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.

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.

The Theory of Linear Prediction

CERN Document Server

Vaidyanathan, PP

2007-01-01

Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vecto

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....

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

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

Science.gov (United States)

Antown, Fadi; Dragičević, Davor; Froyland, Gary

2018-03-01

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

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

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 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.

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 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.

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.

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.

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.

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...

Linear response at the 4-component relativistic level

DEFF Research Database (Denmark)

Saue, T.; Jensen, Hans Jørgen Aagaard

2003-01-01

The theory, implementation, and application of linear response at the 4-component relativistic closed-shell Hartree-Fock level based on the concept of quasienergy and time averaging are reported. As such, an efficient AO-driven algorithm is obtained by assigning specific Hermiticity and time...

Theory of orbital magnetoelectric response

International Nuclear Information System (INIS)

Malashevich, Andrei; Souza, Ivo; Coh, Sinisa; Vanderbilt, David

2010-01-01

We extend the recently developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric (ME) response of periodic insulators. Working in the independent-particle framework, we find that the finite-field orbital magnetization can be written as a sum of three gauge-invariant contributions, one of which has no counterpart at zero field. The extra contribution is collinear with and explicitly dependent on the electric field. The expression for the orbital magnetization is suitable for first-principles implementations, allowing one to calculate the ME response coefficients by numerical differentiation. Alternatively, perturbation-theory techniques may be used, and for that purpose we derive an expression directly for the linear ME tensor by taking the first field-derivative analytically. Two types of terms are obtained. One, the 'Chern-Simons' term, depends only on the unperturbed occupied orbitals and is purely isotropic. The other, 'Kubo' terms, involve the first-order change in the orbitals and give isotropic as well as anisotropic contributions to the response. In ordinary ME insulators all terms are generally present, while in strong Z 2 topological insulators only the Chern-Simons term is allowed, and is quantized. In order to validate the theory, we have calculated under periodic boundary conditions the linear ME susceptibility for a 3D tight-binding model of an ordinary ME insulator, using both the finite-field and perturbation-theory expressions. The results are in excellent agreement with calculations on bounded samples.

Dynamic Response Analysis of Linear Pulse Motor with Closed Loop Control

OpenAIRE

山本, 行雄; 山田, 一

1989-01-01

A linear pulse motor can translate digital signals into linear positions without a gear system. It is important to predict a dynamic response in order to the motor that has the good performance. In this report the maximum pulse rate and the maximum speed on the linear pulse motor are obtained by using the sampling theory.

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.

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.

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.

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

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.

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

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.

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.

The nuclear response in extended RPA theories

International Nuclear Information System (INIS)

Wambach, J.

1991-01-01

Linear response theories for small-amplitude nuclear motion are discussed. A review is given of the Random-Phase-Approximation and its successes and shortcomings are pointed out. Systematic improvements are presented which include two-particle two-hole excitations and account for dissipative effects due to binary collisions of nucleons in the mean field. These improved theories describe inelastic scattering experiments satisfactorily over a wide kinematical range. (author)

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.

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

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 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.

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

Lead-lag relationships between stock and market risk within linear response theory

Science.gov (United States)

Borysov, Stanislav; Balatsky, Alexander

2015-03-01

We study historical correlations and lead-lag relationships between individual stock risks (standard deviation of daily stock returns) and market risk (standard deviation of daily returns of a market-representative portfolio) in the US stock market. We consider the cross-correlation functions averaged over stocks, using historical stock prices from the Standard & Poor's 500 index for 1994-2013. The observed historical dynamics suggests that the dependence between the risks was almost linear during the US stock market downturn of 2002 and after the US housing bubble in 2007, remaining at that level until 2013. Moreover, the averaged cross-correlation function often had an asymmetric shape with respect to zero lag in the periods of high correlation. We develop the analysis by the application of the linear response formalism to study underlying causal relations. The calculated response functions suggest the presence of characteristic regimes near financial crashes, when individual stock risks affect market risk and vice versa. This work was supported by VR 621-2012-2983.

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....

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.

Generalizability theory and item response theory

OpenAIRE

Glas, Cornelis A.W.; Eggen, T.J.H.M.; Veldkamp, B.P.

2012-01-01

Item response theory is usually applied to items with a selected-response format, such as multiple choice items, whereas generalizability theory is usually applied to constructed-response tasks assessed by raters. However, in many situations, raters may use rating scales consisting of items with a selected-response format. This chapter presents a short overview of how item response theory and generalizability theory were integrated to model such assessments. Further, the precision of the esti...

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

Transition to Coherence in Populations of Coupled Chaotic Oscillators: A Linear Response Approach

International Nuclear Information System (INIS)

Topaj, Dmitri; Kye, Won-Ho; Pikovsky, Arkady

2001-01-01

We consider the collective dynamics in an ensemble of globally coupled chaotic maps. The transition to the coherent state with a macroscopic mean field is analyzed in the framework of the linear response theory. The linear response function for the chaotic system is obtained using the perturbation approach to the Frobenius-Perron operator. The transition point is defined from this function by virtue of the self-excitation condition for the feedback loop. Analytical results for the coupled Bernoulli maps are confirmed by the numerics

Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

Science.gov (United States)

Camporesi, Roberto

2011-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

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)

Evaluating and interpreting the chemical relevance of the linear response kernel for atoms II: open shell.

Science.gov (United States)

Boisdenghien, Zino; Fias, Stijn; Van Alsenoy, Christian; De Proft, Frank; Geerlings, Paul

2014-07-28

Most of the work done on the linear response kernel χ(r,r') has focussed on its atom-atom condensed form χAB. Our previous work [Boisdenghien et al., J. Chem. Theory Comput., 2013, 9, 1007] was the first effort to truly focus on the non-condensed form of this function for closed (sub)shell atoms in a systematic fashion. In this work, we extend our method to the open shell case. To simplify the plotting of our results, we average our results to a symmetrical quantity χ(r,r'). This allows us to plot the linear response kernel for all elements up to and including argon and to investigate the periodicity throughout the first three rows in the periodic table and in the different representations of χ(r,r'). Within the context of Spin Polarized Conceptual Density Functional Theory, the first two-dimensional plots of spin polarized linear response functions are presented and commented on for some selected cases on the basis of the atomic ground state electronic configurations. Using the relation between the linear response kernel and the polarizability we compare the values of the polarizability tensor calculated using our method to high-level values.

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.

Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

Science.gov (United States)

Silva, Walter A.

1993-01-01

A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

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.

A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

Science.gov (United States)

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

Generalizability theory and item response theory

NARCIS (Netherlands)

Glas, Cornelis A.W.; Eggen, T.J.H.M.; Veldkamp, B.P.

2012-01-01

Item response theory is usually applied to items with a selected-response format, such as multiple choice items, whereas generalizability theory is usually applied to constructed-response tasks assessed by raters. However, in many situations, raters may use rating scales consisting of items with a

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.

Linear and non-linear infrared response of one-dimensional vibrational Holstein polarons in the anti-adiabatic limit: Optical and acoustical phonon models

Science.gov (United States)

Falvo, Cyril

2018-02-01

The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.

Density and spin linear response of atomic Fermi superfluids with population imbalance in the BCS–BEC crossover

International Nuclear Information System (INIS)

Guo, Hao; Li, Yang; He, Yan; Chien, Chih-Chun

2014-01-01

We present a theoretical study of the density and spin (representing the two components) linear response of Fermi superfluids with tunable attractive interactions and population imbalance. In both linear response theories, we find that the fluctuations of the order parameter must be treated on equal footing with the gauge transformations associated with the symmetries of the Hamiltonian so that important constraints including various sum rules can be satisfied. Both theories can be applied to the whole BCS–Bose–Einstein condensation crossover. The spin linear responses are qualitatively different with and without population imbalance because collective-mode effects from the fluctuations of the order parameter survive in the presence of population imbalance, even though the associated symmetry is not broken by the order parameter. Since a polarized superfluid becomes unstable at low temperatures in the weak and intermediate coupling regimes, we found that the density and spin susceptibilities diverge as the system approaches the unstable regime, but the emergence of phase separation preempts the divergence. (paper)

Competitive inhibition can linearize dose-response and generate a linear rectifier.

Science.gov (United States)

Savir, Yonatan; Tu, Benjamin P; Springer, Michael

2015-09-23

Many biological responses require a dynamic range that is larger than standard bi-molecular interactions allow, yet the also ability to remain off at low input. Here we mathematically show that an enzyme reaction system involving a combination of competitive inhibition, conservation of the total level of substrate and inhibitor, and positive feedback can behave like a linear rectifier-that is, a network motif with an input-output relationship that is linearly sensitive to substrate above a threshold but unresponsive below the threshold. We propose that the evolutionarily conserved yeast SAGA histone acetylation complex may possess the proper physiological response characteristics and molecular interactions needed to perform as a linear rectifier, and we suggest potential experiments to test this hypothesis. One implication of this work is that linear responses and linear rectifiers might be easier to evolve or synthetically construct than is currently appreciated.

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.

Linear response in stochastic mean-field theories and the onset of instabilities

International Nuclear Information System (INIS)

Colonna, M.; Chomaz, Ph.

1993-01-01

The small amplitude response of stochastic one-body theories, such as the Boltzmann-Langevin approach is studied. Whereas the two-time correlation function only describes the propagation of fluctuations initially present, the equal-time correlation function is related to the source of stochasticity. For stable systems it yields the Einstein relation, while for unstable systems it determines the growth of the instabilities. These features are illustrated for unstable nuclear matter in two dimensions. (author) 14 refs.; 5 figs

Finite orbit energetic particle linear response to toroidal Alfven eigenmodes

International Nuclear Information System (INIS)

Berk, H.L.; Ye Huanchun; Breizman, B.N.

1992-01-01

The linear response of energetic particles of the TAE modes is calculated taking into account their finite orbit excursion from the flux surfaces. The general expression reproduces the previously derived theory for small banana width; when the banana width Δ b is much larger than the mode thickness Δ m , we obtain a new compact expression for the linear power transfer. When Δ m /Δ b m /Δ b from that predicted by the narrow orbit theory. A comparison is made of the contribution to the TAE growth rate of energetic particles with a slowing-down distribution arising from an isotropic source, and a balanced-injected beam source when the source speed is close to the Alfven speed. For the same stored energy density, the contribution from the principal resonances (vertical strokev parallel vertical stroke=v A ) is substantially enhanced in the beam case compared to the isotropic case, while the contribution at the higher sidebands (vertical strokev parallel vertical stroke=v A /(2l-1) with l≥2) is substantially reduced. (orig.)

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.

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.

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...

Polarizable embedding with a multiconfiguration short-range density functional theory linear response method

DEFF Research Database (Denmark)

Hedegård, Erik D.; Olsen, Jógvan Magnus Haugaard; Knecht, Stefan

2015-01-01

. To demonstrate the capabilities of PE-MC-srDFT, we also investigated the retinylidene Schiff base chromophore embedded in the channelrhodopsin protein. While using a much more compact reference wave function in terms of active space, our PE-MC-srDFT approach yields excitation energies comparable in quality......We present here the coupling of a polarizable embedding (PE) model to the recently developed multiconfiguration short-range density functional theory method (MC-srDFT), which can treat multiconfigurational systems with a simultaneous account for dynamical and static correlation effects. PE......-MC-srDFT is designed to combine efficient treatment of complicated electronic structures with inclusion of effects from the surrounding environment. The environmental effects encompass classical electrostatic interactions as well as polarization of both the quantum region and the environment. Using response theory...

Linear response theory for long-range interacting systems in quasistationary states.

Science.gov (United States)

Patelli, Aurelio; Gupta, Shamik; Nardini, Cesare; Ruffo, Stefano

2012-02-01

Long-range interacting systems, while relaxing to equilibrium, often get trapped in long-lived quasistationary states which have lifetimes that diverge with the system size. In this work, we address the question of how a long-range system in a quasistationary state (QSS) responds to an external perturbation. We consider a long-range system that evolves under deterministic Hamilton dynamics. The perturbation is taken to couple to the canonical coordinates of the individual constituents. Our study is based on analyzing the Vlasov equation for the single-particle phase-space distribution. The QSS represents a stable stationary solution of the Vlasov equation in the absence of the external perturbation. In the presence of small perturbation, we linearize the perturbed Vlasov equation about the QSS to obtain a formal expression for the response observed in a single-particle dynamical quantity. For a QSS that is homogeneous in the coordinate, we obtain an explicit formula for the response. We apply our analysis to a paradigmatic model, the Hamiltonian mean-field model, which involves particles moving on a circle under Hamiltonian dynamics. Our prediction for the response of three representative QSSs in this model (the water-bag QSS, the Fermi-Dirac QSS, and the Gaussian QSS) is found to be in good agreement with N-particle simulations for large N. We also show the long-time relaxation of the water-bag QSS to the Boltzmann-Gibbs equilibrium state. © 2012 American Physical Society

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.

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.

A Fresh Look at Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

Science.gov (United States)

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

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

Finite orbit energetic particle linear response to toroidal Alfven eigenmodes

International Nuclear Information System (INIS)

Berk, H.L.; Ye, Huanchun; Breizman, B.N.

1991-07-01

The linear response of energetic particles to the TAE modes is calculated taking into account their finite orbit excursion from the flux surfaces. The general expression reproduces the previously derived theory for small banana width: when the banana width triangle b is much larger than the mode thickness triangle m , we obtain a new compact expression for the linear power transfer. When triangle m /triangle b much-lt 1, the banana orbit effect reduces the power transfer by a factor of triangle m /triangle b from that predicted by the narrow orbit theory. A comparison is made of the contribution to the TAE growth rate of energetic particles with a slowing-down distribution arising from an isotropic source, and a balance-injected beam source when the source speed is close to the Alfven speed. For the same stored energy density, the contribution from the principal resonances (|υ parallel | = υ A is substantially enhanced in the beam case compared to the isotropic case, while the contribution at the higher sidebands (|υ parallel |) = υ A /(2 ell - 1) with ell ≥ 2) is substantially reduced. 10 refs

New computational method for non-LTE, the linear response matrix

International Nuclear Information System (INIS)

Fournier, K.B.; Grasiani, F.R.; Harte, J.A.; Libby, S.B.; More, R.M.; Zimmerman, G.B.

1998-01-01

My coauthors have done extensive theoretical and computational calculations that lay the ground work for a linear response matrix method to calculate non-LTE (local thermodynamic equilibrium) opacities. I will give briefly review some of their work and list references. Then I will describe what has been done to utilize this theory to create a computational package to rapidly calculate mild non-LTE emission and absorption opacities suitable for use in hydrodynamic calculations. The opacities are obtained by performing table look-ups on data that has been generated with a non-LTE package. This scheme is currently under development. We can see that it offers a significant computational speed advantage. It is suitable for mild non-LTE, quasi-steady conditions. And it offers a new insertion path for high-quality non-LTE data. Currently, the linear response matrix data file is created using XSN. These data files could be generated by more detailed and rigorous calculations without changing any part of the implementation in the hydro code. The scheme is running in Lasnex and is being tested and developed

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.

Lanczos-driven coupled-cluster damped linear response theory for molecules in polarizable environments

DEFF Research Database (Denmark)

List, Nanna Holmgaard; Coriani, Sonia; Kongsted, Jacob

2014-01-01

are specifically motivated by a twofold aim: (i) computation of core excitations in realistic surroundings and (ii) examination of the effect of the differential response of the environment upon excitation solely related to the CC multipliers (herein denoted the J matrix) in computations of excitation energies......We present an extension of a previously reported implementation of a Lanczos-driven coupled-cluster (CC) damped linear response approach to molecules in condensed phases, where the effects of a surrounding environment are incorporated by means of the polarizable embedding formalism. We...... and transition moments of polarizable-embedded molecules. Numerical calculations demonstrate that the differential polarization of the environment due to the first-order CC multipliers provides only minor contributions to the solvatochromic shift for all transitions considered. We thus complement previous works...

Excitation energies with linear response density matrix functional theory along the dissociation coordinate of an electron-pair bond in N-electron systems

International Nuclear Information System (INIS)

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

2014-01-01

Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ω α and oscillator strengths f α for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ω α (R) curves along the bond dissociation coordinate R for the molecules LiH, Li 2 , and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate

Kovacs effect in the one-dimensional Ising model: A linear response analysis

Science.gov (United States)

Ruiz-García, M.; Prados, A.

2014-01-01

We analyze the so-called Kovacs effect in the one-dimensional Ising model with Glauber dynamics. We consider small enough temperature jumps, for which a linear response theory has been recently derived. Within this theory, the Kovacs hump is directly related to the monotonic relaxation function of the energy. The analytical results are compared with extensive Monte Carlo simulations, and an excellent agreement is found. Remarkably, the position of the maximum in the Kovacs hump depends on the fact that the true asymptotic behavior of the relaxation function is different from the stretched exponential describing the relevant part of the relaxation at low temperatures.

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

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...

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

The mathematical structure of the approximate linear response relation

International Nuclear Information System (INIS)

Yasuda, Muneki; Tanaka, Kazuyuki

2007-01-01

In this paper, we study the mathematical structures of the linear response relation based on Plefka's expansion and the cluster variation method in terms of the perturbation expansion, and we show how this linear response relation approximates the correlation functions of the specified system. Moreover, by comparing the perturbation expansions of the correlation functions estimated by the linear response relation based on these approximation methods with exact perturbative forms of the correlation functions, we are able to explain why the approximate techniques using the linear response relation work well

On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series

Science.gov (United States)

Gottwald, Georg A.; Wormell, J. P.; Wouters, Jeroen

2016-09-01

Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model of the observations, based on results for central limit theorems for deterministic dynamical systems, and used to detect linear response breakdown. We apply the method to discrete maps which do not obey linear response and show that the successful detection of breakdown depends on the length of the time series, the magnitude of the perturbation and on the choice of the observable. We find that in order to reliably reject the assumption of linear response for typical observables sufficiently large data sets are needed. Even for simple systems such as the logistic map, one needs of the order of 106 observations to reliably detect the breakdown with a confidence level of 95 %; if less observations are available one may be falsely led to conclude that linear response theory is valid. The amount of data required is larger the smaller the applied perturbation. For judiciously chosen observables the necessary amount of data can be drastically reduced, but requires detailed a priori knowledge about the invariant measure which is typically not available for complex dynamical systems. Furthermore we explore the use of the fluctuation-dissipation theorem (FDT) in cases with limited data length or coarse-graining of observations. The FDT, if applied naively to a system without linear response, is shown to be very sensitive to the details of the sampling method, resulting in erroneous predictions of the response.

Electromagnetic response in kinetic energy driven cuprate superconductors: Linear response approach

International Nuclear Information System (INIS)

Krzyzosiak, Mateusz; Huang, Zheyu; Feng, Shiping; Gonczarek, Ryszard

2010-01-01

Within the framework of the kinetic energy driven superconductivity, the electromagnetic response in cuprate superconductors is studied in the linear response approach. The kernel of the response function is evaluated and employed to calculate the local magnetic field profile, the magnetic field penetration depth, and the superfluid density, based on the specular reflection model for a purely transverse vector potential. It is shown that the low temperature magnetic field profile follows an exponential decay at the surface, while the magnetic field penetration depth depends linearly on temperature, except for the strong deviation from the linear characteristics at extremely low temperatures. The superfluid density is found to decrease linearly with decreasing doping concentration in the underdoped regime. The problem of gauge invariance is addressed and an approximation for the dressed current vertex, which does not violate local charge conservation is proposed and discussed.

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

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.

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...

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)

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)

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.

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.

