Cepheid pulsation theory and multiperiodic cepheid variables
International Nuclear Information System (INIS)
Cox, A.N.; Cox, J.P.
1975-01-01
In this review of the multiperiodic Cepheid variables, the subject matter is divided into four parts. The first discusses general causes of pulsation of Cepheids and other variable stars, and their locations on the H-R diagram. In the second section, the linear adiabatic and nonadiabatic theory calculation of radial pulsation periods and their application to the problem of masses and double-mode Cepheids are reviewed. Periodic solutions, and their stability, of the nonlinear radial pulsation equations for Cepheids and RR Lyrae stars are considered in the third section. The last section provides the latest results on nonlinear, nonperiodic, radial pulsations for Cepheids and RR Lyrae stars. (BJG)
Nonlinear pulsations of luminous He stars
International Nuclear Information System (INIS)
Proffitt, C.R.; Cox, A.N.
1986-01-01
Radial pulsations in models of R Cor Bor stars and BD + 1 0 4381 have been studied with a nonlinear hydrodynamic pulsation code. Comparisons are made with previous calculations and with observed light and velocity curves. 13 refs., 2 tabs
The history and development of nonlinear stellar pulsation codes
International Nuclear Information System (INIS)
Davis, C.G.
1987-01-01
This review is limited to the history and development of nonlinear stellar pulsation codes and methods. The narrative includes examples of practical interest in the application of these numerical methods to problems in stellar pulsation such as Cepheid mass discrepancy, the delineation of the RR Lyrae instability strip, and the question of the development of double-mode pulsation as observed in Cepheids, RR Lyrae and other variable stars. 15 refs
Linear radial pulsation theory. Lecture 5
International Nuclear Information System (INIS)
Cox, A.N.
1983-01-01
We describe a method for getting an equilibrium stellar envelope model using as input the total mass, the envelope mass, the surface effective temperature, the total surface luminosity, and the composition of the envelope. Then wih the structure of the envelope model known, we present a method for obtaining the raidal pulsation periods and growth rates for low order modes. The large amplitude pulsations observed for the yellow and red giants and supergiants are always these radial models, but for the stars nearer the main sequence, as for all of our stars and for the white dwarfs, there frequently are nonradial modes occuring also. Application of linear theory radial pulsation theory is made to the giant star sigma Scuti variables, while the linear nonradial theory will be used for the B stars in later lectures
Stellar pulsations in beyond Horndeski gravity theories
Energy Technology Data Exchange (ETDEWEB)
Sakstein, Jeremy [Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, 209 S. 33rd St., Philadelphia, PA 19104 (United States); Kenna-Allison, Michael; Koyama, Kazuya, E-mail: sakstein@physics.upenn.edu, E-mail: mka1g13@soton.ac.uk, E-mail: kazuya.koyama@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom)
2017-03-01
Theories of gravity in the beyond Horndeski class recover the predictions of general relativity in the solar system whilst admitting novel cosmologies, including late-time de Sitter solutions in the absence of a cosmological constant. Deviations from Newton's law are predicted inside astrophysical bodies, which allow for falsifiable, smoking-gun tests of the theory. In this work we study the pulsations of stars by deriving and solving the wave equation governing linear adiabatic oscillations to find the modified period of pulsation. Using both semi-analytic and numerical models, we perform a preliminary survey of the stellar zoo in an attempt to identify the best candidate objects for testing the theory. Brown dwarfs and Cepheid stars are found to be particularly sensitive objects and we discuss the possibility of using both to test the theory.
Stellar pulsations in beyond Horndeski gravity theories
Sakstein, Jeremy; Kenna-Allison, Michael; Koyama, Kazuya
2017-03-01
Theories of gravity in the beyond Horndeski class recover the predictions of general relativity in the solar system whilst admitting novel cosmologies, including late-time de Sitter solutions in the absence of a cosmological constant. Deviations from Newton's law are predicted inside astrophysical bodies, which allow for falsifiable, smoking-gun tests of the theory. In this work we study the pulsations of stars by deriving and solving the wave equation governing linear adiabatic oscillations to find the modified period of pulsation. Using both semi-analytic and numerical models, we perform a preliminary survey of the stellar zoo in an attempt to identify the best candidate objects for testing the theory. Brown dwarfs and Cepheid stars are found to be particularly sensitive objects and we discuss the possibility of using both to test the theory.
International Nuclear Information System (INIS)
Schumaker, B.L.
1985-01-01
This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum-mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and momentum variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes arise from two-proton transitions, i.e., are created or destroyed two at a time. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed. The fifth paper considers the validity of the standard quantum limit (SQL) for measurements that monitor the position of a free mass. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models and of the gravitational waves they emit
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
Linear nonradial pulsation theory. Lecture 7
International Nuclear Information System (INIS)
Cox, A.N.
1983-01-01
Many of the upper main-sequence stars pulsate in spheroidal nonradial modes. We know this to be true in numerous cases, as we have tabulated for the #betta# Cephei and delta Scuti variables in previous lectures. However, we cannot identify the actual mode for any star except for the low-order pressure p and f modes of our sun. It remains a great challenge to clearly state what really is occurring, in the process we learn more about how stars evolve and pulsate
Theory of auroral zone PiB pulsation spectra
International Nuclear Information System (INIS)
Lysak, R.L.
1988-01-01
Changes in the auroral zone current system are often accompanied by magnetic pulsations with periods of about 1 s. These so-called bursts of irregular pulsations (PiB) have been observed both on ground magnetograms and with in situ satellite observations. These pulsations can be understood as excitations of a resonant cavity in the topside ionosphere, where the Alfven speed has a strong gradient due to the exponential decrease of density above the ionosphere. These waves have a frequency which scales as the ratio of the Alfven speed at the ionosphere divided by the ionospheric scale height. For a pure exponential Alfven speed profile, the mode frequencies are related to zeros of the zeroth-order Bessel function. For other profiles of the density, and therefore Alfven speed, the frequencies are not exactly given by the simple theory, but the frequency and mode structure are similar provided the Alfven speed sharply increases above the ionosphere
International Nuclear Information System (INIS)
Kono, M.; Kawakita, M.
1990-01-01
A nonlinear equation describing the development of the Buneman instability has been derived and solved with the aid of Hirota's bilinear transform [J. Math. Phys. 14, 810 (1973)] to give a variety of stationary solutions, such as pulsating solitons, temporally localized and spatially periodic solutions, as well as ordinary solitons
On a method of numerical calculation of nonlinear radial pulsations of stars
International Nuclear Information System (INIS)
Kosovichev, A.G.
1984-01-01
Some features of using the finite difference method for numerical investigation of nonradial pulsations of stars were considered. The mathematical model of these pulsations is described by time-dependent gasdynaMic equations with gravity. A one-dimentional (spherically-symmetric) case is considered. It was obtained a two-parametric family of ultimate conservative difference schemes where the diffepence analogy of the main conservative laws as well as the additional relations for the balance to individual kinds of energy are performed. Such difference schemes provide more exact calculation of nonlinear flows with shocks as compared with the other difference schemes with the same order of approximation. The methods of numerical solution of implicit (absolute stable) difference schemes for a given family were considered. The coupled equations are solved through iterative Newton method Using martrix and separate successive eliminations. Numerical method can be used for calculation of large amplitude radial pulsations of stars
Nonlinear optimal control theory
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
Nonlinear effects in Pulsations of Compact Stars and Gravitational Waves
International Nuclear Information System (INIS)
Passamonti, A
2007-01-01
Nonlinear stellar oscillations can be studied by using a multiparameter perturbative approach, which is appropriate for investigating the low and mild nonlinear dynamical regimes. We present the main properties of our perturbative framework for describing, in the time domain, the nonlinear coupling between the radial and nonradial perturbations of spherically symmetric and perfect fluid compact stars. This particular coupling can be described by gauge invariant quantities that obeys a system of partial differential equations with source terms, which are made up of product of first order radial and nonradial perturbations. We report the results of numerical simulations for both the axial and polar coupling perturbations, that exhibit in the stellar dynamics and in the associated gravitational wave signal some interesting nonlinear effects, such as combination harmonics and resonances. In particular, we concentrate on the axial case, where the linear axial perturbations describe a harmonic component of a differentially rotating neutron star. The gravitational wave signal of this stellar configuration mirrors at second perturbative order the spectral features of the linear radial normal modes. In addition, a signal amplification appears when one of the radial frequencies is close to the axial w-mode frequencies of the star
A test of Pulsation Theory in Hot B Subdwarfs
Fontaine, Gilles
There are currently of the order of 15 hot B subdwarf (sdB) stars which are known to exhibit low-amplitude (a few to tens of millimag), short-period (100-500 s), multiperiodic luminosity variations. These pulsations are thought to be driven by an opacity bump linked to the presence of a local enhancement of the iron abundance in the envelopes of sdB stars. Such an enhancement results quite naturally from the diffusive equilibrium between gravitational settling and radiative support in the stellar envelope. Nevertheless, surveys for pulsating sdB stars show that, in several instances, variable and non-variable objects with similar effective temperatures and gravities may coexist in the HR diagram. This result suggests that an additional parameter, perhaps a weak stellar wind, might affect the extent of the iron reservoir and thus the ability of the latter to drive pulsations in sdB stars. Fortunately, it is expected that such a wind might also leave its mark on the photospheric heavy element abundance patterns. The intended FUSE observations will i) permit a direct comparison of the heavy element abundance patterns in variable and nonvariable stars of similar atmospheric parameters; ii) provide a consistency check with our wind models; and iii) provide a test of the currently-favored explanation for the driving of the observed pulsations.
A Test of Pulsation Theory in Hot B Subdwarfs (bis)
Fontaine, G.
There are currently 33 hot B subdwarf (sdB) stars which are known to exhibit low-amplitude (a few to tens of mmag), short-period (100-500 s), multiperiodic luminosity variations caused by acoustic mode instabilities. These pulsations are thought to be driven by an opacity bump linked to the presence of a local enhancement of the iron and other iron-peak elements) abundance in the envelopes of sdB stars. Such an enhancement results quite naturally from the diffusive equilibrium between gravitational settling and radiative support in the stellar envelope. Nevertheless, surveys for pulsating sdB stars show that variable and nonvariable objects with similar effective temperatures and gravities coexist in the log g-Teff diagram. This puzzling result suggests that an additional parameter, perhaps a weak stellar wind, might affect the extent of the iron reservoir and thus the ability of the latter to drive pulsations in sdB stars. Fortunately, it is expected that such a wind might also leave its mark on the photospheric heavy element abundance patterns. The intended FUSE observations will 1) permit a direct comparison of the heavy element abundance patterns in variable and nonvariable stars of similar atmospheric parameters, 2) provide a consistency check with our wind models, and 3) provide a test of the currently-favored explanation for the driving of the observed pulsations.
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
Catelan, M?rcio
2014-01-01
The most recent and comprehensive book on pulsating stars which ties the observations to our present understanding of stellar pulsation and evolution theory. Written by experienced researchers and authors in the field, this book includes the latest observational results and is valuable reading for astronomers, graduate students, nuclear physicists and high energy physicists.
An unusual nonlinear system in the magnetosphere: A possible driver for auroral pulsations
International Nuclear Information System (INIS)
Davidson, G.T.; Chiu, Y.T.
1991-01-01
Many aspects of the relation between spatial and temporal structures in morningside aurorae can be explained with the aid of a nonlinear model that describes the interactions between energetic electrons and VLF waves. The simplest form of the model consists of three differential equations, with time derivatives generated in reference frames moving with either the energetic electrons, the cold plasma; or the VLF waves that interact with the energetic electrons. Although unstable solutions that could explain the origin of spatial structures are not found, the existence of spatial structures having sufficiently fine scales can provide a repetitive perturbation that maintains the temporal variations. An analysis of the behavior of solutions of the nonlinear system reveals that a strange attractor does not occur in the autonomous system; but when the repetitive perturbations are regarded as external periodic forcing terms, unusual forms of nonlinear behavior are revealed. If the frequencies of the forcing terms are not commensurate with the natural periods of the system, the solutions present some of the characteristics of deterministic chaos. The nearest analogy is a driven nonlinear oscillator with asymmetric damping. However, because of the stiffness of the system, even those solutions that are not truly chaotic (in the commonly accepted usage) will be indistinguishable from chaos over tens to hundreds of pulsation cycles. In certain cases, when damping terms are reduced to zero, the system displays a form of behavior with many of the important characteristics of chaos, but the phase trajectories do not appear to be bounded
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)
Mass loss and cepheid pulsation
International Nuclear Information System (INIS)
Davis, C.G. Jr.
1977-01-01
Two purposes are served: to discuss the latest improvements in nonlinear pulsation theory indicating the ability to resolve features such as the ''Christy bump'' on the light curves and to show from the results of a bump model and recent observations that mass loss is one of the possible explanations for the mass discrepancy problem between evolutionary and pulsation theories. Recent observations by Sanford and Gow of Los Alamos and Bernat (McDonald Observatory) show that extensive mass loss has occurred in the evolution of the M supergiant α Orionis
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.
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.
Directory of Open Access Journals (Sweden)
Mati Goldberg
Full Text Available A new paradigm has recently emerged in brain science whereby communications between glial cells and neuron-glia interactions should be considered together with neurons and their networks to understand higher brain functions. In particular, astrocytes, the main type of glial cells in the cortex, have been shown to communicate with neurons and with each other. They are thought to form a gap-junction-coupled syncytium supporting cell-cell communication via propagating Ca(2+ waves. An identified mode of propagation is based on cytoplasm-to-cytoplasm transport of inositol trisphosphate (IP(3 through gap junctions that locally trigger Ca(2+ pulses via IP(3-dependent Ca(2+-induced Ca(2+ release. It is, however, currently unknown whether this intracellular route is able to support the propagation of long-distance regenerative Ca(2+ waves or is restricted to short-distance signaling. Furthermore, the influence of the intracellular signaling dynamics on intercellular propagation remains to be understood. In this work, we propose a model of the gap-junctional route for intercellular Ca(2+ wave propagation in astrocytes. Our model yields two major predictions. First, we show that long-distance regenerative signaling requires nonlinear coupling in the gap junctions. Second, we show that even with nonlinear gap junctions, long-distance regenerative signaling is favored when the internal Ca(2+ dynamics implements frequency modulation-encoding oscillations with pulsating dynamics, while amplitude modulation-encoding dynamics tends to restrict the propagation range. As a result, spatially heterogeneous molecular properties and/or weak couplings are shown to give rise to rich spatiotemporal dynamics that support complex propagation behaviors. These results shed new light on the mechanisms implicated in the propagation of Ca(2+ waves across astrocytes and the precise conditions under which glial cells may participate in information processing in the brain.
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
Theory of ultra-low-frequency magnetic pulsations in the earth's magnetosphere
International Nuclear Information System (INIS)
Chen, Liu.
1991-03-01
Long-period (T = 10-600 s) geomagnetic pulsations are known to be associated with magnetohydrodynamic (MHD) perturbations in the Earth's magnetosphere. Broadly speaking, there are two categories of excitation mechanisms. The first category corresponds to impulsive/external excitations, where MHD waves exhibit the stable discrete as well as continuous spectra. The second category corresponds to spontaneous/internal excitations, where MHD instabilities are excited either reactively or via wave-particle interactions. In this tutorial lecture, we briefly review theories concerning both categories of excitation mechanisms and compare theoretical predictions with available satellite observations. 20 refs
On the theory of weak turbulence for the nonlinear Schrödinger equation
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.
Directory of Open Access Journals (Sweden)
Zong Weikai
2017-01-01
Full Text Available Nonlinear mode interactions are difficult to observe from ground-based telescopes as the typical periods of the modulations induced by those nonlinear phenomena are on timescales of weeks, months, even years. The launch of space telescopes, e.g., Kepler, has tremendously changed the situation and shredded new light on this research field. We present results from Kepler photometry showing evidence that nonlinear interactions between modes occur in the two compact pulsators KIC 8626021, a DB white dwarf, and KIC 10139564, a short period hot B subdwarf. KIC 8626021 and KIC 10139564 had been monitored by Kepler in short-cadence for nearly two years and more than three years without interruption, respectively. By analyzing these high-quality photometric data, we found that the modes within the triplets induced by rotation clearly reveal different behaviors: their frequencies and amplitudes may exhibit either periodic or irregular modulations, or remain constant. These various behaviors of the amplitude and of the frequency modulations of the oscillation modes observed in these two stars are in good agreement with those predicted within the amplitude equation formalism in the case of the nonlinear resonant mode coupling mechanism.
Spectral theory and nonlinear functional analysis
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.
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.
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)
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...
Theory and design of nonlinear metamaterials
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
Nonlinear theory of electroelastic and magnetoelastic interactions
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.
A nonlinear theory of generalized functions
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...
Quantitative theory of driven nonlinear brain dynamics.
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.
Nonlinear system theory: another look at dependence.
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.
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
International Nuclear Information System (INIS)
1989-01-01
The study of stellar pulsations is a major route to the understanding of stellar structure and evolution. At the South African Astronomical Observatory (SAAO) the following stellar pulsation studies were undertaken: rapidly oscillating Ap stars; solar-like oscillations in stars; 8-Scuti type variability in a classical Am star; Beta Cephei variables; a pulsating white dwarf and its companion; RR Lyrae variables and galactic Cepheids. 4 figs
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.)
Nonlinear analysis approximation theory, optimization and applications
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.
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
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)
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...
Spectral theory and nonlinear analysis with applications to spatial ecology
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.
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
Geometric Theory of Reduction of Nonlinear Control Systems
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.).
Lectures in nonlinear mechanics and chaos theory
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...
Energy Technology Data Exchange (ETDEWEB)
Szabó, Róbert; Ivezić, Željko; Kiss, László L.; Kolláth, Zoltán [Konkoly Observatory, MTA CSFK, Konkoly Thege Miklós út 15-17, H-1121 Budapest (Hungary); Jones, Lynne; Becker, Andrew C.; Davenport, James R. A. [Astronomy Department, University of Washington, Box 351580, Seattle, WA 98195-1580 (United States); Sesar, Branimir [Division of Physics, Mathematics and Astronomy, Caltech, Pasadena, CA 91125 (United States); Cutri, Roc M., E-mail: rszabo@konkoly.hu [Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125 (United States)
2014-01-01
We present and discuss an extensive data set for the non-Blazhko ab-type RR Lyrae star SDSS J015450+001501, including optical Sloan Digital Sky Survey ugriz light curves and spectroscopic data, LINEAR and Catalina Sky Survey unfiltered optical light curves, and infrared Two Micron All Sky Survey (2MASS) JHK{sub s} and Wide-field Infrared Survey Explorer W1 and W2 light curves. Most notable is that light curves obtained by 2MASS include close to 9000 photometric measures collected over 3.3 yr and provide an exceedingly precise view of near-infrared variability. These data demonstrate that static atmosphere models are insufficient to explain multiband photometric light-curve behavior and present strong constraints for nonlinear pulsation models for RR Lyrae stars. It is a challenge to modelers to produce theoretical light curves that can explain data presented here, which we make publicly available.
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)
Nonlinear structural mechanics theory, dynamical phenomena and modeling
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...
Nonlinear solar cycle forecasting: theory and perspectives
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.
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.
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.
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.
Trimpi, Robert L
1956-01-01
From a theory developed on a quasi-one-dimensional-flow basis, it is found that the stability of the ram jet is dependent upon the instantaneous values of mass flow and total pressure recovery of the supersonic diffuser and immediate neighboring subsonic diffuser. Conditions for stable and unstable flow are presented. The theory developed in the report is in agreement with the experimental data of NACA-TN-3506 and NACA-RM-L50K30. A simple theory for predicting the approximate amplitude of small pressure pulsation in terms of mass-flow decrement from minimum-stable mass flow is developed and found to agree with experiments. Cold-flow tests at a Mach number of 1.94 of ram-jet models having scale factors of 3.15:1 and Reynolds number ratios of 4.75:1 with several supersonic diffuser configurations showed only small variations in performance between geometrically similar models. The predominant variation in steady-flow performance resulted from the larger boundary layer in the combustion chamber of the low Reynolds number models. The conditions at which buzz originated were nearly the same for the same supersonic diffuser (cowling-position angle) configurations in both large and small diameter models. There was no appreciable variation in stability limits of any of the models when the combustion-chamber length was increased by a factor of three. The unsteady-flow performance and wave patterns were also similar when considered on a reduced-frequency basis determined from the relative lengths of the model. The negligible effect of Reynolds number on stability of the off-design configurations was not anticipated in view of the importance of boundary layer to stability, and this result should not be construed to be generally applicable. (author)
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.)
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
An introduction to nonlinear analysis and fixed point theory
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 ...
Theory of weakly nonlinear self-sustained detonations
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
Nonlinear model predictive control theory and algorithms
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...
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
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
Nonlinear transport theory in the metal with tunnel barrier
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 ?.
Energy flow theory of nonlinear dynamical systems with applications
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 ...
Mathematical Systems Theory : from Behaviors to Nonlinear Control
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...
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
A Survey of Nonlinear Dynamics (Chaos Theory)
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
Nonlinear theory of localized standing waves
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...
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
An enstrophy-based linear and nonlinear receptivity theory
Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata
2018-05-01
In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.
