovese, Luigi; Casida, Mark E.; Deutsch, Thierry; Burchak, Olga N.

2012-01-01

Highlights: ► We has been implemented LR-TD-DFT in the pseudopotential wavelet-based program. ► We have compared the results against all-electron Gaussian-type program. ► Orbital energies converges significantly faster for BigDFT than for DEMON2K. ► We report the X-ray crystal structure of the small organic molecule flugi6. ► Measured and calculated absorption spectrum of flugi6 is also reported. - Abstract: Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BIGDFT and results are compared against those obtained with the all-electron Gaussian-type orbital program DEMON2K for the calculation of electronic absorption spectra of N 2 using the TD local density approximation (LDA). The two programs give comparable excitation energies and absorption spectra once suitably extensive basis sets are used. Convergence of LDA density orbitals and orbital energies to the basis-set limit is significantly faster for BIGDFT than for DEMON2K. However the number of virtual orbitals used in TD-DFT calculations is a parameter in BIGDFT, while all virtual orbitals are included in TD-DFT calculations in DEMON2K. As a reality check, we report the X-ray crystal structure and the measured and calculated absorption spectrum (excitation energies and oscillator strengths) of the small organic molecule N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1, 2-a]pyridin-3-amine.

Van der Waals potentials between metal clusters and helium atoms obtained with density functional theory and linear response methods

International Nuclear Information System (INIS)

Liebrecht, M.

2014-01-01

The importance of van der Waals interactions in many diverse research fields such as, e. g., polymer science, nano--materials, structural biology, surface science and condensed matter physics created a high demand for efficient and accurate methods that can describe van der Waals interactions from first principles. These methods should be able to deal with large and complex systems to predict functions and properties of materials that are technologically and biologically relevant. Van der Waals interactions arise due to quantum mechanical correlation effects and finding appropriate models an numerical techniques to describe this type of interaction is still an ongoing challenge in electronic structure and condensed matter theory. This thesis introduces a new variational approach to obtain intermolecular interaction potentials between clusters and helium atoms by means of density functional theory and linear response methods. It scales almost linearly with the number of electrons and can therefore be applied to much larger systems than standard quantum chemistry techniques. The main focus of this work is the development of an ab-initio method to account for London dispersion forces, which are purely attractive and dominate the interaction of non--polar atoms and molecules at large distances. (author) [de

Linear and non-linear amplification of high-mode perturbations at the ablation front in HiPER targets

Energy Technology Data Exchange (ETDEWEB)

Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)

2011-01-15

The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.

Estimating epidemic arrival times using linear spreading theory

Science.gov (United States)

Chen, Lawrence M.; Holzer, Matt; Shapiro, Anne

2018-01-01

We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is composed of a system of ordinary differential equations describing a meta-population susceptible-infected-recovered compartmental model defined on a network where each node represents a city and the edges represent the flight paths connecting cities. Making use of the linear determinacy of the system, we consider spreading speeds and arrival times in the system linearized about the unstable disease free state and compare these to arrival times in the nonlinear system. Two predictions are presented. The first is based upon expansion of the heat kernel for the linearized system. The second assumes that the dominant transmission pathway between any two cities can be approximated by a one dimensional lattice or a homogeneous tree and gives a uniform prediction for arrival times independent of the specific network features. We test these predictions on a real network describing worldwide airline traffic.

Light propagation in linear optical media

CERN Document Server

Gillen, Glen D; Guha, Shekhar

2013-01-01

Light Propagation in Linear Optical Media describes light propagation in linear media by expanding on diffraction theories beyond what is available in classic optics books. In one volume, this book combines the treatment of light propagation through various media, interfaces, and apertures using scalar and vector diffraction theories. After covering the fundamentals of light and physical optics, the authors discuss light traveling within an anisotropic crystal and present mathematical models for light propagation across planar boundaries between different media. They describe the propagation o

Linear algebra meets Lie algebra: the Kostant-Wallach theory

OpenAIRE

Shomron, Noam; Parlett, Beresford N.

2008-01-01

In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.

Applying Monte Carlo Concept and Linear Programming in Modern Portfolio Theory to Obtain Best Weighting Structure

Directory of Open Access Journals (Sweden)

Tumpal Sihombing

2013-01-01

Full Text Available The world is entering the era of recession when the trend is bearish and market is not so favorable. The capital markets in every major country were experiencing great amount of loss and people suffered in their investment. The Jakarta Composite Index (JCI has shown a great downturn for the past one year but the trend bearish year of the JCI. Therefore, rational investors should consider restructuring their portfolio to set bigger proportion in bonds and cash instead of stocks. Investors can apply modern portfolio theory by Harry Markowitz to find the optimum asset allocation for their portfolio. Higher return is always associated with higher risk. This study shows investors how to find out the lowest risk of a portfolio investment by providing them with several structures of portfolio weighting. By this way, investor can compare and make the decision based on risk-return consideration and opportunity cost as well. Keywords: Modern portfolio theory, Monte Carlo, linear programming

Design and optimization of a Holweck pump via linear kinetic theory

Science.gov (United States)

Naris, Steryios; Koutandou, Eirini; Valougeorgis, Dimitris

2012-05-01

The Holweck pump is widely used in the vacuum pumping industry. It can be a self standing apparatus or it can be part of a more advanced pumping system. It is composed by an inner rotating cylinder (rotor) and an outer stationary cylinder (stator). One of them, has spiral guided grooves resulting to a gas motion from the high towards the low vacuum port. Vacuum pumps may be simulated by the DSMC method but due to the involved high computational cost in many cases manufactures commonly resort to empirical formulas and experimental data. Recently a computationally efficient simulation of the Holweck pump via linear kinetic theory has been proposed by Sharipov et al [1]. Neglecting curvature and end effects the gas flow configuration through the helicoidal channels is decomposed into four basic flows. They correspond to pressure and boundary driven flows through a grooved channel and through a long channel with a T shape cross section. Although the formulation and the methodology are explained in detail, results are very limited and more important they are presented in a normalized way which does not provide the needed information about the pump performance in terms of the involved geometrical and flow parameters. In the present work the four basic flows are solved numerically based on the linearized BGK model equation subjected to diffuse boundary conditions. The results obtained are combined in order to create a database of the flow characteristics for a large spectrum of the rarefaction parameter and various geometrical configurations. Based on this database the performance characteristics which are critical in the design of the Holweck pump are computed and the design parameters such as the angle of the pump and the rotational speed, are optimized. This modeling may be extended to other vacuum pumps.

Design and optimization of a Holweck pump via linear kinetic theory

International Nuclear Information System (INIS)

Naris, Steryios; Koutandou, Eirini; Valougeorgis, Dimitris

2012-01-01

The Holweck pump is widely used in the vacuum pumping industry. It can be a self standing apparatus or it can be part of a more advanced pumping system. It is composed by an inner rotating cylinder (rotor) and an outer stationary cylinder (stator). One of them, has spiral guided grooves resulting to a gas motion from the high towards the low vacuum port. Vacuum pumps may be simulated by the DSMC method but due to the involved high computational cost in many cases manufactures commonly resort to empirical formulas and experimental data. Recently a computationally efficient simulation of the Holweck pump via linear kinetic theory has been proposed by Sharipov et al [1]. Neglecting curvature and end effects the gas flow configuration through the helicoidal channels is decomposed into four basic flows. They correspond to pressure and boundary driven flows through a grooved channel and through a long channel with a T shape cross section. Although the formulation and the methodology are explained in detail, results are very limited and more important they are presented in a normalized way which does not provide the needed information about the pump performance in terms of the involved geometrical and flow parameters. In the present work the four basic flows are solved numerically based on the linearized BGK model equation subjected to diffuse boundary conditions. The results obtained are combined in order to create a database of the flow characteristics for a large spectrum of the rarefaction parameter and various geometrical configurations. Based on this database the performance characteristics which are critical in the design of the Holweck pump are computed and the design parameters such as the angle of the pump and the rotational speed, are optimized. This modeling may be extended to other vacuum pumps.

Matrices and linear algebra

CERN Document Server

Schneider, Hans

1989-01-01

Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t

Damped oscillations of linear systems a mathematical introduction

CERN Document Server

Veselić, Krešimir

2011-01-01

The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and ...

Semidefinite linear complementarity problems

International Nuclear Information System (INIS)

Eckhardt, U.

1978-04-01

Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.) [de

New linear theory of hydrodynamic instability of the Hagen-Poiseuille flow and the blood swirling flows formation

Directory of Open Access Journals (Sweden)

Sergey G. Chefranov

2012-11-01

Full Text Available Aims This paper deals with solving of a century-old paradox of linear stability for the Hagen-Poiseuille flow. A new mechanism of dissipative hydrodynamic instability has been established herein, and a basis for the forming of helical structural organization of bloodstream and respective energy effectiveness of the cardiovascular system functioning has been defined by the authors. Materials and methods Theory of hydrodynamic instability, Galerkin’s approximation. Results A new condition Re > Reth-min ≈ 124 of linear (exponential instability of the Hagen-Poisseuille (HP flow with respect to extremely small by magnitude axially-symmetric disturbances of the tangential component of the velocity field is obtained. The disturbances necessarily shall have quasi-periodic longitudinal variability along the pipe axis that corresponds to the observed data. Conclusion We show that the obtained estimate of value of Reth-min corresponds to the condition of independence of the main result (on the linear instability of the HP flow when Re > Reth-min from the procedure of averaging used in the Galerkin approximation. Thus, we obtain the possible natural mechanism for the blood swirling flows formations observed in the aorta and the large blood vessels.

Linear stochastic neutron transport theory

International Nuclear Information System (INIS)

Lewins, J.

1978-01-01

A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)

Primordial black holes in linear and non-linear regimes

Energy Technology Data Exchange (ETDEWEB)

Allahyari, Alireza; Abolhasani, Ali Akbar [Department of Physics, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

2017-06-01

We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we argue that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbations are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.

Application of perturbation theory to the non-linear vibration analysis of a string including the bending moment effects

International Nuclear Information System (INIS)

Esmaeilzadeh Khadem, S.; Rezaee, M.

2001-01-01

In this paper the large amplitude and non-linear vibration of a string is considered. The initial tension, lateral vibration amplitude, diameter and the modulus of elasticity of the string have main effects on its natural frequencies. Increasing the lateral vibration amplitude makes the assumption of constant initial tension invalid. In this case, therefore, it is impossible to use the classical equation of string with small amplitude transverse motion assumption. On the other hand, by increasing the string diameter, the bending moment effect will increase dramatically, and acts as an impressive restoring moment. Considering the effects of the bending moments, the nonlinear equation governing the large amplitude transverse vibration of a string is derived. The time dependent portion of the governing equation has the from of Duff ing equation is solved using the perturbation theory. The results of the analysis are shown in appropriate graphs, and the natural frequencies of the string due to the non-linear factors are compared with the natural frequencies of the linear vibration os a string without bending moment effects

New approach to solve symmetric fully fuzzy linear systems

Indian Academy of Sciences (India)

concepts of fuzzy set theory and then define a fully fuzzy linear system of equations. .... To represent the above problem as fully fuzzy linear system, we represent x .... Fully fuzzy linear systems can be solved by Linear programming approach, ...