Nano-resonator frequency response based on strain gradient theory

International Nuclear Information System (INIS)

Miandoab, Ehsan Maani; Yousefi-Koma, Aghil; Pishkenari, Hossein Nejat; Fathi, Mohammad

2014-01-01

This paper aims to explore the dynamic behaviour of a nano-resonator under ac and dc excitation using strain gradient theory. To achieve this goal, the partial differential equation of nano-beam vibration is first converted to an ordinary differential equation by the Galerkin projection method and the lumped model is derived. Lumped parameters of the nano-resonator, such as linear and nonlinear springs and damper coefficients, are compared with those of classical theory and it is demonstrated that beams with smaller thickness display greater deviation from classical parameters. Stable and unstable equilibrium points based on classic and non-classical theories are also compared. The results show that, regarding the applied dc voltage, the dynamic behaviours expected by classical and non-classical theories are significantly different, such that one theory predicts the un-deformed shape as the stable condition, while the other theory predicts that the beam will experience bi-stability. To obtain the frequency response of the nano-resonator, a general equation including cubic and quadratic nonlinearities in addition to parametric electrostatic excitation terms is derived, and the analytical solution is determined using a second-order multiple scales method. Based on frequency response analysis, the softening and hardening effects given by two theories are investigated and compared, and it is observed that neglecting the size effect can lead to two completely different predictions in the dynamic behaviour of the resonators. The findings of this article can be helpful in the design and characterization of the size-dependent dynamic behaviour of resonators on small scales. (paper)

Non-linear stochastic response of a shallow cable

DEFF Research Database (Denmark)

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

2004-01-01

The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two...

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.

Lieb-Robinson bounds for multi-commutators and applications to response theory

CERN Document Server

Bru, J -B

2017-01-01

Lieb-Robinson bounds for multi-commutators are effective mathematical tools to handle analytic aspects of infinite volume dynamics of non-relativistic quantum particles with short-range, possibly time-dependent interactions. In particular, the existence of fundamental solutions is shown for those (non-autonomous) C*-dynamical systems for which the usual conditions found in standard theories of (parabolic or hyperbolic) non-autonomous evolution equations are not given. In mathematical physics, bounds on multi-commutators of an order higher than two can be used to study linear and non-linear responses of interacting particles to external perturbations. These bounds are derived for lattice fermions, in view of applications to microscopic quantum theory of electrical conduction discussed in this book. All results also apply to quantum spin systems, with obvious modifications. In order to make the results accessible to a wide audience, in particular to students in mathematics with little Physics background, basics...

Non-linear dynamic response of reactor containment

International Nuclear Information System (INIS)

Takemori, T.; Sotomura, K.; Yamada, M.

1975-01-01

A computer program was developed to investigate the elasto-plastic behavior of structures. This program is outlined and the problems of non-linear response of structures are discussed. Since the mode superposition method is only valid in an elastic analysis, the direct integration method was adopted here. As the sample model, an actual reactor containment (reactor building) of PWR plant was adopted. This building consists of three components, that is, a concrete internal structure, a steel containment vessel and a concrete outer shield wall. These components are resting on a rigid foundation mat. Therefore they were modeled with a lumped mass model respectively and coupled on the foundation. The following assumptions were employed to establish the properties of dynamic model: rocking and swaying springs of soil can be obtained from an elastic half-space solution, and the hysteretic characteristic of springs is bi-linear; springs connecting each mass are dealt with shear beams so that both bending and shear deflections can be included (Hysteretic characteristics of springs are linear, bi-linear and tri-linear for the internal structure, the containment vessel and the outer shield wall, respectively); generally, each damping coefficient is given for each mode in modal superposition (However, a damping matrix must be made directly in a non-linear response). Therefore the damping matrix of the model was made by combining the damping matrices [C] of each component obtained by Caughy's method and a damping value of the rocking and swaying by the half-space solution. On the basis of above conditions, the non-linear response of the structure was obtained and the difference between elastic and elasto-plastic analysis is presented

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.

Linear response calculation using the canonical-basis TDHFB with a schematic pairing functional

International Nuclear Information System (INIS)

Ebata, Shuichiro; Nakatsukasa, Takashi; Yabana, Kazuhiro

2011-01-01

A canonical-basis formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory is obtained with an approximation that the pair potential is assumed to be diagonal in the time-dependent canonical basis. The canonical-basis formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even nuclei. E1 strength distributions for proton-rich Mg isotopes are systematically calculated. The calculation suggests strong Landau damping of giant dipole resonance for drip-line nuclei.

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.

Excited-state absorption in tetrapyridyl porphyrins: comparing real-time and quadratic-response time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Bowman, David N. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Asher, Jason C. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Fischer, Sean A. [William R. Wiley Environmental Molecular Sciences Laboratory; Pacific Northwest National Laboratory; P.O. Box 999; Richland; USA; Cramer, Christopher J. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Govind, Niranjan [William R. Wiley Environmental Molecular Sciences Laboratory; Pacific Northwest National Laboratory; P.O. Box 999; Richland; USA

2017-01-01

Threemeso-substituted tetrapyridyl porphyrins (free base, Ni(ii), and Cu(ii)) were investigated for their optical limiting (OL) capabilities using real-time (RT-), linear-response (LR-), and quadratic-response (QR-) time-dependent density functional theory (TDDFT) methods.

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

Responsive linear-dendritic block copolymers.

Science.gov (United States)

Blasco, Eva; Piñol, Milagros; Oriol, Luis

2014-06-01

The combination of dendritic and linear polymeric structures in the same macromolecule opens up new possibilities for the design of block copolymers and for applications of functional polymers that have self-assembly properties. There are three main strategies for the synthesis of linear-dendritic block copolymers (LDBCs) and, in particular, the emergence of click chemistry has made the coupling of preformed blocks one of the most efficient ways of obtaining libraries of LDBCs. In these materials, the periphery of the dendron can be precisely functionalised to obtain functional LDBCs with self-assembly properties of interest in different technological areas. The incorporation of stimuli-responsive moieties gives rise to smart materials that are generally processed as self-assemblies of amphiphilic LDBCs with a morphology that can be controlled by an external stimulus. Particular emphasis is placed on light-responsive LDBCs. Furthermore, a brief review of the biomedical or materials science applications of LDBCs is presented. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Electronic response and longitudinal phonons of a charge-density-wave distorted linear chain

International Nuclear Information System (INIS)

Giuliani, G.

1978-01-01

The longitudinal-phonon spectrum of an incommensurate charge-density-wave distorted linear chain at T = 0 K are calculated. This is done by direct numerical evaluation of the full static-electronic-response matrix. The electronic band structure assumed for this purpose is that of a mean-field theory 1-D Peierls insulator. The present results show how, within this simplified, but self-consistent picture, the phase and amplitude modes connect to, and interact with, the ordinary longitudinal-phonon branch. Effects due to our inclusion of (0,2ksub(F)) scattering along with the usual (-2ksub(F), 2ksub(F)) are also pointed out. An alternative approximate expression for the 1-D electronic-response matrix is also given. (author)

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

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.)

Thouless-Valatin rotational moment of inertia from linear response theory

Science.gov (United States)

Petrík, Kristian; Kortelainen, Markus

2018-03-01

Spontaneous breaking of continuous symmetries of a nuclear many-body system results in the appearance of zero-energy restoration modes. These so-called spurious Nambu-Goldstone modes represent a special case of collective motion and are sources of important information about the Thouless-Valatin inertia. The main purpose of this work is to study the Thouless-Valatin rotational moment of inertia as extracted from the Nambu-Goldstone restoration mode that results from the zero-frequency response to the total-angular-momentum operator. We examine the role and effects of the pairing correlations on the rotational characteristics of heavy deformed nuclei in order to extend our understanding of superfluidity in general. We use the finite-amplitude method of the quasiparticle random-phase approximation on top of the Skyrme energy density functional framework with the Hartree-Fock-Bogoliubov theory. We have successfully extended this formalism and established a practical method for extracting the Thouless-Valatin rotational moment of inertia from the strength function calculated in the symmetry-restoration regime. Our results reveal the relation between the pairing correlations and the moment of inertia of axially deformed nuclei of rare-earth and actinide regions of the nuclear chart. We have also demonstrated the feasibility of the method for obtaining the moment of inertia for collective Hamiltonian models. We conclude that from the numerical and theoretical perspective, the finite-amplitude method can be widely used to effectively study rotational properties of deformed nuclei within modern density functional approaches.

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

Linear and Non-Linear Dielectric Response of Periodic Systems from Quantum Monte Carlo

Science.gov (United States)

Umari, Paolo

2006-03-01

We present a novel approach that allows to calculate the dielectric response of periodic systems in the quantum Monte Carlo formalism. We employ a many-body generalization for the electric enthalpy functional, where the coupling with the field is expressed via the Berry-phase formulation for the macroscopic polarization. A self-consistent local Hamiltonian then determines the ground-state wavefunction, allowing for accurate diffusion quantum Monte Carlo calculations where the polarization's fixed point is estimated from the average on an iterative sequence. The polarization is sampled through forward-walking. This approach has been validated for the case of the polarizability of an isolated hydrogen atom, and then applied to a periodic system. We then calculate the linear susceptibility and second-order hyper-susceptibility of molecular-hydrogen chains whith different bond-length alternations, and assess the quality of nodal surfaces derived from density-functional theory or from Hartree-Fock. The results found are in excellent agreement with the best estimates obtained from the extrapolation of quantum-chemistry calculations.P. Umari, A.J. Williamson, G. Galli, and N. MarzariPhys. Rev. Lett. 95, 207602 (2005).

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...

Detector response theory and its applications

International Nuclear Information System (INIS)

Keijzer, J.

1992-11-01

Some methods to describe the dynamics of fission reactors are investigated. First the reactivity of a reactor is regarded. The values of an exact calculation of the reactivity are compared with values obtained by first-order perturbation theory. Then a description of the point reactor kinetic theory and the detector response theory is given. A comparison of the two methods is made, using models of some well defined perturbations. Two of the perturbations are such that a physical movement of some absorber is regarded. A new way of modelling these moving objects is proposed. The result of the point reactor kinetic theory and the detecor response theory did not differ too much for perturbations which were far from the detector position. Locally however point reactor kinetic theory was not, in contrast with detector response theory, able to produce reliable results. The results of these calculations are to be compared with experiments, which will be performed later. (orig.)

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)

Item response theory - A first approach

Science.gov (United States)

Nunes, Sandra; Oliveira, Teresa; Oliveira, Amílcar

2017-07-01

The Item Response Theory (IRT) has become one of the most popular scoring frameworks for measurement data, frequently used in computerized adaptive testing, cognitively diagnostic assessment and test equating. According to Andrade et al. (2000), IRT can be defined as a set of mathematical models (Item Response Models - IRM) constructed to represent the probability of an individual giving the right answer to an item of a particular test. The number of Item Responsible Models available to measurement analysis has increased considerably in the last fifteen years due to increasing computer power and due to a demand for accuracy and more meaningful inferences grounded in complex data. The developments in modeling with Item Response Theory were related with developments in estimation theory, most remarkably Bayesian estimation with Markov chain Monte Carlo algorithms (Patz & Junker, 1999). The popularity of Item Response Theory has also implied numerous overviews in books and journals, and many connections between IRT and other statistical estimation procedures, such as factor analysis and structural equation modeling, have been made repeatedly (Van der Lindem & Hambleton, 1997). As stated before the Item Response Theory covers a variety of measurement models, ranging from basic one-dimensional models for dichotomously and polytomously scored items and their multidimensional analogues to models that incorporate information about cognitive sub-processes which influence the overall item response process. The aim of this work is to introduce the main concepts associated with one-dimensional models of Item Response Theory, to specify the logistic models with one, two and three parameters, to discuss some properties of these models and to present the main estimation procedures.

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.

Beck's cognitive theory and the response style theory of depression in adolescents with and without mild to borderline intellectual disability.

Science.gov (United States)

Weeland, Martine M; Nijhof, Karin S; Otten, R; Vermaes, Ignace P R; Buitelaar, Jan K

2017-10-01

This study tests the validity of Beck's cognitive theory and Nolen-Hoeksema's response style theory of depression in adolescents with and without MBID. The relationship between negative cognitive errors (Beck), response styles (Nolen-Hoeksema) and depressive symptoms was examined in 135 adolescents using linear regression. The cognitive error 'underestimation of the ability to cope' was more prevalent among adolescents with MBID than among adolescents with average intelligence. This was the only negative cognitive error that predicted depressive symptoms. There were no differences between groups in the prevalence of the three response styles. In line with the theory, ruminating was positively and problem-solving was negatively related to depressive symptoms. Distractive response styles were not related to depressive symptoms. The relationship between response styles, cognitive errors and depressive symptoms were similar for both groups. The main premises of both theories of depression are equally applicable to adolescents with and without MBID. The cognitive error 'Underestimation of the ability to cope' poses a specific risk factor for developing a depression for adolescents with MBID and requires special attention in treatment and prevention of depression. WHAT THIS PAPER ADDS?: Despite the high prevalence of depression among adolescents with MBID, little is known about the etiology and cognitive processes that play a role in the development of depression in this group. The current paper fills this gap in research by examining the core tenets of two important theories on the etiology of depression (Beck's cognitive theory and Nolen-Hoeksema's response style theory) in a clinical sample of adolescents with and without MBID. This paper demonstrated that the theories are equally applicable to adolescents with MBID, as to adolescents with average intellectual ability. However, the cognitive bias 'underestimation of the ability to cope' was the only cognitive error

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 and non-linear dose-response functions reveal a hormetic relationship between stress and learning.

Science.gov (United States)

Zoladz, Phillip R; Diamond, David M

2008-10-16

Over a century of behavioral research has shown that stress can enhance or impair learning and memory. In the present review, we have explored the complex effects of stress on cognition and propose that they are characterized by linear and non-linear dose-response functions, which together reveal a hormetic relationship between stress and learning. We suggest that stress initially enhances hippocampal function, resulting from amygdala-induced excitation of hippocampal synaptic plasticity, as well as the excitatory effects of several neuromodulators, including corticosteroids, norepinephrine, corticotropin-releasing hormone, acetylcholine and dopamine. We propose that this rapid activation of the amygdala-hippocampus brain memory system results in a linear dose-response relation between emotional strength and memory formation. More prolonged stress, however, leads to an inhibition of hippocampal function, which can be attributed to compensatory cellular responses that protect hippocampal neurons from excitotoxicity. This inhibition of hippocampal functioning in response to prolonged stress is potentially relevant to the well-described curvilinear dose-response relationship between arousal and memory. Our emphasis on the temporal features of stress-brain interactions addresses how stress can activate, as well as impair, hippocampal functioning to produce a hormetic relationship between stress and learning.

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.

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.

Linear dose response curves in fungi and tradescantia

International Nuclear Information System (INIS)

Unrau, P.

1999-07-01

Tradescantia Clone 02 data suggests that linear non-threshold dose responses are expected to the lowest doses and dose rates of low linear energy transfer (LET) radiation. This is likely to be true for other living organisms even though Clone 02 is radiation sensitive. It is concluded that Clone 02 is partially defective in the RAD 6 pathway for the repair of DNA interstrand cross-links (ISCL) and other loss of coding damage (LCD), based on its cross sensitivities to EMS and ionizing radiation. Tradescantia Clone 02 data showing linear non-threshold induction of somatic genetic events in part reflects the repair deficiency of this Clone. More DNA damage is repaired by recombinational mechanisms in Clone 02 than would occur in a wild-type strain. Two important classes of DNA lesions are induced by ionizing radiation in DNA - double strand breaks (DSB) which are repaired by recombination mechanisms, and loss of coding information damage (LCD), which is repaired by error prone mechanisms but may also be a substrate for recombinational repair. Based on data from yeast, there are two different repair pathways which deal with these differing lesions with different somatic genetic consequences. From yeast, yield cross sections can be derived and applied to DNA damage and repair in Tradescantia. For Clone 02, per lesion, more visible genetic events are scored than in wild-type strains. In a radiation-derived sub-clone, Clone 0106, which is more variable than Clone 02, even more events occur per lesion. This derivative clone, plus breeding experiments, indicate that Clone 02 is heterozygous, or a 'carrier' for a mutant version of a gene in the Tradescantia RAD 6 repair pathway. Clone 02 is, therefore, much like a Fanconi's anemia carrier in a human population, while the Clone 0106 derivative is much like a homozygous Fanconi's anemia patient, with respect to its response to ionizing radiation damage. Two anomalies in its dose response curves for 'pink' loss of

Linear dose response curves in fungi and tradescantia

Energy Technology Data Exchange (ETDEWEB)

Unrau, P. [Atomic Energy of Canada Ltd., Chalk River, Ontario (Canada)

1999-07-15

Tradescantia Clone 02 data suggests that linear non-threshold dose responses are expected to the lowest doses and dose rates of low linear energy transfer (LET) radiation. This is likely to be true for other living organisms even though Clone 02 is radiation sensitive. It is concluded that Clone 02 is partially defective in the RAD 6 pathway for the repair of DNA interstrand cross-links (ISCL) and other loss of coding damage (LCD), based on its cross sensitivities to EMS and ionizing radiation. Tradescantia Clone 02 data showing linear non-threshold induction of somatic genetic events in part reflects the repair deficiency of this Clone. More DNA damage is repaired by recombinational mechanisms in Clone 02 than would occur in a wild-type strain. Two important classes of DNA lesions are induced by ionizing radiation in DNA - double strand breaks (DSB) which are repaired by recombination mechanisms, and loss of coding information damage (LCD), which is repaired by error prone mechanisms but may also be a substrate for recombinational repair. Based on data from yeast, there are two different repair pathways which deal with these differing lesions with different somatic genetic consequences. From yeast, yield cross sections can be derived and applied to DNA damage and repair in Tradescantia. For Clone 02, per lesion, more visible genetic events are scored than in wild-type strains. In a radiation-derived sub-clone, Clone 0106, which is more variable than Clone 02, even more events occur per lesion. This derivative clone, plus breeding experiments, indicate that Clone 02 is heterozygous, or a 'carrier' for a mutant version of a gene in the Tradescantia RAD 6 repair pathway. Clone 02 is, therefore, much like a Fanconi's anemia carrier in a human population, while the Clone 0106 derivative is much like a homozygous Fanconi's anemia patient, with respect to its response to ionizing radiation damage. Two anomalies in its dose response curves for &apos

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

Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbations

Energy Technology Data Exchange (ETDEWEB)

Turnbull, A. D.; Ferraro, N. M.; Lao, L. L.; Lanctot, M. J. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Izzo, V. A. [University of California-San Diego, 9500 Gilman Dr., La Jolla, California 92093-0417 (United States); Lazarus, E. A.; Hirshman, S. P. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (United States); Park, J.-K.; Lazerson, S.; Reiman, A. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States); Cooper, W. A. [Association Euratom-Confederation Suisse, Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Federale de Lausanne, Lausanne (Switzerland); Liu, Y. Q. [Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB (United Kingdom); Turco, F. [Columbia University, 116th St and Broadway, New York, New York 10027 (United States)

2013-05-15

With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10{sup −3} relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated nonlinear steady state, appropriate damping mechanisms need to be provided for each normal mode comprising the response. Other issues arise in the technical construction of perturbed flux surfaces from a displacement and from the presence of near nullspace normal modes. For the nearby equilibrium approach, in the absence of a full 3D equilibrium reconstruction with a controlled comparison, constraints relating the 2D system profiles to the final profiles in the 3D system also need to be imposed to assure accessibility. The magnetic helicity profile has been proposed as an appropriate input to a 3D equilibrium calculation and tests of this show the anticipated qualitative behavior.