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
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
Introduction to the theory of nonlinear optimization
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
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
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
Pulsations of delta Scuti stars
International Nuclear Information System (INIS)
Cox, A.N.
1989-01-01
A general review of the pulsating δ Scuti variables is given including the observed light curves and positions of the stars in the Hertzsprung-Russell diagram. Theoretical interpretations from evolution and pulsation calculations give their masses, radii, luminosities, and even their approximate internal compositions. Three models of these stars are discussed and used to study the nonlinear hydrodynamic behavior of these stars. The hydrodynamic equations and the Stellingwerf method for obtaining strictly periodic solutions are outlined. Problems of allowing for time-dependent convection and its great sensitivity to temperature and density are presented. Tentative results to date do not show any tendency for amplitudes to grow to large unobserved amplitudes, in disagreement with an earlier suggestion by Stellingwerf. It is found that the very small growth rates of the pulsations may even be too small to be useful in seeking a periodic solution. 15 refs., 8 figs., 3 tabs
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
Theory for Nonlinear Spectroscopy of Vibrational Polaritons
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...
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.)
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
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)
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...
Non-linear theory of elasticity
Lurie, AI
2012-01-01
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
The research on flow pulsation characteristics of axial piston pump
Wang, Bingchao; Wang, Yulin
2017-01-01
The flow pulsation is an important factor influencing the axial piston pump performance. In this paper we implement modeling and simulation of the axial piston pump with AMESim software to explore the flow pulsation characteristics under various factors . Theory analysis shows the loading pressure, angular speed, piston numbers and the accumulator impose evident influence on the flow pulsation characteristics. This simulation and analysis can be used for reducing the flow pulsation rate via properly setting the related factors.
Backward stochastic differential equations from linear to fully nonlinear theory
Zhang, Jianfeng
2017-01-01
This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.
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.
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.
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.
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
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.
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.
Information theory and stochastics for multiscale nonlinear systems
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...
Composite Beam Theory with Material Nonlinearities and Progressive Damage
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
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
The preparation problem in nonlinear extensions of quantum theory
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...
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
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
Synthesis of robust nonlinear autopilots using differential game theory
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.
Development of a nonlinear unsteady transonic flow theory
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.
Nonlinear dynamical systems for theory and research in ergonomics.
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.
On the non-linear scale of cosmological perturbation theory
Blas, Diego; Konstandin, Thomas
2013-01-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Nonlinear responses of chiral fluids from kinetic theory
Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun
2018-01-01
The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.
On the non-linear scale of cosmological perturbation theory
International Nuclear Information System (INIS)
Blas, Diego; Garny, Mathias; Konstandin, Thomas
2013-04-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Theories of quantum dissipation and nonlinear coupling bath descriptors
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.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
Nonlinear electroelasticity: material properties, continuum theory and applications.
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.
Nonlinear electroelasticity: material properties, continuum theory and applications
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.
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
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.
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.)
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
Nonlinear polarization of ionic liquids: theory, simulations, experiments
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.
Linear theory for filtering nonlinear multiscale systems with model error.
Berry, Tyrus; Harlim, John
2014-07-08
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering
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....
Theory of weakly nonlinear self-sustained detonations
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.
Nonlinear problems of the theory of heterogeneous slightly curved shells
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.
History of nonlinear oscillations theory in France (1880-1940)
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...
Pulsation properties of Mira long period variables
International Nuclear Information System (INIS)
Cahn, J.H.
1980-01-01
A matter of great interest to variable star students concerns the mode of pulsation of Mira long period variables. In this report we first give observational evidence for the pulsation constant Q. We then compare the observations with calculations. Next, we review two interesting groups of papers dealing with hydrodynamic properties of long period variables. In the first, a fully dynamic nonlinear calculation maps out the Mira instability domain. In the second, special attention is paid to shock propagation beyond the photosphere which in large measure accounts for the complex spectra from this region. (orig./WL)
Persad, Aaron H; Sefiane, Khellil; Ward, Charles A
2013-10-29
During sessile droplet evaporation, studies with IR thermography and shadowgraphs have indicated temperature pulsations. We confirm those observations with microthermocouples, but microthermocouples also indicate temperature pulsations in the atmosphere of the droplet. The pressure in this atmosphere pulsated as well and was correlated with the temperature pulsations in the droplet. Also, we find that if a droplet evaporates into its own vapor, there are no temperature or pressure pulsations. The pulsations occur only if the droplet evaporates into an atmosphere with a component having a heat of solution with the droplet when it adsorbs-absorbs. None of the currently proposed mechanisms for the temperature pulsations provide an explanation for the coupling between the temperature pulsations in the droplet and the vapor-phase pressure pulsations, and for the absence of the pulsations when the system is single-component. As a mechanism for the pulsations, we propose that when a droplet is exposed to an atmosphere containing a component that has a heat of solution with the droplet, energy will be released from adsorption-absorption. This energy will cause pulsations in the evaporation flux, and these pulsations could cause the observed temperature and pressure pulsations. We examine this mechanism by showing that, if the measured temperature pulsations in a water droplet exposed to a methanol atmosphere are used as the input to a theory of evaporation kinetics (statistical rate theory), the pressure pulsations of the water vapor in the methanol atmosphere are predicted and agree with those measured with a quadrupole mass analyzer. When the inputs and outputs are reversed in the theory, we find that the temperature pulsations in the droplet are correctly predicted from the measured water vapor pulsations in the atmosphere.
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...
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
Non-linearities in Theory-of-Mind Development.
Blijd-Hoogewys, Els M A; van Geert, Paul L C
2016-01-01
Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72-78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths.
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.
Transient response of nonlinear polymer networks: A kinetic theory
Vernerey, Franck J.
2018-06-01
Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.
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
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.)
International Nuclear Information System (INIS)
Whitelock, P.A.
1990-01-01
The observational characteristics of pulsating red variables are reviewed with particular emphasis on the Miras. These variables represent the last stage in the evolution of stars on the Asymptotic Giant Branch (AGB). A large fraction of the IRAS sources in the Bulge are Mira variables and a subset of these are also OH/IR sources. Their periods range up to 720 days, though most are between 360 and 560 days. At a given period those stars with the highest pulsation amplitudes have the highest mass-loss rates; this is interpreted as evidence for a causal connection between mass-loss and pulsation. It is suggested that once an AGB star has become a Mira it will evolve with increasing pulsation amplitude and mass-loss, but with very little change of luminosity or logarithmic period. 26 refs
International Nuclear Information System (INIS)
Cox, A.N.
1982-01-01
Double mode pulsation is a very pervasive phenomenon in stars all over the Hertzsprung-Russell diagram. In order of increasing radius, examples are: ZZ Ceti stars, the sun, the delta Scuti stars, RR Lyrae variables, the β Cephei variables and those related to them, Cepheids, and maybe even the Mira stars. These many modes have been interpreted as both radial and nonradial modes, but in many cases the actual mode has not been clearly identified. Yellow giants seem to be the most simple pulsators with a large majority of the RR Lyrae variables and Cepheids showing only one pulsation period. We limit this review to those very few cases for classical Cepheids and RR Lyrae variables which display two modes. For these we know many facts about these stars, but the actual cause of the pulsation in two modes simultaneously remains unknown
Explicit Nonlinear Model Predictive Control Theory and Applications
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; �...
Untangling the drivers of nonlinear systems with information theory
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
Pulsations of delta Scuti stars
International Nuclear Information System (INIS)
Cox, A.N.
1990-01-01
In this paper the authors give a general review of the pulsating δ Scuti variables, including the observed light curves and positions of the stars in the Hertzsprung-Russell diagram. Theoretical interpretations from evolution and pulsation calculations give their masses, radii, luminosities, and even their approximate internal compositions. Then we discuss three models of these stars, and use them to study the nonlinear hydrodynamic behavior of these stars, after which the authors outline the hydrodynamic equations and the Stellingwerf method for obtaining strictly periodic solutions. The authors also present the problems of allowing for time-dependent convection and its great sensitivity to temperature and density. Tentative results to data do not show any tendency for amplitudes to grow to large unobserved amplitudes, in disagreement with an earlier suggestion by Stellingwerf. Finally, the authors find that the very small growth rates of the pulsations may even be too small to be useful in seeking a periodic solution. The δ Scuti variables are the most common type of variable star in our galaxy except for the white dwarfs. This is because stars in the mass range from just over one M circle-dot up to at least several M circle-dot pass through the yellow giant instability strip in the Hertzsprung-Russell diagram as they evolve off the main sequence to the red. Actually, stars up to the maximum main sequence mass also evolve through this region at higher luminosities, but there are so few of them, and they evolve so rapidly to the red, that they are almost unknown. At the higher luminosity, they probably would be called first-instability strip-crossing Cepheids anyway. Such cepheids are difficult to separate from those that are on the second blueward instability strip crossing that is much slower. Really, the δ Scuti variables are just low-luminosity Cepheids
Zong, Weikai; Charpinet, Stéphane; Fu, Jian-Ning; Vauclair, Gérard; Niu, Jia-Shu; Su, Jie
2018-02-01
We present the first results of an ensemble and systematic survey of oscillation mode variability in pulsating hot B subdwarf (sdB) and white dwarf stars observed with the original Kepler mission. The satellite provides uninterrupted high-quality photometric data with a time baseline that can reach up to 4 yr collected on pulsating stars. This is a unique opportunity to characterize long-term behaviors of oscillation modes. A mode modulation in amplitude and frequency can be independently inferred by its fine structure in the Fourier spectrum, from the sLSP, or with prewhitening methods applied to various parts of the light curve. We apply all these techniques to the sdB star KIC 3527751, a long-period-dominated hybrid pulsator. We find that all the detected modes with sufficiently large amplitudes to be thoroughly studied show amplitude and/or frequency variations. Components of three identified quintuplets around 92, 114, and 253 μHz show signatures that can be linked to nonlinear interactions according to the resonant mode coupling theory. This interpretation is further supported by the fact that many oscillation modes are found to have amplitudes and frequencies showing correlated or anticorrelated variations, a behavior that can be linked to the amplitude equation formalism, where nonlinear frequency corrections are determined by their amplitude variations. Our results suggest that oscillation modes varying with diverse patterns are a very common phenomenon in pulsating sdB stars. Close structures around main frequencies therefore need to be carefully interpreted in light of this finding to secure a robust identification of real eigenfrequencies, which is crucial for seismic modeling. The various modulation patterns uncovered should encourage further developments in the field of nonlinear stellar oscillation theory. It also raises a warning to any long-term project aiming at measuring the rate of period change of pulsations caused by stellar evolution, or at
Theoretical pulsation of metallic-line stars
International Nuclear Information System (INIS)
Cox, A.N.; King, D.S.; Hodson, S.W.
1979-01-01
The linear-theory radial-pulsation stability of low-helium delta Scuti variable models (1.0--2.5 Msun) has been investigated to see if metallicism and pulsation can occur simultaneously. Metallicism, which occurs in slowly rotating stars after the gravitational settling of He and the loss of the He II convection zone and its deep mixing for Y< or approx. =0.1, can then be established rapidly compared with the evolution time scale. Pulsation can still occur with driving due to the residual helium and the enhanced hydrogen. With the reduced helium giving no connection zone, the pulsation instability strip, whose blue and edges are estimated in this paoer, is about half as wide as with a normal helium abundance. Zero helium in the surface driving regions, however, produces blue edges so red that probably no instability strip exists at all. The red edge, predicted theoretically on the basis of the importance of convection in the outer zone, agrees well with the observational one. Cool, low-helium and metallic-line stars are then predicted to pulsate in a 200--500 K wide strip that is widest between the main-sequence luminosity of 5 Lsun and 15 Lsun. This strip reasonably includes the observed pulsating delta Del and mild Am stars, but there may be conflicts. Since blue edges for varying ionization-zone helium content occur across the entire instability strip, bluer first and higher overtone pulsations are also predicted everywhere from less than 7000 K to over 8000 K, the redder ones probably showing metallicism
Pulsation of high luminosity helium stars
International Nuclear Information System (INIS)
King, D.S.; Wheeler, J.C.; Cox, J.P.; Cox, A.N.; Hodson, S.W.
1979-01-01
Preliminary calculations are made on a systematic restudy of the linear and nonlinear pulsations of helium stars allowing for more recent and higher estimates of the effective temperature and for the high carbon abundance. Linear and nonlinear models are used. Results show qualitative agreement with earlier ones, models with sufficiently large L/M have a very hot blue edge for their instability strip, very large L/M values lead to dynamically unstable models which would appear to eject mass and therefore may not be realistic models for the pulsating RCrB stars, for the sequence studied a reasonable mass could be greater than or equal to 1.5 Msub solar. 12 references
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.
Robust methods and asymptotic theory in nonlinear econometrics
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 ...
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
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.
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
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
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 ...
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
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
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)
Strongly nonlinear theory of rapid solidification near absolute stability
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
Excitation of Stellar Pulsations
DEFF Research Database (Denmark)
Houdek, G.
2012-01-01
In this review I present an overview of our current understanding of the physical mechanisms that are responsible for the excitation of pulsations in stars with surface convection zones. These are typically cooler stars such as the δ Scuti stars, and stars supporting solar-like oscillations....
Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory
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)…
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...
A nonlinear theory for elastic plates with application to characterizing paper properties
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...
Masses and pulsations of BL Herculis variables
International Nuclear Information System (INIS)
Hodson, S.W.; Cox, A.N.; King, D.S.
1981-01-01
From linear results, the masses of BL Her variables must be nearer to 0.55 M /sub sun/ than 0.75 M /sub sun/ if the bump phase transition (resonance) is to be located anywhere near the observed period range of 1./sup d/5 to 1./sup d/7. The nonlinear results are consistent with the Simon resonance concept, but demonstrate that light and velocity curve shapes are a nonlinear phenomenon that require nonlinear period ratios to display the resonances only in the narrow, observed range of 1./sup d/5 to 1./sup d/7. The mass near 0.55 M /sub sun/ is in good agreement with evolution calculations (Sweigart and Gross, 1976) and nonlinear pulsation studies of Carson, Stothers, and Vemury (1981) and Stothers
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.
White dwarf evolution - Cradle-to-grave constraints via pulsation
Kawaler, Steven D.
1990-01-01
White dwarf evolution, particularly in the early phases, is not very strongly constrained by observation. Fortunately, white dwarfs undergo nonradial pulsation in three distinct regions of the H-R diagram. These pulsations provide accurate masses, surface compositional structure and rotation velocities, and help constrain other important physical properties. We demonstrate the application of the tools of stellar seismology to white dwarf evolution using the hot white dwarf star PG 1159-035 and the cool DAV (or ZZ Ceti) stars as examples. From pulsation studies, significant challenges to the theory of white dwarf evolution emerge.
White dwarf evolution - Cradle-to-grave constraints via pulsation
International Nuclear Information System (INIS)
Kawaler, S.D.
1990-01-01
White dwarf evolution, particularly in the early phases, is not very strongly constrained by observation. Fortunately, white dwarfs undergo nonradial pulsation in three distinct regions of the H-R diagram. These pulsations provide accurate masses, surface compositional structure and rotation velocities, and help constrain other important physical properties. We demonstrate the application of the tools of stellar seismology to white dwarf evolution using the hot white dwarf star PG 1159-035 and the cool DAV (or ZZ Ceti) stars as examples. From pulsation studies, significant challenges to the theory of white dwarf evolution emerge. 44 refs
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...
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
Nonlinear time series theory, methods and applications with R examples
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
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
Articulated pipes conveying fluid pulsating with high frequency
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
1999-01-01
Stability and nonlinear dynamics of two articulated pipes conveying fluid with a high-frequency pulsating component is investigated. The non-autonomous model equations are converted into autonomous equations by approximating the fast excitation terms with slowly varying terms. The downward hanging...... pipe position will lose stability if the mean flow speed exceeds a certain critical value. Adding a pulsating component to the fluid flow is shown to stabilize the hanging position for high values of the ratio between fluid and pipe-mass, and to marginally destabilize this position for low ratios....... An approximate nonlinear solution for small-amplitude flutter oscillations is obtained using a fifth-order multiple scales perturbation method, and large-amplitude oscillations are examined by numerical integration of the autonomous model equations, using a path-following algorithm. The pulsating fluid component...
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.)
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
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
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.
Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory
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'.
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.
Nonlinear Dynamic Theory of Acute Cell Injuries and Brain Ischemia
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.
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.
On the temporal fluctuations of pulsating auroral luminosity
International Nuclear Information System (INIS)
Yamamoto, Tatsundo
1988-01-01
From a study of all-sky TV records, it is shown that the luminosity fluctuations of pulsating auroras can be understood in terms of a series of pulses with rapid on-off switchings in burstlike fashion and that the widths of successive pulses (pulsation on times) are fairly constant. This is common even when luminosity fluctuations consist of complex-irregular variations, in contrast to the pulsation off time that is significantly variable. Complex-irregular variations are ground to be due to simultaneous appearance of more pulsating patches that exhibit movements eastward and westward over the site, and each of the patches shows primarily isolated luminosity pulses. Several examples are presented and described in detail. A natural consequence of these observations is that the classical concept of period does not mean much and the luminosity fluctuations should be treated as a series of individual isolated pulses where the pulsation on time is the most essential quantity. These characteristics are briefly discussed in relation to VLF/ELF wave-particle interactions in the magnetosphere. Then a new interpretation of the nonlinear relaxation oscillation model is proposed, where the propagation effect of VLF/ELF waves in low energy plasm irregularities near the magnetospheric equatorial plane plays an essential role to produce rapid on-off switchings of precipitating energetic electron fluxes. Both electromagnetic and electrostatic waves are possibly related to the precipitation pulsations
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....
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.
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.)
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
Auroral pulsations and accompanying VLF emissions
Directory of Open Access Journals (Sweden)
V. R. Tagirov
Full Text Available Results of simultaneous TV observations of pulsating auroral patches and ELF-VLF-emissions in the morning sector carried out in Sodankylä (Finland on February 15, 1991 are presented. Auroral pulsating activity was typical having pulsating patches with characteristic periods of about 7 s. Narrow-band hiss emissions and chorus elements at intervals of 0.3–0.4 s formed the main ELF-VLF activity in the frequency range 1.0–2.5 kHz at the same time. The analysis of auroral images with time resolution of 0.04 s allowed perfectly separate analysis of spatial and temporal variations in the auroral luminosity. Mutual correspondence between the behaviour of the luminous auroral patches and the appearance of ELF noise type hiss emissions and VLF chorus trains was found in two intervals chosen for analysis. While the hiss emissions were associated with the appearance of luminosity inside a limited area close to the zenith, the structured VLF emissions were accompanied by rapid motion of luminosity inside the area. The spatial dimension of the pulsating area was about 45–50 km and luminosity propagated inside it with velocity of about 10–12 kms. We discuss a new approach to explain the 5–15 s auroral pulsation based on the theory of flowing cyclotron maser and relaxation characteristics of ionosphere.
Key words. Magnetospheric physics (auroral phenomena; magnetosphere-ionosphere interactions · Space plasma physics (wave-particle interactions
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)
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
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
Stochastic Control Theory, Nonlinear Structural Mechanics and Applied Combinatorics
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
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.
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)
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.
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.)
Using system theory and energy methods to prove existence of non-linear PDE's
Zwart, H.J.
2015-01-01
In this discussion paper we present an idea of combining techniques known from systems theory with energy estimates to show existence for a class of non-linear partial differential equations (PDE's). At the end of the paper a list of research questions with possible approaches is given.
Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory
DEFF Research Database (Denmark)
Frier, Christian; Sørensen, John Dalsgaard
2003-01-01
A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...
Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes
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…
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...
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.
White noise theory of robust nonlinear filtering with correlated state and observation noises
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
White noise theory of robust nonlinear filtering with correlated state and observation noises
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
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
On the role of resonances in double-mode pulsation
International Nuclear Information System (INIS)
Dziembowski, W.; Kovacs, G.
1984-01-01
Simultaneous effects of resonant coupling and non-linear saturation of linear driving mechanism on the finite amplitude solution of multi-modal pulsation problem and on its stability are investigated. Both effects are calculated in the lowest order of approximation in terms of amplitudes. It is shown that the 2:1 resonance between one of the two linearly unstable modes and a higher frequency mode causes double-mode (fundamental and first overtone) pulsation. In a certain range of parameters, such as the frequency mismatch, the linear growth and damping rates, it is the only stable solution of the problem. (author)
Pulsation, Mass Loss and the Upper Mass Limit
Klapp, J.; Corona-Galindo, M. G.