Some relations of parameters in quantum field theory

International Nuclear Information System (INIS)

Ishikawa, K.

1986-01-01

Two schemes of parameter relations, linear relation and non-linear relation are discussed. The linear relation of coupling constants is derived directly from an underlying symmetry of the classical theory and is preserved usually in the quantum theory. The non-linear relation is not derived by a same manner but is derived by more involved way which is intrinsically connected with quantum theory. An underlying symmetry which leads the linear relation is shown to be essential in the non-linear relation too. Some extension is also discussed

The Growing Importance of Linear Algebra in Undergraduate Mathematics.

Science.gov (United States)

Tucker, Alan

1993-01-01

Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

Linear circuit theory matrices in computer applications

CERN Document Server

Vlach, Jiri

2014-01-01

Basic ConceptsNodal and Mesh AnalysisMatrix MethodsDependent SourcesNetwork TransformationsCapacitors and InductorsNetworks with Capacitors and InductorsFrequency DomainLaplace TransformationTime DomainNetwork FunctionsActive NetworksTwo-PortsTransformersModeling and Numerical MethodsSensitivitiesModified Nodal FormulationFourier Series and TransformationAppendix: Scaling of Linear Networks.

ORACLS: A system for linear-quadratic-Gaussian control law design

Science.gov (United States)

Armstrong, E. S.

1978-01-01

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Decomposition Theory in the Teaching of Elementary Linear Algebra.

Science.gov (United States)

London, R. R.; Rogosinski, H. P.

1990-01-01

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)

Analytical results for post-buckling behaviour of plates in compression and in shear

Science.gov (United States)

Stein, M.

1985-01-01

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Introduction to linear systems of differential equations

CERN Document Server

Adrianova, L Ya

1995-01-01

The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent. In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1)�autonomous, 2)�periodic, 3)�reducible to autonomous, 4)�nearly reducible to autonomous, 5)�regular. In addition, Adrianova considers the following: stability of linear systems and the influence of perturbations of the coefficients on the stability the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions several estimates of the growth rate of solutions of a linear system in terms of its coefficients How perturbations of the coefficients change all the elements of the spectrum of the system is defin...

A non-linear kinematic hardening function

International Nuclear Information System (INIS)

Ottosen, N.S.

1977-05-01

Based on the classical theory of plasticity, and accepting the von Mises criterion as the initial yield criterion, a non-linear kinematic hardening function applicable both to Melan-Prager's and to Ziegler's hardening rule is proposed. This non-linear hardening function is determined by means of the uniaxial stress-strain curve, and any such curve is applicable. The proposed hardening function considers the problem of general reversed loading, and a smooth change in the behaviour from one plastic state to another nearlying plastic state is obtained. A review of both the kinematic hardening theory and the corresponding non-linear hardening assumptions is given, and it is shown that material behaviour is identical whether Melan-Prager's or Ziegler's hardening rule is applied, provided that the von Mises yield criterion is adopted. (author)

Metrical results on systems of small linear forms

DEFF Research Database (Denmark)

Hussain, M.; Kristensen, Simon

In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine--Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating function.......In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine--Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating function....

An Application of Linear Algebra over Lattices

OpenAIRE

M. Hosseinyazdi

2008-01-01

In this paper, first we consider L n as a semimodule over a complete bounded distributive lattice L. Then we define the basic concepts of module theory for L n. After that, we proved many similar theorems in linear algebra for the space L n. An application of linear algebra over lattices for solving linear systems, was given

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Vecharynski, Eugene [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Brabec, Jiri [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Shao, Meiyue [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Govind, Niranjan [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab.; Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division

2017-12-01

We present two efficient iterative algorithms for solving the linear response eigen- value problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously. The efficiency of the new algorithms is demonstrated by numerical examples.

Modern linear control design a time-domain approach

CERN Document Server

Caravani, Paolo

2013-01-01

This book offers a compact introduction to modern linear control design.  The simplified overview presented of linear time-domain methodology paves the road for the study of more advanced non-linear techniques. Only rudimentary knowledge of linear systems theory is assumed - no use of Laplace transforms or frequency design tools is required. Emphasis is placed on assumptions and logical implications, rather than abstract completeness; on interpretation and physical meaning, rather than theoretical formalism; on results and solutions, rather than derivation or solvability.  The topics covered include transient performance and stabilization via state or output feedback; disturbance attenuation and robust control; regional eigenvalue assignment and constraints on input or output variables; asymptotic regulation and disturbance rejection. Lyapunov theory and Linear Matrix Inequalities (LMI) are discussed as key design methods. All methods are demonstrated with MATLAB to promote practical use and comprehension. ...

Anti-D3 branes and moduli in non-linear supergravity

Science.gov (United States)

Garcia del Moral, Maria P.; Parameswaran, Susha; Quiroz, Norma; Zavala, Ivonne

2017-10-01

Anti-D3 branes and non-perturbative effects in flux compactifications spontaneously break supersymmetry and stabilise moduli in a metastable de Sitter vacua. The low energy 4D effective field theory description for such models would be a supergravity theory with non-linearly realised supersymmetry. Guided by string theory modular symmetry, we compute this non-linear supergravity theory, including dependence on all bulk moduli. Using either a constrained chiral superfield or a constrained vector field, the uplifting contribution to the scalar potential from the anti-D3 brane can be parameterised either as an F-term or Fayet-Iliopoulos D-term. Using again the modular symmetry, we show that 4D non-linear supergravities that descend from string theory have an enhanced protection from quantum corrections by non-renormalisation theorems. The superpotential giving rise to metastable de Sitter vacua is robust against perturbative string-loop and α' corrections.

Energy of linear quasineutral electrostatic drift waves

International Nuclear Information System (INIS)

Pfirsch, D.; Correa-Restrepo, D.

1993-01-01

Certain kinds of nonlinear instabilities are related to the existence of negative-energy perturbations. In this paper, an exact energy expression for linear quasineutral electrostatic perturbations is derived within the framework of dissipationless multifluid theory that is valid for any geometry. Taking the mass formally as a tensor with, in general, different masses parallel and perpendicular to an ambient magnetic field allows one to treat in a convenient way different approximations such as the full dynamics and restriction to parallel dynamics or the completely adiabatic case. Application to slab configurations yields the result that the adiabatic approximation does not allow negative energy for perturbations which are perfectly localized at a mode resonant surface, whereas inclusion of the parallel dynamics does. This is in agreement with a recent numerical study of drift-wave turbulence within the framework of collisional two-fluid theory by B. Scott [Phys. Rev. Lett. 65, 3289 (1990); Phys. Fluids B 4, 2468 (1992)]. A dissipationless theory can be formulated in terms of a Lagrangian, from which the energy is immediately obtained. We start with the nonlinear theory. The theory is formulated via a Lagrangian which is written in terms of displacement vectors ξ ν (x,t) such that all constraints are taken into account. The nonlinear energy is obtained from the Lagrangian by standard methods. The procedure used is the same as that developed in a forthcoming paper by Pfirsch and Sudan [Phys. Fluids B (to be published)] for ideal nonlinear magnetohydrodynamics theory. From the exact Lagrangian one obtains the Lagrangian of the linearized theory by simple expansion to second order in ξ ν . This Lagrangian then yields the energy of the linearized theory

Uniqueness theorems in linear elasticity

CERN Document Server

Knops, Robin John

1971-01-01

The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...

Groups, matrices, and vector spaces a group theoretic approach to linear algebra

CERN Document Server

Carrell, James B

2017-01-01

This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory ...

Charge and pairing dynamics in the attractive Hubbard model: Mode coupling and the validity of linear-response theory

Science.gov (United States)

Bünemann, Jörg; Seibold, Götz

2017-12-01

Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to nonequilibrium situations. Here we examine the validity of such an approach for the charge and pairing response of systems with charge-density wave and (or) superconducting (SC) order. Our investigations are based on the attractive Hubbard model which we study within the time-dependent Hartree-Fock approximation. In particular, we calculate the quench and pump-probe dynamics for SC and charge order parameters in order to analyze the frequency spectra and the coupling of the probe field to the specific excitations. Our calculations reveal that the "linear-response assumption" is justified for small to moderate nonequilibrium situations (i.e., pump pulses) in the case of a purely charge-ordered ground state. However, the pump-probe dynamics on top of a superconducting ground state is determined by phase and amplitude modes which get coupled far from the equilibrium state indicating the failure of the linear-response assumption.

Linear regression

CERN Document Server

Olive, David J

2017-01-01

This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...

Dissipative open systems theory as a foundation for the thermodynamics of linear systems.

Science.gov (United States)

Delvenne, Jean-Charles; Sandberg, Henrik

2017-03-06

In this paper, we advocate the use of open dynamical systems, i.e. systems sharing input and output variables with their environment, and the dissipativity theory initiated by Jan Willems as models of thermodynamical systems, at the microscopic and macroscopic level alike. We take linear systems as a study case, where we show how to derive a global Lyapunov function to analyse networks of interconnected systems. We define a suitable notion of dynamic non-equilibrium temperature that allows us to derive a discrete Fourier law ruling the exchange of heat between lumped, discrete-space systems, enriched with the Maxwell-Cattaneo correction. We complete these results by a brief recall of the steps that allow complete derivation of the dissipation and fluctuation in macroscopic systems (i.e. at the level of probability distributions) from lossless and deterministic systems.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time

Science.gov (United States)

Wang, Yu

1995-08-01

The dynamic response and stability of a single-degree-of-freedom system with unsymmetric piecewise-linear/non-linear stiffness are analyzed using the finite element method in the time domain. Based on a Hamilton's weak principle, this method provides a simple and efficient approach for predicting all possible fundamental and sub-periodic responses. The stability of the steady state response is determined by using Floquet's theory without any special effort for calculating transition matrices. This method is applied to a number of examples, demonstrating its effectiveness even for a strongly non-linear problem involving both clearance and continuous stiffness non-linearities. Close agreement is found between available published findings and the predictions of the finite element in time approach, which appears to be an efficient and reliable alternative technique for non-linear dynamic response and stability analysis of periodic systems.

A Linear Theory for Pretwisted Elastic Beams

DEFF Research Database (Denmark)

Krenk, Steen

1983-01-01

contains a general system of differential equations and gives explicit solutions for homogenous extension, torsion, and bending. The theory accounts explicitly for the shear center, the elastic center, and the axis of pretwist. The resulting torsion-extension coupling is in agreement with a recent...

