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Sample records for nonlinear programming theory

  1. Nonlinear programming analysis and methods

    CERN Document Server

    Avriel, Mordecai

    2012-01-01

    This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.

  2. Nonlinear optimal control theory

    CERN Document Server

    Berkovitz, Leonard David

    2012-01-01

    Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also dis

  3. Nonlinear theory of elastic shells

    International Nuclear Information System (INIS)

    Costa Junior, J.A.

    1979-08-01

    Nonlinear theory of elastic shells is developed which incorporates both geometric and physical nonlinearities and which does not make use of the well known Love-Kirchhoff hypothesis. The resulting equations are formulated in tensorial notation and are reduced to the ones of common use when simplifying assumptions encountered in the especific litterature are taken. (Author) [pt

  4. Nonlinear classical theory of electromagnetism

    International Nuclear Information System (INIS)

    Pisello, D.

    1977-01-01

    A topological theory of electric charge is given. Einstein's criteria for the completion of classical electromagnetic theory are summarized and their relation to quantum theory and the principle of complementarity is indicated. The inhibiting effect that this principle has had on the development of physical thought is discussed. Developments in the theory of functions on nonlinear spaces provide the conceptual framework required for the completion of electromagnetism. The theory is based on an underlying field which is a continuous mapping of space-time into points on the two-sphere. (author)

  5. Using Nonlinear Programming in International Trade Theory: The Factor-Proportions Model

    Science.gov (United States)

    Gilbert, John

    2004-01-01

    Students at all levels benefit from a multi-faceted approach to learning abstract material. The most commonly used technique in teaching the pure theory of international trade is a combination of geometry and algebraic derivations. Numerical simulation can provide a valuable third support to these approaches. The author describes a simple…

  6. The Nonlinear Field Space Theory

    Energy Technology Data Exchange (ETDEWEB)

    Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)

    2016-08-10

    In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

  7. The Nonlinear Field Space Theory

    International Nuclear Information System (INIS)

    Mielczarek, Jakub; Trześniewski, Tomasz

    2016-01-01

    In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

  8. Nonlinear gravitons and curved twistor theory

    International Nuclear Information System (INIS)

    Penrose, R.

    1976-01-01

    A new approach to the quantization of general relativity is suggested in which a state consisting of just one graviton can be described, but in a way which involves both the curvature and nonlinearities of Einstein's theory. It is felt that this approach can be justified solely on its own merits but it also receives striking encouragement from another direction: a surprising mathematical result enables one to construct the general such nonlinear gravitation state from a curved twistor space, the construction being given in terms of one arbitrary holomorphic function of three complex variables. In this way, the approach fits naturally into the general twistor program for the description of quantized fields. (U.K.)

  9. Spectral theory and nonlinear functional analysis

    CERN Document Server

    Lopez-Gomez, Julian

    2001-01-01

    This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.

  10. A Geometrically—Nonlinear Plate Theory 12

    Institute of Scientific and Technical Information of China (English)

    AlbertC.J.LUO

    1999-01-01

    An approximate plate theory developed in this paper is based on an assumed displacement field,the strains described by a Taylor series in the normal distance from the middle surface,the exact strains of the middle surface and the equations of equilibrium governing the exact configuration of the deformed middle surface,In this theory the exact geometry of the deformed middle surface is used to derive the strains and equilibrium of the plate.Application of this theory does not depend on the constitutive law.THis theory can reduce to some existing nonlinear theories through imposition of constraints.

  11. Nonlinear Lorentz-invariant theory of gravitation

    International Nuclear Information System (INIS)

    Petry, W.

    1976-01-01

    A nonlinear Lorentz-invariant theory of gravitation and a Lorentz-invariant Hamiltonian for a particle with spin in the gravitational field are developed. The equations of motions are studied. The theory is applied to the three well known tests of General Relativity. In the special case of the red shift of spectral lines and of the deflection of light, the theory gives the same results as the General Theory of Relativity, whereas in the case of the perihelion of the Mercury, the theory gives 40,3'', in good agreement with experimental results of Dicke. (author)

  12. Nonlinearity and disorder: Theory and applications

    DEFF Research Database (Denmark)

    Bang, Ole; Sørensen, Mads Peter

    Proceedings of the NATO Advanced Research Workshop (ARW) entitled Nonlinearity and Disorder: Theory and Applications, held in Tashkent, Uzbekistan, October 2-6, 2001. Phenomena of coherent structures in nonlinear systems and disorder are considered opposite in nature. For example one of the most...... of the photorefractive solitons. Another very fast growing area induced by the technological development is statistical phenomena in nonlinear pulse propagation in optical fibers. Intrinsic randomness of existing optical communication systems has an important impact on the performance of planned soliton communication...

  13. Lectures in nonlinear mechanics and chaos theory

    CERN Document Server

    Stetz, Albert W

    2016-01-01

    This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...

  14. Theory and design of nonlinear metamaterials

    Science.gov (United States)

    Rose, Alec Daniel

    If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers

  15. Nonlinear theory of electroelastic and magnetoelastic interactions

    CERN Document Server

    Dorfmann, Luis

    2014-01-01

    This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.

  16. A nonlinear theory of generalized functions

    CERN Document Server

    1990-01-01

    This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applicati...

  17. Quantitative theory of driven nonlinear brain dynamics.

    Science.gov (United States)

    Roberts, J A; Robinson, P A

    2012-09-01

    Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

  18. Nonlinear system theory: another look at dependence.

    Science.gov (United States)

    Wu, Wei Biao

    2005-10-04

    Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms.

  19. Topics in nonlinear wave theory with applications

    International Nuclear Information System (INIS)

    Tracy, E.R.

    1984-01-01

    Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly

  20. Nonlinear analysis approximation theory, optimization and applications

    CERN Document Server

    2014-01-01

    Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

  1. 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

  2. Nonlinear closed-loop control theory

    International Nuclear Information System (INIS)

    Perez, R.B.; Otaduy, P.J.; Abdalla, M.

    1992-01-01

    Traditionally, the control of nuclear power plants has been implemented by the use of proportional-integral (PI) control systems. PI controllers are both simple and, within their calibration range, highly reliable. However, PIs provide little performance information that could be used to diagnose out-of-range events or the nature of unanticipated transients that may occur in the plant. To go beyond the PI controller, the new control algorithms must deal with the physical system nonlinearities and with the reality of uncertain dynamics terms in its mathematical model. The tool to develop a new kind of control algorithm is provided by Optimal Control Theory. In this theory, a norm is minimized which incorporates the constraint that the model equations should be satisfied at all times by means of the Lagrange multipliers. Optimal control algorithms consist of two sets of coupled equations: (1) the model equations, integrated forward in time; and (2) the equations for the Lagrange multipliers (adjoints), integrated backwards in time. There are two challenges: dealing with large sets of coupled nonlinear equations and with a two-point boundary value problem that must be solved iteratively. In this paper, the rigorous conversion of the two-point boundary value problem into an initial value problem is presented. In addition, the incorporation into the control algorithm of ''real world'' constraints such as sensors and actuators, dynamic response functions and time lags introduced by the digitalization of analog signals is presented. (Author)

  3. Stochastic control theory dynamic programming principle

    CERN Document Server

    Nisio, Makiko

    2015-01-01

    This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-ma...

  4. Waves and Structures in Nonlinear Nondispersive Media General Theory and Applications to Nonlinear Acoustics

    CERN Document Server

    Gurbatov, S N; Saichev, A I

    2012-01-01

    "Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...

  5. Spectral theory and nonlinear analysis with applications to spatial ecology

    CERN Document Server

    Cano-Casanova, S; Mora-Corral , C

    2005-01-01

    This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.

  6. Recent advances in multiparametric nonlinear programming

    KAUST Repository

    Domí nguez, Luis F.; Narciso, Diogo A.; Pistikopoulos, Efstratios N.

    2010-01-01

    In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

  7. Recent advances in multiparametric nonlinear programming

    KAUST Repository

    Domínguez, Luis F.

    2010-05-01

    In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

  8. Rigorous theory of molecular orientational nonlinear optics

    International Nuclear Information System (INIS)

    Kwak, Chong Hoon; Kim, Gun Yeup

    2015-01-01

    Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955)] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO) through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1) the derivation of rigorous tensorial components of the effective molecular hyperpolarizabilities, (2) the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect), optical Kerr effect (OKE), dc electric field induced second harmonic generation (EFISH), degenerate four wave mixing (DFWM) and third harmonic generation (THG). We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR), Pockels effect and difference frequency generation (DFG) are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR), dc electric field induced difference frequency generation (EFIDFG) and pump-probe transmission are presented

  9. Geometric Theory of Reduction of Nonlinear Control Systems

    Science.gov (United States)

    Elkin, V. I.

    2018-02-01

    The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).

  10. Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

    International Nuclear Information System (INIS)

    Zhang Zhijie; Jiang Dongguang; Wang Wei

    2011-01-01

    Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)

  11. Nonlinear structural mechanics theory, dynamical phenomena and modeling

    CERN Document Server

    Lacarbonara, Walter

    2013-01-01

    Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

  12. Elementary number theory with programming

    CERN Document Server

    Lewinter, Marty

    2015-01-01

    A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and con

  13. Nonlinear solar cycle forecasting: theory and perspectives

    Science.gov (United States)

    Baranovski, A. L.; Clette, F.; Nollau, V.

    2008-02-01

    In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters - the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.

  14. Nonlinear solar cycle forecasting: theory and perspectives

    Directory of Open Access Journals (Sweden)

    A. L. Baranovski

    2008-02-01

    Full Text Available In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters – the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.

  15. Charges in nonlinear higher-spin theory

    Energy Technology Data Exchange (ETDEWEB)

    Didenko, V.E. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Misuna, N.G. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Moscow Institute of Physics and Technology,Institutsky lane 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)

    2017-03-30

    Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS{sub 4} Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.

  16. Charges in nonlinear higher-spin theory

    International Nuclear Information System (INIS)

    Didenko, V.E.; Misuna, N.G.; Vasiliev, M.A.

    2017-01-01

    Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS 4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.

  17. Relaxation and decomposition methods for mixed integer nonlinear programming

    CERN Document Server

    Nowak, Ivo; Bank, RE

    2005-01-01

    This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.

  18. The constructive approach to nonlinear quantum field theory

    International Nuclear Information System (INIS)

    Segal, I.

    1976-01-01

    The general situation in nonlinear quantum field theory is outlined. The author discusses a reversion to the canonical quantization formalism and develops it to the maximal level attainable on the basis of advances in the past decade in nonlinear scattering and functional integration. (B.R.H.)

  19. Nonlinear theory of the free-electron laser

    International Nuclear Information System (INIS)

    Chian, A.C.-L.; Padua Brito Serbeto, A. de.

    1984-01-01

    A theory of Raman free-electron laser using a circularly polarized electromagnetic pump is investigated. Coupled wave equations that describe both linear and nonlinear evolution of stimulated Raman scattering are derived. The dispersion relation and the growth rate for the parametric instability are obtained. Nonlinear processes that may lead to saturation of the free-electron laser are discussed. (Author) [pt

  20. An introduction to nonlinear analysis and fixed point theory

    CERN Document Server

    Pathak, Hemant Kumar

    2018-01-01

    This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for ...

  1. Theory of weakly nonlinear self-sustained detonations

    KAUST Repository

    Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

    2015-01-01

    We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced

  2. Nonlinear model predictive control theory and algorithms

    CERN Document Server

    Grüne, Lars

    2017-01-01

    This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...

  3. On nonequilibrium many-body systems III: nonlinear transport theory

    International Nuclear Information System (INIS)

    Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.

    1986-01-01

    A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt

  4. 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

  5. Nonlinear PI control of chaotic systems using singular perturbation theory

    International Nuclear Information System (INIS)

    Wang Jiang; Wang Jing; Li Huiyan

    2005-01-01

    In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit

  6. Nonlinear transport theory in the metal with tunnel barrier

    Science.gov (United States)

    Zubov, E. E.

    2018-02-01

    Within the framework of the scattering matrix formalism, the nonlinear Kubo theory for electron transport in the metal with a tunnel barrier has been considered. A general expression for the mean electrical current was obtained. It significantly simplifies the calculation of nonlinear contributions to the conductivity of various hybrid structures. In the model of the tunnel Hamiltonian, all linear and nonlinear contributions to a mean electrical current are evaluated. The linear approximation agrees with results of other theories. For effective barrier transmission ?, the ballistic transport is realised with a value of the Landauer conductivity equal to ?.

  7. Energy flow theory of nonlinear dynamical systems with applications

    CERN Document Server

    Xing, Jing Tang

    2015-01-01

    This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...

  8. Mathematical Systems Theory : from Behaviors to Nonlinear Control

    CERN Document Server

    Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien

    2015-01-01

    This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...

  9. Nonlinear programming with feedforward neural networks.

    Energy Technology Data Exchange (ETDEWEB)

    Reifman, J.

    1999-06-02

    We provide a practical and effective method for solving constrained optimization problems by successively training a multilayer feedforward neural network in a coupled neural-network/objective-function representation. Nonlinear programming problems are easily mapped into this representation which has a simpler and more transparent method of solution than optimization performed with Hopfield-like networks and poses very mild requirements on the functions appearing in the problem. Simulation results are illustrated and compared with an off-the-shelf optimization tool.

  10. Overview of nonlinear theory of kinetically driven instabilities

    International Nuclear Information System (INIS)

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

    1998-09-01

    An overview is presented of the theory for the nonlinear behavior of instabilities driven by the resonant wave particle interaction. The approach should be applicable to a wide variety of kinetic systems in magnetic fusion devices and accelerators. Here the authors emphasize application to Alfven were driven instability, and the principles of the theory are used to interpret experimental data

  11. Explicit Nonlinear Model Predictive Control Theory and Applications

    CERN Document Server

    Grancharova, Alexandra

    2012-01-01

    Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

  12. A Survey of Nonlinear Dynamics (Chaos Theory)

    Science.gov (United States)

    1991-04-01

    example of an n = 1 Hamiltonian system does have separatrices. This is the 1D pendulum (Fig. 4.2): 9=p, p=-asin9;H(9,p) =p2 /2- acosO . (4-5) Phase space...method. There is no substitute for the actual labor of applying the nonlinear operator to a sum of normal modes, producing a general Galerkin vector

  13. Nonlinear theory of localized standing waves

    OpenAIRE

    Denardo, Bruce; Larraza, Andrés; Putterman, Seth; Roberts, Paul

    1992-01-01

    An investigation of the nonlinear dispersive equations of continuum mechanics reveals localized standing-wave solutions that are domain walls between regions of different wave number. These states can appear even when the dispersion law is a single-valued function of the wave number. In addition, we calculate solutions for kinks in cutoff and noncutoff modes, as well as cutoff breather solitons. Division of Engineering and Geophysics of the Office of Basic Energy Science of U.S. DOE for su...

  14. Nonlinear theory of collisionless trapped ion modes

    International Nuclear Information System (INIS)

    Hahm, T.S.; Tang, W.M.

    1996-01-01

    A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level δn/n 0 is lower than the conventional mixing length estimate, Δr/L n (ii) the ion temperature fluctuation level δT i /T i significantly exceeds the density fluctuation level δn/n 0 ; and (iii) the parallel ion velocity fluctuation level δv iparallel /v Ti is expected to be negligible

  15. An enstrophy-based linear and nonlinear receptivity theory

    Science.gov (United States)

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

    2018-05-01

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

  16. 96 International Conference on Nonlinear Programming

    CERN Document Server

    1998-01-01

    About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu­ tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi­ nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi­ hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by...

  17. An introduction to geometric theory of fully nonlinear parabolic equations

    International Nuclear Information System (INIS)

    Lunardi, A.

    1991-01-01

    We study a class of nonlinear evolution equations in general Banach space being an abstract version of fully nonlinear parabolic equations. In addition to results of existence, uniqueness and continuous dependence on the data, we give some qualitative results about stability of the stationary solutions, existence and stability of the periodic orbits. We apply such results to some parabolic problems arising from combustion theory. (author). 24 refs

  18. Inverse operator theory method and its applications in nonlinear physics

    International Nuclear Information System (INIS)

    Fang Jinqing

    1993-01-01

    Inverse operator theory method, which has been developed by G. Adomian in recent years, and its applications in nonlinear physics are described systematically. The method can be an unified effective procedure for solution of nonlinear and/or stochastic continuous dynamical systems without usual restrictive assumption. It is realized by Mathematical Mechanization by us. It will have a profound on the modelling of problems of physics, mathematics, engineering, economics, biology, and so on. Some typical examples of the application are given and reviewed

  19. Introduction to the theory of nonlinear optimization

    CERN Document Server

    Jahn, Johannes

    2007-01-01

    This book serves as an introductory text to optimization theory in normed spaces. The topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a ba

  20. A non-linear field theory

    International Nuclear Information System (INIS)

    Skyrme, T.H.R.

    1994-01-01

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

  1. Quantization of a nonlinearly realized supersymmetric theory

    International Nuclear Information System (INIS)

    Shima, K.

    1977-01-01

    The two-dimensional version of the Volkov-Akulov Lagrangian, where the supersymmetry is realized nonlinearly by means of a single Majorana spinor psi (x), is quantized. The equal-time anticommutators for the field are not c numbers but are functions of the field itself. By explicit calculation we shall show that the supersymmetry charges of the model form the supersymmetry algebra (the graded Lie algebra); therefore the Hamiltonian of the system P 0 is written as a bilinear sum of products of supersymmetry charges. We shall also show that the supersymmetry charges exactly generate a constant translation of psi (x) in the spinor space

  2. Program Theory for Participatory Design

    DEFF Research Database (Denmark)

    Bossen, Claus; Dindler, Christian; Iversen, Ole Sejer

    2018-01-01

    How does participatory design work and what are the links between investments in terms of time, people and skills, the processes and the resulting effects? This paper explores program theory as a way for Participatory Design (PD) to investigate and evaluate these issues. Program theory comes out...

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

    Science.gov (United States)

    Silva, Walter A.

    1993-01-01

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

  4. 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

  5. Theory for Nonlinear Spectroscopy of Vibrational Polaritons

    OpenAIRE

    Ribeiro, RF; Dunkelberger, AD; Xiang, B; Xiong, W; Simpkins, BS; Owrutsky, JC; Yuen-Zhou, J

    2017-01-01

    Molecular polaritons have gained considerable attention due to their potential to control nanoscale molecular processes by harnessing electromagnetic coherence. Although recent experiments with liquid-phase vibrational polaritons have shown great promise for exploiting these effects, significant challenges remain in interpreting their spectroscopic signatures. In this letter, we develop a quantum-mechanical theory of pump-probe spectroscopy for this class of polaritons based on the quantum La...

  6. Nonlinear neoclassical theory for toroidal edge plasmas

    International Nuclear Information System (INIS)

    Fueloep, T.; Helander, P.

    2001-01-01

    Edge plasma processes play a critical role for the global confinement of the plasma. In the edge region, where impurity ions are abundant and the temperature and density gradients are large, the assumptions of the standard neoclassical theory break down. We have extended the theory of neoclassical transport in an impure plasma with arbitrary cross section and aspect ratio to allow for steeper pressure and temperature gradients than are usually considered in the conventional theory. The gradients are allowed to be so large that the friction force between the bulk ions and heavy impurities is comparable to the parallel impurity pressure gradient. In this case the impurity ions are found to undergo a spontaneous rearrangement on each flux surface. This reduces their parallel friction with the bulk ions and causes the neoclassical ion flux to become a non-monotonic function of the gradients for plasma parameters typical of the tokamak edge. Thus, the neoclassical confinement is improved in regions where the gradients are large, such as in the edge pedestal. The theoretical predictions are compared with experimental data from several tokamaks. (orig.)

  7. Soliton excitations in a class of nonlinear field theory models

    International Nuclear Information System (INIS)

    Makhan'kov, V.G.; Fedyanin, V.K.

    1985-01-01

    Investigation results of nonlinear models of the field theory with a lagrangian are described. The theory includes models both with zero stable vacuum epsilon=1 and with condensate epsilon=-1 (of disturbed symmetry). Conditions of existence of particle-like solutions (PLS), stability of these solutions are investigated. Soliton dynamics is studied. PLS formfactors are calculated. Statistical mechanics of solitons is built and their dynamic structure factors are calculated

  8. A new integrability theory for certain nonlinear physical problems

    International Nuclear Information System (INIS)

    Berger, M.S.

    1993-01-01

    A new mathematically sound integrability theory for certain nonlinear problems defined by ordinary or partial differential equations is defined. The new theory works in an arbitrary finite number of space dimensions. Moreover, if a system is integrable in the new sense described here, it has a remarkable stability property that distinguishes if from any previously known integrability ideas. The new theory proceeds by establishing a ''global normal form'' for the problem at hand. This normal form holds subject to canonical coordinate transformations, extending such classical ideas by using new nonlinear methods of infinite dimensional functional analysis. The global normal form in question is related to the mathematical theory of singularities of mappings of H. Whitney and R. Thom extended globally and form finite to infinite dimensions. Thus bifurcation phenomena are naturally included in the new integrability theory. Typical examples include the classically nonintegrable Riccati equation, certain non-Euclidean mean field theories, certain parabolic reaction diffusion equations and the hyperbolic nonlinear telegrapher's equation. (Author)

  9. de Sitter limit of inflation and nonlinear perturbation theory

    DEFF Research Database (Denmark)

    R. Jarnhus, Philip; Sloth, Martin Snoager

    2007-01-01

    We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug...

  10. Non-linear theory of elasticity

    CERN Document Server

    Lurie, AI

    2012-01-01

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

  11. Many body theory program

    International Nuclear Information System (INIS)

    Balatsky, A.V.; Scalapino, D.; Wilkins, J.; Pines, D.; Bedell, K.; Schrieffer, J.R.; Fisk, Z.

    1998-01-01

    This is the final report of a two-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors have obtained a description of symmetry of the order parameter and pairing state in high-Tc superconductors. They developed a theory of ferromagnetic instability of Fermi-liquid. They have conducted an experimental investigation of the intermetallic compounds and Zintl-type compound. They investigated the properties of Cu-0 ladders. They have developed the theory of liftshitz tails in superconductors. They have conducted a number of summer workshops

  12. Backward stochastic differential equations from linear to fully nonlinear theory

    CERN Document Server

    Zhang, Jianfeng

    2017-01-01

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

  13. Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

    Science.gov (United States)

    Meair, Jonathan; Jacquod, Philippe

    2013-02-27

    We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.

  14. SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

    1998-09-01

    This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

  15. Properties of some nonlinear Schroedinger equations motivated through information theory

    International Nuclear Information System (INIS)

    Yuan, Liew Ding; Parwani, Rajesh R

    2009-01-01

    We update our understanding of nonlinear Schroedinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q = 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value η = 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, η might be encoding relativistic effects.

  16. Computer programs for nonlinear algebraic equations

    International Nuclear Information System (INIS)

    Asaoka, Takumi

    1977-10-01

    We have provided principal computer subroutines for obtaining numerical solutions of nonlinear algebraic equations through a review of the various methods. Benchmark tests were performed on these subroutines to grasp the characteristics of them compared to the existing subroutines. As computer programs based on the secant method, subroutines of the Muller's method using the Chambers' algorithm were newly developed, in addition to the equipment of subroutines of the Muller's method itself. The programs based on the Muller-Chambers' method are useful especially for low-order polynomials with complex coefficients except for the case of finding the triple roots, three close roots etc. In addition, we have equipped subroutines based on the Madsen's algorithm, a variant of the Newton's method. The subroutines have revealed themselves very useful as standard programs because all the roots are found accurately for every case though they take longer computing time than other subroutines for low-order polynomials. It is shown also that an existing subroutine of the Bairstow's method gives the fastest algorithm for polynomials with complex coefficients, except for the case of finding the triple roots etc. We have provided also subroutines to estimate error bounds for all the roots produced with the various algorithms. (auth.)

  17. Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity

    International Nuclear Information System (INIS)

    Granovsky, Alexander B.; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru

    2003-01-01

    We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D i =ε i (0) E i +χ i (3) |E i | 2 E i . We assume that linear ε i (0) and cubic nonlinear χ i (3) dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function χ eff (3) can be significantly greater (up to 10 3 times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity

  18. Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Granovsky, Alexander B. E-mail: granov@magn.ru; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru

    2003-03-01

    We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D{sub i}={epsilon}{sub i}{sup (0)}E{sub i} +{chi}{sub i}{sup (3)}|E{sub i}|{sup 2}E{sub i}. We assume that linear {epsilon}{sub i}{sup (0)} and cubic nonlinear {chi}{sub i}{sup (3)} dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function {chi}{sub eff}{sup (3)} can be significantly greater (up to 10{sup 3} times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity.

  19. Nonlinear turbulence theory and simulation of Buneman instability

    International Nuclear Information System (INIS)

    Yoon, P. H.; Umeda, T.

    2010-01-01

    In the present paper, the weak turbulence theory for reactive instabilities, formulated in a companion paper [P. H. Yoon, Phys. Plasmas 17, 112316 (2010)], is applied to the strong electron-ion two-stream (or Buneman) instability. The self-consistent theory involves quasilinear velocity space diffusion equation for the particles and nonlinear wave kinetic equation that includes quasilinear (or induced emission) term as well as nonlinear wave-particle interaction term (or a term that represents an induced scattering off ions). We have also performed one-dimensional electrostatic Vlasov simulation in order to benchmark the theoretical analysis. Under the assumption of self-similar drifting Gaussian distribution function for the electrons it is shown that the current reduction and the accompanying electron heating as well as electric field turbulence generation can be discussed in a self-consistent manner. Upon comparison with the Vlasov simulation result it is found that quasilinear wave kinetic equation alone is insufficient to account for the final saturation amplitude. Upon including the nonlinear scattering term in the wave kinetic equation, however, we find that a qualitative agreement with the simulation is recovered. From this, we conclude that the combined quasilinear particle diffusion plus induced emission and scattering (off ions) processes adequately account for the nonlinear development of the Buneman instability.

  20. Information theory and stochastics for multiscale nonlinear systems

    CERN Document Server

    Majda, Andrew J; Grote, Marcus J

    2005-01-01

    This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...

  1. Composite Beam Theory with Material Nonlinearities and Progressive Damage

    Science.gov (United States)

    Jiang, Fang

    Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping

  2. A general sensitivity theory for simulations of nonlinear systems

    International Nuclear Information System (INIS)

    Kenton, M.A.

    1981-01-01

    A general sensitivity theory is developed for nonlinear lumped-parameter system simulations. The point-of-departure is general perturbation theory, which has long been used for linear systems in nuclear engineering and reactor physics. The theory allows the sensitivity of particular figures-of-merit of the system behavior to be calculated with respect to any parameter.An explicit procedure is derived for applying the theory to physical systems undergoing sudden events (e.g., reactor scrams, tank ruptures). A related problem, treating figures-of-merit defined as functions of extremal values of system variables occurring at sudden events, is handled by the same procedure. The general calculational scheme for applying the theory to numerical codes is discussed. It is shown that codes which use pre-packaged implicit integration subroutines can be augmented to include sensitivity theory: a companion set of subroutines to solve the sensitivity problem is listed. This combined system analysis code is applied to a simple model for loss of post-accident heat removal in a liquid metal-cooled fast breeder reactor. The uses of the theory for answering more general sensitivity questions are discussed. One application of the theory is to systematically determine whether specific physical processes in a model contribute significantly to the figures-of-merit. Another application of the theory is for selecting parameter values which enable a model to match experimentally observed behavior

  3. The preparation problem in nonlinear extensions of quantum theory

    OpenAIRE

    Cavalcanti, Eric G.; Menicucci, Nicolas C.; Pienaar, Jacques L.

    2012-01-01

    Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to possible exotic information-theoretic effects, including breaking quantum cryptography and radically speeding up both classical and quantum computers. The physical interpretation of such theories, however, is still unclear. We consider a large class of operationa...

  4. Second quantization of classical nonlinear relativistic field theory. Pt. 2

    International Nuclear Information System (INIS)

    Balaban, T.

    1976-01-01

    The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field PHI is obtained. (orig./BJ) [de

  5. Two-dimensional nonlinear equations of supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1985-01-01

    Supersymmetric generalization of two-dimensional nonlinear dynamical equations of gauge theories is presented. The nontrivial dynamics of a physical system in the supersymmetry and supergravity theories for (2+2)-dimensions is described by the integrable embeddings of Vsub(2/2) superspace into the flat enveloping superspace Rsub(N/M), supplied with the structure of a Lie superalgebra. An equation is derived which describes a supersymmetric generalization of the two-dimensional Toda lattice. It contains both super-Liouville and Sinh-Gordon equations

  6. Synthesis of robust nonlinear autopilots using differential game theory

    Science.gov (United States)

    Menon, P. K. A.

    1991-01-01

    A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.

  7. Development of a nonlinear unsteady transonic flow theory

    Science.gov (United States)

    Stahara, S. S.; Spreiter, J. R.

    1973-01-01

    A nonlinear, unsteady, small-disturbance theory capable of predicting inviscid transonic flows about aerodynamic configurations undergoing both rigid body and elastic oscillations was developed. The theory is based on the concept of dividing the flow into steady and unsteady components and then solving, by method of local linearization, the coupled differential equation for unsteady surface pressure distribution. The equations, valid at all frequencies, were derived for two-dimensional flows, numerical results, were obtained for two classses of airfoils and two types of oscillatory motions.

  8. Nonlinear dynamical systems for theory and research in ergonomics.

    Science.gov (United States)

    Guastello, Stephen J

    2017-02-01

    Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.

  9. Nonlinear beam dynamics experimental program at SPEAR

    International Nuclear Information System (INIS)

    Tran, P.; Pellegrini, C.; Cornacchia, M.; Lee, M.; Corbett, W.

    1995-01-01

    Since nonlinear effects can impose strict performance limitations on modern colliders and storage rings, future performance improvements depend on further understanding of nonlinear beam dynamics. Experimental studies of nonlinear beam motion in three-dimensional space have begun in SPEAR using turn-by-turn transverse and longitudinal phase-space monitors. This paper presents preliminary results from an on-going experiment in SPEAR

  10. Non-linear programming method in optimization of fast reactors

    International Nuclear Information System (INIS)

    Pavelesku, M.; Dumitresku, Kh.; Adam, S.

    1975-01-01

    Application of the non-linear programming methods on optimization of nuclear materials distribution in fast reactor is discussed. The programming task composition is made on the basis of the reactor calculation dependent on the fuel distribution strategy. As an illustration of this method application the solution of simple example is given. Solution of the non-linear program is done on the basis of the numerical method SUMT. (I.T.)

  11. On the non-linear scale of cosmological perturbation theory

    CERN Document Server

    Blas, Diego; Konstandin, Thomas

    2013-01-01

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

  12. Nonlinear responses of chiral fluids from kinetic theory

    Science.gov (United States)

    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.

  13. 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.

  14. 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.

  15. Theories of quantum dissipation and nonlinear coupling bath descriptors

    Science.gov (United States)

    Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing

    2018-03-01

    The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.

