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)

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)

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

OpenAIRE

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

2009-01-01

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

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.

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

Science.gov (United States)

Meair, Jonathan; Jacquod, Philippe

2013-02-27

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

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

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

Geometric Theory of Reduction of Nonlinear Control Systems

Science.gov (United States)

Elkin, V. I.

2018-02-01

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

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

Energy flow theory of nonlinear dynamical systems with applications

CERN Document Server

Xing, Jing Tang

2015-01-01

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

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.)

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

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....

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

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...

Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence

Energy Technology Data Exchange (ETDEWEB)

Heusen, M.; Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com [Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)

2017-04-20

In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.

Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence

International Nuclear Information System (INIS)

Heusen, M.; Shalchi, A.

2017-01-01

In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.

Nonlinear dynamical systems for theory and research in ergonomics.

Science.gov (United States)

Guastello, Stephen J

2017-02-01

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

Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity

International Nuclear Information System (INIS)

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

2007-01-01

We report observations of the dynamics of electromagnetically induced transparency (EIT) in a Λ system when the ground states are Stark shifted. Interactions of this type exhibit large optical nonlinearities called Kerr nonlinearities, and have numerous applications. The EIT Kerr nonlinearity is relatively slow, which is a limiting factor that may make many potential applications impossible. Using rubidium atoms, we observe the dynamics of the EIT Kerr nonlinearity using a Mach-Zehnder interferometer to measure phase modulation of the EIT fields resulting from a pulsed signal beam Stark shifting the ground state energy levels. The rise times and transients agree well with theory

A nonlinear theory of generalized functions

CERN Document Server

1990-01-01

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

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.

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.)

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

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.)

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

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

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

Agreeing on expectations

DEFF Research Database (Denmark)

Nielsen, Christian; Bentsen, Martin Juul

Commitment and trust are often mentioned as important aspects of creating a perception of reliability between counterparts. In the context of university-industry collaborations (UICs), agreeing on ambitions and expectations are adamant to achieving outcomes that are equally valuable to all parties...... involved. Despite this, our initial probing indicated that such covenants rarely exist. As such, this paper draws on project management theory and proposes the possibility of structuring assessments of potential partners before university-industry collaborations are brought to life. Our analysis suggests...

Information theory and stochastics for multiscale nonlinear systems

CERN Document Server

Majda, Andrew J; Grote, Marcus J

2005-01-01

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

Nonlinear system theory: another look at dependence.

Science.gov (United States)

Wu, Wei Biao

2005-10-04

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

Theory of weakly nonlinear self-sustained detonations

KAUST Repository

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

2015-01-01

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

Theory and design of nonlinear metamaterials

Science.gov (United States)

Rose, Alec Daniel

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

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.

Backward stochastic differential equations from linear to fully nonlinear theory

CERN Document Server

Zhang, Jianfeng

2017-01-01

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

Quantitative theory of driven nonlinear brain dynamics.

Science.gov (United States)

Roberts, J A; Robinson, P A

2012-09-01

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

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)

Composite Beam Theory with Material Nonlinearities and Progressive Damage

Science.gov (United States)

Jiang, Fang

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

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

Science.gov (United States)

Bridges, Thomas J.; Ratliff, Daniel J.

2018-04-01

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

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

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

Science.gov (United States)

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

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

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.

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

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

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

International Nuclear Information System (INIS)

Doering, C.R.

1985-01-01

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

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.

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

Science.gov (United States)

Silva, Walter A.

1993-01-01

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

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

Development of a nonlinear unsteady transonic flow theory

Science.gov (United States)

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

1973-01-01

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

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....

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

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

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...

Nonlinear analysis approximation theory, optimization and applications

CERN Document Server

2014-01-01

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

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

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.

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

Synthesis of robust nonlinear autopilots using differential game theory

Science.gov (United States)

Menon, P. K. A.

1991-01-01

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

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.)

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.

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

Science.gov (United States)

Nemeth, Michael P.

2013-01-01

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

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

International Nuclear Information System (INIS)

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

2014-01-01

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

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

Science.gov (United States)

Bloch, Deborah P.

2005-01-01

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

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

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 polarization of ionic liquids: theory, simulations, experiments

Science.gov (United States)

Kornyshev, Alexei

2010-03-01

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

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

Science.gov (United States)

M. W. Johnson; Thomas J. Urbanik

1984-03-01

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

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.

Theories of quantum dissipation and nonlinear coupling bath descriptors

Science.gov (United States)

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

2018-03-01

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

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

Science.gov (United States)

Wang, Liming; Zheng, Shijie

2018-02-01

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

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

CERN Document Server

Takahashi, Wataru

1995-01-01

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

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

Science.gov (United States)

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

2018-05-01

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

The preparation problem in nonlinear extensions of quantum theory

OpenAIRE

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

2012-01-01

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

Lectures in nonlinear mechanics and chaos theory

CERN Document Server

Stetz, Albert W

2016-01-01

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

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

Nonlinear responses of chiral fluids from kinetic theory

Science.gov (United States)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

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

Nonlinear wavenumber of an electron plasma wave

International Nuclear Information System (INIS)

Vidmar, P.J.; Malmberg, J.H.; Starke, T.P.

1976-01-01

The wavenumber of a large-amplitude electron plasma wave propagating on a collisionless plasma column is measured. The wavenumber is shifted from that of a small-amplitude wave of the same frequency. This nonlinear wavenumber shift, deltak/subr/, depends on position, frequency, and initial wave amplitude, Phi. The observed spatial oscillations of deltak/subr/ agree qualitatively with recent theories. Experimentally deltak/subr/proportionalk/subi/S (Phi) rootPhi where k/subi/ is the linear Landau damping coefficient, S (Phi) equivalentk/subi/(Phi)/k/subi/, and k/subi/(Phi) is the initial damping coefficient which depends on Phi

Microcanonical ensemble formulation of lattice gauge theory

International Nuclear Information System (INIS)

Callaway, D.J.E.; Rahman, A.

1982-01-01

A new formulation of lattice gauge theory without explicit path integrals or sums is obtained by using the microcanonical ensemble of statistical mechanics. Expectation values in the new formalism are calculated by solving a large set of coupled, nonlinear, ordinary differential equations. The average plaquette for compact electrodynamics calculated in this fashion agrees with standard Monte Carlo results. Possible advantages of the microcanonical method in applications to fermionic systems are discussed

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

Science.gov (United States)

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

2010-12-01

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

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

Science.gov (United States)

Kharin, Nikolay A.

2000-04-01

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

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.)

Nonlinear electroelasticity: material properties, continuum theory and applications.

Science.gov (United States)

Dorfmann, Luis; Ogden, Ray W

2017-08-01

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

Nonlinear electroelasticity: material properties, continuum theory and applications

Science.gov (United States)

Dorfmann, Luis; Ogden, Ray W.

2017-08-01

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

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

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.

Quantum theory from a nonlinear perspective Riccati equations in fundamental physics

CERN Document Server

Schuch, Dieter

2018-01-01

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

On the non-linear scale of cosmological perturbation theory

Energy Technology Data Exchange (ETDEWEB)

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

2013-04-15

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

On the non-linear scale of cosmological perturbation theory

International Nuclear Information System (INIS)

Blas, Diego; Garny, Mathias; Konstandin, Thomas

2013-04-01

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

On the non-linear scale of cosmological perturbation theory

CERN Document Server

Blas, Diego; Konstandin, Thomas

2013-01-01

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

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)

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

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...

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

International Nuclear Information System (INIS)

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

2013-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-12-15

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

On the interaction of small-scale linear waves with nonlinear solitary waves

Science.gov (United States)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow

Non-linear theory of elasticity and optimal design

CERN Document Server

Ratner, LW

2003-01-01

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

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

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...

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

Science.gov (United States)

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

1983-01-01

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

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

Science.gov (United States)

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

2015-01-01

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

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

Science.gov (United States)

de Paor, A. M.

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

Effect of nonlinear stress-strain relationship on bending strength of isotropic graphite

International Nuclear Information System (INIS)

Arai, Taketoshi; Oku, Tatsuo

1978-05-01

Four-point bending tests were made on rectangular isotropic 7477PT graphite specimens of different sizes to observe the relation between load and outermost fiber strain. Analytical methods, allowing for nonlinear stress-strain relationships different between tension and compression, were developed for calculating the fiber stress distribution in a beam and the failure probability based on the Weibull statistical theory for bending fracture. With increase of the stress, the stress-strain curves for tension deviate from the linearity and also from those for compression. The true bending strengths of the rectangular bars are 10 -- 20 percent lower than elastic bending strengths. Revised Weibull theory gives failure probability distributions agreeing with measured ones, compared with the theory based on elastic behavior. (auth.)