An Application of Linear Algebra over Lattices

Directory of Open Access Journals (Sweden)

M. Hosseinyazdi

2008-03-01

Full Text Available In this paper, first we consider L n as a semimodule over a complete bounded distributive lattice L. Then we define the basic concepts of module theory for L n. After that, we proved many similar theorems in linear algebra for the space L n. An application of linear algebra over lattices for solving linear systems, was given

Asymmetric Vibration of Polar Orthotropic Annular Circular Plates of Quadratically Varying Thickness with Same Boundary Conditions

Directory of Open Access Journals (Sweden)

N. Bhardwaj

2008-01-01

Full Text Available In the present paper, asymmetric vibration of polar orthotropic annular circular plates of quadratically varying thickness resting on Winkler elastic foundation is studied by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method. Convergence of the results is tested and comparison is made with results already available in the existing literature. Numerical results for the first ten frequencies for various values of parameters describing width of annular plate, thickness profile, material orthotropy and foundation constant for all three possible combinations of clamped, simply supported and free edge conditions are shown and discussed. It is found that (a higher elastic property in circumferential direction leads to higher stiffness against lateral vibration; (b Lateral vibration characteristics of F-Fplates is more sensitive towards parametric changes in material orthotropy and foundation stiffness than C-C and S-Splates; (c Effect of quadratical thickness variation on fundamental frequency is more significant in cases of C-C and S-S plates than that of F-Fplates. Thickness profile which is convex relative to plate center-line tends to result in higher stiffness of annular plates against lateral vibration than the one which is concave and (d Fundamental mode of vibration of C-C and S-Splates is axisymmetrical while that of F-Fplates is asymmetrical.

Recent developments in linear theta-pinch research: experiment and theory

International Nuclear Information System (INIS)

McKenna, K.F.; Bartsch, R.R.; Commisso, R.J.

1978-01-01

High energy plasmas offusion interest can be generated in linear theta pinches. However, end losses present a fundamental limitation on the plasma containment time. This paper discusses recent progress in end-loss and end-stoppering experiments and in the theoretical understanding of linear theta-pinch physics

Further linear algebra

CERN Document Server

Blyth, T S

2002-01-01

Most of the introductory courses on linear algebra develop the basic theory of finite­ dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num­ ber of illustrative and worked examples, as well as many exercises that are strategi­ cally placed throughout the text. Solutions to the ex...

EDITORIAL: Non-linear and non-Gaussian cosmological perturbations Non-linear and non-Gaussian cosmological perturbations

Science.gov (United States)

Sasaki, Misao; Wands, David

2010-06-01

In recent years there has been a resurgence of interest in the study of non-linear perturbations of cosmological models. This has been the result of both theoretical developments and observational advances. New theoretical challenges arise at second and higher order due to mode coupling and the need to develop new gauge-invariant variables beyond first order. In particular, non-linear interactions lead to deviations from a Gaussian distribution of primordial perturbations even if initial vacuum fluctuations are exactly Gaussian. These non-Gaussianities provide an important probe of models for the origin of structure in the very early universe. We now have a detailed picture of the primordial distribution of matter from surveys of the cosmic microwave background, notably NASA's WMAP satellite. The situation will continue to improve with future data from the ESA Planck satellite launched in 2009. To fully exploit these data cosmologists need to extend non-linear cosmological perturbation theory beyond the linear theory that has previously been sufficient on cosmological scales. Another recent development has been the realization that large-scale structure, revealed in high-redshift galaxy surveys, could also be sensitive to non-linearities in the primordial curvature perturbation. This focus section brings together a collection of invited papers which explore several topical issues in this subject. We hope it will be of interest to theoretical physicists and astrophysicists alike interested in understanding and interpreting recent developments in cosmological perturbation theory and models of the early universe. Of course it is only an incomplete snapshot of a rapidly developing field and we hope the reader will be inspired to read further work on the subject and, perhaps, fill in some of the missing pieces. This focus section is dedicated to the memory of Lev Kofman (1957-2009), an enthusiastic pioneer of inflationary cosmology and non-Gaussian perturbations.

Theoretical prediction on corrugated sandwich panels under bending loads

Science.gov (United States)

Shu, Chengfu; Hou, Shujuan

2018-05-01

In this paper, an aluminum corrugated sandwich panel with triangular core under bending loads was investigated. Firstly, the equivalent material parameters of the triangular corrugated core layer, which could be considered as an orthotropic panel, were obtained by using Castigliano's theorem and equivalent homogeneous model. Secondly, contributions of the corrugated core layer and two face panels were both considered to compute the equivalent material parameters of the whole structure through the classical lamination theory, and these equivalent material parameters were compared with finite element analysis solutions. Then, based on the Mindlin orthotropic plate theory, this study obtain the closed-form solutions of the displacement for a corrugated sandwich panel under bending loads in specified boundary conditions, and parameters study and comparison by the finite element method were executed simultaneously.

Non-linear dynamics of wind turbine wings

DEFF Research Database (Denmark)

Larsen, Jesper Winther; Nielsen, Søren R.K.

2006-01-01

The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced...

The conceptual basis of mathematics in cardiology III: linear systems theory and integral transforms.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-05-01

This is the third in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas.This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to

c-Map for Born–Infeld theories

Directory of Open Access Journals (Sweden)

L. Andrianopoli

2016-07-01

Full Text Available The c-map of four dimensional non-linear theories of electromagnetism is considered both in the rigid case and in its coupling to gravity. In this way theories with antisymmetric tensors and scalars are obtained, and the three non-linear representations of N = 2 supersymmetry partially broken to N = 1 related. The manifest Sp(2n and U(n covariance of these theories in their multifield extensions is also exhibited. This construction extends to H-invariant non-linear theories of Born–Infeld type with non-dynamical scalars spanning a symmetric coset manifold G/H and the vector field strengths and their duals in a symplectic representation of G as is the case for extended supergravity.

Non-linear realizations and bosonic branes

International Nuclear Information System (INIS)

West, P.

2001-01-01

In this very short note, following hep-th/0001216, we express the well known bosonic brane as a non-linear realization. The reader may also consult hep-th/9912226, 0001216 and 0005270 where the branes of M theory are constructed as a non-linear realisation. The automorphisms of the supersymmetry algebra play an essential role. (author)

Some new ternary linear codes

Directory of Open Access Journals (Sweden)

Rumen Daskalov

2017-07-01

Full Text Available Let an $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$ and minimum Hamming distance $d$ over $GF(q$. One of the most important problems in coding theory is to construct codes with optimal minimum distances. In this paper 22 new ternary linear codes are presented. Two of them are optimal. All new codes improve the respective lower bounds in [11].

Phi-value analysis of a linear, sequential reaction mechanism: theory and application to ion channel gating.

Science.gov (United States)

Zhou, Yu; Pearson, John E; Auerbach, Anthony

2005-12-01

We derive the analytical form of a rate-equilibrium free-energy relationship (with slope Phi) for a bounded, linear chain of coupled reactions having arbitrary connecting rate constants. The results confirm previous simulation studies showing that Phi-values reflect the position of the perturbed reaction within the chain, with reactions occurring earlier in the sequence producing higher Phi-values than those occurring later in the sequence. The derivation includes an expression for the transmission coefficients of the overall reaction based on the rate constants of an arbitrary, discrete, finite Markov chain. The results indicate that experimental Phi-values can be used to calculate the relative heights of the energy barriers between intermediate states of the chain but provide no information about the energies of the wells along the reaction path. Application of the equations to the case of diliganded acetylcholine receptor channel gating suggests that the transition-state ensemble for this reaction is nearly flat. Although this mechanism accounts for many of the basic features of diliganded and unliganded acetylcholine receptor channel gating, the experimental rate-equilibrium free-energy relationships appear to be more linear than those predicted by the theory.

Elasticity theory and applications

CERN Document Server

Saada, Adel S; Hartnett, James P; Hughes, William F

2013-01-01

Elasticity: Theory and Applications reviews the theory and applications of elasticity. The book is divided into three parts. The first part is concerned with the kinematics of continuous media; the second part focuses on the analysis of stress; and the third part considers the theory of elasticity and its applications to engineering problems. This book consists of 18 chapters; the first of which deals with the kinematics of continuous media. The basic definitions and the operations of matrix algebra are presented in the next chapter, followed by a discussion on the linear transformation of points. The study of finite and linear strains gradually introduces the reader to the tensor concept. Orthogonal curvilinear coordinates are examined in detail, along with the similarities between stress and strain. The chapters that follow cover torsion; the three-dimensional theory of linear elasticity and the requirements for the solution of elasticity problems; the method of potentials; and topics related to cylinders, ...

Spectroscopic investigations using density functional theory on 2-methoxy- 4(phenyliminomethyl)phenol: A non linear optical material

Science.gov (United States)

Hijas, K. M.; Madan Kumar, S.; Byrappa, K.; Geethakrishnan, T.; Jeyaram, S.; Nagalakshmi, R.

2018-03-01

Single crystals of 2-methoxy-4(phenyliminomethyl)phenol were grown from ethanol by slow evaporation solution growth technique. Single crystal X-ray diffraction experiment reveals the crystallization in orthorhombic system having non-centrosymmetric space group C2221. Geometrical optimization by density functional theory method was carried out using Gaussian program and compared with experimental results. Detailed experimental and theoretical vibrational analyses were carried out and the results were correlated to find close agreement. Thermal analyses show the material is thermally stable with a melting point of 159 °C. Natural bond orbital analysis was carried out to explain charge transfer interactions through hydrogen bonding. Relatively smaller HOMO-LUMO band gap favors the non linear optical activity of the molecule. Natural population analysis and molecular electrostatic potential calculations visualize the charge distribution in an isolated molecule. Calculated first-order molecular hyperpolarizability and preliminary second harmonic generation test carried out using Kurtz-Perry technique establish 2-methoxy-4(phenyliminomethyl)phenol crystal as a good non linear optical material. Z-scan proposes the material for reverse saturable absorption.

Linear Algebra Thoroughly Explained

CERN Document Server

Vujičić, Milan

2008-01-01

Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a comprehensive resource book for the subject.