  16. Non-linear theory of elasticity and optimal design

    CERN Document Server

    Ratner, LW

    2003-01-01

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

  17. Nonlinear electroelasticity: material properties, continuum theory and applications.

    Science.gov (United States)

    Dorfmann, Luis; Ogden, Ray W

    2017-08-01

    In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

  18. Nonlinear electroelasticity: material properties, continuum theory and applications

    Science.gov (United States)

    Dorfmann, Luis; Ogden, Ray W.

    2017-08-01

    In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

  19. Analytic theory of the nonlinear M = 1 tearing mode

    International Nuclear Information System (INIS)

    Hazeltine, R.D.; Meiss, J.D.; Morrison, P.J.

    1985-09-01

    Numerical studies show that the m = 1 tearing mode continues to grow exponentially well into the nonlinear regime, in contrast with the slow, ''Rutherford,'' growth of m > 1 modes. We present a single helicity calculation which generalizes that of Rutherford to the case when the constant-psi approximation is invalid. As in that theory, the parallel current becomes an approximate flux function when the island size, W, exceeds the linear tearing layer width. However for the m = 1 mode, W becomes proportional to deltaB, rather than (deltaB)/sup 1/2/ above this critical amplitude. This implies that the convective nonlinearity in Ohm's law, which couples the m = 0 component to the m = 1 component, dominates the resistive diffusion term. The balance between the inductive electric field and this convective nonlinearity results in exponential growth. Assuming the form of the perturbed fields to be like that of the linear mode, we find that the growth occurs at 71% of the linear rate

  20. Nonlinear closure relations theory for transport processes in nonequilibrium systems

    International Nuclear Information System (INIS)

    Sonnino, Giorgio

    2009-01-01

    A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ('Onsager') transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.

  1. Nonlinear mean field theory for nuclear matter and surface properties

    International Nuclear Information System (INIS)

    Boguta, J.; Moszkowski, S.A.

    1983-01-01

    Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)

  2. Research program in elementary particle theory: Outstanding Junior Investigator Program

    International Nuclear Information System (INIS)

    Bowick, M.J.

    1990-01-01

    This report discusses the following topics: aspects of string theory; nonlinear sigma models and high-T c superconductivity; axionic black holes; topological mass generation; and quantum gravity in 2 + 1 dimensions

  3. 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

  4. Nonlinear polarization of ionic liquids: theory, simulations, experiments

    Science.gov (United States)

    Kornyshev, Alexei

    2010-03-01

    Room temperature ionic liquids (RTILs) composed of large, often asymmetric, organic cations and simple or complex inorganic or organic anions do not freeze at ambient temperatures. Their rediscovery some 15 years ago is widely accepted as a ``green revolution'' in chemistry, offering an unlimited number of ``designer'' solvents for chemical and photochemical reactions, homogeneous catalysis, lubrication, and solvent-free electrolytes for energy generation and storage. As electrolytes they are non-volatile, some can sustain without decomposition up to 6 times higher voltages than aqueous electrolytes, and many are environmentally friendly. The studies of RTILs and their applications have reached a critical stage. So many of them can be synthesized - about a thousand are known already - their mixtures can further provide ``unlimited'' number of combinations! Thus, establishing some general laws that could direct the best choice of a RTIL for a given application became crucial; guidance is expected from theory and modelling. But for a physical theory, RTILs comprise a peculiar and complex class of media, the description of which lies at the frontier line of condensed matter theoretical physics: dense room temperature ionic plasmas with ``super-strong'' Coulomb correlations, which behave like glasses at short time-scale, but like viscous liquids at long-time scale. This talk will introduce RTILs to physicists and overview the current understanding of the nonlinear response of RTILs to electric field. It will focus on the theory, simulations, and experimental characterisation of the structure and nonlinear capacitance of the electrical double layer at a charged electrode. It will also discuss pros and contras of supercapacitor applications of RTILs.

  5. Linear theory for filtering nonlinear multiscale systems with model error.

    Science.gov (United States)

    Berry, Tyrus; Harlim, John

    2014-07-08

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

  6. 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....

  7. ROTAX: a nonlinear optimization program by axes rotation method

    International Nuclear Information System (INIS)

    Suzuki, Tadakazu

    1977-09-01

    A nonlinear optimization program employing the axes rotation method has been developed for solving nonlinear problems subject to nonlinear inequality constraints and its stability and convergence efficiency were examined. The axes rotation method is a direct search of the optimum point by rotating the orthogonal coordinate system in a direction giving the minimum objective. The searching direction is rotated freely in multi-dimensional space, so the method is effective for the problems represented with the contours having deep curved valleys. In application of the axes rotation method to the optimization problems subject to nonlinear inequality constraints, an improved version of R.R. Allran and S.E.J. Johnsen's method is used, which deals with a new objective function composed of the original objective and a penalty term to consider the inequality constraints. The program is incorporated in optimization code system SCOOP. (auth.)

  8. Theory of weakly nonlinear self-sustained detonations

    KAUST Repository

    Faria, Luiz

    2015-11-03

    We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations.

  9. Nonlinear problems of the theory of heterogeneous slightly curved shells

    Science.gov (United States)

    Kantor, B. Y.

    1973-01-01

    An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

  10. History of nonlinear oscillations theory in France (1880-1940)

    CERN Document Server

    Ginoux, Jean-Marc

    2017-01-01

    This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own...

  11. A general theory of two-wave mixing in nonlinear media

    DEFF Research Database (Denmark)

    Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael

    2009-01-01

    A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...

  12. Nonlinear theory of the collisional Rayleigh-Taylor instability in equatorial spread F

    International Nuclear Information System (INIS)

    Chaturvedi, P.K.; Ossakow, S.L.

    1977-01-01

    The nonlinear behavior of the collisional Rayleigh-Taylor instability is studied in equatorial Spread F by including a dominant two-dimensional nonlinearity. It is found that on account of this nonlinearity the instability saturates by generating damped higher spatial harmonics. The saturated power spectrum for the density fluctuations is discussed. A comparison between experimental observations and theory is presented

  13. Applications and algorithms for mixed integer nonlinear programming

    International Nuclear Information System (INIS)

    Leyffer, Sven; Munson, Todd; Linderoth, Jeff; Luedtke, James; Miller, Andrew

    2009-01-01

    The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scientific applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.

  14. Non-linearities in Theory-of-Mind Development.

    Science.gov (United States)

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

    2016-01-01

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

  15. WHAMSE: a program for three-dimensional nonlinear structural dynamics

    International Nuclear Information System (INIS)

    Belytschko, T.; Tsay, C.S.

    1982-02-01

    WHAMSE is a computer program for the nonlinear, transient analysis of structures. The formulation includes both geometric and material nonlinearities, so problems with large displacements and elastic-plastic behavior can be treated. Explicit time integration is used, so the program is most suitable for implusive loads. Energy balance calculations are provided to check numerical stability. The mass matrix is lumped. A finite element format is used for the description of the problem geometry, so the program is quite versatile in treating complex engineering structures. The following elements are included: a triangular element for thin plates and shells, a beam element, a spring element and a rigid body. Mesh generation features are provided to simplify program input. Other features of the program are: (1) a restart capability; (2) a variety of output options, such as printer plots or CALCOMP plots of selected time histories, picture (snapshot) output, and CALCOMP plots of the undeformed and deformed structure

  16. 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.

  17. Duality in non-linear programming

    Science.gov (United States)

    Jeyalakshmi, K.

    2018-04-01

    In this paper we consider duality and converse duality for a programming problem involving convex objective and constraint functions with finite dimensional range. We do not assume any constraint qualification. The dual is presented by reducing the problem to a standard Lagrange multiplier problem.

  18. θ-convex nonlinear programming problems

    International Nuclear Information System (INIS)

    Emam, T.

    2008-01-01

    A class of sets and a class of functions called θ-convex sets and θ-convex functions are introduced by relaxing the definitions of convex sets and operator θ on the sets and domain of definition of the functions. The optimally results for θ-convex programming problems are established.

  19. Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification

    Czech Academy of Sciences Publication Activity Database

    Mordukhovich, B. S.; Outrata, Jiří

    2013-01-01

    Roč. 49, č. 3 (2013), s. 446-464 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : variational analysis * second-order theory * generalized differentiation * tilt stability Subject RIV: BA - General Mathematics Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/MTR/outrata-tilt stability in nonlinear programming under mangasarian-fromovitz constraint qualification.pdf

  20. Genetic Algorithm for Mixed Integer Nonlinear Bilevel Programming and Applications in Product Family Design

    OpenAIRE

    Chenlu Miao; Gang Du; Yi Xia; Danping Wang

    2016-01-01

    Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP) to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP), which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard pr...

  1. Transient response of nonlinear polymer networks: A kinetic theory

    Science.gov (United States)

    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.

  2. Interior Point Methods for Large-Scale Nonlinear Programming

    Czech Academy of Sciences Publication Activity Database

    Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

    2005-01-01

    Roč. 20, č. 4-5 (2005), s. 569-582 ISSN 1055-6788 R&D Projects: GA AV ČR IAA1030405 Institutional research plan: CEZ:AV0Z10300504 Keywords : nonlinear programming * interior point methods * KKT systems * indefinite preconditioners * filter methods * algorithms Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2005

  3. Quantum theory of a one-dimensional laser with output coupling. 2. Nonlinear theory

    International Nuclear Information System (INIS)

    Penaforte, J.C.; Baseia, B.

    1984-01-01

    A previous paper describing the quantum theory of a laser in linear approximation is here extended to the nonlinear case. Instead of the approach of conventional theory - which deals with discrete 'cavity-modes' and includes artificial mechanisms to simulates radiation field losses due to beam extraction - a more realistic model of optical cavity having output coupling is used that works entirely within the continuous spectrum, allowing one to obtain the equations for the field both inside and outside the laser cavity. Besides the quantum noise due to spontaneous emission, a noise term of classical nature due to transmission losses automatically emerges from the present treatment. For single-collective-mode operation the equations for laser field are solved exactly, yielding the transient and steady-state solutions. Inside the laser cavity, the results of nonlinear analysis agree with those found in conventional theory once the conventional 'mode-amplitude' is reinterpreted as a collective variable. Outside the cavity - unaccessible region in the conventional treatment - the solution for the laser field is also exhibited. Further considerations as concerning the role played by the noise terms in the field buildup are discussed. (Author) [pt

  4. 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.)

  5. Nonlinear Knowledge in Kernel-Based Multiple Criteria Programming Classifier

    Science.gov (United States)

    Zhang, Dongling; Tian, Yingjie; Shi, Yong

    Kernel-based Multiple Criteria Linear Programming (KMCLP) model is used as classification methods, which can learn from training examples. Whereas, in traditional machine learning area, data sets are classified only by prior knowledge. Some works combine the above two classification principle to overcome the defaults of each approach. In this paper, we propose a model to incorporate the nonlinear knowledge into KMCLP in order to solve the problem when input consists of not only training example, but also nonlinear prior knowledge. In dealing with real world case breast cancer diagnosis, the model shows its better performance than the model solely based on training data.

  6. Untangling the drivers of nonlinear systems with information theory

    Science.gov (United States)

    Wing, S.; Johnson, J.

    2017-12-01

    Many systems found in nature are nonlinear. The drivers of the system are often nonlinearly correlated with one another, which makes it a challenge to understand the effects of an individual driver. For example, solar wind velocity (Vsw) and density (nsw) are both found to correlate well with radiation belt fluxes and are thought to be drivers of the magnetospheric dynamics; however, the Vsw is anti-correlated with nsw, which can potentially confuse interpretation of these relationships as causal or coincidental. Information theory can untangle the drivers of these systems, describe the underlying dynamics, and offer constraints to modelers and theorists, leading to better understanding of the systems. Two examples are presented. In the first example, the solar wind drivers of geosynchronous electrons with energy range of 1.8-3.5 MeV are investigated using mutual information (MI), conditional mutual information (CMI), and transfer entropy (TE). The information transfer from Vsw to geosynchronous MeV electron flux (Je) peaks with a lag time (t) of 2 days. As previously reported, Je is anticorrelated with nsw with a lag of 1 day. However, this lag time and anticorrelation can be attributed mainly to the Je(t + 2 days) correlation with Vsw(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time < 24 hr, suggesting that the loss mechanism due to nsw or solar wind dynamic pressure has to start operating in < 24 hr. nsw transfers about 36% as much information as Vsw (the primary driver) to Je. Nonstationarity in the system dynamics are investigated using windowed TE. When the data is ordered according to high or low transfer entropy it is possible to understand details of the triangle distribution that has been identified between Je(t + 2

  7. Nonlinear theory of scattering by localized potentials in metals

    Energy Technology Data Exchange (ETDEWEB)

    Howard, I A [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); March, N H [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); Oxford University, Oxford (United Kingdom); Echenique, P M [Donostia International Physics Center (DIPC), 20018 San Sebastian, Basque Country (Spain); Departamento de Fisica de Materiales and Centro Mixto CSIC-UPV/EHU, Facultad de Quimicas, UPV/EHU, Apartado 1072, 20080, San Sebastian (Spain)

    2003-11-14

    In early work, March and Murray gave a perturbation theory of the Dirac density matrix {gamma}(r, r') generated by a localized potential V(r) embedded in an initially uniform Fermi gas to all orders in V(r). For potentials sufficiently slowly varying in space, they summed the resulting series for r' = r to regain the Thomas-Fermi density {rho}(r) {proportional_to} [{mu} - V(r)]{sup 3/2}, with {mu} the chemical potential of the Fermi gas. For an admittedly simplistic repulsive central potential V(r) = vertical bar A vertical bar exp(-cr), it is first shown here that what amounts to the sum of the March-Murray series for the s-wave (only) contribution to the density, namely {rho}{sub s}(r, {mu}), can be obtained in closed form. Furthermore, for specific numerical values of A and c in this exponential potential, the long-range behaviour of {rho}{sub s}(r, {mu}) is related to the zero-potential form of March and Murray, which merely suffers a {mu}-dependent phase shift. This result is interpreted in relation to the recent high density screening theorem of Zaremba, Nagy and Echenique. A brief discussion of excess electrical resistivity caused by nonlinear scattering in a Fermi gas is added; this now involves an off-diagonal local density of states. Finally, for periodic lattices, contact is made with the quantum-mechanical defect centre models of Koster and Slater (1954 Phys. Rev. 96 1208) and of Beeby (1967 Proc. R. Soc. A 302 113), and also with the semiclassical approximation of Friedel (1954 Adv. Phys. 3 446). In appendices, solvable low-dimensional models are briefly summarized.

  8. Robust methods and asymptotic theory in nonlinear econometrics

    CERN Document Server

    Bierens, Herman J

    1981-01-01

    This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non­ linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...

  9. Theory of Nonlinear Dispersive Waves and Selection of the Ground State

    International Nuclear Information System (INIS)

    Soffer, A.; Weinstein, M.I.

    2005-01-01

    A theory of time-dependent nonlinear dispersive equations of the Schroedinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, 'selection of the ground state', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides

  10. Origin of soft limits from nonlinear supersymmetry in Volkov-Akulov theory

    Energy Technology Data Exchange (ETDEWEB)

    Kallosh, Renata; Karlsson, Anna; Murli, Divyanshu [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305 (United States)

    2017-03-15

    We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.

  11. Geometrical phases from global gauge invariance of nonlinear classical field theories

    International Nuclear Information System (INIS)

    Garrison, J.C.; Chiao, R.Y.

    1988-01-01

    We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics

  12. Bonus algorithm for large scale stochastic nonlinear programming problems

    CERN Document Server

    Diwekar, Urmila

    2015-01-01

    This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...

  13. Integer programming theory, applications, and computations

    CERN Document Server

    Taha, Hamdy A

    1975-01-01

    Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming.Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other

  14. Separable programming theory and methods

    CERN Document Server

    Stefanov, Stefan M

    2001-01-01

    In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered Convex separable programs subject to inequality equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs Numerical approximation with respect to I1 and I4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well Audience Advanced undergraduate and graduate students, mathematical programming operations research specialists

  15. Semantic theory for logic programming

    Energy Technology Data Exchange (ETDEWEB)

    Brown, F M

    1981-01-01

    The author axiomatizes a number of meta theoretic concepts which have been used in logic programming, including: meaning, logical truth, nonentailment, assertion and erasure, thus showing that these concepts are logical in nature and need not be defined as they have previously been defined in terms of the operations of any particular interpreter for logic programs. 10 references.

  16. Fusion Research Center, theory program. Progress report

    International Nuclear Information System (INIS)

    1982-01-01

    The Texas FRC theory program is directed primarily toward understanding the initiation, heating, and confinement of tokamak plasmas. It supports and complements the experimental programs on the TEXT and PRETEXT devices, as well as providing information generally applicable to the national tokamak program. A significant fraction of the Center's work has been carried out in collaboration with, or as a part of, the program of the Institute for Fusion Studies (IFS). During the past twelve months, 14 FRC theory reports and 12 IFS reports with partial FRC support have been issued

  17. A Recurrent Neural Network for Nonlinear Fractional Programming

    Directory of Open Access Journals (Sweden)

    Quan-Ju Zhang

    2012-01-01

    Full Text Available This paper presents a novel recurrent time continuous neural network model which performs nonlinear fractional optimization subject to interval constraints on each of the optimization variables. The network is proved to be complete in the sense that the set of optima of the objective function to be minimized with interval constraints coincides with the set of equilibria of the neural network. It is also shown that the network is primal and globally convergent in the sense that its trajectory cannot escape from the feasible region and will converge to an exact optimal solution for any initial point being chosen in the feasible interval region. Simulation results are given to demonstrate further the global convergence and good performance of the proposing neural network for nonlinear fractional programming problems with interval constraints.

  18. An Asymptotic Derivation of Weakly Nonlinear Ray Theory

    Indian Academy of Sciences (India)

    The transport equation for the amplitude has been deduced with an error (2) where is the small parameter appearing in the high frequency approximation. On a length scale over which Choquet–Bruhat's theory is valid, this theory reduces to the former. The theory is valid on a much larger length scale and the leading ...

  19. 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

  20. Symmetry properties of some nonlinear field theory models

    International Nuclear Information System (INIS)

    Shvachka, A.B.

    1984-01-01

    Various approaches towards the study of symmetry properties of some nonlinear evolution equations as well as possible ways of their computer implementation using the computer algebra systems langage are discussed. Special attention is paid to the method of pseudopotential investigation of formal integrability and isovector method for the equations of balance

  1. Nonlinear theory of diffusive acceleration of particles by shock waves

    Energy Technology Data Exchange (ETDEWEB)

    Malkov, M.A. [University of California at San Diego, La Jolla, CA (United States)]. E-mail: mmalkov@ucsd.edu; Drury, L. O' C. [Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2 (Ireland)

    2001-04-01

    Among the various acceleration mechanisms which have been suggested as responsible for the nonthermal particle spectra and associated radiation observed in many astrophysical and space physics environments, diffusive shock acceleration appears to be the most successful. We review the current theoretical understanding of this process, from the basic ideas of how a shock energizes a few reactionless particles to the advanced nonlinear approaches treating the shock and accelerated particles as a symbiotic self-organizing system. By means of direct solution of the nonlinear problem we set the limit to the test-particle approximation and demonstrate the fundamental role of nonlinearity in shocks of astrophysical size and lifetime. We study the bifurcation of this system, proceeding from the hydrodynamic to kinetic description under a realistic condition of Bohm diffusivity. We emphasize the importance of collective plasma phenomena for the global flow structure and acceleration efficiency by considering the injection process, an initial stage of acceleration and, the related aspects of the physics of collisionless shocks. We calculate the injection rate for different shock parameters and different species. This, together with differential acceleration resulting from nonlinear large-scale modification, determines the chemical composition of accelerated particles. The review concentrates on theoretical and analytical aspects but our strategic goal is to link the fundamental theoretical ideas with the rapidly growing wealth of observational data. (author)

  2. Strongly nonlinear theory of rapid solidification near absolute stability

    Science.gov (United States)

    Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

    2017-10-01

    We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the

  3. Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory

    Science.gov (United States)

    Bloch, Deborah P.

    2005-01-01

    The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…

  4. 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...

  5. A nonlinear theory for elastic plates with application to characterizing paper properties

    Science.gov (United States)

    M. W. Johnson; Thomas J. Urbanik

    1984-03-01

    A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...

  6. Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory

    DEFF Research Database (Denmark)

    Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav

    model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable...

  7. New solutions of a nonlinear classical field theory

    International Nuclear Information System (INIS)

    Marques, G.C.; Ventura, I.

    1975-01-01

    New solutions of a relativistic, classical, field theoretical model having logarithmic nonlinearities are obtained. Some of these solutions correspond to field not bounded in time but having finite energy and charge. There are no bounded solutions (bound states and resonances in particular) if the charge exceeds a certain value. This effect is due to the existance of a 'charge barrier' in this field theoretical model. All calculations are performed in a number of spatial dimensions [pt

  8. Nonlinear time series theory, methods and applications with R examples

    CERN Document Server

    Douc, Randal; Stoffer, David

    2014-01-01

    FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre

  9. Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Doering, C.R.

    1985-01-01

    Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory

  10. 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.)

  11. Nonlinear Theory of Nonparaxial Laser Pulse Propagation in Plasma Channels

    International Nuclear Information System (INIS)

    Esarey, E.; Schroeder, C. B.; Shadwick, B. A.; Wurtele, J. S.; Leemans, W. P.

    2000-01-01

    Nonparaxial propagation of ultrashort, high-power laser pulses in plasma channels is examined. In the adiabatic limit, pulse energy conservation, nonlinear group velocity, damped betatron oscillations, self-steepening, self-phase modulation, and shock formation are analyzed. In the nonadiabatic limit, the coupling of forward Raman scattering (FRS) and the self-modulation instability (SMI) is analyzed and growth rates are derived, including regimes of reduced growth. The SMI is found to dominate FRS in most regimes of interest. (c) 2000 The American Physical Society

  12. Nonlinear theory of transverse-multimode plasma accelerators

    International Nuclear Information System (INIS)

    Kuzelev, M.V.; Panin, V.A.; Plotnikov, A.P.

    1991-01-01

    The excitation of the higher transverse modes in a plasma-filled waveguide by a high-power electron beam is considered. General nonlinear equations are obtained which treat the excitation of the higher transverse plasma waves by a high-current relativistic beam. Results are presented of the numerical solutions of these equations. In the case of ultrarelativistic beams analytical expressions are found for the maximum amplitudes of the excited modes and the Q of the amplification. Numerical estimates are presented for realistic parameters

  13. Beyond the SM with nonlinearly realized gauge theories

    International Nuclear Information System (INIS)

    ERRARI, R.

    2014-01-01

    A Stuckelberg Mass Term (SMT) is introduced in a SU(2) non-abelian gauge theory as an alternative to the Higgs mechanism. A lattice model is used in order to investigate the mass spectrum of the theory, in particular the presence of Higgs-like bound states. Simulations indicate the presence of neutral bound states. Further investigations are needed in order to compare the model with experiments.

  14. Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

    Science.gov (United States)

    Bridges, Thomas J.; Ratliff, Daniel J.

    2018-04-01

    The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

  15. Considering "Nonlinearity" Across the Continuum in Medical Education Assessment: Supporting Theory, Practice, and Future Research Directions.

    Science.gov (United States)

    Durning, Steven J; Lubarsky, Stuart; Torre, Dario; Dory, Valérie; Holmboe, Eric

    2015-01-01

    The purpose of this article is to propose new approaches to assessment that are grounded in educational theory and the concept of "nonlinearity." The new approaches take into account related phenomena such as "uncertainty," "ambiguity," and "chaos." To illustrate these approaches, we will use the example of assessment of clinical reasoning, although the principles we outline may apply equally well to assessment of other constructs in medical education. Theoretical perspectives include a discussion of script theory, assimilation theory, self-regulated learning theory, and situated cognition. Assessment examples to include script concordance testing, concept maps, self-regulated learning microanalytic technique, and work-based assessment, which parallel the above-stated theories, respectively, are also highlighted. We conclude with some practical suggestions for approaching nonlinearity. © 2015 The Alliance for Continuing Education in the Health Professions, the Society for Academic Continuing Medical Education, and the Council on Continuing Medical Education, Association for Hospital Medical Education.

  16. Nonlinear Dynamic Theory of Acute Cell Injuries and Brain Ischemia

    Science.gov (United States)

    Taha, Doaa; Anggraini, Fika; Degracia, Donald; Huang, Zhi-Feng

    2015-03-01

    Cerebral ischemia in the form of stroke and cardiac arrest brain damage affect over 1 million people per year in the USA alone. In spite of close to 200 clinical trials and decades of research, there are no treatments to stop post-ischemic neuron death. We have argued that a major weakness of current brain ischemia research is lack of a deductive theoretical framework of acute cell injury to guide empirical studies. A previously published autonomous model based on the concept of nonlinear dynamic network was shown to capture important facets of cell injury, linking the concept of therapeutic to bistable dynamics. Here we present an improved, non-autonomous formulation of the nonlinear dynamic model of cell injury that allows multiple acute injuries over time, thereby allowing simulations of both therapeutic treatment and preconditioning. Our results are connected to the experimental data of gene expression and proteomics of neuron cells. Importantly, this new model may be construed as a novel approach to pharmacodynamics of acute cell injury. The model makes explicit that any pro-survival therapy is always a form of sub-lethal injury. This insight is expected to widely influence treatment of acute injury conditions that have defied successful treatment to date. This work is supported by NIH NINDS (NS081347) and Wayne State University President's Research Enhancement Award.

  17. Nonlinear spectral mixing theory to model multispectral signatures

    Energy Technology Data Exchange (ETDEWEB)

    Borel, C.C. [Los Alamos National Lab., NM (United States). Astrophysics and Radiation Measurements Group

    1996-02-01

    Nonlinear spectral mixing occurs due to multiple reflections and transmissions between discrete surfaces, e.g. leaves or facets of a rough surface. The radiosity method is an energy conserving computational method used in thermal engineering and it models nonlinear spectral mixing realistically and accurately. In contrast to the radiative transfer method the radiosity method takes into account the discreteness of the scattering surfaces (e.g. exact location, orientation and shape) such as leaves and includes mutual shading between them. An analytic radiosity-based scattering model for vegetation was developed and used to compute vegetation indices for various configurations. The leaf reflectance and transmittance was modeled using the PROSPECT model for various amounts of water, chlorophyll and variable leaf structure. The soil background was modeled using SOILSPEC with a linear mixture of reflectances of sand, clay and peat. A neural network and a geometry based retrieval scheme were used to retrieve leaf area index and chlorophyll concentration for dense canopies. Only simulated canopy reflectances in the 6 visible through short wave IR Landsat TM channels were used. The authors used an empirical function to compute the signal-to-noise ratio of a retrieved quantity.

  18. Tail estimates for stochastic fixed point equations via nonlinear renewal theory

    DEFF Research Database (Denmark)

    Collamore, Jeffrey F.; Vidyashankar, Anand N.

    2013-01-01

    estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....

  19. Simulation of creep effects in framework of a geometrically nonlinear endochronic theory of inelasticity

    Science.gov (United States)

    Zabavnikova, T. A.; Kadashevich, Yu. I.; Pomytkin, S. P.

    2018-05-01

    A geometric non-linear endochronic theory of inelasticity in tensor parametric form is considered. In the framework of this theory, the creep strains are modelled. The effect of various schemes of applying stresses and changing of material properties on the development of creep strains is studied. The constitutive equations of the model are represented by non-linear systems of ordinary differential equations which are solved in MATLAB environment by implicit difference method. Presented results demonstrate a good qualitative agreement of theoretical data and experimental observations including the description of the tertiary creep and pre-fracture of materials.

  20. Theory for stationary nonlinear wave propagation in complex magnetic geometry

    International Nuclear Information System (INIS)

    Watanabe, T.; Hojo, H.; Nishikawa, Kyoji.

    1977-08-01

    We present our recent efforts to derive a systematic calculation scheme for nonlinear wave propagation in the self-consistent plasma profile in complex magnetic-field geometry. Basic assumptions and/or approximations are i) use of the collisionless two-fluid model with an equation of state; ii) restriction to a steady state propagation and iii) existence of modified magnetic surface, modification due to Coriolis' force. We discuss four situations: i) weak-field propagation without static flow, ii) arbitrary field strength with flow in axisymmetric system, iii) weak field limit of case ii) and iv) arbitrary field strength in nonaxisymmetric torus. Except for case iii), we derive a simple variation principle, similar to that of Seligar and Whitham, by introducing appropriate coordinates. In cases i) and iii), we derive explicit results for quasilinear profile modification. (auth.)

  1. Geometrical theory of nonlinear phase distortion of intense laser beams

    International Nuclear Information System (INIS)

    Glaze, J.A.; Hunt, J.T.; Speck, D.R.

    1975-01-01

    Phase distortion arising from whole beam self-focusing of intense laser pulses with arbitrary spatial profiles is treated in the limit of geometrical optics. The constant shape approximation is used to obtain the phase and angular distribution of the geometrical rays in the near field. Conditions for the validity of this approximation are discussed. Geometrical focusing of the aberrated beam is treated for the special case of a beam with axial symmetry. Equations are derived that show both the shift of the focus and the distortion of the intensity distribution that are caused by the nonlinear index of refraction of the optical medium. An illustrative example treats the case of beam distortion in a Nd:Glass amplifier

  2. Linear and nonlinear theory study of Alpha Virginis

    International Nuclear Information System (INIS)

    Cox, A.N.; Hodson, S.W.; Clancy, S.P.

    1981-01-01

    Nonlinear radiation hydrodynamic calculations using a model for α Virginis, a β Cephei star, have been made to see if the cause of the recurrent radial pulsation epochs can be discovered. The basic observed characteristics of β Cephei variables are presented. A review of the various proposals to make these stars pulsate concludes that the excitation mechanism must be in the central convective core or variable composition regions. The envelope damps radial fundamental mode pulsations in 4 years and in even shorter periods for radial overtones. It is proposed here that the mixing of envelope hydrogen into the hydrogen depleted (or even exhausted) core can produce periodic pressure pulses which drive the pulsation amplitude up to the observed value. During the decay of the pulsations, evolution toward higher luminosities enables further episodes of mixing and driving to occur. We predict rapid amplitude increases when mixing occurs and a slow decay of radial (and nonradial modes for other β Cephei variables) between mixing episodes

  3. Development of nonlinear dynamic analysis program for nuclear piping systems

    International Nuclear Information System (INIS)

    Kamichika, Ryoichi; Izawa, Masahiro; Yamadera, Masao

    1980-01-01

    In the design for nuclear power piping, pipe-whip protection shall be considered in order to keep the function of safety related system even when postulated piping rupture occurs. This guideline was shown in U.S. Regulatory Guide 1.46 for the first time and has been applied in Japanese nuclear power plants. In order to analyze the dynamic behavior followed by pipe rupture, nonlinear analysis is required for the piping system including restraints which play the role of an energy absorber. REAPPS (Rupture Effective Analysis of Piping Systems) has been developed for this purpose. This program can be applied to general piping systems having branches etc. Pre- and post- processors are prepared in this program in order to easily input the data for the piping engineer and show the results optically by use of a graphic display respectively. The piping designer can easily solve many problems in his daily work by use of this program. This paper describes about the theoretical background and functions of this program and shows some examples. (author)

  4. Nonlinear aeroelastic modelling for wind turbine blades based on blade element momentum theory and geometrically exact beam theory

    International Nuclear Information System (INIS)

    Wang, Lin; Liu, Xiongwei; Renevier, Nathalie; Stables, Matthew; Hall, George M.