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

Science.gov (United States)

Takahashi, Taiki

2011-01-01

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

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

Science.gov (United States)

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

2000-08-01

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

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

Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability

Science.gov (United States)

Zhao, K. G.; Wang, L. F.; Xue, C.; Ye, W. H.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.

2018-03-01

On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.

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

Directory of Open Access Journals (Sweden)

A. M. de Paor

1998-01-01

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

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

International Nuclear Information System (INIS)

Qian, Hong

2011-01-01

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

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

International Nuclear Information System (INIS)

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

1984-01-01

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

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

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...

Nonlinearity management in higher dimensions

International Nuclear Information System (INIS)

Kevrekidis, P G; Pelinovsky, D E; Stefanov, A

2006-01-01

In the present paper, we revisit nonlinearity management of the time-periodic nonlinear Schroedinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schroedinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H 1 norm remains bounded, in contrast with the usual blow-up mechanism for the focusing Schroedinger equation. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management

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.

Multiple nonlinear Bragg diffraction of femtosecond laser pulses in a {\\chi^{(2)}} photonic lattice with hexagonal domains

Science.gov (United States)

Vyunishev, A. M.; Arkhipkin, V. G.; Baturin, I. S.; Akhmatkhanov, A. R.; Shur, V. Ya; Chirkin, A. S.

2018-04-01

The frequency doubling of femtosecond laser pulses in a two-dimensional (2D) rectangular nonlinear photonic lattice with hexagonal domains is studied experimentally and theoretically. The broad fundamental spectrum enables frequency conversion under nonlinear Bragg diffraction for a series of transverse orders at a fixed longitudinal quasi-phase-matching order. The consistent nonstationary theory of the frequency doubling of femtosecond laser pulses is developed using the representation based on the reciprocal lattice of the structure. The calculated spatial distribution of the second-harmonic spectral intensity agrees well with the experimental data. The condition for multiple nonlinear Bragg diffraction in a 2D nonlinear photonic lattice is offered. The hexagonal shape of the domains contributes to multibeam second harmonic excitation. The maximum conversion efficiency for a series of transverse orders in the range 0.01%-0.03% is obtained.

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

NARCIS (Netherlands)

Zwart, H.J.

2015-01-01

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

Nonlinear hyperbolic waves in multidimensions

CERN Document Server

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...

Nonlinear elastic waves in materials

CERN Document Server

Rushchitsky, Jeremiah J

2014-01-01

The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...

Theory of weakly nonlinear self-sustained detonations

KAUST Repository

Faria, Luiz

2015-11-03

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

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

Science.gov (United States)

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

1991-01-01

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

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

NARCIS (Netherlands)

Bagchi, Arunabha; Karandikar, Rajeeva

1992-01-01

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

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

NARCIS (Netherlands)

Bagchi, Arunabha; Karandikar, Rajeeva

1994-01-01

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

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

International Nuclear Information System (INIS)

Fang Jinqing; Yao Weiguang

1992-12-01

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

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.

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.

Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

Science.gov (United States)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

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

Science.gov (United States)

Hall, P.; Malik, M. R.

1984-01-01

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

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

Science.gov (United States)

Hall, P.; Malik, M. R.

1986-01-01

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

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

Directory of Open Access Journals (Sweden)

2007-01-01

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

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

Science.gov (United States)

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

2018-06-01

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

TBA equations for the mass gap in the O(2r) non-linear σ-models

International Nuclear Information System (INIS)

Balog, Janos; Hegedues, Arpad

2005-01-01

We propose TBA integral equations for 1-particle states in the O(n) non-linear σ-model for even n. The equations are conjectured on the basis of the analytic properties of the large volume asymptotics of the problem, which is explicitly constructed starting from Luscher's asymptotic formula. For small volumes the mass gap values computed numerically from the TBA equations agree very well with results of three-loop perturbation theory calculations, providing support for the validity of the proposed TBA system

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

Science.gov (United States)

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

2014-04-01

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

Nonlinear optimization

CERN Document Server

Ruszczynski, Andrzej

2011-01-01

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

Non-linearities in Theory-of-Mind Development.

Science.gov (United States)

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

2016-01-01

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

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

Science.gov (United States)

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

2015-10-01

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

Numerical Test of Different Approximations Used in the Transport Theory of Energetic Particles

Science.gov (United States)

Qin, G.; Shalchi, A.

2016-05-01

Recently developed theories for perpendicular diffusion work remarkably well. The diffusion coefficients they provide agree with test-particle simulations performed for different turbulence setups ranging from slab and slab-like models to two-dimensional and noisy reduced MHD turbulence. However, such theories are still based on different analytical approximations. In the current paper we use a test-particle code to explore the different approximations used in diffusion theory. We benchmark different guiding center approximations, simplifications of higher-order correlations, and the Taylor-Green-Kubo formula. We demonstrate that guiding center approximations work very well as long as the particle's unperturbed Larmor radius is smaller than the perpendicular correlation length of the turbulence. Furthermore, the Taylor-Green-Kubo formula and the definition of perpendicular diffusion coefficients via mean square displacements provide the same results. The only approximation that was used in the past in nonlinear diffusion theory that fails is to replace fourth-order correlations by a product of two second-order correlation functions. In more advanced nonlinear theories, however, this type of approximation is no longer used. Therefore, we confirm the validity of modern diffusion theories as a result of the work presented in the current paper.

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

Science.gov (United States)

Bussolari, Cori J.; Goodell, Judith A.

2009-01-01

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

Generalized solutions of nonlinear partial differential equations

CERN Document Server

Rosinger, EE

1987-01-01

During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin

Time-Sliced Perturbation Theory II: Baryon Acoustic Oscillations and Infrared Resummation

CERN Document Server

Blas, Diego; Ivanov, Mikhail M.; Sibiryakov, Sergey

2016-01-01

We use time-sliced perturbation theory (TSPT) to give an accurate description of the infrared non-linear effects affecting the baryonic acoustic oscillations (BAO) present in the distribution of matter at very large scales. In TSPT this can be done via a systematic resummation that has a simple diagrammatic representation and does not involve uncontrollable approximations. We discuss the power counting rules and derive explicit expressions for the resummed matter power spectrum up to next-to leading order and the bispectrum at the leading order. The two-point correlation function agrees well with N-body data at BAO scales. The systematic approach also allows to reliably assess the shift of the baryon acoustic peak due to non-linear effects.

Measurement and fitting techniques for the assessment of material nonlinearity using nonlinear Rayleigh waves

Energy Technology Data Exchange (ETDEWEB)

Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)

2015-03-31

This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

Science.gov (United States)

Arendt, V.; Shalchi, A.

2018-06-01

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

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)

Nonlinear analysis

CERN Document Server

Gasinski, Leszek

2005-01-01

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

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

DEFF Research Database (Denmark)

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

2016-01-01

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

Exact Solution of a Strongly Coupled Gauge Theory in 0 +1 Dimensions

Science.gov (United States)

Krishnan, Chethan; Kumar, K. V. Pavan

2018-05-01

Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely, the smallest colored tensor model due to Gurau and Witten that exhibits nonlinearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of N , exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the technical details will appear in companion paper [C. Krishnan and K. V. Pavan Kumar, Complete solution of a gauged tensor model, arXiv:1804.10103].

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

OpenAIRE

A. M. de Paor

1998-01-01

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

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

Directory of Open Access Journals (Sweden)

Shahriar Dastjerdi

2016-06-01

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

Nonlinear Science

CERN Document Server

Yoshida, Zensho

2010-01-01

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

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)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-09-01

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

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

Science.gov (United States)

Tsuchida, Satoshi; Kuratsuji, Hiroshi

2018-05-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2010-05-15

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

'Nothing is agreed until everything is agreed'

DEFF Research Database (Denmark)

McQuaid, Sara Dybris

In terms of conflict resolution, we may think of Northern Ireland as a case of (deferring conflict by) institutionalising radical disagreement, in particular through the Agreement from 1998. The violence has largely if not completely stopped, but the key constitutional question of whether Northern...... Ireland should be British or Irish, is only settled for now. In the language of dialogue, the parties have “agreed to disagree” with an understanding that these matters can be reopened at some future date if there is a majority wish to do so. In the meantime, a system of designated power-sharing has been...

