Linear response theory for quantum open systems
Wei, J. H.; Yan, YiJing
2011-01-01
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
Modification of linear response theory for mean-field approximations
Hütter, M.; Öttinger, H.C.
1996-01-01
In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the
Linear response theory for magnetic Schrodinger operators in disordered media
Bouclet, J M; Klein, A; Schenker, J
2004-01-01
We justify the linear response theory for an ergodic Schrodinger operator with magnetic field within the non-interacting particle approximation, and derive a Kubo formula for the electric conductivity tensor. To achieve that, we construct suitable normed spaces of measurable covariant operators where the Liouville equation can be solved uniquely. If the Fermi level falls into a region of localization, we recover the well-known Kubo-Streda formula for the quantum Hall conductivity at zero temperature.
Linear response theory of activated surface diffusion with interacting adsorbates
Energy Technology Data Exchange (ETDEWEB)
Marti' nez-Casado, R. [Department of Chemistry, Imperial College London, South Kensington, London SW7 2AZ (United Kingdom); Sanz, A.S.; Vega, J.L. [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); Rojas-Lorenzo, G. [Instituto Superior de Tecnologi' as y Ciencias Aplicadas, Ave. Salvador Allende, esq. Luaces, 10400 La Habana (Cuba); Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain); Miret-Artes, S., E-mail: s.miret@imaff.cfmac.csic.es [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain)
2010-05-12
Graphical abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed. - Abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed.
Quantum optimal control theory in the linear response formalism
International Nuclear Information System (INIS)
Castro, Alberto; Tokatly, I. V.
2011-01-01
Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice, this normally means optimizing the value of some observable, a so-called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization: the unperturbed Hamiltonian is allowed to be time dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in terms of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for nonequilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems.
Linear response theory an analytic-algebraic approach
De Nittis, Giuseppe
2017-01-01
This book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3–5: the relevant von Neumann algebras, noncommutative $L^p$- and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and Kubo-Streda formulas. The book closes with a chapter about...
The spin polarized linear response from density functional theory: Theory and application to atoms
Energy Technology Data Exchange (ETDEWEB)
Fias, Stijn, E-mail: sfias@vub.ac.be; Boisdenghien, Zino; De Proft, Frank; Geerlings, Paul [General Chemistry (ALGC), Vrije Universiteit Brussel (Free University Brussels – VUB), Pleinlaan 2, 1050 Brussels (Belgium)
2014-11-14
Within the context of spin polarized conceptual density functional theory, the spin polarized linear response functions are introduced both in the [N, N{sub s}] and [N{sub α}, N{sub β}] representations. The mathematical relations between the spin polarized linear response functions in both representations are examined and an analytical expression for the spin polarized linear response functions in the [N{sub α}, N{sub β}] representation is derived. The spin polarized linear response functions were calculated for all atoms up to and including argon. To simplify the plotting of our results, we integrated χ(r, r′) to a quantity χ(r, r{sup ′}), circumventing the θ and ϕ dependence. This allows us to plot and to investigate the periodicity throughout the first three rows in the periodic table within the two different representations. For the first time, χ{sub αβ}(r, r{sup ′}), χ{sub βα}(r, r{sup ′}), and χ{sub SS}(r, r{sup ′}) plots have been calculated and discussed. By integration of the spin polarized linear response functions, different components to the polarisability, α{sub αα}, α{sub αβ}, α{sub βα}, and α{sub ββ} have been calculated.
DEFF Research Database (Denmark)
Yan, Wei
2015-01-01
We investigate the hydrodynamic theory of metals, offering systematic studies of the linear-response dynamics for an inhomogeneous electron gas. We include the quantum functional terms of the Thomas-Fermi kinetic energy, the von Weizsa¨cker kinetic energy, and the exchange-correlation Coulomb...... energies under the local density approximation. The advantages, limitations, and possible improvements of the hydrodynamic theory are transparently demonstrated. The roles of various parameters in the theory are identified. We anticipate that the hydrodynamic theory can be applied to investigate the linear...... response of complex metallic nanostructures, including quantum effects, by adjusting theory parameters appropriately....
A quantum-mechanical perspective on linear response theory within polarizable embedding
DEFF Research Database (Denmark)
List, Nanna Holmgaard; Norman, Patrick; Kongsted, Jacob
2017-01-01
We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole...
Molenaar, Dylan; Tuerlinckx, Francis; van der Maas, Han L J
2015-01-01
A generalized linear modeling framework to the analysis of responses and response times is outlined. In this framework, referred to as bivariate generalized linear item response theory (B-GLIRT), separate generalized linear measurement models are specified for the responses and the response times that are subsequently linked by cross-relations. The cross-relations can take various forms. Here, we focus on cross-relations with a linear or interaction term for ability tests, and cross-relations with a curvilinear term for personality tests. In addition, we discuss how popular existing models from the psychometric literature are special cases in the B-GLIRT framework depending on restrictions in the cross-relation. This allows us to compare existing models conceptually and empirically. We discuss various extensions of the traditional models motivated by practical problems. We also illustrate the applicability of our approach using various real data examples, including data on personality and cognitive ability.
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...
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
Non-linear wave loads and ship responses by a time-domain strip theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...
Linear-response theory of Coulomb drag in coupled electron systems
DEFF Research Database (Denmark)
Flensberg, Karsten; Hu, Ben Yu-Kuang; Jauho, Antti-Pekka
1995-01-01
We report a fully microscopic theory for the transconductivity, or, equivalently, the momentum transfer rate, of Coulomb coupled electron systems. We use the Kubo linear-response formalism and our main formal result expresses the transconductivity in terms of two fluctuation diagrams, which...
Airfoil wake and linear theory gust response including sub and superresonant flow conditions
Henderson, Gregory H.; Fleeter, Sanford
1992-01-01
The unsteady aerodynamic gust response of a high solidity stator vane row is examined in terms of the fundamental gust modeling assumptions with particular attention given to the effects near an acoustic resonance. A series of experiments was performed with gusts generated by rotors comprised of perforated plates and airfoils. It is concluded that, for both the perforated plate and airfoil wake generated gusts, the unsteady pressure responses do not agree with the linear-theory gust predictions near an acoustic resonance. The effects of the acoustic resonance phenomena are clearly evident on the airfoil surface unsteady pressure responses. The transition of the measured lift coefficients across the acoustic resonance from the subresonant regime to the superresonant regime occurs in a simple linear fashion.
Sequential double excitations from linear-response time-dependent density functional theory
Energy Technology Data Exchange (ETDEWEB)
Mosquera, Martín A.; Ratner, Mark A.; Schatz, George C., E-mail: g-schatz@northwestern.edu [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States); Chen, Lin X. [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States); Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 South Cass Ave., Lemont, Illinois 60439 (United States)
2016-05-28
Traditional UV/vis and X-ray spectroscopies focus mainly on the study of excitations starting exclusively from electronic ground states. However there are many experiments where transitions from excited states, both absorption and emission, are probed. In this work we develop a formalism based on linear-response time-dependent density functional theory to investigate spectroscopic properties of excited states. We apply our model to study the excited-state absorption of a diplatinum(II) complex under X-rays, and transient vis/UV absorption of pyrene and azobenzene.
Selected topics in the quantum theory of solids: collective excitations and linear response
International Nuclear Information System (INIS)
Balakrishnan, V.
1977-08-01
This report is based on the lecture notes of a course given at the Department of Physics, Indian Institute of Technology, Madras, during the period January-April 1976 for M.Sc. students. The emphasis is on the concept of elementary excitations in many-body systems, and on the technique of linear response theory. Various topics are covered in 7 sections. The second section following the introductory section is on 'second quantization' and includes discussion on creation and destruction operators, multiparticle states, time-dependent operators etc. Section 3 deals with the 'electron gas' and includes discussion on non-interacting Fermi gas, Coulomb interaction and exchange energy, the two-electron correlation function etc. Section 4 deals with the dielectric response analysis of the electron gas and includes discussion on Coulomb interaction in terms of density fluctuations, self-consistent field dielectric function etc. In section 5 the 'linear response theory' is explained. The Liouville operator, Boltzmann's superposition integral, dispersion relations etc. are explained. Quasiparticles and plasmous are discussed in the Section 6. Section 7 deals with 'lattice dynamics and phonons'. In the last section 8, spin waves are explained. The Heisenberg exchange hamiltonian, Green Function for noninteracting magnons etc. are discussed. (author)
Relevance of sampling schemes in light of Ruelle's linear response theory
International Nuclear Information System (INIS)
Lucarini, Valerio; Wouters, Jeroen; Faranda, Davide; Kuna, Tobias
2012-01-01
We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We first show that using a general functional decomposition for space–time dependent forcings, we can define elementary susceptibilities that allow us to construct the linear response of the system to general perturbations. Starting from the definition of SRB measure, we then study the consequence of taking different sampling schemes for analysing the response of the system. We show that only a specific choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows us to obtain the formula first presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be fine-tuned to make the definition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analysing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick
Non-Markovian linear response theory for quantum open systems and its applications.
Shen, H Z; Li, D X; Yi, X X
2017-01-01
The Kubo formula is an equation that expresses the linear response of an observable due to a time-dependent perturbation. It has been extended from closed systems to open systems in recent years under the Markovian approximation, but is barely explored for open systems in non-Markovian regimes. In this paper, we derive a formula for the linear response of an open system to a time-independent external field. This response formula is available for both Markovian and non-Markovian dynamics depending on parameters in the spectral density of the environment. As an illustration of the theory, the Hall conductance of a two-band system subjected to environments is derived and discussed. With the tight-binding model, we point out the Hall conductance changes from Markovian to non-Markovian dynamics by modulating the spectral density of the environment. Our results suggest a way to the controlling of the system response, which has potential applications for quantum statistical mechanics and condensed matter physics.
Van Meer, R.; Gritsenko, O. V.; Baerends, E. J.
2017-01-01
Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In
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
Time-dependent density functional theory of open quantum systems in the linear-response regime.
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.
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.
Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum
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.
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.
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
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
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.
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.
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.
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 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
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...
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...
Lead-lag relationships between stock and market risk within linear response theory
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.
Linear spaces: history and theory
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.
Linear response theory for long-range interacting systems in quasistationary 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
The Theory of Linear Prediction
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
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.
Global hybrids from the semiclassical atom theory satisfying the local density linear response.
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.
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....
Thouless-Valatin rotational moment of inertia from linear response theory
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.
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
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.
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
Directory of Open Access Journals (Sweden)
Manuel Offidani
2018-05-01
Full Text Available We present a unified theoretical framework for the study of spin dynamics and relativistic transport phenomena in disordered two-dimensional Dirac systems with pseudospin-spin coupling. The formalism is applied to the paradigmatic case of graphene with uniform Bychkov-Rashba interaction and shown to capture spin relaxation processes and associated charge-to-spin interconversion phenomena in response to generic external perturbations, including spin density fluctuations and electric fields. A controlled diagrammatic evaluation of the generalized spin susceptibility in the diffusive regime of weak spin-orbit interaction allows us to show that the spin and momentum lifetimes satisfy the standard Dyakonov-Perel relation for both weak (Gaussian and resonant (unitary nonmagnetic disorder. Finally, we demonstrate that the spin relaxation rate can be derived in the zero-frequency limit by exploiting the SU(2 covariant conservation laws for the spin observables. Our results set the stage for a fully quantum-mechanical description of spin relaxation in both pristine graphene samples with weak spin-orbit fields and in graphene heterostructures with enhanced spin-orbital effects currently attracting much attention.
Bayes linear statistics, theory & methods
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...
Linear algebra and group theory
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.
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...
Linear stochastic neutron transport theory
International Nuclear Information System (INIS)
Lewins, J.
1978-01-01
A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)
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
Linear programming mathematics, theory and algorithms
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.
Numerical linear algebra theory and applications
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.
The linearization method in hydrodynamical stability theory
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.
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
Employing Theories Far beyond Their Limits - Linear Dichroism Theory.
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
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
Linear algebra and group theory for physicists
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...
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
Linear control theory for gene network modeling.
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.
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
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.
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
Theory of linear operators in Hilbert space
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.
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)
Generalizability theory and item response theory
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 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.
Linearized propulsion theory of flapping airfoils revisited
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.
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.
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.
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
Linear canonical transforms theory and applications
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.
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
Stochastic linear programming models, theory, and computation
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...
Generalizability theory and item response theory
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
Linear optical response of finite systems using multishift linear system solvers
Energy Technology Data Exchange (ETDEWEB)
Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
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.
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...
Problems of linear electron (polaron) transport theory in semiconductors
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
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.
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...
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
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
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)
A Linear Theory for Pretwisted Elastic Beams
DEFF Research Database (Denmark)
Krenk, Steen
1983-01-01
contains a general system of differential equations and gives explicit solutions for homogenous extension, torsion, and bending. The theory accounts explicitly for the shear center, the elastic center, and the axis of pretwist. The resulting torsion-extension coupling is in agreement with a recent...
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 ubiquitination signals in adaptive immune responses.
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.
Linear circuit theory matrices in computer applications
Vlach, Jiri
2014-01-01
Basic ConceptsNodal and Mesh AnalysisMatrix MethodsDependent SourcesNetwork TransformationsCapacitors and InductorsNetworks with Capacitors and InductorsFrequency DomainLaplace TransformationTime DomainNetwork FunctionsActive NetworksTwo-PortsTransformersModeling and Numerical MethodsSensitivitiesModified Nodal FormulationFourier Series and TransformationAppendix: Scaling of Linear Networks.
Non-linear theory of elasticity
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.
DEFF Research Database (Denmark)
Norman, Patrick; Schimmelpfennig, Bernd; Ruud, Kenneth
2002-01-01
A systematic investigation of a hierarchy of methods for including relativistic effects in the calculation of linear and nonlinear optical properties was carried out. The simple ECP method and the more involved spin-averaged Douglas-Kroll approximation were compared to benchmark results obtained...
Inverse problems in linear transport theory
International Nuclear Information System (INIS)
Dressler, K.
1988-01-01
Inverse problems for a class of linear kinetic equations are investigated. The aim is to identify the scattering kernel of a transport equation (corresponding to the structure of a background medium) by observing the 'albedo' part of the solution operator for the corresponding direct initial boundary value problem. This means to get information on some integral operator in an integrodifferential equation through on overdetermined boundary value problem. We first derive a constructive method for solving direct halfspace problems and prove a new factorization theorem for the solutions. Using this result we investigate stationary inverse problems with respect to well posedness (e.g. reduce them to classical ill-posed problems, such as integral equations of first kind). In the time-dependent case we show that a quite general inverse problem is well posed and solve it constructively. (orig.)
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)
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.
International Nuclear Information System (INIS)
Perez-Moreno, Javier; Hung, Sheng-Ting; Kuzyk, Mark G.; Zhou, Juefei; Ramini, Shiva K.; Clays, Koen
2011-01-01
We show that a combination of linear absorption spectroscopy, hyper-Rayleigh scattering, and a theoretical analysis using sum rules to reduce the size of the parameter space leads to a prediction of the imaginary part of the second hyperpolarizability of the dye AF-455 that agrees with the experimental data gathered through two-photon absorption spectroscopy. Our procedure, which demands self-consistency between several measurement techniques and does not use adjustable parameters, provides a means for determining transition moments between the dominant excited states based strictly on experimental characterization. This is made possible by our new approach that uses sum rules and molecular symmetry to rigorously reduce the number of required physical quantities.
Diagnostics for Linear Models With Functional Responses
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...
An enstrophy-based linear and nonlinear receptivity theory
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.
Shear-transformation-zone theory of linear glassy dynamics.
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.
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
When is quasi-linear theory exact. [particle acceleration
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.
Dynamic Response Analysis of Linear Pulse Motor with Closed Loop Control
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.
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.
Hydration thermodynamics beyond the linear response approximation.
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
Responsive linear-dendritic block copolymers.
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.
Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control
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...
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.)
Turnpike theory of continuous-time linear optimal control problems
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 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.
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
A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.
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.
Linearly Polarized IR Spectroscopy Theory and Applications for Structural Analysis
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
Symmetric linear systems - An application of algebraic systems theory
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.
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)
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
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.
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)
Plane answers to complex questions the theory of linear models
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...
Linear {GLP}-algebras and their elementary theories
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.
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
General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles.
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.
On the non-linear scale of cosmological perturbation theory
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.
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
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.
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…
Non-linear electrodynamics in Kaluza-Klein theory
International Nuclear Information System (INIS)
Kerner, R.