    2014-01-01

    Due to the increasing size and flexibility of large wind turbine blades, accurate and reliable aeroelastic modelling is playing an important role for the design of large wind turbines. Most existing aeroelastic models are linear models based on assumption of small blade deflections. This assumption is not valid anymore for very flexible blade design because such blades often experience large deflections. In this paper, a novel nonlinear aeroelastic model for large wind turbine blades has been developed by combining BEM (blade element momentum) theory and mixed-form formulation of GEBT (geometrically exact beam theory). The nonlinear aeroelastic model takes account of large blade deflections and thus greatly improves the accuracy of aeroelastic analysis of wind turbine blades. The nonlinear aeroelastic model is implemented in COMSOL Multiphysics and validated with a series of benchmark calculation tests. The results show that good agreement is achieved when compared with experimental data, and its capability of handling large deflections is demonstrated. Finally the nonlinear aeroelastic model is applied to aeroelastic modelling of the parked WindPACT 1.5 MW baseline wind turbine, and reduced flapwise deflection from the nonlinear aeroelastic model is observed compared to the linear aeroelastic code FAST (Fatigue, Aerodynamics, Structures, and Turbulence). - Highlights: • A novel nonlinear aeroelastic model for wind turbine blades is developed. • The model takes account of large blade deflections and geometric nonlinearities. • The model is reliable and efficient for aeroelastic modelling of wind turbine blades. • The accuracy of the model is verified by a series of benchmark calculation tests. • The model provides more realistic aeroelastic modelling than FAST (Fatigue, Aerodynamics, Structures, and Turbulence)

  5. Electric generating capacity planning: A nonlinear programming approach

    Energy Technology Data Exchange (ETDEWEB)

    Yakin, M.Z.; McFarland, J.W.

    1987-02-01

    This paper presents a nonlinear programming approach for long-range generating capacity expansion planning in electrical power systems. The objective in the model is the minimization of total cost consisting of investment cost plus generation cost for a multi-year planning horizon. Reliability constraints are imposed by using standard and practical reserve margin requirements. State equations representing the dynamic aspect of the problem are included. The electricity demand (load) and plant availabilities are treated as random variables, and the method of cumulants is used to calculate the expected energy generated by each plant in each year of the planning horizon. The resulting model has a (highly) nonlinear objective function and linear constraints. The planning model is solved over the multiyear planning horizon instead of decomposing it into one-year period problems. This approach helps the utility decision maker to carry out extensive sensitivity analysis easily. A case study example is provided using EPRI test data. Relationships among the reserve margin, total cost and surplus energy generating capacity over the planning horizon are explored by analyzing the model.

  6. Inverse operator theory method mathematics-mechanization for the solutions of nonlinear equations and some typical applications in nonlinear physics

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    1992-12-01

    Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science

  7. ARSTEC, Nonlinear Optimization Program Using Random Search Method

    International Nuclear Information System (INIS)

    Rasmuson, D. M.; Marshall, N. H.

    1979-01-01

    1 - Description of problem or function: The ARSTEC program was written to solve nonlinear, mixed integer, optimization problems. An example of such a problem in the nuclear industry is the allocation of redundant parts in the design of a nuclear power plant to minimize plant unavailability. 2 - Method of solution: The technique used in ARSTEC is the adaptive random search method. The search is started from an arbitrary point in the search region and every time a point that improves the objective function is found, the search region is centered at that new point. 3 - Restrictions on the complexity of the problem: Presently, the maximum number of independent variables allowed is 10. This can be changed by increasing the dimension of the arrays

  8. Advanced nonlinear theory: Long-term stability at the SSC

    International Nuclear Information System (INIS)

    Heifets, S.

    1987-01-01

    This paper discussed the long-term stability of the particle beams in the Superconducting Super Collider. In particular the dynamics of a single particle beam is considered in depth. The topics of this paper include: the Hamiltonian of this particle approach, perturbation theory, canonical transformations, interaction of the resonances, structure of the phase space, synchro-Betatron oscillations, modulation diffusion and noise-resonance interaction. 36 refs

  9. Stochastic Control Theory, Nonlinear Structural Mechanics and Applied Combinatorics

    Science.gov (United States)

    1989-05-12

    More specifically: (") x 3 PAS and Steiner triple systems; (") x 4 PAS and Steiner triple systems which can be nested; and (’) x 5 PAS and Steiner ...am Rudolf Wille CONCEPTUAL SCALING Technische Hochschule Darmstadt Abstract: Scaling of empirical data uses formal patterns to lead to a better...of Arizona Jan 18 - 22 Wille, Rudolf Technische Hochschule Darmstadt Jan 17 - 23 21 APPLICATIONS OF COMBINATORICS AND GRAPH THEORY TO THE BIOLOGICAL

  10. Kinetic theory of nonlinear transport phenomena in complex plasmas

    International Nuclear Information System (INIS)

    Mishra, S. K.; Sodha, M. S.

    2013-01-01

    In contrast to the prevalent use of the phenomenological theory of transport phenomena, a number of transport properties of complex plasmas have been evaluated by using appropriate expressions, available from the kinetic theory, which are based on Boltzmann's transfer equation; in particular, the energy dependence of the electron collision frequency has been taken into account. Following the recent trend, the number and energy balance of all the constituents of the complex plasma and the charge balance on the particles is accounted for; the Ohmic loss has also been included in the energy balance of the electrons. The charging kinetics for the complex plasma comprising of uniformly dispersed dust particles, characterized by (i) uniform size and (ii) the Mathis, Rumpl, and Nordsieck power law of size distribution has been developed. Using appropriate expressions for the transport parameters based on the kinetic theory, the system of equations has been solved to investigate the parametric dependence of the complex plasma transport properties on the applied electric field and other plasma parameters; the results are graphically illustrated.

  11. Nucleon-nucleon scattering in the functional quantum theory of the nonlinear spinor field

    International Nuclear Information System (INIS)

    Haegele, G.

    1979-01-01

    The author calculates the S matrix for the elastic nucleon-nucleon scattering in the lowest approximation using the quantum theory of nonlinear spinor fields with special emphasis to the ghost configuration of this theory. Introducing a general scalar product a new functional channel calculus is considered. From the results the R and T matrix elements and the differential and integral cross sections are derived. (HSI)

  12. Linear programming mathematics, theory and algorithms

    CERN Document Server

    1996-01-01

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

  13. Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy

    Institute of Scientific and Technical Information of China (English)

    TANG Zhilie; XING Da; LIU Songhao

    2004-01-01

    The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single-and two-photon confocal microscopy.

  14. Nonlinear many-body reaction theories from nuclear mean field approximations

    International Nuclear Information System (INIS)

    Griffin, J.J.

    1983-01-01

    Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)

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

    NARCIS (Netherlands)

    Zwart, H.J.

    2015-01-01

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

  16. 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...

  17. Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes

    Science.gov (United States)

    Bussolari, Cori J.; Goodell, Judith A.

    2009-01-01

    Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to…

  18. 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...

  19. An approximation theory for nonlinear partial differential equations with applications to identification and control

    Science.gov (United States)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  20. White noise theory of robust nonlinear filtering with correlated state and observation noises

    NARCIS (Netherlands)

    Bagchi, Arunabha; Karandikar, Rajeeva

    1992-01-01

    In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling

  1. White noise theory of robust nonlinear filtering with correlated state and observation noises

    NARCIS (Netherlands)

    Bagchi, Arunabha; Karandikar, Rajeeva

    1994-01-01

    In the existing `direct¿ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a `finitely additive¿ white noise is used to model the observation noise. We remove this asymmetry by modelling the

  2. 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

  3. Classical and Quantum Nonlinear Integrable Systems: Theory and Application

    International Nuclear Information System (INIS)

    Brzezinski, Tomasz

    2003-01-01

    This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems such as the KdV equation, vertex models, RSOS and IRF models, spin chains, integrable differential equations, discrete systems, Ising, Potts and other lattice models and reaction--diffusion processes, as well as outlining major methods of solving integrable systems. These include Lax pairs, Baecklund and Miura transformations, the inverse scattering method, various types of the Bethe Ansatz, Painleve methods, the dbar method and fusion methods to mention just a few. The book is divided into two parts, each containing five chapters. The first part is devoted to classical integrable systems and introduces the subject through the KdV equation, and then proceeds through Painleve analysis, discrete systems and two-dimensional integrable partial differential equations, to culminate in the review of solvable lattice models in statistical physics, solved through the coordinate and algebraic Bethe Ansatz methods. The second part deals with quantum integrable systems, and begins with an outline of unifying approaches to quantum, statistical, ultralocal and non-ultralocal systems. The theory and methods of solving quantum integrable spin chains are then described. Recent developments in applying Bethe Ansatz methods in condensed matter physics, including superconductivity and nanoscale physics, are reviewed. The book concludes with an introduction to diffusion-reaction processes. Every chapter is devoted to a different subject and is self-contained, and thus can be read separately. A reader interesting in classical methods of solitons, such as the methods of solving the KdV equation, can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5, and so on. Thus the book should appeal and be useful to a wide range of theoretical

  4. FATAL, General Experiment Fitting Program by Nonlinear Regression Method

    International Nuclear Information System (INIS)

    Salmon, L.; Budd, T.; Marshall, M.

    1982-01-01

    1 - Description of problem or function: A generalized fitting program with a free-format keyword interface to the user. It permits experimental data to be fitted by non-linear regression methods to any function describable by the user. The user requires the minimum of computer experience but needs to provide a subroutine to define his function. Some statistical output is included as well as 'best' estimates of the function's parameters. 2 - Method of solution: The regression method used is based on a minimization technique devised by Powell (Harwell Subroutine Library VA05A, 1972) which does not require the use of analytical derivatives. The method employs a quasi-Newton procedure balanced with a steepest descent correction. Experience shows this to be efficient for a very wide range of application. 3 - Restrictions on the complexity of the problem: The current version of the program permits functions to be defined with up to 20 parameters. The function may be fitted to a maximum of 400 points, preferably with estimated values of weight given

  5. Computer programs for solving systems of nonlinear equations

    International Nuclear Information System (INIS)

    Asaoka, Takumi

    1978-03-01

    Computer programs to find a solution, usually the one closest to some guess, of a system of simultaneous nonlinear equations are provided for real functions of the real arguments. These are based on quasi-Newton methods or projection methods, which are briefly reviewed in the present report. Benchmark tests were performed on these subroutines to grasp their characteristics. As the program not requiring analytical forms of the derivatives of the Jacobian matrix, we have dealt with NS01A of Powell, NS03A of Reid for a system with the sparse Jacobian and NONLIN of Brown. Of these three subroutines of quasi-Newton methods, NONLIN is shown to be the most useful because of its stable algorithm and short computation time. On the other hand, as the subroutine for which the derivatives of the Jacobian are to be supplied analytically, we have tested INTECH of a quasi-Newton method based on the Boggs' algorithm, PROJA of Georg and Keller based on the projection method and an option of NS03A. The results have shown that INTECH, treating variables which appear only linearly in the functions separately, takes the shortest computation time, on the whole, while the projection method requires further research to find an optimal algorithm. (auth.)

  6. Theory of plasmonic effects in nonlinear optics: the case of graphene

    Science.gov (United States)

    Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

    The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

  7. 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.))

  8. Development of ultrasound transducer diffractive field theory for nonlinear propagation-based imaging

    Science.gov (United States)

    Kharin, Nikolay A.

    2000-04-01

    In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.

  9. Maximized gust loads for a nonlinear airplane using matched filter theory and constrained optimization

    Science.gov (United States)

    Scott, Robert C.; Perry, Boyd, III; Pototzky, Anthony S.

    1991-01-01

    This paper describes and illustrates two matched-filter-theory based schemes for obtaining maximized and time-correlated gust-loads for a nonlinear airplane. The first scheme is computationally fast because it uses a simple one-dimensional search procedure to obtain its answers. The second scheme is computationally slow because it uses a more complex multidimensional search procedure to obtain its answers, but it consistently provides slightly higher maximum loads than the first scheme. Both schemes are illustrated with numerical examples involving a nonlinear control system.

  10. Microscopic nonlinear relativistic quantum theory of absorption of powerful x-ray radiation in plasma.

    Science.gov (United States)

    Avetissian, H K; Ghazaryan, A G; Matevosyan, H H; Mkrtchian, G F

    2015-10-01

    The microscopic quantum theory of plasma nonlinear interaction with the coherent shortwave electromagnetic radiation of arbitrary intensity is developed. The Liouville-von Neumann equation for the density matrix is solved analytically considering a wave field exactly and a scattering potential of plasma ions as a perturbation. With the help of this solution we calculate the nonlinear inverse-bremsstrahlung absorption rate for a grand canonical ensemble of electrons. The latter is studied in Maxwellian, as well as in degenerate quantum plasma for x-ray lasers at superhigh intensities and it is shown that one can achieve the efficient absorption coefficient in these cases.

  11. Comment on the consistency of truncated nonlinear integral equation based theories of freezing

    International Nuclear Information System (INIS)

    Cerjan, C.; Bagchi, B.; Rice, S.A.

    1985-01-01

    We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim--Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions

  12. Nonlinear theory for the parametric instability with comparable electron and ion temperatures

    International Nuclear Information System (INIS)

    Oberman, C.

    1972-01-01

    The basic linear theory of the parametric instability driven by a pump E 0 sin ω 0 t oscillating near the electron plasma frequency is reviewed. An expression is derived for the temporal nonlinear development of the fluctuation spectrum of the excited waves. For plasma with comparable electron and ion temperatures nonlinear Landau damping of electron plasma waves on ions provides the dominant nonlinearity. The steady state solutions are examined both analytically and numerically in the limit when the spontaneous emission term is small. The characteristics of the plasma wave spectrum agrees well with the general features of ionospheric observations. The enhanced dissipation rate of the pump due to the presence of the fluctuations agrees with laboratory observations. (U.S.)

  13. Theory of nonlinear acoustic forces acting on fluids and particles in microsystems

    DEFF Research Database (Denmark)

    Karlsen, Jonas Tobias

    fundamentally new capabilities in chemical, biomedical, or clinical studies of single cells and bioparticles. This thesis, entitled Theory of nonlinear acoustic forces acting on fluids and particles in microsystems, advances the fundamental understanding of acoustofluidics by addressing the origin...... of the nonlinear acoustic forces acting on fluids and particles. Classical results in nonlinear acoustics for the non-dissipative acoustic radiation force acting on a particle or an interface, as well as the dissipative acoustic force densities driving acoustic streaming, are derived and discussed in terms...... in the continuous fluid parameters of density and compressibility, e.g., due to a solute concentration field, the thesis presents novel analytical results on the acoustic force density acting on inhomogeneous fluids in acoustic fields. This inhomogeneity-induced acoustic force density is non-dissipative in origin...

  14. Quantum theory from a nonlinear perspective Riccati equations in fundamental physics

    CERN Document Server

    Schuch, Dieter

    2018-01-01

    This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in ...

  15. Nonlinear scattering from a plasma column. I - Theory. II Special cases

    Science.gov (United States)

    Crawford, F. W.; Harker, K. J.

    1983-01-01

    The scattered signal excited by nonlinear mixing of two plane waves normally incident on an infinitely long column of plasma is investigated. A general solution is obtained for the polarization in which the electric field vectors of the waves are perpendicular to the column axis and the column is assumed to be radically inhomogeneous. This general theory is then applied to the special cases of the inhomogeneous column in the long-wavelength limit, and the homogeneous column both for the general case and in the long-wavelength limit. It is determined that dipole and quadrupole components should predominate in the polar radiation pattern for the long-wavelength case. The special case of second harmonic generation due to a single incident wave is analyzed in detail. Nonlinear scattering coefficients are computed, and the corresponding polar radiation patterns are determined. The findings of this study are employed to evaluate the feasibility of observing nonlinear scattering from meteor trails.

  16. 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.

  17. PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

    Science.gov (United States)

    Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.

    1977-01-01

    The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.

  18. Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory

    International Nuclear Information System (INIS)

    Qian, Hong

    2011-01-01

    The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)

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

    International Nuclear Information System (INIS)

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

    1978-01-01

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

  20. On the theory of weak turbulence for the nonlinear Schrödinger equation

    CERN Document Server

    Escobedo, M

    2015-01-01

    The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.

  1. The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems

    International Nuclear Information System (INIS)

    Di Dong; Yiming Long.

    1994-10-01

    In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous periodic and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems. (author). 40 refs

  2. Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory

    Science.gov (United States)

    Xu, Yan; Hu, Bin; Wu, Jiang; Zhang, Jianhua

    2014-04-01

    The excitation intervention of strategic alliance may change with the changes in the parameters of circumstance (e.g., external alliance tasks). As a result, the stable cooperation between members may suffer a complete unplanned betrayal at last. However, current perspectives on strategic alliances cannot adequately explain this transition mechanism. This study is a first attempt to analyze this nonlinear phenomenon through stochastic catastrophe theory (SCT). A stochastic dynamics model is constructed based on the cooperation of strategic alliance from the perspective of evolutionary game theory. SCT explains the discontinuous changes caused by the changes in environmental parameters. Theoretically, we identify conditions where catastrophe can occur in the cooperation of alliance members.

  3. T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory

    CERN Document Server

    Takahashi, Wataru

    1995-01-01

    The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza­ tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the­ ories. Although our special emphasis was laid upon "nonlinearity" and "con­ vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark­ able rapid growth of this dis...

  4. Method of asymptotic expansions and qualitative analysis of finite-dimensional models in the nonlinear field theory

    International Nuclear Information System (INIS)

    Eleonskij, V.M.; Kulagin, N.E.; Novozhilova, N.S.; Silin, V.P.

    1984-01-01

    The reasons which prevent the existence of periodic in time and self-localised in space solutions of the nonlinear wave equation u=F (u) are determined by the methods of qualitative theory of dynamical systems. The correspondence between the qualitative behaviour of special (separatrix) trajectories in the phase space and asymptotic solutions of the nonlinear wave equation is analysed

  5. φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations

    Science.gov (United States)

    Sornette, D.; Simonetti, P.; Andersen, J. V.

    2000-08-01

    Physics and finance are both fundamentally based on the theory of random walks (and their generalizations to higher dimensions) and on the collective behavior of large numbers of correlated variables. The archetype examplifying this situation in finance is the portfolio optimization problem in which one desires to diversify on a set of possibly dependent assets to optimize the return and minimize the risks. The standard mean-variance solution introduced by Markovitz and its subsequent developments is basically a mean-field Gaussian solution. It has severe limitations for practical applications due to the strongly non-Gaussian structure of distributions and the nonlinear dependence between assets. Here, we present in details a general analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto Gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a nonlinear covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good conditioning. The portfolio distribution is then obtained as the solution of a mapping to a so-called φq field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The interaction (non-mean field) structure in this field theory is a direct consequence of the non-Gaussian nature of the distribution of asset price returns. We find that minimizing the portfolio variance (i.e. the relatively “small” risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive

  6. Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

    Science.gov (United States)

    Tsuchida, Satoshi; Kuratsuji, Hiroshi

    2018-05-01

    A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

  7. Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.

    Energy Technology Data Exchange (ETDEWEB)

    Robinson, Brandon [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Rocha da Costa, Leandro Jose [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Poirel, Dominique [Royal Military College of Canada, Kingston (Canada). Dept. of Mechanical and Aerospace Engineering; Pettit, Chris [US Naval Academy, Annapolis, MD (United States). Dept. of Mechanical and Aerospace Engineering; Khalil, Mohammad [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sarkar, Abhijit [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering

    2017-09-01

    Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.

  8. Nonlinear vibration of rectangular atomic force microscope cantilevers by considering the Hertzian contact theory

    Energy Technology Data Exchange (ETDEWEB)

    Sadeghi, A., E-mail: a_sadeghi@srbiau.ac.ir [Islamic Azad Univ., Dept. of Mechanical and Aerospace Engineering, Science and Research Branch, Tehran (Iran, Islamic Republic of); Zohoor, H. [Sharif Univ. of Technology, Center of Excellence in Design, Robotics and Automation, Tehran (Iran, Islamic Republic of); The Academy of Sciences if I.R. Iran (Iran, Islamic Republic of)

    2010-05-15

    The nonlinear flexural vibration for a rectangular atomic force microscope cantilever is investigated by using Timoshenko beam theory. In this paper, the normal and tangential tip-sample interaction forces are found from a Hertzian contact model and the effects of the contact position, normal and lateral contact stiffness, tip height, thickness of the beam, and the angle between the cantilever and the sample surface on the nonlinear frequency to linear frequency ratio are studied. The differential quadrature method is employed to solve the nonlinear differential equations of motion. The results show that softening behavior is seen for most cases and by increasing the normal contact stiffness, the frequency ratio increases for the first mode, but for the second mode, the situation is reversed. The nonlinear-frequency to linear-frequency ratio increases by increasing the Timoshenko beam parameter, but decreases by increasing the contact position for constant amplitude for the first and second modes. For the first mode, the frequency ratio decreases by increasing both of the lateral contact stiffness and the tip height, but increases by increasing the angle α between the cantilever and sample surface. (author)

  9. Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

    Science.gov (United States)

    de Paor, A. M.

    Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.

  10. JAC, 2-D Finite Element Method Program for Quasi Static Mechanics Problems by Nonlinear Conjugate Gradient (CG) Method

    International Nuclear Information System (INIS)

    Biffle, J.H.

    1991-01-01

    1 - Description of program or function: JAC is a two-dimensional finite element program for solving large deformation, temperature dependent, quasi-static mechanics problems with the nonlinear conjugate gradient (CG) technique. Either plane strain or axisymmetric geometry may be used with material descriptions which include temperature dependent elastic-plastic, temperature dependent secondary creep, and isothermal soil models. The nonlinear effects examined include material and geometric nonlinearities due to large rotations, large strains, and surface which slide relative to one another. JAC is vectorized to perform efficiently on the Cray1 computer. A restart capability is included. 2 - Method of solution: The nonlinear conjugate gradient method is employed in a two-dimensional plane strain or axisymmetric setting with various techniques for accelerating convergence. Sliding interface conditions are also implemented. A four-node Lagrangian uniform strain element is used with orthogonal hourglass viscosity to control the zero energy modes. Three sets of continuum equations are needed - kinematic statements, constitutive equations, and equations of equilibrium - to describe the deformed configuration of the body. 3 - Restrictions on the complexity of the problem - Maxima of: 10 load and solution control functions, 4 materials. The strain rate is assumed constant over a time interval. Current large rotation theory is applicable to a maximum shear strain of 1.0. JAC should be used with caution for large shear strains. Problem size is limited only by available memory

  11. Application of H∞ control theory to power control of a nonlinear reactor model

    International Nuclear Information System (INIS)

    Suzuki, Katsuo; Shimazaki, Junya; Shinohara, Yoshikuni

    1993-01-01

    The H∞ control theory is applied to the compensator design of a nonlinear nuclear reactor model, and the results are compared with standard linear quadratic Gaussian (LQG) control. The reactor model is assumed to be provided with a control rod drive system having the compensation of rod position feedback. The nonlinearity of the reactor model exerts a great influence on the stability of the control system, and hence, it is desirable for a power control system of a nuclear reactor to achieve robust stability and to improve the sensitivity of the feedback control system. A computer simulation based on a power control system synthesized by LQG control was performed revealing that the control system has some stationary offset and less stability. Therefore, here, attention is given to the development of a methodology for robust control that can withstand exogenous disturbances and nonlinearity in view of system parameter changes. The developed methodology adopts H∞ control theory in the feedback system and shows interesting features of robustness. The results of the computer simulation indicate that the feedback control system constructed by the developed H∞ compensator possesses sufficient robustness of control on the stability and disturbance attenuation, which are essential for the safe operation of a nuclear reactor

  12. 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.)

  13. A universal nonlinear relation among boundary states in closed string field theory

    International Nuclear Information System (INIS)

    Kishimoto, Isao; Matsuo, Yutaka; Watanabe, Eitoku

    2004-01-01

    We show that the boundary states satisfy a nonlinear relation (the idempotency equation) with respect to the star product of closed string field theory. This relation is universal in the sense that various D-branes, including the infinitesimally deformed ones, satisfy the same equation, including the coefficient. This paper generalizes our analysis [hep-th/0306189] in the following senses. (1) We present a background-independent formulation based on conformal field theory. It illuminates the geometric nature of the relation and allows us to more systematically analyze the variations around the D-brane background. (2) We show that the Witten-type star product satisfies a similar relation but with a more divergent coefficient. (3) We determine the coefficient of the relation analytically. The result shows that the α parameter can be formally factored out, and the relation becomes universal. We present a conjecture on vacuum theory based on this computation. (author)

  14. COYOTE: a finite element computer program for nonlinear heat conduction problems

    International Nuclear Information System (INIS)

    Gartling, D.K.

    1978-06-01

    COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program

  15. 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.

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

    Science.gov (United States)

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

    2018-06-01

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

  17. One-dimensional nonlinear theory for rectangular helix traveling-wave tube

    Energy Technology Data Exchange (ETDEWEB)

    Fu, Chengfang, E-mail: fchffchf@126.com; Zhao, Bo; Yang, Yudong; Ju, Yongfeng [Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huai' an 223003 (China); Wei, Yanyu [School of Physical Electronics, University of Electronic and Technology of China, Chengdu 610054 (China)

    2016-08-15

    A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numerically using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.

  18. Nonlinear theory of trapped electron temperature gradient driven turbulence in flat density H-mode plasmas

    International Nuclear Information System (INIS)

    Hahm, T.S.

    1990-12-01

    Ion temperature gradient turbulence based transport models have difficulties reconciling the recent DIII-D H-mode results where the density profile is flat, but χ e > χ i in the core region. In this work, a nonlinear theory is developed for recently discovered ion temperature gradient trapped electron modes propagating in the electron diamagnetic direction. This instability is predicted to be linearly unstable for L Ti /R approx-lt κ θ ρ s approx-lt (L Ti /R) 1/4 . They are also found to be strongly dispersive even at these long wavelengths, thereby suggesting the importance of the wave-particle-wave interactions in the nonlinear saturation phase. The fluctuation spectrum and anomalous fluxes are calculated. In accordance with the trends observed in DIII-D, the predicted electron thermal diffusivity can be larger than the ion thermal diffusivity. 17 refs., 3 figs

  19. Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory

    Science.gov (United States)

    Wang, Liming; Zheng, Shijie

    2018-02-01

    In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.

  20. Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory.

    Science.gov (United States)

    Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tomé, W A

    2011-04-07

    The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.

  1. Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory

    Energy Technology Data Exchange (ETDEWEB)

    Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tome, W A, E-mail: tewatia@wisc.edu [Department of Human Oncology, University of Wisconsin, Madison, WI (United States)

    2011-04-07

    The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay '{tau}' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed

  2. Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory

    International Nuclear Information System (INIS)

    Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tome, W A

    2011-01-01

    The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.

  3. A self-consistent nonlinear theory of resistive-wall instability in a relativistic electron beam

    International Nuclear Information System (INIS)

    Uhm, H.S.

    1994-01-01

    A self-consistent nonlinear theory of resistive-wall instability is developed for a relativistic electron beam propagating through a grounded cylindrical resistive tube. The theory is based on the assumption that the frequency of the resistive-wall instability is lower than the cutoff frequency of the waveguide. The theory is concentrated on study of the beam current modulation directly related to the resistive-wall klystron, in which a relativistic electron beam is modulated at the first cavity and propagates downstream through the resistive wall. Because of the self-excitation of the space charge waves by the resistive-wall instability, a highly nonlinear current modulation of the electron beam is accomplished as the beam propagates downstream. A partial integrodifferential equation is obtained in terms of the initial energy modulation (ε), the self-field effects (h), and the resistive-wall effects (κ). Analytically investigating the partial integrodifferential equation, a scaling law of the propagation distance z m at which the maximum current modulation occurs is obtained. It is found in general that the self-field effects dominate over the resistive-wall effects at the beginning of the propagation. As the beam propagates farther downstream, the resistive-wall effects dominate. Because of a relatively large growth rate of the instability, the required tube length of the klystron is short for most applications

  4. A normal form approach to the theory of nonlinear betatronic motion

    International Nuclear Information System (INIS)

    Bazzani, A.; Todesco, E.; Turchetti, G.; Servizi, G.

    1994-01-01

    The betatronic motion of a particle in a circular accelerator is analysed using the transfer map description of the magnetic lattice. In the linear case the transfer matrix approach is shown to be equivalent to the Courant-Snyder theory: In the normal coordinates' representation the transfer matrix is a pure rotation. When the nonlinear effects due to the multipolar components of the magnetic field are taken into account, a similar procedure is used: a nonlinear change of coordinates provides a normal form representation of the map, which exhibits explicit symmetry properties depending on the absence or presence of resonance relations among the linear tunes. The use of normal forms is illustrated in the simplest but significant model of a cell with a sextupolar nonlinearity which is described by the quadratic Henon map. After recalling the basic theoretical results in Hamiltonian dynamics, we show how the normal forms describe the different topological structures of phase space such as KAM tori, chains of islands and chaotic regions; a critical comparison with the usual perturbation theory for Hamilton equations is given. The normal form theory is applied to compute the tune shift and deformation of the orbits for the lattices of the SPS and LHC accelerators, and scaling laws are obtained. Finally, the correction procedure of the multipolar errors of the LHC, based on the analytic minimization of the tune shift computed via the normal forms, is described and the results for a model of the LHC are presented. This application, relevant for the lattice design, focuses on the advantages of normal forms with respect to tracking when parametric dependences have to be explored. (orig.)

  5. 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.

  6. On the treatment of nonlinear local feedbacks within advanced nodal generalized perturbation theory

    International Nuclear Information System (INIS)

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

    1993-01-01

    Recent efforts to upgrade the underlying neutronics formulations within the in-core nuclear fuel management optimization code FORMOSA (Ref. 1) have produced two important developments; first, a computationally efficient and second-order-accurate advanced nodal generalized perturbation theory (GPT) model [derived from the nonlinear iterative nodal expansion method (NEM)] for evaluating core attributes (i.e., k eff and power distribution versus cycle burnup), and second, an equally efficient and accurate treatment of local thermal-hydraulic and fission product feedbacks embedded within NEM GPT. The latter development is the focus of this paper

  7. 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...

  8. Nonlinear field theories and non-Gaussian fluctuations for near-critical many-body systems

    International Nuclear Information System (INIS)

    Tuszynski, J.A.; Dixon, J.M.; Grundland, A.M.

    1994-01-01

    This review article outlines a number of efforts made over the past several decades to understand the physics of near critical many-body systems. Beginning with the phenomenological theories of Landau and Ginzburg the paper discusses the two main routes adopted in the past. The first approach is based on statistical calculations while the second investigates the underlying nonlinear field equations. In the last part of the paper we outline a generalisation of these methods which combines classical and quantum properties of the many-body systems studied. (orig.)