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

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.

Explicit Nonlinear Model Predictive Control Theory and Applications

CERN Document Server

Grancharova, Alexandra

2012-01-01

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

Nonlinear model predictive control theory and algorithms

CERN Document Server

Grüne, Lars

2017-01-01

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

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

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

Directory of Open Access Journals (Sweden)

Iman Eshraghi

2016-09-01

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

Glimpses of soliton theory the algebra and geometry of nonlinear PDEs

CERN Document Server

Kasman, Alex

2010-01-01

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

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

Science.gov (United States)

Banks, H. T.; Kunisch, K.

1982-01-01

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

Nonlinear optics principles and applications

CERN Document Server

Rottwitt, Karsten

2014-01-01

IntroductionReview of linear opticsInduced polarizationHarmonic oscillator modelLocal field correctionsEstimated nonlinear responseSummaryTime-domain material responseThe polarization time-response functionThe Born-Oppenheimer approximationRaman scattering response function of silicaSummaryMaterial response in the frequency domain, susceptibility tensorsThe susceptibility tensorThe induced polarization in the frequency domainSum of monochromatic fieldsThe prefactor to the induced polarizationThird-order polarization in the Born-Oppenheimer approximation in the frequency domainKramers-Kronig relationsSummarySymmetries in nonlinear opticsSpatial symmetriesSecond-order materialsThird-order nonlinear materialsCyclic coordinate-systemContracted notation for second-order susceptibility tensorsSummaryThe nonlinear wave equationMono and quasi-monochromatic beamsPlane waves - the transverse problemWaveguidesVectorial approachNonlinear birefringenceSummarySecond-order nonlinear effectsGeneral theoryCoupled wave theoryP...

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.

Linear theory for filtering nonlinear multiscale systems with model error.

Science.gov (United States)

Berry, Tyrus; Harlim, John

2014-07-08

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

Context, Complexity and Contestation: Birmingham's Agreed Syllabuses for Religious Education since the 1970s

Science.gov (United States)

Parker, Stephen G.; Freathy, Rob J. K.

2011-01-01

The present article offers an historical perspective on the 1975, 1995 and 2007 Birmingham Agreed Syllabuses for Religious Education. It draws upon historical evidence uncovered as part of "The hidden history of curriculum change in religious education in English schools, 1969-1979" project, and curriculum history theories, especially…

24 CFR 241.1070 - Agreed interest rate.

Science.gov (United States)

2010-04-01

... 24 Housing and Urban Development 2 2010-04-01 2010-04-01 false Agreed interest rate. 241.1070...-Eligibility Requirements § 241.1070 Agreed interest rate. The equity or acquisition loan shall bear interest at the rate agreed upon by the borrower and the lender. ...

Goertler vortices in growing boundary layers: The leading edge receptivity problem, linear growth and the nonlinear breakdown stage

Science.gov (United States)

Hall, Philip

1989-01-01

Goertler vortices are thought to be the cause of transition in many fluid flows of practical importance. A review of the different stages of vortex growth is given. In the linear regime, nonparallel effects completely govern this growth, and parallel flow theories do not capture the essential features of the development of the vortices. A detailed comparison between the parallel and nonparallel theories is given and it is shown that at small vortex wavelengths, the parallel flow theories have some validity; otherwise nonparallel effects are dominant. New results for the receptivity problem for Goertler vortices are given; in particular vortices induced by free stream perturbations impinging on the leading edge of the walls are considered. It is found that the most dangerous mode of this type can be isolated and it's neutral curve is determined. This curve agrees very closely with the available experimental data. A discussion of the different regimes of growth of nonlinear vortices is also given. Again it is shown that, unless the vortex wavelength is small, nonparallel effects are dominant. Some new results for nonlinear vortices of 0(1) wavelengths are given and compared to experimental observations.

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

International Nuclear Information System (INIS)

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

1978-01-01

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

On the theory of weak turbulence for the nonlinear Schrödinger equation

CERN Document Server

Escobedo, M

2015-01-01

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

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 dynamics and complexity

CERN Document Server

Luo, Albert; Fu, Xilin

2014-01-01

This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

Robust methods and asymptotic theory in nonlinear econometrics

CERN Document Server

Bierens, Herman J

1981-01-01

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

24 CFR 242.26 - Agreed interest rate.

Science.gov (United States)

2010-04-01

... 24 Housing and Urban Development 2 2010-04-01 2010-04-01 false Agreed interest rate. 242.26... MORTGAGE INSURANCE FOR HOSPITALS Mortgage Requirements § 242.26 Agreed interest rate. (a) The mortgage shall bear interest at the rate or rates agreed upon by the mortgagee and the mortgagor. (b) The amount...

24 CFR 203.20 - Agreed interest rate.

Science.gov (United States)

2010-04-01

... 24 Housing and Urban Development 2 2010-04-01 2010-04-01 false Agreed interest rate. 203.20... § 203.20 Agreed interest rate. (a) The mortgage shall bear interest at the rate agreed upon by the mortgagee and the mortgagor. (b) Interest shall be payable in monthly installments on the principal amount...

24 CFR 241.560 - Agreed interest rate.

Science.gov (United States)

2010-04-01

... 24 Housing and Urban Development 2 2010-04-01 2010-04-01 false Agreed interest rate. 241.560... § 241.560 Agreed interest rate. (a) The mortgage shall bear interest at the rate agreed upon by the lender and the borrower. (b) Interest shall be payable in monthly installments on the principal amount of...

Nonlinear dynamics aspects of particle accelerators

International Nuclear Information System (INIS)

Jowett, J.M.; Turner, S.; Month, M.

1986-01-01

These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI)

Ward Identities of W_{\\infty} Symmetry and Higher Genus Amplitudes in 2D String Theory

OpenAIRE

Hamada, Ken-ji

1995-01-01

The Ward identities of the $W_{\\infty}$ symmetry in two dimensional string theory in the tachyon background are studied in the continuum approach. We consider amplitudes different from 2D string ones by the external leg factor and derive the recursion relations among them. The recursion relations have non-linear terms which give relations among the amplitudes defined on different genus. The solutions agree with the matrix model results even in higher genus. We also discuss differences of role...

Quantum Nonlinear Optics

CERN Document Server

Hanamura, Eiichi; Yamanaka, Akio

2007-01-01

This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.

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

International Nuclear Information System (INIS)

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

1995-01-01

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

Relation between nonlinear models and gauge ambiguities

International Nuclear Information System (INIS)

Balachandran, A.P.; Ramachandran, R.; Rupertsberger, H.; Skagerstam, B.S.

1980-01-01

We show that the solutions of a class of nonlinear models also generate gauge ambiguities in the vacuum sector of Yang-Mills theories. Our results extend known connections between gauge ambiguities and certain nonlinear sigma-models, and clarify the underlying group theory. For many nonlinear models, we also give a simple, intrinsic parametrization of physical fields (which have values in a homogeneous space of a group). (orig.)

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...

Advances in nonlinear optics

CERN Document Server

Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong

2015-01-01

This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.

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.

Device Applications of Nonlinear Dynamics

CERN Document Server

Baglio, Salvatore

2006-01-01

This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.

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

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

CERN Document Server

Farantos, Stavros C

2014-01-01

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

Degenerate nonlinear diffusion equations

CERN Document Server

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...

Averaging of nonlinearity-managed pulses

International Nuclear Information System (INIS)

Zharnitsky, Vadim; Pelinovsky, Dmitry

2005-01-01

We consider the nonlinear Schroedinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons

Nonlinear Deformable-body Dynamics

CERN Document Server

Luo, Albert C J

2010-01-01

"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...

The non-linear power spectrum of the Lyman alpha forest

International Nuclear Information System (INIS)

Arinyo-i-Prats, Andreu; Miralda-Escudé, Jordi; Viel, Matteo; Cen, Renyue

2015-01-01

The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate the comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula

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

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.)