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

An introduction to linear ordinary differential equations using the impulsive response method and factorization

CERN Document Server

Camporesi, Roberto

2016-01-01

This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

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

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)

Global hybrids from the semiclassical atom theory satisfying the local density linear response.

Science.gov (United States)

Fabiano, Eduardo; Constantin, Lucian A; Cortona, Pietro; Della Sala, Fabio

2015-01-13

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 2011, 106, 186406] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetic and structural testing, including thermochemistry and geometry, transition metal complexes, noncovalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semiempirical dispersion corrections are also provided.

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.

Linear ubiquitination signals in adaptive immune responses.

Science.gov (United States)

Ikeda, Fumiyo

2015-07-01

Ubiquitin can form eight different linkage types of chains using the intrinsic Met 1 residue or one of the seven intrinsic Lys residues. Each linkage type of ubiquitin chain has a distinct three-dimensional topology, functioning as a tag to attract specific signaling molecules, which are so-called ubiquitin readers, and regulates various biological functions. Ubiquitin chains linked via Met 1 in a head-to-tail manner are called linear ubiquitin chains. Linear ubiquitination plays an important role in the regulation of cellular signaling, including the best-characterized tumor necrosis factor (TNF)-induced canonical nuclear factor-κB (NF-κB) pathway. Linear ubiquitin chains are specifically generated by an E3 ligase complex called the linear ubiquitin chain assembly complex (LUBAC) and hydrolyzed by a deubiquitinase (DUB) called ovarian tumor (OTU) DUB with linear linkage specificity (OTULIN). LUBAC linearly ubiquitinates critical molecules in the TNF pathway, such as NEMO and RIPK1. The linear ubiquitin chains are then recognized by the ubiquitin readers, including NEMO, which control the TNF pathway. Accumulating evidence indicates an importance of the LUBAC complex in the regulation of apoptosis, development, and inflammation in mice. In this article, I focus on the role of linear ubiquitin chains in adaptive immune responses with an emphasis on the TNF-induced signaling pathways. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

The basics of item response theory using R

CERN Document Server

Baker, Frank B

2017-01-01

This graduate-level textbook is a tutorial for item response theory that covers both the basics of item response theory and the use of R for preparing graphical presentation in writings about the theory. Item response theory has become one of the most powerful tools used in test construction, yet one of the barriers to learning and applying it is the considerable amount of sophisticated computational effort required to illustrate even the simplest concepts. This text provides the reader access to the basic concepts of item response theory freed of the tedious underlying calculations. It is intended for those who possess limited knowledge of educational measurement and psychometrics. Rather than presenting the full scope of item response theory, this textbook is concise and practical and presents basic concepts without becoming enmeshed in underlying mathematical and computational complexities. Clearly written text and succinct R code allow anyone familiar with statistical concepts to explore and apply item re...

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

A heteroscedastic generalized linear model with a non-normal speed factor for responses and response times.

Science.gov (United States)

Molenaar, Dylan; Bolsinova, Maria

2017-05-01

In generalized linear modelling of responses and response times, the observed response time variables are commonly transformed to make their distribution approximately normal. A normal distribution for the transformed response times is desirable as it justifies the linearity and homoscedasticity assumptions in the underlying linear model. Past research has, however, shown that the transformed response times are not always normal. Models have been developed to accommodate this violation. In the present study, we propose a modelling approach for responses and response times to test and model non-normality in the transformed response times. Most importantly, we distinguish between non-normality due to heteroscedastic residual variances, and non-normality due to a skewed speed factor. In a simulation study, we establish parameter recovery and the power to separate both effects. In addition, we apply the model to a real data set. © 2017 The Authors. British Journal of Mathematical and Statistical Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.

Beyond the linear fluctuation-dissipation theorem: the role of causality

International Nuclear Information System (INIS)

Lucarini, Valerio; Colangeli, Matteo

2012-01-01

In this paper we tackle the traditional problem of relating the fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also nonlinear processes. With this goal, we try to build on Kubo's linear response theory and the response theory recently developed by Ruelle for nonequilibrium systems equipped with an invariant Sinai–Ruelle–Bowen (SRB) measure. Our derivation also sheds light on the link between causality and the possibility of relating fluctuations and response, both at the linear and nonlinear level. We first show, in a rather general setting, how the formalism of Ruelle's response theory can be used to derive in a novel way a generalization of the Kramers–Kronig relations. We then provide a formal extension at each order of nonlinearity of the fluctuation-dissipation theorem for general systems endowed with a smooth invariant measure. Finally, we focus on the physically relevant case of systems weakly perturbed from equilibrium, for which we present explicit fluctuation-dissipation relations linking the susceptibility describing the nth order response of the system with suitably defined correlations taken in the equilibrium ensemble

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.

A linear chromatic mechanism drives the pupillary response.

Science.gov (United States)

Tsujimura, S.; Wolffsohn, J. S.; Gilmartin, B.

2001-01-01

Previous studies have shown that a chromatic mechanism can drive pupil responses. The aim of this research was to clarify whether a linear or nonlinear chromatic mechanism drives pupillary responses by using test stimuli of various colours that are defined in cone contrast space. The pupil and accommodation responses evoked by these test stimuli were continuously and simultaneously objectively measured by photorefraction. The results with isochromatic and isoluminant stimuli showed that the accommodative level remained approximately constant (< 0.25 D change in mean level) even when the concurrent pupillary response was large (ca. 0.30 mm). The pupillary response to an isoluminant grating was sustained, delayed (by ca. 60 ms) and larger in amplitude than that for a isochromatic uniform stimulus, which supports previous work suggesting that the chromatic mechanism contributes to the pupillary response. In a second experiment, selected chromatic test gratings were used and isoresponse contours in cone contrast space were obtained. The results showed that the isoresponse contour in cone contrast space is well described (r(2) = 0.99) by a straight line with a positive slope. The results indicate that a /L - M/ linear chromatic mechanism, whereby a signal from the long wavelength cone is subtracted from that of the middle wavelength cone and vice versa, drives pupillary responses. PMID:11674867

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.

Impurity strength and impurity domain modulated frequency-dependent linear and second non-linear response properties of doped quantum dots

Energy Technology Data Exchange (ETDEWEB)

Datta, Nirmal Kumar [Department of Physics, Suri Vidyasagar College, Suri, Birbhum 731 101, West Bengal (India); Ghosh, Manas [Department of Chemistry, Physical Chemistry Section, Visva Bharati University, Santiniketan, Birbhum 731 235, West Bengal (India)

2011-08-15

We explore the pattern of frequency-dependent linear and second non-linear optical responses of repulsive impurity doped quantum dots harmonically confined in two dimensions. The dopant impurity potential chosen assumes a Gaussian form and it is doped into an on-center location. The quantum dot is subject to a periodically oscillating external electric field. For some fixed values of transverse magnetic field strength ({omega}{sub c}) and harmonic confinement potential ({omega}{sub 0}), the influence of impurity strength (V{sub 0}) and impurity domain ({xi}) on the diagonal components of the frequency-dependent linear ({alpha}{sub xx} and {alpha}{sub yy}) and second non-linear ({gamma}{sub xxxx} and {gamma}{sub yyyy}) responses of the dot are computed through a linear variational route. The investigations reveal that the optical responses undergo enhancement with increase in both V{sub 0} and {xi} values. However, in the limitingly small dopant strength regime one observes a drop in the optical responses with increase in V{sub 0}. A time-average rate of energy transfer to the system is often invoked to support the findings. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Semiclassical theory for the nuclear response function

International Nuclear Information System (INIS)

Stroth, U.

1986-01-01

In the first part of this thesis it was demonstrated how on a semiclassical base a RPA theory is developed and applied to electron scattering. It was shown in which fields of nuclear physics this semiclassical theory can be applied and how it is to be understood. In this connection we dedicated an extensive discussion to the Fermi gas model. From the free response function we calculated the RPA response with a finite-range residual interaction which we completely antisymmetrize. In the second part of this thesis we studied with our theory (e,e') data for the separated response functions. (orig./HSI) [de

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....

Endoreversible quantum heat engines in the linear response regime.

Science.gov (United States)

Wang, Honghui; He, Jizhou; Wang, Jianhui

2017-07-01

We analyze general models of quantum heat engines operating a cycle of two adiabatic and two isothermal processes. We use the quantum master equation for a system to describe heat transfer current during a thermodynamic process in contact with a heat reservoir, with no use of phenomenological thermal conduction. We apply the endoreversibility description to such engine models working in the linear response regime and derive expressions of the efficiency and the power. By analyzing the entropy production rate along a single cycle, we identify the thermodynamic flux and force that a linear relation connects. From maximizing the power output, we find that such heat engines satisfy the tight-coupling condition and the efficiency at maximum power agrees with the Curzon-Ahlborn efficiency known as the upper bound in the linear response regime.

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.

How linear response shaped models of neural circuits and the quest for alternatives.

Science.gov (United States)

Herfurth, Tim; Tchumatchenko, Tatjana

2017-10-01

In the past decades, many mathematical approaches to solve complex nonlinear systems in physics have been successfully applied to neuroscience. One of these tools is the concept of linear response functions. However, phenomena observed in the brain emerge from fundamentally nonlinear interactions and feedback loops rather than from a composition of linear filters. Here, we review the successes achieved by applying the linear response formalism to topics, such as rhythm generation and synchrony and by incorporating it into models that combine linear and nonlinear transformations. We also discuss the challenges encountered in the linear response applications and argue that new theoretical concepts are needed to tackle feedback loops and non-equilibrium dynamics which are experimentally observed in neural networks but are outside of the validity regime of the linear response formalism. Copyright © 2017 Elsevier Ltd. All rights reserved.

Four-Component Damped Density Functional Response Theory Study of UV/Vis Absorption Spectra and Phosphorescence Parameters of Group 12 Metal-Substituted Porphyrins.

Science.gov (United States)

Fransson, Thomas; Saue, Trond; Norman, Patrick

2016-05-10

The influences of group 12 (Zn, Cd, Hg) metal-substitution on the valence spectra and phosphorescence parameters of porphyrins (P) have been investigated in a relativistic setting. In order to obtain valence spectra, this study reports the first application of the damped linear response function, or complex polarization propagator, in the four-component density functional theory framework [as formulated in Villaume et al. J. Chem. Phys. 2010 , 133 , 064105 ]. It is shown that the steep increase in the density of states as due to the inclusion of spin-orbit coupling yields only minor changes in overall computational costs involved with the solution of the set of linear response equations. Comparing single-frequency to multifrequency spectral calculations, it is noted that the number of iterations in the iterative linear equation solver per frequency grid-point decreases monotonously from 30 to 0.74 as the number of frequency points goes from one to 19. The main heavy-atom effect on the UV/vis-absorption spectra is indirect and attributed to the change of point group symmetry due to metal-substitution, and it is noted that substitutions using heavier atoms yield small red-shifts of the intense Soret-band. Concerning phosphorescence parameters, the adoption of a four-component relativistic setting enables the calculation of such properties at a linear order of response theory, and any higher-order response functions do not need to be considered-a real, conventional, form of linear response theory has been used for the calculation of these parameters. For the substituted porphyrins, electronic coupling between the lowest triplet states is strong and results in theoretical estimates of lifetimes that are sensitive to the wave function and electron density parametrization. With this in mind, we report our best estimates of the phosphorescence lifetimes to be 460, 13.8, 11.2, and 0.00155 s for H2P, ZnP, CdP, and HgP, respectively, with the corresponding transition

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.

Analyzing force concept inventory with item response theory

Science.gov (United States)

Wang, Jing; Bao, Lei

2010-10-01

Item response theory is a popular assessment method used in education. It rests on the assumption of a probability framework that relates students' innate ability and their performance on test questions. Item response theory transforms students' raw test scores into a scaled proficiency score, which can be used to compare results obtained with different test questions. The scaled score also addresses the issues of ceiling effects and guessing, which commonly exist in quantitative assessment. We used item response theory to analyze the force concept inventory (FCI). Our results show that item response theory can be useful for analyzing physics concept surveys such as the FCI and produces results about the individual questions and student performance that are beyond the capability of classical statistics. The theory yields detailed measurement parameters regarding the difficulty, discrimination features, and probability of correct guess for each of the FCI questions.

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

Nonlinear response of dense colloidal suspensions under oscillatory shear: mode-coupling theory and Fourier transform rheology experiments.

Science.gov (United States)

Brader, J M; Siebenbürger, M; Ballauff, M; Reinheimer, K; Wilhelm, M; Frey, S J; Weysser, F; Fuchs, M

2010-12-01

Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.

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

Time-domain Hydroelasticity Theory of Ships Responding to Waves

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui

1997-01-01

free surface flow. The general interface boundary condition is used in the mathematical formulation of the fluid motion around the flexible structure. The general time-domain theory is simplified to a slender-body theory for the analysis of wave-induced global responses of monohull ships. The structure...... is represented by a non-uniform beam, while the generalized hydrodynamic coefficients can be obtained from two-dimensional potential flow theory. The linear slender body theory is generalized to treat the non-linear loading effects of rigid motion and structural response of ships travelling in rough seas....... The non-linear hydrostatic restoring force and hydrodynamic momentum action are considered. A numerical solution is presented for the slender body theory. Numerical examples are given for two ship cases with different geometry features, a warship hull and the S175 containership with two different bow...

CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

Science.gov (United States)

Jamison, J. W.

1994-01-01

CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

Comparison of equivalent linear and non linear methods on ground response analysis: case study at West Bangka site

International Nuclear Information System (INIS)

Eko Rudi Iswanto; Eric Yee

2016-01-01

Within the framework of identifying NPP sites, site surveys are performed in West Bangka (WB), Bangka-Belitung Island Province. Ground response analysis of a potential site has been carried out using peak strain profiles and peak ground acceleration. The objective of this research is to compare Equivalent Linear (EQL) and Non Linear (NL) methods of ground response analysis on the selected NPP site (West Bangka) using Deep Soil software. Equivalent linear method is widely used because requires soil data in simple way and short time of computational process. On the other hand, non linear method is capable of representing the actual soil behaviour by considering non linear soil parameter. The results showed that EQL method has similar trends to NL method. At surface layer, the acceleration values for EQL and NL methods are resulted as 0.425 g and 0.375 g respectively. NL method is more reliable in capturing higher frequencies of spectral acceleration compared to EQL method. (author)

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

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...

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....

The duality in the topological vector spaces and the linear physical system theory

International Nuclear Information System (INIS)

Oliveira Castro, F.M. de.

1980-01-01

The excitation-response relation in a linear, passive, and causal physical system who has the property of this relation be invariant for a time translation is univocally determined by the general form of the linear and continuous functionals defined on the linear topological space chosen for the representation of the excitations. (L.C.) [pt

Linear and Non-Linear Dose-Response Functions Reveal a Hormetic Relationship Between Stress and Learning

OpenAIRE

Zoladz, Phillip R.; Diamond, David M.

2008-01-01

Over a century of behavioral research has shown that stress can enhance or impair learning and memory. In the present review, we have explored the complex effects of stress on cognition and propose that they are characterized by linear and non-linear dose-response functions, which together reveal a hormetic relationship between stress and learning. We suggest that stress initially enhances hippocampal function, resulting from amygdala-induced excitation of hippocampal synaptic plasticity, as ...

Note: A high dynamic range, linear response transimpedance amplifier.

Science.gov (United States)

Eckel, S; Sushkov, A O; Lamoreaux, S K

2012-02-01

We have built a high dynamic range (nine decade) transimpedance amplifier with a linear response. The amplifier uses junction-gate field effect transistors (JFETs) to switch between three different resistors in the feedback of a low input bias current operational amplifier. This allows for the creation of multiple outputs, each with a linear response and a different transimpedance gain. The overall bandwidth of the transimpedance amplifier is set by the bandwidth of the most sensitive range. For our application, we demonstrate a three-stage amplifier with transimpedance gains of approximately 10(9)Ω, 3 × 10(7)Ω, and 10(4)Ω with a bandwidth of 100 Hz.

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.

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.

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

On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

Directory of Open Access Journals (Sweden)

Jun Wang

2011-01-01

Full Text Available A nonlinear time-varying (NLTV dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

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)

Optimal approximation of linear systems by artificial immune response

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstracts four elements, namely, antigen, antibody, reaction rules among antibodies, and driving algorithm describing how the rules are applied to antibodies, to simulate the process of immune response. Some reaction rules including clonal selection rules, immunological memory rules and immune regulation rules are introduced. Using the theorem of Markov chain, it is proofed that the new model is convergent. The experimental study on the optimal approximation of a stable linear system and an unstable one show that the approximate models searched by the new model have better performance indices than those obtained by some existing algorithms including the differential evolution algorithm and the multi-agent genetic algorithm.

Quantum work relations and response theory in parity-time-symmetric quantum systems

Science.gov (United States)

Wei, Bo-Bo

2018-01-01

In this work, we show that a universal quantum work relation for a quantum system driven arbitrarily far from equilibrium extends to a parity-time- (PT -) symmetric quantum system with unbroken PT symmetry, which is a consequence of microscopic reversibility. The quantum Jarzynski equality, linear response theory, and Onsager reciprocal relations for the PT -symmetric quantum system are recovered as special cases of the universal quantum work relation in a PT -symmetric quantum system. In the regime of broken PT symmetry, the universal quantum work relation does not hold because the norm is not preserved during the dynamics.

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.

On multidimensional item response theory -- a coordinate free approach

OpenAIRE

Antal, Tamás

2007-01-01

A coordinate system free definition of complex structure multidimensional item response theory (MIRT) for dichotomously scored items is presented. The point of view taken emphasizes the possibilities and subtleties of understanding MIRT as a multidimensional extension of the ``classical'' unidimensional item response theory models. The main theorem of the paper is that every monotonic MIRT model looks the same; they are all trivial extensions of univariate item response theory.

Linear density response function in the projector augmented wave method

DEFF Research Database (Denmark)

Yan, Jun; Mortensen, Jens Jørgen; Jacobsen, Karsten Wedel

2011-01-01

We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single...... functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001...

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...

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.

Item Response Theory: A Basic Concept

Science.gov (United States)

Mahmud, Jumailiyah

2017-01-01

With the development in computing technology, item response theory (IRT) develops rapidly, and has become a user friendly application in psychometrics world. Limitation in classical theory is one aspect that encourages the use of IRT. In this study, the basic concept of IRT will be discussed. In addition, it will briefly review the ability…

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.

Superradiance Effects in the Linear and Nonlinear Optical Response of Quantum Dot Molecules

Science.gov (United States)

Sitek, A.; Machnikowski, P.

2008-11-01

We calculate the linear optical response from a single quantum dot molecule and the nonlinear, four-wave-mixing response from an inhomogeneously broadened ensemble of such molecules. We show that both optical signals are affected by the coupling-dependent superradiance effect and by optical interference between the two polarizations. As a result, the linear and nonlinear responses are not identical.

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)

Linear Algebra Revisited: An Attempt to Understand Students' Conceptual Difficulties

Science.gov (United States)

Britton, Sandra; Henderson, Jenny

2009-01-01

This article looks at some of the conceptual difficulties that students have in a linear algebra course. An overview of previous research in this area is given, and the various theories that have been espoused regarding the reasons that students find linear algebra so difficult are discussed. Student responses to two questions testing the ability…

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.

Comparing light sensitivity, linearity and step response of electronic cameras for ophthalmology.