  9. Naturalness of Nonlinear Scalar Self-Couplings in a Relativistic Mean Field Theory for Neutron Stars

    International Nuclear Information System (INIS)

    Maekawa, Claudio; Razeira, Moises; Vasconcellos, Cesar A. Z.; Dillig, Manfred; Bodmann, Bardo E. J.

    2004-01-01

    We investigate the role of naturalness in effective field theory. We focus on dense hadronic matter using a generalized relativistic multi-baryon lagrangian density mean field approach which contains nonlinear self-couplings of the σ, δ meson fields and the fundamental baryon octet. We adjust the model parameters to describe bulk static properties of ordinary nuclear matter. Then, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as the ones found in the interior of neutron stars

  10. Extensions to a nonlinear finite-element axisymmetric shell model based on Reissner's shell theory

    International Nuclear Information System (INIS)

    Cook, W.A.

    1981-01-01

    Extensions to shell analysis not usually associated with shell theory are described in this paper. These extensions involve thick shells, nonlinear materials, a linear normal stress approximation, and a changing shell thickness. A finite element shell-of-revolution model has been developed to analyze nuclear material shipping containers under severe impact conditions. To establish the limits for this shell model, the basic assumptions used in its development were studied; these are listed in this paper. Several extensions were evident from the study of these limits: a thick shell, a plastic hinge, and a linear normal stress

  11. Current and Future Constraints on Higgs Couplings in the Nonlinear Effective Theory

    Energy Technology Data Exchange (ETDEWEB)

    de Blas, Jorge [INFN, Padua; Eberhardt, Otto [Valencia U., IFIC; Krause, Claudius [Fermilab

    2018-03-02

    We perform a Bayesian statistical analysis of the constraints on the nonlinear Effective Theory given by the Higgs electroweak chiral Lagrangian. We obtain bounds on the effective coefficients entering in Higgs observables at the leading order, using all available Higgs-boson signal strengths from the LHC runs 1 and 2. Using a prior dependence study of the solutions, we discuss the results within the context of natural-sized Wilson coefficients. We further study the expected sensitivities to the different Wilson coefficients at various possible future colliders. Finally, we interpret our results in terms of some minimal composite Higgs models.

  12. Generalized effective potential in nonlinear theories of the 4-th order

    International Nuclear Information System (INIS)

    Ananikyan, N.S.; Savvidy, G.K.

    1980-01-01

    By means of the Legendre transformations in the framework of nonlinear theories of the 4-th order a generalized effective potential GITA(phi, G, H, S) is constructed. It depends on PHI, a possible expectation value of the quantum field; on G, H, possible expectation values of the 2- a.nd 3-point connected Green functions and on S= a possible expectation value of the classical action. The expansion for the functional GITA(phi, G, H, S) is obtained, which is similar to the loop expansion for the effective action GITA(phi)

  13. A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

    KAUST Repository

    Domí nguez, Luis F.; Pistikopoulos, Efstratios N.

    2012-01-01

    An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear

  14. Formal Theory versus Stakeholder Theory: New Insights from a Tobacco-Focused Prevention Program Evaluation

    Science.gov (United States)

    Chen, Huey T.; Turner, Nannette C.

    2012-01-01

    Health promotion and social betterment program interventions are based on either formal theory from academia or stakeholder theory from stakeholders' observations and experiences in working with clients. Over time, formal theory-based interventions have acquired high prestige, while stakeholder theory-based interventions have been held in low…

  15. Nonlinear programming for classification problems in machine learning

    Science.gov (United States)

    Astorino, Annabella; Fuduli, Antonio; Gaudioso, Manlio

    2016-10-01

    We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model. While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.

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

    Science.gov (United States)

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

    2014-12-01

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

  17. Application of nonlinear nodal diffusion generalized perturbation theory to nuclear fuel reload optimization

    International Nuclear Information System (INIS)

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

    1995-01-01

    The determination of the family of optimum core loading patterns for pressurized water reactors (PWRs) involves the assessment of the core attributes for thousands of candidate loading patterns. For this reason, the computational capability to efficiently and accurately evaluate a reactor core's eigenvalue and power distribution versus burnup using a nodal diffusion generalized perturbation theory (GPT) model is developed. The GPT model is derived from the forward nonlinear iterative nodal expansion method (NEM) to explicitly enable the preservation of the finite difference matrix structure. This key feature considerably simplifies the mathematical formulation of NEM GPT and results in reduced memory storage and CPU time requirements versus the traditional response-matrix approach to NEM. In addition, a treatment within NEM GPT can account for localized nonlinear feedbacks, such as that due to fission product buildup and thermal-hydraulic effects. When compared with a standard nonlinear iterative NEM forward flux solve with feedbacks, the NEM GPT model can execute between 8 and 12 times faster. These developments are implemented within the PWR in-core nuclear fuel management optimization code FORMOSA-P, combining the robustness of its adaptive simulated annealing stochastic optimization algorithm with an NEM GPT neutronics model that efficiently and accurately evaluates core attributes associated with objective functions and constraints of candidate loading patterns

  18. Game Theory of Tumor–Stroma Interactions in Multiple Myeloma: Effect of Nonlinear Benefits

    Directory of Open Access Journals (Sweden)

    Javad Salimi Sartakhti

    2018-05-01

    Full Text Available Cancer cells and stromal cells often exchange growth factors with paracrine effects that promote cell growth: a form of cooperation that can be studied by evolutionary game theory. Previous models have assumed that interactions between cells are pairwise or that the benefit of a growth factor is a linear function of its concentration. Diffusible factors, however, affect multiple cells and generally have nonlinear effects, and these differences are known to have important consequences for evolutionary dynamics. Here, we study tumor–stroma paracrine signaling using a model with multiplayer collective interactions in which growth factors have nonlinear effects. We use multiple myeloma as an example, modelling interactions between malignant plasma cells, osteoblasts, and osteoclasts. Nonlinear benefits can lead to results not observed in linear models, including internal mixed stable equilibria and cyclical dynamics. Models with linear effects, therefore, do not lead to a meaningful characterization of the dynamics of tumor–stroma interactions. To understand the dynamics and the effect of therapies it is necessary to estimate the shape of the benefit functions experimentally and parametrize models based on these functions.

  19. Glimpses of soliton theory the algebra and geometry of nonlinear PDEs

    CERN Document Server

    Kasman, Alex

    2010-01-01

    Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstr...

  20. Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory

    International Nuclear Information System (INIS)

    Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi; Yamamoto, Yuki

    2009-01-01

    Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to 'pion' fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.

  1. A neuroeconomic theory of rational addiction and nonlinear time-perception.

    Science.gov (United States)

    Takahashi, Taiki

    2011-01-01

    Neuroeconomic conditions for "rational addiction" (Becker & Murphy 1988) have been unknown. This paper derived the conditions for "rational addiction" by utilizing a nonlinear time-perception theory of "hyperbolic" discounting, which is mathematically equivalent to the q-exponential intertemporal choice model based on Tsallis' statistics. It is shown that (i) Arrow-Pratt measure for temporal cognition corresponds to the degree of irrationality (i.e., Prelec's "decreasing impatience" parameter of temporal discounting) and (ii) rationality in addicts is controlled by a nondimensionalization parameter of the logarithmic time-perception function. Furthermore, the present theory illustrates the possibility that addictive drugs increase impulsivity via dopaminergic neuroadaptation without increasing irrationality. Future directions in the application of the model to studies in neuroeconomics are discussed.

  2. Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models.

    Directory of Open Access Journals (Sweden)

    Ryo Oizumi

    Full Text Available Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.

  3. Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models.

    Science.gov (United States)

    Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi

    2016-01-01

    Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.

  4. TRUMP3-JR: a finite difference computer program for nonlinear heat conduction problems

    International Nuclear Information System (INIS)

    Ikushima, Takeshi

    1984-02-01

    Computer program TRUMP3-JR is a revised version of TRUMP3 which is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Pre- and post-processings for input data generation and graphical representations of calculation results of TRUMP3 are avaiable in TRUMP3-JR. The calculation equations, program descriptions and user's instruction are presented. A sample problem is described to demonstrate the use of the program. (author)

  5. Connection between Einstein equations, nonlinear sigma models, and self-dual Yang-Mills theory

    International Nuclear Information System (INIS)

    Sanchez, N.; Whiting, B.

    1986-01-01

    The authors analyze the connection between nonlinear sigma models self-dual Yang-Mills theory, and general relativity (self-dual and non-self-dual, with and without killing vectors), both at the level of the equations and at the level of the different type of solutions (solitons and calorons) of these theories. They give a manifestly gauge invariant formulation of the self-dual gravitational field analogous to that given by Yang for the self-dual Yang-Mills field. This formulation connects in a direct and explicit way the self-dual Yang-Mills and the general relativity equations. They give the ''R gauge'' parametrization of the self-dual gravitational field (which corresponds to modified Yang's-type and Ernst equations) and analyze the correspondence between their different types of solutions. No assumption about the existence of symmetries in the space-time is needed. For the general case (non-self-dual), they show that the Einstein equations contain an O nonlinear sigma model. This connection with the sigma model holds irrespective of the presence of symmetries in the space-time. They found a new class of solutions of Einstein equations depending on holomorphic and antiholomorphic functions and we relate some subclasses of these solutions to solutions of simpler nonlinear field equations that are well known in other branches of physics, like sigma models, SineGordon, and Liouville equations. They include gravitational plane wave solutions. They analyze the response of different accelerated quantum detector models, compare them to the case when the detectors are linterial in an ordinary Planckian gas at a given temperature, and discuss the anisotropy of the detected response for Rindler observers

  6. Stochastic linear programming models, theory, and computation

    CERN Document Server

    Kall, Peter

    2011-01-01

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

  7. Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

    OpenAIRE

    A. M. de Paor

    1998-01-01

    International audience; Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ? has the value 1 is proved via ...

  8. A program in BASIC for calclation of cavity theory corrections

    International Nuclear Information System (INIS)

    Bugge Christensen, E.; Miller, A.

    1982-05-01

    A program in BASIC for a desk-top calculator HP 9830A is described. The program allows calculation of cavity theory corrections according to Burlin's general cavity theory. The calculations are made by using tabulated values for stopping powers and energy absorption coefficients, stored either as coefficients to a fitted polynomial or as the actual table data. (author)

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

    International Nuclear Information System (INIS)

    Zavaljevski, N.

    1985-01-01

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

  10. Genetic Algorithm for Mixed Integer Nonlinear Bilevel Programming and Applications in Product Family Design

    Directory of Open Access Journals (Sweden)

    Chenlu Miao

    2016-01-01

    Full Text Available Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP, which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard problem. Consequently, using traditional methods to solve such problems is difficult. Genetic algorithms (GAs have great value in solving BLP problems, and many studies have designed GAs to solve BLP problems; however, such GAs are typically designed for special cases that do not involve MINLBLP with one or multiple followers. Therefore, we propose a bilevel GA to solve these particular MINLBLP problems, which are widely used in product family problems. We give numerical examples to demonstrate the effectiveness of the proposed algorithm. In addition, a reducer family case study is examined to demonstrate practical applications of the proposed BLGA.

  11. Research program in elementary particle theory

    International Nuclear Information System (INIS)

    1989-01-01

    The Syracuse High Energy Theory group has continued to make significant contributions to many areas. Many novel aspects of Chern-Simons terms and effective Lagrangians were investigated. Various interesting aspects of quantum gravity and string theory were explored. Gauge models of elementary particles were studied in depth. The investigations of QCD at finite temperatures and multiply connected configuration spaces continued. 24 refs

  12. Testing universal relations of neutron stars with a nonlinear matter-gravity coupling theory

    International Nuclear Information System (INIS)

    Sham, Y.-H.; Lin, L.-M.; Leung, P. T.

    2014-01-01

    Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of NSs can exist. Lau et al. found that the frequency of the f-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Due to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff, we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.

  13. Testing Universal Relations of Neutron Stars with a Nonlinear Matter-Gravity Coupling Theory

    Science.gov (United States)

    Sham, Y.-H.; Lin, L.-M.; Leung, P. T.

    2014-02-01

    Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of NSs can exist. Lau et al. found that the frequency of the f-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Due to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff, we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.

  14. The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread

    International Nuclear Information System (INIS)

    Kong, Ling-Bao; Wang, Hong-Yu; Hou, Zhi-Ling; Jin, Hai-Bo; Du, Chao-Hai

    2013-01-01

    The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained

  15. Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

    Directory of Open Access Journals (Sweden)

    A. M. de Paor

    1998-01-01

    Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.

  16. The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread

    Energy Technology Data Exchange (ETDEWEB)

    Kong, Ling-Bao, E-mail: konglingbao@gmail.com [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Wang, Hong-Yu [School of Physics, Anshan Normal University, Anshan 114005 (China); Hou, Zhi-Ling, E-mail: houzl@mail.buct.edu.cn [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Jin, Hai-Bo [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); Du, Chao-Hai [Institute of Electronics, Chinese Academy of Sciences, Beijing 100190 (China)

    2013-12-15

    The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained.

  17. Non-linear nuclear engineering models as genetic programming application

    International Nuclear Information System (INIS)

    Domingos, Roberto P.; Schirru, Roberto; Martinez, Aquilino S.

    1997-01-01

    This work presents a Genetic Programming paradigm and a nuclear application. A field of Artificial Intelligence, based on the concepts of Species Evolution and Natural Selection, can be understood as a self-programming process where the computer is the main agent responsible for the discovery of a program able to solve a given problem. In the present case, the problem was to find a mathematical expression in symbolic form, able to express the existent relation between equivalent ratio of a fuel cell, the enrichment of fuel elements and the multiplication factor. Such expression would avoid repeatedly reactor physics codes execution for core optimization. The results were compared with those obtained by different techniques such as Neural Networks and Linear Multiple Regression. Genetic Programming has shown to present a performance as good as, and under some features superior to Neural Network and Linear Multiple Regression. (author). 10 refs., 8 figs., 1 tabs

  18. PENNON: A code for convex nonlinear and semidefinite programming

    Czech Academy of Sciences Publication Activity Database

    Kočvara, Michal; Stingl, M.

    2003-01-01

    Roč. 18, č. 3 (2003), s. 317-333 ISSN 1055-6788 R&D Projects: GA ČR GA201/00/0080 Grant - others:BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : convex programming * semidefinite programming * large-scale problems Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.306, year: 2003

  19. Finding a nonlinear lattice with improved integrability using Lie transform perturbation theory

    International Nuclear Information System (INIS)

    Sonnad, Kiran G.; Cary, John R.

    2004-01-01

    A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This condition leads to reduced chaos and improved confinement when compared to a system that is not close to integrability. Numerical calculations of single-particle trajectories and phase space projections of the dynamic aperture performed for a lattice with quadrupoles and sextupoles confirm that this is indeed the case

  20. Turning points in nonlinear business cycle theories, financial crisis and the 2007-2008 downturn.

    Science.gov (United States)

    Dore, Mohammed H I; Singh, Ragiv G

    2009-10-01

    This paper reviews three nonlinear dynamical business cycle theories of which only one (The Goodwin model) reflects the stylized facts of observed business cycles and has a plausible turning point mechanism. The paper then examines the US (and now global) financial crisis of 2008 and the accompanying downturn in the US. The paper argues that a skewed income distribution could not sustain effective demand and that over the 2001-2006 expansion demand was maintained through massive amounts of credit, with more than 50 percent of sales in the US being maintained through credit. A vector autoregression model confirms the crucial role played by credit. However legislative changes that dismantled the restrictions placed on the financial sector after the crash of 1929 and the consequent structural changes in the financial sector after 1980 enabled the growth of new debt instruments and credit. But overexpansion of credit when profits and house prices were declining in 2005/06 led to a nonlinear shift due to a new realization of the poor quality of some of this debt, namely mortgage backed securities. Bankruptcies, followed by retrenchment at the banks, then led to the bursting of the credit bubble, with the possibility of a severe recession.

  1. Nonlinear theory of a cyclotron autoresonance maser (CARM) amplifier with outer-slotted-coaxial waveguide

    International Nuclear Information System (INIS)

    Qiu Chunrong; Ouyang Zhengbiao; Zhang Shichang; Zhang Huibo; Jin Jianbo; Lai Yingxin

    2005-01-01

    A self-consistent nonlinear theory for the outer-slotted-coaxial-waveguide cyclotron autoresonance maser (CARM) amplifier is presented, which includes the characteristic equation of the wave, coupling equation of the wave with the relativistic electron beam and the simulation model. The influences of the magnetic field, the slot depth and width are investigated. The interesting characteristic of the device is that the mode competition can be efficiently suppressed by slotting the outer wall of the coaxial waveguide. A typical example is given by the theoretical design of a 137 GHz outer-slotted-coaxial-waveguide CARM amplifier by utilizing an electron beam with a voltage of 90 kV, current of 50 A, velocity pitch angle of 0.85 and a magnetic field of 43.0 kG. The nonlinear simulation predicts a power of 467.9 kW, an electronic efficiency of 10.4% and a saturated gain of 46.7 dB, if the electron beam has no velocity spread. However, the axial velocity spread deteriorates the device; for example, if the axial velocity spread is 2%, the peak power decreases to 332.4 kW with an efficiency of 7.4% and a saturated gain of 45.22 dB. Simulation shows that the efficiency of the outer-slotted-coaxial-waveguide CARM amplifier may be increased from 10.4% to 29.6% by tapering the magnetic field

  2. Buckling Analysis for Stiffened Anisotropic Circular Cylinders Based on Sanders Nonlinear Shell Theory

    Science.gov (United States)

    Nemeth, Michael P.

    2014-01-01

    Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.

  3. Nonlinear theory of ion-acoustic waves in an ideal plasma with degenerate electrons

    International Nuclear Information System (INIS)

    Dubinov, A. E.; Dubinova, A. A.

    2007-01-01

    A nonlinear theory is constructed that describes steady-state ion-acoustic waves in an ideal plasma in which the electron component is a degenerate Fermi gas and the ion component is a classical gas. The parameter ranges in which such a plasma can exist are determined, and dispersion relations for ion-acoustic waves are obtained that make it possible to find the linear ion-acoustic velocity. Analytic gas-dynamic models of ion sound are developed for a plasma with the ion component as a cold, an isothermal, or an adiabatic gas, and moreover, the solutions to the equations of all the models are brought to a quadrature form. Profiles of a subsonic periodic and a supersonic solitary wave are calculated, and the upper critical Mach numbers of a solitary wave are determined. For a plasma with cold ions, the critical Mach number is expressed by an explicit exact formula

  4. [Analysis of the heart sound with arrhythmia based on nonlinear chaos theory].

    Science.gov (United States)

    Ding, Xiaorong; Guo, Xingming; Zhong, Lisha; Xiao, Shouzhong

    2012-10-01

    In this paper, a new method based on the nonlinear chaos theory was proposed to study the arrhythmia with the combination of the correlation dimension and largest Lyapunov exponent, through computing and analyzing these two parameters of 30 cases normal heart sound and 30 cases with arrhythmia. The results showed that the two parameters of the heart sounds with arrhythmia were higher than those with the normal, and there was significant difference between these two kinds of heart sounds. That is probably due to the irregularity of the arrhythmia which causes the decrease of predictability, and it's more complex than the normal heart sound. Therefore, the correlation dimension and the largest Lyapunov exponent can be used to analyze the arrhythmia and for its feature extraction.

  5. Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.

    Science.gov (United States)

    Levinson, Howard W; Markel, Vadim A

    2016-10-01

    We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.

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

    Science.gov (United States)

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

    2010-12-01

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

  7. Use of Program Theory in a Nutrition Program for Grandchildren and Grandparents

    Science.gov (United States)

    Koenings, Mallory; Arscott, Sara

    2013-01-01

    Grandparents University ® (GPU) is a 2-day campus-based nutrition education program for grandparents and grandchildren based on constructs from Social Cognitive Theory and the Theory of Planned Behavior. This article describes how program theory was used to develop a working model, design activities, and select outcome measures of a 2-day…

  8. A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

    Science.gov (United States)

    Nemeth, Michael P.

    2013-01-01

    A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

  9. The program ORTOCARTAN for applications in the relativity theory

    International Nuclear Information System (INIS)

    Krasinski, A.

    1985-01-01

    A general outline of the program ORTOCARTAN for algebraic computing in the relativity theory is presented. A short history of the program is given. The base-programming language is LISP. The details of the calculation are presented. An example of application of the ORTOCARTAN is given

  10. Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

    Directory of Open Access Journals (Sweden)

    Iman Eshraghi

    2016-09-01

    Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.

  11. A Theory Based Introductory Programming Course

    DEFF Research Database (Denmark)

    Hansen, Michael Reichhardt; Kristensen, Jens Thyge; Rischel, Hans

    1999-01-01

    This paper presents an introductory programming course designed to teach programming as an intellectual activity. The course emphasizes understandable concepts which can be useful in designing programs, while the oddities of today's technology are considered of secondary importance. An important...... goal is to fight the trial-and-error approach to programming which is a result of the students battles with horribly designed and documented systems and languages prior to their studies at university. Instead, the authors strive for giving the students a good experience of programming as a systematic......, intellectual activity where the solution of a programming problem can be described in an understandable way. The approach is illustrated by an example which is a commented solution of a problem posed to the students in the course....

  12. Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems

    Czech Academy of Sciences Publication Activity Database

    Lukšan, Ladislav; Vlček, Jan

    1998-01-01

    Roč. 5, č. 3 (1998), s. 219-247 ISSN 1070-5325 R&D Projects: GA ČR GA201/96/0918 Keywords : nonlinear programming * sparse problems * equality constraints * truncated Newton method * augmented Lagrangian function * indefinite systems * indefinite preconditioners * conjugate gradient method * residual smoothing Subject RIV: BA - General Mathematics Impact factor: 0.741, year: 1998

  13. A nonlinear programming approach to lower bounds for the ground-state energy of helium

    International Nuclear Information System (INIS)

    Porras, I.; Feldmann, D.M.; King, F.W.

    1999-01-01

    Lower-bound estimates for the ground-state energy of the helium atom are determined using nonlinear programming techniques. Optimized lower bounds are determined for single-particle, radially correlated, and general correlated wave functions. The local nature of the method employed makes it a very severe test of the accuracy of the wave function

  14. A Smooth Newton Method for Nonlinear Programming Problems with Inequality Constraints

    Directory of Open Access Journals (Sweden)

    Vasile Moraru

    2012-02-01

    Full Text Available The paper presents a reformulation of the Karush-Kuhn-Tucker (KKT system associated nonlinear programming problem into an equivalent system of smooth equations. Classical Newton method is applied to solve the system of equations. The superlinear convergence of the primal sequence, generated by proposed method, is proved. The preliminary numerical results with a problems test set are presented.

  15. On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

    Science.gov (United States)

    Hall, P.; Malik, M. R.

    1984-01-01

    The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

  16. On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

    Science.gov (United States)

    Hall, P.; Malik, M. R.

    1986-01-01

    The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

  17. On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications

    International Nuclear Information System (INIS)

    Mahmoud, Gamal M; Mahmoud, Emad E; Arafa, Ayman A

    2013-01-01

    In this paper we deal with the projective synchronization (PS) of hyperchaotic complex nonlinear systems and its application in secure communications based on passive theory. The unpredictability of the scaling factor in PS can additionally enhance the security of communications. In this paper, a scheme for secure message transmission is proposed, and we try to transmit more than one large or bounded message from the transmitter to the receiver. The new hyperchaotic complex Lorenz system is employed to encrypt these messages. In the transmitter, the original messages are modulated into its parameter. In the receiver, we assume that the parameter of the receiver system is uncertain. The controllers and corresponding parameter update law are constructed to achieve PS between the transmitter and receiver system with an uncertain parameter, and identify the unknown parameter via passive theory. The original messages can be recovered successfully through some simple operations by the estimated parameter. Numerical results have verified the effectiveness and feasibility of the presented method. (paper)

  18. Theory of coherent Stark nonlinear spectroscopy in a three-level system

    International Nuclear Information System (INIS)

    Loiko, Yurii; Serrat, Carles

    2007-01-01

    Coherent Stark nonlinear spectroscopy (CSNS) is a spectroscopic tool based on the cancellation of the phase sensitivity at frequency 5ω in the ultrafast four-wave mixing (FWM) of two-color pulses with frequencies ω and 3ω. We develop a theory for CSNS in three-level V-type systems, and reveal that the mechanism for the phase sensitivity at 5ω is the quantum interference between the two primary paths in the FWM of the ω and 3ω fields. We find that the cancellation phenomenon occurs when the probability amplitude of one of these two primary pathways becomes equal to zero due to the competition effect between the two allowed transitions in the V-type system. The analytical expressions that describe the phase-sensitivity phenomenon and the conditions for its cancellation have been derived on the basis of perturbation theory, and are confirmed by numerical integration of the density matrix and Maxwell equations. We argue that CSNS can be utilized, in particular, for the investigation of optically dense media

  19. Floyd's principle, correctness theories and program equivalence

    NARCIS (Netherlands)

    Bergstra, J.A.; Tiuryn, J.; Tucker, J.V.

    1982-01-01

    A programming system is a language made from a fixed class of data abstractions and a selection of familiar deterministic control and assignment constructs. It is shown that the sets of all ‘before-after’ first-order assertions which are true of programs in any such language can uniquely determine

  20. Research program in elementary particle theory

    International Nuclear Information System (INIS)

    Balachandran, A.P.; Rosenzweig, C.; Schechter, J.; Wali, K.C.

    1992-01-01

    In this paper we give a brief account of the work of the group during the past year. The topics covered here include (1) Effective Lagrangians and Solitons; (2) Chern-Simons and Conformal Field Theories; (3) Spin and Statistics; (4) The Standard Model and Beyond; (5) Non-Abelian Monopoles; (6) The Inflationary Universe; (7) The Hubbard Model, and (8) Miscellaneous

  1. Research program in elementary particle theory: Outstanding junior investigator program

    International Nuclear Information System (INIS)

    Bowick, M.J.

    1989-01-01

    This report briefly discusses the following topics: high-temperature strings; axionic black holes and wormholes; equations of motion for massless modes as vanishing curvature; vertex algebras and string theory; and massive axions

  2. Genetic programming theory and practice XII

    CERN Document Server

    Riolo, Rick; Kotanchek, Mark

    2015-01-01

    These contributions, written by the foremost international researchers and practitioners of Genetic Programming (GP), explore the synergy between theoretical and empirical results on real-world problems, producing a comprehensive view of the state of the art in GP. Topics in this volume include: gene expression regulation, novel genetic models for glaucoma, inheritable epigenetics, combinators in genetic programming, sequential symbolic regression, system dynamics, sliding window symbolic regression, large feature problems, alignment in the error space, HUMIE winners, Boolean multiplexer funct

  3. Theory and praxis of map analsys in CHEF part 2: Nonlinear normal form

    International Nuclear Information System (INIS)

    Michelotti, Leo

    2009-01-01

    This is the second of three memos describing how normal form map analysis is implemented in CHEF. The first (1) explained the manipulations required to assure that initial, linear transformations preserved Poincare invariants, thereby confirming correct normalization of action-angle coordinates. In this one, the transformation will be extended to nonlinear terms. The third, describing how the algorithms were implemented within the software of CHEF's libraries, most likely will never be written. The first section, Section 2, quickly lays out preliminary concepts and relationships. In Section 3, we shall review the perturbation theory - an iterative sequence of transformations that converts a nonlinear mapping into its normal form - and examine the equation which moves calculations from one step to the next. Following that is a section titled 'Interpretation', which identifies connections between the normalized mappings and idealized, integrable, fictitious Hamiltonian models. A final section contains closing comments, some of which may - but probably will not - preview work to be done later. My reasons for writing this memo and its predecessor have already been expressed. (1) To them can be added this: 'black box code' encourages users to proceed with little or no understanding of what it does or how it operates. So far, CHEF has avoided this trap admirably by failing to attract potential users. However, we reached a watershed last year: even I now have difficulty following the software through its maze of operations. Extensions to CHEF's physics functionalities, software upgrades, and even simple maintenance are becoming more difficult than they should. I hope these memos will mark parts of the maze for easier navigation in the future. Despite appearances to the contrary, I tried to include no (or very little) more than the minimum needed to understand what CHEF's nonlinear analysis modules do.1 As with the first memo, material has been lifted - and modified - from

  4. Theory and praxis of map analsys in CHEF part 2: Nonlinear normal form

    Energy Technology Data Exchange (ETDEWEB)

    Michelotti, Leo; /FERMILAB

    2009-04-01

    This is the second of three memos describing how normal form map analysis is implemented in CHEF. The first [1] explained the manipulations required to assure that initial, linear transformations preserved Poincare invariants, thereby confirming correct normalization of action-angle coordinates. In this one, the transformation will be extended to nonlinear terms. The third, describing how the algorithms were implemented within the software of CHEF's libraries, most likely will never be written. The first section, Section 2, quickly lays out preliminary concepts and relationships. In Section 3, we shall review the perturbation theory - an iterative sequence of transformations that converts a nonlinear mapping into its normal form - and examine the equation which moves calculations from one step to the next. Following that is a section titled 'Interpretation', which identifies connections between the normalized mappings and idealized, integrable, fictitious Hamiltonian models. A final section contains closing comments, some of which may - but probably will not - preview work to be done later. My reasons for writing this memo and its predecessor have already been expressed. [1] To them can be added this: 'black box code' encourages users to proceed with little or no understanding of what it does or how it operates. So far, CHEF has avoided this trap admirably by failing to attract potential users. However, we reached a watershed last year: even I now have difficulty following the software through its maze of operations. Extensions to CHEF's physics functionalities, software upgrades, and even simple maintenance are becoming more difficult than they should. I hope these memos will mark parts of the maze for easier navigation in the future. Despite appearances to the contrary, I tried to include no (or very little) more than the minimum needed to understand what CHEF's nonlinear analysis modules do.1 As with the first memo, material

  5. The Volterra's integral equation theory for accelerator single-freedom nonlinear components

    International Nuclear Information System (INIS)

    Wang Sheng; Xie Xi

    1996-01-01

    The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed

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

    Directory of Open Access Journals (Sweden)

    2007-01-01

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

  7. Nonlinear analysis

    CERN Document Server

    Gasinski, Leszek

    2005-01-01

    Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.

  8. Using a systems orientation and foundational theory to enhance theory-driven human service program evaluations.

    Science.gov (United States)

    Wasserman, Deborah L

    2010-05-01

    This paper offers a framework for using a systems orientation and "foundational theory" to enhance theory-driven evaluations and logic models. The framework guides the process of identifying and explaining operative relationships and perspectives within human service program systems. Self-Determination Theory exemplifies how a foundational theory can be used to support the framework in a wide range of program evaluations. Two examples illustrate how applications of the framework have improved the evaluators' abilities to observe and explain program effect. In both exemplars improvements involved addressing and organizing into a single logic model heretofore seemingly disparate evaluation issues regarding valuing (by whose values); the role of organizational and program context; and evaluation anxiety and utilization. Copyright 2009 Elsevier Ltd. All rights reserved.