1990-11-01
RESUMEN. La existencia de estrellas con masas en exceso de 100 M0 ha sido cuestionada por mucho tiempo. Lfmites superiores para la masa de 100 M0 han sido obtenidos de teorfas de pulsaci6n y formaci6n estelar. En este trabajo nosotros primero investigamos la estabilidad radial de estrellas masivas utilizando la aproximaci6n clasica cuasiadiabatica de Ledoux, la aproximaci6n cuasiadiabatica de Castor y un calculo completamente no-adiabatico. Hemos encontrado que los tres metodos de calculo dan resultados similares siempre y cuando una pequefia regi6n de las capas externas de la estrella sea despreciada para la aproximaci6n clasica. La masa crftica para estabilidad de estrellas masivas ha sido encontrada en acuerdo a trabajos anteriores. Explicamos Ia discrepancia entre este y trabajos anteriores por uno de los autores. Discunmos calculos no-lineales y perdida de masa con respecto a) lfmite superior de masa. The existence of stars with masses in excess of 100 M0 has been questioned for a very long time. Upper mass limits of 100 Me have been obtained from pulsation and star formation theories. In this work we first investigate the radial stability of massive stars using the classical Ledoux's quasiadiabatic approximation. the Castor quasiadiabatic approximation and a fully nonadiabatic calculation. We have found that the three methods of calculation give similar results provided that a small region in outer layers of the star be neglected for the classical approximation. The critical mass for stability of massive stars is found to be in agreement with previous work. We explain the reason for the discrepancy between this and previous work by one of the authors. We discuss non-linear calculations and mass loss with regard to the upper mass limit. Key words: STARS-MASS FUNCTION - STARS-MASS LOSS - STARS-PULSATION
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
Theory of plasmonic effects in nonlinear optics: the case of graphene
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.).
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.))
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.
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.
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.
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
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.)
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...
Quantum theory from a nonlinear perspective Riccati equations in fundamental physics
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 ...
Nonlinear scattering from a plasma column. I - Theory. II Special cases
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.
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)
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
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
Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory
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.
T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory
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...
Pulsations in white dwarf stars
Van Grootel, Valérie; Fontaine, Gilles; Brassard, Pierre; Dupret, Marc-Antoine
2017-01-01
I will present a description of the six distinct families of pulsating white dwarfs that are currently known. Pulsations are present at various stages of the evolution (from hot, pre-white dwarfs to cool white dwarfs), at various stellar masses, and for various atmospheric compositions. In all of them, a mechanism linked to opacity changes along the evolution drives the oscillations. The existence of these oscillations offers the opportunity to apply asteroseismology for constraining physics ...
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
φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations
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
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.
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.
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)
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.
Massive B-type pulsators in low-metallicity environments
Karoff, C.; Arentoft, T.; Glowienka, L.; Coutures, C.; Nielsen, T. B.; Dogan, G.; Grundahl, F.; Kjeldsen, H.
2009-07-01
Massive B-type pulsators such as β Cep and slowly pulsating B (SPB) stars pulsate due to layers of increased opacity caused by partial ionization. The increased opacity blocks the energy flux to the surface of the stars which causes the layers to rise and the opacity to drop. This cyclical behavior makes the star act as a heat engine and the star will thus pulsate. For β Cep and SPB stars the increased opacity is believed to be caused by partial ionization of iron and these stars should therefore contain non-insignificant quantities of the metal. A good test of this theory is to search for β Cep and SPB stars in low-metallicity environments. If no stars are found the theory is supported, but, on the other hand, if a substantial number of β Cep and SPB stars are found in these environments then the theory is not supported and a %solutions solution is needed. With a growing number of identified β Cep and SPB stars in the low-metallicity Magellanic Clouds we seem to be left with the second case. We will in this context discuss recent findings of β Cep and SPB stars in the Magellanic Clouds and some possible solutions to the discrepancy between these observations and the theory. We also describe an ambitious project that we have initiated on the Small Magellanic Cloud open cluster NGC 371 which will help to evaluate these solutions.
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
Linear and nonlinear instability theory of a noble gas MHD generator
International Nuclear Information System (INIS)
Mesland, A.J.
1982-01-01
This thesis deals with the stability of the working medium of a seeded noble gas magnetohydrodynamic generator. The aim of the study is to determine the instability mechanism which is most likely to occur in experimental MHD generators and to describe its behaviour with linear and nonlinear theories. In chapter I a general introduction is given. The pertinent macroscopic basic equations are derived in chapter II, viz. the continuity, the momentum and the energy equation for the electrons and the heavy gas particles, consisting of the seed particles and the noble gas atoms. Chapter III deals with the linear plane wave analysis of small disturbances of a homogeneous steady state. The steady state is discussed in chapter IV. The values for the steady state parameters used for the calculations both for the linear analysis as for the nonlinear analysis are made plausible with the experimental values. Based on the results of the linear plane wave theory a nonlinear plane wave model of the electrothermal instability is introduced in chapter V. (Auth.)
A 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)
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.
Influence of magnetic flutter on tearing growth in linear and nonlinear theory
Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.
2018-06-01
Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.
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.
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
The effect of tides on self-driven stellar pulsations
Balona, L. A.
2018-06-01
In addition to rotation, a tidal force in a binary introduces another axis of symmetry joining the two centres of mass. If the stars are in circular orbit and synchronous rotation, a pulsation with spherical harmonic degree l is split into l + 1 frequencies. In the observer's frame of reference, these in turn are further split into equidistant frequencies spaced by multiples of the orbital frequency. In the periodogram of a pulsating star, tidal action can be seen as low-amplitude equidistant splitting of each oscillation mode which are not harmonics of the orbital frequency. This effect is illustrated using Kepler observations of the heartbeat variable, KIC 4142768, which is also a δ Scuti star. Even though the theory is only applicable to circular orbits, the expected equidistant splitting is clearly seen in all four of the highest amplitude modes. This results in amplitude variability of each pulsation mode with a period equal to the orbital period.
Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory
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.
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.
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
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.
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
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.)
Modeling of pulsating heat pipes.
Energy Technology Data Exchange (ETDEWEB)
Givler, Richard C.; Martinez, Mario J.
2009-08-01
This report summarizes the results of a computer model that describes the behavior of pulsating heat pipes (PHP). The purpose of the project was to develop a highly efficient (as compared to the heat transfer capability of solid copper) thermal groundplane (TGP) using silicon carbide (SiC) as the substrate material and water as the working fluid. The objective of this project is to develop a multi-physics model for this complex phenomenon to assist with an understanding of how PHPs operate and to be able to understand how various parameters (geometry, fill ratio, materials, working fluid, etc.) affect its performance. The physical processes describing a PHP are highly coupled. Understanding its operation is further complicated by the non-equilibrium nature of the interplay between evaporation/condensation, bubble growth and collapse or coalescence, and the coupled response of the multiphase fluid dynamics among the different channels. A comprehensive theory of operation and design tools for PHPs is still an unrealized task. In the following we first analyze, in some detail, a simple model that has been proposed to describe PHP behavior. Although it includes fundamental features of a PHP, it also makes some assumptions to keep the model tractable. In an effort to improve on current modeling practice, we constructed a model for a PHP using some unique features available in FLOW-3D, version 9.2-3 (Flow Science, 2007). We believe that this flow modeling software retains more of the salient features of a PHP and thus, provides a closer representation of its behavior.
Amplitude Modulation of Pulsation Modes in Delta Scuti Stars
Bowman, Dominic M.
2017-10-01
The pulsations in δ Sct stars are excited by a heat engine driving mechanism caused by increased opacity in their surface layers, and have pulsation periods of order a few hours. Space based observations in the last decade have revealed a diverse range of pulsational behaviour in these stars, which is investigated using an ensemble of 983 δ Sct stars observed continuously for 4 yr by the Kepler Space Telescope. A statistical search for amplitude modulation of pulsation modes is carried out and it is shown that 61.3 per cent of the 983 δ Sct stars exhibit significant amplitude modulation in at least a single pulsation mode, and that this is uncorrelated with effective temperature and surface gravity. Hence, the majority of δ Sct stars exhibit amplitude modulation, with time-scales of years and longer demonstrated to be significant in these stars both observationally and theoretically. An archetypal example of amplitude modulation in a δ Sct star is KIC 7106205, which contains only a single pulsation mode that varies significantly in amplitude whilst all other pulsation modes stay constant in amplitude and phase throughout the 4-yr Kepler data set. Therefore, the visible pulsational energy budget in this star, and many others, is not conserved over 4 yr. Models of beating of close-frequency pulsation modes are used to identify δ Sct stars with frequencies that lie closer than 0.001 d^{-1}, which are barely resolved using 4 yr of Kepler observations, and maintain their independent identities over 4 yr. Mode coupling models are used to quantify the strength of coupling and distinguish between non-linearity in the form of combination frequencies and non-linearity in the form of resonant mode coupling for families of pulsation modes in several stars. The changes in stellar structure caused by stellar evolution are investigated for two high amplitude δ Sct (HADS) stars in the Kepler data set, revealing a positive quadratic change in phase for the fundamental and
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
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...
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.)
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
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
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.
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)
The mechanism of pulsating aurora
International Nuclear Information System (INIS)
Johnstone, A.D.
1983-01-01
New measurement using ground-based techniques, sounding-rockets and geostationary satellites show that pulsating aurora is almost certainly caused by a modulation of the precipitating electron beam. The modulation is probably imposed near the magnetic equator by an interaction with ELF waves which are observed to be modulated at the same frequency. The measured wave intensity is not strong enough to cause pulsations by variation of the rate of pitch angle diffusion so it is suggested that the pulsation is caused by a coherent interaction involving the generation of ELF chorus. The periodicity arises because the chorus is shut-off after approximately half a bounce period when the increased rate of precipitation removes most of the resonant electrons. The supply is then replenished by pitch angle diffusion
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.
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
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.
Glimpses of soliton theory the algebra and geometry of nonlinear PDEs
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...
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.
A neuroeconomic theory of rational addiction and nonlinear time-perception.
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.
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.
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.
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
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 ...
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.
Testing Universal Relations of Neutron Stars with a Nonlinear Matter-Gravity Coupling Theory
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.
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
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.
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.
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
Turning points in nonlinear business cycle theories, financial crisis and the 2007-2008 downturn.
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.
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
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.
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
[Analysis of the heart sound with arrhythmia based on nonlinear chaos theory].
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.
Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.
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.
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.
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.
Kiviniemi, Vesa; Wang, Xindi; Korhonen, Vesa; Keinänen, Tuija; Tuovinen, Timo; Autio, Joonas; LeVan, Pierre; Keilholz, Shella; Zang, Yu-Feng; Hennig, Jürgen; Nedergaard, Maiken
2016-06-01
The theory on the glymphatic convection mechanism of cerebrospinal fluid holds that cardiac pulsations in part pump cerebrospinal fluid from the peri-arterial spaces through the extracellular tissue into the peri-venous spaces facilitated by aquaporin water channels. Since cardiac pulses cannot be the sole mechanism of glymphatic propulsion, we searched for additional cerebrospinal fluid pulsations in the human brain with ultra-fast magnetic resonance encephalography. We detected three types of physiological mechanisms affecting cerebral cerebrospinal fluid pulsations: cardiac, respiratory, and very low frequency pulsations. The cardiac pulsations induce a negative magnetic resonance encephalography signal change in peri-arterial regions that extends centrifugally and covers the brain in ≈1 Hz cycles. The respiratory ≈0.3 Hz pulsations are centripetal periodical pulses that occur dominantly in peri-venous areas. The third type of pulsation was very low frequency (VLF 0.001-0.023 Hz) and low frequency (LF 0.023-0.73 Hz) waves that both propagate with unique spatiotemporal patterns. Our findings using critically sampled magnetic resonance encephalography open a new view into cerebral fluid dynamics. Since glymphatic system failure may precede protein accumulations in diseases such as Alzheimer's dementia, this methodological advance offers a novel approach to image brain fluid dynamics that potentially can enable early detection and intervention in neurodegenerative diseases. © The Author(s) 2015.
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.
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.
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.
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)
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
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
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
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
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.
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.
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.
Simulations of pulsating one-dimensional detonations with true fifth order accuracy
International Nuclear Information System (INIS)
Henrick, Andrew K.; Aslam, Tariq D.; Powers, Joseph M.
2006-01-01
A novel, highly accurate numerical scheme based on shock-fitting coupled with fifth order spatial and temporal discretizations is applied to a classical unsteady detonation problem to generate solutions with unprecedented accuracy. The one-dimensional reactive Euler equations for a calorically perfect mixture of ideal gases whose reaction is described by single-step irreversible Arrhenius kinetics are solved in a series of calculations in which the activation energy is varied. In contrast with nearly all known simulations of this problem, which converge at a rate no greater than first order as the spatial and temporal grid is refined, the present method is shown to converge at a rate consistent with the fifth order accuracy of the spatial and temporal discretization schemes. This high accuracy enables more precise verification of known results and prediction of heretofore unknown phenomena. To five significant figures, the scheme faithfully recovers the stability boundary, growth rates, and wave-numbers predicted by an independent linear stability theory in the stable and weakly unstable regime. As the activation energy is increased, a series of period-doubling events are predicted, and the system undergoes a transition to chaos. Consistent with general theories of non-linear dynamics, the bifurcation points are seen to converge at a rate for which the Feigenbaum constant is 4.66 ± 0.09, in close agreement with the true value of 4.669201... As activation energy is increased further, domains are identified in which the system undergoes a transition from a chaotic state back to one whose limit cycles are characterized by a small number of non-linear oscillatory modes. This result is consistent with behavior of other non-linear dynamical systems, but not typically considered in detonation dynamics. The period and average detonation velocity are calculated for a variety of asymptotically stable limit cycles. The average velocity for such pulsating detonations is found
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.
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.
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.
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials
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.
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
Generalizing a nonlinear geophysical flood theory to medium-sized river networks
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.
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
Time-dependent density functional theory for nonlinear properties of open-shell systems.
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.
Electron energy measurements in pulsating auroras
International Nuclear Information System (INIS)
McEwan, D.J.; Yee, E.; Whalen, B.A.; Yau, A.W.
1981-01-01
Electron spectra were obtained during two rocket flights into pulsating aurora from Southend, Saskatchewan. The first rocket launched at 1143:24 UT on February 15, 1980 flew into an aurora of background intensity 275 R of N 2 + 4278 A and showing regular pulsations with about a 17 s period. Electron spectra of Maxwellian energy distributions were observed with an average E 0 = 1.5 keV, rising to 1.8 keV during the pulsations. There was one-to-one correspondence between the electron energy modulation and the observed optical pulsations. The second rocket, launched at 1009:10 UT on February 23, flew into a diffuse auroral surface of intensity 800 R of N 2 + 4278 A and with somewhat irregular pulsations. The electron spectra were again of Maxwellian energy distribution with an average E 0 = 1.8 keV increasing to 2.1 keV during the pulsations. The results from these flights suggest that pulsating auroras occurring in the morning sector may be quite commonly excited by low energy electrons. The optical pulsations are due to periodic increases in the energy of the electrons with the source of modulation in the vicintiy of the geomagnetic equatorial plane. (auth)
Self-pulsation in Raman fiber amplifiers
DEFF Research Database (Denmark)
Pedersen, Martin Erland Vestergaard; Ott, Johan Raunkjær; Rottwitt, Karsten
2009-01-01
Dynamic behavior caused by Brillouin scattering in Raman fiber amplifiers is studied. Modes of self-pulsation steady state oscillations are found. Their dependence on amplification scheme is demonstrated.......Dynamic behavior caused by Brillouin scattering in Raman fiber amplifiers is studied. Modes of self-pulsation steady state oscillations are found. Their dependence on amplification scheme is demonstrated....
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...
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
Occurrence and average behavior of pulsating aurora
Partamies, N.; Whiter, D.; Kadokura, A.; Kauristie, K.; Nesse Tyssøy, H.; Massetti, S.; Stauning, P.; Raita, T.
2017-05-01
Motivated by recent event studies and modeling efforts on pulsating aurora, which conclude that the precipitation energy during these events is high enough to cause significant chemical changes in the mesosphere, this study looks for the bulk behavior of auroral pulsations. Based on about 400 pulsating aurora events, we outline the typical duration, geomagnetic conditions, and change in the peak emission height for the events. We show that the auroral peak emission height for both green and blue emission decreases by about 8 km at the start of the pulsating aurora interval. This brings the hardest 10% of the electrons down to about 90 km altitude. The median duration of pulsating aurora is about 1.4 h. This value is a conservative estimate since in many cases the end of event is limited by the end of auroral imaging for the night or the aurora drifting out of the camera field of view. The longest durations of auroral pulsations are observed during events which start within the substorm recovery phases. As a result, the geomagnetic indices are not able to describe pulsating aurora. Simultaneous Antarctic auroral images were found for 10 pulsating aurora events. In eight cases auroral pulsations were seen in the southern hemispheric data as well, suggesting an equatorial precipitation source and a frequent interhemispheric occurrence. The long lifetimes of pulsating aurora, their interhemispheric occurrence, and the relatively high-precipitation energies make this type of aurora an effective energy deposition process which is easy to identify from the ground-based image data.
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.
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.
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.
Pulsating combustion - Combustion characteristics and reduction of emissions
Energy Technology Data Exchange (ETDEWEB)
Lindholm, Annika
1999-11-01
In the search for high efficiency combustion systems pulsating combustion has been identified as one of the technologies that potentially can meet the objectives of clean combustion and good fuel economy. Pulsating combustion offers low emissions of pollutants, high heat transfer and efficient combustion. Although it is an old technology, the interest in pulsating combustion has been renewed in recent years, due to its unique features. Various applications of pulsating combustion can be found, mainly as drying and heating devices, of which the latter also have had commercial success. It is, however, in the design process of a pulse combustor, difficult to predict the operating frequency, the heat release etc., due to the lack of a well founded theory of the phenomenon. Research concerning control over the combustion process is essential for developing high efficiency pulse combustors with low emissions. Natural gas fired Helmholtz type pulse combustors have been the experimental objects of this study. In order to investigate the interaction between the fluid dynamics and the chemistry in pulse combustors, laser based measuring techniques as well as other conventional measuring techniques have been used. The experimental results shows the possibilities to control the combustion characteristics of pulsating combustion. It is shown that the time scales in the large vortices created at the inlet to the combustion chamber are very important for the operation of the pulse combustor. By increasing/decreasing the time scale for the large scale mixing the timing of the heat release is changed and the operating characteristics of the pulse combustor changes. Three different means for NO{sub x} reduction in Helmholtz type pulse combustors have been investigated. These include exhaust gas recirculation, alteration of air/fuel ratio and changed inlet geometry in the combustion chamber. All used methods achieved less than 10 ppm NO{sub x} emitted (referred to stoichiometric
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
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
Freytag, B.; Liljegren, S.; Höfner, S.
2017-04-01
Context. Observations of asymptotic giant branch (AGB) stars with increasing spatial resolution reveal new layers of complexity of atmospheric processes on a variety of scales. Aims: To analyze the physical mechanisms that cause asymmetries and surface structures in observed images, we use detailed 3D dynamical simulations of AGB stars; these simulations self-consistently describe convection and pulsations. Methods: We used the CO5BOLD radiation-hydrodynamics code to produce an exploratory grid of global "star-in-a-box" models of the outer convective envelope and the inner atmosphere of AGB stars to study convection, pulsations, and shock waves and their dependence on stellar and numerical parameters. Results: The model dynamics are governed by the interaction of long-lasting giant convection cells, short-lived surface granules, and strong, radial, fundamental-mode pulsations. Radial pulsations and shorter wavelength, traveling, acoustic waves induce shocks on various scales in the atmosphere. Convection, waves, and shocks all contribute to the dynamical pressure and, thus, to an increase of the stellar radius and to a levitation of material into layers where dust can form. Consequently, the resulting relation of pulsation period and stellar radius is shifted toward larger radii compared to that of non-linear 1D models. The dependence of pulsation period on luminosity agrees well with observed relations. The interaction of the pulsation mode with the non-stationary convective flow causes occasional amplitude changes and phase shifts. The regularity of the pulsations decreases with decreasing gravity as the relative size of convection cells increases. The model stars do not have a well-defined surface. Instead, the light is emitted from a very extended inhomogeneous atmosphere with a complex dynamic pattern of high-contrast features. Conclusions: Our models self-consistently describe convection, convectively generated acoustic noise, fundamental-mode radial
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.
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.
Pulsations of the R Coronae Borealis stars
International Nuclear Information System (INIS)
Cox, J.P.; King, D.S.; Cox, A.N.; Wheeler, J.C.; Hansen, C.J.; Hodson, S.W.
1980-01-01
The radial pulsations of very luminous, low-mass models (L/M approx. 10 4 , solar units), which are possible representatives of the R CrB stars, have been examined. These pulsations are extremely nonadiabatic. There are in some cases at least one extra (strange) mode which makes interpretation difficult. The blue instability edges are also peculiar, in that there is an abrupt excursion of the blue edge to the blue for L/M sufficiently large. The range of periods of the model encompasses observed periods of the Cepheid-like pulsations of actual R CrB stars
Rodríguez-López, C.; MacDonald, J.; Moya, A.
2011-01-01
We present the results of the first theoretical non-radial non-adiabatic pulsational study of M dwarf stellar models with masses in the range 0.1 to 0.5M_solar. We find the fundamental radial mode to be unstable due to an \\epsilon mechanism caused by deuterium (D-) burning for the young 0.1 and 0.2M_solar models, by non-equilibrium He^3 burning for the 0.2 and 0.25M_solar models of 10^4Myr, and by a flux blocking mechanism for the partially convective 0.4 and 0.5M_solar models once they reach...
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
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...
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)
Pulsations of white dwarf stars with thick hydrogen or helium surface layers
Energy Technology Data Exchange (ETDEWEB)
Cox, A.N.; Starrfield, S.G.; Kidman, R.B.; Pesnell, W.D.