Nonlinear systems

National Research Council Canada - National Science Library

Drazin, P. G

1992-01-01

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

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

CERN Document Server

Ginoux, Jean-Marc

2017-01-01

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

Perturbation theory for BAO reconstructed fields: One-loop results in the real-space matter density field

Science.gov (United States)

Hikage, Chiaki; Koyama, Kazuya; Heavens, Alan

2017-08-01

We compute the power spectrum at one-loop order in standard perturbation theory for the matter density field to which a standard Lagrangian baryonic acoustic oscillation (BAO) reconstruction technique is applied. The BAO reconstruction method corrects the bulk motion associated with the gravitational evolution using the inverse Zel'dovich approximation (ZA) for the smoothed density field. We find that the overall amplitude of one-loop contributions in the matter power spectrum substantially decreases after reconstruction. The reconstructed power spectrum thereby approaches the initial linear spectrum when the smoothed density field is close enough to linear, i.e., the smoothing scale Rs≳10 h-1 Mpc . On smaller Rs, however, the deviation from the linear spectrum becomes significant on large scales (k ≲Rs-1 ) due to the nonlinearity in the smoothed density field, and the reconstruction is inaccurate. Compared with N-body simulations, we show that the reconstructed power spectrum at one-loop order agrees with simulations better than the unreconstructed power spectrum. We also calculate the tree-level bispectrum in standard perturbation theory to investigate non-Gaussianity in the reconstructed matter density field. We show that the amplitude of the bispectrum significantly decreases for small k after reconstruction and that the tree-level bispectrum agrees well with N-body results in the weakly nonlinear regime.

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

Science.gov (United States)

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

2014-12-01

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

Nonlinear dynamics aspects of particle accelerators. Proceedings

Energy Technology Data Exchange (ETDEWEB)

Jowett, J M; Turner, S; Month, M

1986-01-01

These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI).

Introduction to nonlinear dispersive equations

CERN Document Server

Linares, Felipe

2015-01-01

This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

L2-gain and passivity techniques in nonlinear control

CERN Document Server

van der Schaft, Arjan

2017-01-01

This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity. The potential of L2-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization...

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

Nonlinear systems

CERN Document Server

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

2018-01-01

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

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

Directory of Open Access Journals (Sweden)

Adailton S. Borges

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

Nonlinear problems of the theory of heterogeneous slightly curved shells

Science.gov (United States)

Kantor, B. Y.

1973-01-01

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

Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

CERN Document Server

Aliyu, MDS

2011-01-01

A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter

Introduction to nonlinear finite element analysis

CERN Document Server

Kim, Nam-Ho

2015-01-01

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

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

International Nuclear Information System (INIS)

Di Dong; Yiming Long.

1994-10-01

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

Global solutions of nonlinear Schrödinger equations

CERN Document Server

Bourgain, J

1999-01-01

This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrödinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented. Several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research r

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

Science.gov (United States)

Levinson, Howard W; Markel, Vadim A

2016-10-01

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

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

International Nuclear Information System (INIS)

Hahm, T.S.

1990-12-01

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

AGREED-UPON PROCEDURES, PROCEDURES FOR AUDITING EUROPEAN GRANTS

Directory of Open Access Journals (Sweden)

Daniel Petru VARTEIU

2016-12-01

The audit of EU-funded projects is an audit based on agreed-upon procedures, which are established by the Managing Authority or the Intermediate Body. Agreed-upon procedures can be defined as engagements made in accordance with ISRS 4400, applicable to agreed-upon procedures, where the auditor undertakes to carry out the agreed-upon procedures and issue a report on factual findings. The report provided by the auditor does not express any assurance. It allows users to form their own opinions about the conformity of the expenses with the project budget as well as the eligibility of the expenses.

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

Science.gov (United States)

Neilson, Peter D; Neilson, Megan D

2005-09-01

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

Nonlinear solar cycle forecasting: theory and perspectives

Science.gov (United States)

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

2008-02-01

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

The AGREE Enterprise: a decade of advancing clinical practice guidelines.

Science.gov (United States)

Makarski, Julie; Brouwers, Melissa C

2014-08-15

The original AGREE (Appraisal of Guidelines for REsearch and Evaluation) Instrument was published in 2003, and its revision, the AGREE II, in 2009. Together, they filled an important gap in the guideline and quality of care fields. Ten years later, the AGREE Enterprise reflects on a trajectory of projects and international collaboration that have contributed to advancing the science and quality of practice guidelines and the uptake of AGREE/AGREE II. The AGREE Enterprise has undertaken activities to improve the tool and to develop resources to support its use. Since 2003, the uptake and adoption of AGREE by the international community has been swift and broad. A total of 33 language translations of the original AGREE Instrument and the current AGREE II are available and were initiated by the international community. A recent scan of the published literature identified over 600 articles that referenced the AGREE tools. The AGREE tools have been widely received and applied, with several organizations having incorporated the AGREE as part of their formal practice guideline programs. Since its redevelopment in 2010, the AGREE Enterprise website (www.agreetrust.org) continues to experience steady increases in visitors per month and currently has over 10,000 registered users. The AGREE Enterprise has contributed to the advancements of guidelines through research activities and international participation by scientific and user communities. As we enter a new decade, we look forward to ongoing collaborations and contributing to further advancements to improve quality of care and health care systems.

Prolongation Structure of Semi-discrete Nonlinear Evolution Equations

International Nuclear Information System (INIS)

Bai Yongqiang; Wu Ke; Zhao Weizhong; Guo Hanying

2007-01-01

Based on noncommutative differential calculus, we present a theory of prolongation structure for semi-discrete nonlinear evolution equations. As an illustrative example, a semi-discrete model of the nonlinear Schroedinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

Science.gov (United States)

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity

Science.gov (United States)

Mostafazadeh, Ali; Oflaz, Neslihan

2017-11-01

We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.

Recent topics in non-linear partial differential equations 4

CERN Document Server

Mimura, M

1989-01-01

This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.

Nonlinear control and filtering using differential flatness approaches applications to electromechanical systems

CERN Document Server

Rigatos, Gerasimos G

2015-01-01

This monograph presents recent advances in differential flatness theory and analyzes its use for nonlinear control and estimation. It shows how differential flatness theory can provide solutions to complicated control problems, such as those appearing in highly nonlinear multivariable systems and distributed-parameter systems. Furthermore, it shows that differential flatness theory makes it possible to perform filtering and state estimation for a wide class of nonlinear dynamical systems and provides several descriptive test cases. The book focuses on the design of nonlinear adaptive controllers and nonlinear filters, using exact linearization based on differential flatness theory. The adaptive controllers obtained can be applied to a wide class of nonlinear systems with unknown dynamics, and assure reliable functioning of the control loop under uncertainty and varying operating conditions. The filters obtained outperform other nonlinear filters in terms of accuracy of estimation and computation speed. The bo...

Nonlinear effects during sound propagation in n-InSb at 4.20K

International Nuclear Information System (INIS)

Ilisavskij, Yu.V.; Chiplis, D.

1975-01-01

The absorption of transverse sound and the influence of longitudinal electric and magnetic fields thereon were studied in n-InSb at 4.2 0 K over a wide range of frequencies and intensities. The electron absorption of sound was found to depend strongly on input intensity due to the heating of electrons by the sound wave. It was discovered that the observed non-linearity was suppressed by the electric field. On the basis of comparison of the experimental results with the existing theories it is concluded that during the heating of electrons by sound, apart from changes in mobility, the carrier concentration in the conductivity band is also substantially changed. The measurements in the magnetic field agree qualitatively with the two-band conductivity model. (author)

Nonlinearity without superluminality

International Nuclear Information System (INIS)

Kent, Adrian

2005-01-01

Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schroedinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality

Nonlinear wave collapse and strong turbulence

International Nuclear Information System (INIS)

Robinson, P.A.

1997-01-01

The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions. copyright 1997 The American Physical Society

Recent topics in nonlinear PDE

International Nuclear Information System (INIS)

Mimura, Masayasu; Nishida, Takaaki

1984-01-01

The meeting on the subject of nonlinear partial differential equations was held at Hiroshima University in February, 1983. Leading and active mathematicians were invited to talk on their current research interests in nonlinear pdes occuring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. This volume contains the theory of nonlinear pdes and the related topics which have been recently developed in Japan. (Auth.)

Symmetry, phase modulation and nonlinear waves

CERN Document Server

Bridges, Thomas J

2017-01-01

Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.

A non-linear field theory

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

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

Determination of the spiral Galaxy structure parameters based on neutral hydrogen radiowave radiation in 21 cm line. 2. Nonlinear theory. 30 deg <= |l| <= 60 deg

International Nuclear Information System (INIS)

Berman, V.G.; Mishurov, Yu.N.