  9. Nonlinear Hamiltonian mechanics applied to molecular dynamics theory and computational methods for understanding molecular spectroscopy and chemical reactions

    CERN Document Server

    Farantos, Stavros C

    2014-01-01

    This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.

  10. Research program in elementary particle theory

    International Nuclear Information System (INIS)

    Balachandran, A.P.; Rosenzweig, C.; Schechter, J.; Wali, K.C.

    1990-01-01

    Discussed in this paper is a brief account of the research work of the principal investigators and their co-workers during the past few years. The topics covered include: Topology in Physics; Skyrme Model; High Temperature Superconductivity; fractional statistics, and generalized spin statistics theorem; QCD as a dual chromomagnetic superconductor; confinement and string picture in QCD; quark gluon plasmas; cosmic strings; effective Lagrangians for QCD; ''proton spin,'' ''strange content'' and related topics; physical basis of the Skyrme model; gauge theories and weak interactions; grand unification; Universal ''see saw mechanism''; abelian and non-abelian interactions of a test string

  11. 1981 Magnetic-fusion theory program project summaries

    International Nuclear Information System (INIS)

    1982-02-01

    The theory program supports research projects at three different types of sites: DOE and other government laboratories, universities, and industrial contractors. This report is organized into three sections corresponding to the three types of sites and within each section is organized alphabetically by site name. Summaries of each program are given

  12. Explicating Practicum Program Theory: A Case Example in Human Ecology

    Science.gov (United States)

    Chandler, Kathryn M. M.; Williamson, Deanna L.

    2013-01-01

    This study explicated the theory underpinning the Human Ecology Practicum Program offered in the Department of Human Ecology at the University of Alberta. The program has operated for 40 years but never been formally evaluated. Using a document analysis, focus group and individual interviews, and a stakeholder working group, we explored…

  13. Learning Theories Applied to Teaching Technology: Constructivism versus Behavioral Theory for Instructing Multimedia Software Programs

    Science.gov (United States)

    Reed, Cajah S.

    2012-01-01

    This study sought to find evidence for a beneficial learning theory to teach computer software programs. Additionally, software was analyzed for each learning theory's applicability to resolve whether certain software requires a specific method of education. The results are meant to give educators more effective teaching tools, so students…

  14. The genetic algorithm for the nonlinear programming of water pollution control system

    Energy Technology Data Exchange (ETDEWEB)

    Wei, J.; Zhang, J. [China University of Geosciences (China)

    1999-08-01

    In the programming of water pollution control system the combined method of optimization with simulation is used generally. It is not only laborious in calculation, but also the global optimum of the obtained solution is guaranteed difficult. In this paper, the genetic algorithm (GA) used in the nonlinear programming of water pollution control system is given, by which the preferred conception for the programming of waste water system is found in once-through operation. It is more succinct than the conventional method and the global optimum of the obtained solution could be ensured. 6 refs., 4 figs., 3 tabs.

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

    Science.gov (United States)

    Tutcuoglu, A.; Majidi, C.

    2014-12-01

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

  16. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

    Energy Technology Data Exchange (ETDEWEB)

    Matouš, Karel, E-mail: kmatous@nd.edu [Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556 (United States); Geers, Marc G.D.; Kouznetsova, Varvara G. [Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven (Netherlands); Gillman, Andrew [Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556 (United States)

    2017-02-01

    Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

  17. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

    International Nuclear Information System (INIS)

    Matouš, Karel; Geers, Marc G.D.; Kouznetsova, Varvara G.; Gillman, Andrew

    2017-01-01

    Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

  18. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

    Science.gov (United States)

    Matouš, Karel; Geers, Marc G. D.; Kouznetsova, Varvara G.; Gillman, Andrew

    2017-02-01

    Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

  19. A nonlinear theory of relativistic klystrons connected to a coaxial waveguide

    International Nuclear Information System (INIS)

    Uhm, H.S.; Hendricks, K.J.; Arman, M.J.; Bowers, L.; Hackett, K.E.; Spencer, T.A.; Coleman, P.D.; Lemke, R.W.

    1997-01-01

    A self-consistent nonlinear theory of current modulation in an electron beam propagating through relativistic klystrons connected to a coaxial waveguide is developed. A theoretical model of the beam-energy increase Δγ near the extraction cavity is also developed, based on the self-potential depression. The potential depression κ can be significantly reduced in the vicinity of the extraction cavity from its value at the injection point. In appropriate system parameters, the kinetic-energy increase can easily be more than 50 keV, thereby eliminating the possibility of virtual cathode in the extraction cavity. Properties of the current modulation in a klystron are also investigated, assuming that a regular cylindrical waveguide is connected to a coaxial waveguide at the propagation distance z=z 1 . Due to proximity of a grounded conductor, the beam close-quote s potential depression κ in the coaxial region is considerably less than that in the regular region. It is shown in the present analysis that amplitude of the current modulation increases drastically as the coaxial inner-conductor approaches the driving cavity. Moreover, the amplitude of the current modulation in the coaxial region changes slowly in comparison with that in the regular region

  20. Generalizing a nonlinear geophysical flood theory to medium-sized river networks

    Science.gov (United States)

    Gupta, Vijay K.; Mantilla, Ricardo; Troutman, Brent M.; Dawdy, David; Krajewski, Witold F.

    2010-01-01

    The central hypothesis of a nonlinear geophysical flood theory postulates that, given space-time rainfall intensity for a rainfall-runoff event, solutions of coupled mass and momentum conservation differential equations governing runoff generation and transport in a self-similar river network produce spatial scaling, or a power law, relation between peak discharge and drainage area in the limit of large area. The excellent fit of a power law for the destructive flood event of June 2008 in the 32,400-km2 Iowa River basin over four orders of magnitude variation in drainage areas supports the central hypothesis. The challenge of predicting observed scaling exponent and intercept from physical processes is explained. We show scaling in mean annual peak discharges, and briefly discuss that it is physically connected with scaling in multiple rainfall-runoff events. Scaling in peak discharges would hold in a non-stationary climate due to global warming but its slope and intercept would change.

  1. Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory

    International Nuclear Information System (INIS)

    Pack, M. V.; Camacho, R. M.; Howell, J. C.

    2006-01-01

    We present a theory describing the transients and rise times of the refractive Kerr nonlinearity which is enhanced using electromagnetically induced transparency (EIT). We restrict our analysis to the case of a pulsed signal field with continuous-wave EIT fields, and all fields are well below saturation. These restrictions enable the reduction of an EIT Kerr, four-level, density-matrix equation to a two-level Bloch-vector equation which has a simple and physically intuitive algebraic solution. The physically intuitive picture of a two-level Bloch vector provides insights that are easily generalized to more complex and experimentally realistic models. We consider generalization to the cases of Doppler broadening, many-level EIT systems (we consider the D1 line of 87 Rb), and optically thick media. For the case of optically thick media we find that the rise time of the refractive EIT Kerr effect is proportional to the optical thickness. The rise time of the refractive EIT Kerr effect sets important limitations for potential few-photon applications

  2. Time-dependent density functional theory for nonlinear properties of open-shell systems.

    Science.gov (United States)

    Rinkevicius, Zilvinas; Jha, Prakash Chandra; Oprea, Corneliu I; Vahtras, Olav; Agren, Hans

    2007-09-21

    This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.

  3. CASKETSS-HEAT: a finite difference computer program for nonlinear heat conduction problems

    International Nuclear Information System (INIS)

    Ikushima, Takeshi

    1988-12-01

    A heat conduction program CASKETSS-HEAT has been developed. CASKETSS-HEAT is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Main features of CASKETSS-HEAT are as follows. (1) One, two and three-dimensional geometries for heat conduction calculation are available. (2) Convection and radiation heat transfer of boundry can be specified. (3) Phase change and chemical change can be treated. (4) Finned surface heat transfer can be treated easily. (5) Data memory allocation in the program is variable according to problem size. (6) The program is a compatible heat transfer analysis program to the stress analysis program SAP4 and SAP5. (7) Pre- and post-processing for input data generation and graphic representation of calculation results are available. In the paper, brief illustration of calculation method, input data and sample calculation are presented. (author)

  4. Genetic programming theory and practice X

    CERN Document Server

    Riolo, Rick; Ritchie, Marylyn D; Moore, Jason H

    2013-01-01

    These contributions, written by the foremost international researchers and practitioners of Genetic Programming (GP), explore the synergy between theoretical and empirical results on real-world problems, producing a comprehensive view of the state of the art in GP. Topics in this volume include: evolutionary constraints, relaxation of selection mechanisms, diversity preservation strategies, flexing fitness evaluation, evolution in dynamic environments, multi-objective and multi-modal selection, foundations of evolvability, evolvable and adaptive evolutionary operators, foundation of  injecting

  5. On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

    DEFF Research Database (Denmark)

    True, Hans

    1999-01-01

    We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed......., and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice...

  6. Nonlinear theory of surface-wave--particle interactions in a cylindrical plasma

    International Nuclear Information System (INIS)

    Dengra, A.; Palop, J.I.F.

    1994-01-01

    This work is an application of the specular reflection hypothesis to the study of the nonlinear surface-wave--particle interactions in a cylindrical plasma. The model is based on nonlinear resolution of the Vlasov equation by the method of characteristics. The expression obtained for the rate of increase of kinetic energy per electron has permitted us to investigate the temporal behavior of nonlinear collisionless damping for different situations as a function of the critical parameters

  7. Nonlinear Time Series Prediction Using LS-SVM with Chaotic Mutation Evolutionary Programming for Parameter Optimization

    International Nuclear Information System (INIS)

    Xu Ruirui; Chen Tianlun; Gao Chengfeng

    2006-01-01

    Nonlinear time series prediction is studied by using an improved least squares support vector machine (LS-SVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization. We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.

  8. Nonlinear response time-dependent density functional theory combined with the effective fragment potential method

    Energy Technology Data Exchange (ETDEWEB)

    Zahariev, Federico; Gordon, Mark S., E-mail: mark@si.msg.chem.iastate.edu [Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)

    2014-05-14

    This work presents an extension of the linear response TDDFT/EFP method to the nonlinear-response regime together with the implementation of nonlinear-response TDDFT/EFP in the quantum-chemistry computer package GAMESS. Included in the new method is the ability to calculate the two-photon absorption cross section and to incorporate solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method is able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties.

  9. Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach

    Directory of Open Access Journals (Sweden)

    Olav Slupphaug

    2001-01-01

    Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.

  10. SPSS and SAS programs for generalizability theory analyses.

    Science.gov (United States)

    Mushquash, Christopher; O'Connor, Brian P

    2006-08-01

    The identification and reduction of measurement errors is a major challenge in psychological testing. Most investigators rely solely on classical test theory for assessing reliability, whereas most experts have long recommended using generalizability theory instead. One reason for the common neglect of generalizability theory is the absence of analytic facilities for this purpose in popular statistical software packages. This article provides a brief introduction to generalizability theory, describes easy to use SPSS, SAS, and MATLAB programs for conducting the recommended analyses, and provides an illustrative example, using data (N = 329) for the Rosenberg Self-Esteem Scale. Program output includes variance components, relative and absolute errors and generalizability coefficients, coefficients for D studies, and graphs of D study results.

  11. Time Domain Modeling and Simulation of Nonlinear Slender Viscoelastic Beams Associating Cosserat Theory and a Fractional Derivative Model

    Directory of Open Access Journals (Sweden)

    Adailton S. Borges

    Full Text Available Abstract A broad class of engineering systems can be satisfactory modeled under the assumptions of small deformations and linear material properties. However, many mechanical systems used in modern applications, like structural elements typical of aerospace and petroleum industries, have been characterized by increased slenderness and high static and dynamic loads. In such situations, it becomes indispensable to consider the nonlinear geometric effects and/or material nonlinear behavior. At the same time, in many cases involving dynamic loads, there comes the need for attenuation of vibration levels. In this context, this paper describes the development and validation of numerical models of viscoelastic slender beam-like structures undergoing large displacements. The numerical approach is based on the combination of the nonlinear Cosserat beam theory and a viscoelastic model based on Fractional Derivatives. Such combination enables to derive nonlinear equations of motion that, upon finite element discretization, can be used for predicting the dynamic behavior of the structure in the time domain, accounting for geometric nonlinearity and viscoelastic damping. The modeling methodology is illustrated and validated by numerical simulations, the results of which are compared to others available in the literature.

  12. An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

    Science.gov (United States)

    Neilson, Peter D; Neilson, Megan D

    2005-09-01

    Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

  13. Assessment of non-linear analysis finite element program (NONSAP) for inelastic analysis

    International Nuclear Information System (INIS)

    Chang, T.Y.; Prachuktam, S.; Reich, M.

    1976-11-01

    An assessment on a nonlinear structural analysis finite element program called NONSAP is given with respect to its inelastic analysis capability for pressure vessels and components. The assessment was made from the review of its theoretical basis and bench mark problem runs. It was found that NONSAP has only limited capability for inelastic analysis. However, the program was written flexible enough that it can be easily extended or modified to suit the user's need. Moreover, some of the numerical difficulties in using NONSAP are pointed out

  14. Online Financial Education Programs: Theory, Research, and Recommendations

    Directory of Open Access Journals (Sweden)

    Jinhee Kim

    2017-03-01

    Full Text Available Technological advances have created unprecedented opportunities for online financial education that can be used to improve financial literacy and money management practices. While online financial education programs have become popular, relevant research and theoretical frameworks have rarely been considered in the development of such programs. This article synthesizes lessons from literature and theories for the development of an effective online financial education program. Drawing from literature on financial literacy education and online education, implications and recommendations for integrating technology into online financial education programs for adults are discussed.

  15. Technical program to study the benefits of nonlinear analysis methods in LWR component designs. Technical report TR-3723-1

    International Nuclear Information System (INIS)

    Raju, P.P.

    1980-05-01

    This report summarizes the results of the study program to assess the benefits of nonlinear analysis methods in Light Water Reactor (LWR) component designs. The current study reveals that despite its increased cost and other complexities, nonlinear analysis is a practical and valuable tool for the design of LWR components, especially under ASME Level D service conditions (faulted conditions) and it will greatly assist in the evaluation of ductile fracture potential of pressure boundary components. Since the nonlinear behavior is generally a local phenomenon, the design of complex components can be accomplished through substructuring isolated localized regions and evaluating them in detail using nonlinear analysis methods

  16. Mathematical programming and game theory for decision making

    CERN Document Server

    Bapat, R B; Das, A K; Parthasarathy, T

    2008-01-01

    This edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel pro

  17. The Development of a Program Engagement Theory for Group Offending Behavior Programs.

    Science.gov (United States)

    Holdsworth, Emma; Bowen, Erica; Brown, Sarah; Howat, Douglas

    2017-10-01

    Offender engagement in group offending behavior programs is poorly understood and under-theorized. In addition, there is no research on facilitators' engagement. This article presents the first ever theory to address this gap. A Program Engagement Theory (PET) was derived from a constructivist grounded theory analysis that accounts for both facilitators' and offenders' engagement in group offending behavior programs (GOBPs). Interviews and session observations were used to collect data from 23 program facilitators and 28 offenders (group members). The analysis revealed that group members' engagement involved shared identities and moving on as a group. In turn, this was dependent on facilitators personalising treatment frameworks and establishing a hook to help group members move on. The PET emphasizes the importance of considering change during treatment as a process rather than simply a program outcome. Solution-focused (SF) programs were more conducive to engagement and the change process than offence-focused programs.

  18. Electron beam instabilities in unmagnetized plasmas via the Stieltjes transform (linear theory and nonlinear mode coupling)

    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

  19. Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

    Energy Technology Data Exchange (ETDEWEB)

    Klimachkov, D. A., E-mail: klimchakovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru [Russian Academy of Sciences, Space Research Institute (Russian Federation)

    2016-09-15

    Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the

  20. The complement of research and theory in practice: contact theory at work in nonfamilial intergenerational programs.

    Science.gov (United States)

    Jarrott, Shannon E; Smith, Cynthia L

    2011-02-01

    We assessed whether a shared site intergenerational care program informed by contact theory contributed to more desirable social behaviors of elders and children during intergenerational programming than a center with a more traditional programming approach that lacks some or all of the contact theory tenets. We observed 59 elder and child participants from the two sites during intergenerational activities. Using the Intergenerational Observation Scale, we coded participants' predominant behavior in 15-s intervals through each activity's duration. We then calculated for each individual the percentage of time frames each behavior code was predominant. Participants at the theory-based program demonstrated higher rates of intergenerational interaction, higher rates of solitary behavior, and lower rates of watching than at the traditional program. Contact theory tenets were optimized when coupled with evidence-based practices. Intergenerational programs with stakeholder support that promotes equal group status, cooperation toward a common goal, and mechanisms of friendship among participants can achieve important objectives for elder and child participants in care settings.

  1. Nonlinear adaptive robust back stepping force control of hydraulic load simulator: Theory and experiments

    International Nuclear Information System (INIS)

    Yao, Jianyong; Jiao, Zongxia; Yao, Bin

    2014-01-01

    High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.

  2. Nonlinear adaptive robust back stepping force control of hydraulic load simulator: Theory and experiments

    Energy Technology Data Exchange (ETDEWEB)

    Yao, Jianyong [Nanjing University of Science and Technology, Nanjing (China); Jiao, Zongxia [Beihang University, Beijing (China); Yao, Bin [Purdue University, West Lafayette (United States)

    2014-04-15

    High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.

  3. Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment

    International Nuclear Information System (INIS)

    Sousa, V C; De M Anicézio, M; De Marqui Jr, C; Erturk, A

    2011-01-01

    Converting aeroelastic vibrations into electricity for low power generation has received growing attention over the past few years. In addition to potential applications for aerospace structures, the goal is to develop alternative and scalable configurations for wind energy harvesting to use in wireless electronic systems. This paper presents modeling and experiments of aeroelastic energy harvesting using piezoelectric transduction with a focus on exploiting combined nonlinearities. An airfoil with plunge and pitch degrees of freedom (DOF) is investigated. Piezoelectric coupling is introduced to the plunge DOF while nonlinearities are introduced through the pitch DOF. A state-space model is presented and employed for the simulations of the piezoaeroelastic generator. A two-state approximation to Theodorsen aerodynamics is used in order to determine the unsteady aerodynamic loads. Three case studies are presented. First the interaction between piezoelectric power generation and linear aeroelastic behavior of a typical section is investigated for a set of resistive loads. Model predictions are compared to experimental data obtained from the wind tunnel tests at the flutter boundary. In the second case study, free play nonlinearity is added to the pitch DOF and it is shown that nonlinear limit-cycle oscillations can be obtained not only above but also below the linear flutter speed. The experimental results are successfully predicted by the model simulations. Finally, the combination of cubic hardening stiffness and free play nonlinearities is considered in the pitch DOF. The nonlinear piezoaeroelastic response is investigated for different values of the nonlinear-to-linear stiffness ratio. The free play nonlinearity reduces the cut-in speed while the hardening stiffness helps in obtaining persistent oscillations of acceptable amplitude over a wider range of airflow speeds. Such nonlinearities can be introduced to aeroelastic energy harvesters (exploiting

  4. The nonlinear finite element analysis program NUCAS (NUclear Containment Analysis System) for reinforced concrete containment building

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Sang Jin; Lee, Hong Pyo; Seo, Jeong Moon [Korea Atomic Energy Research Institute, Taejeon (Korea)

    2002-03-01

    The maim goal of this research is to develop a nonlinear finite element analysis program NUCAS to accurately predict global and local failure modes of containment building subjected to internal pressure. In this report, we describe the techniques we developed throught this research. An adequate model to the analysis of containment building such as microscopic material model is adopted and it applied into the development Reissner-Mindlin degenerated shell element. To avoid finite element deficiencies, the substitute strains based on the assumed strain method is used in the shell formulation. Arc-length control method is also adopted to fully trace the peak load-displacement path due to crack formation. In addition, a benchmark test suite is developed to investigate the performance of NUCAS and proposed as the future benchmark tests for nonlinear analysis of reinforced concrete. Finally, the input format of NUCAS and the examples of input/output file are described. 39 refs., 65 figs., 8 tabs. (Author)

  5. Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming

    Science.gov (United States)

    Liu, Derong; Huang, Yuzhu; Wang, Ding; Wei, Qinglai

    2013-09-01

    In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

  6. Towards a Theory for Testing Non-terminating Programs

    DEFF Research Database (Denmark)

    Gotlieb, Arnaud; Petit, Matthieu

    2009-01-01

    Non-terminating programs are programs that legally perform unbounded computations. Though they are ubiquitous in real-world applications, testing these programs requires new theoretic developments as usual definitions of test data adequacy criteria ignore infinite paths. This paper develops...... a theory of program-based structural testing based on operational semantics. Reasoning at the program semantics level permits to cope with infinite paths (and non-feasible paths) when defining test data adequacy criteria. As a result, our criteria respect the first Weyuker’s property on finite...... applicability, even for non-terminating programs. We discuss the consequences of this re-interpretation of test data adequacy criteria w.r.t. existing test coverage criteria....

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

    DEFF Research Database (Denmark)

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

    2016-01-01

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

  8. Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1

    International Nuclear Information System (INIS)

    Krivitsky, V.S.; Vladimirov, S.V.

    1991-01-01

    An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a 'direct' nonlinear interaction of particles and waves, and the influence of the non-stationary of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one. (author)

  9. Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

    Science.gov (United States)

    Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping

    2018-01-01

    An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

  10. The Behavior Intervention Support Team (BIST) Program: Underlying Theories

    Science.gov (United States)

    Boulden, Walter T.

    2010-01-01

    The Behavior Intervention Support Team (BIST) is a proactive school-wide behavior management plan for all students, emphasizing schools partnering with students and parents through caring relationships and high expectations. The BIST program is well-grounded in behavioral theory and combines strength-based and resiliency principles within the…

  11. Theory and analysis of nonlinear dynamics and stability in storage rings: A working group summary

    International Nuclear Information System (INIS)

    Chattopadhyay, S.; Audy, P.; Courant, E.D.

    1988-07-01

    A summary and commentary of the available theoretical and analytical tools and recent advances in the nonlinear dynamics, stability and aperture issues in storage rings are presented. 11 refs., 4 figs

  12. Stability of the static solitons in a pure spinor theory with fractional power nonlinearities

    International Nuclear Information System (INIS)

    Akdeniz, K.G.; Tezgor, G.; Barut, A.O.; Kalayci, J.; Okan, S.E.

    1988-08-01

    Soliton solutions are obtained in a pure fermionic model with fractional power nonlinear self-interactions. The stability properties of the minimum solutions have also been investigated within the framework of the Shatah-Strauss formalism. (author). 10 refs

  13. 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

  14. Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

    Science.gov (United States)

    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.

  15. Stability analysis of nonlinear autonomous systems - General theory and application to flutter

    Science.gov (United States)

    Smith, L. L.; Morino, L.

    1975-01-01

    The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

  16. Density nonlinearities and a field theory for the dynamics of simple fluids

    OpenAIRE

    Mazenko, Gene F.; Yeo, Joonhyun

    1994-01-01

    We study the role of the Jacobian arising from a constraint enforcing the nonlinear relation: ${\\bf g}=\\rho{\\bf V}$, where $\\rho,\\: {\\bf g}$ and ${\\bf V}$ are the mass density, the momentum density and the local velocity field, respectively, in the field theoretic formulation of the nonlinear fluctuating hydrodynamics of simple fluids. By investigating the Jacobian directly and by developing a field theoretic formulation without the constraint, we find that no changes in dynamics result as co...

  17. Introduction to nonlinear finite element analysis

    CERN Document Server

    Kim, Nam-Ho

    2015-01-01

    This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

  18. Algebraic computing program for studying the gauge theory

    International Nuclear Information System (INIS)

    Zet, G.

    2005-01-01

    An algebraic computing program running on Maple V platform is presented. The program is devoted to the study of the gauge theory with an internal Lie group as local symmetry. The physical quantities (gauge potentials, strength tensors, dual tensors etc.) are introduced either as equations in terms of previous defined quantities (tensors), or by manual entry of the component values. The components of the strength tensor and of its dual are obtained with respect to a given metric of the space-time used for describing the gauge theory. We choose a Minkowski space-time endowed with spherical symmetry and give some example of algebraic computing that are adequate for studying electroweak or gravitational interactions. The field equations are also obtained and their solutions are determined using the DEtools facilities of the Maple V computing program. (author)

  19. Intuitionistic Fuzzy Goal Programming Technique for Solving Non-Linear Multi-objective Structural Problem

    Directory of Open Access Journals (Sweden)

    Samir Dey

    2015-07-01

    Full Text Available This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.

  20. General Rotorcraft Aeromechanical Stability Program (GRASP): Theory manual

    Science.gov (United States)

    Hodges, Dewey H.; Hopkins, A. Stewart; Kunz, Donald L.; Hinnant, Howard E.

    1990-01-01

    The general rotorcraft aeromechanical stability program (GRASP) was developed to calculate aeroelastic stability for rotorcraft in hovering flight, vertical flight, and ground contact conditions. GRASP is described in terms of its capabilities and its philosophy of modeling. The equations of motion that govern the physical system are described, as well as the analytical approximations used to derive them. The equations include the kinematical equation, the element equations, and the constraint equations. In addition, the solution procedures used by GRASP are described. GRASP is capable of treating the nonlinear static and linearized dynamic behavior of structures represented by arbitrary collections of rigid-body and beam elements. These elements may be connected in an arbitrary fashion, and are permitted to have large relative motions. The main limitation of this analysis is that periodic coefficient effects are not treated, restricting rotorcraft flight conditions to hover, axial flight, and ground contact. Instead of following the methods employed in other rotorcraft programs. GRASP is designed to be a hybrid of the finite-element method and the multibody methods used in spacecraft analysis. GRASP differs from traditional finite-element programs by allowing multiple levels of substructure in which the substructures can move and/or rotate relative to others with no small-angle approximations. This capability facilitates the modeling of rotorcraft structures, including the rotating/nonrotating interface and the details of the blade/root kinematics for various types. GRASP differs from traditional multibody programs by considering aeroelastic effects, including inflow dynamics (simple unsteady aerodynamics) and nonlinear aerodynamic coefficients.

  1. Trajectory Planning of Satellite Formation Flying using Nonlinear Programming and Collocation

    Directory of Open Access Journals (Sweden)

    Hyung-Chu Lim

    2008-12-01

    Full Text Available Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a large spacecraft. Some techniques have been proposed to design optimal formation trajectories minimizing fuel consumption in the process of formation configuration or reconfiguration. In this study, a method is introduced to build fuel-optimal trajectories minimizing a cost function that combines the total fuel consumption of all satellites and assignment of fuel consumption rate for each satellite. This approach is based on collocation and nonlinear programming to solve constraints for collision avoidance and the final configuration. New constraints of nonlinear equality or inequality are derived for final configuration, and nonlinear inequality constraints are established for collision avoidance. The final configuration constraints are that three or more satellites should form a projected circular orbit and make an equilateral polygon in the horizontal plane. Example scenarios, including these constraints and the cost function, are simulated by the method to generate optimal trajectories for the formation configuration and reconfiguration of multiple satellites.

  2. Multiscale asymmetric orthogonal wavelet kernel for linear programming support vector learning and nonlinear dynamic systems identification.

    Science.gov (United States)

    Lu, Zhao; Sun, Jing; Butts, Kenneth

    2014-05-01

    Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

  3. NASA's Heliophysics Theory Program - Accomplishments in Life Cycle Ending 2011

    Science.gov (United States)

    Grebowsky, J.

    2011-01-01

    NASA's Heliophysics Theory Program (HTP) is now into a new triennial cycle of funded research, with new research awards beginning in 2011. The theory program was established by the (former) Solar Terrestrial Division in 1980 to redress a weakness of support in the theory area. It has been a successful, evolving scientific program with long-term funding of relatively large "critical mass groups" pursuing theory and modeling on a scale larger than that available within the limits of traditional NASA Supporting Research and Technology (SR&T) awards. The results of the last 3 year funding cycle, just ended, contributed to ever more cutting edge theoretical understanding of all parts of the Sun-Earth Connection chain. Advances ranged from the core of the Sun out into the corona, through the solar wind into the Earth's magnetosphere and down to the ionosphere and lower atmosphere, also contributing to understanding the environments of other solar system bodies. The HTP contributions were not isolated findings but continued to contribute to the planning and implementation of NASA spacecraft missions and to the development of the predictive computer models that have become the workhorses for analyzing satellite and ground-based measurements.

  4. Dynamic pull-in instability of geometrically nonlinear actuated micro-beams based on the modified couple stress theory

    Directory of Open Access Journals (Sweden)

    Hamid M. Sedighi

    Full Text Available This paper investigates the dynamic pull-in instability of vibrating micro-beams undergoing large deflection under electrosatically actuation. The governing equation of motion is derived based on the modified couple stress theory. Homotopy Perturbation Method is employed to produce the high accuracy approximate solution as well as the second-order frequency- amplitude relationship. The nonlinear governing equation of micro beam vibrations predeformed by an electric field includes both even and odd nonlinearities. The influences of basic non-dimensional parameters on the pull-in instability as well as the natural frequency are studied. It is demonstrated that two terms in series expansions are sufficient to produce high accuracy solution of the micro-structure. The accuracy of proposed asymptotic approach is validated via numerical results. The phase portrait of the system exhibits periodic and homoclinic orbits.

  5. H∞ Excitation Control Design for Stochastic Power Systems with Input Delay Based on Nonlinear Hamiltonian System Theory

    Directory of Open Access Journals (Sweden)

    Weiwei Sun

    2015-01-01

    Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.

  6. Computational Performance Analysis of Nonlinear Dynamic Systems using Semi-infinite Programming

    Directory of Open Access Journals (Sweden)

    Tor A. Johansen

    2001-01-01

    Full Text Available For nonlinear systems that satisfy certain regularity conditions it is shown that upper and lower bounds on the performance (cost function can be computed using linear or quadratic programming. The performance conditions derived from Hamilton-Jacobi inequalities are formulated as linear inequalities defined pointwise by discretizing the state-space when assuming a linearly parameterized class of functions representing the candidate performance bounds. Uncertainty with respect to some system parameters can be incorporated by also gridding the parameter set. In addition to performance analysis, the method can also be used to compute Lyapunov functions that guarantees uniform exponential stability.

  7. Linear combination of forecasts with numerical adjustment via MINIMAX non-linear programming

    Directory of Open Access Journals (Sweden)

    Jairo Marlon Corrêa

    2016-03-01

    Full Text Available This paper proposes a linear combination of forecasts obtained from three forecasting methods (namely, ARIMA, Exponential Smoothing and Artificial Neural Networks whose adaptive weights are determined via a multi-objective non-linear programming problem, which seeks to minimize, simultaneously, the statistics: MAE, MAPE and MSE. The results achieved by the proposed combination are compared with the traditional approach of linear combinations of forecasts, where the optimum adaptive weights are determined only by minimizing the MSE; with the combination method by arithmetic mean; and with individual methods

  8. Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming

    DEFF Research Database (Denmark)

    Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven

    2005-01-01

    The design of sheet pile walls by lower bound limit analysis is considered. The design problem involves the determination of the necessary yield moment of the wall, the wall depth and the anchor force such that the structure is able to sustain the given loads. This problem is formulated...... as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....