1987-01-01
The most general variational principle based on the invariants of the Riemann tensor and leading to the second order differential equations should contain, in dimensions higher than four, the invariants of the Gauss-Bonnet type. In five dimensions the lagrangian should be a linear combination of the scalar curvature and the second-order invariant. The equations of the electromagnetic field are derived in the absence of scalar and gravitational fields of the Kaluza-Klein model. They yield the unique extension of Maxwell's system in the Kaluza-Klein theory. Some properties of eventual solutions are discussed [fr
Non-linear theory of elasticity and optimal design
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
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...
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
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.)
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
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
Responsive gelation of hydrophobized linear polymer
DEFF Research Database (Denmark)
Madsen, Claus Greve; Toeth, Joachim; Jørgensen, Lene
In this study we present the rheological properties of a physically linked polymer network, composed of linear hydrophilic chains, modified with hydrophobic moieties in each end. Solutions of the polymer in ethanol-water mixtures showed Newtonian behaviour up to about 99 % ethanol, with the highest...
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
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....
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)
A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media
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.
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.
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.
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...
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.)
Checking the foundation: recent radiobiology and the linear no-threshold theory.
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.
Competitive inhibition can linearize dose-response and generate a linear rectifier.
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.
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 theory for filtering nonlinear multiscale systems with model error.
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
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.
A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs
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...
Non-linearities in Theory-of-Mind Development.
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.
Hrouzek, Pavel; Štys, Dalibor; Martens, Harald
2013-01-01
Responsivity is a conversion qualification of a measurement device given by the functional dependence between the input and output quantities. A concentration-response-dependent calibration curve represents the most simple experiment for the measurement of responsivity in mass spectrometry. The cyanobacterial hepatotoxin microcystin-LR content in complex biological matrices of food additives was chosen as a model example of a typical problem. The calibration curves for pure microcystin and its mixtures with extracts of green alga and fish meat were reconstructed from the series of measurement. A novel approach for the quantitative estimation of ion competition in ESI is proposed in this paper. We define the correlated responsivity offset in the intensity values using the approximation of minimal correlation given by the matrix to the target mass values of the analyte. The estimation of the matrix influence enables the approximation of the position of a priori unknown responsivity and was easily evaluated using a simple algorithm. The method itself is directly derived from the basic attributes of the theory of measurements. There is sufficient agreement between the theoretical and experimental values. However, some theoretical issues are discussed to avoid misinterpretations and excessive expectations. PMID:23586036
Directory of Open Access Journals (Sweden)
Jan Urban
2013-01-01
Full Text Available Responsivity is a conversion qualification of a measurement device given by the functional dependence between the input and output quantities. A concentration-response-dependent calibration curve represents the most simple experiment for the measurement of responsivity in mass spectrometry. The cyanobacterial hepatotoxin microcystin-LR content in complex biological matrices of food additives was chosen as a model example of a typical problem. The calibration curves for pure microcystin and its mixtures with extracts of green alga and fish meat were reconstructed from the series of measurement. A novel approach for the quantitative estimation of ion competition in ESI is proposed in this paper. We define the correlated responsivity offset in the intensity values using the approximation of minimal correlation given by the matrix to the target mass values of the analyte. The estimation of the matrix influence enables the approximation of the position of a priori unknown responsivity and was easily evaluated using a simple algorithm. The method itself is directly derived from the basic attributes of the theory of measurements. There is sufficient agreement between the theoretical and experimental values. However, some theoretical issues are discussed to avoid misinterpretations and excessive expectations.
Urban, Jan; Hrouzek, Pavel; Stys, Dalibor; Martens, Harald
2013-01-01
Responsivity is a conversion qualification of a measurement device given by the functional dependence between the input and output quantities. A concentration-response-dependent calibration curve represents the most simple experiment for the measurement of responsivity in mass spectrometry. The cyanobacterial hepatotoxin microcystin-LR content in complex biological matrices of food additives was chosen as a model example of a typical problem. The calibration curves for pure microcystin and its mixtures with extracts of green alga and fish meat were reconstructed from the series of measurement. A novel approach for the quantitative estimation of ion competition in ESI is proposed in this paper. We define the correlated responsivity offset in the intensity values using the approximation of minimal correlation given by the matrix to the target mass values of the analyte. The estimation of the matrix influence enables the approximation of the position of a priori unknown responsivity and was easily evaluated using a simple algorithm. The method itself is directly derived from the basic attributes of the theory of measurements. There is sufficient agreement between the theoretical and experimental values. However, some theoretical issues are discussed to avoid misinterpretations and excessive expectations.
Linear and Non-Linear Dielectric Response of Periodic Systems from Quantum Monte Carlo
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).
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.)
Comparison of Linear Induction Motor Theories for the LIMRV and TLRV Motors
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 ...
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
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.
Decomposition Theory in the Teaching of Elementary Linear Algebra.
London, R. R.; Rogosinski, H. P.
1990-01-01
Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)
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
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...
Linear algebra meets Lie algebra: the Kostant-Wallach theory
Shomron, Noam; Parlett, Beresford N.
2008-01-01
In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.
Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems
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.
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 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
Randomized Item Response Theory Models
Fox, Gerardus J.A.
2005-01-01
The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR technique is the probability of the true response modeled by
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.
Towards a Culturally Situated Reader Response Theory
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…
Item Response Theory: A Basic Concept
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…
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
Note: A high dynamic range, linear response transimpedance amplifier.
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 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...
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.
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 Morava E-theories of finite general linear groups
Mattafirri, Sara
The feasibility of producing an image of radioactivity distribution within a patient or confined region of space using information carried by the gamma-rays emitted from the source is investigated. The imaging approach makes use of parameters related to the gamma-rays which undergo Compton scattering within a detection system, it does not involve the use of pin-holes, and it employs gamma-rays of energy ranging from a few hundreds of keVs to MeVs. Energy range of the photons and absence of pin-holes aim to provide larger pool of radioisotopes and larger efficiency than other emission imaging modalities, such as single photon emission computed tomography and positron emission tomography, making it possible to investigate larger pool of functions and smaller radioactivity doses. The observables available to produce the image are the gamma-ray position of interaction and energy deposition during Compton scattering within the detection systems. Image reconstruction methodologies such as backprojection and list-mode maximum likelihood expectation maximization algorithm are characterized and applied to produce images of simulated and experimental sources on the basis of the observed parameters. Given the observables and image reconstruction methodologies, imaging systems based on minimizing the variation of the impulse response with position within the field of view are developed. The approach allows imaging of three-dimensional sources when an imaging system which provides full 4 pi view of the object is used and imaging of two-dimensional sources when a single block-type detector which provides one view of the object is used. Geometrical resolution of few millimeters is obtained at few centimeters from the detection system if employing gamma-rays of energy in the order of few hundreds of keVs and current state of the art semi-conductor detectors; At this level of resolution, detection efficiency is in the order of 10-3 at few centimeters from the detector when a single
Galois theory and algorithms for linear differential equations
Put, Marius van der
2005-01-01
This paper is an informal introduction to differential Galois theory. It surveys recent work on differential Galois groups, related algorithms and some applications. (c) 2005 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Taheri M.
2015-09-01
Full Text Available Background: Drug resistance is widely believed to be an increasingly serious threat to global public health. We have previously reported that short term exposure of microorganisms to diagnostic ultrasound waves could significantly alter their sensitivity to antibiotics. In our previous studies, Klebsiella pneumoniae showed major differences in the sensitivity to antibiotics in exposed and non-exposed samples. This study was aimed at investigating the alteration of antibiotic resistance of Klebsiella pneumonia, after exposure to Wi-Fi 2.4 GHz electromagnetic radiofrequency radiation. Materials and Methods: In this in vitro study, three replicate agar plates were used for each test. The antibiotic susceptibility test was carried out using disc diffusion method on Mueller Hinton agar plates and the inhibition zones in both control and exposed groups were measured. A common Wi-Fi router was used in this study as the radiofrequency exposure source. Irradiated samples were exposed to Wi-Fi radiofrequency radiation for 3, 4.5 and 8 hours. Results: Statistically significant variations of sensitivity to antibiotics were found for all studied antibiotics after 4.5 hours of RF exposure, compared to non-exposed bacteria. Interestingly, the mean diameters of the inhibition zones after 3 hours of exposure were less than those exposed for 4.5 hours. Following this rise in the sensitivity to antibiotics, a fall was observed in the bacteria exposed for 8 hours for all studied antibiotics. Conclusion: The findings of this study show a statistically significant rise in the sensitivity of Klebsiella pneumoniae to different antibiotics after 4.5 hours of exposure to 2.4 GHz Wi-Fi radiation, followed by a fall after 8 hours of exposure. These observations can be interpreted by the concept of non-linearity in the responses of Klebsiella pneumoniae to different antibiotics after exposure to electromagnetic radiofrequency radiation. As in this study a minimum level of
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
Endoreversible quantum heat engines in the linear response regime.
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.
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…
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.
Linear theory radial and nonradial pulsations of DA dwarf stars
International Nuclear Information System (INIS)
Starrfield, S.; Cox, A.N.; Hodson, S.; Pesnell, W.D.
1982-01-01
The Los Alamos stellar envelope and radial linear non-adiabatic computer code, along with a new Los Alamos non-radial code are used to investigate the total hydrogen mass necessary to produce the non-radial instability of DA dwarfs
Linear theory of plasma filled backward wave oscillator
Indian Academy of Sciences (India)
An analytical and numerical study of backward wave oscillator (BWO) in linear regime is presented to get an insight into the excitation of electromagnetic waves as a result of the interaction of the relativistic electron beam with a slow wave structure. The effect of background plasma on the BWO instability is also presented.
Lectures on algebraic system theory: Linear systems over rings
Kamen, E. W.
1978-01-01
The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.
Structure formation with massive neutrinos. Going beyond linear theory
International Nuclear Information System (INIS)
Blas, Diego; Garny, Mathias; Konstandin, Thomas; Lesgourgues, Julien; Institut de Theorie Phenomenes Physiques EPFL, Lausanne; Savoie Univ., CNRS, Annecy-le-Vieux
2014-08-01
We compute non-linear corrections to the matter power spectrum taking the time- and scale-dependent free-streaming length of neutrinos into account. We adopt a hybrid scheme that matches the full Boltzmann hierarchy to an effective two-fluid description at an intermediate redshift. The non-linearities in the neutrino component are taken into account by using an extension of the time-flow framework. We point out that this remedies a spurious behaviour that occurs when neglecting non-linear terms for neutrinos. This behaviour is related to how efficiently short modes decouple from long modes and can be traced back to the violation of momentum conservation if neutrinos are treated linearly. Furthermore, we compare our results at next to leading order to various other methods and quantify the accuracy of the fluid description. Due to the correct decoupling behaviour of short modes, the two-fluid scheme is a suitable starting point to compute higher orders in perturbations or for resummation methods.
Structure formation with massive neutrinos: going beyond linear theory
Blas, Diego; Konstandin, Thomas; Lesgourgues, Julien
2014-01-01
We compute non-linear corrections to the matter power spectrum taking the time- and scale-dependent free-streaming length of neutrinos into account. We adopt a hybrid scheme that matches the full Boltzmann hierarchy to an effective two-fluid description at an intermediate redshift. The non-linearities in the neutrino component are taken into account by using an extension of the time-flow framework. We point out that this remedies a spurious behaviour that occurs when neglecting non-linear terms for neutrinos. This behaviour is related to how efficiently short modes decouple from long modes and can be traced back to the violation of momentum conservation if neutrinos are treated linearly. Furthermore, we compare our results at next to leading order to various other methods and quantify the accuracy of the fluid description. Due to the correct decoupling behaviour of short modes, the two-fluid scheme is a suitable starting point to compute higher orders in perturbations or for resummation methods.
Backward stochastic differential equations from linear to fully nonlinear theory
Zhang, Jianfeng
2017-01-01
This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
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.
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
Item response theory - A first approach
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.
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.
A look inside the theory of the linear approximation
Bel, Ll.
2006-01-01
We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This allows to introduce geometrical objects that are not invariant under General gauge transformations but they are under Special ones. We develop then a formalism that strengthens the analogy of the formalisms of the electromagnetic and the gravitational theo...
Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory
Richtarik, Peter; Taká č, Martin
2017-01-01
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.
Estimating epidemic arrival times using linear spreading theory
Chen, Lawrence M.; Holzer, Matt; Shapiro, Anne
2018-01-01
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is composed of a system of ordinary differential equations describing a meta-population susceptible-infected-recovered compartmental model defined on a network where each node represents a city and the edges represent the flight paths connecting cities. Making use of the linear determinacy of the system, we consider spreading speeds and arrival times in the system linearized about the unstable disease free state and compare these to arrival times in the nonlinear system. Two predictions are presented. The first is based upon expansion of the heat kernel for the linearized system. The second assumes that the dominant transmission pathway between any two cities can be approximated by a one dimensional lattice or a homogeneous tree and gives a uniform prediction for arrival times independent of the specific network features. We test these predictions on a real network describing worldwide airline traffic.
Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory
Richtarik, Peter
2017-06-04
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.
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.
A linear chromatic mechanism drives the pupillary response.
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
Quantization of a non-linearly realized supersymmetric theory
International Nuclear Information System (INIS)
Shima, Kazunari
1976-01-01
The two-dimensional version of the Volkov-Akulov's Lagrngian, where the super-symmetry is realized non-linearly by means of a single Majorana spinor psi(x), is quantized. The equal time anti-commutators for the field are not c-numbers but functions of the field itself. By the explicite calculation we shall show that supersymmetry charges of the model form the supersymmetry algebra(the graded Lie algebra) and the supersymmetry charges exactly generate a constant translation of psi(x) in the spinor space. In this work we restrict our investigation to the two-dimensional space-time for the sake of simplicity. (auth.)
A quasi-linear control theory analysis of timesharing skills
Agarwal, G. C.; Gottlieb, G. L.
1977-01-01
The compliance of the human ankle joint is measured by applying 0 to 50 Hz band-limited gaussian random torques to the foot of a seated human subject. These torques rotate the foot in a plantar-dorsal direction about a horizontal axis at a medial moleolus of the ankle. The applied torques and the resulting angular rotation of the foot are measured, digitized and recorded for off-line processing. Using such a best-fit, second-order model, the effective moment of inertia of the ankle joint, the angular viscosity and the stiffness are calculated. The ankle joint stiffness is shown to be a linear function of the level of tonic muscle contraction, increasing at a rate of 20 to 40 Nm/rad/Kg.m. of active torque. In terms of the muscle physiology, the more muscle fibers that are active, the greater the muscle stiffness. Joint viscosity also increases with activation. Joint stiffness is also a linear function of the joint angle, increasing at a rate of about 0.7 to 1.1 Nm/rad/deg from plantar flexion to dorsiflexion rotation.
Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information
Directory of Open Access Journals (Sweden)
Naoki Yamamoto
2014-11-01
Full Text Available To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
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
Item Response Data Analysis Using Stata Item Response Theory Package
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…
Kovacs effect in the one-dimensional Ising model: A linear response analysis
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.
Linear theory of plasma Čerenkov masers
Birau, M.
1996-11-01
A different theoretical model of Čerenkov instability in the linear amplification regime of plasma Čerenkov masers is developed. The model assumes a cold relativistic annular electron beam propagating through a column of cold dense plasma, the two bodies being immersed in an infinite magnetic guiding field inside a perfect cylindrical waveguide. In order to simplify the calculations, a radial rectangular distribution of plasma and beam density is assumed and only azimuthal symmetric modes are under investigation. The model's difference consists of taking into account the whole plasma and beam electromagnetic structures in the interpretation of the Čerenkov instability. This model leads to alternative results such as the possibility of emission at several frequencies. In addition, the electric field is calculated taking into account its radial phase dependence, so that a map of the field in the interaction region can be presented.
Linear theory of beam depolarization due to vertical betatron motion
International Nuclear Information System (INIS)
Chao, A.W.; Schwitters, R.F.