Science.gov (United States)

Kopp, O; Markert, S; Tornow, R P

2002-01-01

To develop and test a procedure to measure and compare light sensitivity, linearity and step response of electronic cameras. The pixel value (PV) of digitized images as a function of light intensity (I) was measured. The sensitivity was calculated from the slope of the P(I) function, the linearity was estimated from the correlation coefficient of this function. To measure the step response, a short sequence of images was acquired. During acquisition, a light source was switched on and off using a fast shutter. The resulting PV was calculated for each video field of the sequence. A CCD camera optimized for the near-infrared (IR) spectrum showed the highest sensitivity for both, visible and IR light. There are little differences in linearity. The step response depends on the procedure of integration and read out.

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.

Linear response in the nonequilibrium zero range process

International Nuclear Information System (INIS)

Maes, Christian; Salazar, Alberto

2014-01-01

We explore a number of explicit response formulæ around the boundary driven zero range process to changes in the exit and entrance rates. In such a nonequilibrium regime kinetic (and not only thermodynamic) aspects make a difference in the response. Apart from a number of formal approaches, we illustrate a general decomposition of the linear response into entropic and frenetic contributions, the latter being realized from changes in the dynamical activity at the boundaries. In particular in this way one obtains nonlinear modifications to the Green–Kubo relation. We end by bringing some general remarks about the situation where that nonequilibrium response remains given by the (equilibrium) Kubo formula such as for the density profile in the boundary driven Lorentz gas

Linearization of Positional Response Curve of a Fiber-optic Displacement Sensor

Science.gov (United States)

Babaev, O. G.; Matyunin, S. A.; Paranin, V. D.

2018-01-01

Currently, the creation of optical measuring instruments and sensors for measuring linear displacement is one of the most relevant problems in the area of instrumentation. Fiber-optic contactless sensors based on the magneto-optical effect are of special interest. They are essentially contactless, non-electrical and have a closed optical channel not subject to contamination. The main problem of this type of sensors is the non-linearity of their positional response curve due to the hyperbolic nature of the magnetic field intensity variation induced by moving the magnetic source mounted on the controlled object relative to the sensing element. This paper discusses an algorithmic method of linearizing the positional response curve of fiber-optic displacement sensors in any selected range of the displacements to be measured. The method is divided into two stages: 1 - definition of the calibration function, 2 - measurement and linearization of the positional response curve (including its temperature stabilization). The algorithm under consideration significantly reduces the number of points of the calibration function, which is essential for the calibration of temperature dependence, due to the use of the points that randomly deviate from the grid points with uniform spacing. Subsequent interpolation of the deviating points and piecewise linear-plane approximation of the calibration function reduces the microcontroller storage capacity for storing the calibration function and the time required to process the measurement results. The paper also presents experimental results of testing real samples of fiber-optic displacement sensors.

Open-ended response theory with polarizable embedding

DEFF Research Database (Denmark)

Steindal, Arnfinn Hykkerud; Beerepoot, Maarten T P; Ringholm, Magnus

2016-01-01

We present the theory and implementation of an open-ended framework for electric response properties at the level of Hartree-Fock and Kohn-Sham density functional theory that includes effects from the molecular environment modeled by the polarizable embedding (PE) model. With this new state......-of-the-art multiscale functionality, electric response properties to any order can be calculated for molecules embedded in polarizable atomistic molecular environments ranging from solvents to complex heterogeneous macromolecules such as proteins. In addition, environmental effects on multiphoton absorption (MPA...

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.

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.)

Atomic theory of viscoelastic response and memory effects in metallic glasses

Science.gov (United States)

Cui, Bingyu; Yang, Jie; Qiao, Jichao; Jiang, Minqiang; Dai, Lanhong; Wang, Yun-Jiang; Zaccone, Alessio

2017-09-01

An atomic-scale theory of the viscoelastic response of metallic glasses is derived from first principles, using a Zwanzig-Caldeira-Leggett system-bath Hamiltonian as a starting point within the framework of nonaffine linear response to mechanical deformation. This approach provides a generalized Langevin equation (GLE) as the average equation of motion for an atom or ion in the material, from which non-Markovian nonaffine viscoelastic moduli are extracted. These can be evaluated using the vibrational density of states (DOS) as input, where the boson peak plays a prominent role in the mechanics. To compare with experimental data for binary ZrCu alloys, a numerical DOS was obtained from simulations of this system, which also take electronic degrees of freedom into account via the embedded-atom method for the interatomic potential. It is shown that the viscoelastic α -relaxation, including the α -wing asymmetry in the loss modulus, can be very well described by the theory if the memory kernel (the non-Markovian friction) in the GLE is taken to be a stretched-exponential decaying function of time. This finding directly implies strong memory effects in the atomic-scale dynamics and suggests that the α -relaxation time is related to the characteristic time scale over which atoms retain memory of their previous collision history. This memory time grows dramatically below the glass transition.

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)

Diagnostics for Linear Models With Functional Responses

OpenAIRE

Xu, Hongquan; Shen, Qing

2005-01-01

Linear models where the response is a function and the predictors are vectors are useful in analyzing data from designed experiments and other situations with functional observations. Residual analysis and diagnostics are considered for such models. Studentized residuals are defined and their properties are studied. Chi-square quantile-quantile plots are proposed to check the assumption of Gaussian error process and outliers. Jackknife residuals and an associated test are proposed to det...

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.

LINEAR KERNEL SUPPORT VECTOR MACHINES FOR MODELING PORE-WATER PRESSURE RESPONSES

Directory of Open Access Journals (Sweden)

KHAMARUZAMAN W. YUSOF

2017-08-01

Full Text Available Pore-water pressure responses are vital in many aspects of slope management, design and monitoring. Its measurement however, is difficult, expensive and time consuming. Studies on its predictions are lacking. Support vector machines with linear kernel was used here to predict the responses of pore-water pressure to rainfall. Pore-water pressure response data was collected from slope instrumentation program. Support vector machine meta-parameter calibration and model development was carried out using grid search and k-fold cross validation. The mean square error for the model on scaled test data is 0.0015 and the coefficient of determination is 0.9321. Although pore-water pressure response to rainfall is a complex nonlinear process, the use of linear kernel support vector machine can be employed where high accuracy can be sacrificed for computational ease and time.

Comparison of Classical Test Theory and Item Response Theory in Individual Change Assessment

NARCIS (Netherlands)

Jabrayilov, Ruslan; Emons, Wilco H. M.; Sijtsma, Klaas

2016-01-01

Clinical psychologists are advised to assess clinical and statistical significance when assessing change in individual patients. Individual change assessment can be conducted using either the methodologies of classical test theory (CTT) or item response theory (IRT). Researchers have been optimistic

Linear response to long wavelength fluctuations using curvature simulations

Energy Technology Data Exchange (ETDEWEB)

Baldauf, Tobias; Zaldarriaga, Matias [School of Natural Sciences, Institute for Advanced Study, Princeton, NJ (United States); Seljak, Uroš [Physics Department, Astronomy Department and Lawrence Berkeley National Laboratory, University of California, Berkeley, CA (United States); Senatore, Leonardo, E-mail: baldauf@ias.edu, E-mail: useljak@berkeley.edu, E-mail: senatore@stanford.edu, E-mail: matiasz@ias.edu [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA (United States)

2016-09-01

We study the local response to long wavelength fluctuations in cosmological N -body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, more direct, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the response of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naïve derivation assuming a universal mass function by approximately 8–20%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.

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

Time-dependent density-functional theory in the projector augmented-wave method

DEFF Research Database (Denmark)

Walter, Michael; Häkkinen, Hannu; Lehtovaara, Lauri

2008-01-01

We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we...

Item level diagnostics and model - data fit in item response theory ...

African Journals Online (AJOL)

Item response theory (IRT) is a framework for modeling and analyzing item response data. Item-level modeling gives IRT advantages over classical test theory. The fit of an item score pattern to an item response theory (IRT) models is a necessary condition that must be assessed for further use of item and models that best fit ...

Item Response Data Analysis Using Stata Item Response Theory Package

Science.gov (United States)

Yang, Ji Seung; Zheng, Xiaying

2018-01-01

The purpose of this article is to introduce and review the capability and performance of the Stata item response theory (IRT) package that is available from Stata v.14, 2015. Using a simulated data set and a publicly available item response data set extracted from Programme of International Student Assessment, we review the IRT package from…

Towards a Culturally Situated Reader Response Theory

Science.gov (United States)

Brooks, Wanda; Browne, Susan

2012-01-01

This article describes a theory of how culture enables literary interpretations of texts. We begin with a brief overview of the reader response field. From there, we introduce the theory and provide illustrative participant data examples. These data examples illustrate the four cultural positions middle grade students in our research assumed when…

Violations of local equilibrium and linear response in classical lattice systems

International Nuclear Information System (INIS)

Aoki, Kenichiro; Kusnezov, Dimitri

2003-01-01

We quantitatively and systematically analyze how local equilibrium, and linear response in transport are violated as systems move far from equilibrium. This is done by studying heat flow in classical lattice models with and without bulk transport behavior, in 1-3 dimensions, at various temperatures. Equations of motion for the system are integrated numerically to construct the non-equilibrium steady states. Linear response and local equilibrium assumptions are seen to break down in a similar manner. We quantify the breakdown through the analysis of both microscopic and macroscopic observables and examine its transformation properties under general redefinitions of the non-equilibrium temperature

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

A nanolens-type enhancement in the linear and second harmonic response of a metallic dimer

International Nuclear Information System (INIS)

Pustovit, Vitaliy; Biswas, Sushmita; Vaia, Richard; Urbas, Augustine

2014-01-01

In this paper we explore the linear and second-order nonlinear response of gold nanoparticle pairs (dimers). Despite that even-order nonlinear processes are forbidden in bulk centrosymmetric media like metals, second order nonlinear response exhibits a high degree of sensitivity for spherical nanoparticles where inversion symmetry is broken at the surface. Recent experiments demonstrate significant dependence of linear response and second-harmonic surface nonlinear response arising from the local fundamental field distribution in a dimer configuration. Our calculations are carried out taking into account high order multipolar interactions between metal nanoparticles, and demonstrate that linear and nonlinear optical responses of the dimer exhibit periodic behavior dependent on the separation distance between nanoparticles. This response increases for dimers with a large difference between particle sizes. (paper)

The non-linear response of the magnetosphere: 30 October 1978

International Nuclear Information System (INIS)

Price, C.P.; Prichard, D.

1993-01-01

The authors address the question of whether the response of the earth magnetosphere to the solar wind can be viewed as a nonlinear phenomena, rather than a linear response. The difficulty in answering this question is that the driving function, namely the solar wind, is very aperiodic, and it is difficult to argue that the system has time to go to any sort of a steady state in response to the driving force, prior to its making another random change. The application of nonlinear analysis methods in the face of this type of system is very limited. The authors pick a particular day, namely October 30, 1978, when the solar wind was very uniform for an extended period of time, and there is the possibility the system could converge to some type of strange attractor state within this period. They look at the auroral electrojet as a measure of the potential nonlinear response of the magnetosphere, and apply both nonlinear and linear analysis procedures to the data to try to determine if the data would support a nonlinear response of the magnetosphere to the solar wind driver, taken as the product of the solar wind speed v, and the southward component of the interplanetary magnetic field B s

Dynamic Response of Non-Linear Inelsatic Systems to Poisson-Driven Stochastic Excitations

DEFF Research Database (Denmark)

Nielsen, Søren R. K.; Iwankiewicz, R.

of an equivalent linearization techni que and substituting the non-analytical non-linearity in the original system by the cubic form in the pertinent state variables. The response moments are evaluated for the equivalent systems with the help of a generalized Ito's differential rule. The analytical results...

A generalized non-local optical response theory for plasmonic nanostructures

DEFF Research Database (Denmark)

Mortensen, N. Asger; Raza, Søren; Wubs, Martijn

2014-01-01

for their description. Here instead we present a comparatively simple semiclassical generalized non-local optical response theory that unifies quantum pressure convection effects and induced charge diffusion kinetics, with a concomitant complex-valued generalized non-local optical response parameter. Our theory...

On the Relationship between Classical Test Theory and Item Response Theory: From One to the Other and Back

Science.gov (United States)

Raykov, Tenko; Marcoulides, George A.

2016-01-01

The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…

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

Toward a Responsibility-Catering Prioritarian Ethical Theory of Risk.

Science.gov (United States)

Wikman-Svahn, Per; Lindblom, Lars

2018-03-05

Standard tools used in societal risk management such as probabilistic risk analysis or cost-benefit analysis typically define risks in terms of only probabilities and consequences and assume a utilitarian approach to ethics that aims to maximize expected utility. The philosopher Carl F. Cranor has argued against this view by devising a list of plausible aspects of the acceptability of risks that points towards a non-consequentialist ethical theory of societal risk management. This paper revisits Cranor's list to argue that the alternative ethical theory responsibility-catering prioritarianism can accommodate the aspects identified by Cranor and that the elements in the list can be used to inform the details of how to view risks within this theory. An approach towards operationalizing the theory is proposed based on a prioritarian social welfare function that operates on responsibility-adjusted utilities. A responsibility-catering prioritarian ethical approach towards managing risks is a promising alternative to standard tools such as cost-benefit analysis.

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.

MINIMUM ENTROPY DECONVOLUTION OF ONE-AND MULTI-DIMENSIONAL NON-GAUSSIAN LINEAR RANDOM PROCESSES

Institute of Scientific and Technical Information of China (English)

程乾生

1990-01-01

The minimum entropy deconvolution is considered as one of the methods for decomposing non-Gaussian linear processes. The concept of peakedness of a system response sequence is presented and its properties are studied. With the aid of the peakedness, the convergence theory of the minimum entropy deconvolution is established. The problem of the minimum entropy deconvolution of multi-dimensional non-Gaussian linear random processes is first investigated and the corresponding theory is given. In addition, the relation between the minimum entropy deconvolution and parameter method is discussed.

Hydration thermodynamics beyond the linear response approximation.

Science.gov (United States)

Raineri, Fernando O

2016-10-19

The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute

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.

Strawsonian Libertarianism: A Theory of Free Will and Moral Responsibility

OpenAIRE

Franklin, Christopher

2010-01-01

My dissertation develops a novel theory of free will and moral responsibility, Strawsonian libertarianism, which combines Strawsonianism about the concept of moral responsibility with event-causal libertarianism concerning its conditions of application. I construct this theory in light of and response to the three main objections to libertarianism: the moral shallowness objection, the intelligibility objection, and the empirical plausibility objection.The moral shallowness objection contends...

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...

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

A density functional theory-based chemical potential equalisation

Indian Academy of Sciences (India)

A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole polarizability within the framework of density functional theory based linear response theory. The resulting polarizability is expressed in terms of the contributions from individual atoms in the molecule. A few ...

Application of elasticity theory at Sandia Labortories

International Nuclear Information System (INIS)

Davison, L.

1975-01-01

Examples are given of the application of linear elasticity theory to the solution of practical problems encountered at Sandia Laboratories. It is being applied to a very broad range of problems: those in one, two, and three spatial dimensions, some involving static and some dynamic response, to materials having isotropic and anisotropic symmetry, to homogeneous and inhomogeneous bodies, etc. Various extensions of the theory to include electric, magnetic and thermal effects, to account for material microstructure, for radiation and spall damage, chemical reactions, and other phenomena have been developed and/or applied. In some applications linear elasticity represents the physics of a problem well and is the theory of choice. In others the theory was used because it lent insight into a larger problem that was also attacked by means of other theories and/or experiment, and in some cases it serves as a part of a more encompassing theory

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

Recovery coefficients as a test of system linearity of response in PET

International Nuclear Information System (INIS)

Geworski, L.; Munz, D.L.; Knoop, B.; Hofmann, M.; Knapp, W.H.

2002-01-01

Aim: New imaging protocols have created an increasing demand for quantitation in dedicated PET. Besides attenuation and scatter correction the recovery correction, accounting for the instrument's limited spatial resolution, has gained importance. For clinical practicability these corrections should work independent from the object, i.e. from the actual distribution of emitter and absorber. Aim of the study was to test this object independency, i.e. system linearity of response, by comparing recovery coefficients (RC) determined for different object geometries. In fact, this comparison may serve as a final test on system linearity of response, as measured on the quantitative accuracy by which the activity concentration in small lesions can be recovered. Method: For hot and cold spot imaging situations spatial distribution of activity is different. Therefore, scatter correction algorithm has to deal with different scatter distributions. If all factors disturbing system linearity, specifically scatter and attenuation, are corrected to a sufficient degree of accuracy, the system behaves linearly resulting in the theoretical relationship. CSRC = (1-HSRC). Thus, this equation, applied hot and cold spot measurements, will serve as a test on the effectiveness of the corrections and, hence, as a test of system linearity of response. Following IEC standard procedures (IEC 61675-1) measurements were done with and without interplane septa (2D/3D) on an ECAT EXACT 922 using a cylindrical phantom containing six spheres of different diameters (10 mm - 40 mm). All data were corrected for attenuation (transmission scan) and scatter (2D: deconvolution, 3D: scatter model), as implemented in the scanner's standard software. Recovery coefficients were determined for cold (CSRC) and hot (HSRC) lesions using both 2D and 3D acquisition mode. Results: CSRC directly measured versus CSRC calculated according to eq. (1) from HSRC resulted in an excellent agreement for both 2D and 3D data

Assessing item fit for unidimensional item response theory models using residuals from estimated item response functions.

Science.gov (United States)

Haberman, Shelby J; Sinharay, Sandip; Chon, Kyong Hee

2013-07-01

Residual analysis (e.g. Hambleton & Swaminathan, Item response theory: principles and applications, Kluwer Academic, Boston, 1985; Hambleton, Swaminathan, & Rogers, Fundamentals of item response theory, Sage, Newbury Park, 1991) is a popular method to assess fit of item response theory (IRT) models. We suggest a form of residual analysis that may be applied to assess item fit for unidimensional IRT models. The residual analysis consists of a comparison of the maximum-likelihood estimate of the item characteristic curve with an alternative ratio estimate of the item characteristic curve. The large sample distribution of the residual is proved to be standardized normal when the IRT model fits the data. We compare the performance of our suggested residual to the standardized residual of Hambleton et al. (Fundamentals of item response theory, Sage, Newbury Park, 1991) in a detailed simulation study. We then calculate our suggested residuals using data from an operational test. The residuals appear to be useful in assessing the item fit for unidimensional IRT models.

A biological basis for the linear non-threshold dose-response relationship for low-level carcinogen exposure

International Nuclear Information System (INIS)

Albert, R.E.

1981-01-01

This chapter examines low-level dose-response relationships in terms of the two-stage mouse tumorigenesis model. Analyzes the feasibility of the linear non-threshold dose-response model which was first adopted for use in the assessment of cancer risks from ionizing radiation and more recently from chemical carcinogens. Finds that both the interaction of B(a)P with epidermal DNA of the mouse skin and the dose-response relationship for the initiation stage of mouse skin tumorigenesis showed a linear non-threshold dose-response relationship. Concludes that low level exposure to environmental carcinogens has a linear non-threshold dose-response relationship with the carcinogen acting as an initiator and the promoting action being supplied by the factors that are responsible for the background cancer rate in the target tissue

Item response theory analysis of the mechanics baseline test

Science.gov (United States)

Cardamone, Caroline N.; Abbott, Jonathan E.; Rayyan, Saif; Seaton, Daniel T.; Pawl, Andrew; Pritchard, David E.