A time-dependent density functional theory investigation of plasmon resonances of linear Au atomic chains

International Nuclear Information System (INIS)

Liu Dan-Dan; Zhang Hong

2011-01-01

We report theoretical studies on the plasmon resonances in linear Au atomic chains by using ab initio time-dependent density functional theory. The dipole responses are investigated each as a function of chain length. They converge into a single resonance in the longitudinal mode but split into two transverse modes. As the chain length increases, the longitudinal plasmon mode is redshifted in energy while the transverse modes shift in the opposite direction (blueshifts). In addition, the energy gap between the two transverse modes reduces with chain length increasing. We find that there are unique characteristics, different from those of other metallic chains. These characteristics are crucial to atomic-scale engineering of single-molecule sensing, optical spectroscopy, and so on. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

Lessons to be learned from a contentious challenge to mainstream radiobiological science (the linear no-threshold theory of genetic mutations)

International Nuclear Information System (INIS)

Beyea, Jan

2017-01-01

There are both statistically valid and invalid reasons why scientists with differing default hypotheses can disagree in high-profile situations. Examples can be found in recent correspondence in this journal, which may offer lessons for resolving challenges to mainstream science, particularly when adherents of a minority view attempt to elevate the status of outlier studies and/or claim that self-interest explains the acceptance of the dominant theory. Edward J. Calabrese and I have been debating the historical origins of the linear no-threshold theory (LNT) of carcinogenesis and its use in the regulation of ionizing radiation. Professor Calabrese, a supporter of hormesis, has charged a committee of scientists with misconduct in their preparation of a 1956 report on the genetic effects of atomic radiation. Specifically he argues that the report mischaracterized the LNT research record and suppressed calculations of some committee members. After reviewing the available scientific literature, I found that the contemporaneous evidence overwhelmingly favored a (genetics) LNT and that no calculations were suppressed. Calabrese's claims about the scientific record do not hold up primarily because of lack of attention to statistical analysis. Ironically, outlier studies were more likely to favor supra-linearity, not sub-linearity. Finally, the claim of investigator bias, which underlies Calabrese's accusations about key studies, is based on misreading of text. Attention to ethics charges, early on, may help seed a counter narrative explaining the community's adoption of a default hypothesis and may help focus attention on valid evidence and any real weaknesses in the dominant paradigm. - Highlights: • Edward J Calabrese has made a contentious challenge to mainstream radiobiological science. • Such challenges should not be neglected, lest they enter the political arena without review. • Key genetic studies from the 1940s, challenged by Calabrese, were

Lessons to be learned from a contentious challenge to mainstream radiobiological science (the linear no-threshold theory of genetic mutations)

Energy Technology Data Exchange (ETDEWEB)

Beyea, Jan, E-mail: jbeyea@cipi.com

2017-04-15

There are both statistically valid and invalid reasons why scientists with differing default hypotheses can disagree in high-profile situations. Examples can be found in recent correspondence in this journal, which may offer lessons for resolving challenges to mainstream science, particularly when adherents of a minority view attempt to elevate the status of outlier studies and/or claim that self-interest explains the acceptance of the dominant theory. Edward J. Calabrese and I have been debating the historical origins of the linear no-threshold theory (LNT) of carcinogenesis and its use in the regulation of ionizing radiation. Professor Calabrese, a supporter of hormesis, has charged a committee of scientists with misconduct in their preparation of a 1956 report on the genetic effects of atomic radiation. Specifically he argues that the report mischaracterized the LNT research record and suppressed calculations of some committee members. After reviewing the available scientific literature, I found that the contemporaneous evidence overwhelmingly favored a (genetics) LNT and that no calculations were suppressed. Calabrese's claims about the scientific record do not hold up primarily because of lack of attention to statistical analysis. Ironically, outlier studies were more likely to favor supra-linearity, not sub-linearity. Finally, the claim of investigator bias, which underlies Calabrese's accusations about key studies, is based on misreading of text. Attention to ethics charges, early on, may help seed a counter narrative explaining the community's adoption of a default hypothesis and may help focus attention on valid evidence and any real weaknesses in the dominant paradigm. - Highlights: • Edward J Calabrese has made a contentious challenge to mainstream radiobiological science. • Such challenges should not be neglected, lest they enter the political arena without review. • Key genetic studies from the 1940s, challenged by Calabrese, were

General solution of linear vector supersymmetry

International Nuclear Information System (INIS)

Blasi, Alberto; Maggiore, Nicola

2007-01-01

We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such a solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology, usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example

Lessons to be learned from a contentious challenge to mainstream radiobiological science (the linear no-threshold theory of genetic mutations).

Science.gov (United States)

Beyea, Jan

2017-04-01

There are both statistically valid and invalid reasons why scientists with differing default hypotheses can disagree in high-profile situations. Examples can be found in recent correspondence in this journal, which may offer lessons for resolving challenges to mainstream science, particularly when adherents of a minority view attempt to elevate the status of outlier studies and/or claim that self-interest explains the acceptance of the dominant theory. Edward J. Calabrese and I have been debating the historical origins of the linear no-threshold theory (LNT) of carcinogenesis and its use in the regulation of ionizing radiation. Professor Calabrese, a supporter of hormesis, has charged a committee of scientists with misconduct in their preparation of a 1956 report on the genetic effects of atomic radiation. Specifically he argues that the report mischaracterized the LNT research record and suppressed calculations of some committee members. After reviewing the available scientific literature, I found that the contemporaneous evidence overwhelmingly favored a (genetics) LNT and that no calculations were suppressed. Calabrese's claims about the scientific record do not hold up primarily because of lack of attention to statistical analysis. Ironically, outlier studies were more likely to favor supra-linearity, not sub-linearity. Finally, the claim of investigator bias, which underlies Calabrese's accusations about key studies, is based on misreading of text. Attention to ethics charges, early on, may help seed a counter narrative explaining the community's adoption of a default hypothesis and may help focus attention on valid evidence and any real weaknesses in the dominant paradigm. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

On pole structure assignment in linear systems

Czech Academy of Sciences Publication Activity Database

Loiseau, J.-J.; Zagalak, Petr

2009-01-01

Roč. 82, č. 7 (2009), s. 1179-1192 ISSN 0020-7179 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : linear systems * linear state feedback * pole structure assignment Subject RIV: BC - Control Systems Theory Impact factor: 1.124, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-on pole structure assignment in linear systems.pdf

Linear kinetic theory and particle transport in stochastic mixtures. Third year and final report, June 15, 1993--December 14, 1996

International Nuclear Information System (INIS)

Pomraning, G.C.

1997-05-01

The goal in this research was to continue the development of a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. Such a theory should predict the ensemble average and higher moments, such as the variance, of the particle or energy density described by the underlying transport/kinetic equation. The statistics studied correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components in the mixture. The mixing statistics considered were Markovian as well as more general statistics. In the absence of time dependence and scattering, the theory is well developed and described exactly by the master (Liouville) equation for Markovian mixing, and by renewal equations for non-Markovian mixing. The intent of this research was to generalize these treatments to include both time dependence and scattering. A further goal of this research was to develop approximate, but simpler, models from any comprehensive theory. In particular, a specific goal was to formulate a renormalized transport/kinetic theory of the usual nonstochastic form, but with effective interaction coefficients and sources to account for the stochastic nature of the problem. In the three and one-half year period of research summarized in this final report, they have made substantial progress in the development of a comprehensive theory of kinetic processes in stochastic mixtures. This progress is summarized in 16 archival journal articles, 7 published proceedings papers, and 2 comprehensive review articles. In addition, 17 oral presentations were made describing these research results

Introduction to representation theory

CERN Document Server

Etingof, Pavel; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex

2011-01-01

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a "holistic" introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic k...

Non-linear assessment and deficiency of linear relationship for healthcare industry

Science.gov (United States)

Nordin, N.; Abdullah, M. M. A. B.; Razak, R. C.

2017-09-01

This paper presents the development of the non-linear service satisfaction model that assumes patients are not necessarily satisfied or dissatisfied with good or poor service delivery. With that, compliment and compliant assessment is considered, simultaneously. Non-linear service satisfaction instrument called Kano-Q and Kano-SS is developed based on Kano model and Theory of Quality Attributes (TQA) to define the unexpected, hidden and unspoken patient satisfaction and dissatisfaction into service quality attribute. A new Kano-Q and Kano-SS algorithm for quality attribute assessment is developed based satisfaction impact theories and found instrumentally fit the reliability and validity test. The results were also validated based on standard Kano model procedure before Kano model and Quality Function Deployment (QFD) is integrated for patient attribute and service attribute prioritization. An algorithm of Kano-QFD matrix operation is developed to compose the prioritized complaint and compliment indexes. Finally, the results of prioritized service attributes are mapped to service delivery category to determine the most prioritized service delivery that need to be improved at the first place by healthcare service provider.

The potential in general linear electrodynamics. Causal structure, propagators and quantization

Energy Technology Data Exchange (ETDEWEB)

Siemssen, Daniel [Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw (Poland); Pfeifer, Christian [Institute for Theoretical Physics, Leibniz Universitaet Hannover (Germany); Center of Applied Space Technology and Microgravity (ZARM), Universitaet Bremen (Germany)

2016-07-01

From an axiomatic point of view, the fundamental input for a theory of electrodynamics are Maxwell's equations dF=0 (or F=dA) and dH=J, and a constitutive law H=F, which relates the field strength 2-form F and the excitation 2-form H. In this talk we consider general linear electrodynamics, the theory of electrodynamics defined by a linear constitutive law. The best known application of this theory is the effective description of electrodynamics inside (linear) media (e.g. birefringence). We analyze the classical theory of the electromagnetic potential A before we use methods familiar from mathematical quantum field theory in curved spacetimes to quantize it. Our analysis of the classical theory contains the derivation of retarded and advanced propagators, the analysis of the causal structure on the basis of the constitutive law (instead of a metric) and a discussion of the classical phase space. This classical analysis sets the stage for the construction of the quantum field algebra and quantum states, including a (generalized) microlocal spectrum condition.

Modules as Learning Tools in Linear Algebra

Science.gov (United States)

Cooley, Laurel; Vidakovic, Draga; Martin, William O.; Dexter, Scott; Suzuki, Jeff; Loch, Sergio

2014-01-01

This paper reports on the experience of STEM and mathematics faculty at four different institutions working collaboratively to integrate learning theory with curriculum development in a core undergraduate linear algebra context. The faculty formed a Professional Learning Community (PLC) with a focus on learning theories in mathematics and…

Galois theory and algorithms for linear differential equations

NARCIS (Netherlands)

Put, Marius van der

2005-01-01

This paper is an informal introduction to differential Galois theory. It surveys recent work on differential Galois groups, related algorithms and some applications. (c) 2005 Elsevier Ltd. All rights reserved.

Acetate and phosphate anion adsorption linear sweep voltammograms simulated using density functional theory

KAUST Repository

Savizi, Iman Shahidi Pour

2011-04-01

Specific adsorption of anions to electrode surfaces may alter the rates of electrocatalytic reactions. Density functional theory (DFT) methods are used to predict the adsorption free energy of acetate and phosphate anions as a function of Pt(1 1 1) electrode potential. Four models of the electrode potential are used including a simple vacuum slab model, an applied electric field model with and without the inclusion of a solvating water bi-layer, and the double reference model. The linear sweep voltammogram (LSV) due to anion adsorption is simulated using the DFT results. The inclusion of solvation at the electrochemical interface is necessary for accurately predicting the adsorption peak position. The Langmuir model is sufficient for predicting the adsorption peak shape, indicating coverage effects are minor in altering the LSV for acetate and phosphate adsorption. Anion adsorption peak positions are determined for solution phase anion concentrations present in microbial fuel cells and microbial electrolysis cells and discussion is provided as to the impact of anion adsorption on oxygen reduction and hydrogen evolution reaction rates in these devices. © 2011 Elsevier Ltd. All rights reserved.