1980-01-01

Gas flow and its density distribution in the Galaxy spiral arm gravitational potential is calculated by means of the nonlinear theory. Line profile of H I emission in 21 cm based on the Galaxy spiral structure models proposed by Lin and Marochnik are constructed for the galactic coordinates 30 deg < or approximately |l| < or approximately 60 deg. It is shown that the conclusion about the possibility of agreement of the Marochnik model with observations made by means of the linear theory is confirmed in the nonlinear theory. In the Marochnik model distributions with R H II regions, CO-clouds, γ-radiation, supernova remnants and so on may also be understood connecting them with variation of gas compression in galactic shock with H radius

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

Science.gov (United States)

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

2011-04-07

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

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

International Nuclear Information System (INIS)

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

2011-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2011-04-07

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

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

International Nuclear Information System (INIS)

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

2003-01-01

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

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.)

Complex motions and chaos in nonlinear systems

CERN Document Server

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.

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

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.

Nonlinear waves and weak turbulence

CERN Document Server

Zakharov, V E

1997-01-01

This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.

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

Science.gov (United States)

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

2012-10-01

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

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

Nonlinear Poisson equation for heterogeneous media.

Science.gov (United States)

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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

Nonlinear temporal modulation of pulsar radioemission

International Nuclear Information System (INIS)

Chian, A.C.-L.

1984-01-01

A nonlinear theory is discussed for self-modulation of pulsar radio pulses. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron-positron plasma. The nonlinearities arising from wave intensity induced relativistic particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary wave forms may account for the formation of pulsar microstructures. (Author) [pt

Solitons in quadratic nonlinear photonic crystals

DEFF Research Database (Denmark)

Corney, Joel Frederick; Bang, Ole

2001-01-01

We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....

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)

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

KAUST Repository

Yavari, Arash

2012-03-09

We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan\\'s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.

Strongly nonlinear theory of rapid solidification near absolute stability

Science.gov (United States)

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

2017-10-01

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

Field-theoretical investigations in nonlinear realizations of gauge symmetry

International Nuclear Information System (INIS)

Lee, Chenhan.

1989-01-01

A review of both linear realization and non-linear realization of gauge symmetries is given and the connection between the two recipes is carefully examined. The author then constructs both linear and non-linear realizations for of supersymmetric theories. The supermultiplets of the Goldstone modes contain Goldstone bosons, quasi-Goldstone bosons and quasi-Goldstone fermions. He makes an attempt to construct a specific model of a supersymmetric non-linear realization for the Nambu-Goldstone superfields and the quasi-Goldstone fermions are identified with the quarks and leptons. Further, he discusses a mechanism by which the components of the Nambu-Goldstone supermultiplets are given non-zero mass splittings by the coupling to a hidden sector. Next, he turns to anti-symmetric tensor gauge theories, which are shown to be classically equivalent to the non-linear models describing the complete symmetry breakdown. To study the quantum mechanical equivalence of these two models, he carries out the tensor gauge fixing and the quantization procedures for the anti-symmetric tensor theories and establish the global symmetry currents which connect the two models. He then builds the supersymmetric extensions of the anti-symmetric tensor gauge theories in both abelian and non-abelian versions. Such super-tensor gauge theories are shown, by using the superfield equations of motion, to be equivalent to the fully doubled supersymmetric non-linear models of complete symmetry breakdown

Nonlinear science as a fluctuating research frontier

International Nuclear Information System (INIS)

He Jihuan

2009-01-01

Nonlinear science has had quite a triumph in all conceivable applications in science and technology, especially in high energy physics and nanotechnology. COBE, which was awarded the physics Nobel Prize in 2006, might be probably more related to nonlinear science than the Big Bang theory. Five categories of nonlinear subjects in research frontier are pointed out.

On the entanglement entropy for gauge theories

International Nuclear Information System (INIS)

Ghosh, Sudip; Soni, Ronak M; Trivedi, Sandip P.

2015-01-01

We propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and Non-Abelian gauge theories. For ℤ_N and U(1) theories, without matter, our definition agrees with a particular case of the definition given by Casini, Huerta and Rosabal. We also argue that in general, both for Abelian and Non-Abelian theories, our definition agrees with the entanglement entropy calculated using a definition of the replica trick. Our definition, however, does not agree with some standard ways to measure entanglement, like the number of Bell pairs which can be produced by entanglement distillation.

Superdiffusions and positive solutions of nonlinear partial differential equations

CERN Document Server

Dynkin, E B

2004-01-01

This book is devoted to the applications of probability theory to the theory of nonlinear partial differential equations. More precisely, it is shown that all positive solutions for a class of nonlinear elliptic equations in a domain are described in terms of their traces on the boundary of the domain. The main probabilistic tool is the theory of superdiffusions, which describes a random evolution of a cloud of particles. A substantial enhancement of this theory is presented that can be of interest for everybody who works on applications of probabilistic methods to mathematical analysis.

Generalized nonlinear Proca equation and its free-particle solutions

Energy Technology Data Exchange (ETDEWEB)

Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)

2016-06-15

We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)

NONLINEAR EVOLUTION OF BEAM-PLASMA INSTABILITY IN INHOMOGENEOUS MEDIUM

International Nuclear Information System (INIS)

Ziebell, L. F.; Pavan, J.; Yoon, P. H.; Gaelzer, R.

2011-01-01

The problem of electron-beam propagation in inhomogeneous solar wind is intimately related to the solar type II and/or type III radio bursts. Many scientists have addressed this issue in the past by means of quasi-linear theory, but in order to fully characterize the nonlinear dynamics, one must employ weak-turbulence theory. Available numerical solutions of the weak-turbulence theory either rely on only one nonlinear process (either decay or scattering), or when both nonlinear terms are included, the inhomogeneity effect is generally ignored. The present paper reports the full solution of weak-turbulence theory that includes both decay and scattering processes, and also incorporating the effects of density gradient. It is found that the quasi-linear effect sufficiently accounts for the primary Langmuir waves, but to properly characterize the back-scattered Langmuir wave, which is important for eventual radiation generation, it is found that both nonlinear decay and scattering processes make comparable contributions. Such a finding may be important in the quantitative analysis of the plasma emission process with application to solar type II and/or type III radio bursts.

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

Directory of Open Access Journals (Sweden)

Hamid M. Sedighi

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

The nonlinear universe chaos, emergence, life

CERN Document Server

Scott, A C

2007-01-01

Written in Alwyn Scott’s inimitable style – lucid and accessible – The Nonlinear Universe surveys and explores the explosion of activity in nonlinear science that began in the 1970s and 1980s and continues today. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science – and an appreciation of its implications – is essential for understanding scientific developments of the twenty-first century.

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

International Nuclear Information System (INIS)

Esmaeilzadeh Khadem, S.; Rezaee, M.

2001-01-01

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

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

Science.gov (United States)

Osherovich, V. A.; Fainberg, J.

2018-01-01

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

Consensus problem in directed networks of multi-agents via nonlinear protocols

International Nuclear Information System (INIS)

Liu Xiwei; Chen Tianping; Lu Wenlian

2009-01-01

In this Letter, the consensus problem via distributed nonlinear protocols for directed networks is investigated. Its dynamical behaviors are described by ordinary differential equations (ODEs). Based on graph theory, matrix theory and the Lyapunov direct method, some sufficient conditions of nonlinear protocols guaranteeing asymptotical or exponential consensus are presented and rigorously proved. The main contribution of this work is that for nonlinearly coupled networks, we generalize the results for undirected networks to directed networks. Consensus under pinning control technique is also developed here. Simulations are also given to show the validity of the theories.

Transient response of nonlinear polymer networks: A kinetic theory

Science.gov (United States)

Vernerey, Franck J.

2018-06-01

Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.

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

Nonlinear (super)symmetries and amplitudes

Energy Technology Data Exchange (ETDEWEB)

Kallosh, Renata [Physics Department, Stanford University,382 Via Pueblo Mall, Stanford, CA 94305-4060 (United States)

2017-03-07

There is an increasing interest in nonlinear supersymmetries in cosmological model building. Independently, elegant expressions for the all-tree amplitudes in models with nonlinear symmetries, like D3 brane Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the generalized background field method we show how, in general, nonlinear symmetries of the action, bosonic and fermionic, constrain amplitudes beyond soft limits. The same identities control, for example, bosonic E{sub 7(7)} scalar sector symmetries as well as the fermionic goldstino symmetries. We present a universal derivation of the vanishing amplitudes in the single (bosonic or fermionic) soft limit. We explain why, universally, the double-soft limit probes the coset space algebra. We also provide identities describing the multiple-soft limit. We discuss loop corrections to N≥5 supergravity, to the D3 brane, and the UV completion of constrained multiplets in string theory.