2012-02-01

Item response theory is useful in both the development and evaluation of assessments and in computing standardized measures of student performance. In item response theory, individual parameters (difficulty, discrimination) for each item or question are fit by item response models. These parameters provide a means for evaluating a test and offer a better measure of student skill than a raw test score, because each skill calculation considers not only the number of questions answered correctly, but the individual properties of all questions answered. Here, we present the results from an analysis of the Mechanics Baseline Test given at MIT during 2005-2010. Using the item parameters, we identify questions on the Mechanics Baseline Test that are not effective in discriminating between MIT students of different abilities. We show that a limited subset of the highest quality questions on the Mechanics Baseline Test returns accurate measures of student skill. We compare student skills as determined by item response theory to the more traditional measurement of the raw score and show that a comparable measure of learning gain can be computed.

Thermospheric dynamics - A system theory approach

Science.gov (United States)

Codrescu, M.; Forbes, J. M.; Roble, R. G.

1990-01-01

A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.

Applications of equivalent linearization approaches to nonlinear piping systems

International Nuclear Information System (INIS)

Park, Y.; Hofmayer, C.; Chokshi, N.

1997-01-01

The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA's are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations

Incorporating Response Times in Item Response Theory Models of Reading Comprehension Fluency

Science.gov (United States)

Su, Shiyang

2017-01-01

With the online assessment becoming mainstream and the recording of response times becoming straightforward, the importance of response times as a measure of psychological constructs has been recognized and the literature of modeling times has been growing during the last few decades. Previous studies have tried to formulate models and theories to…

The log-linear response function of the bounded number-line task is unrelated to the psychological representation of quantity.

Science.gov (United States)

Cohen, Dale J; Quinlan, Philip T

2018-02-01

The bounded number-line task has been used extensively to assess the numerical competence of both children and adults. One consistent finding has been that young children display a logarithmic response function, whereas older children and adults display a more linear response function. Traditionally, these log-linear functions have been interpreted as providing a transparent window onto the nature of the participants' psychological representations of quantity (termed here a direct response strategy). Here we show that the direct response strategy produces the log-linear response function regardless of whether the psychological representation of quantity is compressive or expansive. Simply put, the log-linear response function results from task constraints rather than from the psychological representation of quantities. We also demonstrate that a proportion/subtraction response strategy produces response patterns that almost perfectly correlate with the psychological representation of quantity. We therefore urge researchers not to interpret the log-linear response pattern in terms of numerical representation.

PELAPORAN CORPORATE SOCIAL RESPONSIBILITY PERBANKAN SYARIAH DALAM PERSPEKTIF SYARIAH ENTERPRISE THEORY

OpenAIRE

Syuhada Mansur

2011-01-01

This study aims to analyze the reporting of corporate social responsibility (CSR) in Islamic banking based on concept of sharia enterprise theory. The research was done by analyzing how the Bank Syariah Mandiri (BSM) reported their corporate social responsibility . This study uses a case study of annual reports BSM and then analysis based on the disclosure of social responsibility based on sharia enterprise theory. These results show that the social responsibility reporting of Bank Syariah...

Relationships among Classical Test Theory and Item Response Theory Frameworks via Factor Analytic Models

Science.gov (United States)

Kohli, Nidhi; Koran, Jennifer; Henn, Lisa

2015-01-01

There are well-defined theoretical differences between the classical test theory (CTT) and item response theory (IRT) frameworks. It is understood that in the CTT framework, person and item statistics are test- and sample-dependent. This is not the perception with IRT. For this reason, the IRT framework is considered to be theoretically superior…

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.

Item Response Theory Analyses of the Cambridge Face Memory Test (CFMT)

Science.gov (United States)

Cho, Sun-Joo; Wilmer, Jeremy; Herzmann, Grit; McGugin, Rankin; Fiset, Daniel; Van Gulick, Ana E.; Ryan, Katie; Gauthier, Isabel

2014-01-01

We evaluated the psychometric properties of the Cambridge face memory test (CFMT; Duchaine & Nakayama, 2006). First, we assessed the dimensionality of the test with a bi-factor exploratory factor analysis (EFA). This EFA analysis revealed a general factor and three specific factors clustered by targets of CFMT. However, the three specific factors appeared to be minor factors that can be ignored. Second, we fit a unidimensional item response model. This item response model showed that the CFMT items could discriminate individuals at different ability levels and covered a wide range of the ability continuum. We found the CFMT to be particularly precise for a wide range of ability levels. Third, we implemented item response theory (IRT) differential item functioning (DIF) analyses for each gender group and two age groups (Age ≤ 20 versus Age > 21). This DIF analysis suggested little evidence of consequential differential functioning on the CFMT for these groups, supporting the use of the test to compare older to younger, or male to female, individuals. Fourth, we tested for a gender difference on the latent facial recognition ability with an explanatory item response model. We found a significant but small gender difference on the latent ability for face recognition, which was higher for women than men by 0.184, at age mean 23.2, controlling for linear and quadratic age effects. Finally, we discuss the practical considerations of the use of total scores versus IRT scale scores in applications of the CFMT. PMID:25642930

Nonrigid, Linear Plasma Response Model Based on Perturbed Equilibria for Axisymmetric Tokamak Control Design

International Nuclear Information System (INIS)

Welander, A.S.; Deranian, R.D.; Humphreys, D.A.; Leuer, J.A.; Walker, M.L.

2005-01-01

Tokamak control design relies on an accurate linear model of the plasma response, which can often dominate the local field variations in regions under active feedback control. For example, when fluxes at selected points on the plasma boundary are regulated in DIII-D, the plasma response to a change in a coil current gives rise to a flux change which can be larger than and opposite to the flux change caused by the coil alone.In the past, rigid plasma models have been used for linear stability and shape control design. In a rigid model, the plasma current profile is considered fixed and moves rigidly in response to control coils to maintain radial and vertical force balance. In a nonrigid model, however, changes in the plasma shape and current profile are taken into account. Such models are expected to be important for future advanced tokamak control design. The present work describes development of a nonrigid plasma response model for high-accuracy multivariable control design and provides comparisons of model predictions against DIII-D experimental data. The linear perturbed plasma response model is calculated rapidly from an existing equilibrium solution

Non-linear dose response of a few plant taxa to acute gamma radiation

International Nuclear Information System (INIS)

George, J.T.; Patel, B.B.; Pius, J.; Narula, B.; Shankhadarwar, S.; Rane, V.A.; Venu-Babu, P.; Eapen, S.; Singhal, R.K.

2014-01-01

Micronuclei induction serves as an essential biomarker of radiation stress in a living system, and the simplicity of its detection technique has made it a widely used indicator of radiation damage. The present study was conducted to reveal the cytological dose-response of a few plant taxa, viz., Allium cepa var. aggregatum Linn., Allium sativum Linn., Chlorophytum comosum (Thunb.) Jacques and Eichhornia crassipes (Mart.) Solms, to low LET gamma radiation with special emphasis on the pattern of micronuclei induced across low and high dose regimes. A tri-phasic non-linear dose-response pattern was observed in the four taxa studied, characterized by a low dose linear segment, a plateau and a high dose linear segment. Despite a similar response trend, the critical doses where the phase transitions occurred varied amongst the plant taxa, giving an indication to their relative radiosensitivities. E. crassipes and A. sativum, with their lower critical doses for slope modifications of phase transitions, were concluded as being more radiosensitive as compared to C. comosum and A. cepa, which had relatively higher critical doses. (author)

Predicting near-UV electronic circular dichroism in nucleosomal DNA by means of DFT response theory.

Science.gov (United States)

Norman, Patrick; Parello, Joseph; Polavarapu, Prasad L; Linares, Mathieu

2015-09-14

It is demonstrated that time-dependent density functional theory (DFT) calculations can accurately predict changes in near-UV electronic circular dichroism (ECD) spectra of DNA as the structure is altered from the linear (free) B-DNA form to the supercoiled N-DNA form found in nucleosome core particles. At the DFT/B3LYP level of theory, the ECD signal response is reduced by a factor of 6.7 in going from the B-DNA to the N-DNA form, and it is illustrated how more than 90% of the individual base-pair dimers contribute to this strong hypochromic effect. Of the several inter-base pair parameters, an increase in twist angles is identified as to strongly contribute to a reduced ellipticity. The present work provides first evidence that first-principles calculations can elucidate changes in DNA dichroism due to the supramolecular organization of the nucleoprotein particle and associates these changes with the local structural features of nucleosomal DNA.

Linear response at the 4-component relativistic density-functional level: application to the frequency-dependent dipole polarizability of Hg, AuH and PtH2

International Nuclear Information System (INIS)

Salek, Pawel; Helgaker, Trygve; Saue, Trond

2005-01-01

We report the implementation and application of linear response density-functional theory (DFT) based on the 4-component relativistic Dirac-Coulomb Hamiltonian. The theory is cast in the language of second quantization and is based on the quasienergy formalism (Floquet theory), replacing the initial state dependence of the Runge-Gross theorem by periodic boundary conditions. Contradictions in causality and symmetry of the time arguments are thereby avoided and the exchange-correlation potential and kernel can be expressed as functional derivatives of the quasienergy. We critically review the derivation of the quasienergy analogues of the Hohenberg-Kohn theorem and the Kohn-Sham formalism and discuss the nature of the quasienergy exchange-correlation functional. Structure is imposed on the response equations in terms of Hermiticity and time-reversal symmetry. It is observed that functionals of spin and current densities, corresponding to time-antisymmetric operators, contribute to frequency-dependent and not static electric properties. Physically, this follows from the fact that only a time-dependent electric field creates a magnetic field. It is furthermore observed that hybrid functionals enhance spin polarization since only exact exchange contributes to anti-Hermitian trial vectors. We apply 4-component relativistic linear response DFT to the calculation of the frequency-dependent polarizability of the isoelectronic series Hg, AuH and PtH 2 . Unlike for the molecules, the effect of electron correlation on the polarizability of the mercury atom is very large, about 25%. We observe a remarkable performance of the local-density approximation (LDA) functional in reproducing the experimental frequency-dependent polarizability of this atom, clearly superior to that of the BLYP and B3LYP functionals. This allows us to extract Cauchy moments (S(-4) = 382.82 and S(-6) = 6090.89 a.u.) that we believe are superior to experiment since we go to higher order in the Cauchy

Low voltage RF MEMS variable capacitor with linear C-V response

KAUST Repository

Elshurafa, Amro M.

2012-07-23

An RF MEMS variable capacitor, fabricated in the PolyMUMPS process and tuned electrostatically, possessing a linear capacitance-voltage response is reported. The measured quality factor of the device was 17 at 1GHz, while the tuning range was 1.2:1 and was achieved at an actuation DC voltage of 8V only. Further, the linear regression coefficient was 0.98. The variable capacitor was created such that it has both vertical and horizontal capacitances present. As the top suspended plate moves towards the bottom fixed plate, the vertical capacitance increases whereas the horizontal capacitance decreases simultaneously such that the sum of the two capacitances yields a linear capacitance-voltage relation. © 2012 The Institution of Engineering and Technology.

Linear-quadratic model predictions for tumor control probability

International Nuclear Information System (INIS)

Yaes, R.J.

1987-01-01

Sigmoid dose-response curves for tumor control are calculated from the linear-quadratic model parameters α and Β, obtained from human epidermoid carcinoma cell lines, and are much steeper than the clinical dose-response curves for head and neck cancers. One possible explanation is the presence of small radiation-resistant clones arising from mutations in an initially homogeneous tumor. Using the mutation theory of Delbruck and Luria and of Goldie and Coldman, the authors discuss the implications of such radiation-resistant clones for clinical radiation therapy

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...

Improving linear accelerator service response with a real- time electronic event reporting system.

Science.gov (United States)

Hoisak, Jeremy D P; Pawlicki, Todd; Kim, Gwe-Ya; Fletcher, Richard; Moore, Kevin L

2014-09-08

To track linear accelerator performance issues, an online event recording system was developed in-house for use by therapists and physicists to log the details of technical problems arising on our institution's four linear accelerators. In use since October 2010, the system was designed so that all clinical physicists would receive email notification when an event was logged. Starting in October 2012, we initiated a pilot project in collaboration with our linear accelerator vendor to explore a new model of service and support, in which event notifications were also sent electronically directly to dedicated engineers at the vendor's technical help desk, who then initiated a response to technical issues. Previously, technical issues were reported by telephone to the vendor's call center, which then disseminated information and coordinated a response with the Technical Support help desk and local service engineers. The purpose of this work was to investigate the improvements to clinical operations resulting from this new service model. The new and old service models were quantitatively compared by reviewing event logs and the oncology information system database in the nine months prior to and after initiation of the project. Here, we focus on events that resulted in an inoperative linear accelerator ("down" machine). Machine downtime, vendor response time, treatment cancellations, and event resolution were evaluated and compared over two equivalent time periods. In 389 clinical days, there were 119 machine-down events: 59 events before and 60 after introduction of the new model. In the new model, median time to service response decreased from 45 to 8 min, service engineer dispatch time decreased 44%, downtime per event decreased from 45 to 20 min, and treatment cancellations decreased 68%. The decreased vendor response time and reduced number of on-site visits by a service engineer resulted in decreased downtime and decreased patient treatment cancellations.

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.

Using projector augmented-wave (PAW) formalism inside the density-functional perturbation theory; L'utilisation du formalisme PAW en theorie de la fonctionnelle de la densite perturbee

Energy Technology Data Exchange (ETDEWEB)

Audouze, Ch

2006-07-01

In condensed matter physics, ab-initio simulation allows to get macroscopic quantities (for example equations of state) from microscopic ones, as phonon frequencies which characterize the vibration Eigenmodes of the system. Therefore, one can theoretically predict the behavior of the material at very high pressure conditions, which can be out of reach by experiences. Computations of phonon spectrum are obtained thanks to the linear response theory, where the equations of Density Functional Theory (as the Kohn-Sham model) are perturbed around their fundamental state. The linear response functionality is one of the options included in the ABINIT code, which is an open source package developed in particular by a team of the CEA-DAM (DPTA) and the Catholic University of Louvain-la-Neuve (Belgium). Nevertheless, in spite of using pseudopotentials, computations of phonon spectrum are not tractable for heavy chemical elements, even on massively parallel computers. In order to overcome this difficulty, the linear response theory had to be extended to the PAW (Projector Augmented-Waves) formalism. In this CEA report, we first detail the PAW model, giving to it a more mathematical framework. Then we establish the linear response equations within the PAW formalism, up to the third order derivative of the total energy, for an isolated molecular system and for generic perturbations. Lastly, all these results are specified to the particular case of atom displacements and for perturbations associated to the change of an external potential in which the molecule is set. (author)

Linear response approach to active Brownian particles in time-varying activity fields

Science.gov (United States)

Merlitz, Holger; Vuijk, Hidde D.; Brader, Joseph; Sharma, Abhinav; Sommer, Jens-Uwe

2018-05-01

In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of non-interacting particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.

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...

Using Classical Test Theory and Item Response Theory to Evaluate the LSCI

Science.gov (United States)

Schlingman, Wayne M.; Prather, E. E.; Collaboration of Astronomy Teaching Scholars CATS

2011-01-01

Analyzing the data from the recent national study using the Light and Spectroscopy Concept Inventory (LSCI), this project uses both Classical Test Theory (CTT) and Item Response Theory (IRT) to investigate the LSCI itself in order to better understand what it is actually measuring. We use Classical Test Theory to form a framework of results that can be used to evaluate the effectiveness of individual questions at measuring differences in student understanding and provide further insight into the prior results presented from this data set. In the second phase of this research, we use Item Response Theory to form a theoretical model that generates parameters accounting for a student's ability, a question's difficulty, and estimate the level of guessing. The combined results from our investigations using both CTT and IRT are used to better understand the learning that is taking place in classrooms across the country. The analysis will also allow us to evaluate the effectiveness of individual questions and determine whether the item difficulties are appropriately matched to the abilities of the students in our data set. These results may require that some questions be revised, motivating the need for further development of the LSCI. This material is based upon work supported by the National Science Foundation under Grant No. 0715517, a CCLI Phase III Grant for the Collaboration of Astronomy Teaching Scholars (CATS). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

The theory of a general quantum system interacting with a linear dissipative system

International Nuclear Information System (INIS)

Feynman, R.P.; Vernon, F.L.

2000-01-01

A formalism has been developed, using Feynman's space-time formulation of nonrelativistic quantum mechanics whereby the behavior of a system of interest, which is coupled to other external quantum systems, may be calculated in terms of its own variables only. It is shown that the effect of the external systems in such a formalism can always be included in a general class of functionals (influence functionals) of the coordinates of the system only. The properties of influence functionals for general systems are examined. Then, specific forms of influence functionals representing the effect of definite and random classical forces, linear dissipative systems at finite temperatures, and combinations of these are analyzed in detail. The linear system analysis is first done for perfectly linear systems composed of combinations of harmonic oscillators, loss being introduced by continuous distributions of oscillators. Then approximately linear systems and restrictions necessary for the linear behavior are considered. Influence functionals for all linear systems are shown to have the same form in terms of their classical response functions. In addition, a fluctuation-dissipation theorem is derived relating temperature and dissipation of the linear system to a fluctuating classical potential acting on the system of interest which reduces to the Nyquist-Johnson relation for noise in the case of electric circuits. Sample calculations of transition probabilities for the spontaneous emission of an atom in free space and in a cavity are made. Finally, a theorem is proved showing that within the requirements of linearity all sources of noise or quantum fluctuation introduced by maser-type amplification devices are accounted for by a classical calculation of the characteristics of the maser

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.

Excited electronic states of MnO{sub 4}{sup −}: Challenges for wavefunction and density functional response theories

Energy Technology Data Exchange (ETDEWEB)

Almeida, Nuno M.S.; McKinlay, Russell G.; Paterson, Martin J., E-mail: m.j.paterson@hw.ac.uk

2015-01-13

Highlights: • Linear response coupled cluster hierarchy CCS, CC2, CCSD, CC3 applied to lowest excited states of MnO{sub 4}{sup −}. • Unphysical results obtained for approximate CCn methods. • Failure traced to very large singles amplitudes. • HF and RASSCF calculations on ground state show strong correlations give very poor HF single particle picture. • TD-CAM-B3LYP describes LMCT states with reasonable accuracy. - Abstract: The lowest excited electronic states of the permanganate ion MnO{sub 4}{sup −} are calculated using a hierarchy of coupled cluster response approaches, as well as time-dependent density functional theory. It is shown that while full linear response coupled cluster with singles and doubles (or higher) performs well, that permanganate represents a stern test for approximate coupled cluster response models, and that problems can be traced to very large orbital relaxation effects. TD-DFT is reasonably robust although errors around 0.6 eV are still observed. In order to further investigate the strong correlations prevalent in the electronic ground state large-scale RASSCF calculations were also performed. Again very large orbital relaxation in the correlated wavefunction is observed. Although the system can qualitatively be described by a single configuration, multi-reference diagnostic values show that care must be taken in this and similar metal complexes.

Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics

International Nuclear Information System (INIS)

Hoover, W.G.