Chaos as an intermittently forced linear system.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

Trends in modern system theory

Science.gov (United States)

Athans, M.

1976-01-01

The topics considered are related to linear control system design, adaptive control, failure detection, control under failure, system reliability, and large-scale systems and decentralized control. It is pointed out that the design of a linear feedback control system which regulates a process about a desirable set point or steady-state condition in the presence of disturbances is a very important problem. The linearized dynamics of the process are used for design purposes. The typical linear-quadratic design involving the solution of the optimal control problem of a linear time-invariant system with respect to a quadratic performance criterion is considered along with gain reduction theorems and the multivariable phase margin theorem. The stumbling block in many adaptive design methodologies is associated with the amount of real time computation which is necessary. Attention is also given to the desperate need to develop good theories for large-scale systems, the beginning of a microprocessor revolution, the translation of the Wiener-Hopf theory into the time domain, and advances made in dynamic team theory, dynamic stochastic games, and finite memory stochastic control.

On the linearization of nonlinear supersymmetry based on the commutator algebra

Energy Technology Data Exchange (ETDEWEB)

Tsuda, Motomu, E-mail: tsuda@sit.ac.jp

2017-01-10

We discuss a linearization procedure of nonlinear supersymmetry (NLSUSY) based on the closure of the commutator algebra for variations of functionals of Nambu–Goldstone fermions and their derivative terms under NLSUSY transformations in Volkov–Akulov NLSUSY theory. In the case of a set of bosonic and fermionic functionals, which leads to (massless) vector linear supermultiplets, we explicitly show that general linear SUSY transformations of basic components defined from those functionals are uniquely determined by examining the commutation relation in the NLSUSY theory.

STICAP: A linear circuit analysis program with stiff systems capability. Volume 1: Theory manual. [network analysis

Science.gov (United States)

Cooke, C. H.

1975-01-01

STICAP (Stiff Circuit Analysis Program) is a FORTRAN 4 computer program written for the CDC-6400-6600 computer series and SCOPE 3.0 operating system. It provides the circuit analyst a tool for automatically computing the transient responses and frequency responses of large linear time invariant networks, both stiff and nonstiff (algorithms and numerical integration techniques are described). The circuit description and user's program input language is engineer-oriented, making simple the task of using the program. Engineering theories underlying STICAP are examined. A user's manual is included which explains user interaction with the program and gives results of typical circuit design applications. Also, the program structure from a systems programmer's viewpoint is depicted and flow charts and other software documentation are given.

Foundations of the non-linear mechanics of continua

CERN Document Server

Sedov, L I

1966-01-01

International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable

Simulations of nanocrystals under pressure: Combining electronic enthalpy and linear-scaling density-functional theory

Energy Technology Data Exchange (ETDEWEB)

Corsini, Niccolò R. C., E-mail: niccolo.corsini@imperial.ac.uk; Greco, Andrea; Haynes, Peter D. [Department of Physics and Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Hine, Nicholas D. M. [Department of Physics and Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Cavendish Laboratory, J. J. Thompson Avenue, Cambridge CB3 0HE (United Kingdom); Molteni, Carla [Department of Physics, King' s College London, Strand, London WC2R 2LS (United Kingdom)

2013-08-28

We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure. Based on a definition of the system volume as that enclosed within an electronic density isosurface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett.94, 145501 (2005)], it supports both geometry optimizations and molecular dynamics simulations. We introduce an approach for calibrating the parameters defining the volume in the context of geometry optimizations and discuss their significance. Results in good agreement with simulations using explicit solvents are obtained, validating our approach. Size-dependent pressure-induced structural transformations and variations in the energy gap of hydrogenated silicon nanocrystals are investigated, including one comparable in size to recent experiments. A detailed analysis of the polyamorphic transformations reveals three types of amorphous structures and their persistence on depressurization is assessed.

Energy harvesting with stacked dielectric elastomer transducers: Nonlinear theory, optimization, and linearized scaling law

Science.gov (United States)

Tutcuoglu, A.; Majidi, C.

2014-12-01

Using principles of damped harmonic oscillation with continuous media, we examine electrostatic energy harvesting with a "soft-matter" array of dielectric elastomer (DE) transducers. The array is composed of infinitely thin and deformable electrodes separated by layers of insulating elastomer. During vibration, it deforms longitudinally, resulting in a change in the capacitance and electrical enthalpy of the charged electrodes. Depending on the phase of electrostatic loading, the DE array can function as either an actuator that amplifies small vibrations or a generator that converts these external excitations into electrical power. Both cases are addressed with a comprehensive theory that accounts for the influence of viscoelasticity, dielectric breakdown, and electromechanical coupling induced by Maxwell stress. In the case of a linearized Kelvin-Voigt model of the dielectric, we obtain a closed-form estimate for the electrical power output and a scaling law for DE generator design. For the complete nonlinear model, we obtain the optimal electrostatic voltage input for maximum electrical power output.

Matrix model and time-like linear dila ton matter

International Nuclear Information System (INIS)

Takayanagi, Tadashi

2004-01-01

We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple Fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dila ton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-boranes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string. (author)

Dual double field theory

Energy Technology Data Exchange (ETDEWEB)

Bergshoeff, Eric A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University,Stony Brook, NY 11794-3636 (United States); Penas, Victor A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Riccioni, Fabio [INFN - Sezione di Roma, Dipartimento di Fisica, Università di Roma “La Sapienza”,Piazzale Aldo Moro 2, 00185 Roma (Italy)

2016-06-06

We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for “exotic' dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.

Linear theory of plasma filled backward wave oscillator

Indian Academy of Sciences (India)

An analytical and numerical study of backward wave oscillator (BWO) in linear regime is presented to get an insight into the excitation of electromagnetic waves as a result of the interaction of the relativistic electron beam with a slow wave structure. The effect of background plasma on the BWO instability is also presented.

Mathematical methods linear algebra normed spaces distributions integration

CERN Document Server

Korevaar, Jacob

1968-01-01

Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector

An introduction to fuzzy linear programming problems theory, methods and applications

CERN Document Server

Kaur, Jagdeep

2016-01-01

The book presents a snapshot of the state of the art in the field of fully fuzzy linear programming. The main focus is on showing current methods for finding the fuzzy optimal solution of fully fuzzy linear programming problems in which all the parameters and decision variables are represented by non-negative fuzzy numbers. It presents new methods developed by the authors, as well as existing methods developed by others, and their application to real-world problems, including fuzzy transportation problems. Moreover, it compares the outcomes of the different methods and discusses their advantages/disadvantages. As the first work to collect at one place the most important methods for solving fuzzy linear programming problems, the book represents a useful reference guide for students and researchers, providing them with the necessary theoretical and practical knowledge to deal with linear programming problems under uncertainty.

C-map for Born-Infeld theories

CERN Document Server

Andrianopoli, Laura; Ferrara, Sergio; Trigiante, Mario

2016-01-01

The c-map of four dimensional non-linear theories of electromagnetism is considered both in the rigid case and in its coupling to gravity. In this way theories with antisymmetric tensors and scalars are obtained, and the three non-linear representations of N=2 supersymmetry partially broken to N=1 related. The manifest $\\mathrm{Sp}(2n)$ and $\\mathrm{U}(n)$ covariance of these theories in their multifield extensions is also exhibited.

Introduction to linear elasticity

CERN Document Server

Gould, Phillip L

2013-01-01

Introduction to Linear Elasticity, 3rd Edition, provides an applications-oriented grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical, and biomedical engineering, as well as materials and earth science. The book is distinct from the traditional text aimed at graduate students in solid mechanics by introducing the subject at a level appropriate for advanced undergraduate and beginning graduate students. The author's presentation allows students to apply the basic notions of stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials, viscoelasticity and finite method analysis. This book also:  Emphasizes tensor-based approach while still distilling down to explicit notation Provides introduction to theory of plates, theory of shells, wave propagation, viscoelasticity and plasticity accessible to advanced undergraduate students Appropriate for courses following emerging trend of teaching solid mechan...

Impact Of Elastic Modulus Degradation On Springback In Sheet Metal Forming

International Nuclear Information System (INIS)

Halilovic, Miroslav; Stok, Boris; Vrh, Marko

2007-01-01

Strain recovery after removal of forming loads, commonly defined as springback, is of great concern in sheet metal forming, in particular with regard to proper prediction of the final shape of the part. To control the problem a lot of work has been done, either by minimizing the springback on the material side or by increasing the estimation precision in corresponding process simulations. Unfortunately, by currently available software springback still cannot be adequately predicted, because most analyses of springback are using linear, isotropic and constant Young's modulus and Poisson's ratio. But, as it was measured and reported, none of it is true. The aim of this work is to propose an upgraded mechanical model which takes evolution of damage and related orthotropic stiffness degradation into account. Damage is considered by inclusion of ellipsoidal cavities, and their influence on the stiffness degradation is taken in accordance with the Mori-Tanaka theory, adopting the GTN model for plastic flow. In order to improve the numerical springback prediction, two major things are important: first, the correct evaluation of the stress-strain state at the end of the forming process, and second, correctness of the elastic properties used in the elastic relaxation analysis. Since in modelling of the forming process we adopt a damage constitutive model with orthotropic stiffness degradation considered, a corresponding damage parameters identification upon specific experimental tests data must be performed first, independently of the metal forming modelling. An improved identification of material parameters, which simultaneously considers tensile test results with different type of specimens and using neural network, is proposed. With regard to the case in which damage in material is neglected it is shown in the article how the springback of a formed part differs, when we take orthotropic damage evolution into consideration

Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

KAUST Repository

Richtarik, Peter; Taká č, Martin

2017-01-01

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

KAUST Repository

Richtarik, Peter

2017-06-04

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

Theory of oscillators

CERN Document Server

Andronov, Aleksandr Aleksandrovich; Vitt, Aleksandr Adolfovich

1966-01-01

Theory of Oscillators presents the applications and exposition of the qualitative theory of differential equations. This book discusses the idea of a discontinuous transition in a dynamic process. Organized into 11 chapters, this book begins with an overview of the simplest type of oscillatory system in which the motion is described by a linear differential equation. This text then examines the character of the motion of the representative point along the hyperbola. Other chapters consider examples of two basic types of non-linear non-conservative systems, namely, dissipative systems and self-

Physics prospects at a linear e+e- collider

International Nuclear Information System (INIS)

Rindani, Saurabh D.

2006-01-01

The talk described the prospects of studying standard model parameters as well as scenarios beyond the standard model, like the minimal supersymmetric standard model, theories with extra dimensions and theories with extra neutral gauge bosons, at a future linear e + e - collider. (author)

Convex variational problems linear, nearly linear and anisotropic growth conditions

CERN Document Server

Bildhauer, Michael

2003-01-01

The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.