  9. An application of nonlinear programming to the design of regulators of a linear-quadratic formulation

    Science.gov (United States)

    Fleming, P.

    1983-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

  10. A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

    Science.gov (United States)

    Li, Jinquan; Feng, Shuang; Mi, Honghai

    In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.

  11. Nonlinear evolution of the matter power spectrum in modified theories of gravity

    International Nuclear Information System (INIS)

    Koyama, Kazuya; Taruya, Atsushi; Hiramatsu, Takashi

    2009-01-01

    We present a formalism to calculate the nonlinear matter power spectrum in modified gravity models that explain the late-time acceleration of the Universe without dark energy. Any successful modified gravity models should contain a mechanism to recover general relativity (GR) on small scales in order to avoid the stringent constrains on deviations from GR at solar system scales. Based on our formalism, the quasi-nonlinear power spectrum in the Dvali-Gabadadze-Porratti braneworld models and f(R) gravity models are derived by taking into account the mechanism to recover GR properly. We also extrapolate our predictions to fully nonlinear scales using the parametrized post-Friedmann framework. In the Dvali-Gabadadze-Porratti and f(R) gravity models, the predicted nonlinear power spectrum is shown to reproduce N-body results. We find that the mechanism to recover GR suppresses the difference between the modified gravity models and dark energy models with the same expansion history, but the difference remains large at the weakly nonlinear regime in these models. Our formalism is applicable to a wide variety of modified gravity models and it is ready to use once consistent models for modified gravity are developed.

  12. SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

    Energy Technology Data Exchange (ETDEWEB)

    Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

    1998-08-01

    This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.

  13. Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer

    Science.gov (United States)

    Pikichyan, H. V.

    2017-07-01

    In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.

  14. Nonlinear Analysis of Rotors Supported by Air Foil Journal Bearings – Theory and Experiments

    DEFF Research Database (Denmark)

    Larsen, Jon Steffen

    with a good margin of rotordynamical stable operation. To ensure this, good mathematical models, capable of accurately predicting the dynamic behaviour of the rotor-bearing system, are required at the design stage. This thesis focuses on developing and improving existing mathematical models for predicting...... mechanical behaviour of the bump foils was carefully examined. A mathematical model capable of predicting this nonlinear behaviour was developed and compared to the experimental results with good agreement. With the second test rig, the overall nonlinear behaviour of the rotor-bearing system was investigated...

  15. Nonlinear systems

    National Research Council Canada - National Science Library

    Drazin, P. G

    1992-01-01

    This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...

  16. A theory-informed, process-oriented Resident Scholarship Program.

    Science.gov (United States)

    Thammasitboon, Satid; Darby, John B; Hair, Amy B; Rose, Karen M; Ward, Mark A; Turner, Teri L; Balmer, Dorene F

    2016-01-01

    The Accreditation Council for Graduate Medical Education requires residency programs to provide curricula for residents to engage in scholarly activities but does not specify particular guidelines for instruction. We propose a Resident Scholarship Program that is framed by the self-determination theory (SDT) and emphasize the process of scholarly activity versus a scholarly product. The authors report on their longitudinal Resident Scholarship Program, which aimed to support psychological needs central to SDT: autonomy, competence, and relatedness. By addressing those needs in program aims and program components, the program may foster residents' intrinsic motivation to learn and to engage in scholarly activity. To this end, residents' engagement in scholarly processes, and changes in perceived autonomy, competence, and relatedness were assessed. Residents engaged in a range of scholarly projects and expressed positive regard for the program. Compared to before residency, residents felt more confident in the process of scholarly activity, as determined by changes in increased perceived autonomy, competence, and relatedness. Scholarly products were accomplished in return for a focus on scholarly process. Based on our experience, and in line with the SDT, supporting residents' autonomy, competence, and relatedness through a process-oriented scholarship program may foster the curiosity, inquisitiveness, and internal motivation to learn that drives scholarly activity and ultimately the production of scholarly products.

  17. A theory-informed, process-oriented Resident Scholarship Program

    Science.gov (United States)

    Thammasitboon, Satid; Darby, John B.; Hair, Amy B.; Rose, Karen M.; Ward, Mark A.; Turner, Teri L.; Balmer, Dorene F.

    2016-01-01

    Background The Accreditation Council for Graduate Medical Education requires residency programs to provide curricula for residents to engage in scholarly activities but does not specify particular guidelines for instruction. We propose a Resident Scholarship Program that is framed by the self-determination theory (SDT) and emphasize the process of scholarly activity versus a scholarly product. Methods The authors report on their longitudinal Resident Scholarship Program, which aimed to support psychological needs central to SDT: autonomy, competence, and relatedness. By addressing those needs in program aims and program components, the program may foster residents’ intrinsic motivation to learn and to engage in scholarly activity. To this end, residents’ engagement in scholarly processes, and changes in perceived autonomy, competence, and relatedness were assessed. Results Residents engaged in a range of scholarly projects and expressed positive regard for the program. Compared to before residency, residents felt more confident in the process of scholarly activity, as determined by changes in increased perceived autonomy, competence, and relatedness. Scholarly products were accomplished in return for a focus on scholarly process. Conclusions Based on our experience, and in line with the SDT, supporting residents’ autonomy, competence, and relatedness through a process-oriented scholarship program may foster the curiosity, inquisitiveness, and internal motivation to learn that drives scholarly activity and ultimately the production of scholarly products. PMID:27306995

  18. A nonlinear bi-level programming approach for product portfolio management.

    Science.gov (United States)

    Ma, Shuang

    2016-01-01

    Product portfolio management (PPM) is a critical decision-making for companies across various industries in today's competitive environment. Traditional studies on PPM problem have been motivated toward engineering feasibilities and marketing which relatively pay less attention to other competitors' actions and the competitive relations, especially in mathematical optimization domain. The key challenge lies in that how to construct a mathematical optimization model to describe this Stackelberg game-based leader-follower PPM problem and the competitive relations between them. The primary work of this paper is the representation of a decision framework and the optimization model to leverage the PPM problem of leader and follower. A nonlinear, integer bi-level programming model is developed based on the decision framework. Furthermore, a bi-level nested genetic algorithm is put forward to solve this nonlinear bi-level programming model for leader-follower PPM problem. A case study of notebook computer product portfolio optimization is reported. Results and analyses reveal that the leader-follower bi-level optimization model is robust and can empower product portfolio optimization.

  19. Comparison of linear, mixed integer and non-linear programming methods in energy system dispatch modelling

    DEFF Research Database (Denmark)

    Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian

    2014-01-01

    In the paper, three frequently used operation optimisation methods are examined with respect to their impact on operation management of the combined utility technologies for electric power and DH (district heating) of eastern Denmark. The investigation focusses on individual plant operation...... differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... as a benchmark, as this type is frequently used, and has the lowest amount of constraints of the three. A comparison of the optimised operation of a number of units shows significant differences between the three methods. Compared to the reference, the use of binary integer variables, increases operation...

  20. Adaptive Event-Triggered Control Based on Heuristic Dynamic Programming for Nonlinear Discrete-Time Systems.

    Science.gov (United States)

    Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo

    2017-07-01

    This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.

  1. 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

  2. Nonlinear optical response in condensed phases : A microscopic theory using the multipolar Hamiltonian

    NARCIS (Netherlands)

    Knoester, Jasper; Mukamel, Shaul

    1990-01-01

    A general scheme is presented for calculating the nonlinear optical response in condensed phases that provides a unified picture of excitons, polaritons, retardation, and local-field effects in crystals and in disordered systems. A fully microscopic starting point is taken by considering the

  3. Kinetic theory of nonlinear viscous flow in two and three dimensions

    NARCIS (Netherlands)

    Ernst, M.H.; Cichocki, B.; Dorfman, J.R.; Sharma, J.; Beijeren, H. van

    1978-01-01

    On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form ¦X¦3/2 for hard spheres, or ¦X¦ log ¦X¦ for hard disks. HereX is

  4. Prognostic value of Poincare plot as nonlinear parameter of chaos theory in patients with myocardial infarction

    Directory of Open Access Journals (Sweden)

    Milovanović Branislav

    2007-01-01

    Full Text Available Introduction: There are different proofs about association of autonomic nervous system dysfunction, especially nonlinear parameters, with higher mortality after myocardial infarction. Objective The objective of the study was to determine predictive value of Poincare plot as nonlinear parameter and other significant standard risk predictors: ejection fraction of the left ventricle, late potentials, ventricular arrhythmias, and QT interval. Method The study included 1081 patients with mean follow up of 28 months (ranging fom 0-80 months. End-point of the study was cardiovascular mortality. The following diagnostic methods were used during the second week: ECG with commercial software Schiller AT-10: short time spectral analysis of RR variability with analysis of Poincare plot as nonlinear parameter and late potentials; 24-hour ambulatory ECG monitoring: QT interval, RR interval, QT/RR slope, ventricular arrhythmias (Lown >II; echocardiography examinations: systolic disorder (defined as EF<40 %. Results There were 103 (9.52% cardiovascular deaths during the follow-up. In univariate analysis, the following parameters were significantly correlated with mortality: mean RR interval < 800 ms, QT and RR interval space relationship as mean RR interval < 800 ms and QT interval > 350 ms, positive late potentials, systolic dysfunction, Poincare plot as a point, ventricular arrhythmias (Lown > II. In multivariate analysis, the significant risk predictors were: Poincare plot as a point and mean RR interval lower than 800 ms. Conclusion Mean RR interval lower than 800 ms and nonlinear and space presentation of RR interval as a point Poincare plot were multivariate risk predictors.

  5. General purpose nonlinear analysis program FINAS for elevated temperature design of FBR components

    International Nuclear Information System (INIS)

    Iwata, K.; Atsumo, H.; Kano, T.; Takeda, H.

    1982-01-01

    This paper presents currently available capabilities of a general purpose finite element nonlinear analysis program FINAS (FBR Inelastic Structural Analysis System) which has been developed at Power Reactor and Nuclear Fuel Development Corporation (PNC) since 1976 to support structural design of fast breeder reactor (FBR) components in Japan. This program is capable of treating inelastic responses of arbitrary complex structures subjected to static and dynamic load histories. Various types of finite element covering rods, beams, pipes, axisymmetric, two and three dimensional solids, plates and shells, are implemented in the program. The thermal elastic-plastic creep analysis is possible for each element type, with primary emphasis on the application to FBR components subjected to sustained or cyclic loads at elevated temperature. The program permits large deformation, buckling, fracture mechanics, and dynamic analyses for some of the element types and provides a number of options for automatic mesh generation and computer graphics. Some examples including elevated temperature effects are shown to demonstrate the accuracy and the efficiency of the program

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

    International Nuclear Information System (INIS)

    Esmaeilzadeh Khadem, S.; Rezaee, M.

    2001-01-01

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

  7. Nonlinear theory for axisymmetric self-similar two-dimensional oscillations of electrons in cold plasma with constant proton background

    Science.gov (United States)

    Osherovich, V. A.; Fainberg, J.

    2018-01-01

    We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.

  8. Nonlinear Aeroelastic Analysis of the HIAD TPS Coupon in the NASA 8' High Temperature Tunnel: Theory and Experiment

    Science.gov (United States)

    Goldman, Benjamin D.; Scott, Robert C,; Dowell, Earl H.

    2014-01-01

    The purpose of this work is to develop a set of theoretical and experimental techniques to characterize the aeroelasticity of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A square TPS coupon experiences trailing edge oscillatory behavior during experimental testing in the 8' High Temperature Tunnel (HTT), which may indicate the presence of aeroelastic flutter. Several theoretical aeroelastic models have been developed, each corresponding to a different experimental test configuration. Von Karman large deflection theory is used for the plate-like components of the TPS, along with piston theory for the aerodynamics. The constraints between the individual TPS layers and the presence of a unidirectional foundation at the back of the coupon are included by developing the necessary energy expressions and using the Rayleigh Ritz method to derive the nonlinear equations of motion. Free vibrations and limit cycle oscillations are computed and the frequencies and amplitudes are compared with accelerometer and photogrammetry data from the experiments.

  9. Nonlinear Science

    CERN Document Server

    Yoshida, Zensho

    2010-01-01

    This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl

  10. Evaluation of specific heat for superfluid helium between 0 - 2.1 K based on nonlinear theory

    International Nuclear Information System (INIS)

    Sasaki, Shosuke

    2009-01-01

    The specific heat of liquid helium was calculated theoretically in the Landau theory. The results deviate from experimental data in the temperature region of 1.3 - 2.1 K. Many theorists subsequently improved the results of the Landau theory by applying temperature dependence of the elementary excitation energy. As well known, many-body system has a total energy of Galilean covariant form. Therefore, the total energy of liquid helium has a nonlinear form for the number distribution function. The function form can be determined using the excitation energy at zero temperature and the latent heat per helium atom at zero temperature. The nonlinear form produces new temperature dependence for the excitation energy from Bose condensate. We evaluate the specific heat using iteration method. The calculation results of the second iteration show good agreement with the experimental data in the temperature region of 0 - 2.1 K, where we have only used the elementary excitation energy at 1.1 K.

  11. Investigations of the role of nonlinear couplings in structure formation and transport regulation: Experiment, simulation, and theory

    International Nuclear Information System (INIS)

    Holland, C.; Kim, E.J.; Champeaux, S.; Gurcan, O.; Rosenbluth, M.N.; Diamond, P.H.; Tynan, G.R.; Nevins, W.; Candy, J.

    2003-01-01

    Understanding the physics of shear flow and structure formation in plasmas is a central problem for the advancement of magnetic fusion because of the roles such flows are believed to play in regulating turbulence and transport levels. In this paper, we report on integrated experimental, computational, and theoretical studies of sheared zonal flows and radially extended convective cells, with the aim of assessing the results of theory experiment and theory-simulation comparisons. In particular, simulations are used as test beds for verifying analytical predictions and demonstrating the suitability of techniques such as bispectral analysis for isolating nonlinear couplings in data. Based on intriguing initial results suggesting increased levels of nonlinear coupling occur during L-H transitions, we have undertaken a comprehensive study of bispectral quantities in fluid and gyrokinetic simulations, and compared these results with theoretical expectations. Topics of study include locality and directionality of energy transfer, amplitude scaling, and parameter dependences. Techniques for inferring nonlinear coupling coefficients from data are discussed, and initial results from experimental data are presented. Future experimental studies are motivated. We also present work investigating the role of structures in transport. Analysis of simulation data indicates that the turbulent heat flux can be represented as an ensemble of 'heat pulses' of varying sizes, with a power law distribution. The slope of the power law is shown to determine global transport scaling (i.e. Bohm or gyro-Bohm). Theoretical work studying the dynamics of the largest cells (termed 'streamers') is presented, as well as results from ongoing analysis studying connections between heat pulse distribution and bispectral quantities. (author)

  12. SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

    1999-03-01

    This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.

  13. Nonlinear Dynamics in Complex Systems Theory and Applications for the Life-, Neuro- and Natural Sciences

    CERN Document Server

    Fuchs, Armin

    2013-01-01

    With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz ...

  14. A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-08-01

    Full Text Available In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional differential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorems of Dhage (2014 in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional differential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.

  15. Theory of nonlinear harmonic generation in free-electron lasers with helical wigglers

    International Nuclear Information System (INIS)

    Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.

    2007-05-01

    CoherentHarmonicGeneration (CHG), and in particularNonlinearHarmonicGeneration (NHG), is of importance for both short wavelength Free-Electron Lasers (FELs), in relation with the achievement of shorter wavelengths with a fixed electron-beam energy, and high-average power FEL resonators, in relation with destructive effects of higher harmonics radiation on mirrors. In this paper we present a treatment of NHG from helical wigglers with particular emphasis on the second harmonic. Our study is based on an exact analytical solution of Maxwell's equations, derived with the help of a Green's function method. In particular, we demonstrate that nonlinear harmonic generation (NHG) fromhelicalwigglers vanishes on axis. Our conclusion is in open contrast with results in literature, that include a kinematical mistake in the description of the electron motion. (orig.)

  16. A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials

    Science.gov (United States)

    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.

  17. Emergence of complex space-temporal order in nonlinear field theories

    International Nuclear Information System (INIS)

    Gleiser, Marcelo

    2006-01-01

    We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex space-temporal behavior emerges as the system seeks to establish equipartition after a fast quench. We show that fast quenches may dramatically modify the decay rate of metastable states in first order phase transitions. We discuss possible applications in condensed matter systems and in inflationary cosmology. (author)

  18. Emergence of Complex Spatio-Temporal Behavior in Nonlinear Field Theories

    International Nuclear Information System (INIS)

    Gleiser, Marcelo; Howell, Rafael C.

    2006-01-01

    We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex spatio-temporal behavior emerges as the system seeks to establish equipartition after a fast quench. We show that fast quenches may dramatically modify the decay rate of metastable states in first order phase transitions. We discuss possible applications in condensed matter systems and early universe cosmology

  19. Path selection and bandwidth allocation in MPLS networks: a nonlinear programming approach

    Science.gov (United States)

    Burns, J. E.; Ott, Teunis J.; de Kock, Johan M.; Krzesinski, Anthony E.

    2001-07-01

    Multi-protocol Label Switching extends the IPv4 destination-based routing protocols to provide new and scalable routing capabilities in connectionless networks using relatively simple packet forwarding mechanisms. MPLS networks carry traffic on virtual connections called label switched paths. This paper considers path selection and bandwidth allocation in MPLS networks in order to optimize the network quality of service. The optimization is based upon the minimization of a non-linear objective function which under light load simplifies to OSPF routing with link metrics equal to the link propagation delays. The behavior under heavy load depends on the choice of certain parameters: It can essentially be made to minimize maximal expected utilization, or to maximize minimal expected weighted slacks (both over all links). Under certain circumstances it can be made to minimize the probability that a link has an instantaneous offered load larger than its transmission capacity. We present a model of an MPLS network and an algorithm to find and capacitate optimal LSPs. The algorithm is an improvement of the well-known flow deviation non-linear programming method. The algorithm is applied to compute optimal LSPs for several test networks carrying a single traffic class.

  20. Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

    Science.gov (United States)

    Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

    2017-03-01

    H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

  1. Using Program Theory-Driven Evaluation Science to Crack the Da Vinci Code

    Science.gov (United States)

    Donaldson, Stewart I.

    2005-01-01

    Program theory-driven evaluation science uses substantive knowledge, as opposed to method proclivities, to guide program evaluations. It aspires to update, clarify, simplify, and make more accessible the evolving theory of evaluation practice commonly referred to as theory-driven or theory-based evaluation. The evaluator in this chapter provides a…

  2. Optimal Decision-Making in Fuzzy Economic Order Quantity (EOQ Model under Restricted Space: A Non-Linear Programming Approach

    Directory of Open Access Journals (Sweden)

    M. Pattnaik

    2013-08-01

    Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.

  3. On the Reliability of Nonlinear Modeling using Enhanced Genetic Programming Techniques

    Science.gov (United States)

    Winkler, S. M.; Affenzeller, M.; Wagner, S.

    The use of genetic programming (GP) in nonlinear system identification enables the automated search for mathematical models that are evolved by an evolutionary process using the principles of selection, crossover and mutation. Due to the stochastic element that is intrinsic to any evolutionary process, GP cannot guarantee the generation of similar or even equal models in each GP process execution; still, if there is a physical model underlying to the data that are analyzed, then GP is expected to find these structures and produce somehow similar results. In this paper we define a function for measuring the syntactic similarity of mathematical models represented as structure trees; using this similarity function we compare the results produced by GP techniques for a data set representing measurement data of a BMW Diesel engine.

  4. A chaos-based evolutionary algorithm for general nonlinear programming problems

    International Nuclear Information System (INIS)

    El-Shorbagy, M.A.; Mousa, A.A.; Nasr, S.M.

    2016-01-01

    In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.

  5. Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems

    International Nuclear Information System (INIS)

    Lee, Se Jung; Park, Gyung Jin

    2014-01-01

    In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency

  6. Hamiltonian-Driven Adaptive Dynamic Programming for Continuous Nonlinear Dynamical Systems.

    Science.gov (United States)

    Yang, Yongliang; Wunsch, Donald; Yin, Yixin

    2017-08-01

    This paper presents a Hamiltonian-driven framework of adaptive dynamic programming (ADP) for continuous time nonlinear systems, which consists of evaluation of an admissible control, comparison between two different admissible policies with respect to the corresponding the performance function, and the performance improvement of an admissible control. It is showed that the Hamiltonian can serve as the temporal difference for continuous-time systems. In the Hamiltonian-driven ADP, the critic network is trained to output the value gradient. Then, the inner product between the critic and the system dynamics produces the value derivative. Under some conditions, the minimization of the Hamiltonian functional is equivalent to the value function approximation. An iterative algorithm starting from an arbitrary admissible control is presented for the optimal control approximation with its convergence proof. The implementation is accomplished by a neural network approximation. Two simulation studies demonstrate the effectiveness of Hamiltonian-driven ADP.

  7. A nonlinear theory of cosmic ray pitch angle diffusion in homogeneous magnetostatic turbulence

    International Nuclear Information System (INIS)

    Goldstein, M.L.

    1975-04-01

    A plasma strong turbulence, weak coupling theory is applied to the problem of cosmic ray pitch angle scattering in magnetostatic turbulence. The theory used is a rigorous generalization of Weinstock's resonance-broadening theory and contains no ad hoc approximations. A detailed calculation is presented for a model of slab turbulence with an exponential correlation function. The results agree well with numerical simulations. The rigidity dependence of the pitch angle scattering coefficient differs from that found by previous researchers. The differences result from an inadequate treatment of particle trajectories near 90 0 pitch angle in earlier work

  8. Designing and optimising anaerobic digestion systems: A multi-objective non-linear goal programming approach

    International Nuclear Information System (INIS)

    Nixon, J.D.

    2016-01-01

    This paper presents a method for optimising the design parameters of an anaerobic digestion (AD) system by using first-order kinetics and multi-objective non-linear goal programming. A model is outlined that determines the ideal operating tank temperature and hydraulic retention time, based on objectives for minimising levelised cost of electricity, and maximising energy potential and feedstock mass reduction. The model is demonstrated for a continuously stirred tank reactor processing food waste in two case study locations. These locations are used to investigate the influence of different environmental and economic climates on optimal conditions. A sensitivity analysis is performed to further examine the variation in optimal results for different financial assumptions and objective weightings. The results identify the conditions for the preferred tank temperature to be in the psychrophilic, mesophilic or thermophilic range. For a tank temperature of 35 °C, ideal hydraulic retention times, in terms of achieving a minimum levelised electricity cost, were found to range from 29.9 to 33 days. Whilst there is a need for more detailed information on rate constants for use in first-order models, multi-objective optimisation modelling is considered to be a promising option for AD design. - Highlights: • Nonlinear goal programming is used to optimise anaerobic digestion systems. • Multiple objectives are set including minimising the levelised cost of electricity. • A model is developed and applied to case studies for the UK and India. • Optimal decisions are made for tank temperature and retention time. • A sensitivity analysis is carried out to investigate different model objectives.

  9. Theory of heart biomechanics, biophysics, and nonlinear dynamics of cardiac function

    CERN Document Server

    Hunter, Peter; McCulloch, Andrew

    1991-01-01

    In recent years there has been a growth in interest in studying the heart from the perspective of the physical sciences: mechanics, fluid flow, electromechanics. This volume is the result of a workshop held in July 1989 at the Institute for Nonlinear Sciences at the University of California at San Diego that brought together scientists and clinicians with graduate students and postdoctoral fellows who shared an interest in the heart. The chapters were prepared by the invited speakers as didactic reviews of their subjects but also include the structure, mechanical properties, and function of the heart and the myocardium, electrical activity of the heart and myocardium, and mathematical models of heart function.

  10. Reactor noise analysis based on nonlinear dynamic theory - application to power oscillation

    International Nuclear Information System (INIS)

    Suzudo, Tomoaki

    1993-01-01

    The information dimension is one of the simplest quantities that can be used to determine the asymptotic motion of the time evolution of a nonlinear system. The application of this quantity to reactor noise analysis is proposed, and the possibility of its application to power oscillation analysis is examined. The information dimension of this regime is equal to the number of independent oscillating modes, which is an intuitive physical variable. Time series data from computer experiments and experiments with an actual physical system are used for the analysis. The results indicate that the method is useful for a detailed analysis of reactor power oscillation

  11. Properties of Energy Spectra of Molecular Crystals Investigated by Nonlinear Theory

    Science.gov (United States)

    Pang, Xiao-Feng; Zhang, Huai-Wu

    We calculate the quantum energy spectra of molecular crystals, such as acetanilide, by using discrete nonlinear Schrodinger equation, containing various interactions, appropriate to the systems. The energy spectra consist of many energy bands, in each energy band there are a lot of energy levels including some higher excited states. The result of energy spectrum is basically consistent with experimental values obtained by infrared absorption and Raman scattering in acetanilide and can also explain some experimental results obtained by Careri et al. Finally, we further discuss the influences of variously characteristic parameters on the energy spectra of the systems.

  12. Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory

    Science.gov (United States)

    2017-03-01

    Koopman operator theory to systems with memory in time made during Year 1, during Year 2 we worked toward developing a test capable of determining...using this term. Approved for public release; distribution is unlimited. 6 Furthermore, a key element of an approach that is fully capable of dealing...Operator Theory by Bryan Glaz and Adam Svenkeson Approved for public release; distribution is unlimited. NOTICES

  13. Nonlinear behavior of capacitive micro-beams based on strain gradient theory

    International Nuclear Information System (INIS)

    Fathalilou, Mohammad; Sadeghi, Morteza; Rezazadeh, Ghader

    2014-01-01

    This paper studies the size dependent behavior of materials in MEMS structures. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter and is insignificant for the high ratio of the characteristic size to the length-scale parameter, which is the case of the silicon base micro-beams. However, in some types of micro-beams like gold or nickel bases, the size dependent effect cannot be overlooked. In such cases, ignoring this behavior in modeling will lead to incorrect results. Some previous researchers have applied classic beam theory on their models and imposed a considerable hypothetical value of residual stress to match their theoretical results with the experimental ones. The equilibrium positions or fixed points of the gold and nickel micro-beams are obtained and shown that for a given DC voltage, there is a considerable difference between the obtained fixed points using classic beam theory, modified couple stress theory, and modified strain gradient theory. In addition, it is shown that the calculated static and dynamic pull-in voltages using higher order theories are much closer to the experimental results and are higher several times than those obtained by classic beam theory.

  14. BNL NONLINEAR PRE TEST SEISMIC ANALYSIS FOR THE NUPEC ULTIMATE STRENGTH PIPING TEST PROGRAM

    International Nuclear Information System (INIS)

    DEGRASSI, G.; HOFMAYER, C.; MURPHY, C.; SUZUKI, K.; NAMITA, Y.

    2003-01-01

    The Nuclear Power Engineering Corporation (NUPEC) of Japan has been conducting a multi-year research program to investigate the behavior of nuclear power plant piping systems under large seismic loads. The objectives of the program are: to develop a better understanding of the elasto-plastic response and ultimate strength of nuclear piping; to ascertain the seismic safety margin of current piping design codes; and to assess new piping code allowable stress rules. Under this program, NUPEC has performed a large-scale seismic proving test of a representative nuclear power plant piping system. In support of the proving test, a series of materials tests, static and dynamic piping component tests, and seismic tests of simplified piping systems have also been performed. As part of collaborative efforts between the United States and Japan on seismic issues, the US Nuclear Regulatory Commission (USNRC) and its contractor, the Brookhaven National Laboratory (BNL), are participating in this research program by performing pre-test and post-test analyses, and by evaluating the significance of the program results with regard to safety margins. This paper describes BNL's pre-test analysis to predict the elasto-plastic response for one of NUPEC's simplified piping system seismic tests. The capability to simulate the anticipated ratcheting response of the system was of particular interest. Analyses were performed using classical bilinear and multilinear kinematic hardening models as well as a nonlinear kinematic hardening model. Comparisons of analysis results for each plasticity model against test results for a static cycling elbow component test and for a simplified piping system seismic test are presented in the paper

  15. Uncertainty analysis of time-dependent nonlinear systems: theory and application to transient thermal hydraulics

    International Nuclear Information System (INIS)

    Barhen, J.; Bjerke, M.A.; Cacuci, D.G.; Mullins, C.B.; Wagschal, G.G.

    1982-01-01

    An advanced methodology for performing systematic uncertainty analysis of time-dependent nonlinear systems is presented. This methodology includes a capability for reducing uncertainties in system parameters and responses by using Bayesian inference techniques to consistently combine prior knowledge with additional experimental information. The determination of best estimates for the system parameters, for the responses, and for their respective covariances is treated as a time-dependent constrained minimization problem. Three alternative formalisms for solving this problem are developed. The two ''off-line'' formalisms, with and without ''foresight'' characteristics, require the generation of a complete sensitivity data base prior to performing the uncertainty analysis. The ''online'' formalism, in which uncertainty analysis is performed interactively with the system analysis code, is best suited for treatment of large-scale highly nonlinear time-dependent problems. This methodology is applied to the uncertainty analysis of a transient upflow of a high pressure water heat transfer experiment. For comparison, an uncertainty analysis using sensitivities computed by standard response surface techniques is also performed. The results of the analysis indicate the following. Major reduction of the discrepancies in the calculation/experiment ratios is achieved by using the new methodology. Incorporation of in-bundle measurements in the uncertainty analysis significantly reduces system uncertainties. Accuracy of sensitivities generated by response-surface techniques should be carefully assessed prior to using them as a basis for uncertainty analyses of transient reactor safety problems

  16. Control theory-based regulation of hippocampal CA1 nonlinear dynamics.

    Science.gov (United States)

    Hsiao, Min-Chi; Song, Dong; Berger, Theodore W

    2008-01-01

    We are developing a biomimetic electronic neural prosthesis to replace regions of the hippocampal brain area that have been damaged by disease or insult. Our previous study has shown that the VLSI implementation of a CA3 nonlinear dynamic model can functionally replace the CA3 subregion of the hippocampal slice. As a result, the propagation of temporal patterns of activity from DG-->VLSI-->CA1 reproduces the activity observed experimentally in the biological DG-->CA3-->CA1 circuit. In this project, we incorporate an open-loop controller to optimize the output (CA1) response. Specifically, we seek to optimize the stimulation signal to CA1 using a predictive dentate gyrus (DG)-CA1 nonlinear model (i.e., DG-CA1 trajectory model) and a CA1 input-output model (i.e., CA1 plant model), such that the ultimate CA1 response (i.e., desired output) can be first predicted by the DG-CA1 trajectory model and then transformed to the desired stimulation through the inversed CA1 plant model. Lastly, the desired CA1 output is evoked by the estimated optimal stimulation. This study will be the first stage of formulating an integrated modeling-control strategy for the hippocampal neural prosthetic system.