1980-01-01

Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility

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)

Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation

Energy Technology Data Exchange (ETDEWEB)

List, Nanna Holmgaard, E-mail: nhl@sdu.dk; Jensen, Hans Jørgen Aagaard [Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M (Denmark); Kauczor, Joanna; Norman, Patrick, E-mail: panor@ifm.liu.se [Department of Physics, Chemistry and Biology, Linköping University, Linköping SE 58183 (Sweden); Saue, Trond [Laboratoire de Chimie et Physique Quantiques, UMR 5626—CNRS/Université Toulouse III (Paul Sabatier), 118 route de Narbonne, F-31062 Toulouse Cedex (France)

2015-06-28

We present a formulation of molecular response theory for the description of a quantum mechanical molecular system in the presence of a weak, monochromatic, linearly polarized electromagnetic field without introducing truncated multipolar expansions. The presentation focuses on a description of linear absorption by adopting the energy-loss approach in combination with the complex polarization propagator formulation of response theory. Going beyond the electric-dipole approximation is essential whenever studying electric-dipole-forbidden transitions, and in general, non-dipolar effects become increasingly important when addressing spectroscopies involving higher-energy photons. These two aspects are examined by our study of the near K-edge X-ray absorption fine structure of the alkaline earth metals (Mg, Ca, Sr, Ba, and Ra) as well as the trans-polyenes. In following the series of alkaline earth metals, the sizes of non-dipolar effects are probed with respect to increasing photon energies and a detailed assessment of results is made in terms of studying the pertinent transition electron densities and in particular their spatial extension in comparison with the photon wavelength. Along the series of trans-polyenes, the sizes of non-dipolar effects are probed for X-ray spectroscopies on organic molecules with respect to the spatial extension of the chromophore.

Beyond the electric-dipole approximation: A formulation and implementation of molecular response theory for the description of absorption of electromagnetic field radiation.

Science.gov (United States)

List, Nanna Holmgaard; Kauczor, Joanna; Saue, Trond; Jensen, Hans Jørgen Aagaard; Norman, Patrick

2015-06-28

We present a formulation of molecular response theory for the description of a quantum mechanical molecular system in the presence of a weak, monochromatic, linearly polarized electromagnetic field without introducing truncated multipolar expansions. The presentation focuses on a description of linear absorption by adopting the energy-loss approach in combination with the complex polarization propagator formulation of response theory. Going beyond the electric-dipole approximation is essential whenever studying electric-dipole-forbidden transitions, and in general, non-dipolar effects become increasingly important when addressing spectroscopies involving higher-energy photons. These two aspects are examined by our study of the near K-edge X-ray absorption fine structure of the alkaline earth metals (Mg, Ca, Sr, Ba, and Ra) as well as the trans-polyenes. In following the series of alkaline earth metals, the sizes of non-dipolar effects are probed with respect to increasing photon energies and a detailed assessment of results is made in terms of studying the pertinent transition electron densities and in particular their spatial extension in comparison with the photon wavelength. Along the series of trans-polyenes, the sizes of non-dipolar effects are probed for X-ray spectroscopies on organic molecules with respect to the spatial extension of the chromophore.

Fitting Diffusion Item Response Theory Models for Responses and Response Times Using the R Package diffIRT

Directory of Open Access Journals (Sweden)

Dylan Molenaar

2015-08-01

Full Text Available In the psychometric literature, item response theory models have been proposed that explicitly take the decision process underlying the responses of subjects to psychometric test items into account. Application of these models is however hampered by the absence of general and flexible software to fit these models. In this paper, we present diffIRT, an R package that can be used to fit item response theory models that are based on a diffusion process. We discuss parameter estimation and model fit assessment, show the viability of the package in a simulation study, and illustrate the use of the package with two datasets pertaining to extraversion and mental rotation. In addition, we illustrate how the package can be used to fit the traditional diffusion model (as it has been originally developed in experimental psychology to data.

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

2-D response mapping of multi-linear silicon drift detectors

International Nuclear Information System (INIS)

Castoldi, A.; Guazzoni, C.; Hartmann, R.; Mezza, D.; Strueder, L.; Tassan Garofolo, F.

2010-01-01

Multi-linear silicon drift detectors (MLSDDs) are good candidates to fulfill simultaneous requirements for 2-D position-sensing and spectroscopy applications. The optimization of their design and performance as 2-D imagers requires a detailed study of timing properties of the charge cloud in the MLSDD architecture. In particular it is important to experimentally determine the dependence of the measured amplitude and time-of-arrival on the photon position of interaction so as to derive the 2D detector response. In this paper we will present a detailed experimental characterization aimed at measuring the detector amplitude response and its timing response. The dependence of charge cloud drift time on precise position of interaction has been measured as a function of detector biasing conditions.

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.

Beck's cognitive theory and the response style theory of depression in adolescents with and without mild to borderline intellectual disability

NARCIS (Netherlands)

Weeland, M.M.; Nijhof, K.S.; Otten, R.; Vermaes, I.P.R.; Buitelaar, J.K.

2017-01-01

Aim: This study tests the validity of Beck’s cognitive theory and Nolen-Hoeksema's response style theory of depression in adolescents with and without MBID. Methods: The relationship between negative cognitive errors (Beck), response styles (Nolen-Hoeksema) and depressive symptoms was examined in

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.

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

Non-Linear Dose Response Relationships in Biology, Toxicology, and Medicine (June 8-10, 2004). Final Report

International Nuclear Information System (INIS)

Calabrese, Edward J.

2004-01-01

The conference attracts approximately 500 scientists researching in the area of non-linear low dose effects. These scientists represent a wide range of biological/medical fields and technical disciplines. Observations that biphasic dose responses are frequently reported in each of these areas but that the recognition of similar dose response relationships across disciplines is very rarely appreciated and exploited. By bringing scientist of such diverse backgrounds together who are working on the common area of non-linear dose response relationships this will enhance our understanding of the occurrence, origin, mechanism, significance and practical applications of such dose response relationships

Orbital-motion-limited theory of dust charging and plasma response

International Nuclear Information System (INIS)

Tang, Xian-Zhu; Luca Delzanno, Gian

2014-01-01

The foundational theory for dusty plasmas is the dust charging theory that provides the dust potential and charge arising from the dust interaction with a plasma. The most widely used dust charging theory for negatively charged dust particles is the so-called orbital motion limited (OML) theory, which predicts the dust potential and heat collection accurately for a variety of applications, but was previously found to be incapable of evaluating the dust charge and plasma response in any situation. Here, we report a revised OML formulation that is able to predict the plasma response and hence the dust charge. Numerical solutions of the new OML model show that the widely used Whipple approximation of dust charge-potential relationship agrees with OML theory in the limit of small dust radius compared with plasma Debye length, but incurs large (order-unity) deviation from the OML prediction when the dust size becomes comparable with or larger than plasma Debye length. This latter case is expected for the important application of dust particles in a tokamak plasma

Extending Item Response Theory to Online Homework

Science.gov (United States)

Kortemeyer, Gerd

2014-01-01

Item response theory (IRT) becomes an increasingly important tool when analyzing "big data" gathered from online educational venues. However, the mechanism was originally developed in traditional exam settings, and several of its assumptions are infringed upon when deployed in the online realm. For a large-enrollment physics course for…

A signal detection-item response theory model for evaluating neuropsychological measures.

Science.gov (United States)

Thomas, Michael L; Brown, Gregory G; Gur, Ruben C; Moore, Tyler M; Patt, Virginie M; Risbrough, Victoria B; Baker, Dewleen G

2018-02-05

Models from signal detection theory are commonly used to score neuropsychological test data, especially tests of recognition memory. Here we show that certain item response theory models can be formulated as signal detection theory models, thus linking two complementary but distinct methodologies. We then use the approach to evaluate the validity (construct representation) of commonly used research measures, demonstrate the impact of conditional error on neuropsychological outcomes, and evaluate measurement bias. Signal detection-item response theory (SD-IRT) models were fitted to recognition memory data for words, faces, and objects. The sample consisted of U.S. Infantry Marines and Navy Corpsmen participating in the Marine Resiliency Study. Data comprised item responses to the Penn Face Memory Test (PFMT; N = 1,338), Penn Word Memory Test (PWMT; N = 1,331), and Visual Object Learning Test (VOLT; N = 1,249), and self-report of past head injury with loss of consciousness. SD-IRT models adequately fitted recognition memory item data across all modalities. Error varied systematically with ability estimates, and distributions of residuals from the regression of memory discrimination onto self-report of past head injury were positively skewed towards regions of larger measurement error. Analyses of differential item functioning revealed little evidence of systematic bias by level of education. SD-IRT models benefit from the measurement rigor of item response theory-which permits the modeling of item difficulty and examinee ability-and from signal detection theory-which provides an interpretive framework encompassing the experimentally validated constructs of memory discrimination and response bias. We used this approach to validate the construct representation of commonly used research measures and to demonstrate how nonoptimized item parameters can lead to erroneous conclusions when interpreting neuropsychological test data. Future work might include the

Berry Fermi liquid theory

Energy Technology Data Exchange (ETDEWEB)

Chen, Jing-Yuan, E-mail: chjy@uchicago.edu [Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637 (United States); Stanford Institute for Theoretical Physics, Stanford University, CA 94305 (United States); Son, Dam Thanh, E-mail: dtson@uchicago.edu [Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637 (United States)

2017-02-15

We develop an extension of the Landau Fermi liquid theory to systems of interacting fermions with non-trivial Berry curvature. We propose a kinetic equation and a constitutive relation for the electromagnetic current that together encode the linear response of such systems to external electromagnetic perturbations, to leading and next-to-leading orders in the expansion over the frequency and wave number of the perturbations. We analyze the Feynman diagrams in a large class of interacting quantum field theories and show that, after summing up all orders in perturbation theory, the current–current correlator exactly matches with the result obtained from the kinetic theory. - Highlights: • We extend Landau’s kinetic theory of Fermi liquid to incorporate Berry phase. • Berry phase effects in Fermi liquid take exactly the same form as in Fermi gas. • There is a new “emergent electric dipole” contribution to the anomalous Hall effect. • Our kinetic theory is matched to field theory to all orders in Feynman diagrams.

Linear and nonlinear viscous flow in two-dimensional fluids

International Nuclear Information System (INIS)

Gravina, D.; Ciccotti, G.; Holian, B.L.

1995-01-01

We report on molecular dynamics simulations of shear viscosity η of a dense two-dimensional fluid as a function of the shear rate γ. We find an analytic dependence of η on γ, and do not find any evidence whatsoever of divergence in the Green-Kubo (GK) value that would be caused by the well-known long-time tail for the shear-stress autocorrelation function, as predicted by the mode-coupling theory. In accordance with the linear response theory, the GK value of η agrees remarkably well with nonequilibrium values at small shear rates. (c) 1995 The American Physical Society

Stochastic Parameter Estimation of Non-Linear Systems Using Only Higher Order Spectra of the Measured Response

Science.gov (United States)

Vasta, M.; Roberts, J. B.

1998-06-01

Methods for using fourth order spectral quantities to estimate the unknown parameters in non-linear, randomly excited dynamic systems are developed. Attention is focused on the case where only the response is measurable and the excitation is unmeasurable and known only in terms of a stochastic process model. The approach is illustrated through application to a non-linear oscillator with both non-linear damping and stiffness and with excitation modelled as a stationary Gaussian white noise process. The methods have applications in studies of the response of structures to random environmental loads, such as wind and ocean wave forces.

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.

Kinetic theory of gases and plasmas

International Nuclear Information System (INIS)

Schram, P.P.J.M.

1991-01-01

Kinetic theory provides the link between the non-equilibrium statistical mechanics of many-particle systems and macroscopic or phenomenological physics. This volume deals with the derivation of kinetic equations, their limitations and generalizations,and with the applications of kinetic theory to physical phenomena and the calculation of transport coefficients. This book is divided in 12 chapters which discuss a wide range of topics such as balanced equations, the Klimontovich, Vlasov-Maxwell, and Boltzmann equations, Chapman-Enskog theory, the kinetic theory of plasmas, B.G.K. models, linear response theory, Brownian motion and renormalized kinetic theory. Each chapter is concluded with exercises, which not only enable the readers to test their understanding of the theory, but also present additional examples which complement the text. 151 refs.; 35 figs.; 5 tabs

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...

Item response theory scoring and the detection of curvilinear relationships.

Science.gov (United States)

Carter, Nathan T; Dalal, Dev K; Guan, Li; LoPilato, Alexander C; Withrow, Scott A

2017-03-01

Psychologists are increasingly positing theories of behavior that suggest psychological constructs are curvilinearly related to outcomes. However, results from empirical tests for such curvilinear relations have been mixed. We propose that correctly identifying the response process underlying responses to measures is important for the accuracy of these tests. Indeed, past research has indicated that item responses to many self-report measures follow an ideal point response process-wherein respondents agree only to items that reflect their own standing on the measured variable-as opposed to a dominance process, wherein stronger agreement, regardless of item content, is always indicative of higher standing on the construct. We test whether item response theory (IRT) scoring appropriate for the underlying response process to self-report measures results in more accurate tests for curvilinearity. In 2 simulation studies, we show that, regardless of the underlying response process used to generate the data, using the traditional sum-score generally results in high Type 1 error rates or low power for detecting curvilinearity, depending on the distribution of item locations. With few exceptions, appropriate power and Type 1 error rates are achieved when dominance-based and ideal point-based IRT scoring are correctly used to score dominance and ideal point response data, respectively. We conclude that (a) researchers should be theory-guided when hypothesizing and testing for curvilinear relations; (b) correctly identifying whether responses follow an ideal point versus dominance process, particularly when items are not extreme is critical; and (c) IRT model-based scoring is crucial for accurate tests of curvilinearity. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Multilevel Higher-Order Item Response Theory Models

Science.gov (United States)

Huang, Hung-Yu; Wang, Wen-Chung

2014-01-01

In the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The…

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.

Framing anomaly in the effective theory of the fractional quantum Hall effect.

Science.gov (United States)

Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G; Fradkin, Eduardo

2015-01-09

We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.

Item Response Theory: Overview, Applications, and Promise for Institutional Research

Science.gov (United States)

Bowman, Nicholas A.; Herzog, Serge; Sharkness, Jessica

2014-01-01

Item Response Theory (IRT) is a measurement theory that is ideal for scale and test development in institutional research, but it is not without its drawbacks. This chapter provides an overview of IRT, describes an example of its use, and highlights the pros and cons of using IRT in applied settings.

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

Responses to James Tully’s “Deparochializing Political Theory and Beyond”

Directory of Open Access Journals (Sweden)

Garrick Cooper

2017-06-01

Full Text Available In their responses to James Tully’s article “Deparochializing Political Theory and Beyond,” Garrick Cooper, Charles W. Mills, Sudipta Kaviraj and Sor-hoon Tan engage with different aspects of Tully’s “genuine dialogue.” While they seem to concur with Tully on the urgency of deparochializing political theory, their responses bring to light salient issues which would have to be thought through in taking this project forward.

Measuring Anxiety in Visually-Impaired People: A Comparison between the Linear and the Nonlinear IRT Approaches

Science.gov (United States)

Ferrando, Pere J.; Pallero, Rafael; Anguiano-Carrasco, Cristina

2013-01-01

The present study has two main interests. First, some pending issues about the psychometric properties of the CTAC (an anxiety questionnaire for blind and visually-impaired people) are assessed using item response theory (IRT). Second, the linear model is compared to the graded response model (GRM) in terms of measurement precision, sensitivity…

The time-walk of analog constant fraction discriminators using very fast scintillator detectors with linear and non-linear energy response

Energy Technology Data Exchange (ETDEWEB)

Regis, J.-M., E-mail: regis@ikp.uni-koeln.de [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); Rudigier, M.; Jolie, J.; Blazhev, A.; Fransen, C.; Pascovici, G.; Warr, N. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany)

2012-08-21

The electronic {gamma}-{gamma} fast timing technique allows for direct nuclear lifetime determination down to the few picoseconds region by measuring the time difference between two coincident {gamma}-ray transitions. Using high resolution ultra-fast LaBr{sub 3}(Ce) scintillator detectors in combination with the recently developed mirror symmetric centroid difference method, nuclear lifetimes are measured with a time resolving power of around 5 ps. The essence of the method is to calibrate the energy dependent position (centroid) of the prompt response function of the setup which is obtained for simultaneously occurring events. This time-walk of the prompt response function induced by the analog constant fraction discriminator has been determined by systematic measurements using different photomultiplier tubes and timing adjustments of the constant fraction discriminator. We propose a universal calibration function which describes the time-walk or the combined {gamma}-{gamma} time-walk characteristics, respectively, for either a linear or a non-linear amplitude versus energy dependency of the scintillator detector output pulses.

THE RESPONSIBILITY TO PROTECT. A JUST WAR THEORY BASED ANALYSIS

Directory of Open Access Journals (Sweden)

Andreea IANCU

2014-11-01

Full Text Available This paper analyzes the Responsibility to protect principle as the paradigm that reinforces the just war theory in the current international relations. The importance of this analysis is given by the fact that in the current change of source of international conflicts, the Responsibility to protect principle affirms the responsibility of the international community to protect all the citizens of the world. In this context we witness a translation toward a Post-Westphalian international system, which values the individual as a security referent. This article discusses the origins of the responsibility to protect principle and problematizes (discusses the legitimacy of use of violence and force in the current international system. Moreover, the paper analyzes the possible humanization of the current international relations and, simultaneously, the persistency of conflict and warfare in the international system. The conclusion of this research states that the Responsibility to protect principle revises the just war theory by centering it on the individual.

Dual symmetry in Born-Infeld theory

International Nuclear Information System (INIS)

Khademi, S; Ayoubi, A

2008-01-01

Born-Infeld theory is a non-linear formalism which has many applications in string and electromagnetic theories. Although, the existence of magnetic monopoles and dyons are suggested by Born-Infeld theory, but this theory is not invariant under the dual transformations. In this theory electric fields for point charged particles are not singular at origin (r = 0), but magnetic fields and vector potentials are still singular. In this paper we show that the vanishing of dual symmetry is responsible for these singularities. Furthermore, we present the dual symmetric Born-Infeld theory, by a symmetric definition of electromagnetic fields in terms of new scalar and vector potentials, as well as the ordinary ones. All singularities of vector potential and magnetic field are removed as an immediate consequence of this symmetry.

Theory of RBE. Progress report, 1 January 1976--31 December 1976

International Nuclear Information System (INIS)

Katz, R.

1976-09-01

Experimental studies of emulsion-processing combinations have demonstrated that a range of hittedness, from 1 to 8-or-more, can be achieved with specially processed nuclear research emulsions of the Ilford K series, encompassing the range of supralinear response displayed by biological cells. In analogy with the response of biological cells to high LET radiations, the processes of ion-kill and gamma-kill have been displayed for these emulsions, in that x-rays blacken emulsion in circumstances that single alpha-particles, or even single fission fragments, leave no visible track. Track structure theory and the theory of RBE have been extended to these multi-hit detectors. Supralinearity in thermoluminescent dosimeters has been tentatively identified as due to a population of 2-or-more hit trapping sites, coexisting with the linear 1-or-more hit sites. Inferences from this identification that the response to high-LET radiations is linear and that 2-hit sites must display an RBE greater than 1 are consistent with some experimental observations. This is a second solid state detector having the capacity to mimic the response of biological systems identified from the theory of RBE

CiOpt: a program for optimization of the frequency response of linear circuits

OpenAIRE

Miró Sans, Joan Maria; Palà Schönwälder, Pere

1991-01-01

An interactive personal-computer program for optimizing the frequency response of linear lumped circuits (CiOpt) is presented. CiOpt has proved to be an efficient tool in improving designs where the inclusion of more accurate device models distorts the desired frequency response, as well as in device modeling. The outputs of CiOpt are the element values which best match the obtained and the desired frequency response. The optimization algorithms used (the Fletcher-Powell and Newton's methods,...