Nonlinear operators and their propagators

International Nuclear Information System (INIS)

Schwartz, C.

1997-01-01

Mathematical physicists are familiar with a large set of tools designed for dealing with linear operators, which are so common in both the classical and quantum theories; but many of those tools are useless with nonlinear equations of motion. In this work a general algebra and calculus is developed for working with nonlinear operators: The basic new tool being the open-quotes slash product,close quotes defined by A(1+εB) =A+εA/B+O(ε 2 ). For a generic time development equation, the propagator is constructed and then there follows the formal version of time dependent perturbation theory, in remarkable similarity to the linear situation. A nonperturbative approximation scheme capable of producing high accuracy computations, previously developed for linear operators, is shown to be applicable as well in the nonlinear domain. A number of auxiliary mathematical properties and examples are given. copyright 1997 American Institute of Physics

Theory of quasi-biennial and some other oscillations in meteorological parameters

International Nuclear Information System (INIS)

Njau, E.C.

1990-11-01

We show that quasi-biennial and several other oscillations in meteorological parameters are caused by ''foldover distortions'' in the physical processes represented by the formulations contained in our recent theory. The periods of all these oscillations extend from about 50 days up to over 200,000 years. Additional oscillations within and outside this periodicity range are correspondingly generated primarily as a result of non-linearities in the earth-atmosphere system. Our analysis agrees quite well with past observations as well as results of analyses on climatic records from different locations on the earth and can, therefore, be useful in attempts to make climatic predictions as briefly indicated in the text. (author). 15 refs, 4 figs, 2 tabs

Higher spin gauge theories in any dimension

International Nuclear Information System (INIS)

Vasiliev, M.A.

2004-01-01

Some general properties of higher spin (HS) gauge theories are summarized, with the emphasize on the nonlinear theories in any dimension. The main conclusion is that nonlinear HS theories exist in any dimension. Note that HS gauge symmetries in the nonlinear HS theory differ from the Yang-Mills gauging of the global HS symmetry of a free theory one starts with by HS field strength dependent nonlinear corrections resulting from the partial gauge fixing of spontaneously broken HS symmetries in the extended non-commutative space. The HS geometry is that of the fuzzy hyperboloid in the auxiliary (fiber) non-commutative space. Its radius depends on the Weyl 0-forms which take values in the infinitive-dimensional module dual to the space of single-particle states in the system

New Look at Nonlinear Aerodynamics in Analysis of Hypersonic Panel Flutter

Directory of Open Access Journals (Sweden)

Dan Xie

2017-01-01

Full Text Available A simply supported plate fluttering in hypersonic flow is investigated considering both the airflow and structural nonlinearities. Third-order piston theory is used for nonlinear aerodynamic loading, and von Karman plate theory is used for modeling the nonlinear strain-displacement relation. The Galerkin method is applied to project the partial differential governing equations (PDEs into a set of ordinary differential equations (ODEs in time, which is then solved by numerical integration method. In observation of limit cycle oscillations (LCO and evolution of dynamic behaviors, nonlinear aerodynamic loading produces a smaller positive deflection peak and more complex bifurcation diagrams compared with linear aerodynamics. Moreover, a LCO obtained with the linear aerodynamics is mostly a nonsimple harmonic motion but when the aerodynamic nonlinearity is considered more complex motions are obtained, which is important in the evaluation of fatigue life. The parameters of Mach number, dynamic pressure, and in-plane thermal stresses all affect the aerodynamic nonlinearity. For a specific Mach number, there is a critical dynamic pressure beyond which the aerodynamic nonlinearity has to be considered. For a higher temperature, a lower critical dynamic pressure is required. Each nonlinear aerodynamic term in the full third-order piston theory is evaluated, based on which the nonlinear aerodynamic formulation has been simplified.

A non-linear kinematic hardening function

International Nuclear Information System (INIS)

Ottosen, N.S.

1977-05-01

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

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

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

Science.gov (United States)

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

2010-01-01

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

Ward identities of W{sub {infinity}} symmetry and higher-genus amplitudes in 2D string theory

Energy Technology Data Exchange (ETDEWEB)

Hamada, K. [National Lab. for High Energy Physics, Ibaraki (Japan)

1996-03-04

The Ward identities of the W{sub {infinity}} symmetry in two-dimensional string theory in the tachyon background are studied in the continuum approach. We consider amplitudes different from 2D string ones by the external leg factor and derive the recursion relations among them. The recursion relations have non-linear terms which give relations among the amplitudes defined on different genus. The solutions agree with the matrix model results even in higher genus. We also discuss the differences of the roles of the external leg factor between the c{sub M} = 1 model and the c{sub M} <1 model. (orig.).

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

Feedforward Nonlinear Control Using Neural Gas Network

OpenAIRE

Machón-González, Iván; López-García, Hilario

2017-01-01

Nonlinear systems control is a main issue in control theory. Many developed applications suffer from a mathematical foundation not as general as the theory of linear systems. This paper proposes a control strategy of nonlinear systems with unknown dynamics by means of a set of local linear models obtained by a supervised neural gas network. The proposed approach takes advantage of the neural gas feature by which the algorithm yields a very robust clustering procedure. The direct model of the ...

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

Numerical simulation of the nonlinear dynamics of packets of spiral density waves

International Nuclear Information System (INIS)

Korchagin, V.I.

1987-01-01

In a numerical experiment, the behavior of nonlinear packets of spiral density waves in a gas disk has been investigated for different initial wave amplitudes. If the amplitude of the density perturbations is small (<5%), the wave packet is drawn toward the center or toward the periphery of the disk in accordance with the linear theory. The behavior of linear packets of waves with wavelength comparable to the disk radius (R/sub d//lambda = 4) exhibits good agreement with the conclusions of the linear theory of tightly wound spiral waves. The dynamics of wave packets with initial density amplitudes 16, 30, 50% demonstrates the nonlinear nature of the behavior. THe behavior is governed by whether or not the nonlinear effects of higher than third order in the wave amplitude play a part. If the wave packet dynamics is determined by the cubic nonlinearity, the results of the numerical experiment are in qualitative and quantitative agreement with the nonlinear theory of short waves, although the characteristic scale of the packet and the wavelength are of the order of the disk radius. In the cases when the nonlinear effects of higher orders in the amplitude play an important part, the behavior of a packet does not differ qualitatively from the behavior predicted by the theory of cubic nonlinearity, but the nonlinear spreading of the packet takes place more rapidly

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

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.

Anti-D3 branes and moduli in non-linear supergravity

Science.gov (United States)

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

2017-10-01

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

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

Directory of Open Access Journals (Sweden)

Weiwei Sun

2015-01-01

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

Theory of nonlinear, distortive phenomena in solids: Martensitic, crack, and multiscale structures-phenomenology and physics. Progress summary, 1991--1994

International Nuclear Information System (INIS)

Sethna, J.P.; Krumhansl, J.A.

1994-01-01

We have identified tweed precursors to martensitic phase transformations as a spin glass phase due to composition variations, and used simulations and exact replica theory predictions to predict diffraction peaks and model phase diagrams, and provide real space data for comparison to transmission electron micrograph images. We have used symmetry principles to derive the crack growth laws for mixed-mode brittle fracture, explaining the results for two-dimensional fracture and deriving the growth laws in three dimensions. We have used recent advances in dynamical critical phenomena to study hysteresis in disordered systems, explaining the return-point-memory effect, predicting distributions for Barkhausen noise, and elucidating the transition from athermal to burst behavior in martensites. From a nonlinear lattice-dynamical model of a first-order transition using simulations, finite-size scaling, and transfer matrix methods, it is shown that heterophase transformation precursors cannot occur in a pure homogeneous system, thus emphasizing the role of disorder in real materials. Full integration of nonlinear Landau-Ginzburg continuum theory with experimental neutron-scattering data and first-principles calculations has been carried out to compute semi-quantitative values of the energy and thickness of twin boundaries in InTl and FePd martensites

Non-linear dynamics of wind turbine wings

DEFF Research Database (Denmark)

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

2006-01-01

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

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

International Nuclear Information System (INIS)

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

2013-01-01

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

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

Science.gov (United States)

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

2014-02-01

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

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.