1976-06-01
It is well known that vertical betatron motion in the presence of quantum fluctuations leads to some degree of depolarization of a transversely polarized beam in electron-positron storage rings even for energies away from spin resonances. Analytic formulations of this problem, which require the use of simplifying assumptions, generally have shown that there exist operating energies where typical storage rings should exhibit significant beam polarization. Due to the importance of beam polarization in many experiments, we present here a complete calculation of the depolarization rate to lowest order in the perturbing fields, which are taken to be linear functions of the betatron motion about the equilibrium orbit. The results are applicable to most high energy storage rings. Explicit calculations are given for SPEAR and PEP. 7 refs., 8 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
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
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)
Extending Item Response Theory to Online Homework
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…
Linear theory of sound waves with evaporation and condensation
International Nuclear Information System (INIS)
Inaba, Masashi; Watanabe, Masao; Yano, Takeru
2012-01-01
An asymptotic analysis of a boundary-value problem of the Boltzmann equation for small Knudsen number is carried out for the case when an unsteady flow of polyatomic vapour induces reciprocal evaporation and condensation at the interface between the vapour and its liquid phase. The polyatomic version of the Boltzmann equation of the ellipsoidal statistical Bhatnagar–Gross–Krook (ES-BGK) model is used and the asymptotic expansions for small Knudsen numbers are applied on the assumptions that the Mach number is sufficiently small compared with the Knudsen number and the characteristic length scale divided by the characteristic time scale is comparable with the speed of sound in a reference state, as in the case of sound waves. In the leading order of approximation, we derive a set of the linearized Euler equations for the entire flow field and a set of the boundary-layer equations near the boundaries (the vapour–liquid interface and simple solid boundary). The boundary conditions for the Euler and boundary-layer equations are obtained at the same time when the solutions of the Knudsen layers on the boundaries are determined. The slip coefficients in the boundary conditions are evaluated for water vapour. A simple example of the standing sound wave in water vapour bounded by a liquid water film and an oscillating piston is demonstrated and the effect of evaporation and condensation on the sound wave is discussed. (paper)
Linearized thin-wing theory of gas-centrifuge scoops
International Nuclear Information System (INIS)
Sakurai, T.
1981-01-01
A steady hypersonic rotating flow of a perfect gas past a system of thin stationary scoops in a gas centrifuge of annulus type is studied. The gas is assumed inviscid; its ratio of specific heats is assumed to be approximately 1. The scoops are set at zero angle of attack and are periodic with respect to the azimuthal variable. The flow is assumed to be a three-dimensional small perturbation on a basic state of rigid-body rotation. New scaling laws are proposed as appropriate to realistic operating conditions of gas centrifuges. Basic equations, boundary conditions and shock conditions are linearized for a weakly hypersonic flow by an analytical procedure similar to that used in the thin-wing approximation in high speed aerodynamics. The solution of the basic equations is obtained by the eigenfunction expansion method. The solution provides a simple addition theorem for the scoop drag which makes the resultant drag of a system of several scoops equal to the product of the number of scoops and the drag of a standard system with a single scoop. The solution makes it clear that despite the above addition theorem, the scoops interact in their effects on the flow. (author)
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 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.
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
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.
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.
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
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.
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.
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)
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)
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.
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
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)
How linear features alter predator movement and the functional response.
McKenzie, Hannah W
2012-01-18
In areas of oil and gas exploration, seismic lines have been reported to alter the movement patterns of wolves (Canis lupus). We developed a mechanistic first passage time model, based on an anisotropic elliptic partial differential equation, and used this to explore how wolf movement responses to seismic lines influence the encounter rate of the wolves with their prey. The model was parametrized using 5 min GPS location data. These data showed that wolves travelled faster on seismic lines and had a higher probability of staying on a seismic line once they were on it. We simulated wolf movement on a range of seismic line densities and drew implications for the rate of predator-prey interactions as described by the functional response. The functional response exhibited a more than linear increase with respect to prey density (type III) as well as interactions with seismic line density. Encounter rates were significantly higher in landscapes with high seismic line density and were most pronounced at low prey densities. This suggests that prey at low population densities are at higher risk in environments with a high seismic line density unless they learn to avoid them.
How linear features alter predator movement and the functional response.
McKenzie, Hannah W; Merrill, Evelyn H; Spiteri, Raymond J; Lewis, Mark A
2012-01-01
In areas of oil and gas exploration, seismic lines have been reported to alter the movement patterns of wolves (Canis lupus). We developed a mechanistic first passage time model, based on an anisotropic elliptic partial differential equation, and used this to explore how wolf movement responses to seismic lines influence the encounter rate of the wolves with their prey. The model was parametrized using 5 min GPS location data. These data showed that wolves travelled faster on seismic lines and had a higher probability of staying on a seismic line once they were on it. We simulated wolf movement on a range of seismic line densities and drew implications for the rate of predator-prey interactions as described by the functional response. The functional response exhibited a more than linear increase with respect to prey density (type III) as well as interactions with seismic line density. Encounter rates were significantly higher in landscapes with high seismic line density and were most pronounced at low prey densities. This suggests that prey at low population densities are at higher risk in environments with a high seismic line density unless they learn to avoid them.
Linear response formula for piecewise expanding unimodal maps
International Nuclear Information System (INIS)
Baladi, Viviane; Smania, Daniel
2008-01-01
The average R(t) = ∫φdμ t of a smooth function ψ with respect to the SRB measure μ t of a smooth one-parameter family f t of piecewise expanding interval maps is not always Lipschitz (Baladi 2007 Commun. Math. Phys. 275 839–59, Mazzolena 2007 Master's Thesis Rome 2, Tor Vergata). We prove that if f t is tangent to the topological class of f, and if ∂ t f t | t=0 = X circle f, then R(t) is differentiable at zero, and R'(0) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series given by Ruelle's conjecture. In fact, we show that t map μ t is differentiable within Radon measures. Linear response is violated if and only if f t is transversal to the topological class of f
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.
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
Digital linear control theory applied to automatic stepsize control in electrical circuit simulation
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
Using system theory and energy methods to prove existence of non-linear PDE's
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.
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...
Digital linear control theory applied to automatic stepsize control in electrical circuit simulation
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
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,
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)
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
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.
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)
Non-cooperative stochastic differential game theory of generalized Markov jump linear systems
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...
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 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
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.
Quasi-linear theory and transport theory. [particle acceleration in interplanetary medium
Smith, Charles W.
1992-01-01
The theory of energetic particle scattering by magnetostatic fluctuations is reviewed in so far as it fails to produce the rigidity-independent mean-free-paths observed. Basic aspects of interplanetary magnetic field fluctuations are reviewed with emphasis placed on the existence of dissipation range spectra at high wavenumbers. These spectra are then incorporated into existing theories for resonant magnetostatic scattering and are shown to yield infinite mean-free-paths. Nonresonant scattering in the form of magnetic mirroring is examined and offered as a partial solution to the magnetostatic problem. In the process, mean-free-paths are obtained in good agreement with observations in the interplanetary medium at 1 AU and upstream of planetary bow shocks.
Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?
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.
Linear response formula for piecewise expanding unimodal maps
Baladi, Viviane; Smania, Daniel
2008-04-01
The average R(t)=\\int \\varphi\\,\\rmd \\mu_t of a smooth function phiv with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz (Baladi 2007 Commun. Math. Phys. 275 839-59, Mazzolena 2007 Master's Thesis Rome 2, Tor Vergata). We prove that if ft is tangent to the topological class of f, and if ∂t ft|t = 0 = X circle f, then R(t) is differentiable at zero, and R'(0) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series \\sum_{n=0}^\\infty \\int X(y) \\partial_y (\\varphi \\circ f^n)(y)\\,\\rmd \\mu_0(y) given by Ruelle's conjecture. In fact, we show that t map μt is differentiable within Radon measures. Linear response is violated if and only if ft is transversal to the topological class of f.
A noble refractive optical scanner with linear response
Mega, Yair J.; Lai, Zhenhua; DiMarzio, Charles A.
2013-03-01
Many applications in various fields of science and engineering use steered optical beam systems. Currently, many methods utilize mirrors in order to steer the beam. However, this approach is an off-axis solution, which normally increases the total size of the system as well as its error and complexity. Other methods use a "Risely Prisms" based solution, which is on-axis solution, however it poses some difficulties from an engineering standpoint, and therefore isn't widely used. We present here a novel technique for steering a beam on its optical axis with a linear deflection response. We derived the formulation for the profile required of the refractive optical component necessary for preforming the beam steering. The functionality of the device was simulated analytically using Matlab, as well as using a ray-tracing software, Zemax, and showed agreement with the analytical model. An optical element was manufactured based on the proposed design and the device was tested. The results show agreement with our hypothesis. We also present some proposed geometries of the several other devices, all based on the same concept, which can be used for higher performance applications such as two-dimensional scanner, video rate scanner etc.
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.
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...
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....
Extending item response theory to online homework
Directory of Open Access Journals (Sweden)
Gerd Kortemeyer
2014-05-01
Full Text Available 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 scientists and engineers, the study compares outcomes from IRT analyses of exam and homework data, and then proceeds to investigate the effects of each confounding factor introduced in the online realm. It is found that IRT yields the correct trends for learner ability and meaningful item parameters, yet overall agreement with exam data is moderate. It is also found that learner ability and item discrimination is robust over a wide range with respect to model assumptions and introduced noise. Item difficulty is also robust, but over a narrower range.
Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence.
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.
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 ...
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.
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)
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.
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
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....
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
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.
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
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.
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
Influence of magnetic flutter on tearing growth in linear and nonlinear theory
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.
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.
Linear and Non-Linear Response of Liquid and Solid Particles to Energetic Radiation
1991-03-11
but with the beam left within and upon the surface of a spherical particle illuminat - circularly polarized. (The fifth-order corrected, linearly po...specific situation. Figure 1 shows a schematic of the imaging system under consideration. The incident illuminat - ing radiation is generated from a pulsed
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.)
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
Spectral theory of linear operators and spectral systems in Banach algebras
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...
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)
Nuclear response beyond mean field theory
International Nuclear Information System (INIS)
Brand, M.G.E.; Allaart, K.; Dickhoff, W.H.
1990-01-01
An extension of the RPA equations is derived, with emphasis on the relation between the single-particle Green function and the polarization propagator. Including second order self-energy contributions the resulting particle-hole interaction includes the coupling to two-particle-two-hole (2p2h) states and the resulting response satisfies relevant conservation laws. This aspect of the theory is shown to be essential to obtain reliable and meaningful results for excitation strengths and to avoid ghost solutions. This method is applied to electromagnetic and charge exchange excitations in 48 Ca up to 100 MeV. A G-matrix interaction based on meson exchange is used which takes care of short-range correlations. The results compare favourably with measured excitation strengths and electromagnetic form factors both at low energy as well as in the giant resonance region. Remaining discrepancies point in the direction of further strength reduction due to short-range correlations as well as a possible stronger coupling to 2p2h states at low energy. (orig.)
On multidimensional item response theory -- a coordinate free approach
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.
Superradiance Effects in the Linear and Nonlinear Optical Response of Quantum Dot Molecules
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.
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.
Comparison of Classical Test Theory and Item Response Theory in Individual Change Assessment
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 optical response of carbon nanotubes under axial magnetic field
Moradian, Rostam; Chegel, Raad; Behzad, Somayeh
2010-04-01
We considered single walled carbon naotubes (SWCNTs) as real three dimensional (3D) systems in a cylindrical coordinate. The optical matrix elements and linear susceptibility, χ(ω), in the tight binding approximation in terms of one-dimensional wave vector, kz and subband index, l are calculated. In an external axial magnetic field optical frequency dependence of linear susceptibility are investigated. We found that axial magnetic field has two effects on the imaginary part of the linear susceptibility spectrum, in agreement with experimental results. The first effect is broadening and the second, splitting. Also we found that for all metallic zigzag and armchair SWCNTs, the axial magnetic field leads to the creation of a peak with energy less than 1.5 eV, contrary to what is observed in the absence of a magnetic field.
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.
From 6D superconformal field theories to dynamic gauged linear sigma models
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.
Stability and response bounds of non-conservative linear systems
DEFF Research Database (Denmark)
Pommer, Christian
2003-01-01
For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...
The basics of item response theory using R
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...
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
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)
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
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
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.
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.
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
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.
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.
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
Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth
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.
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 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
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
Directory of Open Access Journals (Sweden)
Tumpal Sihombing
2013-01-01
Full Text Available The world is entering the era of recession when the trend is bearish and market is not so favorable. The capital markets in every major country were experiencing great amount of loss and people suffered in their investment. The Jakarta Composite Index (JCI has shown a great downturn for the past one year but the trend bearish year of the JCI. Therefore, rational investors should consider restructuring their portfolio to set bigger proportion in bonds and cash instead of stocks. Investors can apply modern portfolio theory by Harry Markowitz to find the optimum asset allocation for their portfolio. Higher return is always associated with higher risk. This study shows investors how to find out the lowest risk of a portfolio investment by providing them with several structures of portfolio weighting. By this way, investor can compare and make the decision based on risk-return consideration and opportunity cost as well. Keywords: Modern portfolio theory, Monte Carlo, linear programming
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
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.
How linear response shaped models of neural circuits and the quest for alternatives.
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.
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.
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.
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)
Solar Wind Proton Temperature Anisotropy: Linear Theory and WIND/SWE Observations
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).
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
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 Optical Response of Silicon Nanotubes Under Axial Magnetic Field
Chegel, Raad; Behzad, Somayeh
2013-01-01
We investigated the optical properties of silicon nanotubes (SiNTs) in the low energy region, E < 0.5 eV, and middle energy region, 1.8 eV < E < 2 eV. The dependence of optical matrix elements and linear susceptibility on radius and magnetic field, in terms of one-dimensional (1-d) wavevector and subband index, is calculated using the tight-binding approximation. It is found that, on increasing the nanotube diameter, the low-energy peaks show red-shift and their intensities are decreased. Also, we found that in the middle energy region all tubes have two distinct peaks, where the energy position of the second peak is approximately constant and independent of the nanotube diameter. Comparing the band structure of these tubes in different magnetic fields, several differences are clearly seen, such as splitting of degenerate bands, creation of additional band-edge states, and bandgap modification. It is found that applying the magnetic field leads to a phase transition in zigzag silicon hexagonal nanotubes (Si h-NTs), unlike in zigzag silicon gear-like nanotubes (Si g-NTs), which remain semiconducting in any magnetic field. We found that the axial magnetic field has two effects on the linear susceptibility spectrum, namely broadening and splitting. The axial magnetic field leads to the creation of a peak with energy less than 0.2 eV in metallic Si h-NTs, whereas in the absence of a magnetic field such a transition is not allowed.
Strawsonian Libertarianism: A Theory of Free Will and Moral Responsibility
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...
Analyzing force concept inventory with item response theory
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.
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...
debating toynbee's theory of challenge and response
African Journals Online (AJOL)
American forces were pitted against North Koreans backed by divi- sions of Mao's army ... of Guilt” and that many people of his generation believed that religion offered the only ... Toynbee developed his “challenge and response” theory of the history of civilisations, a ... God as the enduring summit of world history. Neither ...
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.
Reproducibility and signal response linearity of Alanine gel dosimeter
International Nuclear Information System (INIS)
Silva, Cleber Feijo Silva; Campos, Leticia Lucente
2008-01-01
Gel Dosimetry has been studied mainly for medical applications, because it presents signal response in the dose range used in radiotherapy treatments and it can be applied for three dimensional dosimetry. Alanine gel dosimeter is a new gel material developed at IPEN that presents significant improvement on previous alanine systems developed by Costa (1994). The DL-Alanine (C 3 H 7 NO 2 ) is an amino acid tissue equivalent that improves the production of ferric ions in the solution. These ferric ions concentration can be measured by spectrophotometry technique. This work aims to study the reproducibility of the alanine gel solutions and the signal response as a function of gamma radiation dose, considering that these two properties are very important for characterizing and standardizing any dosimeter. (author)
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)
The giant resonances in hot nuclei. Linear response calculations
International Nuclear Information System (INIS)
Braghin, F.L.; Vautherin, D.; Abada, A.
1995-01-01
The isovector response function of hot nuclear matter is calculated using various effective Skyrme interactions. For Skyrme forces with a small effective mass the strength distribution is found to be nearly independent of temperature, and shows little collective effects. In contrast effective forces with an effective mass close to unity produce at zero temperature sizeable collective effects which disappear at temperatures of a few MeV. The relevance of these results for the saturation of the multiplicity of photons emitted by the giant dipole resonance in hot nuclei observed in recent experiments beyond T = 3 MeV is discussed. (authors). 12 refs., 3 figs
Modeling and non-linear responses of MEMS capacitive accelerometer
Directory of Open Access Journals (Sweden)
Sri Harsha C.
2014-01-01
Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.