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

The linear and nonlinear response of infinite periodic systems to static and/or dynamic electric fields. Implementation in CRYSTAL code

Energy Technology Data Exchange (ETDEWEB)

Kirtman, Bernard [Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106 (United States); Springborg, Michael [Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken (Germany); Rérat, Michel [Equipe de Chimie Physique, IPREM UMR5254, Université de Pau et des Pays de l' Adour, 64000 Pau (France); Ferrero, Mauro; Lacivita, Valentina; Dovesi, Roberto [Departimeno di Chimica, IFM, Università di Torino and NIS - Nanostructure Interfaces and Surfaces - Centre of Excellence, Via P. Giuria 7, 10125 Torino (Italy); Orlando, Roberto [Departimento di Scienze e Tecnologie Avanzati, Università del Piemonte Orientale, Viale T. Michel 11, 15121 Alessandria (Italy)

2015-01-22

An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.

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.

Behavioral Theory and Culture Special Issue: Authors' Response to Commentaries

Science.gov (United States)

Pasick, Rena J.; Burke, Nancy J.; Joseph, Galen

2009-01-01

This article presents the authors' response to commentaries that focus on the "Behavioral Constructs and Culture in Cancer Screening" (3Cs) study. The 3Cs study had an unremarkable beginning, with two colleagues discussing their frustration over the narrow range of behavioral theories and the limited guidance the theories offered for a study…

An Introduction to Item Response Theory for Health Behavior Researchers

Science.gov (United States)

Warne, Russell T.; McKyer, E. J. Lisako; Smith, Matthew L.

2012-01-01

Objective: To introduce item response theory (IRT) to health behavior researchers by contrasting it with classical test theory and providing an example of IRT in health behavior. Method: Demonstrate IRT by fitting the 2PL model to substance-use survey data from the Adolescent Health Risk Behavior questionnaire (n = 1343 adolescents). Results: An…

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 ...

Fluctuations of two-time quantities and non-linear response functions

International Nuclear Information System (INIS)

Corberi, F; Lippiello, E; Sarracino, A; Zannetti, M

2010-01-01

We study the fluctuations of the autocorrelation and autoresponse functions and, in particular, their variances and covariance. In a first general part of the paper, we show the equivalence of the variance of the response function to the second-order susceptibility of a composite operator, and we derive an equilibrium fluctuation-dissipation theorem beyond linear order, relating it to the other variances. In a second part of the paper we apply the formalism in the study of non-disordered ferromagnets, in equilibrium or in the coarsening kinetics following a critical or sub-critical quench. We show numerically that the variances and the non-linear susceptibility obey scaling with respect to the coherence length ξ in equilibrium, and with respect to the growing length L(t) after a quench, similar to what is known for the autocorrelation and the autoresponse functions

Theoretic simulation for CMOS device on total dose radiation response

International Nuclear Information System (INIS)

He Baoping; Zhou Heqin; Guo Hongxia; He Chaohui; Zhou Hui; Luo Yinhong; Zhang Fengqi

2006-01-01

Total dose effect is simulated for C4007B, CC4007RH and CC4011 devices at different absorbed dose rate by using linear system theory. When irradiation response and dose are linear, total dose radiation and post-irradiation annealing at room temperature are determined for one random by choosing absorbed dose rate, and total dose effect at other absorbed dose rate can be predicted by using linear system theory. The simulating results agree with the experimental results at different absorbed dose rate. (authors)

Linear population allocation by bistable switches in response to transient stimulation.

Science.gov (United States)

Srimani, Jaydeep K; Yao, Guang; Neu, John; Tanouchi, Yu; Lee, Tae Jun; You, Lingchong

2014-01-01

Many cellular decision processes, including proliferation, differentiation, and phenotypic switching, are controlled by bistable signaling networks. In response to transient or intermediate input signals, these networks allocate a population fraction to each of two distinct states (e.g. OFF and ON). While extensive studies have been carried out to analyze various bistable networks, they are primarily focused on responses of bistable networks to sustained input signals. In this work, we investigate the response characteristics of bistable networks to transient signals, using both theoretical analysis and numerical simulation. We find that bistable systems exhibit a common property: for input signals with short durations, the fraction of switching cells increases linearly with the signal duration, allowing the population to integrate transient signals to tune its response. We propose that this allocation algorithm can be an optimal response strategy for certain cellular decisions in which excessive switching results in lower population fitness.

Kovacs-Like Memory Effect in Athermal Systems: Linear Response Analysis

Science.gov (United States)

Plata, Carlos; Prados, Antonio

2017-10-01

We analyse the emergence of Kovacs-like memory effects in athermal systems within the linear response regime. This is done by starting from both the master equation for the probability distribution and the equations for the physically relevant moments. The general results are applied to a general class of models with conserved momentum and non-conserved energy. Our theoretical predictions, obtained within the first Sonine approximation, show an excellent agreement with the numerical results.

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.

Equivalent linear and nonlinear site response analysis for design and risk assessment of safety-related nuclear structures

International Nuclear Information System (INIS)

Bolisetti, Chandrakanth; Whittaker, Andrew S.; Mason, H. Benjamin; Almufti, Ibrahim; Willford, Michael

2014-01-01

Highlights: • Performed equivalent linear and nonlinear site response analyses using industry-standard numerical programs. • Considered a wide range of sites and input ground motions. • Noted the practical issues encountered while using these programs. • Examined differences between the responses calculated from different programs. • Results of biaxial and uniaxial analyses are compared. - Abstract: Site response analysis is a precursor to soil-structure interaction analysis, which is an essential component in the seismic analysis of safety-related nuclear structures. Output from site response analysis provides input to soil-structure interaction analysis. Current practice in calculating site response for safety-related nuclear applications mainly involves the equivalent linear method in the frequency-domain. Nonlinear time-domain methods are used by some for the assessment of buildings, bridges and petrochemical facilities. Several commercial programs have been developed for site response analysis but none of them have been formally validated for large strains and high frequencies, which are crucial for the performance assessment of safety-related nuclear structures. This study sheds light on the applicability of some industry-standard equivalent linear (SHAKE) and nonlinear (DEEPSOIL and LS-DYNA) programs across a broad range of frequencies, earthquake shaking intensities, and sites ranging from stiff sand to hard rock, all with a focus on application to safety-related nuclear structures. Results show that the equivalent linear method is unable to reproduce the high frequency acceleration response, resulting in almost constant spectral accelerations in the short period range. Analysis using LS-DYNA occasionally results in some unrealistic high frequency acceleration ‘noise’, which can be removed by smoothing the piece-wise linear backbone curve. Analysis using DEEPSOIL results in abrupt variations in the peak strains of consecutive soil layers

Linear combination of auditory steady-state responses evoked by co-modulated tones

DEFF Research Database (Denmark)

Guérit, François; Marozeau, Jeremy; Epp, Bastian

2017-01-01

Up to medium intensities and in the 80–100-Hz region, the auditory steady-state response (ASSR) to a multi-tone carrier is commonly considered to be a linear sum of the dipoles from each tone specific ASSR generator. Here, this hypothesis was investigated when a unique modulation frequency is used...... for all carrier components. Listeners were presented with a co-modulated dual-frequency carrier (1 and 4 kHz), from which the modulator starting phase Ui of the 1-kHz component was systematically varied. The results support the hypothesis of a linear superposition of the dipoles originating from different...

Thermally activated post-glitch response of the neutron star inner crust and core. I. Theory

Energy Technology Data Exchange (ETDEWEB)

Link, Bennett, E-mail: link@physics.montana.edu [Department of Physics, Montana State University, Bozeman, MT 59717 (United States)

2014-07-10

Pinning of superfluid vortices is predicted to prevail throughout much of a neutron star. Based on the idea of Alpar et al., I develop a description of the coupling between the solid and liquid components of a neutron star through thermally activated vortex slippage, and calculate the response to a spin glitch. The treatment begins with a derivation of the vortex velocity from the vorticity equations of motion. The activation energy for vortex slippage is obtained from a detailed study of the mechanics and energetics of vortex motion. I show that the 'linear creep' regime introduced by Alpar et al. and invoked in fits to post-glitch response is not realized for physically reasonable parameters, a conclusion that strongly constrains the physics of a post-glitch response through thermal activation. Moreover, a regime of 'superweak pinning', crucial to the theory of Alpar et al. and its extensions, is probably precluded by thermal fluctuations. The theory given here has a robust conclusion that can be tested by observations: for a glitch in the spin rate of magnitude Δν, pinning introduces a delay in the post-glitch response time. The delay time is t{sub d} = 7(t{sub sd}/10{sup 4} yr)((Δν/ν)/10{sup –6}) d, where t{sub sd} is the spin-down age; t{sub d} is typically weeks for the Vela pulsar and months in older pulsars, and is independent of the details of vortex pinning. Post-glitch response through thermal activation cannot occur more quickly than this timescale. Quicker components of post-glitch response, as have been observed in some pulsars, notably, the Vela pulsar, cannot be due to thermally activated vortex motion but must represent a different process, such as drag on vortices in regions where there is no pinning. I also derive the mutual friction force for a pinned superfluid at finite temperature for use in other studies of neutron star hydrodynamics.

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

Strong-coupling theory of superconductivity

International Nuclear Information System (INIS)

Rainer, D.; Sauls, J.A.

1995-01-01

The electronic properties of correlated metals with a strong electron-phonon coupling may be understood in terms of a combination of Landau''s Fermi liquid theory and the strong-coupling theory of Migdal and Eliashberg. In these lecture notes we discuss the microscopic foundations of this phenomenological Fermi-liquid model of correlated, strong-coupling metals. We formulate the basic equations of the model, which are quasiclassical transport equations that describe both equilibrium and non-equilibrium phenomena for the normal and superconducting states of a metal. Our emphasis is on superconductors close to equilibrium, for which we derive the general linear response theory. As an application we calculate the dynamical conductivity of strong-coupling superconductors. (author)

Similarity transformed coupled cluster response (ST-CCR) theory--a time-dependent similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach.

Science.gov (United States)

Landau, Arie

2013-07-07

This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.

Properties of a novel linear sulfur response mode in a multiple flame photometric detector.

Science.gov (United States)

Clark, Adrian G; Thurbide, Kevin B

2014-01-24

A new linear sulfur response mode was established in the multiple flame photometric detector (mFPD) by monitoring HSO* emission in the red spectral region above 600nm. Optimal conditions for this mode were found by using a 750nm interference filter and oxygen flows to the worker flames of this device that were about 10mL/min larger than those used for monitoring quadratic S2* emission. By employing these parameters, this mode provided a linear response over about 4 orders of magnitude, with a detection limit near 5.8×10(-11)gS/s and a selectivity of sulfur over carbon of about 3.5×10(3). Specifically, the minimum detectable masses for 10 different sulfur analytes investigated ranged from 0.4 to 3.6ng for peak half-widths spanning 4-6s. The response toward ten different sulfur compounds was examined and produced an average reproducibility of 1.7% RSD (n=10) and an average equimolarity value of 1.0±0.1. In contrast to this, a conventional single flame S2* mode comparatively yielded respective values of 6.7% RSD (n=10) and 1.1±0.4. HSO* emission in the mFPD was also found to be relatively much less affected by response quenching due to hydrocarbons compared to a conventional single flame S2* emission mode. Results indicate that this new alternative linear mFPD response mode could be beneficial for sulfur monitoring applications. Copyright © 2013 Elsevier B.V. All rights reserved.

Overview of Classical Test Theory and Item Response Theory for Quantitative Assessment of Items in Developing Patient-Reported Outcome Measures

Science.gov (United States)

Cappelleri, Joseph C.; Lundy, J. Jason; Hays, Ron D.

2014-01-01

Introduction The U.S. Food and Drug Administration’s patient-reported outcome (PRO) guidance document defines content validity as “the extent to which the instrument measures the concept of interest” (FDA, 2009, p. 12). “Construct validity is now generally viewed as a unifying form of validity for psychological measurements, subsuming both content and criterion validity” (Strauss & Smith, 2009, p. 7). Hence both qualitative and quantitative information are essential in evaluating the validity of measures. Methods We review classical test theory and item response theory approaches to evaluating PRO measures including frequency of responses to each category of the items in a multi-item scale, the distribution of scale scores, floor and ceiling effects, the relationship between item response options and the total score, and the extent to which hypothesized “difficulty” (severity) order of items is represented by observed responses. Conclusion Classical test theory and item response theory can be useful in providing a quantitative assessment of items and scales during the content validity phase of patient-reported outcome measures. Depending on the particular type of measure and the specific circumstances, either one or both approaches should be considered to help maximize the content validity of PRO measures. PMID:24811753

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

Computerized Adaptive Test (CAT) Applications and Item Response Theory Models for Polytomous Items

Science.gov (United States)

Aybek, Eren Can; Demirtasli, R. Nukhet

2017-01-01

This article aims to provide a theoretical framework for computerized adaptive tests (CAT) and item response theory models for polytomous items. Besides that, it aims to introduce the simulation and live CAT software to the related researchers. Computerized adaptive test algorithm, assumptions of item response theory models, nominal response…

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

Science.gov (United States)

Schuecker, Clara; Davila, Carlos G.; Pettermann, Heinz E.

2008-01-01

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

Equilibrium finite-frequency noise of an interacting mesoscopic capacitor studied in time-dependent density functional theory

Science.gov (United States)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-03-01

We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time perturbation theory and find excellent agreement for noise frequencies below the reservoir temperature.

Theory of thermoluminescence gamma dose response: The unified interaction model

International Nuclear Information System (INIS)

Horowitz, Y.S.

2001-01-01

We describe the development of a comprehensive theory of thermoluminescence (TL) dose response, the unified interaction model (UNIM). The UNIM is based on both radiation absorption stage and recombination stage mechanisms and can describe dose response for heavy charged particles (in the framework of the extended track interaction model - ETIM) as well as for isotropically ionising gamma rays and electrons (in the framework of the TC/LC geminate recombination model) in a unified and self-consistent conceptual and mathematical formalism. A theory of optical absorption dose response is also incorporated in the UNIM to describe the radiation absorption stage. The UNIM is applied to the dose response supralinearity characteristics of LiF:Mg,Ti and is especially and uniquely successful in explaining the ionisation density dependence of the supralinearity of composite peak 5 in TLD-100. The UNIM is demonstrated to be capable of explaining either qualitatively or quantitatively all of the major features of TL dose response with many of the variable parameters of the model strongly constrained by ancilliary optical absorption and sensitisation measurements

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)

Modeling exposure–lag–response associations with distributed lag non-linear models

Science.gov (United States)

Gasparrini, Antonio

2014-01-01

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094

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

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

Science.gov (United States)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Improving measurement of injection drug risk behavior using item response theory.

Science.gov (United States)

Janulis, Patrick

2014-03-01

Recent research highlights the multiple steps to preparing and injecting drugs and the resultant viral threats faced by drug users. This research suggests that more sensitive measurement of injection drug HIV risk behavior is required. In addition, growing evidence suggests there are gender differences in injection risk behavior. However, the potential for differential item functioning between genders has not been explored. To explore item response theory as an improved measurement modeling technique that provides empirically justified scaling of injection risk behavior and to examine for potential gender-based differential item functioning. Data is used from three studies in the National Institute on Drug Abuse's Criminal Justice Drug Abuse Treatment Studies. A two-parameter item response theory model was used to scale injection risk behavior and logistic regression was used to examine for differential item functioning. Item fit statistics suggest that item response theory can be used to scale injection risk behavior and these models can provide more sensitive estimates of risk behavior. Additionally, gender-based differential item functioning is present in the current data. Improved measurement of injection risk behavior using item response theory should be encouraged as these models provide increased congruence between construct measurement and the complexity of injection-related HIV risk. Suggestions are made to further improve injection risk behavior measurement. Furthermore, results suggest direct comparisons of composite scores between males and females may be misleading and future work should account for differential item functioning before comparing levels of injection risk behavior.

Systematic study of doping dependence on linear magnetoresistance in p-PbTe

International Nuclear Information System (INIS)

Schneider, J. M.; Chitta, V. A.; Oliveira, N. F.; Peres, M. L.; Castro, S. de; Soares, D. A. W.; Wiedmann, S.; Zeitler, U.; Abramof, E.; Rappl, P. H. O.; Mengui, U. A.

2014-01-01

We report on a large linear magnetoresistance effect observed in doped p-PbTe films. While undoped p-PbTe reveals a sublinear magnetoresistance, p-PbTe films doped with BaF 2 exhibit a transition to a nearly perfect linear magnetoresistance behaviour that is persistent up to 30 T. The linear magnetoresistance slope ΔR/ΔB is to a good approximation, independent of temperature. This is in agreement with the theory of Quantum Linear Magnetoresistance. We also performed magnetoresistance simulations using a classical model of linear magnetoresistance. We found that this model fails to explain the experimental data. A systematic study of the doping dependence reveals that the linear magnetoresistance response has a maximum for small BaF 2 doping levels and diminishes rapidly for increasing doping levels. Exploiting the huge impact of doping on the linear magnetoresistance signal could lead to new classes of devices with giant magnetoresistance behavior.

A generalized linear factor model approach to the hierarchical framework for responses and response times.

Science.gov (United States)

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

2015-05-01

We show how the hierarchical model for responses and response times as developed by van der Linden (2007), Fox, Klein Entink, and van der Linden (2007), Klein Entink, Fox, and van der Linden (2009), and Glas and van der Linden (2010) can be simplified to a generalized linear factor model with only the mild restriction that there is no hierarchical model at the item side. This result is valuable as it enables all well-developed modelling tools and extensions that come with these methods. We show that the restriction we impose on the hierarchical model does not influence parameter recovery under realistic circumstances. In addition, we present two illustrative real data analyses to demonstrate the practical benefits of our approach. © 2014 The British Psychological Society.

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

Response of the Shockley surface state to an external electrical field: A density-functional theory study of Cu(111)

Science.gov (United States)

Berland, K.; Einstein, T. L.; Hyldgaard, P.

2012-01-01

The response of the Cu(111) Shockley surface state to an external electrical field is characterized by combining a density-functional theory calculation for a slab geometry with an analysis of the Kohn-Sham wave functions. Our analysis is facilitated by a decoupling of the Kohn-Sham states via a rotation in Hilbert space. We find that the surface state displays isotropic dispersion, quadratic until the Fermi wave vector but with a significant quartic contribution beyond. We calculate the shift in energetic position and effective mass of the surface state for an electrical field perpendicular to the Cu(111) surface; the response is linear over a broad range of field strengths. We find that charge transfer occurs beyond the outermost copper atoms and that accumulation of electrons is responsible for a quarter of the screening of the electrical field. This allows us to provide well converged determinations of the field-induced changes in the surface state for a moderate number of layers in the slab geometry.

A solution to the varying response of the linear power monitor induced by xenon poisoning

Energy Technology Data Exchange (ETDEWEB)

Godsey, T A; Randall, J D [Texas A and M University (United States)

1974-07-01

After conversion to FLIP fuel at Texas A and M, the fuel temperatures were examined very carefully. It was observed that the fuel temperature at 1 Mw varied over a wide range during the week. This variation was shown to be due to the variation in response of the linear CIC which was used to establish reactor power level. A modification of the linear power monitor was designed and installed. The response of this system was verified by using cobalt wires, fuel temperature, and a fission chamber located at 6 feet from the reactor core. The system has proven to be operationally satisfactory. (author)

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

An NCME Instructional Module on Polytomous Item Response Theory Models

Science.gov (United States)

Penfield, Randall David

2014-01-01

A polytomous item is one for which the responses are scored according to three or more categories. Given the increasing use of polytomous items in assessment practices, item response theory (IRT) models specialized for polytomous items are becoming increasingly common. The purpose of this ITEMS module is to provide an accessible overview of…

Responsible Business: A Textbook for Theory; Practice and Change

OpenAIRE

Laasch, Oliver; Conaway, Roger

2014-01-01

his eBook provides a theoretically sound, but highly relevant, introduction to the topic of socially and environmentally responsible business. While the eBook strongly draws from the classic background theories such as business ethics, sustainable development, and corporate social responsibility, those concepts are applied to the most current practices. Practice boxes highlight interesting details, cases and statistics; figures extensively illustrate the theoretical concepts; and end-of-chapt...