Nonlinear theory of localized standing waves

OpenAIRE

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

1992-01-01

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

Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation

Science.gov (United States)

Kandula, Max

2010-01-01

The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of Omega(Tau)(sub d), where Omega is the circular frequency, and Tau(sub d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction

Guideline appraisal with AGREE II: online survey of the potential influence of AGREE II items on overall assessment of guideline quality and recommendation for use.

Science.gov (United States)

Hoffmann-Eßer, Wiebke; Siering, Ulrich; Neugebauer, Edmund A M; Brockhaus, Anne Catharina; McGauran, Natalie; Eikermann, Michaela

2018-02-27

The AGREE II instrument is the most commonly used guideline appraisal tool. It includes 23 appraisal criteria (items) organized within six domains. AGREE II also includes two overall assessments (overall guideline quality, recommendation for use). Our aim was to investigate how strongly the 23 AGREE II items influence the two overall assessments. An online survey of authors of publications on guideline appraisals with AGREE II and guideline users from a German scientific network was conducted between 10th February 2015 and 30th March 2015. Participants were asked to rate the influence of the AGREE II items on a Likert scale (0 = no influence to 5 = very strong influence). The frequencies of responses and their dispersion were presented descriptively. Fifty-eight of the 376 persons contacted (15.4%) participated in the survey and the data of the 51 respondents with prior knowledge of AGREE II were analysed. Items 7-12 of Domain 3 (rigour of development) and both items of Domain 6 (editorial independence) had the strongest influence on the two overall assessments. In addition, Items 15-17 (clarity of presentation) had a strong influence on the recommendation for use. Great variations were shown for the other items. The main limitation of the survey is the low response rate. In guideline appraisals using AGREE II, items representing rigour of guideline development and editorial independence seem to have the strongest influence on the two overall assessments. In order to ensure a transparent approach to reaching the overall assessments, we suggest the inclusion of a recommendation in the AGREE II user manual on how to consider item and domain scores. For instance, the manual could include an a-priori weighting of those items and domains that should have the strongest influence on the two overall assessments. The relevance of these assessments within AGREE II could thereby be further specified.

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

Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

Science.gov (United States)

Hoefer, Mark A.

that the experimentally observed blast waves may be viewed as dispersive shock waves. A nonlinear mathematical model of spin-wave excitation using a point contact in a thin ferromagnetic film is introduced. This work incorporates a recently proposed spin-torque contribution to classical magnetodynamic theory with a variable coefficient terra in the magnetic torque equation. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the full nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm. Simulations also predict a saturation and red shift of the frequency at currents large enough to invert the magnetization tinder the point contact. In the weak nonlinear limit, the theory is approximated by a cubic complex Ginzburg-Landau type equation. The mode's nonlinear frequency shift is found by use of perturbation techniques, whose results agree with those of direct numerical simulations.

Non-linear realizations and bosonic branes

International Nuclear Information System (INIS)

West, P.

2001-01-01

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

Quasi-periodic solutions of nonlinear beam equations with quintic quasi-periodic nonlinearities

Directory of Open Access Journals (Sweden)

Qiuju Tuo

2015-01-01

Full Text Available In this article, we consider the one-dimensional nonlinear beam equations with quasi-periodic quintic nonlinearities $$ u_{tt}+u_{xxxx}+(B+ \\varepsilon\\phi(tu^5=0 $$ under periodic boundary conditions, where B is a positive constant, $\\varepsilon$ is a small positive parameter, $\\phi(t$ is a real analytic quasi-periodic function in t with frequency vector $\\omega=(\\omega_1,\\omega_2,\\dots,\\omega_m$. It is proved that the above equation admits many quasi-periodic solutions by KAM theory and partial Birkhoff normal form.

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

Science.gov (United States)

Nemeth, Michael P.

2014-01-01

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

c-Map for Born–Infeld theories

Directory of Open Access Journals (Sweden)

L. Andrianopoli

2016-07-01

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

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

Science.gov (United States)

Dore, Mohammed H I; Singh, Ragiv G

2009-10-01

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

Oscillations in nonlinear systems

CERN Document Server

Hale, Jack K

2015-01-01

By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

Science.gov (United States)

Bache, Morten; Lavrinenko, Andrei V.

2017-09-01

Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

KAUST Repository

Crosta, M

2012-09-12

By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.

The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

KAUST Repository

Crosta, M; Trillo, S; Fratalocchi, Andrea

2012-01-01

By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.

Single-Wire Electric-Field Coupling Power Transmission Using Nonlinear Parity-Time-Symmetric Model with Coupled-Mode Theory

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.

Exponential Growth of Nonlinear Ballooning Instability

International Nuclear Information System (INIS)

Zhu, P.; Hegna, C. C.; Sovinec, C. R.

2009-01-01

Recent ideal magnetohydrodynamic (MHD) theory predicts that a perturbation evolving from a linear ballooning instability will continue to grow exponentially in the intermediate nonlinear phase at the same linear growth rate. This prediction is confirmed in ideal MHD simulations. When the Lagrangian compression, a measure of the ballooning nonlinearity, becomes of the order of unity, the intermediate nonlinear phase is entered, during which the maximum plasma displacement amplitude as well as the total kinetic energy continues to grow exponentially at the rate of the corresponding linear phase.

The nonlinear gyroresonance interaction between energetic electrons and coherent VLF waves propagating at an arbitrary angle with respect to the earth's magnetic field

Science.gov (United States)

Bell, T. F.

1984-01-01

A theory is presented of the nonlinear gyroresonance interaction that takes place in the magnetosphere between energetic electrons and coherent VLF waves propagating in the whistler mode at an arbitrary angle psi with respect to the earth's magnetic field B-sub-0. Particularly examined is the phase trapping (PT) mechanism believed to be responsible for the generation of VLF emissions. It is concluded that near the magnetic equatorial plane gradients of psi may play a very important part in the PT process for nonducted waves. Predictions of a higher threshold value for PT for nonducted waves generally agree with experimental data concerning VLF emission triggering by nonducted waves.

Parametric autoresonant excitation of the nonlinear Schrödinger equation.

Science.gov (United States)

Friedland, L; Shagalov, A G

2016-10-01

Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the driving wave for entering the autoresonant regime. It is shown that above the threshold, a flat (spatially independent) NLS solution can be fully converted into a traveling wave. A simplified, few spatial harmonics expansion approach is also developed for studying this nonlinear mode conversion process, allowing interpretation as autoresonant interaction within triads of spatial harmonics.

Born-Infeld Nonlinear Electrodynamics

International Nuclear Information System (INIS)

Bialynicki-Birula, I.

1999-01-01

This is only a summary of a lecture delivered at the Infeld Centennial Meeting. In the lecture the history of the Born-Infeld nonlinear electrodynamics was presented and some general features of the theory were discussed. (author)

Wave transmission in nonlinear lattices

International Nuclear Information System (INIS)

Hennig, D.; Tsironis, G.P.

1999-01-01

The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Nonlinear electrodynamics and cosmology

International Nuclear Information System (INIS)

Breton, Nora

2010-01-01

Nonlinear electrodynamics (NLED) generalizes Maxwell's theory for strong fields. When coupled to general relativity NLED presents interesting features like the non-vanishing of the trace of the energy-momentum tensor that leads to the possibility of violation of some energy conditions and of acting as a repulsive contribution in the Raychaudhuri equation. This theory is worth to study in cosmological and astrophysical situations characterized by strong electromagnetic and gravitational fields.

Complex dynamics and morphogenesis an introduction to nonlinear science

CERN Document Server

Misbah, Chaouqi

2017-01-01

This book offers an introduction to the physics of nonlinear phenomena through two complementary approaches: bifurcation theory and catastrophe theory. Readers will be gradually introduced to the language and formalisms of nonlinear sciences, which constitute the framework to describe complex systems. The difficulty with complex systems is that their evolution cannot be fully predicted because of the interdependence and interactions between their different components. Starting with simple examples and working toward an increasing level of universalization, the work explores diverse scenarios of bifurcations and elementary catastrophes which characterize the qualitative behavior of nonlinear systems. The study of temporal evolution is undertaken using the equations that characterize stationary or oscillatory solutions, while spatial analysis introduces the fascinating problem of morphogenesis. Accessible to undergraduate university students in any discipline concerned with nonlinear phenomena (physics, mathema...

Nonlinear singular perturbation problems of arbitrary real orders

International Nuclear Information System (INIS)

Bijura, Angelina M.