Stress wave propagation in linear viscoelasticity

International Nuclear Information System (INIS)

Asada, Kazuo; Fukuoka, Hidekazu.

1992-01-01

Decreasing characteristics of both stress and stress gradient with propagation distance at a 2-dimensional linear viscoelasticity wavefront are derived by using our 3-dimensional theoretical equation for particle velocity discontinuities. By finite-element method code DYNA3D, stress at a noncurvature dilatation wavefront of linear viscoelasticity is shown to decrease exponentially. This result is in good accordance with our theory. By dynamic photoelasticity experiment, stress gradients of urethane rubber plates at 3 types of wavefronts are shown to decrease exponentially at a noncurvature wavefront and are shown to be a decreasing function of (1/√R) exp (α 1 2 /(2α 0 3 ξ)) at a curvature wavefront. These experiment results are in good accordance with our theory. (author)

Inverse problems in linear transport theory

International Nuclear Information System (INIS)

Dressler, K.

1988-01-01

Inverse problems for a class of linear kinetic equations are investigated. The aim is to identify the scattering kernel of a transport equation (corresponding to the structure of a background medium) by observing the 'albedo' part of the solution operator for the corresponding direct initial boundary value problem. This means to get information on some integral operator in an integrodifferential equation through on overdetermined boundary value problem. We first derive a constructive method for solving direct halfspace problems and prove a new factorization theorem for the solutions. Using this result we investigate stationary inverse problems with respect to well posedness (e.g. reduce them to classical ill-posed problems, such as integral equations of first kind). In the time-dependent case we show that a quite general inverse problem is well posed and solve it constructively. (orig.)

Linear algebra and linear operators in engineering with applications in Mathematica

CERN Document Server

Davis, H Ted

2000-01-01

Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and practical application of linear algebra and functional analysis. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. The important theorems of the subject are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert spaces are introduced from analogy. Wherever possible, theorems and definitions from matrix theory are called upon to drive the analogy home. The result is a clear and intuitive segue to functional analysis, culminating in a practical introduction to the functional theory of integral and differential operators. Numerous examples, problems, and illustrations highlight applications from all over engineering and the physical ...

Extending the linear model with R generalized linear, mixed effects and nonparametric regression models

CERN Document Server

Faraway, Julian J

2005-01-01

Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway''s critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author''s treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the ...

Product state resolved excitation spectroscopy of He-, Ne-, and Ar-Br2 linear isomers: experiment and theory.

Science.gov (United States)

Pio, Jordan M; van der Veer, Wytze E; Bieler, Craig R; Janda, Kenneth C

2008-04-07

Valence excitation spectra for the linear isomers of He-, Ne-, and Ar-Br2 are reported and compared to a two-dimensional simulation using the currently available potential energy surfaces. Excitation spectra from the ground electronic state to the region of the inner turning point of the Rg-Br2 (B,nu') stretching coordinate are recorded while probing the asymptotic Br2 (B,nu') state. Each spectrum is a broad continuum extending over hundreds of wavenumbers, becoming broader and more blueshifted as the rare gas atom is changed from He to Ne to Ar. In the case of Ne-Br2, the threshold for producing the asymptotic product state reveals the X-state linear isomer bond energy to be 71+/-3 cm(-1). The qualitative agreement between experiment and theory shows that the spectra can be correctly regarded as revealing the one-atom solvent shifts and also provides new insight into the one-atom cage effect on the halogen vibrational relaxation. The measured spectra provide data to test future ab initio potential energy surfaces in the interaction of rare gas atoms with the halogen valence excited state.

Theory and praxis pf map analsys in CHEF part 1: Linear normal form

Energy Technology Data Exchange (ETDEWEB)

Michelotti, Leo; /Fermilab

2008-10-01

This memo begins a series which, put together, could comprise the 'CHEF Documentation Project' if there were such a thing. The first--and perhaps only--three will telegraphically describe theory, algorithms, implementation and usage of the normal form map analysis procedures encoded in CHEF's collection of libraries. [1] This one will begin the sequence by explaining the linear manipulations that connect the Jacobian matrix of a symplectic mapping to its normal form. It is a 'Reader's Digest' version of material I wrote in Intermediate Classical Dynamics (ICD) [2] and randomly scattered across technical memos, seminar viewgraphs, and lecture notes for the past quarter century. Much of its content is old, well known, and in some places borders on the trivial.1 Nevertheless, completeness requires their inclusion. The primary objective is the 'fundamental theorem' on normalization written on page 8. I plan to describe the nonlinear procedures in a subsequent memo and devote a third to laying out algorithms and lines of code, connecting them with equations written in the first two. Originally this was to be done in one short paper, but I jettisoned that approach after its first section exceeded a dozen pages. The organization of this document is as follows. A brief description of notation is followed by a section containing a general treatment of the linear problem. After the 'fundamental theorem' is proved, two further subsections discuss the generation of equilibrium distributions and issue of 'phase'. The final major section reviews parameterizations--that is, lattice functions--in two and four dimensions with a passing glance at the six-dimensional version. Appearances to the contrary, for the most part I have tried to restrict consideration to matters needed to understand the code in CHEF's libraries.

Assessment of the excitelet algorithm for in-situ mechanical characterization of orthotropic structures

Science.gov (United States)

Ostiguy, Pierre-Claude; Quaegebeur, Nicolas; Masson, Patrice

2012-04-01

Damage detection and localization on composites can be impaired by inaccurate knowledge of the mechanical properties of the structure. This paper demonstrates the feasibility of using a chirplet-based correlation technique, called Excitelet, to evaluate the mechanical properties of orthotropic carbon fibre-based composite laminates. The method relies on the identification of an optimal correlation coefficient between measured and simulated dispersed signals measured on a structure using piezoceramic (PZT) transducers. Finite Element Model (FEM) is first conducted to demonstrate the capability of the approach to evaluate the mechanical properties of a composite structure. Experimental validation is then conducted on a unidirectionnal 2.30 mm thick laminate composed of unidirectional plies and a 2.35 mm thick laminate composed of unidirectional plies oriented at [0, 90]4s. Surface bonded PZT transducers were used both for actuation and sensing of guided waves bursts measured at 0° and 90° with respect to upper ply fibre orientation. The characterization is performed at various frequencies below 100 kHz using A0 or S0 modes and comparison with the material properties measured following ASTM standard testing is presented. The results indicate that large correlation coefficients are obtained between the measurements and simulated signals for both A0 and S0 modes when accurate properties are used as inputs for the model. Strategies based on multiple modes correlation are also assessed in order to improve the accuracy of the characterization approach. The results obtained using the proposed approach for the unidirectional plate and most of the results obtained using the proposed approach for the [0, 90]4s laminate are in agreement with the uncertainty associated with ASTM tests results while the proposed method is non destructive and can be performed prior to each imaging processing.

Operator approach to linear control systems

CERN Document Server

Cheremensky, A

1996-01-01

Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and relatively simple principles, and readers with less experience in the field of operator theory will find enough material to give them a good overview of the current state of LQP theory and its applications. Audience: Graduate students and researchers in the fields of mathematical systems theory, operator theory, cybernetics, and control systems.

Improvement of linear reactivity methods and application to long range fuel management

International Nuclear Information System (INIS)

Woehlke, R.A.; Quan, B.L.

1982-01-01

The original development of the linear reactivity theory assumes flat burnup, batch by batch. The validity of this assumption is explored using multicycle burnup data generated with a detailed 3-D SIMULATE model. The results show that the linear reactivity method can be improved by correcting for batchwise power sharing. The application of linear reactivity to long range fuel management is demonstrated in several examples. Correcting for batchwise power sharing improves the accuracy of the analysis. However, with regard to the sensitivity of fuel cost to changes in various parameters, the corrected and uncorrected linear reactivity theories give remarkably similar results

Schwarz maps of algebraic linear ordinary differential equations

Science.gov (United States)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

E11 and the non-linear dual graviton

Science.gov (United States)

Tumanov, Alexander G.; West, Peter

2018-04-01

The non-linear dual graviton equation of motion as well as the duality relation between the gravity and dual gravity fields are found in E theory by carrying out E11 variations of previously found equations of motion. As a result the equations of motion in E theory have now been found at the full non-linear level up to, and including, level three, which contains the dual graviton field. When truncated to contain fields at levels three and less, and the spacetime is restricted to be the familiar eleven dimensional space time, the equations are equivalent to those of eleven dimensional supergravity.

PWR in-core nuclear fuel management optimization utilizing nodal (non-linear NEM) generalized perturbation theory

International Nuclear Information System (INIS)

Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.

1993-01-01

The computational capability of efficiently and accurately evaluate reactor core attributes (i.e., k eff and power distributions as a function of cycle burnup) utilizing a second-order accurate advanced nodal Generalized Perturbation Theory (GPT) model has been developed. The GPT model is derived from the forward non-linear iterative Nodal Expansion Method (NEM) strategy, thereby extending its inherent savings in memory storage and high computational efficiency to also encompass GPT via the preservation of the finite-difference matrix structure. The above development was easily implemented into the existing coarse-mesh finite-difference GPT-based in-core fuel management optimization code FORMOSA-P, thus combining the proven robustness of its adaptive Simulated Annealing (SA) multiple-objective optimization algorithm with a high-fidelity NEM GPT neutronics model to produce a powerful computational tool used to generate families of near-optimum loading patterns for PWRs. (orig.)

Synthesis of models for order-sorted first-order theories using linear algebra and constraint solving

Directory of Open Access Journals (Sweden)

Salvador Lucas

2015-12-01

Full Text Available Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In this setting, Order-Sorted First-Order Logic provides a powerful framework to represent declarative programs. It also provides a target logic to obtain models for other logics via transformations. We investigate the automatic generation of numerical models for order-sorted first-order logics and its use in program analysis, in particular in termination analysis of declarative programs. We use convex domains to give domains to the different sorts of an order-sorted signature; we interpret the ranked symbols of sorted signatures by means of appropriately adapted convex matrix interpretations. Such numerical interpretations permit the use of existing algorithms and tools from linear algebra and arithmetic constraint solving to synthesize the models.

A Hybrid Density Functional Theory/Molecular Mechanics Approach for Linear Response Properties in Heterogeneous Environments.

Science.gov (United States)

Rinkevicius, Zilvinas; Li, Xin; Sandberg, Jaime A R; Mikkelsen, Kurt V; Ågren, Hans

2014-03-11

We introduce a density functional theory/molecular mechanical approach for computation of linear response properties of molecules in heterogeneous environments, such as metal surfaces or nanoparticles embedded in solvents. The heterogeneous embedding environment, consisting from metallic and nonmetallic parts, is described by combined force fields, where conventional force fields are used for the nonmetallic part and capacitance-polarization-based force fields are used for the metallic part. The presented approach enables studies of properties and spectra of systems embedded in or placed at arbitrary shaped metallic surfaces, clusters, or nanoparticles. The capability and performance of the proposed approach is illustrated by sample calculations of optical absorption spectra of thymidine absorbed on gold surfaces in an aqueous environment, where we study how different organizations of the gold surface and how the combined, nonadditive effect of the two environments is reflected in the optical absorption spectrum.