1986-07-01
In order to see if there could be agreement between results of stellar evolution theory and those of nonradial pulsation theory, calculations of white dwarf models have been made for hydrogen surface masses of 10/sup -4/ solar masses. Earlier results indicated that surface masses greater than 10/sup -8/ solar masses would not allow nonradial pulsations, even though all the driving and damping is in surface layers only 10/sup -12/ of the mass thick. It is shown that the surface mass of hydrogen in the pulsating white dwarfs (ZZ Ceti variables) can be any value as long as it is thick enough to contain the surface convection zone. 10 refs., 6 figs.
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
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
Non-linear analytic and coanalytic problems (Lp-theory, Clifford analysis, examples)
International Nuclear Information System (INIS)
Dubinskii, Yu A; Osipenko, A S
2000-01-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the 'orthogonal' sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented
Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)
Dubinskii, Yu A.; Osipenko, A. S.
2000-02-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.
Stability analysis of nonlinear autonomous systems - General theory and application to flutter
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).
Density nonlinearities and a field theory for the dynamics of simple fluids
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...
Solar wind controlled pulsations: A review
International Nuclear Information System (INIS)
Odera, T.J.
1986-01-01
Studies of the solar wind controlled Pc 3, 4 pulsations by early and recent researchers are highlighted. The review focuses on the recent observations, which cover the time during the International Magnetospheric Study (IMS). Results from early and recent observations agree on one point, that is, that the Pc 3, 4 pulsations are influenced by three main solar wind parameters, namely, the solar wind velocity V/sub 5w/, the IMF orientation theta/sub x/B, and magnitude B. The results can be interpreted, preferably, in terms of an external origin for Pc 3, 4 pulsations. This implies, essentially, the signal model, which means that the pulsations originate in the upstream waves (in the interplanetary medium) and are transported by convection to the magnetopause, where they couple to oscillations of the magnetospheric field lines
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.
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.
Pulsations of Energetic Electron Pulsations In Association With Substorm Onset
Åsnes, A.; Stadsnes, J.; Bjordal, J.; Østgaard, N.; Haaland, S.; Rosenberg, T. J.; Detrick, D. L.
The Polar Ionospheric X-ray Imaging Experiment (PIXIE) is giving detailed images of the energetic electron precipitation when the POLAR satellite is near perigee over the Antarctica. In this area the PIXIE images have a spatial resolution of the order of 100 km, and a temporal resolution of 10 s can be obtained. In this paper we present the results of a study focusing on the onset and expansion of a substorm occuring on July 24, 1998. In this event we observe strong modulations of the energetic electron precipitation with period around 1 minute following substorm onset. The pulsations were restricted to a narrow magnetic local time sector in the pre-midnight region, about 0.5 hours wide, and showed movement towards higher latitudes and earlier lo- cal times. The event will be discussed in context of measurements from ground sta- tions and satellites in geosynchronous orbit. Precipitation of energetic electrons will be compared with VLF/ELF ground measurements. Features in the energetic elec- tron precipitation will be mapped to the magnetospheric equatorial plane by field line tracing.
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.
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
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.
Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer
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.
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...
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...
Dynamical zoning within a Lagrangian mesh by use of DYN, a stellar pulsation code
International Nuclear Information System (INIS)
Castor, J.I.; Davis, C.G.; Davison, D.K.
1977-02-01
A method of dynamical zoning within a Lagrangian mesh is used to resolve the motion of the hydrogen ionization front in a time-dependent nonlinear model of a pulsating star. The resulting coupling with the radiative-transfer improves the calculated light curves. The method is described is some detail and then applied to a model of the Cepheid eta Aq1. 8 figures, 1 table
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
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
Kinetic theory of nonlinear viscous flow in two and three dimensions
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
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.
Study on pressure pulsation and piping vibration of complex piping of reciprocating compressor
International Nuclear Information System (INIS)
Xu Bin; Feng Quanke; Yu Xiaoling
2008-01-01
This paper presents a preliminary research on the piping vibration and pressure pulsation of reciprocating compressor piping system. On the basis of plane wave theory, the calculation of gas column natural frequency and pressure pulsation in complex pipelines is done by using the transfer matrix method and stiffness matrix method, respectively. With the discretization method of FEM, a mathematical model for calculating the piping vibration and stress of reciprocating compressor piping system is established, and proper boundary conditions are proposed. Then the structural modal and stress of the piping system are calculated with CAESAR II. The comparison of measured and calculated values found that the one dimensional wave equation can accurately calculate the natural frequency and pressure pulsation in gas column of piping system for reciprocating compressor. (authors)
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
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.
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: smancas@mail.ucf.edu; Roy Choudhury, S. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: choudhur@longwood.cs.ucf.edu
2009-04-15
Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic-quintic Ginzburg-Landau Equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied. In this paper, we address the issues of central interest in the area, i.e., the conditions for the occurrence of the five categories of dissipative solitons, as well the dependence of both their shape and their stability on the various parameters of the CGLE, viz. the nonlinearity, dispersion, linear and nonlinear gain, loss and spectral filtering parameters. Our predictions on the variation of the soliton amplitudes, widths and periods with the CGLE parameters agree with simulation results. First, we elucidate the Hopf bifurcation mechanism responsible for the various pulsating solitary waves, as well as its absence in Hamiltonian and integrable systems where such structures are absent. Next, we develop and discuss a variational formalism within which to explore the various classes of dissipative solitons. Given the complex dynamics of the various dissipative solutions, this formulation is, of necessity, significantly generalized over all earlier approaches in several crucial ways. Firstly, the starting formulation
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.
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
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.
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)
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.
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 ...
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.
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.)
A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials
Li, Chen; Liao, Yufei
2018-03-01
Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.
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)
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
Romero, Alejandra D.; Córsico, A. H.; Althaus, L. G.; Pelisoli, I.; Kepler, S. O.
2018-06-01
The blue large-amplitude pulsators (BLAPs) constitute a new class of pulsating stars. They are hot stars with effective temperatures of ˜30 000 K and surface gravities of log g ˜ 4.9, that pulsate with periods in the range 20-40 min. Until now, their origin and evolutionary state, as well as the nature of their pulsations, were not been unveiled. In this paper, we propose that the BLAPs are the hot counterpart of the already known pulsating pre-extremely low mass (pre-ELM) white dwarf (WD) stars, that are He-core low-mass stars resulting from interacting binary evolution. Using fully evolutionary sequences, we show that the BLAPs are well represented by pre-ELM WD models with high effective temperature and stellar masses ˜0.34 M⊙. From the analysis of their pulsational properties, we find that the observed variabilities can be explained by high-order non-radial g-mode pulsations or, in the case of the shortest periods, also by low-order radial modes, including the fundamental radial mode. The theoretical modes with periods in the observed range are unstable due to the κ mechanism associated with the Z-bump in the opacity at log T ˜ 5.25.
Directory of Open Access Journals (Sweden)
Marius Alexandru PANAIT
2014-06-01
Full Text Available The pulsating heated flows are traditionally a difficult subject to treat with conventional hot wire or film methods. Special factors that complicate matters are flow reversal and non linear flow effects of vortices and wire probe wake disturbances on the heat transfer to the hot film or wire sensor in heated pulsating flows. The presence of these strongly nonlinear and unknown terms leads to great difficulties in calibration of hot film probes in this particular regime. The paper analyses the current state of matters in the field and reports a series of solutions that have been practically tested in a case of a high speed pulsated heated flow. Normally such measurements are made in a non-contact fashion using a LDV system or various visualization techniques but there have been recent attempts to use a constant temperature hot wire anemometer system (CTA.To obtain meaningful calibration for hot wire films in hot pulsating flows, a comparison system on other principles (LDV was used, as well as a specially designed nozzle to replace the calibrator unit that could not be operated with heated fluid due to structural integrity reasons. The method as described below works well for the expected speed range that could be generated using the special nozzle.
Flow control by combining radial pulsation and rotation of a cylinder in uniform flow
Oualli, H.; Hanchi, S.; Bouabdallah, A.; Gad-El-Hak, M.
2008-11-01
Flow visualizations and hot-wire measurements are carried out to study a circular cylinder undergoing simultaneous radial pulsation and rotation and placed in a uniform flow. The Reynolds number is in the range of 1,000--22,000, for which transition in the shear layers and near wake is expected. Our previous experimental and numerical investigations in this subcritical flow regime have established the existence of an important energy transfer mechanism from the mean flow to the fluctuations. Radial pulsations cause and enhance that energy transfer. Certain values of the amplitude and frequency of the pulsations lead to negative drag (i.e. thrust). The nonlinear interaction between the Magnus effect induced by the steady rotation of the cylinder and the near-wake modulated by the bluff body's pulsation leads to alteration of the omnipresent Kármán vortices and the possibility of optimizing the lift-to-drag ratio as well as the rates of heat and mass transfer. Other useful applications include the ability to enhance or suppress the turbulence intensity, and to avoid the potentially destructive lock-in phenomenon in the wake of bridges, electric cables and other structures.
Recent developments in pulsating aurora studies
International Nuclear Information System (INIS)
Sandahl, I.
1985-11-01
The field of pulsating aurora studies is reviewed. The paper begins with a short description of the characteristics of pulsating auroras and the theoretical ideas which, in view of existing experimental results, seem most important. A selection of new theoretical results and experimental results from both ground based instruments and instruments on rockets and satellites is then presented. There is now convincing evidence that the luminosity modulation is caused by a modulated flux of electron. The electron flux modulation seems to arise from a modulated resonant interaction between electrons and whistler mode waves in the equatorial plane, but the reason for the modulation is not known. Measurements concerning the drift and location of patches and the creation of Pi1 micropulsations are also deiscussed. Finally some suggestions for future research work are outlined. Optical measurements, especially with low light level TV, have proven to be of great importance in experimental studies of pulsating auroras. (author)
Pulsating star research and the Gaia revolution
Directory of Open Access Journals (Sweden)
Eyer Laurent
2017-01-01
Full Text Available In this article we present an overview of the ESA Gaia mission and of the unprecedented impact that Gaia will have on the field of variable star research. We summarise the contents and impact of the first Gaia data release on the description of variability phenomena, with particular emphasis on pulsating star research. The Tycho-Gaia astrometric solution, although limited to 2.1 million stars, has been used in many studies related to pulsating stars. Furthermore a set of 3,194 Cepheids and RR Lyrae stars with their times series have been released. Finally we present the plans for the ongoing study of variable phenomena with Gaia and highlight some of the possible impacts of the second data release on variable, and specifically, pulsating stars.
Pulsating star research and the Gaia revolution
Eyer, Laurent; Clementini, Gisella; Guy, Leanne P.; Rimoldini, Lorenzo; Glass, Florian; Audard, Marc; Holl, Berry; Charnas, Jonathan; Cuypers, Jan; Ridder, Joris De; Evans, Dafydd W.; de Fombelle, Gregory Jevardat; Lanzafame, Alessandro; Lecoeur-Taibi, Isabelle; Mowlavi, Nami; Nienartowicz, Krzysztof; Riello, Marco; Ripepi, Vincenzo; Sarro, Luis; Süveges, Maria
2017-09-01
In this article we present an overview of the ESA Gaia mission and of the unprecedented impact that Gaia will have on the field of variable star research. We summarise the contents and impact of the first Gaia data release on the description of variability phenomena, with particular emphasis on pulsating star research. The Tycho-Gaia astrometric solution, although limited to 2.1 million stars, has been used in many studies related to pulsating stars. Furthermore a set of 3,194 Cepheids and RR Lyrae stars with their times series have been released. Finally we present the plans for the ongoing study of variable phenomena with Gaia and highlight some of the possible impacts of the second data release on variable, and specifically, pulsating stars.
Four new massive pulsating white dwarfs including an ultramassive DAV
Curd, Brandon; Gianninas, A.; Bell, Keaton J.; Kilic, Mukremin; Romero, A. D.; Allende Prieto, Carlos; Winget, D. E.; Winget, K. I.
2017-06-01
We report the discovery of four massive (M > 0.8 M⊙) ZZ Ceti white dwarfs, including an ultramassive 1.16 M⊙ star. We obtained ground-based, time series photometry for 13 white dwarfs from the Sloan Digital Sky Survey Data Release 7 and Data Release 10 whose atmospheric parameters place them within the ZZ Ceti instability strip. We detect monoperiodic pulsations in three of our targets (J1015, J1554 and J2038) and identify three periods of pulsation in J0840 (173, 327 and 797 s). Fourier analysis of the remaining nine objects does not indicate variability above the 4 detection threshold. Our preliminary asteroseismic analysis of J0840 yields a stellar mass M = 1.14 ± 0.01 M⊙, hydrogen and helium envelope masses of MH = 5.8 × 10-7 M⊙ and MHe = 4.5 × 10-4 M⊙ and an expected core crystallized mass ratio of 50-70 per cent. J1015, J1554 and J2038 have masses in the range 0.84-0.91 M⊙ and are expected to have a CO core; however, the core of J0840 could consist of highly crystallized CO or ONeMg given its high mass. These newly discovered massive pulsators represent a significant increase in the number of known ZZ Ceti white dwarfs with mass M > 0.85 M⊙, and detailed asteroseismic modelling of J0840 will allow for significant tests of crystallization theory in CO and ONeMg core white dwarfs.
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
The coupling between pulsation and mass loss in massive stars
Townsend, Rich
2007-01-01
To what extent can pulsational instabilities resolve the mass-loss problem of massive stars? How important is pulsation in structuring and modulating the winds of these stars? What role does pulsation play in redistributing angular momentum in massive stars? Although I cannot offer answers to these questions, I hope at the very least to explain how they come to be asked.
Gas compressor with side branch absorber for pulsation control
Harris, Ralph E [San Antonio, TX; Scrivner, Christine M [San Antonio, TX; Broerman, III, Eugene L.
2011-05-24
A method and system for reducing pulsation in lateral piping associated with a gas compressor system. A tunable side branch absorber (TSBA) is installed on the lateral piping. A pulsation sensor is placed in the lateral piping, to measure pulsation within the piping. The sensor output signals are delivered to a controller, which controls actuators that change the acoustic dimensions of the SBA.
Theory of heart biomechanics, biophysics, and nonlinear dynamics of cardiac function
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.
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
Properties of Energy Spectra of Molecular Crystals Investigated by Nonlinear Theory
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.
Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory
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
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.
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
Control theory-based regulation of hippocampal CA1 nonlinear dynamics.
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.
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
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)
Yoon, Sung Hwan
2017-10-12
According to previous theory, pulsating propagation in a premixed flame only appears when the reduced Lewis number, β(Le-1), is larger than a critical value (Sivashinsky criterion: 4(1 +3) ≈ 11), where β represents the Zel\\'dovich number (for general premixed flames, β ≈ 10), which requires Lewis number Le > 2.1. However, few experimental observation have been reported because the critical reduced Lewis number for the onset of pulsating instability is beyond what can be reached in experiments. Furthermore, the coupling with the unavoidable hydrodynamic instability limits the observation of pure pulsating instabilities in flames. Here, we describe a novel method to observe the pulsating instability. We utilize a thermoacoustic field caused by interaction between heat release and acoustic pressure fluctuations of the downward-propagating premixed flames in a tube to enhance conductive heat loss at the tube wall and radiative heat loss at the open end of the tube due to extended flame residence time by diminished flame surface area, i.e., flat flame. The thermoacoustic field allowed pure observation of the pulsating motion since the primary acoustic force suppressed the intrinsic hydrodynamic instability resulting from thermal expansion. By employing this method, we have provided new experimental observations of the pulsating instability for premixed flames. The Lewis number (i.e., Le ≈ 1.86) was less than the critical value suggested previously.
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.
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
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...
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
TIDALLY INDUCED PULSATIONS IN KEPLER ECLIPSING BINARY KIC 3230227
Energy Technology Data Exchange (ETDEWEB)
Guo, Zhao; Gies, Douglas R. [Center for High Angular Resolution Astronomy and Department of Physics and Astronomy, Georgia State University, P.O. Box 5060, Atlanta, GA 30302-5060 (United States); Fuller, Jim, E-mail: guo@astro.gsu.edu, E-mail: gies@chara.gsu.edu, E-mail: jfuller@caltech.edu [TAPIR, Walter Burke Institute for Theoretical Physics, Mailcode 350-17, Caltech, Pasadena, CA 91125 (United States)
2017-01-01
KIC 3230227 is a short period (P ≈ 7.0 days) eclipsing binary with a very eccentric orbit ( e = 0.6). From combined analysis of radial velocities and Kepler light curves, this system is found to be composed of two A-type stars, with masses of M {sub 1} = 1.84 ± 0.18 M {sub ⊙}, M {sub 2} = 1.73 ± 0.17 M {sub ⊙} and radii of R {sub 1} = 2.01 ± 0.09 R {sub ⊙}, R {sub 2} = 1.68 ± 0.08 R {sub ⊙} for the primary and secondary, respectively. In addition to an eclipse, the binary light curve shows a brightening and dimming near periastron, making this a somewhat rare eclipsing heartbeat star system. After removing the binary light curve model, more than 10 pulsational frequencies are present in the Fourier spectrum of the residuals, and most of them are integer multiples of the orbital frequency. These pulsations are tidally driven, and both the amplitudes and phases are in agreement with predictions from linear tidal theory for l = 2, m = −2 prograde modes.
TIDALLY INDUCED PULSATIONS IN KEPLER ECLIPSING BINARY KIC 3230227
International Nuclear Information System (INIS)
Guo, Zhao; Gies, Douglas R.; Fuller, Jim
2017-01-01
KIC 3230227 is a short period (P ≈ 7.0 days) eclipsing binary with a very eccentric orbit ( e = 0.6). From combined analysis of radial velocities and Kepler light curves, this system is found to be composed of two A-type stars, with masses of M 1 = 1.84 ± 0.18 M ⊙ , M 2 = 1.73 ± 0.17 M ⊙ and radii of R 1 = 2.01 ± 0.09 R ⊙ , R 2 = 1.68 ± 0.08 R ⊙ for the primary and secondary, respectively. In addition to an eclipse, the binary light curve shows a brightening and dimming near periastron, making this a somewhat rare eclipsing heartbeat star system. After removing the binary light curve model, more than 10 pulsational frequencies are present in the Fourier spectrum of the residuals, and most of them are integer multiples of the orbital frequency. These pulsations are tidally driven, and both the amplitudes and phases are in agreement with predictions from linear tidal theory for l = 2, m = −2 prograde modes.
Compressional Pc5 type pulsations in the morningside plasma sheet
Energy Technology Data Exchange (ETDEWEB)
Vaivads, A.; Baumjohann, W.; Haerendel, G.; Nakamura, R.; Kucharek, H.; Klecker, B. [Max-Planck-Institut fuer Extraterrestrische Physik, Garching (Germany); Lessard, M.R. [Dartmouth Coll., Hanover, NH (United States). Thayer School of Engineering; Kistler, L.M. [New Hampshire Univ., Durham (United States). Space Science Center; Mukai, T.; Nishida, A. [Institute of Space and Astronautical Science, Sagamihara, Kanagawa (Japan)
2001-03-01
We study compressional pulsations in Pc5 frequency range observed in the dawn-side at distances of about 10 R{sub E}, close to the magnetic equator. We use data obtained during two events of conjunctions between Equator-S and Geotail: 1000-1700 UT on 9 March 1998, and 0200-0600 UT on 25 April 1998. In both events, pulsations are observed after substorm activity. The pulsations are antisymmetric with respect to the equatorial plane (even mode), and move eastward with phase velocity close to plasma velocity. The pulsations tend to be pressure balanced. We also discuss possible generation mechanisms of the pulsations. (orig.)
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.)
Impact of pulsations on vortex flowmeters
Peters, M.C.A.M.; Bokhorst, E. van; Limpens, C.H.L.
1998-01-01
The impact of imposed pulsations on the output of five 3”-industrial vortex flow meters with a triangular bluff body and various type of sensors was experimentally investigated in a gas flow over a wide range of frequencies from 20 Hz to 400 Hz and amplitudes ranging from 1% to 30% rms of the
Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics
Directory of Open Access Journals (Sweden)
Daniel W.F. Alves
2017-10-01
Full Text Available We examine knotted solutions, the most simple of which is the “Hopfion”, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.
Phantom solution in a non-linear Israel-Stewart theory
Cruz, Miguel; Cruz, Norman; Lepe, Samuel
2017-06-01
In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p = ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than -1 and constant in time.
Application of NARX neural networks in thermal dynamics identification of a pulsating heat pipe
International Nuclear Information System (INIS)
Lee Yawei; Chang Tienli
2009-01-01
The pulsating heat pipe (PHP) receiving much attention in industries is a novel type of cooling device. The distinguishing feature of PHPs is the unsteady flow oscillations formed by the passing non-uniform distributions of vapour plugs and liquid slugs. This study introduces a methodology of a non-linear auto-regressive with exogenous (NARX) neural network to analyze the thermal dynamics of a PHP in both the time and frequency domains. Three heating powers: 30, 70, and 110 W are tested, and all the predicted results are presented in quite good agreement with the measured results. Herein, the harmonic analysis of the non-linear structure can be equivalently conducted with generalized frequency response functions (GFRFs). Based on the non-linear coupling between the various input spectral components, the interpretations of the higher order GFRFs have been extensively presented for demonstrating the non-linear effects on the heat transfer of a PHP at different operating conditions
Spinning phenomena and energetics of spherically pulsating patterns in stratified fluids
International Nuclear Information System (INIS)
Ibragimov, Ranis N; Dameron, Michael
2011-01-01
The nonlinear solutions of the two-dimensional Boussinesq equations describing internal waves in rotating stratified fluids were obtained as group invariant solutions. The latter nonlinear solutions correspond to the rotation transformation preserving the form of the original nonlinear equations of motion. It is shown that the obtained class of exact solutions can be associated with the spherically pulsating patterns observed in uniformly stratified fluids. It is also shown that the obtained rotationally symmetric solutions are bounded functions that can be visualized as spinning patterns in stratified fluids. It is also shown that the rotational transformation provides the energy conservation law together with other conservation laws for which the spinning phenomena is observed. The effects of nonlinearity and the Earth's rotation on such a phenomenon are also discussed.