Energy Technology Data Exchange (ETDEWEB)
Corsini, Niccolò R. C., E-mail: niccolo.corsini@imperial.ac.uk; Greco, Andrea; Haynes, Peter D. [Department of Physics and Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Hine, Nicholas D. M. [Department of Physics and Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Cavendish Laboratory, J. J. Thompson Avenue, Cambridge CB3 0HE (United Kingdom); Molteni, Carla [Department of Physics, King' s College London, Strand, London WC2R 2LS (United Kingdom)
2013-08-28
We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure. Based on a definition of the system volume as that enclosed within an electronic density isosurface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett.94, 145501 (2005)], it supports both geometry optimizations and molecular dynamics simulations. We introduce an approach for calibrating the parameters defining the volume in the context of geometry optimizations and discuss their significance. Results in good agreement with simulations using explicit solvents are obtained, validating our approach. Size-dependent pressure-induced structural transformations and variations in the energy gap of hydrogenated silicon nanocrystals are investigated, including one comparable in size to recent experiments. A detailed analysis of the polyamorphic transformations reveals three types of amorphous structures and their persistence on depressurization is assessed.
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.
Dissipative open systems theory as a foundation for the thermodynamics of linear systems.
Delvenne, Jean-Charles; Sandberg, Henrik
2017-03-06
In this paper, we advocate the use of open dynamical systems, i.e. systems sharing input and output variables with their environment, and the dissipativity theory initiated by Jan Willems as models of thermodynamical systems, at the microscopic and macroscopic level alike. We take linear systems as a study case, where we show how to derive a global Lyapunov function to analyse networks of interconnected systems. We define a suitable notion of dynamic non-equilibrium temperature that allows us to derive a discrete Fourier law ruling the exchange of heat between lumped, discrete-space systems, enriched with the Maxwell-Cattaneo correction. We complete these results by a brief recall of the steps that allow complete derivation of the dissipation and fluctuation in macroscopic systems (i.e. at the level of probability distributions) from lossless and deterministic systems.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).
Behavioral Theory and Culture Special Issue: Authors' Response to Commentaries
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
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…
Item Response Theory: Overview, Applications, and Promise for Institutional Research
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.
Rights and Responsibilities in the Light of Social Contract Theory
La Morte, Michael W.
1977-01-01
Discusses the influence of the social contract on American institutions, due process when liberty and property are involved, the nature of an individual's responsibility to the government, and the application of social contract theory to education. (Author/IRT)
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
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)
Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains.
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
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.
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...
Bates, Jason H T; Sobel, Burton E
2003-05-01
This is the third in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas.This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to
Nuclear excitations in the nuclear response theory
International Nuclear Information System (INIS)
Nguyen Van Giai.
1983-01-01
The Random Phase Approximation is used to calculate the response of a nucleus to an external field. The method allows a full treatment of continuum effects. Effective interactions to be used are discussed, and the consistency between the mean field and the residual interaction is stressed. Some applications to excitation properties of spherical nuclei are shown
Item Response Theory for Peer Assessment
Uto, Masaki; Ueno, Maomi
2016-01-01
As an assessment method based on a constructivist approach, peer assessment has become popular in recent years. However, in peer assessment, a problem remains that reliability depends on the rater characteristics. For this reason, some item response models that incorporate rater parameters have been proposed. Those models are expected to improve…
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)
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.
High Power Klystrons: Theory and Practice at the Stanford Linear Accelerator CenterPart I
Energy Technology Data Exchange (ETDEWEB)
Caryotakis, G.
2004-12-15
This is Part I of a two-part report on design and manufacturing methods used at SLAC to produce accelerator klystrons. Chapter 1 begins with the history and applications for klystrons, in both of which Stanford University was extensively involved. The remaining chapters review the theory of klystron operation, derive the principal formulae used in their design, and discuss the assumptions that they involve. These formulae are subsequently used in small-signal calculations of the frequency response of a particular klystron, whose performance is also simulated by two different computer codes. The results of calculations and simulations are compared to the actual performance of the klystron.
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
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…
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.
An NCME Instructional Module on Polytomous Item Response Theory Models
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…
Linear and Nonlinear Response of a Rotating Tokamak Plasma to a Resonant Error-Field
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.
On the theory of the two-photon linear photovoltaic effect in n-GaP
Energy Technology Data Exchange (ETDEWEB)
Rasulov, V. R.; Rasulov, R. Ya., E-mail: r-rasulov51@mail.ru [Fergana State University (Uzbekistan)
2016-02-15
A quantitative theory of the diagonal (ballistic) and nondiagonal (shift) band index contributions to the two-photon current of the linear photovoltaic effect in a semiconductor with a complex band due to the asymmetry of events of electron scattering at phonons and photons is developed. It is shown that processes caused by the simultaneous absorption of two photons do not contribute to the ballistic photocurrent in n-GaP. This is due to the fact that, in this case, there is no asymmetric distribution of the momentum of electrons excited with photons; this distribution arises upon the sequential absorption of two photons with the involvement of LO phonons. It is demonstrated that the temperature dependence of the shift contribution to the two-photon photocurrent in n-GaP is determined by the temperature dependence of the light-absorption coefficient caused by direct optical transitions of electrons between subbands X{sub 1} and X{sub 3}. It is shown that the spectral dependence of the photocurrent has a feature in the light frequency range ω → Δ/2ℏ, which is related to the hump-like shape of subband X{sub 1} in n-GaP{sup 1} and the root-type singularity of the state density determined as k{sub ω}{sup -1}= (2ℏω–Δ){sup –1/2}, where Δ is the energy gap between subbands X{sub 1} and X{sub 3}. The spectral and temperature dependences of the coefficient of absorption of linearly polarized light in n-GaP are obtained with regard to the cone-shaped lower subband of the conduction band.
Theory and praxis pf map analsys in CHEF part 1: Linear normal form
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /Fermilab
2008-10-01
This memo begins a series which, put together, could comprise the 'CHEF Documentation Project' if there were such a thing. The first--and perhaps only--three will telegraphically describe theory, algorithms, implementation and usage of the normal form map analysis procedures encoded in CHEF's collection of libraries. [1] This one will begin the sequence by explaining the linear manipulations that connect the Jacobian matrix of a symplectic mapping to its normal form. It is a 'Reader's Digest' version of material I wrote in Intermediate Classical Dynamics (ICD) [2] and randomly scattered across technical memos, seminar viewgraphs, and lecture notes for the past quarter century. Much of its content is old, well known, and in some places borders on the trivial.1 Nevertheless, completeness requires their inclusion. The primary objective is the 'fundamental theorem' on normalization written on page 8. I plan to describe the nonlinear procedures in a subsequent memo and devote a third to laying out algorithms and lines of code, connecting them with equations written in the first two. Originally this was to be done in one short paper, but I jettisoned that approach after its first section exceeded a dozen pages. The organization of this document is as follows. A brief description of notation is followed by a section containing a general treatment of the linear problem. After the 'fundamental theorem' is proved, two further subsections discuss the generation of equilibrium distributions and issue of 'phase'. The final major section reviews parameterizations--that is, lattice functions--in two and four dimensions with a passing glance at the six-dimensional version. Appearances to the contrary, for the most part I have tried to restrict consideration to matters needed to understand the code in CHEF's libraries.
Design and optimization of a Holweck pump via linear kinetic theory
Naris, Steryios; Koutandou, Eirini; Valougeorgis, Dimitris
2012-05-01
The Holweck pump is widely used in the vacuum pumping industry. It can be a self standing apparatus or it can be part of a more advanced pumping system. It is composed by an inner rotating cylinder (rotor) and an outer stationary cylinder (stator). One of them, has spiral guided grooves resulting to a gas motion from the high towards the low vacuum port. Vacuum pumps may be simulated by the DSMC method but due to the involved high computational cost in many cases manufactures commonly resort to empirical formulas and experimental data. Recently a computationally efficient simulation of the Holweck pump via linear kinetic theory has been proposed by Sharipov et al [1]. Neglecting curvature and end effects the gas flow configuration through the helicoidal channels is decomposed into four basic flows. They correspond to pressure and boundary driven flows through a grooved channel and through a long channel with a T shape cross section. Although the formulation and the methodology are explained in detail, results are very limited and more important they are presented in a normalized way which does not provide the needed information about the pump performance in terms of the involved geometrical and flow parameters. In the present work the four basic flows are solved numerically based on the linearized BGK model equation subjected to diffuse boundary conditions. The results obtained are combined in order to create a database of the flow characteristics for a large spectrum of the rarefaction parameter and various geometrical configurations. Based on this database the performance characteristics which are critical in the design of the Holweck pump are computed and the design parameters such as the angle of the pump and the rotational speed, are optimized. This modeling may be extended to other vacuum pumps.
Design and optimization of a Holweck pump via linear kinetic theory
International Nuclear Information System (INIS)
Naris, Steryios; Koutandou, Eirini; Valougeorgis, Dimitris
2012-01-01
The Holweck pump is widely used in the vacuum pumping industry. It can be a self standing apparatus or it can be part of a more advanced pumping system. It is composed by an inner rotating cylinder (rotor) and an outer stationary cylinder (stator). One of them, has spiral guided grooves resulting to a gas motion from the high towards the low vacuum port. Vacuum pumps may be simulated by the DSMC method but due to the involved high computational cost in many cases manufactures commonly resort to empirical formulas and experimental data. Recently a computationally efficient simulation of the Holweck pump via linear kinetic theory has been proposed by Sharipov et al [1]. Neglecting curvature and end effects the gas flow configuration through the helicoidal channels is decomposed into four basic flows. They correspond to pressure and boundary driven flows through a grooved channel and through a long channel with a T shape cross section. Although the formulation and the methodology are explained in detail, results are very limited and more important they are presented in a normalized way which does not provide the needed information about the pump performance in terms of the involved geometrical and flow parameters. In the present work the four basic flows are solved numerically based on the linearized BGK model equation subjected to diffuse boundary conditions. The results obtained are combined in order to create a database of the flow characteristics for a large spectrum of the rarefaction parameter and various geometrical configurations. Based on this database the performance characteristics which are critical in the design of the Holweck pump are computed and the design parameters such as the angle of the pump and the rotational speed, are optimized. This modeling may be extended to other vacuum pumps.
International Nuclear Information System (INIS)
Lazar, M.; Schlickeiser, R.
2006-01-01
The properties of transverse waves parallel propagating in magnetized plasmas with arbitrary composition and thermally anisotropic, are investigated on the basis of relativistic Vlasov-Maxwell equations. The transverse dispersion relations for plasmas with arbitrary distribution functions are derived. These dispersion relations describe the linear response of the system to the initial perturbations and thus define all existing linear (transverse) plasma modes in the system. By analytic continuation the dispersion relations in the whole complex frequency plane are constructed. Further analysis is restricted to the important case of anisotropic bi-Maxwellian equilibrium plasma distribution functions. Explicit forms of the relativistically correct transverse dispersion relations are derived that hold for any values of the plasma temperatures and the temperature anisotropy. In the limit of nonrelativistic plasma temperatures the dispersion relations are expressed in terms of plasma dispersion function, however, the dependence on frequency and wave numbers is markedly different from the standard noncovariant nonrelativistic analysis. Only in the strictly unphysical formal limit of an infinitely large speed of light, c→∞, does the nonrelativistic dispersion relations reduce to the standard noncovariant dispersion relations
Corporate Social Responsibility and Stakeholder Theory: Learning From Each Other
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...
Tutcuoglu, A.; Majidi, C.
2014-12-01
Using principles of damped harmonic oscillation with continuous media, we examine electrostatic energy harvesting with a "soft-matter" array of dielectric elastomer (DE) transducers. The array is composed of infinitely thin and deformable electrodes separated by layers of insulating elastomer. During vibration, it deforms longitudinally, resulting in a change in the capacitance and electrical enthalpy of the charged electrodes. Depending on the phase of electrostatic loading, the DE array can function as either an actuator that amplifies small vibrations or a generator that converts these external excitations into electrical power. Both cases are addressed with a comprehensive theory that accounts for the influence of viscoelasticity, dielectric breakdown, and electromechanical coupling induced by Maxwell stress. In the case of a linearized Kelvin-Voigt model of the dielectric, we obtain a closed-form estimate for the electrical power output and a scaling law for DE generator design. For the complete nonlinear model, we obtain the optimal electrostatic voltage input for maximum electrical power output.
Effect of liquid surface tension on circular and linear hydraulic jumps; theory and experiments
Bhagat, Rajesh Kumar; Jha, Narsing Kumar; Linden, Paul F.; Wilson, David Ian
2017-11-01
The hydraulic jump has attracted considerable attention since Rayleigh published his account in 1914. Watson (1964) proposed the first satisfactory explanation of the circular hydraulic jump by balancing the momentum and hydrostatic pressure across the jump, but this solution did not explain what actually causes the jump to form. Bohr et al. (1992) showed that the hydraulic jump happens close to the point where the local Froude number equals to one, suggesting a balance between inertial and hydrostatic contributions. Bush & Aristoff (2003) subsequently incorporated the effect of surface tension and showed that this is important when the jump radius is small. In this study, we propose a new account to explain the formation and evolution of hydraulic jumps under conditions where the jump radius is strongly influenced by the liquid surface tension. The theory is compared with experiments employing liquids of different surface tension and different viscosity, in circular and linear configurations. The model predictions and the experimental results show excellent agreement. Commonwealth Scholarship Commission, St. John's college, University of Cambridge.
Savizi, Iman Shahidi Pour
2011-04-01
Specific adsorption of anions to electrode surfaces may alter the rates of electrocatalytic reactions. Density functional theory (DFT) methods are used to predict the adsorption free energy of acetate and phosphate anions as a function of Pt(1 1 1) electrode potential. Four models of the electrode potential are used including a simple vacuum slab model, an applied electric field model with and without the inclusion of a solvating water bi-layer, and the double reference model. The linear sweep voltammogram (LSV) due to anion adsorption is simulated using the DFT results. The inclusion of solvation at the electrochemical interface is necessary for accurately predicting the adsorption peak position. The Langmuir model is sufficient for predicting the adsorption peak shape, indicating coverage effects are minor in altering the LSV for acetate and phosphate adsorption. Anion adsorption peak positions are determined for solution phase anion concentrations present in microbial fuel cells and microbial electrolysis cells and discussion is provided as to the impact of anion adsorption on oxygen reduction and hydrogen evolution reaction rates in these devices. © 2011 Elsevier Ltd. All rights reserved.
Solution to the Diffusion equation for multi groups in X Y geometry using Linear Perturbation theory
International Nuclear Information System (INIS)
Mugica R, C.A.
2004-01-01
Diverse methods exist to solve numerically the neutron diffusion equation for several energy groups in stationary state among those that highlight those of finite elements. In this work the numerical solution of this equation is presented using Raviart-Thomas nodal methods type finite element, the RT0 and RT1, in combination with iterative techniques that allow to obtain the approached solution in a quick form. Nevertheless the above mentioned, the precision of a method is intimately bound to the dimension of the approach space by cell, 5 for the case RT0 and 12 for the RT1, and/or to the mesh refinement, that makes the order of the problem of own value to solve to grow considerably. By this way if it wants to know an acceptable approach to the value of the effective multiplication factor of the system when this it has experimented a small perturbation it was appeal to the Linear perturbation theory with which is possible to determine it starting from the neutron flow and of the effective multiplication factor of the not perturbed case. Results are presented for a reference problem in which a perturbation is introduced in an assemble that simulates changes in the control bar. (Author)
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)
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.
International Nuclear Information System (INIS)
Duan, Chaowei; Zhan, Yafeng
2016-01-01
The output characteristics of a linear monostable system driven with a periodic signal and an additive white Gaussian noise are studied in this paper. Theoretical analysis shows that the output signal-to-noise ratio (SNR) decreases monotonously with the increasing noise intensity but the output SNR-gain is stable. Inspired by this high SNR-gain phenomenon, this paper applies the linear monostable system in the parameters estimation algorithm for phase shift keying (PSK) signals and improves the estimation performance. - Highlights: • The response of a linear monostable system driven with a periodic signal and an additive white Gaussian noise is analyzed. • The optimal parameter of this linear monostable system to maximum the output SNR-gain is obtained. • Application of this linear monostable system in parameters estimation algorithm for PSK signals obtains performance improvement.
CiOpt: a program for optimization of the frequency response of linear circuits
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,...
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...
Lieb-Robinson bounds for multi-commutators and applications to response theory
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...