  17. Nonlinear power spectrum from resummed perturbation theory: a leap beyond the BAO scale

    International Nuclear Information System (INIS)

    Anselmi, Stefano; Pietroni, Massimo

    2012-01-01

    A new computational scheme for the nonlinear cosmological matter power spectrum (PS) is presented. Our method is based on evolution equations in time, which can be cast in a form extremely convenient for fast numerical evaluations. A nonlinear PS is obtained in a time comparable to that needed for a simple 1-loop computation, and the numerical implementation is very simple. Our results agree with N-body simulations at the percent level in the BAO range of scales, and at the few-percent level up to k ≅ 1 h/Mpc at z∼>0.5, thereby opening the possibility of applying this tool to scales interesting for weak lensing. We clarify the approximations inherent to this approach as well as its relations to previous ones, such as the Time Renormalization Group, and the multi-point propagator expansion. We discuss possible lines of improvements of the method and its intrinsic limitations by multi streaming at small scales and low redshifts

  18. Phase-space description of plasma waves. Linear and nonlinear theory

    International Nuclear Information System (INIS)

    Biro, T.

    1992-11-01

    We develop an (r,k) phase space description of waves in plasmas by introducing Gaussian window functions to separate short scale oscillations from long scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation also in an inhomogeneous and time varying background plasma, we first discuss the proper form of the current response function. On the analogy of the particle distribution function f(v,r,t), we introduce a wave density N(k,r,t) on phase space. This function is proven to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density' along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible. Within the phase space representation, we obtain a very general formula for the second order nonlinear current in terms of the vector potential. This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasma, including the effects of inhomogeneous turbulence, wave convection and refraction. (author)

  19. A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation.

    Science.gov (United States)

    Louisnard, O

    2012-01-01

    The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium. Copyright © 2011 Elsevier B.V. All rights reserved.

  20. LDRD final report on theory and exploration of quantum-dot optical nonlinearities and coherences

    International Nuclear Information System (INIS)

    Chow, Weng Wah

    2008-01-01

    A microscopic theory for investigating quantum-dot optical properties was developed. The theory incorporated advances on various aspects of quantum-dot physics developed at Sandia and elsewhere. Important components are a non-Markovian treatment of polarization dephasing due to carrier-carrier scattering (developed at Sandia) and a nonperturbative treatment within a polaron picture of the scattering of carriers by longitudinal-optical phonons (developed at Bremen University). A computer code was also developed that provides a detailed accounting of electronic structure influences and a consistent treatment of many-body effects, the latter via the incorporation of results from the microscopic theory. This code was used to explore quantum coherence physics in a quantum-dot system. The investigation furthers the understanding of the underlying differences between atomic quantum coherence and semiconductor quantum coherence, and helps improve the potential of using quantum coherences in quantum computing, coherent control and high-resolution spectroscopy

  1. On the use of contraction theory for the design of nonlinear observers for ocean vehicles

    DEFF Research Database (Denmark)

    Jouffroy, Jerome; Lottin, Jacques

    and practice. This paper addresses the question of the applicability of contraction theory to the design of UGES observers for ocean vehicles. A relation between the concept of exponential convergence of a contracting system and uniform global exponential stability (UGES) is rst given. Then two contraction......Guaranteeing that traditional concepts of stability like uniform global exponential or asymptotic stability (UGES or UGAS) are veri ed when using design tools based on new concepts of stability may be of signicant importance. It is especially so when attempting to bridge the gap between theory...

  2. 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

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

    International Nuclear Information System (INIS)

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

    1993-01-01

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

  4. 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.

  5. Phantom solution in a non-linear Israel-Stewart theory

    Science.gov (United States)

    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.

  6. Interfacing theories of program with theories of evaluation for advancing evaluation practice: Reductionism, systems thinking, and pragmatic synthesis.

    Science.gov (United States)

    Chen, Huey T

    2016-12-01

    Theories of program and theories of evaluation form the foundation of program evaluation theories. Theories of program reflect assumptions on how to conceptualize an intervention program for evaluation purposes, while theories of evaluation reflect assumptions on how to design useful evaluation. These two types of theories are related, but often discussed separately. This paper attempts to use three theoretical perspectives (reductionism, systems thinking, and pragmatic synthesis) to interface them and discuss the implications for evaluation practice. Reductionism proposes that an intervention program can be broken into crucial components for rigorous analyses; systems thinking view an intervention program as dynamic and complex, requiring a holistic examination. In spite of their contributions, reductionism and systems thinking represent the extreme ends of a theoretical spectrum; many real-world programs, however, may fall in the middle. Pragmatic synthesis is being developed to serve these moderate- complexity programs. These three theoretical perspectives have their own strengths and challenges. Knowledge on these three perspectives and their evaluation implications can provide a better guide for designing fruitful evaluations, improving the quality of evaluation practice, informing potential areas for developing cutting-edge evaluation approaches, and contributing to advancing program evaluation toward a mature applied science. Copyright © 2016 Elsevier Ltd. All rights reserved.

  7. Quantitive theory of the Fermi-Pasta-Ulam recurrence in the nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Infeld, E.

    1981-01-01

    By limiting attention to the lowest-order Fourier modes we obtain a theory of the Fermi-Pasta-Ulam recurrence that gives excellent agreement with recent numerical results. Both the predicted period of the recurrence and the temporal development of the n = 0 mode are very good fits. The maximum of the n = 1 mode, however, is off by about 30%

  8. Solving large nonlinear generalized eigenvalue problems from Density Functional Theory calculations in parallel

    DEFF Research Database (Denmark)

    Bendtsen, Claus; Nielsen, Ole Holm; Hansen, Lars Bruno

    2001-01-01

    The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...

  9. Nonlinear systems

    CERN Document Server

    Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús

    2018-01-01

    This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many  new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...

  10. Constraints on Nonlinear and Stochastic Growth Theories for Type 3 Solar Radio Bursts from the Corona to 1 AU

    Science.gov (United States)

    Cairns, Iver H.; Robinson, P. A.

    1998-01-01

    Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for

  11. Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

    Science.gov (United States)

    Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady

    2008-02-01

    We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald

  12. Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance

    OpenAIRE

    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...

  13. Nonlinear optimization

    CERN Document Server

    Ruszczynski, Andrzej

    2011-01-01

    Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...

  14. Hamilton-Ostrogradsky principle in the theory of nonlinear elasticity with the combined approach

    International Nuclear Information System (INIS)

    Sporykhin, A.N.

    1995-01-01

    The assignment of a portion of the edge conditions in the deformed state and a portion of them in the initial state so that the initial and deformed states of the body are unknowns is a characteristic feature of the statement of a number of technological problems. Haber and Haber and Abel have performed studies in this direction, where constitutive relationships have been constructed within the framework of a linearly elastic material. Use of the displacements of individual particles as variable parameters in these relationships has required additional conditions that do not follow from the formulated problem. Use of familiar variational principles described in Euler coordinates is rendered difficult by the complexity of edge-condition formulation in the special case when the initial state is unknown. The latter is governed by the fact that variational principles are derived from the initial formulations open-quotes in Lagrangian coordinates,close quotes by recalculating the operation functional. Using Lagrange's principle, Novikov and Sporykhin constructed constitutive equations in the general case of a nonlinearly elastic body with edge conditions assigned in different configurations. An analogous problem is solved in this paper using the Hamilton-Ostrogradsky principle

  15. Detection of seizures from small samples using nonlinear dynamic system theory.

    Science.gov (United States)

    Yaylali, I; Koçak, H; Jayakar, P

    1996-07-01

    The electroencephalogram (EEG), like many other biological phenomena, is quite likely governed by nonlinear dynamics. Certain characteristics of the underlying dynamics have recently been quantified by computing the correlation dimensions (D2) of EEG time series data. In this paper, D2 of the unbiased autocovariance function of the scalp EEG data was used to detect electrographic seizure activity. Digital EEG data were acquired at a sampling rate of 200 Hz per channel and organized in continuous frames (duration 2.56 s, 512 data points). To increase the reliability of D2 computations with short duration data, raw EEG data were initially simplified using unbiased autocovariance analysis to highlight the periodic activity that is present during seizures. The D2 computation was then performed from the unbiased autocovariance function of each channel using the Grassberger-Procaccia method with Theiler's box-assisted correlation algorithm. Even with short duration data, this preprocessing proved to be computationally robust and displayed no significant sensitivity to implementation details such as the choices of embedding dimension and box size. The system successfully identified various types of seizures in clinical studies.

  16. Theory for nonlinear magnetosonic waves in a two-ion-species plasma

    International Nuclear Information System (INIS)

    Toida, Mieko; Ohsawa, Yukiharu

    1997-01-01

    Magnetosonic waves propagating perpendicular to a magnetic field in a plasma containing two ion species is studied theoretically. The magnetosonic wave is split into two modes in a two-ion-species plasma; low- and high- frequency modes. The frequency of the low-frequency mode tends to zero as the wave number k goes to zero. A KdV equation is derived for this mode by the conventional reductive perturbation method. The frequency of high-frequency mode does not go to zero as k → 0. However, using a new expansion scheme, a KdV equation for the nonlinear high-frequency mode has also been derived. This shows that KdV equations are not limited to waves whose frequencies tend to zero as k → 0. The KdV equation for the low-frequency mode is valid when the amplitudes ε are quite small, while that for the high-frequency mode is valid when (m. e /m. i ) 1/2 e /m. i is a measure of electron-to-ion mass ratios. The characteristic soliton widths are the ion inertia length for the low-frequency mode and the electron skin depth for the high-frequency mode. (author)

  17. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    Science.gov (United States)

    Bogdan, V. M.; Bond, V. B.

    1980-01-01

    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  18. Nonlinear dynamics of a pseudoelastic shape memory alloy system—theory and experiment

    International Nuclear Information System (INIS)

    Enemark, S; F Santos, I; A Savi, M

    2014-01-01

    In this work, a helical spring made from a pseudoelastic shape memory alloy was embedded in a dynamic system also composed of a mass, a linear spring and an excitation system. The mechanical behaviour of shape memory alloys is highly complex, involving hysteresis, which leads to damping capabilities and varying stiffness. Besides, these properties depend on the temperature and pretension conditions. Because of these capabilities, shape memory alloys are interesting in relation to engineering design of dynamic systems. A theoretical model based on a modification of the 1D Brinson model was established. Basically, the hardening and the sub-loop behaviour were altered. The model parameters were extracted from force–displacement tests of the spring at different constant temperatures as well as from differential scanning calorimetry. Model predictions were compared with experimental results of free and forced vibrations of the system setup under different temperature conditions. The experiments give a thorough insight into dynamic systems involving pseudoelastic shape memory alloys. Comparison between experimental results and the proposed model shows that the model is able to explain and predict the overall nonlinear behaviour of the system. (paper)

  19. Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation

    Directory of Open Access Journals (Sweden)

    V. O. Vakhnenko

    2016-01-01

    Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.

  20. On the problem of the existence of the solutions of the nonlinear nonsingular equations of quantum field theory

    International Nuclear Information System (INIS)

    Nelipa, N.F.

    1978-01-01

    The existence of the solution of the nonlinear, singular equations of quantum field theory is discussed. By making use of the Banach's and Schauder's fixed point theorems, the condition of the existence of these equations is found. As some illustration, these methods were applied to the equations for the π-scattering on static nucleon. The investigations of the other equations of quantum field theory (Chew-Low, double dispersin relation, Green's function) lead to the similar result. The application of the Newton-Kantorovich method to the Chew-Low equations also gives the similar result. What are the causes of such situation[ The main suggestions which the author has used were that the Banach's, the Schauder's, and the Newton-Kantorovich methods were applied and the Hoelder space was choosen. It may be that the method are crude. It may be that the solutions do not belong to the Hoelder space. Now it is rather difficult to say which role each of these two suggestions plays. (Kobatake, H.)

  1. Large-scale perturbations of magnetohydrodynamic regimes linear and weakly nonlinear stability theory

    CERN Document Server

    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.

  2. Exact solutions to nonlinear symmetron theory: One- and two-mirror systems

    Science.gov (United States)

    Brax, Philippe; Pitschmann, Mario

    2018-03-01

    We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one- or two-mirror system. The one-dimensional equations of motion are integrated exactly for both systems and their solutions can be expressed in terms of Jacobi elliptic functions. Surprisingly, in the case of two parallel mirrors, the equations of motion generically provide not a unique solution but a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to q BOUNCE experiments, neutron interferometry and for the calculation of the symmetron-field-induced "Casimir force" in the CANNEX experiment.

  3. Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

    Science.gov (United States)

    Wei, Qinglai; Liu, Derong; Lin, Hanquan

    2016-03-01

    In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

  4. The nurse scheduling problem: a goal programming and nonlinear optimization approaches

    Science.gov (United States)

    Hakim, L.; Bakhtiar, T.; Jaharuddin

    2017-01-01

    Nurses scheduling is an activity of allocating nurses to conduct a set of tasks at certain room at a hospital or health centre within a certain period. One of obstacles in the nurse scheduling is the lack of resources in order to fulfil the needs of the hospital. Nurse scheduling which is undertaken manually will be at risk of not fulfilling some nursing rules set by the hospital. Therefore, this study aimed to perform scheduling models that satisfy all the specific rules set by the management of Bogor State Hospital. We have developed three models to overcome the scheduling needs. Model 1 is designed to schedule nurses who are solely assigned to a certain inpatient unit and Model 2 is constructed to manage nurses who are assigned to an inpatient room as well as at Polyclinic room as conjunct nurses. As the assignment of nurses on each shift is uneven, then we propose Model 3 to minimize the variance of the workload in order to achieve equitable assignment on every shift. The first two models are formulated in goal programming framework, while the last model is in nonlinear optimization form.

  5. Automatic Design of Synthetic Gene Circuits through Mixed Integer Non-linear Programming

    Science.gov (United States)

    Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias

    2012-01-01

    Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits. PMID:22536398

  6. The Theory and Practice of Programmed Instruction; A Guide for Teachers.

    Science.gov (United States)

    Pocztar, Jerry

    A historical sketch which traces behavioral theory from Pavlov to Skinner and explains the application of Skinner's theory to teaching begins this introduction to programed instruction. Next, three models of programed courses, Skinner's, Crowder's, and skip-branching, are described. The third section, techniques for elaborating programed courses,…

  7. Summaries of FY 1986 research in the Applied Plasma Physics Fusion Theory Program

    International Nuclear Information System (INIS)

    1987-12-01

    The Theory Program is charged with supporting the development of theories and models of plasmas for the fusion research effort. This work ranges from first-principles analysis of elementary plasma processes to empirical simulation of specific experiments. The Theory Program supports research by industrial contractors, US government laboratories, and universities. The university support also helps to fulfill the DOE mission of training scientists for the fusion program. The Theory Program is funded through the Fusion Theory Branch, Division of Applied Plasma Physics in the Office of Fusion Energy. The work is divided among 31 institutions, of which 19 are universities, five are industrial contractors, and seven are US government laboratories; see Table 1 for a complete list. The FY 1986 Theory Program budget was divided among theory types: toroidal, mirror, alternate concept, generic, and atomic. Device modeling is included among the other funding categories, and is not budgeted separately

  8. Analytical theory and nonlinear δf perturbative simulations of temperature anisotropy instability in intense charged particle beams

    Directory of Open Access Journals (Sweden)

    Edward A. Startsev

    2003-08-01

    Full Text Available In plasmas with strongly anisotropic distribution functions (T_{∥b}/T_{⊥b}≪1 a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9, 3138 (2002] of the stability properties of intense non-neutral charged particle beams with large temperature anisotropy (T_{⊥b}≫T_{∥b} to allow for nonaxisymmetric perturbations with ∂/∂θ≠0. The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined. The simulation results clearly show that moderately intense beams with s_{b}=ω[over ^]_{pb}^{2}/2γ_{b}^{2}ω_{β⊥}^{2}≳0.5 are linearly unstable to short-wavelength perturbations with k_{z}^{2}r_{b}^{2}≳1, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ω[over ^]_{pb}^{2}=4πn[over ^]_{b}e_{b}^{2}/γ_{b}m_{b} is the relativistic plasma frequency squared, and ω_{β⊥} is the betatron frequency associated with the applied smooth-focusing field. A theoretical model is developed based on the Vlasov-Maxwell equations which describes the essential features of the linear stages of instability. Both the simulations and the analytical theory predict that the dipole mode (azimuthal mode number m=1 is the most unstable mode. In the nonlinear stage, tails develop in the longitudinal momentum distribution function, and the kinetic instability saturates due to resonant wave-particle interactions.

  9. A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

    KAUST Repository

    Domínguez, Luis F.

    2012-06-25

    An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).

  10. CASKETSS-DYNA2D: a nonlinear impact analysis computer program for nuclear fuel transport casks in two dimensional geometries

    International Nuclear Information System (INIS)

    Ikushima, Takeshi

    1988-10-01

    A nonlinear impact analysis computer program DYNA2D, which was developed by Hallquist, has been introduced from Lawrence Livermore National Laboratory for the purpose of using impact analysis of nuclear fuel transport casks. DYNA2D has been built in CASKETSS code system (CASKETSS means a modular code system for CASK Evaluation code system for Thermal and Structural Safety). Main features of DYNA2D are as follows; (1) This program has been programmed to provide near optimal speed on vector processing computers. (2) An explicit time integration method is used for fast calculation. (3) Many material models are available in the program. (4) A contact-impact algorithm permits gap and sliding along structural interfaces. (5) A rezoner has been embedded in the program. (6) The graphic program for representations of calculation is provided. In the paper, brief illustration of calculation method, input data and sample calculations are presented. (author)

  11. Determination of the spiral Galaxy structure parameters based on neutral hydrogen radiowave radiation in 21 cm line. 2. Nonlinear theory. 30 deg <= |l| <= 60 deg

    International Nuclear Information System (INIS)

    Berman, V.G.; Mishurov, Yu.N.

    1980-01-01

    Gas flow and its density distribution in the Galaxy spiral arm gravitational potential is calculated by means of the nonlinear theory. Line profile of H I emission in 21 cm based on the Galaxy spiral structure models proposed by Lin and Marochnik are constructed for the galactic coordinates 30 deg < or approximately |l| < or approximately 60 deg. It is shown that the conclusion about the possibility of agreement of the Marochnik model with observations made by means of the linear theory is confirmed in the nonlinear theory. In the Marochnik model distributions with R H II regions, CO-clouds, γ-radiation, supernova remnants and so on may also be understood connecting them with variation of gas compression in galactic shock with H radius

  12. Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

    Science.gov (United States)

    Basko, D M

    2014-02-01

    We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

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

    Directory of Open Access Journals (Sweden)

    Shahriar Dastjerdi

    2016-06-01

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

  14. Interval Solution for Nonlinear Programming of Maximizing the Fatigue Life of V-Belt under Polymorphic Uncertain Environment

    Directory of Open Access Journals (Sweden)

    Zhong Wan

    2013-01-01

    Full Text Available In accord with the practical engineering design conditions, a nonlinear programming model is constructed for maximizing the fatigue life of V-belt drive in which some polymorphic uncertainties are incorporated. For a given satisfaction level and a confidence level, an equivalent formulation of this uncertain optimization model is obtained where only interval parameters are involved. Based on the concepts of maximal and minimal range inequalities for describing interval inequality, the interval parameter model is decomposed into two standard nonlinear programming problems, and an algorithm, called two-step based sampling algorithm, is developed to find an interval optimal solution for the original problem. Case study is employed to demonstrate the validity and practicability of the constructed model and the algorithm.

  15. [High energy particle physics]: Task A, High energy physics program: Experiment and theory; Task B, High energy physics program: Numerical simulation of quantum field theories

    International Nuclear Information System (INIS)

    Lannutti, J.E.

    1991-01-01

    This report discusses the following research: fixed target experiments; collider experiments; computing, networking and VAX upgrade; SSC preparation, detector development and detector construction; solid argon calorimetry; absorption of CAD system geometries into GEANT for SSC; and particle theory programs

  16. EURDYN: computer programs for the nonlinear transient analysis of structures submitted to dynamic loading. EURDYN (Release 3): users' manual

    International Nuclear Information System (INIS)

    Halleux, J.P.

    1983-01-01

    The EURDYN computer codes are mainly designed for the simulation of nonlinear dynamic response of fast-reactor compoments submitted to impulse loading due to abnormal working conditions. Two releases of the structural computer codes EURDYN 01 (2-D beams and triangles and axisymmetric conical shells and triangular tores), 02 (axisymmetric and 2-D quadratic isoparametric elements) and 03 (triangular plate elements) have already been produced. They include material (elasto-plasticity using the classical flow theory approach) and geometrical (large displacements and rotations treated by a corotational technique) nonlinearities. The new features of Release 3 roughly consist in: full large strain capability for 9-node isoparametric elements, generalized array dimensions, introduction of the radial return algorithm for elasto-plastic material modelling, extension of the energy check facility to the case of prescribed displacements, and, possible interface to a post-processing package including time plot facilities

  17. Nonlinear Boltzmann equation for the homogeneous isotropic case: Minimal deterministic Matlab program

    Science.gov (United States)

    Asinari, Pietro

    2010-10-01

    .gz Programming language: Tested with Matlab version ⩽6.5. However, in principle, any recent version of Matlab or Octave should work Computer: All supporting Matlab or Octave Operating system: All supporting Matlab or Octave RAM: 300 MBytes Classification: 23 Nature of problem: The problem consists in integrating the homogeneous Boltzmann equation for a generic collisional kernel in case of isotropic symmetry, by a deterministic direct method. Difficulties arise from the multi-dimensionality of the collisional operator and from satisfying the conservation of particle number and energy (momentum is trivial for this test case) as accurately as possible, in order to preserve the late dynamics. Solution method: The solution is based on the method proposed by Aristov (2001) [1], but with two substantial improvements: (a) the original problem is reformulated in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium). Both these corrections make possible to derive very accurate reference solutions for this test case. Restrictions: The nonlinear Boltzmann equation is extremely challenging from the computational point of view, in particular for deterministic methods, despite the increased computational power of recent hardware. In this work, only the homogeneous isotropic case is considered, for making possible the development of a minimal program (by a simple scripting language) and allowing the user to check the advantages of the proposed improvements beyond Aristov's (2001) method [1]. The initial conditions are supposed parameterized according to a fixed analytical expression, but this can be

  18. Nonlinear dynamic behaviour of a rotor-foundation system coupled through passive magnetic bearings with magnetic anisotropy - Theory and experiment

    DEFF Research Database (Denmark)

    Enemark, Søren; Santos, Ilmar F.

    2016-01-01

    In this work, the nonlinear dynamic behaviour of a vertical rigid rotor interacting with a flexible foundation by means of two passive magnetic bearings is quantified and evaluated. The quantification is based on theoretical and experimental investigation of the non-uniformity (anisotropy......) of the magnetic field and the weak nonlinearity of the magnetic forces. Through mathematical modelling the nonlinear equations of motion are established for describing the shaft and bearing housing lateral dynamics coupled via the nonlinear and non-uniform magnetic forces. The equations of motion are solved...

  19. Towards program theory validation: Crowdsourcing the qualitative analysis of participant experiences.

    Science.gov (United States)

    Harman, Elena; Azzam, Tarek

    2018-02-01

    This exploratory study examines a novel tool for validating program theory through crowdsourced qualitative analysis. It combines a quantitative pattern matching framework traditionally used in theory-driven evaluation with crowdsourcing to analyze qualitative interview data. A sample of crowdsourced participants are asked to read an interview transcript and identify whether program theory components (Activities and Outcomes) are discussed and to highlight the most relevant passage about that component. The findings indicate that using crowdsourcing to analyze qualitative data can differentiate between program theory components that are supported by a participant's experience and those that are not. This approach expands the range of tools available to validate program theory using qualitative data, thus strengthening the theory-driven approach. Copyright © 2017 Elsevier Ltd. All rights reserved.

  20. The Father Friendly Initiative within Families: Using a logic model to develop program theory for a father support program.

    Science.gov (United States)

    Gervais, Christine; de Montigny, Francine; Lacharité, Carl; Dubeau, Diane

    2015-10-01

    The transition to fatherhood, with its numerous challenges, has been well documented. Likewise, fathers' relationships with health and social services have also begun to be explored. Yet despite the problems fathers experience in interactions with healthcare services, few programs have been developed for them. To explain this, some authors point to the difficulty practitioners encounter in developing and structuring the theory of programs they are trying to create to promote and support father involvement (Savaya, R., & Waysman, M. (2005). Administration in Social Work, 29(2), 85), even when such theory is key to a program's effectiveness (Chen, H.-T. (2005). Practical program evaluation. Thousand Oaks, CA: Sage Publications). The objective of the present paper is to present a tool, the logic model, to bridge this gap and to equip practitioners for structuring program theory. This paper addresses two questions: (1) What would be a useful instrument for structuring the development of program theory in interventions for fathers? (2) How would the concepts of a father involvement program best be organized? The case of the Father Friendly Initiative within Families (FFIF) program is used to present and illustrate six simple steps for developing a logic model that are based on program theory and demonstrate its relevance. Crown Copyright © 2015. Published by Elsevier Ltd. All rights reserved.

  1. Advances in nonlinear optics

    CERN Document Server

    Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong

    2015-01-01

    This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.

  2. Automation of nonlinear calculations in the theory of fusion reactor; Automatisation des calculs non lineaires dans la theorie des reacteurs a fusion

    Energy Technology Data Exchange (ETDEWEB)

    Braffort, P; Chaigne, M [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1958-07-01

    1) Introduction: The difficulties of the formulation of the equations of phenomena occurring during the operation of a fusion reactor are underlined. 2) The possibilities presented by analog computation of the solution of nonlinear differential equations are enumerated. The accuracy and limitations of this method are discussed. 3) The analog solution in the stationary problem of the measurement of the discharge confinement is given and comparison with experimental results. 4) The analog solution of the dynamic problem of the evolution of the discharge current in a simple case is given and it is compared with experimental data. 5) The analog solution of the motion of an isolated ion in the electromagnetic field is given. A spatial field simulator used for this problem (bidimensional problem) is described. 6) The analog solution of the preceding problem for a tridimensional case for particular geometrical configurations using simultaneously 2 field simulators is given. 7) A method of computation derived from Monte Carlo method for the study of dynamic of plasma is described. 8) Conclusion: the essential differences between the analog computation of fission reactors and fusion reactors are analysed. In particular the theory of control of a fusion reactor as described by SCHULTZ is discussed and the results of linearized formulations are compared with those of nonlinear simulation. (author)Fren. [French] 1) Introduction. On souligne les difficultes que presente la mise en equation des phenomenes mis en jeu lors du fonctionnement d'un reacteur a fusion. On selectionne un certain nombre d'equations generalement utilisees et on montre les impossibilites analytiques auxquelles on se heurte alors. 2) On rappelle les possibilites du calcul analogique pour la resolution des systemes differentiels non lineaires et on indique la precision de la methode ainsi que ses limitations. 3) On decrit esolution analogique du probleme statique de la mesure du confinement de la decharge

  3. Implications of the Goal Theory on air show programs planning

    Directory of Open Access Journals (Sweden)

    Dewald Venter

    2014-01-01

    Full Text Available Events have long played an important role in human society (Shone & Parry, 2010: 3. The toils and efforts of daily lives have often been broken up by events of all kinds as humans seek an escape from the harsh reality of existence and events provide the outlet. Events are classified into four categories according to Shone and Parry (2010: 5 namely leisure (sport, recreation, personal (weddings, birthdays, cultural (art, folklore and organizational (politics, commercial. Successful events either match or exceed visitor motives and goals. It is critical that data be collected from visitors to determine their motives and goals in order to satisfy them and thereby encouraging repeat visits. One such event is the annual air show held at the Zwartkop Air Force Base (AFB in Pretoria, South Africa. Zwartkop AFB is also home to the South African Air Force (SAAF museum that also the hosts of the air show. Much of the museum‟s funds are generated through hosting the air show and sponsor contributions. Visitor goal satisfaction should therefore be of critically importance to the program planners. Military hardware has long held a fascination for those who used them and inspired the imagination of young and old. Such hardware often serves as a remembrance of times passed and as a testament to those who perished. For many visiting museums and air shows, curiosity plays a big role. The particular focus of this article will be on how the goal theory of leisure travel can be utilized by the air show organizers to enhance visitor experience to an air show.

  4. [Research programs on elementary particle and field theories and superconductivity

    International Nuclear Information System (INIS)

    Khuri, N.N.

    1992-01-01

    Research of staff members in theoretical physics is presented in the following areas: super string theory, a new approach to path integrals, new ideas on the renormalization group, nonperturbative chiral gauge theories, the standard model, K meson decays, and the CP problem. Work on high-T c superconductivity and protein folding is also related

  5. Research program in elementary particle theory, 1980. Progress report

    International Nuclear Information System (INIS)

    Sudarshan, E.C.G.; Ne'eman, Y.

    1980-01-01

    Research is reported for these subject areas: particle physics in relativistic astrophysics and cosmology; phenomenology of weak and electromagnetic interactions; strong interaction physics, QCD, and quark-parton physics; quantum field theory, quantum mechanics and fundamental problems; groups, gauges, and grand unified theories; and supergeometry, superalgebra, and unification

  6. Research program in elementary particle theory, 1980. Progress report

    Energy Technology Data Exchange (ETDEWEB)

    Sudarshan, E. C.G.; Ne' eman, Y.

    1980-01-01

    Research is reported for these subject areas: particle physics in relativistic astrophysics and cosmology; phenomenology of weak and electromagnetic interactions; strong interaction physics, QCD, and quark-parton physics; quantum field theory, quantum mechanics and fundamental problems; groups, gauges, and grand unified theories; and supergeometry, superalgebra, and unification. (GHT)

  7. THE GENERAL ATOMICS FUSION THEORY PROGRAM ANNUAL REPORT FOR FISCAL YEAR 2002

    International Nuclear Information System (INIS)

    PROJECT STAFF

    2002-01-01

    OAK B202 THE GENERAL ATOMICS FUSION THEORY PROGRAM ANNUAL REPORT FOR FISCAL YEAR 2002. The dual objective of the fusion theory program at General Atomics (GA) is to significantly advance the scientific understanding of the physics of fusion plasmas and to support the DIII-D and other tokamak experiments. The program plan is aimed at contributing significantly to the Fusion Energy Science and the Tokamak Concept Improvement goals of the Office of Fusion Energy Sciences (OFES)

  8. Foundations and Applications of Theory in the First Impressions Program

    Science.gov (United States)

    Brown, Laura E.; McDonald, John; Chase, Lisa C.; Sewake, Geoffrey; Stencel, Beverly; Northrop, Andy; Kelly, Miriah; Faulkner, Ryan

    2018-01-01

    The First Impressions program was designed to help communities learn about their strengths and shortcomings through the "fresh eyes" of first-time visitors. This Extension-led community assessment program has been implemented in over 500 communities since the 1990s, yet scant literature exists regarding the program's theoretical…

  9. Bilevel programming problems theory, algorithms and applications to energy networks

    CERN Document Server

    Dempe, Stephan; Pérez-Valdés, Gerardo A; Kalashnykova, Nataliya; Kalashnikova, Nataliya

    2015-01-01

    This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

  10. Research program in elementary-particle theory, 1981. Progress report

    International Nuclear Information System (INIS)

    Sudarshan, E.C.G.; Ne'eman, Y.