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%
Using Nonlinear Programming in International Trade Theory: The Factor-Proportions Model
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…
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...
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...
A Pulsation Mechanism for GW Virginis Variables
Cox, Arthur N.
2003-03-01
The mechanism that produces pulsations in the hottest pre-white dwarfs has been uncertain since the early work indicated that helium is a poison that smooths opacity bumps in the opacity-temperature plane caused by the ionizations of the large observed amounts of carbon and oxygen. Very little helium seemed to be needed to prevent the kappa effect pulsation driving, but helium amounts of almost half of the mass in the surface composition are observed in the pulsating PG 1159-035 stars called the GW Virginis variables. Rather little change in the C and O surface abundances is observed from the hottest (RX J2117.1+3412 at 170,000 K) to the coolest (PG 0122+200 at 80,000 K) GW Vir variables. Actually the shortest observed periods (300-400 s) of these variables are generally predicted to be unstable in all models, but the longest observed periods (up to 1000 s) are difficult to excite. Three recent investigations differ in their conclusions, with two finding that helium and even a slight amount of hydrogen does not prevent the kappa effect of C and O ionizations. A more detailed study reported here confirms the poisoning effect of helium. However, the ionization K- and L-edge opacity of the original iron, whose global abundance is unaffected by all previous evolution, especially if enhanced by radiation absorption levitation, can give different, previously unexplored, opacity driving that can explain the observed pulsations. But even this iron ionization driving can be somewhat poisoned by bump smoothing if the C and O abundances are large. Nonvariable GW Vir stars in the observed instability strip could be the result of small composition variations in the pulsation driving layers.
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
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
Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance
Yu Nakayama
2009-01-01
We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the non-relativistic conformal invariance. We discuss applications to scaling regime of Reggeo...
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...
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
Detection of seizures from small samples using nonlinear dynamic system theory.
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.
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)
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.
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)
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.
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.)
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.
Exact solutions to nonlinear symmetron theory: One- and two-mirror systems
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.
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.
Neutron star pulsations and instabilities
International Nuclear Information System (INIS)
Lindblom, L.
2001-01-01
Gravitational radiation (GR) drives an instability in certain modes of rotating stars. This instability is strong enough in the case of the r-modes to cause their amplitudes to grow on a timescale of tens of seconds in rapidly rotating neutron stars. GR emitted by these modes removes angular momentum from the star at a rate which would spin it down to a relatively small angular velocity within about one year, if the dimensionless amplitude of the mode grows to order unity. A pedagogical level discussion is given here on the mechanism of GR instability in rotating stars, on the relevant properties of the r-modes, and on our present understanding of the dissipation mechanisms that tend to suppress this instability in neutron stars. The astrophysical implications of this GR driven instability are discussed for young neutron stars, and for older systems such as low mass x-ray binaries. Recent work on the non-linear evolution of the r-modes is also presented. (author)
Modeling pulsations in hot stars with winds
Energy Technology Data Exchange (ETDEWEB)
Noels, Arlette; Godart, Melanie [Institut d' Astrophysique et de Geophysique, Liege (Belgium); Dupret, Marc-Antoine [Observatoire de Paris-Meudon, LESIA (France)], E-mail: Arlette.Noels@ulg.ac.be, E-mail: ma.dupret@obspm.fr, E-mail: Melanie.Godart@ulg.ac.be
2008-10-15
The interaction pulsation/mass loss takes different aspects. Pulsations can trigger mass loss as in LBVs and Miras; on the other hand, mass loss can modify the driving conditions within the stars. But the most spectacular aspect is the effect on stellar models which, in turn, opens a royal way to asteroseismology to test physical conditions inside massive stars, such as the extent of convective cores or the appearance of new driving mechanisms. We start with a discussion on MS stars and their strange mode instabilities. We then move on to the excitation of the LBV phenomenon. WR stars and the newly observed MOST period in WR123 are discussed in view of the power of asteroseismology. We then turn to B supergiants, in particular HD163899, and show how asteroseismology can really probe convection, semiconvection and mass loss.
Constraints on stellar evolution from pulsations
International Nuclear Information System (INIS)
Cox, A.N.
1984-01-01
Consideration of the many types of intrinsic variable stars, that is, those that pulsate, reveals that perhaps a dozen classes can indicate some constraints that affect the results of stellar evolution calculations, or some interpretations of observations. Many of these constraints are not very strong or may not even be well defined yet. The author discusses the case for six classes: classical Cepheids with their measured Wesselink radii, the observed surface effective temperatures of the known eleven double-mode Cepheids, the pulsation periods and measured surface effective temperatures of three R CrB variables, the delta Scuti variable VZ Cnc with a very large ratio of its two observed periods, the nonradial oscillations of the Sun, and the period ratios of the newly discovered double-mode RR Lyrae variables. (Auth.)
Modeling pulsations in hot stars with winds
International Nuclear Information System (INIS)
Noels, Arlette; Godart, Melanie; Dupret, Marc-Antoine
2008-01-01
The interaction pulsation/mass loss takes different aspects. Pulsations can trigger mass loss as in LBVs and Miras; on the other hand, mass loss can modify the driving conditions within the stars. But the most spectacular aspect is the effect on stellar models which, in turn, opens a royal way to asteroseismology to test physical conditions inside massive stars, such as the extent of convective cores or the appearance of new driving mechanisms. We start with a discussion on MS stars and their strange mode instabilities. We then move on to the excitation of the LBV phenomenon. WR stars and the newly observed MOST period in WR123 are discussed in view of the power of asteroseismology. We then turn to B supergiants, in particular HD163899, and show how asteroseismology can really probe convection, semiconvection and mass loss.
Nonlinear calculations for bump Cepheids
International Nuclear Information System (INIS)
Hodson, S.W.; Cox, A.N.
1979-01-01
Hydrodynamic calculations to find strictly periodic solutions for the fundamental mode pulsations of 7 M/sub sun/ models were made using the von Sengbusch--Stellingwerf relaxation method. The models have a helium enrichment in the surface convection zones to Y = 0.78, which from the linear theory period ratio π 2 /π 0 and the Simon and Schmidt resonance hypothesis, should give the observed Hertzsprung progression of light and velocity curve bump phase with period. These surface helium enhanced models show the proper nonlinear bump phase behavior without resort to any mass loss before or during the blue loop phases of yellow giant evolution. At 6000 K and the evolution theory luminosity of 4744 L/sub sun/ for 7 M/sub sun/, that is, at a fundamental mode period of 8.5 day, the velocity curve bump is well after the maximum expansion velocity. At 5400 K and at the same luminosity (period of 12.5 days), there is a bump on the velocity curve well before maximum expansion velocity time. The latter case seems to exhibit the Christy echos but not the former. The echo interpretation may not be appropriate for these masses which are larger than the anomalous masses used by Christy, Stobie, and Adams. Resonance of the fundamental and second overtone modes should not necessarily show echos of surface disturbances from the center. The conclusion is that helium enrichment in the surface convection zones can adequately explain observations of bump Cepheids at evolution theory masses. 12 references
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
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.
Pulsating strings from two-dimensional CFT on (T4N/S(N
Directory of Open Access Journals (Sweden)
Carlos Cardona
2015-04-01
Full Text Available We propose a state from the two-dimensional conformal field theory on the orbifold (T4N/S(N as a dual description for a pulsating string moving in AdS3. We show that, up to first order in the deforming parameter, the energy in both descriptions has the same dependence on the mode number, but with a non-trivial function of the coupling.
Nonradial pulsations of hot evolved stars
International Nuclear Information System (INIS)
Starrfield, S.G.
1987-01-01
There are three classes of faint blue variable stars: the ZZ Ceti variables (DAV degenerate dwarfs), the DBV variables (DB degenerate dwarfs), and the GW Vir variables (DOV degenerate dwarfs). None of these classes of variable stars were known at the time of the last blue star meeting. Observational and theoretical studies of the ZZ Ceti variables, the DBV variables, and the GW Vir variables have shown them to be pulsating in nonradial g-modes. The cause of the pulsation has been determined for each class of variable star and, in all cases, also involves predictions of the stars envelope composition. The predictions are that the ZZ Ceti variables must have pure hydrogen surface layers, the DBV stars must have pure helium surface layers, and the GW Vir stars must have carbon and oxygen rich surface layers with less than 30% (by mass) of helium. Given these compositions, it is found that pulsation driving occurs as a result of the kappa and gamma effects operating in the partial ionization zones of either hydrogen or helium. In addition, a new driving mechanism, called convection blocking, also occurs in these variables. For the GW Vir variables, it is the kappa and gamma effects in the partial ionization regions of carbon and oxygen. 45 refs
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.
Contamination of RR Lyrae stars from Binary Evolution Pulsators
Karczmarek, Paulina; Pietrzyński, Grzegorz; Belczyński, Krzysztof; Stępień, Kazimierz; Wiktorowicz, Grzegorz; Iłkiewicz, Krystian
2016-06-01
Binary Evolution Pulsator (BEP) is an extremely low-mass member of a binary system, which pulsates as a result of a former mass transfer to its companion. BEP mimics RR Lyrae-type pulsations but has different internal structure and evolution history. We present possible evolution channels to produce BEPs, and evaluate the contamination value, i.e. how many objects classified as RR Lyrae stars can be undetected BEPs. In this analysis we use population synthesis code StarTrack.
TV morphology of some episodes of pulsating auroras
International Nuclear Information System (INIS)
Vallance Jones, A.; Gattinger, R.L.
1981-01-01
Sets of all-sky TV images of pulsating auroras obtained during the displays through which the sounding rockets of the Pulsating Aurora Campaign were fired are presented and discussed. It is emphasized that these displays are considerably more complex and variable than might seem to be the case on the basis of zenith photometer records. The pulsation modulation pattern was observed to be travelling westward during the first flight; later in the same display this apparent motion ceased. For the second flight the pulsation modulation pattern was almost stationary. (auth)
Musical scale estimation for some multiperiodic pulsating stars
Ulaş, B.
2009-03-01
The agreement between frequency arrangements of some multiperiodic pulsating stars and musical scales is investigated in this study. The ratios of individual pulsation frequencies of 28 samples of various types of pulsating stars are compared to 57 musical scales by using two different methods. The residual sum of squares of stellar observational frequency ratios is chosen as the indicator of the accordance. The result shows that the arrangements of pulsation frequencies of Y Cam and HD 105458 are similar to Diminished Whole Tone Scale and Arabian(b) Scale, respectively.
FOLLOW-UP OBSERVATIONS OF THE SECOND AND THIRD KNOWN PULSATING HOT DQ WHITE DWARFS
International Nuclear Information System (INIS)
Dufour, P.; Green, E. M.; Fontaine, G.; Brassard, P.; Francoeur, M.; Latour, M.
2009-01-01
We present follow-up time-series photometric observations that confirm and extend the results of the significant discovery made by Barlow et al. that the Hot DQ white dwarfs SDSS J220029.08 - 074121.5 and SDSS J234843.30 - 094245.3 are luminosity variable. These are the second and third known members of a new class of pulsating white dwarfs, after the prototype SDSS J142625.71+575218.3. We find that the light curve of SDSS J220029.08 - 074121.5 is dominated by an oscillation at 654.397 ± 0.056 s, and that the light pulse folded on that period is highly nonlinear due to the presence of the first and second harmonic of the main pulsation. We also present evidence for the possible detection of two additional pulsation modes with low amplitudes and periods of 577.576 ± 0.226 s and 254.732 ± 0.048 s in that star. Likewise, we find that the light curve of SDSS J234843.30 - 094245.3 is dominated by a pulsation with a period of 1044.168 ± 0.012 s, but with no sign of harmonic components. A new oscillation, with a low amplitude and a period of 416.919 ± 0.004 s, is also probably detected in that second star. We argue, on the basis of the very different folded pulse shapes, that SDSS J220029.08 - 074121.5 is likely magnetic, while SDSS J234843.30 - 094245.3 is probably not.
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...
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.
Period--luminosity--color relations and pulsation modes of pulsating variable stars
International Nuclear Information System (INIS)
Breger, M.; Bregman, J.N.
1975-01-01
The periods of delta Scuti, RR Lyrae, dwarf Cepheid, and W Virginis variables have been investigated for their dependence on luminosity, color, mass, and pulsation modes. A maximum-likelihood method, which includes consideration of the observational errors in each coordinate, has been applied to obtain observational period-luminosity-color (P-L-C) relations
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
Evolutionary pulsational mode dynamics in nonthermal turbulent viscous astrofluids
Karmakar, Pralay Kumar; Dutta, Pranamika
2017-11-01
The pulsational mode of gravitational collapse in a partially ionized self-gravitating inhomogeneous viscous nonthermal nonextensive astrofluid in the presence of turbulence pressure is illustratively analyzed. The constitutive thermal species, lighter electrons and ions, are thermostatistically treated with the nonthermal κ-distribution laws. The inertial species, such as identical heavier neutral and charged dust microspheres, are modelled in the turbulent fluid framework. All the possible linear processes responsible for dust-dust collisions are accounted. The Larson logatropic equations of state relating the dust thermal (linear) and turbulence (nonlinear) pressures with dust densities are included. A regular linear normal perturbation analysis (local) over the complex astrocloud ensues in a generalized quartic dispersion relation with unique nature of plasma-dependent multi-parametric coefficients. A numerical standpoint is provided to showcase the basic mode features in a judicious astronomical paradigm. It is shown that both the kinematic viscosity of the dust fluids and nonthermality parameter (kappa, the power-law tail index) of the thermal species act as stabilizing (damping) agent against the gravity; and so forth. The underlying evolutionary microphysics is explored. The significance of redistributing astrofluid material via waveinduced accretion in dynamic nonhomologic structureless cloud collapse leading to hierarchical astrostructure formation is actualized.
O-C analysis of the pulsating subdwarf B star PG 1219 + 534
Otani, Tomomi; Stone-Martinez, Alexander; Oswalt, Terry D.; Morello, Claudia; Moss, Adam; Singh, Dana; Sampson, Kenneth; DeAbreu, Caila; Khan, Aliyah; Seepersad, Austin; Shaikh, Mehvesh; Wilson, Linda
2017-01-01
PG 1219 + 534 (KY Uma) is a subdwarf B pulsating star with multiple periodicities between 120 - 175 s. So far, the most promising theory for the origin of subdwarf B (sdB) stars is that they result from binary mass transfer near the Helium Flash stage of evolution. The observations of PG 1219 +534 reported here are part of our program to constrain this evolutional theory by searching for companions and determining orbital separations around sdB pulsators using the Observed-minus-Calculated (O-C) method. A star’s position in space will wobble due to the gravitational forces of any companion or planet. If the star emits a periodic signal like pulsations, its orbital motion around the system’s center of mass causes periodic changes in the light pulse arrival times. PG 1219 + 534 was monitored for 90 hours during 2010-1 and 2016 using the 0.9m SARA-KP telescope at Kitt Peak National Observatory (KPNO), Arizona, and the 0.8 m Ortega telescope at Florida Institute of Technology in Melbourne. In this poster we present our time-series photometry and O-C analysis of this data.
Pulsations in white dwarfs: Selected topics
Directory of Open Access Journals (Sweden)
Saio H.
2013-03-01
Full Text Available This paper presents a very brief overview of the observed properties of g-mode pulsations in variable white dwarfs. We then discuss a few selected topics: Excitation mechanisms (kappa- and convection- mechanisms, and briefly the effect of a strong magnetic field (∼ 1 MG on g-modes as recently found in a hot DQ (carbon-rich atmosphere white dwarf. In the discussion of excitation mechanisms, a simple interpretation for the convection mechanism is given.
Construction of Database for Pulsating Variable Stars
Chen, B. Q.; Yang, M.; Jiang, B. W.
2011-07-01
A database for the pulsating variable stars is constructed for Chinese astronomers to study the variable stars conveniently. The database includes about 230000 variable stars in the Galactic bulge, LMC and SMC observed by the MACHO (MAssive Compact Halo Objects) and OGLE (Optical Gravitational Lensing Experiment) projects at present. The software used for the construction is LAMP, i.e., Linux+Apache+MySQL+PHP. A web page is provided to search the photometric data and the light curve in the database through the right ascension and declination of the object. More data will be incorporated into the database.
Acoustic radiation force control: Pulsating spherical carriers.
Rajabi, Majid; Mojahed, Alireza
2018-02-01
The interaction between harmonic plane progressive acoustic beams and a pulsating spherical radiator is studied. The acoustic radiation force function exerted on the spherical body is derived as a function of the incident wave pressure and the monopole vibration characteristics (i.e., amplitude and phase) of the body. Two distinct strategies are presented in order to alter the radiation force effects (i.e., pushing and pulling states) by changing its magnitude and direction. In the first strategy, an incident wave field with known amplitude and phase is considered. It is analytically shown that the zero- radiation force state (i.e., radiation force function cancellation) is achievable for specific pulsation characteristics belong to a frequency-dependent straight line equation in the plane of real-imaginary components (i.e., Nyquist Plane) of prescribed surface displacement. It is illustrated that these characteristic lines divide the mentioned displacement plane into two regions of positive (i.e., pushing) and negative (i.e., pulling) radiation forces. In the second strategy, the zero, negative and positive states of radiation force are obtained through adjusting the incident wave field characteristics (i.e., amplitude and phase) which insonifies the radiator with prescribed pulsation characteristics. It is proved that zero radiation force state occurs for incident wave pressure characteristics belong to specific frequency-dependent circles in Nyquist plane of incident wave pressure. These characteristic circles divide the Nyquist plane into two distinct regions corresponding to positive (out of circles) and negative (in the circles) values of radiation force function. It is analytically shown that the maximum amplitude of negative radiation force is exactly equal to the amplitude of the (positive) radiation force exerted upon the sphere in the passive state, by the same incident field. The developed concepts are much more deepened by considering the required
The Cepheid mass discrepancy and pulsation-driven mass loss
Neilson, H.R.; Cantiello, M.; Langer, N.
2011-01-01
Context. A longstanding challenge for understanding classical Cepheids is the Cepheid mass discrepancy, where theoretical mass estimates using stellar evolution and stellar pulsation calculations have been found to differ by approximately 10−20%. Aims. We study the role of pulsation-driven mass loss
Compressional Pc5 type pulsations in the morningside plasma sheet
Directory of Open Access Journals (Sweden)
A. Vaivads
Full Text Available We study compressional pulsations in Pc5 frequency range observed in the dawn-side at distances of about 10 RE , close to the magnetic equator. We use data obtained during two events of conjunctions between Equator-S and Geotail: 1000–1700 UT on 9 March 1998, and 0200–0600 UT on 25 April 1998. In both events, pulsations are observed after substorm activity. The pulsations are antisymmetric with respect to the equatorial plane (even mode, and move eastward with phase velocity close to plasma velocity. The pulsations tend to be pressure balanced. We also discuss possible generation mechanisms of the pulsations.
Key words. Magnetospheric physics (magnetospheric configuration and dynamics; MHD waves and instabilities; plasma sheet
Compressional Pc5 type pulsations in the morningside plasma sheet
Directory of Open Access Journals (Sweden)
A. Vaivads
2001-03-01
Full Text Available We study compressional pulsations in Pc5 frequency range observed in the dawn-side at distances of about 10 RE , close to the magnetic equator. We use data obtained during two events of conjunctions between Equator-S and Geotail: 1000–1700 UT on 9 March 1998, and 0200–0600 UT on 25 April 1998. In both events, pulsations are observed after substorm activity. The pulsations are antisymmetric with respect to the equatorial plane (even mode, and move eastward with phase velocity close to plasma velocity. The pulsations tend to be pressure balanced. We also discuss possible generation mechanisms of the pulsations.Key words. Magnetospheric physics (magnetospheric configuration and dynamics; MHD waves and instabilities; plasma sheet
DEFF Research Database (Denmark)
Reed, M.D.; Kawaler, Stephen D.; Østensen, Roy H.
2010-01-01
1093 Her (PG 1716) class or a hybrid star with both short and long periods. The apparently non-binary long-period and hybrid pulsators are described here. The V1093 Her periods range from 1 to 4.5 h and are associated with g-mode pulsations. Three stars also exhibit short periods indicative of p...