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...
Comparing light sensitivity, linearity and step response of electronic cameras for ophthalmology.
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.
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.
Validity of the linear no-threshold theory of radiation carcinogenesis at low doses
International Nuclear Information System (INIS)
Cohen, B.L.
1999-01-01
A great deal is known about the cancer risk of high radiation doses from studies of Japanese A-bomb survivors, patients exposed for medical therapy, occupational exposures, etc. But the vast majority of important applications deal with much lower doses, usually accumulated at much lower dose rates, referred to as 'low-level radiation' (LLR). Conventionally, the cancer risk from LLR has been estimated by the use of linear no-threshold theory (LNT). For example, it is assumed that the cancer risk from 0 01 Sr (100 mrem) of dose is 0 01 times the risk from 1 Sv (100 rem). In recent years, the former risk estimates have often been reduced by a 'dose and dose rate reduction factor', which is taken to be a factor of 2. But otherwise, the LNT is frequently used for doses as low as one hundred-thousandth of those for which there is direct evidence of cancer induction by radiation. It is the origin of the commonly used expression 'no level of radiation is safe' and the consequent public fear of LLR. The importance of this use of the LNT can not be exaggerated and is used in many applications in the nuclear industry. The LNT paradigm has also been carried over to chemical carcinogens, leading to severe restrictions on use of cleaning fluids, organic chemicals, pesticides, etc. If the LNT were abandoned for radiation, it would probably also be abandoned for chemical carcinogens. In view of these facts, it is important to consider the validity of the LNT. That is the purpose of this paper. (author)
Analysis of 2D reactor core using linear perturbation theory and nodal finite element methods
International Nuclear Information System (INIS)
Adrian Mugica; Edmundo del Valle
2005-01-01
In this work the multigroup steady state neutron diffusion equations are solved using the nodal finite element method (NFEM) and the Linear Perturbation Theory (LPT) for XY geometry. The NFEM used corresponds to the Raviart-Thomas schemes RT0 and RT1, interpolating 5 and 12 parameters respectively in each node of the space discretization. The accuracy of these methods is related with the dimension of the space approximation and the mesh size. Therefore, using fine meshes and the RT0 or RT1 nodal methods leads to a large an interesting eigenvalue problem. The finite element method used to discretize the weak formulation of the diffusion equations is the Galerkin one. The algebraic structure of the discrete eigenvalue problem is obtained and solved using the Wielandt technique and the BGSTAB iterative method using the SPARSKIT package developed by Yousef Saad. The results obtained with LPT show good agreement with the results obtained directly for the perturbed problem. In fact, the cpu time to solve a single problem, the unperturbed and the perturbed one, is practically the same but when one is focused in shuffling many times two different assemblies in the core then the LPT technique becomes quite useful to get good approximations in a short time. This particular problem was solved for one quarter-core with NFEM. Thus, the computer program based on LPT can be used to perform like an analysis tool in the fuel reload optimization or combinatory analysis to get reload patterns in nuclear power plants once that it had been incorporated with the thermohydraulic aspects needed to simulate accurately a real problem. The maximum differences between the NFEM and LPT for the three LWR reactor cores are about 250 pcm. This quantity is considered an acceptable value for this kind of analysis. (authors)
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)
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
Responsible Business: A Textbook for Theory; Practice and Change
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...
Item Response Theory in the context of Improving Student Reasoning
Goddard, Chase; Davis, Jeremy; Pyper, Brian
2011-10-01
We are interested to see if Item Response Theory can help to better inform the development of reasoning ability in introductory physics. A first pass through our latest batch of data from the Heat and Temperature Conceptual Evaluation, the Lawson Classroom Test of Scientific Reasoning, and the Epistemological Beliefs About Physics Survey may help in this effort.
Characterizing Sources of Uncertainty in Item Response Theory Scale Scores
Yang, Ji Seung; Hansen, Mark; Cai, Li
2012-01-01
Traditional estimators of item response theory scale scores ignore uncertainty carried over from the item calibration process, which can lead to incorrect estimates of the standard errors of measurement (SEMs). Here, the authors review a variety of approaches that have been applied to this problem and compare them on the basis of their statistical…
Bad Questions: An Essay Involving Item Response Theory
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…
Practical Guide to Conducting an Item Response Theory Analysis
Toland, Michael D.
2014-01-01
Item response theory (IRT) is a psychometric technique used in the development, evaluation, improvement, and scoring of multi-item scales. This pedagogical article provides the necessary information needed to understand how to conduct, interpret, and report results from two commonly used ordered polytomous IRT models (Samejima's graded…
Using SAS PROC MCMC for Item Response Theory Models
Ames, Allison J.; Samonte, Kelli
2015-01-01
Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian…
Multilevel Higher-Order Item Response Theory Models
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…
Item Response Theory Models for Performance Decline during Testing
Jin, Kuan-Yu; Wang, Wen-Chung
2014-01-01
Sometimes, test-takers may not be able to attempt all items to the best of their ability (with full effort) due to personal factors (e.g., low motivation) or testing conditions (e.g., time limit), resulting in poor performances on certain items, especially those located toward the end of a test. Standard item response theory (IRT) models fail to…
Item Response Theory Modeling of the Philadelphia Naming Test
Fergadiotis, Gerasimos; Kellough, Stacey; Hula, William D.
2015-01-01
Purpose: In this study, we investigated the fit of the Philadelphia Naming Test (PNT; Roach, Schwartz, Martin, Grewal, & Brecher, 1996) to an item-response-theory measurement model, estimated the precision of the resulting scores and item parameters, and provided a theoretical rationale for the interpretation of PNT overall scores by relating…
Goodness-of-Fit Assessment of Item Response Theory Models
Maydeu-Olivares, Alberto
2013-01-01
The article provides an overview of goodness-of-fit assessment methods for item response theory (IRT) models. It is now possible to obtain accurate "p"-values of the overall fit of the model if bivariate information statistics are used. Several alternative approaches are described. As the validity of inferences drawn on the fitted model…
Large Sample Confidence Intervals for Item Response Theory Reliability Coefficients
Andersson, Björn; Xin, Tao
2018-01-01
In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability…
Theory and computation of disturbance invariant sets for discrete-time linear systems
Directory of Open Access Journals (Sweden)
Kolmanovsky Ilya
1998-01-01
Full Text Available This paper considers the characterization and computation of invariant sets for discrete-time, time-invariant, linear systems with disturbance inputs whose values are confined to a specified compact set but are otherwise unknown. The emphasis is on determining maximal disturbance-invariant sets X that belong to a specified subset Γ of the state space. Such d-invariant sets have important applications in control problems where there are pointwise-in-time state constraints of the form χ ( t ∈ Γ . One purpose of the paper is to unite and extend in a rigorous way disparate results from the prior literature. In addition there are entirely new results. Specific contributions include: exploitation of the Pontryagin set difference to clarify conceptual matters and simplify mathematical developments, special properties of maximal invariant sets and conditions for their finite determination, algorithms for generating concrete representations of maximal invariant sets, practical computational questions, extension of the main results to general Lyapunov stable systems, applications of the computational techniques to the bounding of state and output response. Results on Lyapunov stable systems are applied to the implementation of a logic-based, nonlinear multimode regulator. For plants with disturbance inputs and state-control constraints it enlarges the constraint-admissible domain of attraction. Numerical examples illustrate the various theoretical and computational results.
Theory of Kerr and Faraday rotations and linear dichroism in Topological Weyl Semimetals.
Kargarian, Mehdi; Randeria, Mohit; Trivedi, Nandini
2015-08-03
We consider the electromagnetic response of a topological Weyl semimetal (TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the surface Brillouin zone. We compute the frequency-dependent complex conductivities σαβ(ω) and also take into account the modification of Maxwell equations by the topological θ-term to obtain the Kerr and Faraday rotations in a variety of geometries. For TWS films thinner than the wavelength, the Kerr and Faraday rotations, determined by the separation between Weyl nodes, are significantly larger than in topological insulators. In thicker films, the Kerr and Faraday angles can be enhanced by choice of film thickness and substrate refractive index. We show that, for radiation incident on a surface with Fermi arcs, there is no Kerr or Faraday rotation but the electric field develops a longitudinal component inside the TWS, and there is linear dichroism signal. Our results have implications for probing the TWS phase in various experimental systems.
Linearization of Positional Response Curve of a Fiber-optic Displacement Sensor
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.
Item response theory scoring and the detection of curvilinear relationships.
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).
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.
On the Linear Relation between the Mean and the Standard Deviation of a Response Time Distribution
Wagenmakers, Eric-Jan; Brown, Scott
2007-01-01
Although it is generally accepted that the spread of a response time (RT) distribution increases with the mean, the precise nature of this relation remains relatively unexplored. The authors show that in several descriptive RT distributions, the standard deviation increases linearly with the mean. Results from a wide range of tasks from different…
A Capacitor-Free, Fast Transient Response Linear Voltage Regulator In a 180nm CMOS
DEFF Research Database (Denmark)
Deleuran, Alexander N.; Lindbjerg, Nicklas; Pedersen, Martin K.
2015-01-01
A 1.8 V capacitor-free linear regulator with fast transient response based on a new topology with a fast and slow regulation loop is presented. The design has been laid out and simulated in a 0.18 µm CMOS process. The design has a low component count and is tailored for system-on-chip integration...
Optical measurement of the weak non-linearity in the eardrum vibration response to auditory stimuli
Aerts, Johan
The mammalian hearing organ consists of the external ear (auricle and ear canal) followed by the middle ear (eardrum and ossicles) and the inner ear (cochlea). Its function is to convert the incoming sound waves and convert them into nerve pulses which are processed in the final stage by the brain. The main task of the external and middle ear is to concentrate the incoming sound waves on a smaller surface to reduce the loss that would normally occur in transmission from air to inner ear fluid. In the past it has been shown that this is a linear process, thus without serious distortions, for sound waves going up to pressures of 130 dB SPL (˜90 Pa). However, at large pressure changes up to several kPa, the middle ear movement clearly shows non-linear behaviour. Thus, it is possible that some small non-linear distortions are also present in the middle ear vibration at lower sound pressures. In this thesis a sensitive measurement set-up is presented to detect this weak non-linear behaviour. Essentially, this set-up consists of a loud-speaker which excites the middle ear, and the resulting vibration is measured with an heterodyne vibrometer. The use of specially designed acoustic excitation signals (odd random phase multisines) enables the separation of the linear and non-linear response. The application of this technique on the middle ear demonstrates that there are already non-linear distortions present in the vibration of the middle ear at a sound pressure of 93 dB SPL. This non-linear component also grows strongly with increasing sound pressure. Knowledge of this non-linear component can contribute to the improvement of modern hearing aids, which operate at higher sound pressures where the non-linearities could distort the signal considerably. It is also important to know the contribution of middle ear non-linearity to otoacoustic emissions. This are non-linearities caused by the active feedback amplifier in the inner ear, and can be detected in the external and
Toward a Responsibility-Catering Prioritarian Ethical Theory of Risk.
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.
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.
Recent developments in linear theta-pinch research: experiment and theory
International Nuclear Information System (INIS)
McKenna, K.F.; Bartsch, R.R.; Commisso, R.J.
1978-01-01
High energy plasmas offusion interest can be generated in linear theta pinches. However, end losses present a fundamental limitation on the plasma containment time. This paper discusses recent progress in end-loss and end-stoppering experiments and in the theoretical understanding of linear theta-pinch physics
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…
Item response theory analysis of the mechanics baseline test
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.
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
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...
Profile-likelihood Confidence Intervals in Item Response Theory Models.
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.
Robustness-tracking control based on sliding mode and H∞ theory for linear servo system
Institute of Scientific and Technical Information of China (English)
TIAN Yan-feng; GUO Qing-ding
2005-01-01
A robustness-tracking control scheme based on combining H∞ robust control and sliding mode control is proposed for a direct drive AC permanent-magnet linear motor servo system to solve the conflict between tracking and robustness of the linear servo system. The sliding mode tracking controller is designed to ensure the system has a fast tracking characteristic to the command, and the H∞ robustness controller suppresses the disturbances well within the close loop( including the load and the end effect force of linear motor etc. ) and effectively minimizes the chattering of sliding mode control which influences the steady state performance of the system. Simulation results show that this control scheme enhances the track-command-ability and the robustness of the linear servo system, and in addition, it has a strong robustness to parameter variations and resistance disturbances.
An introduction to fuzzy linear programming problems theory, methods and applications
Kaur, Jagdeep
2016-01-01
The book presents a snapshot of the state of the art in the field of fully fuzzy linear programming. The main focus is on showing current methods for finding the fuzzy optimal solution of fully fuzzy linear programming problems in which all the parameters and decision variables are represented by non-negative fuzzy numbers. It presents new methods developed by the authors, as well as existing methods developed by others, and their application to real-world problems, including fuzzy transportation problems. Moreover, it compares the outcomes of the different methods and discusses their advantages/disadvantages. As the first work to collect at one place the most important methods for solving fuzzy linear programming problems, the book represents a useful reference guide for students and researchers, providing them with the necessary theoretical and practical knowledge to deal with linear programming problems under uncertainty.
Non-linear analytic and coanalytic problems (Lp-theory, Clifford analysis, examples)
International Nuclear Information System (INIS)
Dubinskii, Yu A; Osipenko, A S
2000-01-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the 'orthogonal' sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented
Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)
Dubinskii, Yu A.; Osipenko, A. S.
2000-02-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.
Modeling Composite Assessment Data Using Item Response Theory
Ueckert, Sebastian
2018-01-01
Composite assessments aim to combine different aspects of a disease in a single score and are utilized in a variety of therapeutic areas. The data arising from these evaluations are inherently discrete with distinct statistical properties. This tutorial presents the framework of the item response theory (IRT) for the analysis of this data type in a pharmacometric context. The article considers both conceptual (terms and assumptions) and practical questions (modeling software, data requirements, and model building). PMID:29493119
Incorporating Response Times in Item Response Theory Models of Reading Comprehension Fluency
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…
Low voltage RF MEMS variable capacitor with linear C-V response
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.
Quantum work relations and response theory in parity-time-symmetric quantum systems
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.
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
Improving linear accelerator service response with a real- time electronic event reporting system.
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.
Response statistics of rotating shaft with non-linear elastic restoring forces by path integration
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.
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
Linear population allocation by bistable switches in response to transient stimulation.
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.
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.
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.
Using Classical Test Theory and Item Response Theory to Evaluate the LSCI
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.
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 response approach to active Brownian particles in time-varying activity fields
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.
Quasi-linear theory for a tokamak plasma in the presence of cyclotron resonance
International Nuclear Information System (INIS)
Belikov, V.S.; Kolesnichenko, Ya.I.
1993-01-01
Quasi-linear diffusion equations for the distribution function of trapped and circulating particles interacting with waves in a tokamak by means of cyclotron resonance are derived. The resulting equations reveal new features of quasi-linear diffusion and are of two kinds, one which involves bounce resonances overlapping in velocity space and one with well separated bounce resonances. These two cases correspond to situations where the phase of the wave-particle interaction between successive resonances can be considered as random or deterministic, respectively. An analysis of the conditions of applicability of the new equations is carried out and previous well-known forms of the quasi-linear diffusion equations are shown to be recovered in the proper limits. (10 refs., 3 figs.)
International Nuclear Information System (INIS)
Mika, J.
1975-09-01
Originally the work was oriented towards two main topics: a) difference and integral methods in neutron transport theory. Two computers were used for numerical calculations GIER and CYBER-72. During the first year the main effort was shifted towards basic theoretical investigations. At the first step the ANIS code was adopted and later modified to check various finite difference approaches against each other. Then the general finite element method and the singular perturbation method were developed. The analysis of singularities of the one-dimensional neutron transport equation in spherical geometry has been done and presented. Later the same analysis for the case of cylindrical symmetry has been carried out. The second and the third year programme included the following topics: 1) finite difference methods in stationary neutron transport theory; 2)mathematical fundamentals of approximate methods for solving the transport equation; 3) singular perturbation method for the time-dependent transport equation; 4) investigation of various iterative procedures in reactor calculations. This investigation will help to better understanding of the mathematical basis for existing and developed numerical methods resulting in more effective algorithms for reactor computer codes
Kovacs-Like Memory Effect in Athermal Systems: Linear Response Analysis
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.
Immune oncology, immune responsiveness and the theory of everything.