Forms and Linear Network Codes

DEFF Research Database (Denmark)

Hansen, Johan P.

We present a general theory to obtain linear network codes utilizing forms and obtain explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces intersect in the same small dimension. The theory is inspired by the methods of the author utilizing the osculating...... spaces of Veronese varieties. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possibly altered vector space. Ralf Koetter and Frank R. Kschischang introduced a metric on the set af vector spaces and showed that a minimal...... distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The vector spaces in our construction are equidistant in the above metric and the distance between any pair of vector spaces is large making...

Applied linear algebra

CERN Document Server

Olver, Peter J

2018-01-01

This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the un...

Lectures on operator theory and its applications

CERN Document Server

Böttcher, Albrecht; Dritschel, Michael A; Langer, Heinz; Lancaster, Peter

1995-01-01

Much of the importance of mathematics lies in its ability to provide theories which are useful in widely different fields of endeavor. A good example is the large and amorphous body of knowledge known as "the theory of linear operators" or "operator theory", which came to life about a century ago as a theory to encompass properties common to matrix, differential, and integral operators. Thus, it is a primary purpose of operator theory to provide a coherent body of knowledge which can explain phenomena common to the enormous variety of problems in which such linear operators play a part. The th

Linear response coupled cluster theory with the polarizable continuum model within the singles approximation for the solvent response

Science.gov (United States)

Caricato, Marco

2018-04-01

We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.

Linearizing feedforward/feedback attitude control

Science.gov (United States)

Paielli, Russell A.; Bach, Ralph E.

1991-01-01

An approach to attitude control theory is introduced in which a linear form is postulated for the closed-loop rotation error dynamics, then the exact control law required to realize it is derived. The nonminimal (four-component) quaternion form is used to attitude because it is globally nonsingular, but the minimal (three-component) quaternion form is used for attitude error because it has no nonlinear constraints to prevent the rotational error dynamics from being linearized, and the definition of the attitude error is based on quaternion algebra. This approach produces an attitude control law that linearizes the closed-loop rotational error dynamics exactly, without any attitude singularities, even if the control errors become large.

Quasi-linear equation for magnetoplasma oscillations in the weakly relativistic approximation

International Nuclear Information System (INIS)

Rizzato, F.B.

1985-01-01

Some limitations which are present in the dynamical equations for collisionless plasmas are discussed. Some elementary corrections to the linear theories are obtained in a heuristic form, which directly lead to the so-called quasi-linear theories in its non-relativistic and relativistic forms. The effect of the relativistic variation of the gyrofrequency on the diffusion coefficient is examined in a typically perturbative approximation. (author)

Basic linear partial differential equations

CERN Document Server

Treves, Francois

1975-01-01

Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their

Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications

Science.gov (United States)

Wang, Wenjun; Li, Peng; Jin, Feng

2016-09-01

A novel two-dimensional linear elastic theory of magneto-electro-elastic (MEE) plates, considering both surface and nonlocal effects, is established for the first time based on Hamilton’s principle and the Lee plate theory. The equations derived are more general, suitable for static and dynamic analyses, and can also be reduced to the piezoelectric, piezomagnetic, and elastic cases. As a specific application example, the influences of the surface and nonlocal effects, poling directions, piezoelectric phase materials, volume fraction, damping, and applied magnetic field (i.e., constant applied magnetic field and time-harmonic applied magnetic field) on the magnetoelectric (ME) coupling effects are first investigated based on the established two-dimensional plate theory. The results show that the ME coupling coefficient has an obvious size-dependent characteristic owing to the surface effects, and the surface effects increase the ME coupling effects significantly when the plate thickness decreases to its critical thickness. Below this critical thickness, the size-dependent effect is obvious and must be considered. In addition, the output power density of a magnetic energy nanoharvester is also evaluated using the two-dimensional plate theory obtained, with the results showing that a relatively larger output power density can be achieved at the nanoscale. This study provides a mathematical tool which can be used to analyze the mechanical properties of nanostructures theoretically and numerically, as well as evaluating the size effect qualitatively and quantitatively.

Vibration Theory, Vol. 3

DEFF Research Database (Denmark)

Nielsen, Søren R. K.

The present textbook has been written based on previous lecture notes for a course on stochastic vibration theory that is being given on the 9th semester at Aalborg University for M. Sc. students in structural engineering. The present 4th edition of this textbook on linear stochastic vibration th...... theory is unchanged in comparison to the 3rd edition. Only a few errors have been corrected.......The present textbook has been written based on previous lecture notes for a course on stochastic vibration theory that is being given on the 9th semester at Aalborg University for M. Sc. students in structural engineering. The present 4th edition of this textbook on linear stochastic vibration...

Non-linear frequency and amplitude modulation of a nano-contact spin torque oscillator

OpenAIRE

Muduli, P. K.; Pogoryelov, Ye.; Bonetti, S.; Consolo, G.; Mancoff, Fred; Åkerman, Johan

2009-01-01

We study the current controlled modulation of a nano-contact spin torque oscillator. Three principally different cases of frequency non-linearity ($d^{2}f/dI^{2}_{dc}$ being zero, positive, and negative) are investigated. Standard non-linear frequency modulation theory is able to accurately describe the frequency shifts during modulation. However, the power of the modulated sidebands only agrees with calculations based on a recent theory of combined non-linear frequency and amplitude modulation.

Backward stochastic differential equations from linear to fully nonlinear theory

CERN Document Server

Zhang, Jianfeng

2017-01-01

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

On the theory of the two-photon linear photovoltaic effect in n-GaP

Energy Technology Data Exchange (ETDEWEB)

Rasulov, V. R.; Rasulov, R. Ya., E-mail: r-rasulov51@mail.ru [Fergana State University (Uzbekistan)

2016-02-15

A quantitative theory of the diagonal (ballistic) and nondiagonal (shift) band index contributions to the two-photon current of the linear photovoltaic effect in a semiconductor with a complex band due to the asymmetry of events of electron scattering at phonons and photons is developed. It is shown that processes caused by the simultaneous absorption of two photons do not contribute to the ballistic photocurrent in n-GaP. This is due to the fact that, in this case, there is no asymmetric distribution of the momentum of electrons excited with photons; this distribution arises upon the sequential absorption of two photons with the involvement of LO phonons. It is demonstrated that the temperature dependence of the shift contribution to the two-photon photocurrent in n-GaP is determined by the temperature dependence of the light-absorption coefficient caused by direct optical transitions of electrons between subbands X{sub 1} and X{sub 3}. It is shown that the spectral dependence of the photocurrent has a feature in the light frequency range ω → Δ/2ℏ, which is related to the hump-like shape of subband X{sub 1} in n-GaP{sup 1} and the root-type singularity of the state density determined as k{sub ω}{sup -1}= (2ℏω–Δ){sup –1/2}, where Δ is the energy gap between subbands X{sub 1} and X{sub 3}. The spectral and temperature dependences of the coefficient of absorption of linearly polarized light in n-GaP are obtained with regard to the cone-shaped lower subband of the conduction band.

Numerical algebra, matrix theory, differential-algebraic equations and control theory festschrift in honor of Volker Mehrmann

CERN Document Server

Bollhöfer, Matthias; Kressner, Daniel; Mehl, Christian; Stykel, Tatjana

2015-01-01

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on ...

Large magnetic coils-design accompanying calculation and optimization. Regarding orthotropic interlayers, temperature and elastic supports-derivation of a special finite element

International Nuclear Information System (INIS)

Stelzer, J.F.; Sievers, A.; Welzel, R.

1976-10-01

This paper deals with finite element calculations of large coils as they are used as main coils in Tokamaks. They consist of copper layers with glass fibre reinforced resin interlayers inbedded in a strong steel ring. In a first analysis model the several epoxy layers are condensed to only one the tickness of which is equal to the sum of the single sizes. This fictitious layer is assumed to lie in the middle of the copper and is treated as an orthotropic material. In a following changed model the epoxy layer is situated between the steel ring and the copper. In this location the epoxy was suspected to suffer from the highest shear stresses. Both models employ springy trusses as supporting features which simulate the real elastic behaviour of a sustaining vault. Special attentions are given a) to the shear stresses in the epoxy, b) to the hot and cold states of the coils, and c) to the forces transferred from the coils to the sustaining vault. An optimal structure design is carried out concerning the steel ring. (orig./GG) [de

Introduction to optimal control theory

International Nuclear Information System (INIS)

Agrachev, A.A.

2002-01-01

These are lecture notes of the introductory course in Optimal Control theory treated from the geometric point of view. Optimal Control Problem is reduced to the study of controls (and corresponding trajectories) leading to the boundary of attainable sets. We discuss Pontryagin Maximum Principle, basic existence results, and apply these tools to concrete simple optimal control problems. Special sections are devoted to the general theory of linear time-optimal problems and linear-quadratic problems. (author)

Macroscopic and non-linear quantum games

International Nuclear Information System (INIS)

Aerts, D.; D'Hooghe, A.; Posiewnik, A.; Pykacz, J.

2005-01-01

Full text: We consider two models of quantum games. The first one is Marinatto and Weber's 'restricted' quantum game in which only the identity and the spin-flip operators are used. We show that this quantum game allows macroscopic mechanistic realization with the use of a version of the 'macroscopic quantum machine' described by Aerts already in 1980s. In the second model we use non-linear quantum state transformations which operate on points of spin-1/2 on the Bloch sphere and which can be used to distinguish optimally between two non-orthogonal states. We show that efficiency of these non-linear strategies out-perform any linear ones. Some hints on the possible theory of non-linear quantum games are given. (author)

Supersymmetry breaking in the linear representation of the dilaton

International Nuclear Information System (INIS)

Gaida, I.

1995-01-01

String effective theories with N=1 supersymmetry in 4 dimensions are subject of the discussion. These theories are effective in the sense, that they are low-energy limits of a given higher dimensional string theory after dimensional reduction and integrating out all heavy modes. At tree level the gauge coupling constant can be expressed by the vacuum expectation value of the dilaton superfield S:g 2 =2 -1 . Throughout this text S+ anti S will be denoted as the chiral representation of the dilaton. It has been shown that there exists a supersymmetric legendre transformation called supersymmetric duality, which transforms S+ anti S into a linear superfield L, where L will be called the linear representation of the dilaton. (orig.)