Impulsively started, steady and pulsated annular inflows
Energy Technology Data Exchange (ETDEWEB)
Abdel-Raouf, Emad [General Field Engineer, Halliburton Energy Services 719 Hangar Dr, New Iberia, LA 70560, United States of America (United States); Sharif, Muhammad A R; Baker, John, E-mail: abdelraouf.em@gmail.com, E-mail: msharif@eng.ua.edu, E-mail: john.baker@eng.ua.edu [Aerospace Engineering and Mechanics Department, The University of Alabama, Tuscaloosa, Alabama 35487, United States of America (United States)
2017-04-15
A computational investigation was carried out on low Reynolds number laminar inflow starting annular jets using multiple blocking ratios and atmospheric ambient conditions. The jet exit velocity conditions are imposed as steady, unit pulsed, and sinusoidal pulsed while the jet surroundings and the far-field jet inlet upstream conditions are left atmospheric. The reason is to examine the flow behavior in and around the jet inlet under these conditions. The pulsation mode behavior is analyzed based on the resultant of the momentum and pressure forces at the entry of the annulus, the circulation and vortex formation, and the propulsion efficiency of the inflow jets. The results show that under certain conditions, the net force of inflow jets (sinusoidal pulsed jets in particular) could point opposite to the flow direction due to the adverse pressure drops in the flow. The propulsion efficiency is also found to increase with pulsation frequency and the sinusoidal pulsed inflow jets are more efficient than the unit pulsed inflow jets. In addition, steady inflow jets did not trigger the formation of vortices, while unit and sinusoidal pulsed inflow jets triggered the formation of vortices under a certain range of frequencies. (paper)
Computational model of miniature pulsating heat pipes
Energy Technology Data Exchange (ETDEWEB)
Martinez, Mario J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Givler, Richard C. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2013-01-01
The modeling work described herein represents Sandia National Laboratories (SNL) portion of a collaborative three-year project with Northrop Grumman Electronic Systems (NGES) and the University of Missouri to develop an advanced, thermal ground-plane (TGP), which is a device, of planar configuration, that delivers heat from a source to an ambient environment with high efficiency. Work at all three institutions was funded by DARPA/MTO; Sandia was funded under DARPA/MTO project number 015070924. This is the final report on this project for SNL. This report presents a numerical model of a pulsating heat pipe, a device employing a two phase (liquid and its vapor) working fluid confined in a closed loop channel etched/milled into a serpentine configuration in a solid metal plate. The device delivers heat from an evaporator (hot zone) to a condenser (cold zone). This new model includes key physical processes important to the operation of flat plate pulsating heat pipes (e.g. dynamic bubble nucleation, evaporation and condensation), together with conjugate heat transfer with the solid portion of the device. The model qualitatively and quantitatively predicts performance characteristics and metrics, which was demonstrated by favorable comparisons with experimental results on similar configurations. Application of the model also corroborated many previous performance observations with respect to key parameters such as heat load, fill ratio and orientation.
Constraints on stellar evolution from pulsations
International Nuclear Information System (INIS)
Cox, A.N.
1983-01-01
Consideration of the many types of intrinsic variable stars, that is, those that pulsate, reveals that perhaps a dozen classes can indicate some constraints that affect the results of stellar evolution calculations, or some interpretations of observations. Many of these constraints are not very strong or may not even be well defined yet. In this review we discuss only the case for six classes: classical Cepheids with their measured Wesselink radii, the observed surface effective temperatures of the known eleven double-mode Cepheids, the pulsation periods and measured surface effective temperatures of three R CrB variables, the delta Scuti variable VZ Cnc with a very large ratio of its two observed periods, the nonradial oscillations of our sun, and the period ratios of the newly discovered double-mode RR Lyrae variables. Unfortunately, the present state of knowledge about the exact compositions; mass loss and its dependence on the mass, radius, luminosity, and composition; ;and internal mixing processes, as well as sometimes the more basic parameters such as luminosities and surface effective temperatures prevent us from applying strong constraints for every case where currently the possibility exists
New pulsating casing collar to improve cementing quality
Energy Technology Data Exchange (ETDEWEB)
Chen, P. [Southwest Petroleum Inst., Nanchong, Sichuan (China); He, K. [JiangHan Petroleum Administration Bureau, Qianjiang, Hubei (China); Wu, J. [Chevron Petroleum Tech. Co., Houston, TX (United States)
1998-12-31
This paper presents the design and test results of a new pulsating casing collar which improves cementing quality. The new pulsating casing collar (PCC) is designed according to the Helmholtz oscillator to generate a pulsating jet flow by self-excitation in the cementing process. By placing this new pulsating casing collar at the bottom of casing string, the generated pulsating jet flow transmits vibrating pressure waves up through the annulus and helps remove drilling mud in the annulus. It can therefore improve cementing quality, especially when eccentric annulus exists due to casing eccentricity where the mud is difficult to remove. The new pulsating casing collar consists of a top nozzle, a resonant chamber, and a bottom nozzle. It can be manufactured easily and is easy to use in the field. It has been tested in Jianghan oil-field, P.R. China. The field-test results support the theoretical analysis and laboratory test, and the cementing quality is shown greatly improved by using the new pulsating casing collar.
The ionospheric signature of Pi 2 pulsations observed by STARE
International Nuclear Information System (INIS)
Sutcliffe, P.R.; Nielsen, E.
1992-01-01
This study extends the work of Sutcliffe and Nielsen (1990) in which a classical Pi 2 pulsation was first isolated in Scandinavian Twin Auroral Radar Experiment (STARE) data. A high-pass-filtering technique is used to remove the background electric field in the STARE data and so reveal the spatial and temporal ionospheric signatures of the Pi 2 pulsation electric fields. A number of events are identified and examples presented in which pulsation electric fields up to 50 mV/m are observed. Magnetic field oscillations computed from the filtered STARE data using the Biot-Savart law correlate well with pulsation magnetometer data. A 180 degree phase difference is observed between high- and low-altitude X component pulsations. The ionospheric signature of a Pi 2 is located slightly poleward of the core of the auroral breakup region where the southward, westward, and northward directed background electric fields coverage; the strongest pulsation fields occur in the region of equatorward directed electric fields. The ionospheric electric field patterns of the Pi 2 pulsations determined from the STARE data correlate well with those modeled for a transverse Alfven wave incident on an east-west aligned high-conductivity strip in the ionosphere
Pitch angle scattering and particle precipitation in a pulsating aurora - an experimental study
International Nuclear Information System (INIS)
Sandahl, I.
1984-10-01
A pulsating aurora occurring during the recovery phase of a substorm on January 27, 1979 was monitored by a large set of instruments. The Swedish sounding rocket S23-L2 was launched at magnetic midnight over pulsating patches, some of which exhibited 3+-1 Hz modulation. The ground based instrumentation included auroral TV cameras, all sky cameras, photometers and magnetometers. The geostationary satellite GEOS-2 was located in the equatorial plane, approximately conjugate to the rocket. The central experiment of this study is the particle experiment on the rocket. Several aspects of pulsating auroras have been investigated. The auroral luminosity variations were very well correlated to variations in the flux of precipitating hot electrons. The 1-20 second pulsations were caused by increased fluxes of 4-40 keV electrons. The 3+-1 Hz modulation was detected in 7-200 keV electrons, but the biggest energy flux modulation occurred for electrons of about 60 keV. Model calculations involving the electron distributions measured by the sounding rocket and GEOS-2, consistently show that the electrons may have been scattered into the loss cone through the Doppler shifted gyroresonance with whistler mode waves. The scattering was not a pure pitch angle scattering as in the classical Coroniti and Kennel theory, but involved also a systematic energy loss from the particles. The waves were probably hiss with some chorus elements. The equatorial plane plasma density was estimated in two independent ways to be about 2x10 6 m- 3 . The 3+-1 Hz modulation was measured both by the particle experiment on the rocket and by the wave experiment on GEOS-2. Properties of the modulated fluxes are described and a qualitative model for the cause of the modulation is proposed. (author)
Finding binaries from phase modulation of pulsating stars with Kepler
Shibahashi, Hiromoto; Murphy, Simon; Bedding, Tim
2017-09-01
Binary orbital motion causes a periodic variation in the path length travelled by light emitted from a star towards us. Hence, if the star is pulsating, the observed phase of the pulsation varies over the orbit. Conversely, once we have observed such phase variation, we can extract information about the binary orbit from photometry alone. Continuous and precise space-based photometry has made it possible to measure these light travel time effects on the pulsating stars in binary systems. This opens up a new way of finding unseen brown dwarfs, planets, or massive compact stellar remnants: neutron stars and black holes.
Copper alloys disintegration using pulsating water jet
Czech Academy of Sciences Publication Activity Database
Lehocká, D.; Klich, Jiří; Foldyna, Josef; Hloch, Sergej; Królczyk, J. B.; Cárach, J.; Krolczyk, G.
2016-01-01
Roč. 82, March 2016 (2016), s. 375-383 ISSN 0263-2241 R&D Projects: GA MŠk(CZ) LO1406; GA MŠk ED2.1.00/03.0082 Institutional support: RVO:68145535 Keywords : pulsating water jet * generation of pulses * disintegration * surface morphology * copper alloys Subject RIV: JQ - Machines ; Tools Impact factor: 2.359, year: 2016 http://ac.els-cdn.com/S0263224116000154/1-s2.0-S0263224116000154-main.pdf?_tid=8f8d1de6-99e9-11e6-afbc-00000aacb362&acdnat=1477314089_59912e52847e91e2030d6a1afd09e7b2
Directory of Open Access Journals (Sweden)
Holdsworth Daniel L.
2017-01-01
Full Text Available SuperWASP is one of the largest ground-based surveys for transiting exoplanets. To date, it has observed over 31 million stars. Such an extensive database of time resolved photometry holds the potential for extensive searches of stellar variability, and provide solid candidates for the upcoming TESS mission. Previous work by e.g. [15], [5], [12] has shown that the WASP archive provides a wealth of pulsationally variable stars. In this talk I will provide an overview of the SuperWASP project, present some of the published results from the survey, and some of the on-going work to identify key targets for the TESS mission.
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.
Nonlinear dynamics and complexity
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.
Nonlinear elastic waves in materials
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...
Pulsations of stellar models in H and He burning phases
International Nuclear Information System (INIS)
Gurm, H.S.; Sukhija, H.M.; Badalia, J.K.
1983-01-01
A study of pulsational properties with evolution has been done for a 15.6 Msub(sun) star with Xsub(e)=0.90 and Ysub(e)=0.08. Pulsational properties in the hydrogen-burning stages have been compared with those in helium-burning stages. A comparison with observed characteristics of #betta# Cepheids, classical Cepheids and supergiant variables has been made during the course of its evolution. In addition, models of 5, 9, and 15 Msub(sun) with Xsub(e)=0.708, Ysub(e)=0.272 have also been studied for pulsational properties during the helium burning stage. It is also seen that pulsational instability is sensitive to changes in initial chemical composition and opacity parameters, n and s. A low helium abundance could be a reason for the stability of the models, even when lying in the instability strip of the H-R diagram. (orig.)
Micro-Channel Embedded Pulsating Heat Pipes, Phase I
National Aeronautics and Space Administration — As the need for thermal control technology becomes more demanding Micro-Channel Embedded Pulsating Heat Pipes (ME-PHPs) represents a sophisticated and enabling...
Pulsating Heat Pipe for Cryogenic Fluid Management, Phase I
National Aeronautics and Space Administration — A passive Pulsating Heat Pipe (PHP) system is proposed to distribute cooling over broad areas with low additional system mass. The PHP technology takes advantage of...
Photometric study of the pulsating, eclipsing binary OO DRA
International Nuclear Information System (INIS)
Zhang, X. B.; Deng, L. C.; Tian, J. F.; Wang, K.; Yan, Z. Z.; Luo, C. Q.; Sun, J. J.; Liu, Q. L.; Xin, H. Q.; Zhou, Q.; Luo, Z. Q.
2014-01-01
We present a comprehensive photometric study of the pulsating, eclipsing binary OO Dra. Simultaneous B- and V-band photometry of the star was carried out on 14 nights. A revised orbital period and a new ephemeris were derived from the data. The first photometric solution of the binary system and the physical parameters of the component stars are determined. They reveal that OO Dra could be a detached system with a less-massive secondary component nearly filling its Roche lobe. By subtracting the eclipsing light changes from the data, we obtained the intrinsic pulsating light curves of the hotter, massive primary component. A frequency analysis of the residual light yields two confident pulsation modes in both B- and V-band data with the dominant frequency detected at 41.865 c/d. A brief discussion concerning the evolutionary status and the pulsation nature of the binary system is finally given.
Pulsations of stellar models in H and He burning phases
Energy Technology Data Exchange (ETDEWEB)
Gurm, H S; Sukhija, H M; Badalia, J K [Punjabi Univ., Patalia (India). Dept. of Astronomy and Space Sciences
1983-02-01
A study of pulsational properties with evolution has been done for a 15.6 Msub(sun) star with Xsub(e)=0.90 and Ysub(e)=0.08. Pulsational properties in the hydrogen-burning stages have been compared with those in helium-burning stages. A comparison with observed characteristics of ..beta.. Cepheids, classical Cepheids and supergiant variables has been made during the course of its evolution. In addition, models of 5, 9, and 15 Msub(sun) with Xsub(e)=0.708, Ysub(e)=0.272 have also been studied for pulsational properties during the helium burning stage. It is also seen that pulsational instability is sensitive to changes in initial chemical composition and opacity parameters, n and s. A low helium abundance could be a reason for the stability of the models, even when lying in the instability strip of the H-R diagram.
Linear theory radial and nonradial pulsations of DA dwarf stars
International Nuclear Information System (INIS)
Starrfield, S.; Cox, A.N.; Hodson, S.; Pesnell, W.D.
1982-01-01
The Los Alamos stellar envelope and radial linear non-adiabatic computer code, along with a new Los Alamos non-radial code are used to investigate the total hydrogen mass necessary to produce the non-radial instability of DA dwarfs
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)
GD 154: White dwarf with multi- and monoperiodic pulsation
Directory of Open Access Journals (Sweden)
Bognár Zs.
2013-03-01
Full Text Available We present the white dwarf GD 154 as an example where either monoperiodic or multiperiodic pulsation were found at different epochs. The mono-multi-monoperiodic stage seems to alternate. Many questions have been raised. Is this behaviour connected to the evolution of DAV stars? How often does it happen? Is there any regularity in this change of the pulsational behaviour or is it irregular?
Structure of Alpha Virginis. III. The pulsation characteristics
International Nuclear Information System (INIS)
Odell, A.P.
1980-01-01
Stellar structure models which were generated to match the photometric and binary properties of the B1.5 IV star Spica (α Vir) are analyzed for pulsation characteristics. The pulsation computations were linear and adiabatic and included both radial and nonradial (l=2) motions. Three sets of models were tested: normal evolution using Cox-Steward opacities, normal evolution using opacities increased substantially over Cox-Stewart, and evolution models using Cox-Stewart opacities but with a nonshrinking convective core
Non-Invasive Measurement of Intracranial Pressure Pulsation using Ultrasound
Ueno, Toshiaki; Ballard, R. E.; Yost, W. T.; Hargens, A. R.
1997-01-01
Exposure to microgravity causes a cephalad fluid shift which may elevate intracranial pressure (ICP). Elevation in ICP may affect cerebral hemodynamics in astronauts during space flight. ICP is, however, a difficult parameter to measure due to the invasiveness of currently available techniques. We already reported our development of a non-invasive ultrasound device for measurement of ICP. We recently modified the device so that we might reproducibly estimate ICP changes in association with cardiac cycles. In the first experiment, we measured changes in cranial distance with the ultrasound device in cadavera while changing ICP by infusing saline into the lateral ventricle. In the second experiment, we measured changes in cranial distance in five healthy volunteers while placing them in 60 deg, 30 deg head-up tilt, supine, and 10 deg head-down tilt position. In the cadaver study, fast Fourier transformation revealed that cranial pulsation is clearly associated with ICP pulsation. The ratio of cranial distance and ICP pulsation is 1.3microns/mmHg. In the tilting study, the magnitudes of cranial pulsation are linearly correlated to tilt angles (r=0.87). The ultrasound device has sufficient sensitivity to detect cranial pulsation in association with cardiac cycles. By analyzing the magnitude of cranial pulsation, estimates of ICP during space flight are possible.
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.
Reed, M. D.; Kawaler, S. D.; Østensen, R. H.; Bloemen, S.; Baran, A.; Telting, J. H.; Silvotti, R.; Charpinet, S.; Quint, A. C.; Handler, G.; Gilliland, R. L.; Borucki, W. J.; Koch, D. G.; Kjeldsen, H.; Christensen-Dalsgaard, J.
2010-12-01
We present the discovery of non-radial pulsations in five hot subdwarf B (sdB) stars based on 27 d of nearly continuous time series photometry using the Kepler spacecraft. We find that every sdB star cooler than ≈27 500 K that Kepler has observed (seven so far) is a long-period pulsator of the V1093 Her (PG 1716) class or a hybrid star with both short and long periods. The apparently non-binary long-period and hybrid pulsators are described here. The V1093 Her periods range from 1 to 4.5 h and are associated with g-mode pulsations. Three stars also exhibit short periods indicative of p-modes with periods of 2-5 min and in addition, these stars exhibit periodicities between both classes from 15 to 45 min. We detect the coolest and longest-period V1093 Her-type pulsator to date, KIC010670103 (Teff≈ 20 900 K, Pmax≈ 4.5 h) as well as a suspected hybrid pulsator, KIC002697388, which is extremely cool (Teff≈ 23 900 K) and for the first time hybrid pulsators which have larger g-mode amplitudes than p-mode ones. All of these pulsators are quite rich with many frequencies and we are able to apply asymptotic relationships to associate periodicities with modes for KIC010670103. Kepler data are particularly well suited for these studies as they are long duration, extremely high duty cycle observations with well-behaved noise properties.
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
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.
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
International Nuclear Information System (INIS)
Grigahcene, A.; Monteiro, M. J. P. F. G.; Antoci, V.; Handler, G.; Houdek, G.; Balona, L.; Catanzaro, G.; Daszynska-Daszkiewicz, J.; Guzik, J. A.; Kurtz, D. W.; Marconi, M.; Ripepi, V.; Moya, A.; Suarez, J.-C.; Uytterhoeven, K.; Borucki, W. J.; Brown, T. M.; Christensen-Dalsgaard, J.; Gilliland, R. L.; Jenkins, J. M.
2010-01-01
Observations of the pulsations of stars can be used to infer their interior structure and test theoretical models. The main-sequence γ Doradus (Dor) and δ Scuti (Sct) stars with masses 1.2-2.5 M sun are particularly useful for these studies. The γ Dor stars pulsate in high-order g-modes with periods of order 1 day, driven by convective blocking at the base of their envelope convection zone. The δ Sct stars pulsate in low-order g- and p-modes with periods of order 2 hr, driven by the κ mechanism operating in the He II ionization zone. Theory predicts an overlap region in the Hertzsprung-Russell diagram between instability regions, where 'hybrid' stars pulsating in both types of modes should exist. The two types of modes with properties governed by different portions of the stellar interior provide complementary model constraints. Among the known γ Dor and δ Sct stars, only four have been confirmed as hybrids. Now, analysis of combined Quarter 0 and Quarter 1 Kepler data for hundreds of variable stars shows that the frequency spectra are so rich that there are practically no pure δ Sct or γ Dor pulsators, i.e., essentially all of the stars show frequencies in both the δ Sct and the γ Dor frequency range. A new observational classification scheme is proposed that takes into account the amplitude as well as the frequency and is applied to categorize 234 stars as δ Sct, γ Dor, δ Sct/γ Dor or γ Dor/δ Sct hybrids.
Constraining the neutrino magnetic dipole moment from white dwarf pulsations
International Nuclear Information System (INIS)
Córsico, A.H.; Althaus, L.G.; Bertolami, M.M. Miller; Kepler, S.O.; García-Berro, E.
2014-01-01
Pulsating white dwarf stars can be used as astrophysical laboratories to constrain the properties of weakly interacting particles. Comparing the cooling rates of these stars with the expected values from theoretical models allows us to search for additional sources of cooling due to the emission of axions, neutralinos, or neutrinos with magnetic dipole moment. In this work, we derive an upper bound to the neutrino magnetic dipole moment (μ ν ) using an estimate of the rate of period change of the pulsating DB white dwarf star PG 1351+489. We employ state-of-the-art evolutionary and pulsational codes which allow us to perform a detailed asteroseismological period fit based on fully DB white dwarf evolutionary sequences. Plasmon neutrino emission is the dominant cooling mechanism for this class of hot pulsating white dwarfs, and so it is the main contributor to the rate of change of period with time (Pidot) for the DBV class. Thus, the inclusion of an anomalous neutrino emission through a non-vanishing magnetic dipole moment in these sequences notably influences the evolutionary timescales, and also the expected pulsational properties of the DBV stars. By comparing the theoretical Pidot value with the rate of change of period with time of PG 1351+489, we assess the possible existence of additional cooling by neutrinos with magnetic dipole moment. Our models suggest the existence of some additional cooling in this pulsating DB white dwarf, consistent with a non-zero magnetic dipole moment with an upper limit of μ ν ∼< 10 -11 μ B . This bound is somewhat less restrictive than, but still compatible with, other limits inferred from the white dwarf luminosity function or from the color-magnitude diagram of the Globular cluster M5. Further improvements of the measurement of the rate of period change of the dominant pulsation mode of PG 1351+489 will be necessary to confirm our bound
Photometric Survey to Search for Field sdO Pulsators
Johnson, C.; Green, E.; Wallace, S.; O'Malley, C.; Amaya, H.; Biddle, L.; Fontaine, G.