Turan, Tolga; Kannan, Deepti; Patel, Maulik; Matthew Barnes, J; Tanlimco, Sonia G; Lu, Rongze; Halliwill, Kyle; Kongpachith, Sarah; Kline, Douglas E; Hendrickx, Wouter; Cesano, Alessandra; Butterfield, Lisa H; Kaufman, Howard L; Hudson, Thomas J; Bedognetti, Davide; Marincola, Francesco; Samayoa, Josue
2018-06-05
Anti-cancer immunotherapy is encountering its own checkpoint. Responses are dramatic and long lasting but occur in a subset of tumors and are largely dependent upon the pre-existing immune contexture of individual cancers. Available data suggest that three landscapes best define the cancer microenvironment: immune-active, immune-deserted and immune-excluded. This trichotomy is observable across most solid tumors (although the frequency of each landscape varies depending on tumor tissue of origin) and is associated with cancer prognosis and response to checkpoint inhibitor therapy (CIT). Various gene signatures (e.g. Immunological Constant of Rejection - ICR and Tumor Inflammation Signature - TIS) that delineate these landscapes have been described by different groups. In an effort to explain the mechanisms of cancer immune responsiveness or resistance to CIT, several models have been proposed that are loosely associated with the three landscapes. Here, we propose a strategy to integrate compelling data from various paradigms into a "Theory of Everything". Founded upon this unified theory, we also propose the creation of a task force led by the Society for Immunotherapy of Cancer (SITC) aimed at systematically addressing salient questions relevant to cancer immune responsiveness and immune evasion. This multidisciplinary effort will encompass aspects of genetics, tumor cell biology, and immunology that are pertinent to the understanding of this multifaceted problem.
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)
Directory of Open Access Journals (Sweden)
Rüdiger Kniep
Full Text Available We explored the functional role of individual otoconia within the otolith system of mammalians responsible for the detection of linear accelerations and head tilts in relation to the gravity vector. Details of the inner structure and the shape of intact human and artificial otoconia were studied using environmental scanning electron microscopy (ESEM, including decalcification by ethylenediaminetetraacetic acid (EDTA to discriminate local calcium carbonate density. Considerable differences between the rhombohedral faces of human and artificial otoconia already indicate that the inner architecture of otoconia is not consistent with the point group -3m. This is clearly confirmed by decalcified otoconia specimen which are characterized by a non-centrosymmetric volume distribution of the compact 3+3 branches. This structural evidence for asymmetric mass distribution was further supported by light microscopy in combination with a high speed camera showing the movement of single otoconia specimen (artificial specimen under gravitational influence within a viscous medium (artificial endolymph. Moreover, the response of otoconia to linear acceleration forces was investigated by particle dynamics simulations. Both, time-resolved microscopy and computer simulations of otoconia acceleration show that the dislocation of otoconia include significant rotational movement stemming from density asymmetry. Based on these findings, we suggest an otolith membrane expansion/stiffening mechanism for enhanced response to linear acceleration transmitted to the vestibular hair cells.
International Nuclear Information System (INIS)
Silva, J.O. da; Magalhaes, C.M.S. de; Santos, L.A.P. dos
2007-01-01
Commercial bipolar phototransistors have been used as detectors for low energy X-rays. However, when they are used in high energy X-ray beams, there is a certain loss of sensitivity to the ionizing radiation. This damage is cumulative and irreversible. There are several factors that yield variations in the phototransistor response when it is under high energy radiation, such as its fabrication technology and its electrical characteristics. The aim of this work is to present experimental results that are used to correlate the response curve of SMT (Surface-Mount Technology) bipolar phototransistors with their loss of sensitivity after irradiation from a Linac (linear accelerator) megavoltage beams. (author)
Cultural Consensus Theory: Aggregating Continuous Responses in a Finite Interval
Batchelder, William H.; Strashny, Alex; Romney, A. Kimball
Cultural consensus theory (CCT) consists of cognitive models for aggregating responses of "informants" to test items about some domain of their shared cultural knowledge. This paper develops a CCT model for items requiring bounded numerical responses, e.g. probability estimates, confidence judgments, or similarity judgments. The model assumes that each item generates a latent random representation in each informant, with mean equal to the consensus answer and variance depending jointly on the informant and the location of the consensus answer. The manifest responses may reflect biases of the informants. Markov Chain Monte Carlo (MCMC) methods were used to estimate the model, and simulation studies validated the approach. The model was applied to an existing cross-cultural dataset involving native Japanese and English speakers judging the similarity of emotion terms. The results sharpened earlier studies that showed that both cultures appear to have very similar cognitive representations of emotion terms.
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
Asymmetry in ecosystem responses to precipitation: Theory, observation and experimentation
Sala, O.; Gherardi, L.; Reichmann, L.; Peters, D.
2017-12-01
Ecosystem processes such as primary production respond to changes in precipitation that occur annually and at longer time scales. The questions guiding this presentation are whether ecosystem responses to wet and dry years are symmetrical. Is the increase in productivity in a wet year similar in absolute value to the decrease in productivity in a dry year following a wet year? Is the response to one dry or wet year similar tot response of several consecutive wet and dry years? Do all plant-functional groups respond in a similar way to changes in precipitation? To address the questions we explore the theory behind a potential asymmetry and report on experimental results. Analysis of the cost and benefits of plant responses to changes in precipitation support the idea asymmetrical responses because the threshold for abscising organs that have already been deployed should be higher than the threshold to deploy new organs. However, experiments in a desert grassland in New Mexico where we experimentally increased and decreased precipitation from one year to the next showed that the response was symmetrical. Another mechanism that may yield asymmetries is the productivity response to changes in precipitation is associated with the shape of the relationship between precipitation and productivity. Straight-line relationship may yield no asymmetries whereas a saturating or concave up relationship may result in different asymmetries. Here, we report results from an experiment that yielded concave down responses for grasses and concave up for shrubs. Finally, we report results from a 10-year experiment showing asymmetric responses of grasses and shrubs. Moreover, the magnitude of the sign of the responses changed with the time since the beginning of the precipitation manipulation.
Finite Abstractions of Max-Plus-Linear Systems : Theory and Algorithms
Adzkiya, D.
2014-01-01
Max-Plus-Linear (MPL) systems are a class of discrete-event systems with a continuous state space characterizing the timing of the underlying sequential discrete events. These systems are predisposed to describe the timing synchronization between interleaved processes. MPL systems are employed in
Student Reactions to Learning Theory Based Curriculum Materials in Linear Algebra--A Survey Analysis
Cooley, Laurel; Vidakovic, Draga; Martin, William O.; Dexter, Scott; Suzuki, Jeff
2016-01-01
In this report we examine students' perceptions of the implementation of carefully designed curriculum materials (called modules) in linear algebra courses at three different universities. The curricular materials were produced collaboratively by STEM and mathematics education faculty as members of a professional learning community (PLC) over…
Theory and Applications of Discontinuous State Feedback Generating Chaos for Linear Systems
International Nuclear Information System (INIS)
Xiao-Dan, Zhang; Zhen, Wang; Pin-Dong, Zhao
2008-01-01
We investigate a kind of chaos generating technique on a type of n-dimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system
Relation between linear and nonlinear N=3,4 supergravity theories
International Nuclear Information System (INIS)
Sevrin, A.; Thielemans, K.; Troost, W.
1993-01-01
The effective actions for d=2, N=3,4 chiral supergravities with a linear and a nonlinear gauge algebra are related to each other by a quantum reduction; the latter is obtained from the former by putting quantum currents equal to zero. This implies that the renormalization factors for the quantum actions are identical
Comparison of nonlinearities in oscillation theory of half-linear differential equations
Czech Academy of Sciences Publication Activity Database
Řehák, Pavel
2008-01-01
Roč. 121, č. 2 (2008), s. 93-105 ISSN 0236-5294 R&D Projects: GA AV ČR KJB100190701 Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential equation * comparison theorem * Riccati technique Subject RIV: BA - General Mathematics Impact factor: 0.317, year: 2008
The H-N method for solving linear transport equation: theory and application
International Nuclear Information System (INIS)
Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.
2002-01-01
The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions
Synchronizing chaos in an experimental chaotic pendulum using methods from linear control theory
Kaart, S.; Schouten, J.C.; Bleek, van den C.M.
1999-01-01
Linear feedback control, specifically model predictive control (MPC), was used successfully to synchronize an experimental chaotic pendulum both on unstable periodic and aperiodic orbits. MPC enables tuning of the controller to give an optimal controller performance. That is, both the fluctuations
Savizi, Iman Shahidi Pour; Janik, Michael J.
2011-01-01
) electrode potential. Four models of the electrode potential are used including a simple vacuum slab model, an applied electric field model with and without the inclusion of a solvating water bi-layer, and the double reference model. The linear sweep
Lagos, Macarena; Bellini, Emilio; Noller, Johannes; Ferreira, Pedro G.; Baker, Tessa
2018-03-01
We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.
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)
Nucleon-nucleon scattering in the functional quantum theory of the non-linear spinor field
International Nuclear Information System (INIS)
Philipp, W.
1975-01-01
The nucleon-nucleon and nucleon-antinucleon scattering cross sections are calculated in the frame of the functional quantum field theory by means of two different approximation methods: averaging by integration of indefinite integrals and pulse averaging. The results for nucleon-nucleon scattering are compared with experimental data, with calculations using a modified functional scalar product and with results in first order perturbation theory (V-A-coupling). As for elastic nucleon-antinucleon scattering, the S matrix is investigated for crossing symmetry. Scattering of 'nucleons' of different mass results in different cross sections even in the lowest-order approximation. (BJ) [de
Directory of Open Access Journals (Sweden)
Ana Calabrese
2011-01-01
Full Text Available In the auditory system, the stimulus-response properties of single neurons are often described in terms of the spectrotemporal receptive field (STRF, a linear kernel relating the spectrogram of the sound stimulus to the instantaneous firing rate of the neuron. Several algorithms have been used to estimate STRFs from responses to natural stimuli; these algorithms differ in their functional models, cost functions, and regularization methods. Here, we characterize the stimulus-response function of auditory neurons using a generalized linear model (GLM. In this model, each cell's input is described by: 1 a stimulus filter (STRF; and 2 a post-spike filter, which captures dependencies on the neuron's spiking history. The output of the model is given by a series of spike trains rather than instantaneous firing rate, allowing the prediction of spike train responses to novel stimuli. We fit the model by maximum penalized likelihood to the spiking activity of zebra finch auditory midbrain neurons in response to conspecific vocalizations (songs and modulation limited (ml noise. We compare this model to normalized reverse correlation (NRC, the traditional method for STRF estimation, in terms of predictive power and the basic tuning properties of the estimated STRFs. We find that a GLM with a sparse prior predicts novel responses to both stimulus classes significantly better than NRC. Importantly, we find that STRFs from the two models derived from the same responses can differ substantially and that GLM STRFs are more consistent between stimulus classes than NRC STRFs. These results suggest that a GLM with a sparse prior provides a more accurate characterization of spectrotemporal tuning than does the NRC method when responses to complex sounds are studied in these neurons.
Properties of a novel linear sulfur response mode in a multiple flame photometric detector.
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.
International Nuclear Information System (INIS)
Pomraning, G.C.
1997-05-01
The goal in this research was to continue the development of a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. Such a theory should predict the ensemble average and higher moments, such as the variance, of the particle or energy density described by the underlying transport/kinetic equation. The statistics studied correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components in the mixture. The mixing statistics considered were Markovian as well as more general statistics. In the absence of time dependence and scattering, the theory is well developed and described exactly by the master (Liouville) equation for Markovian mixing, and by renewal equations for non-Markovian mixing. The intent of this research was to generalize these treatments to include both time dependence and scattering. A further goal of this research was to develop approximate, but simpler, models from any comprehensive theory. In particular, a specific goal was to formulate a renormalized transport/kinetic theory of the usual nonstochastic form, but with effective interaction coefficients and sources to account for the stochastic nature of the problem. In the three and one-half year period of research summarized in this final report, they have made substantial progress in the development of a comprehensive theory of kinetic processes in stochastic mixtures. This progress is summarized in 16 archival journal articles, 7 published proceedings papers, and 2 comprehensive review articles. In addition, 17 oral presentations were made describing these research results
On the reciprocity-like relations in linear neutron transport theory
International Nuclear Information System (INIS)
Modak, R.S.; Sahni, D.C.
1997-01-01
The existence of certain reciprocity-like relations in neutron transport theory was shown earlier under some quite restrictive conditions. Here, these relations are shown to be valid in more general situations by using a different approach based on individual neutron trajectories. (author)
A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials
Li, Chen; Liao, Yufei
2018-03-01
Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.
Self-consistent field theory based molecular dynamics with linear system-size scaling
Energy Technology Data Exchange (ETDEWEB)
Richters, Dorothee [Institute of Mathematics and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 9, D-55128 Mainz (Germany); Kühne, Thomas D., E-mail: kuehne@uni-mainz.de [Institute of Physical Chemistry and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 7, D-55128 Mainz (Germany); Technical and Macromolecular Chemistry, University of Paderborn, Warburger Str. 100, D-33098 Paderborn (Germany)
2014-04-07
We present an improved field-theoretic approach to the grand-canonical potential suitable for linear scaling molecular dynamics simulations using forces from self-consistent electronic structure calculations. It is based on an exact decomposition of the grand canonical potential for independent fermions and does neither rely on the ability to localize the orbitals nor that the Hamilton operator is well-conditioned. Hence, this scheme enables highly accurate all-electron linear scaling calculations even for metallic systems. The inherent energy drift of Born-Oppenheimer molecular dynamics simulations, arising from an incomplete convergence of the self-consistent field cycle, is circumvented by means of a properly modified Langevin equation. The predictive power of the present approach is illustrated using the example of liquid methane under extreme conditions.
Comparison theorems and strong oscillation in the half-linear discrete oscillation theory
Czech Academy of Sciences Publication Activity Database
Řehák, Pavel
2003-01-01
Roč. 33, č. 1 (2003), s. 333-352 ISSN 0035-7596 R&D Projects: GA ČR GA201/98/0677; GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : half-linear difference equation * comparison theorems * strong oscillation Subject RIV: BA - General Mathematics Impact factor: 0.187, year: 2003
Bianchi-Baecklund transformations, conservation laws, and linearization of various field theories
International Nuclear Information System (INIS)
Chau Wang, L.L.
1980-01-01
The discussion includes: the Sine-Gordon equation, parametric Bianchi-Baecklund transformations and the derivation of local conservation laws; chiral fields, parametric Bianchi-Baecklund transformations, local and non-local conservation laws, and linearization; super chiral fields, a parallel development similar to the chiral field; and self-dual Yang-Mills fields in 4-dimensional Euclidean space; loop-cpace chiral equations, parallel development but with subtlety
Nonlocal linear theory of the gradient drift instability in the equatorial electrojet
International Nuclear Information System (INIS)
Ronchi, C.; Similon, P.L.; Sudan, R.N.
1989-01-01
The linear global eigenmodes of the gradient drift instability in the daytime equatorial electrojet are investigated. A main feature of the analysis is the inclusion of ion-neutral and electron-neutral collision frequencies dependent on altitude. It is found that the basic characteristics and localization of the unstable modes are determined mainly by the profiles of the Pedersen and Hall mobilities, which are derived from the Cowling conductivity model and experimental data. The equilibrium density profile is parabolic, which is fairly representative of the actual measurements. The unstable modes are sensitive not to the details of this profile, but only to the average value of the gradient. The results are obtained from a direct numerical integration of nonlocal linearized equations. They are further analyzed through an eikonal analysis, which provides both an interpretation of the transient modes observed by Fu et al. (1986) and some additional physics insight into the linear evolution of the global unstable modes. Finally, it is shown that the previously reported short-wavelength stabilization effect due to velocity shear may be overshadowed by the presence of regions in which the transient modes can develop into absolute instabilities. copyright American Geophysical Union 1989
Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules
Directory of Open Access Journals (Sweden)
Katy L. Chubb
2018-04-01
Full Text Available A numerical application of linear-molecule symmetry properties, described by the D ∞ h point group, is formulated in terms of lower-order symmetry groups D n h with finite n. Character tables and irreducible representation transformation matrices are presented for D n h groups with arbitrary n-values. These groups can subsequently be used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of “reduced” vibrational eigenvalue problems with simplified Hamiltonians is used as a practical example. It is shown how the solutions of these eigenvalue problems can also be extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ of the vibrational angular momentum operator L ^ z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D n h . 12 C 2 H 2 is used as an example of a linear molecule of D ∞ h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE.