    1981-01-01

    Progress is reported for research in the physics of ultra high energies and cosmology, the phenomenology of particle physics, composite models of particles and quantum field theory, quantum mechanics, geometric formulations, fiber bundles, and other algebraic models

  11. Research program in elementary particle theory. Progress report, 1984

    International Nuclear Information System (INIS)

    Sudarshan, E.C.G.; Dicus, D.A.

    1984-04-01

    Research progress is reported on the following topics: gauge theory and monopole physics; supersymmetry and proton decay; strong interactions and model of particles; quantum rotator and spectrum generating group models of particles; geometric foundations of particle physics and optics; and application of particle physics to astrophysics. The titles of DOE reports are listed, and research histories of the scientific staff of the Center for Particle Theory are included

  12. A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

    Science.gov (United States)

    Fleming, P.

    1985-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

  13. Reducing Violence in Non-Controlling Ways: A Change Program Based on Self Determination Theory

    Science.gov (United States)

    Assor, Avi; Feinberg, Ofra; Kanat-Maymon, Yaniv; Kaplan, Haya

    2018-01-01

    This paper presents and examines the first school change program focusing on violence and caring based on self-determination theory (Deci & Ryan, 2012). The program aimed at promoting teachers' capacity to cope with violence and enhance caring without becoming more controlling. Comparisons of the effects of a 22-month-long program in three…

  14. Learning in Context: Technology Integration in a Teacher Preparation Program Informed by Situated Learning Theory

    Science.gov (United States)

    Bell, Randy L.; Maeng, Jennifer L.; Binns, Ian C.

    2013-01-01

    This investigation explores the effectiveness of a teacher preparation program aligned with situated learning theory on preservice science teachers' use of technology during their student teaching experiences. Participants included 26 preservice science teachers enrolled in a 2-year Master of Teaching program. A specific program goal was to…

  15. Review of the Fusion Theory and Computing Program. Fusion Energy Sciences Advisory Committee (FESAC)

    International Nuclear Information System (INIS)

    Antonsen, Thomas M.; Berry, Lee A.; Brown, Michael R.; Dahlburg, Jill P.; Davidson, Ronald C.; Greenwald, Martin; Hegna, Chris C.; McCurdy, William; Newman, David E.; Pellegrini, Claudio; Phillips, Cynthia K.; Post, Douglass E.; Rosenbluth, Marshall N.; Sheffield, John; Simonen, Thomas C.; Van Dam, James

    2001-01-01

    At the November 14-15, 2000, meeting of the Fusion Energy Sciences Advisory Committee, a Panel was set up to address questions about the Theory and Computing program, posed in a charge from the Office of Fusion Energy Sciences (see Appendix A). This area was of theory and computing/simulations had been considered in the FESAC Knoxville meeting of 1999 and in the deliberations of the Integrated Program Planning Activity (IPPA) in 2000. A National Research Council committee provided a detailed review of the scientific quality of the fusion energy sciences program, including theory and computing, in 2000.

  16. Translating Theory Into Practice: Implementing a Program of Assessment.

    Science.gov (United States)

    Hauer, Karen E; O'Sullivan, Patricia S; Fitzhenry, Kristen; Boscardin, Christy

    2018-03-01

    A program of assessment addresses challenges in learner assessment using a centrally planned, coordinated approach that emphasizes assessment for learning. This report describes the steps taken to implement a program of assessment framework within a medical school. A literature review on best practices in assessment highlighted six principles that guided implementation of the program of assessment in 2016-2017: (1) a centrally coordinated plan for assessment aligns with and supports a curricular vision; (2) multiple assessment tools used longitudinally generate multiple data points; (3) learners require ready access to information-rich feedback to promote reflection and informed self-assessment; (4) mentoring is essential to facilitate effective data use for reflection and learning planning; (5) the program of assessment fosters self-regulated learning behaviors; and (6) expert groups make summative decisions about grades and readiness for advancement. Implementation incorporated stakeholder engagement, use of multiple assessment tools, design of a coaching program, and creation of a learner performance dashboard. The assessment team monitors adherence to principles defining the program of assessment and gathers and responds to regular feedback from key stakeholders, including faculty, staff, and students. Next steps include systematically collecting evidence for validity of individual assessments and the program overall. Iterative review of student performance data informs curricular improvements. The program of assessment also highlights technology needs that will be addressed with information technology experts. The outcome ultimately will entail showing evidence of validity that the program produces physicians who engage in lifelong learning and provide high-quality patient care.

  17. Intervention mapping: a process for developing theory- and evidence-based health education programs.

    Science.gov (United States)

    Bartholomew, L K; Parcel, G S; Kok, G

    1998-10-01

    The practice of health education involves three major program-planning activities: needs assessment, program development, and evaluation. Over the past 20 years, significant enhancements have been made to the conceptual base and practice of health education. Models that outline explicit procedures and detailed conceptualization of community assessment and evaluation have been developed. Other advancements include the application of theory to health education and promotion program development and implementation. However, there remains a need for more explicit specification of the processes by which one uses theory and empirical findings to develop interventions. This article presents the origins, purpose, and description of Intervention Mapping, a framework for health education intervention development. Intervention Mapping is composed of five steps: (1) creating a matrix of proximal program objectives, (2) selecting theory-based intervention methods and practical strategies, (3) designing and organizing a program, (4) specifying adoption and implementation plans, and (5) generating program evaluation plans.

  18. A mixed-integer nonlinear programming approach to the optimal design of heat network in a polygeneration energy system

    International Nuclear Information System (INIS)

    Zhang, Jianyun; Liu, Pei; Zhou, Zhe; Ma, Linwei; Li, Zheng; Ni, Weidou

    2014-01-01

    Highlights: • Integration of heat streams with HRSG in a polygeneration system is studied. • A mixed-integer nonlinear programming model is proposed to optimize heat network. • Operating parameters and heat network configuration are optimized simultaneously. • The optimized heat network highly depends on the HRSG type and model specification. - Abstract: A large number of heat flows at various temperature and pressure levels exist in a polygeneration plant which co-produces electricity and chemical products. Integration of these external heat flows in a heat recovery steam generator (HRSG) has great potential to further enhance energy efficiency of such a plant; however, it is a challenging problem arising from the large design space of heat exchanger network. In this paper, a mixed-integer nonlinear programming model is developed for the design optimization of a HRSG with consideration of all alternative matches between the HRSG and external heat flows. This model is applied to four polygeneration cases with different HRSG types, and results indicate that the optimized heat network mainly depends on the HRSG type and the model specification

  19. Policy Iteration for $H_\\infty $ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.

    Science.gov (United States)

    Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao

    2018-02-01

    Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.

  20. Towards a parsimonious program theory of return to work intervention.

    Science.gov (United States)

    Claudi Jensen, Anne Grete

    2013-01-01

    Presentation of a salutogenic theory of return to work (RTW). The study group include 118 unskilled Danish public employees and privately employed house-cleaners on sick leave due to musculoskeletal and/or common mental illnesses. Theory of RTW is discussed from a theoretical and empirical viewpoint, using baseline-data from an intervention study in a longitudinal, non-randomized study design with follow-up after one year. High work ability, strong social support from colleagues and over-commitment are the most important prognostic factors for RTW. An active coping style, high self-efficacy and Sense of Coherence (SOC) are found to increase RTW and high hostility and over-commitment to decrease RTW. Besides health elements in work ability are SOC, self-efficacy, social support and physical activity. Work ability and active coping mediate positive associations between RTW and health, and a negative association with stress. Work ability seems to express the intention to work decisive for RTW, reflecting the interpretation of the work/health situation based on comprehensibility, meaningfulness and manageability. It is influenced by the personal view of life, attitudes and interaction with the workplace. An ecological theory, integrating health promotion is proposed. A later paper will present the intervention study and further validation of the theory.

  1. Implications of learning theory for developing programs to decrease overeating.

    Science.gov (United States)

    Boutelle, Kerri N; Bouton, Mark E

    2015-10-01

    Childhood obesity is associated with medical and psychological comorbidities, and interventions targeting overeating could be pragmatic and have a significant impact on weight. Calorically dense foods are easily available, variable, and tasty which allows for effective opportunities to learn to associate behaviors and cues in the environment with food through fundamental conditioning processes, resulting in measurable psychological and physiological food cue reactivity in vulnerable children. Basic research suggests that initial learning is difficult to erase, and that it is vulnerable to a number of phenomena that will allow the original learning to re-emerge after it is suppressed or replaced. These processes may help explain why it may be difficult to change food cue reactivity and overeating over the long term. Extinction theory may be used to develop effective cue-exposure treatments to decrease food cue reactivity through inhibitory learning, although these processes are complex and require an integral understanding of the theory and individual differences. Additionally, learning theory can be used to develop other interventions that may prove to be useful. Through an integration of learning theory, basic and translational research, it may be possible to develop interventions that can decrease the urges to overeat, and improve the weight status of children. Copyright © 2015 Elsevier Ltd. All rights reserved.

  2. Research program in elementary-particle theory. Progress report

    International Nuclear Information System (INIS)

    Sudarshan, E.C.G.; Ne'eman, Y.

    1982-08-01

    This progress report of the Center for Particle Theory of the University of Texas at Austin reviews the work done over the past year and is part of the renewal proposal for the period from January 1, 1983 to December 31, 1983

  3. Research program in elementary-particle theory, 1983. Progress report

    International Nuclear Information System (INIS)

    Sudarshan, E.C.G.; Ne'eman, Y.

    1983-08-01

    Progress is reviewed on the following topics: physics of ultra high energies and cosmology; phenomenology of particle physics; quantum field theory, supersymmetry and models of particles; and geometric formulations and algebraic models. Recent DOE reports resulting from the contract are listed

  4. Research program in elementary-particle theory, 1983. Progress report

    Energy Technology Data Exchange (ETDEWEB)

    Sudarshan, E C.G.; Ne& #x27; eman, Y

    1983-08-01

    Progress is reviewed on the following topics: physics of ultra high energies and cosmology; phenomenology of particle physics; quantum field theory, supersymmetry and models of particles; and geometric formulations and algebraic models. Recent DOE reports resulting from the contract are listed. (WHK)

  5. Obesity Intervention Programs among Adolescents Using Social Cognitive Theory: A Systematic Literature Review

    Science.gov (United States)

    Bagherniya, Mohammad; Taghipour, Ali; Sharma, Manoj; Sahebkar, Amirhossein; Contento, Isobel R.; Keshavarz, Seyed Ali; Mostafavi Darani, Firoozeh; Safarian, Mohammad

    2018-01-01

    Social cognitive theory (SCT) is a well-known theory for designing nutrition education and physical activity programs for adolescents. This systematic review aimed to evaluate the efficacy of intervention studies based on SCT in reducing or preventing overweight and obesity in adolescents. An electronic literature search in PubMed-Medline, Web of…

  6. Identifying Barriers in Implementing Outcomes-Based Assessment Program Review: A Grounded Theory Analysis

    Science.gov (United States)

    Bresciani, Marilee J.

    2011-01-01

    The purpose of this grounded theory study was to identify the typical barriers encountered by faculty and administrators when implementing outcomes-based assessment program review. An analysis of interviews with faculty and administrators at nine institutions revealed a theory that faculty and administrators' promotion, tenure (if applicable),…

  7. Models for Theory-Based M.A. and Ph.D. Programs.

    Science.gov (United States)

    Botan, Carl; Vasquez, Gabriel

    1999-01-01

    Presents work accomplished at the 1998 National Communication Association Summer Conference. Outlines reasons for theory-based education in public relations. Presents an integrated model of student outcomes, curriculum, pedagogy, and assessment for theory-based master's and doctoral programs, including assumptions made and rationale for such…

  8. The Course Research for the Software Program Based on the Constructivism Teaching Theories

    Science.gov (United States)

    Zhang, Quanyou; Kou, Qiongjie

    The theory of constructivism teaching emphasizes that: firstly, the center of teaching should be students; secondly, teaching should cultivate the student's character of autonomy and cooperation. The constructivism teaching gets rid of some disadvantage in the traditional teaching. Through using constructivism teaching theories to instruct programming course, it can liven up the lesson mood and cultivate the independent study; improve the team spirit and the ability of programming software for students.

  9. Harnessing International Relations Theory to Security Cooperation Program Design

    Science.gov (United States)

    2012-03-22

    behavior. One of the most famous Liberal theorists is the philosopher Immanuel Kant , whose theory of “Perpetual Peace” centered on a vision where “free...democratic states would retain their sovereignty while working together to avoid war.”17 Kant ‟s vision has repeatedly been channeled into a desire...Interdependence and Liberal Institutionalist thinkers share roots with Grotius and Kant , and believe that there is a larger civil society where interstate

  10. Quantum Nonlinear Optics

    CERN Document Server

    Hanamura, Eiichi; Yamanaka, Akio

    2007-01-01

    This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.

  11. Nonlinear dynamics and complexity

    CERN Document Server

    Luo, Albert; Fu, Xilin

    2014-01-01

    This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

  12. Nonlinear elastic waves in materials

    CERN Document Server

    Rushchitsky, Jeremiah J

    2014-01-01

    The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...

  13. Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

    Science.gov (United States)

    Fulcher, Lewis P.

    1979-01-01

    Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)

  14. Multiple utility constrained multi-objective programs using Bayesian theory

    Science.gov (United States)

    Abbasian, Pooneh; Mahdavi-Amiri, Nezam; Fazlollahtabar, Hamed

    2018-03-01

    A utility function is an important tool for representing a DM's preference. We adjoin utility functions to multi-objective optimization problems. In current studies, usually one utility function is used for each objective function. Situations may arise for a goal to have multiple utility functions. Here, we consider a constrained multi-objective problem with each objective having multiple utility functions. We induce the probability of the utilities for each objective function using Bayesian theory. Illustrative examples considering dependence and independence of variables are worked through to demonstrate the usefulness of the proposed model.

  15. The nonlinear treatment in noise analysis and its influence into quality programs

    International Nuclear Information System (INIS)

    Montesino, Maria Elena; Piedra, Margarita; Rolo, Alberto

    2002-01-01

    Analysis by noise technique have been utilized in fact for early detection reactor's anomalies, constituting one of the fundamental tools in maintenance condition. There is an international tendency to use this technique in order to guarantee the quality of maintenance control at present. Essentially this technique is an approach from lineal dynamic and insufficient for limit cycle illustrations, which take place after bifurcation point. As non-lineal dynamic (chaos theory) descriptors consider the dynamic characteristics of studied system, their uses guarantee the quality in predictive maintenance by noise. In this paper was analysed the necessity of theory's use as a tool to supplement the analysis by noise technique. (author)

  16. NRL inertial confinement fusion theory program. 1979 annual report, October 1978 - December 1979

    International Nuclear Information System (INIS)

    1980-01-01

    This is the 1979 annual report of the NRL Inertial Confinement Fusion Theory Program. It covers research performed from October 1978 through December 1979. Research in each of the four current program areas is reported: laser light absorption;fluid dynamics of ablative acceleration; development of computational techniques, and Rayleigh-Taylor stabilization techniques

  17. Intervention mapping protocol for developing a theory-based diabetes self-management education program.

    Science.gov (United States)

    Song, Misoon; Choi, Suyoung; Kim, Se-An; Seo, Kyoungsan; Lee, Soo Jin

    2015-01-01

    Development of behavior theory-based health promotion programs is encouraged with the paradigm shift from contents to behavior outcomes. This article describes the development process of the diabetes self-management program for older Koreans (DSME-OK) using intervention mapping (IM) protocol. The IM protocol includes needs assessment, defining goals and objectives, identifying theory and determinants, developing a matrix to form change objectives, selecting strategies and methods, structuring the program, and planning for evaluation and pilot testing. The DSME-OK adopted seven behavior objectives developed by the American Association of Diabetes Educators as behavioral outcomes. The program applied an information-motivation-behavioral skills model, and interventions were targeted to 3 determinants to change health behaviors. Specific methods were selected to achieve each objective guided by IM protocol. As the final step, program evaluation was planned including a pilot test. The DSME-OK was structured as the 3 determinants of the IMB model were intervened to achieve behavior objectives in each session. The program has 12 weekly 90-min sessions tailored for older adults. Using the IM protocol in developing a theory-based self-management program was beneficial in terms of providing a systematic guide to developing theory-based and behavior outcome-focused health education programs.

  18. Leveraging Sociocultural Theory to Create a Mentorship Program for Doctoral Students

    Science.gov (United States)

    Crosslin, Matt; Wakefield, Jenny S.; Bennette, Phyllis; Black, James William, III

    2013-01-01

    This paper details a proposed doctoral student connections program that is based on sociocultural theory. It is designed to assist new students with starting their educational journey. This program is designed to leverage social interactions, peer mentorship, personal reflection, purposeful planning, and existing resources to assist students in…

  19. PROGRAMMED LEARNING--THEORY AND RESEARCH, AN ENDURING PROBLEM IN PSYCHOLOGY. SELECTED READINGS.

    Science.gov (United States)

    MOORE, J. WILLIAM, ED.; SMITH, WENDELL I., ED.

    THIS IS A COMPILATION OF ARTICLES DEALING WITH PROGRAMED INSTRUCTION AND AUTO-INSTRUCTIONAL DEVICES (TEACHING-MACHINES). THE LITERATURE IS REVIEWED AND AN OVERVIEW OF THE FIELD IS PRESENTED. THE APPLICATION OF INSTRUCTIONAL TECHNOLOGY AND LEARNING THEORY TO TEACHING MACHINES IS DISCUSSED, AND THE PROCEDURE AND RULES OF PROGRAMING METHOD. SAMPLES…

  20. THE GENERAL ATOMICS FUSION THEORY PROGRAM ANNUAL REPORT FOR GRANT YEAR 2004

    International Nuclear Information System (INIS)

    PROJECT STAFF

    2004-01-01

    The dual objective of the fusion theory program at General Atomics (GA) is to significantly advance our scientific understanding of the physics of fusion plasmas and to support the DIII-D and other tokamak experiments. The program plan is aimed at contributing significantly to the Fusion Energy Science and the Tokamak Concept Improvement goals of the Office of Fusion Energy Sciences (OFES)

  1. The Persuasive Program in Adult Education: Theory and Planning.

    Science.gov (United States)

    Atkinson, Thomas Grant

    The purpose of this study was to investigate, develop, and explicate a procedure, theoretical in nature, which adult educators can use for comprehending, analyzing and planning single-event persuasive programs for adults. The study conceptualized persuasion as a behavioral phenomenon consisting of verifiable human action which constitutes, or is…

  2. An inertia-free filter line-search algorithm for large-scale nonlinear programming

    Energy Technology Data Exchange (ETDEWEB)

    Chiang, Nai-Yuan; Zavala, Victor M.

    2016-02-15

    We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.

  3. Some Contributions of General Systems Theory, Cybernetics Theory and Management Control Theory to Evaluation Theory and Practice. Research on Evaluation Program Paper and Report Series. Interim Draft.

    Science.gov (United States)

    Cook, Desmond L.

    This document, one of a series of reports examining the possible contribution of other disciplines to evaluation methodology, describes the major elements of general systems theory (GST), cybernetics theory (CT) and management control theory (MCT). The author suggests that MCT encapsulates major concerns of evaluation since it reveals that…

  4. The theory of dissipative structures of the kinetic system for defects of nonlinear physical system 'metal+loading+irradiation'. Part 3

    International Nuclear Information System (INIS)

    Tarasov, V.A.; Borikov, T.L.; Kryzhanovskaya, T.V.; Chernezhenko, S.A.; Rusov, V.D.

    2007-01-01

    The kinetic system for defects of physical nonlinear system 'metal + load + irradiation' is specified [1, 2, 3]. Developing the approaches offered in [4], where distinctions of mechanisms of radiating creep and areas of their applicability are formalized (depending on external parameters) for fuel and constructional metals, division of kinetic systems for defects of constructional and fuel metals is carrying out. Thus the accent on the autocatalytic features of kinetic system for defects of reactor fuel metals, resulting from the exoenergic autocatalytic character of nuclear fission reactions being the main point defect source is done. In this part of the article the basic attention is given to the kinetic of sink drains for point defects. For kinetic systems of sinks-sources new approaches for the task of boundary conditions are offered. The possible structure of the computer program modelling kinetic system for defects of nonlinear physical system 'metal + load + irradiation' is considered

  5. Distributed cooperative H∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming

    Science.gov (United States)

    Luy, N. T.

    2018-04-01

    The design of distributed cooperative H∞ optimal controllers for multi-agent systems is a major challenge when the agents' models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H∞ optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero-sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilising controllers. It is shown that despite not using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi-robot systems.

  6. Parallel processors and nonlinear structural dynamics algorithms and software

    Science.gov (United States)

    Belytschko, Ted

    1989-01-01

    A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

  7. Nonlinear effects in evolution - an ab initio study: A model in which the classical theory of evolution occurs as a special case.

    Science.gov (United States)

    Clerc, Daryl G

    2016-07-21

    An ab initio approach was used to study the molecular-level interactions that connect gene-mutation to changes in an organism׳s phenotype. The study provides new insights into the evolutionary process and presents a simplification whereby changes in phenotypic properties may be studied in terms of the binding affinities of the chemical interactions affected by mutation, rather than by correlation to the genes. The study also reports the role that nonlinear effects play in the progression of organs, and how those effects relate to the classical theory of evolution. Results indicate that the classical theory of evolution occurs as a special case within the ab initio model - a case having two attributes. The first attribute: proteins and promoter regions are not shared among organs. The second attribute: continuous limiting behavior exists in the physical properties of organs as well as in the binding affinity of the associated chemical interactions, with respect to displacements in the chemical properties of proteins and promoter regions induced by mutation. Outside of the special case, second-order coupling contributions are significant and nonlinear effects play an important role, a result corroborated by analyses of published activity levels in binding and transactivation assays. Further, gradations in the state of perfection of an organ may be small or large depending on the type of mutation, and not necessarily closely-separated as maintained by the classical theory. Results also indicate that organs progress with varying degrees of interdependence, the likelihood of successful mutation decreases with increasing complexity of the affected chemical system, and differences between the ab initio model and the classical theory increase with increasing complexity of the organism. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.

  8. Grading Prediction of Enterprise Financial Crisis Based on Nonlinear Programming Evaluation: A Case Study of Chinese Transportation Industry

    Directory of Open Access Journals (Sweden)

    Zhi-yuan Li

    2014-01-01

    Full Text Available As the core of the effective financial crisis prevention, enterprise finance crisis prediction has been the focal attention of both theorists and businessmen. Financial crisis predictions need to apply a variety of financial and operating indicators for its analysis. Therefore, a new evaluation model based on nonlinear programming is established, the nature of the model is proved, the detailed solution steps of the model are given, and the significance and algorithm of the model are thoroughly discussed in this study. The proposed model can deal with the case of missing data, and has the good isotonic property and profound theoretical background. In the empirical analysis to predict the financial crisis and through the comparison of the analysis of historical data and the real enterprises with financial crisis, we find that the results are in accordance with the real enterprise financial conditions and the proposed model has a good predictive ability.

  9. A solution procedure for mixed-integer nonlinear programming formulation of supply chain planning with quantity discounts under demand uncertainty

    Science.gov (United States)

    Yin, Sisi; Nishi, Tatsushi

    2014-11-01

    Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.

  10. Analysis and monitoring of energy security and prediction of indicator values using conventional non-linear mathematical programming

    Directory of Open Access Journals (Sweden)

    Elena Vital'evna Bykova

    2011-09-01

    Full Text Available This paper describes the concept of energy security and a system of indicators for its monitoring. The indicator system includes more than 40 parameters that reflect the structure and state of fuel and energy complex sectors (fuel, electricity and heat & power, as well as takes into account economic, environmental and social aspects. A brief description of the structure of the computer system to monitor and analyze energy security is given. The complex contains informational, analytical and calculation modules, provides applications for forecasting and modeling energy scenarios, modeling threats and determining levels of energy security. Its application to predict the values of the indicators and methods developed for it are described. This paper presents a method developed by conventional nonlinear mathematical programming needed to address several problems of energy and, in particular, the prediction problem of the security. An example of its use and implementation of this method in the application, "Prognosis", is also given.

  11. Theory of nonlinear, distortive phenomena in solids: Martensitic, crack, and multiscale structures-phenomenology and physics. Progress summary, 1991--1994

    International Nuclear Information System (INIS)

    Sethna, J.P.; Krumhansl, J.A.

    1994-01-01

    We have identified tweed precursors to martensitic phase transformations as a spin glass phase due to composition variations, and used simulations and exact replica theory predictions to predict diffraction peaks and model phase diagrams, and provide real space data for comparison to transmission electron micrograph images. We have used symmetry principles to derive the crack growth laws for mixed-mode brittle fracture, explaining the results for two-dimensional fracture and deriving the growth laws in three dimensions. We have used recent advances in dynamical critical phenomena to study hysteresis in disordered systems, explaining the return-point-memory effect, predicting distributions for Barkhausen noise, and elucidating the transition from athermal to burst behavior in martensites. From a nonlinear lattice-dynamical model of a first-order transition using simulations, finite-size scaling, and transfer matrix methods, it is shown that heterophase transformation precursors cannot occur in a pure homogeneous system, thus emphasizing the role of disorder in real materials. Full integration of nonlinear Landau-Ginzburg continuum theory with experimental neutron-scattering data and first-principles calculations has been carried out to compute semi-quantitative values of the energy and thickness of twin boundaries in InTl and FePd martensites

  12. The "Chaos Theory" and nonlinear dynamics in heart rate variability analysis: does it work in short-time series in patients with coronary heart disease?

    Science.gov (United States)

    Krstacic, Goran; Krstacic, Antonija; Smalcelj, Anton; Milicic, Davor; Jembrek-Gostovic, Mirjana

    2007-04-01

    Dynamic analysis techniques may quantify abnormalities in heart rate variability (HRV) based on nonlinear and fractal analysis (chaos theory). The article emphasizes clinical and prognostic significance of dynamic changes in short-time series applied on patients with coronary heart disease (CHD) during the exercise electrocardiograph (ECG) test. The subjects were included in the series after complete cardiovascular diagnostic data. Series of R-R and ST-T intervals were obtained from exercise ECG data after sampling digitally. The range rescaled analysis method determined the fractal dimension of the intervals. To quantify fractal long-range correlation's properties of heart rate variability, the detrended fluctuation analysis technique was used. Approximate entropy (ApEn) was applied to quantify the regularity and complexity of time series, as well as unpredictability of fluctuations in time series. It was found that the short-term fractal scaling exponent (alpha(1)) is significantly lower in patients with CHD (0.93 +/- 0.07 vs 1.09 +/- 0.04; P chaos theory during the exercise ECG test point out the multifractal time series in CHD patients who loss normal fractal characteristics and regularity in HRV. Nonlinear analysis technique may complement traditional ECG analysis.

  13. In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

    Science.gov (United States)

    Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

    2015-01-01

    Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential

  14. JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

    International Nuclear Information System (INIS)

    Biffle, J.H.; Blanford, M.L.

    1994-05-01

    JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

  15. JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

    International Nuclear Information System (INIS)

    Biffle, J.H.

    1993-02-01

    JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

  16. Linear and nonlinear programming with Maple an interactive, applications-based approach

    CERN Document Server

    Fishback, Paul E

    2009-01-01

    ""… this text could be ideal for the right course and the right group of students. An independent or directed study in mathematical programming using this book could be an excellent introduction to applied optimization for an interested group of undergraduates. …""-MAA Reviews, March 2010

  17. Nonlinear dynamics of shells conveying pulsatile flow with pulse-wave propagation. Theory and numerical results for a single harmonic pulsation

    Science.gov (United States)

    Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.

    2017-05-01

    In deformable shells conveying pulsatile flow, oscillatory pressure changes cause local movements of the fluid and deformation of the shell wall, which propagate downstream in the form of a wave. In biomechanics, it is the propagation of the pulse that determines the pressure gradient during the flow at every location of the arterial tree. In this study, a woven Dacron aortic prosthesis is modelled as an orthotropic circular cylindrical shell described by means of the Novozhilov nonlinear shell theory. Flexible boundary conditions are considered to simulate connection with the remaining tissue. Nonlinear vibrations of the shell conveying pulsatile flow and subjected to pulsatile pressure are investigated taking into account the effects of the pulse-wave propagation. For the first time in literature, coupled fluid-structure Lagrange equations of motion for a non-material volume with wave propagation in case of pulsatile flow are developed. The fluid is modeled as a Newtonian inviscid pulsatile flow and it is formulated using a hybrid model based on the linear potential flow theory and considering the unsteady viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Contributions of pressure and velocity propagation are also considered in the pressure drop along the shell and in the pulsatile frictional traction on the internal wall in the axial direction. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior of a pressurized Dacron aortic graft conveying blood flow. A pulsatile time-dependent blood flow model is considered by applying the first harmonic of the physiological waveforms of velocity and pressure during the heart beating period. Geometrically nonlinear vibration response to pulsatile flow and transmural pulsatile pressure, considering the propagation of pressure and velocity changes inside the shell, is here presented via frequency-response curves, time histories, bifurcation

  18. Implementation of visual programming methods for numerical techniques used in electromagnetic field theory

    Directory of Open Access Journals (Sweden)

    Metin Varan

    2017-08-01

    Full Text Available Field theory is one of the two sub-field theories in electrical and electronics engineering that for creates difficulties for undergraduate students. In undergraduate period, field theory has been taught under the theory of electromagnetic fields by which describes using partial differential equations and integral methods. Analytical methods for solution of field problems on the basis of a mathematical model may result the understanding difficulties for undergraduate students due to their mathematical and physical infrastructure. The analytical methods which can be applied in simple model lose their applicability to more complex models. In this case, the numerical methods are used to solve more complex equations. In this study, by preparing some field theory‘s web-based graphical user interface numerical methods of applications it has been aimed to increase learning levels of field theory problems for undergraduate and graduate students while taking in mind their computer programming capabilities.

  19. Perspectives and Practices of Academics and Students of English Language Teaching Post-Graduate Programs within the Mediation Theory

    Science.gov (United States)

    Asmali, Mehmet

    2018-01-01

    Due to unsatisfactory number of researches investigating ELT post-graduate programs, and perceptions of academics and students in these programs regarding mediation theory of Feuerstein, this study attempted to investigate the aspects of this theory in doctorate and master programs in ELT department of a state university. Methodologically, this…

  20. A Nonvolume Preserving Plasticity Theory with Applications to Powder Metallurgy

    Science.gov (United States)

    Cassenti, B. N.

    1983-01-01

    A plasticity theory has been developed to predict the mechanical response of powder metals during hot isostatic pressing. The theory parameters were obtained through an experimental program consisting of hydrostatic pressure tests, uniaxial compression and uniaxial tension tests. A nonlinear finite element code was modified to include the theory and the results of themodified code compared favorably to the results from a verification experiment.