Flexible Ferroelectric Sensors with Ultrahigh Pressure Sensitivity and Linear Response over Exceptionally Broad Pressure Range.

Science.gov (United States)

Lee, Youngoh; Park, Jonghwa; Cho, Soowon; Shin, Young-Eun; Lee, Hochan; Kim, Jinyoung; Myoung, Jinyoung; Cho, Seungse; Kang, Saewon; Baig, Chunggi; Ko, Hyunhyub

2018-04-24

Flexible pressure sensors with a high sensitivity over a broad linear range can simplify wearable sensing systems without additional signal processing for the linear output, enabling device miniaturization and low power consumption. Here, we demonstrate a flexible ferroelectric sensor with ultrahigh pressure sensitivity and linear response over an exceptionally broad pressure range based on the material and structural design of ferroelectric composites with a multilayer interlocked microdome geometry. Due to the stress concentration between interlocked microdome arrays and increased contact area in the multilayer design, the flexible ferroelectric sensors could perceive static/dynamic pressure with high sensitivity (47.7 kPa -1 , 1.3 Pa minimum detection). In addition, efficient stress distribution between stacked multilayers enables linear sensing over exceptionally broad pressure range (0.0013-353 kPa) with fast response time (20 ms) and high reliability over 5000 repetitive cycles even at an extremely high pressure of 272 kPa. Our sensor can be used to monitor diverse stimuli from a low to a high pressure range including weak gas flow, acoustic sound, wrist pulse pressure, respiration, and foot pressure with a single device.

Non-linear seismic response of base-isolated liquid storage tanks to bi-directional excitation

International Nuclear Information System (INIS)

Shrimali, M.K.; Jangid, R.S.

2002-01-01

Seismic response of the liquid storage tanks isolated by lead-rubber bearings is investigated for bi-directional earthquake excitation (i.e. two horizontal components). The biaxial force-deformation behaviour of the bearings is considered as bi-linear modelled by coupled non-linear differential equations. The continuous liquid mass of the tank is modelled as lumped masses known as convective mass, impulsive mass and rigid mass. The corresponding stiffness associated with these lumped masses has been worked out depending upon the properties of the tank wall and liquid mass. Since the force-deformation behaviour of the bearings is non-linear, as a result, the seismic response is obtained by the Newmark's step-by-step method. The seismic responses of two types of the isolated tanks (i.e. slender and broad) are investigated under several recorded earthquake ground to study the effects of bi-directional interaction. Further, a parametric study is also carried out to study the effects of important system parameters on the effectiveness of seismic isolation for liquid storage tanks. The various important parameters considered are: (i) the period of isolation, (ii) the damping of isolation bearings and (iii) the yield strength level of the bearings. It has been observed that the seismic response of isolated tank is found to be insensitive to interaction effect of the bearing forces. Further, there exists an optimum value of isolation damping for which the base shear in the tank attains the minimum value. Therefore, increasing the bearing damping beyond a certain value may decrease the bearing and sloshing displacements but it may increase the base shear

[Instrument to measure adherence in hypertensive patients: contribution of Item Response Theory].

Science.gov (United States)

Rodrigues, Malvina Thaís Pacheco; Moreira, Thereza Maria Magalhaes; Vasconcelos, Alexandre Meira de; Andrade, Dalton Francisco de; Silva, Daniele Braz da; Barbetta, Pedro Alberto

2013-06-01

To analyze, by means of "Item Response Theory", an instrument to measure adherence to t treatment for hypertension. Analytical study with 406 hypertensive patients with associated complications seen in primary care in Fortaleza, CE, Northeastern Brazil, 2011 using "Item Response Theory". The stages were: dimensionality test, calibrating the items, processing data and creating a scale, analyzed using the gradual response model. A study of the dimensionality of the instrument was conducted by analyzing the polychoric correlation matrix and factor analysis of complete information. Multilog software was used to calibrate items and estimate the scores. Items relating to drug therapy are the most directly related to adherence while those relating to drug-free therapy need to be reworked because they have less psychometric information and low discrimination. The independence of items, the small number of levels in the scale and low explained variance in the adjustment of the models show the main weaknesses of the instrument analyzed. The "Item Response Theory" proved to be a relevant analysis technique because it evaluated respondents for adherence to treatment for hypertension, the level of difficulty of the items and their ability to discriminate between individuals with different levels of adherence, which generates a greater amount of information. The instrument analyzed is limited in measuring adherence to hypertension treatment, by analyzing the "Item Response Theory" of the item, and needs adjustment. The proper formulation of the items is important in order to accurately measure the desired latent trait.

Disorder and non-linear magnetic response of high Tc superconductors

Energy Technology Data Exchange (ETDEWEB)

Burin, J.P. (Lab. de Physique des Solides, INSA, 35 - Rennes (France)); Fouad, Y. (Lab. de Physique des Solides, INSA, 35 - Rennes (France)); Raboutou, A. (Lab. de Physique des Solides, INSA, 35 - Rennes (France)); Peyral, P. (Lab. de Physique des Solides, INSA, 35 - Rennes (France)); Lebeau, C. (Lab. de Physique des Solides, INSA, 35 - Rennes (France)); Rosenblatt, J. (Lab. de Physique des Solides, INSA, 35 - Rennes (France)); Mokhtari, M. (Lab. de Chimie du Solide et inorganique Moleculaire, Univ. Rennes 1, 35 (France)); Pena, O. (Lab. de Chimie du Solide et inorganique Moleculaire, Univ. Rennes 1, 35 (France)); Perrin, C. (Lab. de Chimie du Solide et inorganique Moleculaire, Univ. Rennes 1, 35 (France))

1993-05-10

We measure the low frequency magnetic response of YBa[sub 2]Cu[sub 3]O[sub 6.7]F[sub x] (0 [<=] x < 0.2) ceramics in a wide range of a.c. fields (10[sup -7] T [<=] [mu][sub 0]H[sub 0] [<=] 10[sup -4]). When changing the amount of disorder (varying x) on the microscopic level we find the same non linear response with field amplitude H[sub 0] as in granular conventional superconductors. The real part of the susceptibility appears as a universal function of H[sub 1](T)/H[sub 0] where H[sub 1](T) is the field of first flux penetration. The power law dependence found for H[sub 1](T) can be understood in the framework of the coherence transition of granular superconductors with random couplings. (orig.)

Bad Questions: An Essay Involving Item Response Theory

Science.gov (United States)

Thissen, David

2016-01-01

David Thissen, a professor in the Department of Psychology and Neuroscience, Quantitative Program at the University of North Carolina, has consulted and served on technical advisory committees for assessment programs that use item response theory (IRT) over the past couple decades. He has come to the conclusion that there are usually two purposes…

Item response theory analysis of the Pain Self-Efficacy Questionnaire.

Science.gov (United States)

Costa, Daniel S J; Asghari, Ali; Nicholas, Michael K

2017-01-01

The Pain Self-Efficacy Questionnaire (PSEQ) is a 10-item instrument designed to assess the extent to which a person in pain believes s/he is able to accomplish various activities despite their pain. There is strong evidence for the validity and reliability of both the full-length PSEQ and a 2-item version. The purpose of this study is to further examine the properties of the PSEQ using an item response theory (IRT) approach. We used the two-parameter graded response model to examine the category probability curves, and location and discrimination parameters of the 10 PSEQ items. In item response theory, responses to a set of items are assumed to be probabilistically determined by a latent (unobserved) variable. In the graded-response model specifically, item response threshold (the value of the latent variable for which adjacent response categories are equally likely) and discrimination parameters are estimated for each item. Participants were 1511 mixed, chronic pain patients attending for initial assessment at a tertiary pain management centre. All items except item 7 ('I can cope with my pain without medication') performed well in IRT analysis, and the category probability curves suggested that participants used the 7-point response scale consistently. Items 6 ('I can still do many of the things I enjoy doing, such as hobbies or leisure activity, despite pain'), 8 ('I can still accomplish most of my goals in life, despite the pain') and 9 ('I can live a normal lifestyle, despite the pain') captured higher levels of the latent variable with greater precision. The results from this IRT analysis add to the body of evidence based on classical test theory illustrating the strong psychometric properties of the PSEQ. Despite the relatively poor performance of Item 7, its clinical utility warrants its retention in the questionnaire. The strong psychometric properties of the PSEQ support its use as an effective tool for assessing self-efficacy in people with pain

A simple non-linear model of immune response

International Nuclear Information System (INIS)

Gutnikov, Sergei; Melnikov, Yuri

2003-01-01

It is still unknown why the adaptive immune response in the natural immune system based on clonal proliferation of lymphocytes requires interaction of at least two different cell types with the same antigen. We present a simple mathematical model illustrating that the system with separate types of cells for antigen recognition and patogen destruction provides more robust adaptive immunity than the system where just one cell type is responsible for both recognition and destruction. The model is over-simplified as we did not have an intention of describing the natural immune system. However, our model provides a tool for testing the proposed approach through qualitative analysis of the immune system dynamics in order to construct more sophisticated models of the immune systems that exist in the living nature. It also opens a possibility to explore specific features of highly non-linear dynamics in nature-inspired computational paradigms like artificial immune systems and immunocomputing . We expect this paper to be of interest not only for mathematicians but also for biologists; therefore we made effort to explain mathematics in sufficient detail for readers without professional mathematical background

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.

Developing Integrated Arts Curriculum in Hong Kong: Chaos Theory at Work?

Science.gov (United States)

Wong, Marina

2013-01-01

This article reports the development of integrated arts curriculum in two Hong Kong secondary schools over a 9-year period. Initial findings display a range of individual responses to educational change that are both non-predictable and non-linear. Chaos theory is used to explain these varied responses in terms of bifurcations. The findings of…

The linear transformation model with frailties for the analysis of item response times.

Science.gov (United States)

Wang, Chun; Chang, Hua-Hua; Douglas, Jeffrey A

2013-02-01

The item response times (RTs) collected from computerized testing represent an underutilized source of information about items and examinees. In addition to knowing the examinees' responses to each item, we can investigate the amount of time examinees spend on each item. In this paper, we propose a semi-parametric model for RTs, the linear transformation model with a latent speed covariate, which combines the flexibility of non-parametric modelling and the brevity as well as interpretability of parametric modelling. In this new model, the RTs, after some non-parametric monotone transformation, become a linear model with latent speed as covariate plus an error term. The distribution of the error term implicitly defines the relationship between the RT and examinees' latent speeds; whereas the non-parametric transformation is able to describe various shapes of RT distributions. The linear transformation model represents a rich family of models that includes the Cox proportional hazards model, the Box-Cox normal model, and many other models as special cases. This new model is embedded in a hierarchical framework so that both RTs and responses are modelled simultaneously. A two-stage estimation method is proposed. In the first stage, the Markov chain Monte Carlo method is employed to estimate the parametric part of the model. In the second stage, an estimating equation method with a recursive algorithm is adopted to estimate the non-parametric transformation. Applicability of the new model is demonstrated with a simulation study and a real data application. Finally, methods to evaluate the model fit are suggested. © 2012 The British Psychological Society.

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...

Non-linear temperature-dependent curvature of a phase change composite bimorph beam

Science.gov (United States)

Blonder, Greg

2017-06-01

Bimorph films curl in response to temperature. The degree of curvature typically varies in proportion to the difference in thermal expansion of the individual layers, and linearly with temperature. In many applications, such as controlling a thermostat, this gentle linear behavior is acceptable. In other cases, such as opening or closing a valve or latching a deployable column into place, an abrupt motion at a fixed temperature is preferred. To achieve this non-linear motion, we describe the fabrication and performance of a new bilayer structure we call a ‘phase change composite bimorph (PCBM)’. In a PCBM, one layer in the bimorph is a composite containing small inclusions of phase change materials. When the inclusions melt, their large (generally positive and  >1%) expansion coefficient induces a strong, reversible step function jump in bimorph curvature. The measured jump amplitude and thermal response is consistent with theory, and can be harnessed by a new class of actuators and sensors.

Reevaluation of the Amsterdam Inventory for Auditory Disability and Handicap Using Item Response Theory

Science.gov (United States)

Hospers, J. Mirjam Boeschen; Smits, Niels; Smits, Cas; Stam, Mariska; Terwee, Caroline B.; Kramer, Sophia E.

2016-01-01

Purpose: We reevaluated the psychometric properties of the Amsterdam Inventory for Auditory Disability and Handicap (AIADH; Kramer, Kapteyn, Festen, & Tobi, 1995) using item response theory. Item response theory describes item functioning along an ability continuum. Method: Cross-sectional data from 2,352 adults with and without hearing…

Many-body theory of electrical, thermal and optical response of molecular heterojunctions

Science.gov (United States)

Bergfield, Justin Phillip

In this work, we develop a many-body theory of electronic transport through single molecule junctions based on nonequilibrium Green's functions (NEGFs). The central quantity of this theory is the Coulomb self-energy matrix of the junction SigmaC. SigmaC is evaluated exactly in the sequential-tunneling limit, and the correction due to finite lead-molecule tunneling is evaluated using a conserving approximation based on diagrammatic perturbation theory on the Keldysh contour. In this way, tunneling processes are included to infinite order, meaning that any approximation utilized is a truncation in the physical processes considered rather than in the order of those processes. Our theory reproduces the key features of both the Coulomb blockade and coherent transport regimes simultaneously in a single unified theory. Nonperturbative effects of intramolecular correlations are included, which are necessary to accurately describe the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap, essential for a quantitative theory of transport. This work covers four major topics related to transport in single-molecule junctions. First, we use our many-body theory to calculate the nonlinear electrical response of the archetypal Au-1,4-benzenedithiol-Au junction and find irregularly shaped 'molecular diamonds' which have been experimentally observed in some larger molecules but which are inaccessible to existing theoretical approaches. Next, we extend our theory to include heat transport and develop an exact expression for the heat current in an interacting nanostructure. Using this result, we discover that quantum coherence can strongly enhance the thermoelectric response of a device, a result with a number of technological applications. We then develop the formalism to include multi-orbital lead-molecule contacts and multi-channel leads, both of which strongly affect the observable transport. Lastly, we include a dynamic screening correction to

An empirical comparison of Item Response Theory and Classical Test Theory

Directory of Open Access Journals (Sweden)

Špela Progar

2008-11-01

Full Text Available Based on nonlinear models between the measured latent variable and the item response, item response theory (IRT enables independent estimation of item and person parameters and local estimation of measurement error. These properties of IRT are also the main theoretical advantages of IRT over classical test theory (CTT. Empirical evidence, however, often failed to discover consistent differences between IRT and CTT parameters and between invariance measures of CTT and IRT parameter estimates. In this empirical study a real data set from the Third International Mathematics and Science Study (TIMSS 1995 was used to address the following questions: (1 How comparable are CTT and IRT based item and person parameters? (2 How invariant are CTT and IRT based item parameters across different participant groups? (3 How invariant are CTT and IRT based item and person parameters across different item sets? The findings indicate that the CTT and the IRT item/person parameters are very comparable, that the CTT and the IRT item parameters show similar invariance property when estimated across different groups of participants, that the IRT person parameters are more invariant across different item sets, and that the CTT item parameters are at least as much invariant in different item sets as the IRT item parameters. The results furthermore demonstrate that, with regards to the invariance property, IRT item/person parameters are in general empirically superior to CTT parameters, but only if the appropriate IRT model is used for modelling the data.

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

Corporate Social Responsibility and Stakeholder Theory: Learning From Each Other

OpenAIRE

Freeman, R. Edward; Dmytriyev, Sergiy

2017-01-01

This paper explores the relationship between two major concepts in business ethics - stakeholder theory and corporate social responsibility (CSR). We argue that CSR is a part of corporate responsibilities (company responsibilities to all stakeholders), and show that there is a need for both concepts in business ethics, and their applicability is dependent on a particular problem we want to solve. After reviewing some criticisms of CSR - covering wrongdoing and creating false dichotomies, we s...

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...

Perspective on "Statistical mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems."Kubo R J Phys Soc Jpn 12: 570

NARCIS (Netherlands)

Frenkel, D.

2000-01-01

Kubo's paper on linear-response theory provided a unified language to describe a wide variety of transport phenomena, both quantum and classical, in a suitable "microscopic" language. The paper has been crucial for subsequent developments in numerical simulation.

Microstrip linear phase low pass filter based on defected ground structures for partial response modulation

DEFF Research Database (Denmark)

Cimoli, Bruno; Johansen, Tom Keinicke; Olmos, Juan Jose Vegas

2018-01-01

We report a high performance linear phase low pass filter (LPF) designed for partial response (PR) modulations. For the implementation, we adopted microstrip technology and a variant of the standard stepped‐impedance technique. Defected ground structures (DGS) are used for increasing the characte......We report a high performance linear phase low pass filter (LPF) designed for partial response (PR) modulations. For the implementation, we adopted microstrip technology and a variant of the standard stepped‐impedance technique. Defected ground structures (DGS) are used for increasing...... the characteristic impedance of transmission lines. Experimental results prove that the proposed filter can successfully modulate a non‐return‐to‐zero (NRZ) signal into a five levels PR one....

Linear and Nonlinear Response of a Rotating Tokamak Plasma to a Resonant Error-Field

Science.gov (United States)

Fitzpatrick, Richard

2014-10-01

An in-depth investigation of the effect of a resonant error-field on a rotating, quasi-cylindrical, tokamak plasma is preformed within the context of resistive-MHD theory. General expressions for the response of the plasma at the rational surface to the error-field are derived in both the linear and nonlinear regimes, and the extents of these regimes mapped out in parameter space. Torque-balance equations are also obtained in both regimes. These equations are used to determine the steady-state plasma rotation at the rational surface in the presence of the error-field. It is found that, provided the intrinsic plasma rotation is sufficiently large, the torque-balance equations possess dynamically stable low-rotation and high-rotation solution branches, separated by a forbidden band of dynamically unstable solutions. Moreover, bifurcations between the two stable solution branches are triggered as the amplitude of the error-field is varied. A low- to high-rotation bifurcation is invariably associated with a significant reduction in the width of the magnetic island chain driven at the rational surface, and vice versa. General expressions for the bifurcation thresholds are derived, and their domains of validity mapped out in parameter space. This research was funded by the U.S. Department of Energy under Contract DE-FG02-04ER-54742.

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.

Profile-likelihood Confidence Intervals in Item Response Theory Models.

Science.gov (United States)

Chalmers, R Philip; Pek, Jolynn; Liu, Yang

2017-01-01

Confidence intervals (CIs) are fundamental inferential devices which quantify the sampling variability of parameter estimates. In item response theory, CIs have been primarily obtained from large-sample Wald-type approaches based on standard error estimates, derived from the observed or expected information matrix, after parameters have been estimated via maximum likelihood. An alternative approach to constructing CIs is to quantify sampling variability directly from the likelihood function with a technique known as profile-likelihood confidence intervals (PL CIs). In this article, we introduce PL CIs for item response theory models, compare PL CIs to classical large-sample Wald-type CIs, and demonstrate important distinctions among these CIs. CIs are then constructed for parameters directly estimated in the specified model and for transformed parameters which are often obtained post-estimation. Monte Carlo simulation results suggest that PL CIs perform consistently better than Wald-type CIs for both non-transformed and transformed parameters.

The Faraday effect revisited General theory

CERN Document Server