PENGEMBANGAN TES BERPIKIR KRITIS DENGAN PENDEKATAN ITEM RESPONSE THEORY
Directory of Open Access Journals (Sweden)
Fajrianthi Fajrianthi
2016-06-01
Full Text Available Penelitian ini bertujuan untuk menghasilkan sebuah alat ukur (tes berpikir kritis yang valid dan reliabel untuk digunakan, baik dalam lingkup pendidikan maupun kerja di Indonesia. Tahapan penelitian dilakukan berdasarkan tahap pengembangan tes menurut Hambleton dan Jones (1993. Kisi-kisi dan pembuatan butir didasarkan pada konsep dalam tes Watson-Glaser Critical Thinking Appraisal (WGCTA. Pada WGCTA, berpikir kritis terdiri dari lima dimensi yaitu Inference, Recognition Assumption, Deduction, Interpretation dan Evaluation of arguments. Uji coba tes dilakukan pada 1.453 peserta tes seleksi karyawan di Surabaya, Gresik, Tuban, Bojonegoro, Rembang. Data dikotomi dianalisis dengan menggunakan model IRT dengan dua parameter yaitu daya beda dan tingkat kesulitan butir. Analisis dilakukan dengan menggunakan program statistik Mplus versi 6.11 Sebelum melakukan analisis dengan IRT, dilakukan pengujian asumsi yaitu uji unidimensionalitas, independensi lokal dan Item Characteristic Curve (ICC. Hasil analisis terhadap 68 butir menghasilkan 15 butir dengan daya beda yang cukup baik dan tingkat kesulitan butir yang berkisar antara –4 sampai dengan 2.448. Sedikitnya jumlah butir yang berkualitas baik disebabkan oleh kelemahan dalam menentukan subject matter experts di bidang berpikir kritis dan pemilihan metode skoring. Kata kunci: Pengembangan tes, berpikir kritis, item response theory DEVELOPING CRITICAL THINKING TEST UTILISING ITEM RESPONSE THEORY Abstract The present study was aimed to develop a valid and reliable instrument in assesing critical thinking which can be implemented both in educational and work settings in Indonesia. Following the Hambleton and Jones’s (1993 procedures on test development, the study developed the instrument by employing the concept of critical thinking from Watson-Glaser Critical Thinking Appraisal (WGCTA. The study included five dimensions of critical thinking as adopted from the WGCTA: Inference, Recognition
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.
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.
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
Zilletti, Michele; Marker, Arthur; Elliott, Stephen John; Holland, Keith
2017-05-01
In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.
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
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.
DEFF Research Database (Denmark)
Zhou, Qiang; Nielsen, Søren R.K.; Qu, Weilian
2010-01-01
Considering the coupling between the in-plane and out-of-plane vibration, the stochastic response of an inclined shallow cable with linear viscous dampers subjected to Gaussian white noise excitation is investigated in this paper. Selecting the static deflection shape due to a concentrated force...... together with the C-type Gram-Charlier expansion with a fourth-order closure are applied to obtain statistical moments, power spectral density and probabilistic density function of the cable response, whose availability is verified by Monte Carlo method. Taking a typical cable as an example, the influence...... of several factors, which include excitation level and direction as well as damper size, on the dynamic response of the cable is extensively investigated. It is found that the sum of mean square in-plane and out-of-plane displacement is primarily independent of the load direction when the excitation level...
Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance
Yu Nakayama
2009-01-01
We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the non-relativistic conformal invariance. We discuss applications to scaling regime of Reggeo...
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
Transient response of nonlinear polymer networks: A kinetic theory
Vernerey, Franck J.
2018-06-01
Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.
Contributions to the spectral theory of the linear Boltzmann operator for various geometries
International Nuclear Information System (INIS)
Protopopescu, V.
1975-01-01
The linear monoenergetic Boltzmann operator with isotropic scattering is studied for various geometries and boundary conditions as the infinitesimal generator of a positivity preserving contractive semigroup in an appropriate Hilbert space. General results about the existence and the uniqueness of the solutions of the corresponding evolution problems are reviewed. The spectrum of the Boltzmann operator is analyzed for semi-infinite, slab and parallelepipedic geometries with vacuum, periodic, perfectly reflecting, generalized and diffusely reflecting boundary condition respectively. The main features of these spectra, their importance for determining the asymptotic evolution and possible generalizations to more realistic models are put together in a final section. (author)
International Nuclear Information System (INIS)
Trombetti, T.
1990-01-01
The exact kernel method is presented for linear transport problems with azimuth-dependent angular fluxes. It is based on the evaluation of average scattering densities (ASD's) that fully describe the neutron (or particle) transfer between subsets of the unit sphere of directions by anisotropic scattering. Reciprocity and other ASD functional properties are proved and combined with the symmetry properties of suitable SN quadrature sets. This greatly reduces the number of independent ASD's to be computed and stored. An approach for performing ASD computations with reciprocity checks is presented. ASD expressions of the scattering source for typical 2D geometries are explicitly given. (author)
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 ...
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
Three
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.
The linear transformation model with frailties for the analysis of item response times.
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.
Linear theory of drift-tearing and interchange modes in a screw pinch
International Nuclear Information System (INIS)
Copenhaver, C.
1978-04-01
A drift dispersion relation, as applied to a resistive incompressible plasma in a screw pinch, is derived. This dispersion relation incorporates both drift-tearing and drift-interchange modes and is valid throughout the collisional regime by including kinetic theory factors. The dispersion relation reduces to the drift-tearing dispersion relation in the zero pressure gradient limit, and to the classical resistive dispersion relation in the zero drift limit. The electron temperature gradient instability is still present. Now, however, the introduction of the interchange-drift instability increases the growth rate further above the tearing-drift case. (orig.) [de
Zheligovsky, Vladislav
2011-01-01
New developments for hydrodynamical dynamo theory have been spurred by recent evidence of self-sustained dynamo activity in laboratory experiments with liquid metals. The emphasis in the present volume is on the introduction of powerful mathematical techniques required to tackle modern multiscale analysis of continous systems and there application to a number of realistic model geometries of increasing complexity. This introductory and self-contained research monograph summarizes the theoretical state-of-the-art to which the author has made pioneering contributions.
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...
Energy Technology Data Exchange (ETDEWEB)
Kabashima, Y [Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 226-8502 (Japan)], E-mail: kaba@dis.titech.ac.jp
2008-01-15
A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown.
International Nuclear Information System (INIS)
Kabashima, Y
2008-01-01
A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown
Kabashima, Y.
2008-01-01
A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible to characterize the objective system by a single function of two variables which is determined by the eigenvalue spectrum of the cross-correlation matrix of the pattern matrix. Links to existing methods for analysis of perceptron learning and Gaussian linear vector channels and an application to a simple but nontrivial problem are also shown.
Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics
Directory of Open Access Journals (Sweden)
Daniel W.F. Alves
2017-10-01
Full Text Available We examine knotted solutions, the most simple of which is the “Hopfion”, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.
Phantom solution in a non-linear Israel-Stewart theory
Cruz, Miguel; Cruz, Norman; Lepe, Samuel
2017-06-01
In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p = ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than -1 and constant in time.
Linear response and correlation of a self-propelled particle in the presence of external fields
Caprini, Lorenzo; Marini Bettolo Marconi, Umberto; Vulpiani, Angelo
2018-03-01
We study the non-equilibrium properties of non interacting active Ornstein-Uhlenbeck particles (AOUP) subject to an external nonuniform field using a Fokker-Planck approach with a focus on the linear response and time-correlation functions. In particular, we compare different methods to compute these functions including the unified colored noise approximation (UCNA). The AOUP model, described by the position of the particle and the active force acting on it, is usually mapped into a Markovian process, describing the motion of a fictitious passive particle in terms of its position and velocity, where the effect of the activity is transferred into a position-dependent friction. We show that the form of the response function of the AOUP depends on whether we put the perturbation on the position and keep unperturbed the active force in the original variables or perturb the position and maintain unperturbed the velocity in the transformed variables. Indeed, as a result of the change of variables the perturbation on the position becomes a perturbation both on the position and on the fictitious velocity. We test these predictions by considering the response for three types of convex potentials: quadratic, quartic and double-well potential. Moreover, by comparing the response of the AOUP model with the corresponding response of the UCNA model we conclude that although the stationary properties are fairly well approximated by the UCNA, the non equilibrium properties are not, an effect which is not negligible when the persistence time is large.
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
Directory of Open Access Journals (Sweden)
Sergey G. Chefranov
2012-11-01
Full Text Available Aims This paper deals with solving of a century-old paradox of linear stability for the Hagen-Poiseuille flow. A new mechanism of dissipative hydrodynamic instability has been established herein, and a basis for the forming of helical structural organization of bloodstream and respective energy effectiveness of the cardiovascular system functioning has been defined by the authors. Materials and methods Theory of hydrodynamic instability, Galerkin’s approximation. Results A new condition Re > Reth-min ≈ 124 of linear (exponential instability of the Hagen-Poisseuille (HP flow with respect to extremely small by magnitude axially-symmetric disturbances of the tangential component of the velocity field is obtained. The disturbances necessarily shall have quasi-periodic longitudinal variability along the pipe axis that corresponds to the observed data. Conclusion We show that the obtained estimate of value of Reth-min corresponds to the condition of independence of the main result (on the linear instability of the HP flow when Re > Reth-min from the procedure of averaging used in the Galerkin approximation. Thus, we obtain the possible natural mechanism for the blood swirling flows formations observed in the aorta and the large blood vessels.
International Nuclear Information System (INIS)
Esmaeilzadeh Khadem, S.; Rezaee, M.
2001-01-01
In this paper the large amplitude and non-linear vibration of a string is considered. The initial tension, lateral vibration amplitude, diameter and the modulus of elasticity of the string have main effects on its natural frequencies. Increasing the lateral vibration amplitude makes the assumption of constant initial tension invalid. In this case, therefore, it is impossible to use the classical equation of string with small amplitude transverse motion assumption. On the other hand, by increasing the string diameter, the bending moment effect will increase dramatically, and acts as an impressive restoring moment. Considering the effects of the bending moments, the nonlinear equation governing the large amplitude transverse vibration of a string is derived. The time dependent portion of the governing equation has the from of Duff ing equation is solved using the perturbation theory. The results of the analysis are shown in appropriate graphs, and the natural frequencies of the string due to the non-linear factors are compared with the natural frequencies of the linear vibration os a string without bending moment effects
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.)
Linear, no threshold response at low doses of ionizing radiation: ideology, prejudice and science
International Nuclear Information System (INIS)
Kesavan, P.C.
2014-01-01
The linear, no threshold (LNT) response model assumes that there is no threshold dose for the radiation-induced genetic effects (heritable mutations and cancer), and it forms the current basis for radiation protection standards for radiation workers and the general public. The LNT model is, however, based more on ideology than valid radiobiological data. Further, phenomena such as 'radiation hormesis', 'radioadaptive response', 'bystander effects' and 'genomic instability' are now demonstrated to be radioprotective and beneficial. More importantly, the 'differential gene expression' reveals that qualitatively different proteins are induced by low and high doses. This finding negates the LNT model which assumes that qualitatively similar proteins are formed at all doses. Thus, all available scientific data challenge the LNT hypothesis. (author)
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.
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.
Casero-Alonso, V; López-Fidalgo, J; Torsney, B
2017-01-01
Binary response models are used in many real applications. For these models the Fisher information matrix (FIM) is proportional to the FIM of a weighted simple linear regression model. The same is also true when the weight function has a finite integral. Thus, optimal designs for one binary model are also optimal for the corresponding weighted linear regression model. The main objective of this paper is to provide a tool for the construction of MV-optimal designs, minimizing the maximum of the variances of the estimates, for a general design space. MV-optimality is a potentially difficult criterion because of its nondifferentiability at equal variance designs. A methodology for obtaining MV-optimal designs where the design space is a compact interval [a, b] will be given for several standard weight functions. The methodology will allow us to build a user-friendly computer tool based on Mathematica to compute MV-optimal designs. Some illustrative examples will show a representation of MV-optimal designs in the Euclidean plane, taking a and b as the axes. The applet will be explained using two relevant models. In the first one the case of a weighted linear regression model is considered, where the weight function is directly chosen from a typical family. In the second example a binary response model is assumed, where the probability of the outcome is given by a typical probability distribution. Practitioners can use the provided applet to identify the solution and to know the exact support points and design weights. Copyright Â© 2016 Elsevier Ireland Ltd. All rights reserved.
Modeling exposure–lag–response associations with distributed lag non-linear models
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
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...
Building an Evaluation Scale using Item Response Theory.
Lalor, John P; Wu, Hao; Yu, Hong
2016-11-01
Evaluation of NLP methods requires testing against a previously vetted gold-standard test set and reporting standard metrics (accuracy/precision/recall/F1). The current assumption is that all items in a given test set are equal with regards to difficulty and discriminating power. We propose Item Response Theory (IRT) from psychometrics as an alternative means for gold-standard test-set generation and NLP system evaluation. IRT is able to describe characteristics of individual items - their difficulty and discriminating power - and can account for these characteristics in its estimation of human intelligence or ability for an NLP task. In this paper, we demonstrate IRT by generating a gold-standard test set for Recognizing Textual Entailment. By collecting a large number of human responses and fitting our IRT model, we show that our IRT model compares NLP systems with the performance in a human population and is able to provide more insight into system performance than standard evaluation metrics. We show that a high accuracy score does not always imply a high IRT score, which depends on the item characteristics and the response pattern.
Using item response theory to address vulnerabilities in FFQ.
Kazman, Josh B; Scott, Jonathan M; Deuster, Patricia A
2017-09-01
The limitations for self-reporting of dietary patterns are widely recognised as a major vulnerability of FFQ and the dietary screeners/scales derived from FFQ. Such instruments can yield inconsistent results to produce questionable interpretations. The present article discusses the value of psychometric approaches and standards in addressing these drawbacks for instruments used to estimate dietary habits and nutrient intake. We argue that a FFQ or screener that treats diet as a 'latent construct' can be optimised for both internal consistency and the value of the research results. Latent constructs, a foundation for item response theory (IRT)-based scales (e.g. Patient Reported Outcomes Measurement Information System) are typically introduced in the design stage of an instrument to elicit critical factors that cannot be observed or measured directly. We propose an iterative approach that uses such modelling to refine FFQ and similar instruments. To that end, we illustrate the benefits of psychometric modelling by using items and data from a sample of 12 370 Soldiers who completed the 2012 US Army Global Assessment Tool (GAT). We used factor analysis to build the scale incorporating five out of eleven survey items. An IRT-driven assessment of response category properties indicates likely problems in the ordering or wording of several response categories. Group comparisons, examined with differential item functioning (DIF), provided evidence of scale validity across each Army sub-population (sex, service component and officer status). Such an approach holds promise for future FFQ.
Correlation function for density perturbations in an expanding universe. I. Linear theory
International Nuclear Information System (INIS)
McClelland, J.; Silk, J.
1977-01-01
We derive analytic solutions for the evolution of linearized adiabatic spherically symmetric density perturbations and the two-point correlation function in two regimes of the early universe: the radiation-dominated regime prior to decoupling, and the matter-dominated regime after decoupling. The solutions are for an Einstein--de Sitter universe, and include pressure effects. In the radiation era, we find that individual spherically symmetric adiabatic density perturbations smaller than the Jeans length flow outward like water waves instead of oscillating as infinite plane waves. It seems likely that the only primordial structures on scales smaller than the maximum Jeans length which could survive are very regular waves such as infinite plane waves. However, structure does build up in the correlation function over distances comparable with the maximum Jeans length in the radiation regime, and could lead to the eventual formation of galaxy superclusters. This scale (approx.10 17 Ω -2 M/sub sun)/therefore provides a natural dimension for large-scale structure arising out of the early universe. A general technique is described for constructing solutions for the evolution of the two-point correlation function, and applied to study white noise and power-law initial conditions for primordial inhomogeneities
Valence-bond theory of linear Hubbard and Pariser-Parr-Pople models
Soos, Z. G.; Ramasesha, S.