On the interaction of small-scale linear waves with nonlinear solitary waves

Science.gov (United States)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow

Local and linear chemical reactivity response functions at finite temperature in density functional theory

International Nuclear Information System (INIS)

Franco-Pérez, Marco; Ayers, Paul W.; Gázquez, José L.; Vela, Alberto

2015-01-01

We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model

Effect of liquid surface tension on circular and linear hydraulic jumps; theory and experiments

Science.gov (United States)

Bhagat, Rajesh Kumar; Jha, Narsing Kumar; Linden, Paul F.; Wilson, David Ian

2017-11-01

The hydraulic jump has attracted considerable attention since Rayleigh published his account in 1914. Watson (1964) proposed the first satisfactory explanation of the circular hydraulic jump by balancing the momentum and hydrostatic pressure across the jump, but this solution did not explain what actually causes the jump to form. Bohr et al. (1992) showed that the hydraulic jump happens close to the point where the local Froude number equals to one, suggesting a balance between inertial and hydrostatic contributions. Bush & Aristoff (2003) subsequently incorporated the effect of surface tension and showed that this is important when the jump radius is small. In this study, we propose a new account to explain the formation and evolution of hydraulic jumps under conditions where the jump radius is strongly influenced by the liquid surface tension. The theory is compared with experiments employing liquids of different surface tension and different viscosity, in circular and linear configurations. The model predictions and the experimental results show excellent agreement. Commonwealth Scholarship Commission, St. John's college, University of Cambridge.

Linear feedback controls the essentials

CERN Document Server

Haidekker, Mark A

2013-01-01

The design of control systems is at the very core of engineering. Feedback controls are ubiquitous, ranging from simple room thermostats to airplane engine control. Helping to make sense of this wide-ranging field, this book provides a new approach by keeping a tight focus on the essentials with a limited, yet consistent set of examples. Analysis and design methods are explained in terms of theory and practice. The book covers classical, linear feedback controls, and linear approximations are used when needed. In parallel, the book covers time-discrete (digital) control systems and juxtapos

Generalized, Linear, and Mixed Models

CERN Document Server

McCulloch, Charles E; Neuhaus, John M

2011-01-01

An accessible and self-contained introduction to statistical models-now in a modernized new editionGeneralized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various construction, application, and computational aspects.A clear introduction to the basic ideas of fixed effects models, random effects models, and mixed m

Non-linear analytic and coanalytic problems (Lp-theory, Clifford analysis, examples)

International Nuclear Information System (INIS)

Dubinskii, Yu A; Osipenko, A S

2000-01-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the 'orthogonal' sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented

Spin and diamagnetism in linear and nonlinear optics

International Nuclear Information System (INIS)

Andersen, Torsten; Keller, Ole; Huebner, Wolfgang; Johansson, Boerje

2004-01-01

We present a local-field theory for spin and diamagnetism in linear and nonlinear optics. We examine all the processes contained in the Pauli Hamiltonian and its corresponding microscopic current density, including the terms depending on the electron spin. The resulting general real-space conductivities are presented and discussed. To quantify the implications of including the spin, we study the linear and nonlinear optical properties of free-electron metals, represented by the screened homogeneous electron gas. The real-space formalism is transformed into Fourier space, and the symmetries of the linear and nonlinear optical conductivities in a homogeneous electron gas are discussed. Numerical results are presented for the homogeneous electron gas, in which we treat ω and q as independent variables, thereby opening the theory to near-field optics and the study of evanescent waves. We show that in regions of the ω-q spectrum, the presence of diamagnetism and spin dynamics significantly alters the response in comparison to considering only the paramagnetic response. Additionally, we discuss the effects of screening, and we finish our treatment by a discussion of how to connect the present theory to existing methods in ab initio solid-state physics

JET VELOCITY OF LINEAR SHAPED CHARGES

Directory of Open Access Journals (Sweden)

Vječislav Bohanek

2012-12-01

Full Text Available Shaped explosive charges with one dimension significantly larger than the other are called linear shaped charges. Linear shaped charges are used in various industries and are applied within specific technologies for metal cutting, such as demolition of steel structures, separating spent rocket fuel tanks, demining, cutting holes in the barriers for fire service, etc. According to existing theories and models efficiency of linear shaped charges depends on the kinetic energy of the jet which is proportional to square of jet velocity. The original method for measuring velocity of linear shaped charge jet is applied in the aforementioned research. Measurements were carried out for two different linear materials, and the results are graphically presented, analysed and compared. Measurement results show a discrepancy in the measured velocity of the jet for different materials with the same ratio between linear and explosive mass (M/C per unit of surface, which is not described by presented models (the paper is published in Croatian.

Screening sensitivity theory

International Nuclear Information System (INIS)

Oblow, E.M.; Perey, F.G.

1984-01-01

A comprehensive rigorous theory is developed for screening sensitivity coefficients in largescale modeling applications. The theory uses Bayesian inference and group theory to establish a probabilistic framework for solving an underdetermined system of linear equations. The underdetermined problem is directly related to statistical screening sensitivity theory as developed in recent years. Several examples of the new approach to screening are worked out in detail and comparisons are made with statistical approaches to the problem. The drawbacks of these latter methods are discussed at some length

Heterogeneous dissipative composite structures

Science.gov (United States)

Ryabov, Victor; Yartsev, Boris; Parshina, Ludmila

2018-05-01

The paper suggests mathematical models of decaying vibrations in layered anisotropic plates and orthotropic rods based on Hamilton variation principle, first-order shear deformation laminated plate theory (FSDT), as well as on the viscous-elastic correspondence principle of the linear viscoelasticity theory. In the description of the physical relationships between the materials of the layers forming stiff polymeric composites, the effect of vibration frequency and ambient temperature is assumed as negligible, whereas for the viscous-elastic polymer layer, temperature-frequency relationship of elastic dissipation and stiffness properties is considered by means of the experimentally determined generalized curves. Mitigation of Hamilton functional makes it possible to describe decaying vibration of anisotropic structures by an algebraic problem of complex eigenvalues. The system of algebraic equation is generated through Ritz method using Legendre polynomials as coordinate functions. First, real solutions are found. To find complex natural frequencies of the system, the obtained real natural frequencies are taken as input values, and then, by means of the 3rd order iteration method, complex natural frequencies are calculated. The paper provides convergence estimates for the numerical procedures. Reliability of the obtained results is confirmed by a good correlation between analytical and experimental values of natural frequencies and loss factors in the lower vibration tones for the two series of unsupported orthotropic rods formed by stiff GRP and CRP layers and a viscoelastic polymer layer. Analysis of the numerical test data has shown the dissipation & stiffness properties of heterogeneous composite plates and rods to considerably depend on relative thickness of the viscoelastic polymer layer, orientation of stiff composite layers, vibration frequency and ambient temperature.

Lincx: A Linear Logical Framework with First-class Contexts

DEFF Research Database (Denmark)

Linn Georges, Aina; Murawska, Agata; Otis, Shawn

2017-01-01

Linear logic provides an elegant framework for modelling stateful, imperative and concurrent systems by viewing a context of assumptions as a set of resources. However, mechanizing the meta-theory of such systems remains a challenge, as we need to manage and reason about mixed contexts of linear...

Linearization: Geometric, Complex, and Conditional

Directory of Open Access Journals (Sweden)

Asghar Qadir

2012-01-01

Full Text Available Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it, and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory, are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.

Solution of generalized shifted linear systems with complex symmetric matrices

International Nuclear Information System (INIS)

Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo

2012-01-01

We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green’s function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1–9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126–140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.

Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules

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Katy L. Chubb

2018-04-01

Full Text Available A numerical application of linear-molecule symmetry properties, described by the D ∞ h point group, is formulated in terms of lower-order symmetry groups D n h with finite n. Character tables and irreducible representation transformation matrices are presented for D n h groups with arbitrary n-values. These groups can subsequently be used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of “reduced” vibrational eigenvalue problems with simplified Hamiltonians is used as a practical example. It is shown how the solutions of these eigenvalue problems can also be extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ of the vibrational angular momentum operator L ^ z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D n h . 12 C 2 H 2 is used as an example of a linear molecule of D ∞ h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE.

Linear and Nonlinear Finite Elements.

Science.gov (United States)

1983-12-01

Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y𔃾 , (1-y𔃼)’ 1-y’ 2 - y" (6) that change eq. (5) to V𔃺) = , [yŖ(1 + y") - Qy𔃼

Linear network error correction coding

CERN Document Server

Guang, Xuan

2014-01-01

There are two main approaches in the theory of network error correction coding. In this SpringerBrief, the authors summarize some of the most important contributions following the classic approach, which represents messages by sequences?similar to algebraic coding,?and also briefly discuss the main results following the?other approach,?that uses the theory of rank metric codes for network error correction of representing messages by subspaces. This book starts by establishing the basic linear network error correction (LNEC) model and then characterizes two equivalent descriptions. Distances an

A new active absorption system and its performance to linear and non-linear waves

DEFF Research Database (Denmark)

Andersen, Thomas Lykke; Clavero, M.; Frigaard, Peter Bak

2016-01-01

Highlights •An active absorption system for wavemakers has been developed. •The theory for flush mounted gauges has been extended to cover also small gaps. •The new system has been validated in a wave flume with wavemakers in both ends. •A generation and absorption procedure for highly non-linear...

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

International Nuclear Information System (INIS)

Anjomshoa, Amin; Tahani, Masoud

2016-01-01

In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded ortho tropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.

Linear causal modeling with structural equations

CERN Document Server

Mulaik, Stanley A

2009-01-01

Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal

Influence of Orthotropy on Biomechanics of Peri-Implant Bone in Complete Mandible Model with Full Dentition

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Xi Ding

2014-01-01

Full Text Available Objective. The study was to investigate the impact of orthotropic material on the biomechanics of dental implant, based on a detailed mandible with high geometric and mechanical similarity. Materials and Methods. Multiple data sources were used to elaborate detailed biological structures and implant CAD models. In addition, an extended orthotropic material assignment methodology based on harmonic fields was used to handle the alveolar ridge region to generate compatible orthotropic fields. The influence of orthotropic material was compared with the commonly used isotropic model and simplified orthotropic model. Results. The simulation results showed that the values of stress and strain on the implant-bone interface almost increased in the orthotropic model compared to the isotropic case, especially for the cancellous bone. However, the local stress concentration was more obvious in the isotropic case compared to that in orthotropic case. The simple orthotropic model revealed irregular stress and strain distribution, compared to the isotropic model and the real orthotropic model. The influence of orthotropy was little on the implant, periodontal ligament, tooth enamel, and dentin. Conclusion. The orthotropic material has significant effect on stress and strain of implant-bone interface in the mandible, compared with the isotropic simulation. Real orthotropic mechanical properties of mandible should be emphasized in biomechanical studies of dental implants.

Transition operators in electromagnetic-wave diffraction theory - General theory

Science.gov (United States)

Hahne, G. E.

1992-01-01

A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.