2014-04-01
We present the results of a campaign to search for subdwarf O (sdO) star pulsators among bright field stars. The motivation for this project is the recent discovery by Randall et al. (2011) of four rapidly pulsating sdO stars in the globular cluster ω Cen, with Teff near 50,000 K, 5.4 -0.1 and similar temperatures and gravities. To date, we have found no detectable pulsations at amplitudes above 0.08% (4 times the mean noise level) in any of the 36 field sdO stars that we observed. The presence of pulsations in ω Cen sdO stars and their apparent absence in seemingly comparable field sdO stars is perplexing. While very suggestive, the significance of this result is difficult to assess more completely right now due to remaining uncertainties about the temperature width and purity of the ω Cen instability strip and the existence of any sdO pulsators with weaker amplitudes than the current detection limit in globular clusters.
Nonlinear optics at interfaces
International Nuclear Information System (INIS)
Chen, C.K.
1980-12-01
Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory
Breaking the EOS-gravity degeneracy with masses and pulsating frequencies of neutron stars
International Nuclear Information System (INIS)
Lin, Weikang; Li, Bao-An; Chen, Lie-Wen; Wen, De-Hua; Xu, Jun
2014-01-01
A thorough understanding of many astrophysical phenomena associated with compact objects requires reliable knowledge about both the equation of state (EOS) of super-dense nuclear matter and the theory of strong-field gravity simultaneously because of the EOS-gravity degeneracy. Currently, variations of the neutron star (NS) mass–radius correlation from using alternative gravity theories are much larger than those from changing the NS matter EOS within known constraints. At least two independent observables are required to break the EOS-gravity degeneracy. Using model EOSs for hybrid stars and a Yukawa-type non-Newtonian gravity, we investigate both the mass–radius correlation and pulsating frequencies of NSs. While the maximum mass of NSs increases, the frequencies of the f, p 1 , p 2 , and w I pulsating modes are found to decrease with the increasing strength of the Yukawa-type non-Newtonian gravity, providing a useful reference for future determination simultaneously of both the strong-field gravity and the supranuclear EOS by combining data of x-ray and gravitational wave emissions of NSs. (paper)
Xu, Hao; Pei, Yongmao; Li, Faxin; Fang, Daining
2018-05-01
The magnetic, electric and mechanical behaviors are strongly coupled in magnetoelectric (ME) materials, making them great promising in the application of functional devices. In this paper, the magneto-electro-mechanical fully coupled constitutive behaviors of ME laminates are systematically studied both theoretically and experimentally. A new probabilistic domain switching function considering the surface ferromagnetic anisotropy and the interface charge-mediated effect is proposed. Then a multi-scale multi-field coupling nonlinear constitutive model for layered ME composites is developed with physical measureable parameters. The experiments were performed to compare the theoretical predictions with the experimental data. The theoretical predictions have a good agreement with experimental results. The proposed constitutive relation can be used to describe the nonlinear multi-field coupling properties of both ME laminates and thin films. Several novel coupling experimental phenomena such as the electric-field control of magnetization, and the magnetic-field tuning of polarization are observed and analyzed. Furthermore, the size-effect of the electric tuning behavior of magnetization is predicted, which demonstrates a competition mechanism between the interface strain-mediated effect and the charge-driven effect. Our study offers deep insight into the coupling microscopic mechanism and macroscopic properties of ME layered composites, which is benefit for the design of electromagnetic functional devices.
Epsilon Aur monitoring during predicted pulsation phase
Waagen, Elizabeth O.; Templeton, Matthew R.
2014-09-01
Dr. Robert Stencel (University of Denver Astronomy Program) has requested that AAVSO observers monitor epsilon Aurigae from now through the end of the observing season. "Studies of the long-term, out-of-eclipse photometry of this enigmatic binary suggest that intervals of coherent pulsation occur at roughly 1/3 of the 27.1-year orbital period. Kloppenborg, et al. noted that stable variation patterns develop at 3,200-day intervals' implying that 'the next span of dates when such events might happen are circa JD ~2457000 (2014 December)'. "These out-of-eclipse light variations often have amplitudes of ~0.1 magnitude in U, and ~0.05 in V, with characteristic timescales of 60-100 days. The AAVSO light curve data to the present may indicate that this coherent phenomenon has begun, but we encourage renewed efforts by observers...to help deduce whether these events are internal to the F star, or externally-driven by tidal interaction with the companion star." Nightly observations or one observation every few days (CCD/PEP/DSLR, VUBR (amplitude too small for visual)) are requested. Finder charts with sequence may be created using the AAVSO Variable Star Plotter (http://www.aavso.org/vsp). Observations should be submitted to the AAVSO International Database. Epsilon Aur was the subject of major international campaigns and the AAVSO's Citizen Sky project as it went through its 27.1-year eclipse in 2009-2011. Over 700 observers worldwide submitted over 20,000 multicolor observations to the AAVSO International Database for this project. Much information on eps Aur is available from the AAVSO, including material on the Citizen Sky website (http://www.aavso.org/epsilon-aurigae and http://www.citizensky.org/content/star-our-project). The Journal of the AAVSO, Volume 40, No. 2 (2012) was devoted to discussion of and research results from this event. See full Alert Notice for more details and observations.
Measurement of pressure pulsations in Francis turbines
Energy Technology Data Exchange (ETDEWEB)
Kobro, Einar
2010-11-15
The work presented in this thesis involves preparation and execution of measurements on Francis runners. The measurements were performed by means of onboard measuring equipment both in model runners and full-scale prototype runners. Also, analysis of the measured data, and the discussion of the results, is presented. The measurements resulted in large data sets. These data sets were used by the author to investigate the dynamic pressure and strain in the runners. The results of the analysis can be used as input in future turbine design. Andritz Hydro AG has used the data for verification of their numerical simulation tools. In connection with the refurbishment of Tokke power plant, two model runners were made available for onboard pressure measurements. To investigate the dynamic pressure in these runners, methods for integration of pressure transducers in the runner blades needed to be developed. After initial difficulties during the preparation, successful measurements were obtained from both model runners. At Tokke power plant, both the original and replacement runners were made accessible for onboard pressure and strain gauge measurements. On the original Kvaerner Brug AS runner, the test was prepared and performed by the author. This test failed, due to water intrusion in the logging chain. The second test was performed on the Andritz Hydro AG replacement runner. This test was prepared and performed by the author in close cooperation with Andritz Hydro AG, and the results were successful. The analysis results from both model and prototype runners show that the wake leaving the guide vanes is the most severe source of dynamic pressure in the runner. The draft tube vortex rope pulsation propagates upstream the runner, but does not appear as a significant frequency in the runner strain measurements. (Author)
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
Directory of Open Access Journals (Sweden)
Xujian Shu
2018-03-01
Full Text Available The output power and transmission efficiency of the traditional single-wire electric-field coupling power transmission (ECPT system will drop sharply with the increase of the distance between transmitter and receiver, thus, in order to solve the above problem, in this paper, a new nonlinear parity-time (PT-symmetric model for single-wire ECPT system based on coupled-mode theory (CMT is proposed. The proposed model for single-wire ECPT system not only achieves constant output power but also obtains a high constant transmission efficiency against variable distance, and the steady-state characteristics of the single-wire ECPT system are analyzed. Based on the theoretical analysis and circuit simulation, it shows that the transmission efficiency with constant output power remains 60% over a transmission distance of approximately 34 m without the need for any tuning. Furthermore, the application of a nonlinear PT-symmetric circuit based on CMT enables robust electric power transfer to moving devices or vehicles.
Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.
2007-01-01
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves
International Nuclear Information System (INIS)
Middleditch, J.; Pennypacker, C.R.; Burns, M.S.
1983-01-01
The spectrum of the pulsed optical and infrared flux from HZ Her has been measured to be flat by simultaneous observations with the NASA IRTF 3.0 m and the Lick Crossley 91 cm telescopes. The pulsed fluxes in the 3200-7500 A bandpass and the 1.0-2.5 μm bandpass were both measured to be consistent with 27 μJy and indicate that the reprocessed pulsation spectrum may be optically thin thermal bremsstrahlung radiation, modulated in intensity. However, the temperature required for a good fit is > or =30,000 K. The results of a search for periodic infrared pulsations from other X-ray and radio pulsars, supernova remnants, and the galactic center source IRS 16, are also reported. We have possibly detected 3.5 s infrared pulsations from the X-ray binary pulsar, IE 2259+586. The 285.7 mHz infrared pulsation frequency from IE 2259+586 is consistent with the 286.6 mHz second harmonic X-ray pulsations reprocessed from a companion star in the close binary orbit whose period has been tentatively established to be approx.2300 s
Modelling of temperature distribution and pulsations in fast reactor units
International Nuclear Information System (INIS)
Ushakov, P.A.; Sorokin, A.P.
1994-01-01
Reasons for the occurrence of thermal stresses in reactor units have been analyzed. The main reasons for this analysis are: temperature non-uniformity at the output of reactor core and breeder and the ensuing temperature pulsation; temperature pulsations due to mixing of sodium jets of a different temperature; temperature nonuniformity and pulsations resulting from the part of loops (circuits) un-plug; temperature nonuniformity and fluctuations in transient and accidental shut down of reactor or transfer to cooling by natural circulation. The results of investigating the thermal hydraulic characteristics are obtained by modelling the processes mentioned above. Analysis carried out allows the main lines of investigation to be defined and conclusions can be drawn regarding the problem of temperature distribution and fluctuation in fast reactor units
Doubling the number of pulsating DB white dwarfs
International Nuclear Information System (INIS)
Nitta, Atsuko; Kleinman, S J; Krzenski, J; Kepler, S O; Metcalfe, T S; Mukadam, Anjum S; Mullally, F; Nather, R E; Winget, D E; Sullivan, D; Thompson, Susan E
2009-01-01
We are searching for new pulsating DB white dwarf stars (DBVs) based on the newly found white dwarf stars from the spectra obtained by the Sloan Digital Sky Survey. DBVs pulsate at hotter temperature ranges than their better known cousins, DAVs or ZZ Ceti stars. Since the evolution of white dwarf stars is characterized by cooling, asteroseismological studies of DBVs give us opportunities to study white dwarf structure at a different evolutionary stage than the DAVs. The hottest DBVs are thought to have neutrino luminosities exceeding their photon luminosities (Winget et al. 2004), a quantity measurable through asteroseismology. Therefore, they can also be used to study neutrino physics in the stellar interior. At the time of the meeting, we reported on the nine new DBVs, doubling the number of previously known DBVs. Here we report the new nine pulsators' lightcurves and power spectra.
Transformerless photovoltaic inverters with leakage current and pulsating power elimination
DEFF Research Database (Denmark)
Tang, Yi; Yao, Wenli; Wang, H.
2015-01-01
This paper presents a transformerless inverter topology, which is capable of simultaneously solving leakage current and pulsating power issues in grid-connected photovoltaic (PV) systems. Without adding any additional components to the system, the leakage current caused by the PV......-to-ground parasitic capacitance can be bypassed by introducing a common mode (CM) conducting path to the inverter. The resulting ground leakage current is therefore well controlled to be below the regulation limit. Moreover, the proposed inverter can also eliminate the well-known double line frequency pulsating power....... The mechanism of leakage current suppression and the closed-loop control of pulsating power decoupling are discussed in the paper in details. A 500 W prototype was also built and tested in the laboratory, and both simulation and experimental results are finally presented to show the excellent performance...
Stellar Pulsations, Impact of New Instrumentation and New Insights
Garrido, R; Balona, L; Christensen-Dalsgaard, J; 20th Stellar Pulsation Conference Series
2013-01-01
Analyses of photometric time series obtained from the MOST, CoRoT and Kepler space missions were presented at the 20th conference on Stellar Pulsations (Granada, September 2011). These results are leading to a re-appraisal of our views on stellar pulsation in some stars and posing some new and unexpected challenges. The very important and exciting role played by innovative ground-based observational techniques, such as interferometric measurements of giant pulsating stars and high-resolution spectroscopy in the near infrared, is also discussed. These Proceedings are distinguished by the format of the conference, which brings together a variety of related but different topics not found in other meetings of this nature.
On the pulsation modes and masses of RGB OSARGs
Directory of Open Access Journals (Sweden)
Saio H.
2013-03-01
Full Text Available OSARG (OGLE Small Amplitude Red Giants variables are RGB or AGB stars that show multi-periodic light variations with periods of about 10-100 days. Comparing linear nonadiabatic pulsation periods and period ratios with observed ones, we determined pulsation modes and masses of the RGB OSARG variables in the LMC. We found that pulsations of OSARGs involve radial 1st to 3rd overtones, p4 of l = 1, and p2 of l = 2 modes. The range of mass isfound to be 0.9-1.4M⊙ for RGB OSARGs and their mass-luminosity relation is logL/L⊙ = 0.79 M/M⊙ + 2.2.
Exhaust pressure pulsation observation from turbocharger instantaneous speed measurement
Macián, V.; Luján, J. M.; Bermúdez, V.; Guardiola, C.
2004-06-01
In internal combustion engines, instantaneous exhaust pressure measurements are difficult to perform in a production environment. The high temperature of the exhaust manifold and its pulsating character make its application to exhaust gas recirculation control algorithms impossible. In this paper an alternative method for estimating the exhaust pressure pulsation is presented. A numerical model is built which enables the exhaust pressure pulses to be predicted from instantaneous turbocharger speed measurements. Although the model is data based, a theoretical description of the process is also provided. This combined approach makes it possible to export the model for different engine operating points. Also, compressor contribution in the turbocharger speed pulsation is discussed extensively. The compressor contribution is initially neglected, and effects of this simplified approach are analysed.
Modulation depth analysis in fast pulsations of solar radio emission
International Nuclear Information System (INIS)
Chernov, G.P.; Kurts, Yu.; Akademie der Wissenschaften der DDR, Berlin
1990-01-01
A model of millisecond pulsations due to a pulsation regime of a whistler spectrum is confirmed by the statistical analysis of the modulation depth in five type IV bursts; a modulation depth distribution ΔI/I versus the period (p) grows linearly (with the different slope) up to the maximum at the value ΔI/I ≅ 0.5-0.6. The same dependence ΔI/I(p) for spikes, observed during the same events, testifies also in favour of this model. The overlap on fast pulsations of fiber bursts and of sudden reductions are displayed in the ΔI/I(p) distribution by diffuse tails which are naturally explained by the known models of this fine structure
Davletshin, I. A.; Dushina, O. A.; Mikheev, N. I.; Kolchin, S. A.
2017-11-01
The pulsating flow in a circular channel with semicircular annular ribs as discrete roughness elements has been studied experimentally. Air flow under atmospheric conditions at the channel inlet has been considered. Steady and pulsating air flow has been studied under different frequencies and amplitudes of forced pulsations generated by periodic blockage of the channel cross section by a rotating flap. Flow resistance in pulsating regimes has been estimated from the average static pressure drop. The resistance values attained twice the steady flow ones.
Energy Technology Data Exchange (ETDEWEB)
Speck, Thomas [Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz (Germany); Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut [Institut für Theoretische Physik II, Heinrich-Heine-Universität, D-40225 Düsseldorf (Germany)
2015-06-14
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.
Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles
2011-01-01
Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.
γ DORADUS PULSATIONS IN THE ECLIPSING BINARY STAR KIC 6048106
Energy Technology Data Exchange (ETDEWEB)
Lee, Jae Woo, E-mail: jwlee@kasi.re.kr [Korea Astronomy and Space Science Institute, Daejeon 34113 (Korea, Republic of)
2016-12-20
We present the Kepler photometry of KIC 6048106, which is exhibiting the O’Connell effect and multiperiodic pulsations. Including a starspot on either of the components, light-curve synthesis indicates that this system is a semi-detached Algol with a mass ratio of 0.211, an orbital inclination of 73.°9, and a large temperature difference of 2534 K. To examine in detail both the spot variations and pulsations, we separately analyzed the Kepler time-series data at the interval of an orbital period in an iterative way. The results reveal that the variable asymmetries of the light maxima can be interpreted as the changes with time of a magnetic cool spot on the secondary component. Multiple frequency analyses were performed in the outside-eclipse light residuals after removal of the binarity effects from the observed Kepler data. We detected 30 frequencies with signal to noise amplitude ratios larger than 4.0, of which six ( f {sub 2}– f {sub 6} and f {sub 10}) can be identified as high-order (17 ≤ n ≤ 25) low-degree ( ℓ = 2) gravity-mode pulsations that were stable during the observing run of 200 days. In contrast, the other frequencies may be harmonic and combination terms. For the six frequencies, the pulsation periods and pulsation constants are in the ranges of 0.352–0.506 days and 0.232–0.333 days, respectively. These values and the position on the Hertzsprung–Russell diagram demonstrate that the primary star is a γ Dor variable. The evolutionary status and the pulsation nature of KIC 6048106 are discussed.
International Nuclear Information System (INIS)
Kolesnichenko, A.V.
1980-01-01
An expression for the anomalous dimension of the single-particle Green function is derived in the scalar theory with the interaction Hamiltonian Hsub(int)=g(phisup(n)/n) in the limit n→infinity. It is simultaneously shown that in this model the range of essential distances is of order of nsup(-1/2)
Cycles of self-pulsations in a photonic integrated circuit.
Karsaklian Dal Bosco, Andreas; Kanno, Kazutaka; Uchida, Atsushi; Sciamanna, Marc; Harayama, Takahisa; Yoshimura, Kazuyuki
2015-12-01
We report experimentally on the bifurcation cascade leading to the appearance of self-pulsation in a photonic integrated circuit in which a laser diode is subjected to delayed optical feedback. We study the evolution of the self-pulsing frequency with the increase of both the feedback strength and the injection current. Experimental observations show good qualitative accordance with numerical results carried out with the Lang-Kobayashi rate equation model. We explain the mechanism underlying the self-pulsations by a phenomenon of beating between successive pairs of external cavity modes and antimodes.
Pulsating stars in the region of Carina Nebula
Energy Technology Data Exchange (ETDEWEB)
Steslicki, Marek [Astronomical Institute, University of Wroclaw (Poland)], E-mail: steslicki@astro.uni.wroc.p1
2008-10-15
We present the results of a search for pulsating stars in the region of Carina Nebula which includes three very young open clusters: Trumpler 14, 15 and 16. The search was made with the Wide Field Imager (WFI) on the MPG/ESO 2.2-m telescope in La Silla (Chile). In total, about 16,000 stars have been analyzed using classical Fourier techniques. We found over 20 pulsating {delta}-Scuti type stars in this region. Most of them are probable members of open clusters at the pre-main sequence evolutionary stage.
DEFF Research Database (Denmark)
Kawaler, Stephen D.; Reed, Michael D.; Østensen, Roy H.
2010-01-01
of sdB stars with a close M-dwarf companion with orbital periods of less than half a day. Because the orbital period is so short, the stars should be in synchronous rotation, and if so, the rotation period should imprint itself on the multiplet structure of the pulsations. However, we do not find clear......The survey phase of the Kepler Mission includes a number of hot subdwarf B (sdB) stars to search for non-radial pulsations. We present our analysis of two sdB stars that are found to be g-mode pulsators of the V1093 Her class. These two stars also display the distinct irradiation effect typical...... evidence for such rotational splitting. Though the stars do show some frequency spacings that are consistent with synchronous rotation, they also display multiplets with splittings that are much smaller. Longer-duration time series photometry will be needed to determine if those small splittings...
International Nuclear Information System (INIS)
Haines, M.G.; Bond, D.J.; Chuaqui, H.H.
1983-01-01
The paper reports experimental and theoretical contributions to the understanding of non-linear heat flow and the phenomenon of jet-like filamentary structures in inertial-confinement fusion. When lateral heat flow is minimized, through applying more carefully a radially symmetric irradiation at 1.05 and 0.53 μm on a spherical target, it is found that a heat flux in excess of 10% of the free-streaming limit is consistent with simulations and experimental measurements with particle and X-ray diagnostics. A similar result has been found in a scaled experiment in a plasma of electron density 4x10 16 cm - 3 when the condition Tsub(e) approx.=Tsub(i) is satisfied. These results are in marked contrast to earlier assertions, mainly from plane-target measurements, that the flux limiter is 3%, but in agreement with theoretical calculations of steady non-linear heat flow using a discrete-ordinate method. Thus, no anomalous inhibition of heat flow is found, consistent with theoretical predictions that ion-acoustic turbulence is of no importance in dense (n>=10 21 cm - 3 , T approx.= 1 keV) plasmas. However, in the low-density scaled experiment, under conditions where Tsub(e)>>Tsub(i) is found that ion-acoustic turbulence is present, and the flux limiter is 4%. By using shadowgraphic and schlieren techniques with an optical diagnostic probe, fine-scale jet-like structures have been observed on a scale-length of approx. 10 μm on spherical targets. They occur even outside the laser-irradiated region, and are not connected with irregularities in the laser beam; they are more pronounced with higher-Z materials and with shorter-wavelength lasers, and have megagauss magnetic fields associated with them. Electromagnetic instabilities driven by heat flow are the probable cause of the jets, and of the three known modes the thermal instability, enhanced by radiation loss, agrees more closely with the experiments than the Weibel and thermomagnetic modes, since the latter only occur
Sun, F. Z.; Zhang, P.; Liang, Y. C.; Lu, L. H.