1984-05-01
The ground and low-lying states of finite quantum-cell models with one state per site are obtained exactly through a real-space basis of valence-bond (VB) diagrams that explicitly conserve the total spin. Regular and alternating Hubbard and Pariser-Parr-Pople (PPP) chains and rings with Ne electrons on N(PPP models, but differ from mean-field results. Molecular PPP parameters describe well the excitations of finite polyenes, odd polyene ions, linear cyanine dyes, and slightly overestimate the absorption peaks in polyacetylene (CH)x. Molecular correlations contrast sharply with uncorrelated descriptions of topological solitons, which are modeled by regular polyene radicals and their ions for both wide and narrow alternation crossovers. Neutral solitons have no midgap absorption and negative spin densities, while the intensity of the in-gap excitation of charged solitons is not enhanced. The properties of correlated states in quantum-cell models with one valence state per site are discussed in the adiabatic limit for excited-state geometries and instabilities to dimerization.
Unified theory of damping of linear surface Alfven waves in inhomogeneous incompressible plasmas
International Nuclear Information System (INIS)
Ruderman, M.S.; Goossens, M.
1996-01-01
The viscous damping of surface Alfven waves in a non-uniform plasma is studied in the context of linear and incompressible MHD. It is shown that damping due to resonant absorption and damping on a true discontinuity are two limiting cases of the continuous variation of the damping rate with respect to the dimensionless number Rg = Δλ 2 Re, where Δ is the relative variation of the local Alfven velocity, λ is the ratio of the thickness of the inhomogeneous layer to the wavelength, and Re is the viscous Reynolds number. The analysis is restricted to waves with wavelengths that are long in comparison with the extent of the non-uniform layer (λ '' >'' 1) values of Rg. For very small values of Rg, the damping rate agrees with that found for a true discontinuity, while for very large values of Rg, it agrees with the damping rate due to resonant absorption. The dispersion relation is subsequently studied numerically over a wide range of values of Rg, revealing a continuous but non-monotonic variation of the damping rate with respect to Rg. (Author)
The correlation function for density perturbations in an expanding universe. I - Linear theory
Mcclelland, J.; Silk, J.
1977-01-01
The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.
Nonlinear responses of chiral fluids from kinetic theory
Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun
2018-01-01
The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.
Raab, Melinda; Dunst, Carl J; Hamby, Deborah W
2018-02-27
The purpose of the study was to isolate the sources of variations in the rates of response-contingent learning among young children with multiple disabilities and significant developmental delays randomly assigned to contrasting types of early childhood intervention. Multilevel, hierarchical linear growth curve modelling was used to analyze four different measures of child response-contingent learning where repeated child learning measures were nested within individual children (Level-1), children were nested within practitioners (Level-2), and practitioners were nested within the contrasting types of intervention (Level-3). Findings showed that sources of variations in rates of child response-contingent learning were associated almost entirely with type of intervention after the variance associated with differences in practitioners nested within groups were accounted for. Rates of child learning were greater among children whose existing behaviour were used as the building blocks for promoting child competence (asset-based practices) compared to children for whom the focus of intervention was promoting child acquisition of missing skills (needs-based practices). The methods of analysis illustrate a practical approach to clustered data analysis and the presentation of results in ways that highlight sources of variations in the rates of response-contingent learning among young children with multiple developmental disabilities and significant developmental delays. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.
Lee, Kyungtae; Gu, Geun Ho; Mullen, Charles A; Boateng, Akwasi A; Vlachos, Dionisios G
2015-01-01
Density functional theory is used to study the adsorption of guaiacol and its initial hydrodeoxygenation (HDO) reactions on Pt(111). Previous Brønsted-Evans-Polanyi (BEP) correlations for small open-chain molecules are inadequate in estimating the reaction barriers of phenolic compounds except for the side group (methoxy) carbon-dehydrogenation. New BEP relations are established using a select group of phenolic compounds. These relations are applied to construct a potential-energy surface of guaiacol-HDO to catechol. Analysis shows that catechol is mainly produced via dehydrogenation of the methoxy functional group followed by the CHx (x<3) removal of the functional group and hydrogenation of the ring carbon, in contrast to a hypothesis of a direct demethylation path. Dehydroxylation and demethoxylation are slow, implying that phenol is likely produced from catechol but not through its direct dehydroxylation followed by aromatic carbon-ring hydrogenation. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
The analysis of linear partial differential operators I distribution theory and Fourier analysis
Hörmander, Lars
2003-01-01
The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comm...
Estimating net joint torques from kinesiological data using optimal linear system theory.
Runge, C F; Zajac, F E; Allum, J H; Risher, D W; Bryson, A E; Honegger, F
1995-12-01
Net joint torques (NJT) are frequently computed to provide insights into the motor control of dynamic biomechanical systems. An inverse dynamics approach is almost always used, whereby the NJT are computed from 1) kinematic measurements (e.g., position of the segments), 2) kinetic measurements (e.g., ground reaction forces) that are, in effect, constraints defining unmeasured kinematic quantities based on a dynamic segmental model, and 3) numerical differentiation of the measured kinematics to estimate velocities and accelerations that are, in effect, additional constraints. Due to errors in the measurements, the segmental model, and the differentiation process, estimated NJT rarely produce the observed movement in a forward simulation when the dynamics of the segmental system are inherently unstable (e.g., human walking). Forward dynamic simulations are, however, essential to studies of muscle coordination. We have developed an alternative approach, using the linear quadratic follower (LQF) algorithm, which computes the NJT such that a stable simulation of the observed movement is produced and the measurements are replicated as well as possible. The LQF algorithm does not employ constraints depending on explicit differentiation of the kinematic data, but rather employs those depending on specification of a cost function, based on quantitative assumptions about data confidence. We illustrate the usefulness of the LQF approach by using it to estimate NJT exerted by standing humans perturbed by support-surface movements. We show that unless the number of kinematic and force variables recorded is sufficiently high, the confidence that can be placed in the estimates of the NJT, obtained by any method (e.g., LQF, or the inverse dynamics approach), may be unsatisfactorily low.
The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications
DEFF Research Database (Denmark)
Andreasen, Martin Møller; Fernández-Villaverde, Jesús; Rubio-Ramírez, Juan F.
and impulse response functions. Thus, our analysis introduces GMM estimation for DSGE models approximated up to third-order and provides the foundation for indirect inference and SMM when simulation is required. We illustrate the usefulness of our approach by estimating a New Keynesian model with habits...... and Epstein-Zin preferences by GMM when using …rst and second unconditional moments of macroeconomic and …nancial data and by SMM when using additional third and fourth unconditional moments and non-Gaussian innovations....
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
International Nuclear Information System (INIS)
Krishan, S.
2007-01-01
The Stieltjes transform has been used in place of a more common Laplace transform to determine the time evolution of the self-consistent field (SCF) of an unmagnetized semi-infinite plasma, where the plasma electrons together with a primary and a low-density secondary electron beam move perpendicular to the boundary surface. The secondary beam is produced when the primary beam strikes the grid. Such a plasma system has been investigated by Griskey and Stanzel [M. C. Grisky and R. L. Stenzel, Phys. Rev. Lett. 82, 556 (1999)]. The physical phenomenon, observed in their experiment, has been named by them as ''secondary beam instability.'' The character of the instability observed in the experiment is not the same as predicted by the conventional treatments--the field amplitude does not grow with time. In the frequency spectrum, the theory predicts peak values in the amplitude of SCF at the plasma frequency of plasma and secondary beam electrons, decreasing above and below it. The Stieltjes transform for functions, growing exponentially in the long time limit, does not exist, while the Laplace transform technique gives only exponentially growing solutions. Therefore, it should be interesting to know the kind of solutions that an otherwise physically unstable plasma will yield. In the high-frequency limit, the plasma has been found to respond to any arbitrary frequency of the initial field differentiated only by the strength of the resulting SCF. The condition required for exponential growth in the conventional treatments, and the condition for maximum amplitude (with respect to frequency) in the present treatment, have been found to be the same. Nonlinear mode coupling between the modes excited by the plasma electrons and the low-density secondary beam gives rise to two frequency-dependent peaks in the field amplitude, symmetrically located about the much stronger peak due to the plasma electrons, as predicted by the experiment
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
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.
Hidden Markov Item Response Theory Models for Responses and Response Times.
Molenaar, Dylan; Oberski, Daniel; Vermunt, Jeroen; De Boeck, Paul
2016-01-01
Current approaches to model responses and response times to psychometric tests solely focus on between-subject differences in speed and ability. Within subjects, speed and ability are assumed to be constants. Violations of this assumption are generally absorbed in the residual of the model. As a result, within-subject departures from the between-subject speed and ability level remain undetected. These departures may be of interest to the researcher as they reflect differences in the response processes adopted on the items of a test. In this article, we propose a dynamic approach for responses and response times based on hidden Markov modeling to account for within-subject differences in responses and response times. A simulation study is conducted to demonstrate acceptable parameter recovery and acceptable performance of various fit indices in distinguishing between different models. In addition, both a confirmatory and an exploratory application are presented to demonstrate the practical value of the modeling approach.
Theory and computation of disturbance invariant sets for discrete-time linear systems
Directory of Open Access Journals (Sweden)
Ilya Kolmanovsky
1998-01-01
. One purpose of the paper is to unite and extend in a rigorous way disparate results from the prior literature. In addition there are entirely new results. Specific contributions include: exploitation of the Pontryagin set difference to clarify conceptual matters and simplify mathematical developments, special properties of maximal invariant sets and conditions for their finite determination, algorithms for generating concrete representations of maximal invariant sets, practical computational questions, extension of the main results to general Lyapunov stable systems, applications of the computational techniques to the bounding of state and output response. Results on Lyapunov stable systems are applied to the implementation of a logic-based, nonlinear multimode regulator. For plants with disturbance inputs and state-control constraints it enlarges the constraint-admissible domain of attraction. Numerical examples illustrate the various theoretical and computational results.
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.
1993-01-01
The computational capability of efficiently and accurately evaluate reactor core attributes (i.e., k eff and power distributions as a function of cycle burnup) utilizing a second-order accurate advanced nodal Generalized Perturbation Theory (GPT) model has been developed. The GPT model is derived from the forward non-linear iterative Nodal Expansion Method (NEM) strategy, thereby extending its inherent savings in memory storage and high computational efficiency to also encompass GPT via the preservation of the finite-difference matrix structure. The above development was easily implemented into the existing coarse-mesh finite-difference GPT-based in-core fuel management optimization code FORMOSA-P, thus combining the proven robustness of its adaptive Simulated Annealing (SA) multiple-objective optimization algorithm with a high-fidelity NEM GPT neutronics model to produce a powerful computational tool used to generate families of near-optimum loading patterns for PWRs. (orig.)
Directory of Open Access Journals (Sweden)
Salvador Lucas
2015-12-01
Full Text Available Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In this setting, Order-Sorted First-Order Logic provides a powerful framework to represent declarative programs. It also provides a target logic to obtain models for other logics via transformations. We investigate the automatic generation of numerical models for order-sorted first-order logics and its use in program analysis, in particular in termination analysis of declarative programs. We use convex domains to give domains to the different sorts of an order-sorted signature; we interpret the ranked symbols of sorted signatures by means of appropriately adapted convex matrix interpretations. Such numerical interpretations permit the use of existing algorithms and tools from linear algebra and arithmetic constraint solving to synthesize the models.
DEFF Research Database (Denmark)
Madsen, Lars Bojer; Tolstikhin, Oleg I.; Morishita, Toru
2012-01-01
The recently developed weak-field asymptotic theory [ Phys. Rev. A 84 053423 (2011)] is applied to the analysis of tunneling ionization of a molecular ion (H2+), several homonuclear (H2, N2, O2) and heteronuclear (CO, HF) diatomic molecules, and a linear triatomic molecule (CO2) in a static...... electric field. The dependence of the ionization rate on the angle between the molecular axis and the field is determined by a structure factor for the highest occupied molecular orbital. This factor is calculated using a virtually exact discrete variable representation wave function for H2+, very accurate...... Hartree-Fock wave functions for the diatomics, and a Hartree-Fock quantum chemistry wave function for CO2. The structure factors are expanded in terms of standard functions and the associated structure coefficients, allowing the determination of the ionization rate for any orientation of the molecule...
Directory of Open Access Journals (Sweden)
Jesús García-de-Madariaga
2011-10-01
Full Text Available There has been a lot of discussion about corporate social responsibility (CSR during these last decades. Neoclassical authors support the idea that CSR is not compatible with the objective of profit maximization, and defenders of CSR argue that, in these times of globalization and network economies, the idea of a company managed just to meet shareholders’ interests does not support itself. However, beyond this discussion, how can CSR affect firms’ market value? If we found a positive relationship between these variables, we could conclude that the two theories are reconcilable and the objective of profit maximization, perhaps, should satisfy not only shareholders’ interests, but also stakeholders’. We review previous literature and propose a model to analyze how CSR affects firms’ market value.
Reflections on the nature of non-linear responses of the climate to forcing
Ditlevsen, Peter
2017-04-01
On centennial to multi-millennial time scales the paleoclimatic record shows that climate responds in a very non-linear way to the external forcing. Perhaps most puzzling is the change in glacial period duration at the Middle Pleistocene Transition. From a dynamical systems perspective, this could be a change in frequency locking between the orbital forcing and the climatic response or it could be a non-linear resonance phenomenon. In both cases the climate system shows a non-trivial oscillatory behaviour. From the records it seems that this behaviour can be described by an effective dynamics on a low-dimensional slow manifold. These different possible dynamical behaviours will be discussed. References: Arianna Marchionne, Peter Ditlevsen, and Sebastian Wieczorek, "Three types of nonlinear resonances", arXiv:1605.00858 Peter Ashwin and Peter Ditlevsen, "The middle Pleistocene transition as a generic bifurcation on a slow manifold", Climate Dynamics, 45, 2683, 2015. Peter D. Ditlevsen, "The bifurcation structure and noise assisted transitions in the Pleistocene glacial cycles", Paleoceanography, 24, PA3204, 2009
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.
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.
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
Acoustically determined linear piezoelectric response of lithium niobate up to 1100 V
Energy Technology Data Exchange (ETDEWEB)
Patel, N. [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States); Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87106 (United States); Branch, D. W.; Cular, S. [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States); Schamiloglu, E. [Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87106 (United States)
2014-04-21
We present a method to measure high voltages using the piezoelectric crystal lithium niobate without using voltage dividers. A 36° Y-X cut lithium niobate crystal was coupled to two acoustic transducers, where direct current voltages were applied from 128–1100 V. The time-of-flight through the crystal was determined to be linearly dependent on the applied voltage. A model was developed to predict the time-delay in response to the applied voltage. The results show a sensitivity of 17 fs/V with a measurement error of 1 fs/V was achievable using this method. The sensitivity of this method can be increased by measuring the acoustic wave after multiple passes through the crystal. This method has many advantages over traditional techniques such as: favorable scalability for larger voltages, ease of use, cost effectiveness, and compactness.
Fields of an ultrashort tightly focused radially polarized laser pulse in a linear response plasma
Salamin, Yousef I.
2017-10-01
Analytical expressions for the fields of a radially polarized, ultrashort, and tightly focused laser pulse propagating in a linear-response plasma are derived and discussed. The fields are obtained from solving the inhomogeneous wave equations for the vector and scalar potentials, linked by the Lorenz gauge, in a plasma background. First, the scalar potential is eliminated using the gauge condition, then the vector potential is synthesized from Fourier components of an initial uniform distribution of wavenumbers, and the inverse Fourier transformation is carried out term-by-term in a truncated series (finite sum). The zeroth-order term in, for example, the axial electric field component is shown to model a pulse much better than its widely used paraxial approximation counterpart. Some of the propagation characteristics of the fields are discussed and all fields are shown to have manifested the expected limits for propagation in a vacuum.
Exact asymptotic relations for the effective response of linear viscoelastic heterogeneous media
Gallican, Valentin; Brenner, Renald; Suquet, Pierre
2017-11-01
This article addresses the asymptotic response of viscoelastic heterogeneous media in the frequency domain, at high and low frequencies, for different types of elementary linear viscoelastic constituents. By resorting to stationary principles for complex viscoelasticity and adopting a classification of the viscoelastic behaviours based on the nature of their asymptotic regimes, either elastic or viscous, four exact relations are obtained on the overall viscoelastic complex moduli in each case. Two relations are related to the asymptotic uncoupled heterogeneous problems, while the two remaining ones result from the viscoelastic coupling that manifests itself in the transient regime. These results also provide exact conditions on certain integrals in time of the effective relaxation spectrum. This general setting encompasses the results obtained in preceding studies on mixtures of Maxwell constituents [1,2]. xml:lang="fr"
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.