2014-09-01
In the non-critical phase-matching (NCPM) along the Θ =90° direction, ADP and DKDP crystals which have many advantages, including a large effective nonlinear optical coefficient, a small PM angular sensitivity and non beam walk-off, at the non-critical phase-matching become the competitive candidates in the inertial confinement fusion(ICF) facility, so the reasonable temperature control of crystals has become more and more important .In this paper, the fluid-solid coupling models of ADP crystal and DKDP crystal which both have anisotropic thermal conductivity in the states of vacuum and non-vacuum were established firstly, and then simulated using the fluid analysis software Fluent. The results through the analysis show that the crystal surface temperature distribution is a ring shape, the temperature gradients in the direction of the optical axis both the crystals are 0.02°C and 0.01°C due to the air, the lowest temperature points of the crystals are both at the center of surface, and the temperatures are lower than 0.09°C and 0.05°C compared in the vacuum and non-vacuum environment, then propose two designs for heating apparatus.
Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.
2009-12-01
A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss-Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.
Perdigão, R. A. P.
2017-12-01
Predictability assessments are traditionally made on a case-by-case basis, often by running the particular model of interest with randomly perturbed initial/boundary conditions and parameters, producing computationally expensive ensembles. These approaches provide a lumped statistical view of uncertainty evolution, without eliciting the fundamental processes and interactions at play in the uncertainty dynamics. In order to address these limitations, we introduce a systematic dynamical framework for predictability assessment and forecast, by analytically deriving governing equations of predictability in terms of the fundamental architecture of dynamical systems, independent of any particular problem under consideration. The framework further relates multiple uncertainty sources along with their coevolutionary interplay, enabling a comprehensive and explicit treatment of uncertainty dynamics along time, without requiring the actual model to be run. In doing so, computational resources are freed and a quick and effective a-priori systematic dynamic evaluation is made of predictability evolution and its challenges, including aspects in the model architecture and intervening variables that may require optimization ahead of initiating any model runs. It further brings out universal dynamic features in the error dynamics elusive to any case specific treatment, ultimately shedding fundamental light on the challenging issue of predictability. The formulated approach, framed with broad mathematical physics generality in mind, is then implemented in dynamic models of nonlinear geophysical systems with various degrees of complexity, in order to evaluate their limitations and provide informed assistance on how to optimize their design and improve their predictability in fundamental dynamical terms.
Nonlinear σ-model with non-compact symmetry group and the theory of nonideal bose gas
International Nuclear Information System (INIS)
Pashaev, O.K.
1985-01-01
A continuous classical model of the Heisenberg magnet is constructed on the non-compact SU(1, 1)/U(1) manifold which is gauge equivalent to the nonlinear Schroedinger equation (MLS) of the repulsive type. It is shown that the choice of gauge transformation function as the Jost solutions for the NLS linear problem allows one to obtain solutions of the appropriate Σ-model of the magnet. Spin-wave and soliton solutions are presented. Energy, momentum and magnetization integrals are calculated. Spin waves are determined by the Bogoluybov frequency and describe precession on the hyperboloid surface with a fixed Msub(z) value. Soliton solution describes the magnetization vector yield from the precession plane. When condensate density p → O, then the spectrum coincides with the result obtained for SU(2) Heisenberg ferromagnet and with an exact solution for Bethe spin complex. In the case corresponding to unlimited length of vector S, the soliton spectrum coincides with the hole spectrum of antiferromagnet. There magnetizations related to the upper and lower sheets of the hyperboloid compensate for each other
Directory of Open Access Journals (Sweden)
Jairo A. Paredes
2016-01-01
Full Text Available Ferrocement thin walls are the structural elements that comprise the earthquake resistant system of dwellings built with this material. This article presents the results drawn from an experimental campaign carried out over full-scale precast ferrocement thin walls that were assessed under lateral static loading conditions. The tests allowed the identification of structural parameters and the evaluation of the performance of the walls under static loading conditions. Additionally, an isotropic damage model for modelling the mortar was applied, as well as the classic elasto-plastic theory for modelling the meshes and reinforcing bars. The ferrocement is considered as a composite material, thus the serial/parallel mix theory is used for modelling its mechanical behavior. In this work a methodology for the numerical analysis that allows modeling the nonlinear behavior exhibited by ferrocement walls under static loading conditions, as well as their potential use in earthquake resistant design, is proposed.
Pulsating aurora from electron scattering by chorus waves
Kasahara, S.; Miyoshi, Y.; Yokota, S.; Mitani, T.; Kasahara, Y.; Matsuda, S.; Kumamoto, A.; Matsuoka, A.; Kazama, Y.; Frey, H. U.; Angelopoulos, V.; Kurita, S.; Keika, K.; Seki, K.; Shinohara, I.
2018-02-01
Auroral substorms, dynamic phenomena that occur in the upper atmosphere at night, are caused by global reconfiguration of the magnetosphere, which releases stored solar wind energy. These storms are characterized by auroral brightening from dusk to midnight, followed by violent motions of distinct auroral arcs that suddenly break up, and the subsequent emergence of diffuse, pulsating auroral patches at dawn. Pulsating aurorae, which are quasiperiodic, blinking patches of light tens to hundreds of kilometres across, appear at altitudes of about 100 kilometres in the high-latitude regions of both hemispheres, and multiple patches often cover the entire sky. This auroral pulsation, with periods of several to tens of seconds, is generated by the intermittent precipitation of energetic electrons (several to tens of kiloelectronvolts) arriving from the magnetosphere and colliding with the atoms and molecules of the upper atmosphere. A possible cause of this precipitation is the interaction between magnetospheric electrons and electromagnetic waves called whistler-mode chorus waves. However, no direct observational evidence of this interaction has been obtained so far. Here we report that energetic electrons are scattered by chorus waves, resulting in their precipitation. Our observations were made in March 2017 with a magnetospheric spacecraft equipped with a high-angular-resolution electron sensor and electromagnetic field instruments. The measured quasiperiodic precipitating electron flux was sufficiently intense to generate a pulsating aurora, which was indeed simultaneously observed by a ground auroral imager.
Pulsational instabilities in hot pre-horizontal branch stars
Directory of Open Access Journals (Sweden)
Battich Tiara
2017-01-01
Full Text Available The ϵ mechanism is a self-excitation mechanism of pulsations which acts on the regions where nuclear burning takes place. It has been shown that the ϵ mechanism can excite pulsations in models of hot helium-core flash, and that the pulsations of LS IV-14· 116, a He-enriched hot subdwarf star, could be explained that way. We aim to study the ϵmechanism effects on models of hot pre-horizontal branch stars and determine, if possible, a domain of instability in the log g — log Teff plane. We compute non-adiabatic non-radial pulsations on such stellar models, adopting different values of initial chemical abundances and mass of the hydrogen envelope at the time of the main helium flash. We find an instability domain of long-period (400 s ≲ P ≲ 2500 s g-modes for models with 22000K ≲ Teff ≲ 50000K and 4.67 ≲ log g ≲ 6.15.
Progress of cryogenic pulsating heat pipes at UW-Madison
Diego Fonseca, Luis; Mok, Mason; Pfotenhauer, John; Miller, Franklin
2017-12-01
Space agencies continuously require innovative cooling systems that are lightweight, low powered, physically flexible, easily manufactured and, most importantly, exhibit high heat transfer rates. Therefore, Pulsating Heat Pipes (PHPs) are being investigated to provide these requirements. This paper summarizes the current development of cryogenic Pulsating Heat Pipes with single and multiple evaporator sections built and successfully tested at UW-Madison. Recently, a helium based Pulsating Heat Pipe with three evaporator and three condenser sections has been operated at fill ratios between 20 % and 80 % operating temperature range of 2.9 K to 5.19 K, resulting in a maximum effective thermal conductivity up to 50,000 W/m-K. In addition, a nitrogen Pulsating Heat Pipe has been built with three evaporator sections and one condenser section. This PHP achieved a thermal performance between 32,000 W/m-K and 96,000 W/m-K at fill ratio ranging from 50 % to 80 %. Split evaporator sections are very important in order to spread cooling throughout an object of interest with an irregular temperature distribution or where multiple cooling locations are required. Hence this type of configurations is a proof of concept which hasn’t been attempted before and if matured could be applied to cryo-propellant tanks, superconducting magnets and photon detectors.
A statistical method for draft tube pressure pulsation analysis
International Nuclear Information System (INIS)
Doerfler, P K; Ruchonnet, N
2012-01-01
Draft tube pressure pulsation (DTPP) in Francis turbines is composed of various components originating from different physical phenomena. These components may be separated because they differ by their spatial relationships and by their propagation mechanism. The first step for such an analysis was to distinguish between so-called synchronous and asynchronous pulsations; only approximately periodic phenomena could be described in this manner. However, less regular pulsations are always present, and these become important when turbines have to operate in the far off-design range, in particular at very low load. The statistical method described here permits to separate the stochastic (random) component from the two traditional 'regular' components. It works in connection with the standard technique of model testing with several pressure signals measured in draft tube cone. The difference between the individual signals and the averaged pressure signal, together with the coherence between the individual pressure signals is used for analysis. An example reveals that a generalized, non-periodic version of the asynchronous pulsation is important at low load.
Fu, Y. B.; Ogden, R. W.
2001-05-01
This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.
A non-linear theory for the bubble regime of plasma wake fields in tailored plasma channels
Thomas, Johannes
2016-01-01
We introduce a first full analytical bubble and blow-out model for a radially inhomogeneous plasma in a quasi-static approximation. For both cases we calculate the accelerating and the focusing fields. In our model we also assume a thin electron layer that surrounds the wake field and calculate the field configuration within. Our theory holds for arbitrary radial density profiles and reduces to known models in the limit of a homogeneous plasma. From a previous study of hollow plasma channels with smooth boundaries for laser-driven electron acceleration in the bubble regime we know that pancake-like laser pulses lead to highest electron energies [Pukhov et al, PRL 113, 245003 (2014)]. As it was shown, the bubble fields can be adjusted to balance the laser depletion and dephasing lengths by varying the plasma density profile inside a deep channel. Now we show why the radial fields in the vacuum part of a channel become defocussing.
Jiang, Xingxing; Cheng, Mengfan; Luo, Fengguang; Deng, Lei; Fu, Songnian; Ke, Changjian; Zhang, Minming; Tang, Ming; Shum, Ping; Liu, Deming
2016-12-12
A novel electro-optic chaos source is proposed on the basis of the reverse-time chaos theory and an analog-digital hybrid feedback loop. The analog output of the system can be determined by the numeric states of shift registers, which makes the system robust and easy to control. The dynamical properties as well as the complexity dependence on the feedback parameters are investigated in detail. The correlation characteristics of the system are also studied. Two improving strategies which were established in digital field and analog field are proposed to conceal the time-delay signature. The proposed scheme has the potential to be used in radar and optical secure communication systems.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Effects of self-pulsation on the spray characteristics of gas-liquid swirl coaxial injector
Kang, Zhongtao; Li, Qinglian; Cheng, Peng; Zhang, Xinqiao; Wang, Zhen-guo
2016-10-01
To understand the influence of self-pulsation on the spray characteristics of gas-liquid swirl coaxial injector, a back-lighting photography technique has been employed to capture the instantaneous self-pulsated spray and stable spray images with a high speed camera. The diameter and velocity of the droplets in the spray have been characterized with a Dantec Phase Doppler Anemometry (PDA) system. The effects of self-pulsation on the spray pattern, primary breakup, spray angle, diameter and velocity distribution and mass flow rate distribution are analyzed and discussed. The results show that the spray morphology is greatly influenced by self-pulsation. The stable spray has a cone shape, while the self-pulsated spray looks like a Christmas tree. The main difference of these two sprays is the primary breakup. The liquid film of stable spray keeps stable while that of self-pulsated spray oscillates periodically. The film width of self-pulsated spray varies in a large range with 'neck' and 'shoulder' features existing. The liquid film of self-pulsated spray breaks up at the second neck, and then the second shoulder begins to breakup into ligaments. The self-pulsated spray produces droplet clusters periodically, varies horizontal spray width and mass flux periodically. From the point of spatial distribution, self-pulsation is good for the spray, it uniformizes the mass flux along radius and increases the spray angle. However, when self-pulsation occurs, the SMD distribution varies from an inverted V shape to a hollow cone shape, and SMD increases at all the measuring points. Namely, from the point of atomization performance, self-pulsation has negative effects even when the breakup length is smaller. The effects of self-pulsation on the diameter and velocity distributions of the spray are mainly in the center part of the spray. The periphery of stable and self-pulsated spray has similar diameter and velocity distribution.
Nonlinear dynamics and astrophysics
International Nuclear Information System (INIS)
Vallejo, J. C.; Sanjuan, M. A. F.
2000-01-01
Concepts and techniques from Nonlinear Dynamics, also known as Chaos Theory, have been applied successfully to several astrophysical fields such as orbital motion, time series analysis or galactic dynamics, providing answers to old questions but also opening a few new ones. Some of these topics are described in this review article, showing the basis of Nonlinear Dynamics, and how it is applied in Astrophysics. (Author)
International Nuclear Information System (INIS)
Hinterbichler, Kurt; Joyce, Austin; Khoury, Justin
2012-01-01
The pseudo-conformal scenario is an alternative to inflation in which the early universe is described by an approximate conformal field theory on flat, Minkowski space. Some fields acquire a time-dependent expectation value, which breaks the flat space so(4,2) conformal algebra to its so(4,1) de Sitter subalgebra. As a result, weight-0 fields acquire a scale invariant spectrum of perturbations. The scenario is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics. In this paper, we apply the well-known coset technique to derive the most general effective lagrangian describing the Goldstone field and matter fields, consistent with the assumed symmetries. The resulting action captures the low energy dynamics of any pseudo-conformal realization, including the U(1)-invariant quartic model and the Galilean Genesis scenario. We also derive this lagrangian using an alternative method of curvature invariants, consisting of writing down geometric scalars in terms of the conformal mode. Using this general effective action, we compute the two-point function for the Goldstone and a fiducial weight-0 field, as well as some sample three-point functions involving these fields
Araucaria Project: Pulsating stars in binary systems and as distance indicators
Directory of Open Access Journals (Sweden)
Pilecki Bogumił
2017-01-01
Type II Cepheids are recently becoming more important as distance indicators and astrophysics laboratory, although our knowledge of these stars is quite limited. Their evolutionary status is also not well understood and observational constraints are needed to confirm the current theories. We are presenting here our first results of the spectroscopic analysis of 4 of these systems. The masses of type II Cepheids seem consistent with the expected 0.5 − 0.6 M⊙. We also present first results of the fully modeled pulsator originally classified as peculiar W Vir star. The mass of this star is 1.51 ± 0.09 M⊙ and the p-factor 1.3 ± 0.03. It was eventually found not to belong to any typical Cepheid group.
Thirumurugan, R.; Babu, B.; Anitha, K.; Chandrasekaran, J.
2017-12-01
A novel organic nonlinear optical (NLO) material, creatininium L-tartrate monohydrate (CTM) was synthesized and it was grown as single crystals with optical quality. 1H and 13C NMR spectral studies were performed and molecular structure of synthesized CTM compound was confirmed. Single crystal X-ray diffraction (SXRD) analysis confirmed that CTM was crystallized in orthorhombic system with non-centrosymmetric (NCS), P212121, space group. The grown crystal exhibited admirable properties such as second harmonic generation efficiency (SHG) (1.9 times KDP), and high laser damage threshold (LDT) value of 3.7 GW cm-2. CTM crystal displayed high transparency (∼60%) in the visible and near-IR region with low cut-off wavelength at 249 nm. Photoluminescence study confirmed blue wavelength emission (∼463 nm) of grown crystal. Thermal and mechanical behaviours have been successfully analysed for grown crystals. The dielectric studies were carried out for grown crystal as a function of frequencies at different temperatures. Hirshfeld surface and fingerprint plots provided the percentage of individual interactions contributed by each atom. Moreover, density functional theory (DFT) calculations have been employed to probe the frontier molecular orbitals (FMOs) and first hyperpolarizability (β) analysis of the optimized CTM structure. These results validated CTM as a suitable NLO candidate and were discussed in this work.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems developmen....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304...
Experimental investigation on a pulsating heat pipe with hydrogen
International Nuclear Information System (INIS)
Deng, H R; Liu, Y M; Ma, R F; Han, D Y; Gan, Z H; Pfotenhauer, J M
2015-01-01
The pulsating heat pipe (PHP) has been increasingly studied in cryogenic application, for its high transfer coefficient and quick response. Compared with Nb 3 Sn and NbTi, MgB 2 whose critical transformation temperature is 39 K, is expected to replace some high-temperature superconducting materials at 25 K. In order to cool MgB 2 , this paper designs a Hydrogen Pulsating Heat Pipe, which allows a study of applied heat, filling ratio, turn number, inclination angle and length of adiabatic section on the thermal performance of the PHP. The thermal performance of the hydrogen PHP is investigated for filling ratios of 35%, 51%, 70% at different heat inputs, and provides information regarding the starting process is received at three filling ratios. (paper)
Pressure pulsation measurements in pipe and cluster flows
International Nuclear Information System (INIS)
Benemann, A.; Voj, P.
1976-01-01
Measuring and evaluation techniques of pressure pulsations in pipe and cluster flows are described. The measurements were made on a 1 m long SNR rod-cluster and its feed and drain pipes. At Reynolds numbers in the cluster of 8.9 x 10 4 flow velocities of 14 m/sec were achieved. With the aid of a block diagram recording of the measured values by piezoelectric crystal and piezo-resistive strain gange as well as data processing are explained. For the analytical treatment of the pressure pulsation signals characterizing the turbulence field computer codes of a digital computer and a fast-fourier analyzer (Hewlett-Packard 5450 A) were used. The results show good agreement with theoretical curves on the behaviour of turbulent boundary layers of cluster and pipe flows at high Reynolds numbers. (TK) [de
Comparative pulsation calculations with OP and OPAL opacities
Kanbur, Shashi M.; Simon, Norman R.
1994-01-01
Comparative linear nonadiabatic pulsation calculations are presented using the OPAL and Opacity Project opacities. The two sets of opacities include effects due to intermediate coupling and fine structure as well as new abundances. We used two mass luminosity (M-L) relations, one standard (BIT), and one employing substantial convective core overshoot (COV). The two sets of opacities cannot be differentiated on the basis of the stellar pulsation calculations presented here. The BIT relation can model the beat and bump Cepheids with masses between 4 and 7 solar mass, while if the overshoot relation is used, masses between 2 and 6 solar mass are required. In the RR Lyrae regime, we find the inferred masses of globular cluster RRd stars to be little influenced by the choice of OPAL or OP. Finally, the limited modeling we have done is not able to constrain the Cepheid M-L relation based upon period ratios observed in the beat and bump stars.
Energy confinement in the tokamak devices pulsator and ASDEX
International Nuclear Information System (INIS)
Klueber, O.; Murmann, H.
1982-04-01
The energy confinement of ohmically heated hydrogen plasmas obtained in the ASDEX and Pulsator tokamaks is investigated. In both devices, the confinement time does not follow a simple scaling law of the type tausub(E) approx. equal to nsub(e)a 2 . In the case of Pulsator, a regime is identified in which the transport is governed by electron heat conduction. The experimental data are compared with an analytic solution of the energy balance equation from which a heat diffusivity chisub(e) approx. equal to Zsub(eff)sup(1/3)/nsub(e)(r)Tsub(e)sup(1/2)(r)q(r) is inferred. chisub(i) is supposed to be neoclassical (plateau regime). Heat conduction following these laws is shown to lead to a consistent description of the full data set. (orig.)
Survey of non-linear hydrodynamic models of type-II Cepheids
Smolec, R.
2016-03-01
We present a grid of non-linear convective type-II Cepheid models. The dense model grids are computed for 0.6 M⊙ and a range of metallicities ([Fe/H] = -2.0, -1.5, -1.0), and for 0.8 M⊙ ([Fe/H] = -1.5). Two sets of convective parameters are considered. The models cover the full temperature extent of the classical instability strip, but are limited in luminosity; for the most luminous models, violent pulsation leads to the decoupling of the outermost model shell. Hence, our survey reaches only the shortest period RV Tau domain. In the Hertzsprung-Russell diagram, we detect two domains in which period-doubled pulsation is possible. The first extends through the BL Her domain and low-luminosity W Vir domain (pulsation periods ˜2-6.5 d). The second domain extends at higher luminosities (W Vir domain; periods >9.5 d). Some models within these domains display period-4 pulsation. We also detect very narrow domains (˜10 K wide) in which modulation of pulsation is possible. Another interesting phenomenon we detect is double-mode pulsation in the fundamental mode and in the fourth radial overtone. Fourth overtone is a surface mode, trapped in the outer model layers. Single-mode pulsation in the fourth overtone is also possible on the hot side of the classical instability strip. The origin of the above phenomena is discussed. In particular, the role of resonances in driving different pulsation dynamics as well as in shaping the morphology of the radius variation curves is analysed.
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.