2003-10-01

Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)

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

International Nuclear Information System (INIS)

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

2006-01-01

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

Nonlinear cyclotron absorption and stimulated scattering

International Nuclear Information System (INIS)

Chung, T.H.

1986-01-01

In electron cyclotron resonance heating (ECRH), wave sources heating a plasma linearly with respect to intensity; but as the intensity of ECRH gets larger, there might appear nonlinear effects that would result in cutoff of net absorption. This thesis uses quantum mechanical theory to derive a threshold microwave intensity for nonlinear absorption. The quantum mechanical theory estimates that the threshold microwave intensity for nonlinear absorption is about 10 5 watts/cm 2 for a microwave heating experiment (T/sub e/ = 100 ev, λ = 3,783 cm, B = 2.5 kG). This value seems large considering the present power capabilities of microwave sources (10 2 ∼ 10 3 watts/cm 2 ), but for a low temperature plasma, this threshold will go down. There is another nonlinear phenomenon called stimulated cyclotron scattering that enhances photon scattering by electrons gyrating in a magnetic field. This is expected to prevent incoming photons from arriving at the central region of the fusion plasma, where absorption mainly takes place. Theory based on a photon transport model predicts that the threshold intensity for the stimulated cyclotron scattering is about 10 4 watts/cm 2 for the plasma parameters mentioned above. This value seems large also, but a longer wavelength of microwaves and a larger magnitude magnetic field, which will be the case in reactor type facilities, will lower the threshold intensity to levels comparable with the currently developed microwave sources

Nonlinear transport of accelerator beam phase space

International Nuclear Information System (INIS)

Xie Xi; Xia Jiawen

1995-01-01

Based on the any order analytical solution of accelerator beam dynamics, the general theory for nonlinear transport of accelerator beam phase space is developed by inverse transformation method. The method is general by itself, and hence can also be applied to the nonlinear transport of various dynamic systems in physics, chemistry and biology

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

Science.gov (United States)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

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...

A Survey of Nonlinear Dynamics (Chaos Theory)

Science.gov (United States)

1991-04-01

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

Vibrational mechanics nonlinear dynamic effects, general approach, applications

CERN Document Server

Blekhman, Iliya I

2000-01-01

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat

Lattice cluster theory for dense, thin polymer films.

Science.gov (United States)

Freed, Karl F

2015-04-07

While the application of the lattice cluster theory (LCT) to study the miscibility of polymer blends has greatly expanded our understanding of the monomer scale molecular details influencing miscibility, the corresponding theory for inhomogeneous systems has not yet emerged because of considerable technical difficulties and much greater complexity. Here, we present a general formulation enabling the extension of the LCT to describe the thermodynamic properties of dense, thin polymer films using a high dimension, high temperature expansion. Whereas the leading order of the LCT for bulk polymer systems is essentially simple Flory-Huggins theory, the highly non-trivial leading order inhomogeneous LCT (ILCT) for a film with L layers already involves the numerical solution of 3(L - 1) coupled, highly nonlinear equations for the various density profiles in the film. The new theory incorporates the essential "transport" constraints of Helfand and focuses on the strict imposition of excluded volume constraints, appropriate to dense polymer systems, rather than the maintenance of chain connectivity as appropriate for lower densities and as implemented in self-consistent theories of polymer adsorption at interfaces. The ILCT is illustrated by presenting examples of the computed profiles of the density, the parallel and perpendicular bonds, and the chain ends for free standing and supported films as a function of average film density, chain length, temperature, interaction with support, and chain stiffness. The results generally agree with expected general trends.

Lattice cluster theory for dense, thin polymer films

International Nuclear Information System (INIS)

Freed, Karl F.

2015-01-01

While the application of the lattice cluster theory (LCT) to study the miscibility of polymer blends has greatly expanded our understanding of the monomer scale molecular details influencing miscibility, the corresponding theory for inhomogeneous systems has not yet emerged because of considerable technical difficulties and much greater complexity. Here, we present a general formulation enabling the extension of the LCT to describe the thermodynamic properties of dense, thin polymer films using a high dimension, high temperature expansion. Whereas the leading order of the LCT for bulk polymer systems is essentially simple Flory-Huggins theory, the highly non-trivial leading order inhomogeneous LCT (ILCT) for a film with L layers already involves the numerical solution of 3(L − 1) coupled, highly nonlinear equations for the various density profiles in the film. The new theory incorporates the essential “transport” constraints of Helfand and focuses on the strict imposition of excluded volume constraints, appropriate to dense polymer systems, rather than the maintenance of chain connectivity as appropriate for lower densities and as implemented in self-consistent theories of polymer adsorption at interfaces. The ILCT is illustrated by presenting examples of the computed profiles of the density, the parallel and perpendicular bonds, and the chain ends for free standing and supported films as a function of average film density, chain length, temperature, interaction with support, and chain stiffness. The results generally agree with expected general trends

Nonlinear Dynamics of a Helicopter Model in Ground Resonance

Science.gov (United States)

Tang, D. M.; Dowell, E. H.

1985-01-01

An approximate theoretical method is presented which determined the limit cycle behavior of a helicopter model which has one or two nonlinear dampers. The relationship during unstable ground resonance oscillations between lagging motion of the blades and fuselage motion is discussed. An experiment was carried out on using a helicopter scale model. The experimental results agree with those of the theoretical analysis.

Modeling of nonlinear responses for reciprocal transducers involving polarization switching

DEFF Research Database (Denmark)

Willatzen, Morten; Wang, Linxiang

2007-01-01

Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...... intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling...

Three-dimensional analysis of nonlinear plasma oscillation

International Nuclear Information System (INIS)

Miano, G.

1990-01-01

In an underdense plasma a large-amplitude plasma oscillation may be produced by the beating of two external and colinear electromagnetic waves with a frequency difference approximately equal to the plasma frequency - plasma beat wave (PBW) resonant mechanism. The plasma oscillations are driven by the ponderomotive force arising from the beating of the two imposed electromagnetic waves. In this paper two pump electromagnetic waves with arbitrary transverse profiles have been considered. The plasma is described by using the three dimensinal weakly relativistic fluid equations. The nonlinear plasma oscillation dynamics is studied by using the eulerian description, the averaging and the multiple time scale methods. Unlike the linear theory a strong cross field coupling between longitudinal ans transverse electric field components of the plasma oscillation comes out, resulting in a nonlinear phase change and energy transfer between the two components. Unlike the one-dimensional nonlinear theory, the nonlinear frequency shift is caused by relativistic effects as well as by convective effects and electromagnetic field generated from the three dimensional plasma oscillation. The large amplitude plasma oscillation dynamics produced by a bunched relativistic electron beam with arbitrary transverse profile - plasma wave field (PWF) - or by a high power single frequency short electromagnetic pulse with arbitrary transverse profile - electromagnetic plasma wake field (EPWF) - may be described by means of the present theory. (orig.)

Feedforward Nonlinear Control Using Neural Gas Network

Directory of Open Access Journals (Sweden)

Iván Machón-González

2017-01-01

Full Text Available Nonlinear systems control is a main issue in control theory. Many developed applications suffer from a mathematical foundation not as general as the theory of linear systems. This paper proposes a control strategy of nonlinear systems with unknown dynamics by means of a set of local linear models obtained by a supervised neural gas network. The proposed approach takes advantage of the neural gas feature by which the algorithm yields a very robust clustering procedure. The direct model of the plant constitutes a piece-wise linear approximation of the nonlinear system and each neuron represents a local linear model for which a linear controller is designed. The neural gas model works as an observer and a controller at the same time. A state feedback control is implemented by estimation of the state variables based on the local transfer function that was provided by the local linear model. The gradient vectors obtained by the supervised neural gas algorithm provide a robust procedure for feedforward nonlinear control, that is, supposing the inexistence of disturbances.

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

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 realization of general covariance group

International Nuclear Information System (INIS)

Hamamoto, Shinji

1979-01-01

The structure of the theory resulting from the nonlinear realization of general covariance group is analysed. We discuss the general form of free Lagrangian for Goldstone fields, and propose as a special choice one reasonable form which is shown to describe a gravitational theory with massless tensor graviton and massive vector tordion. (author)

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

International Nuclear Information System (INIS)

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

2005-01-01

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

Two-Fluid and Resistive Nonlinear Simulations of Tokamak Equilibrium, Stability, and Reconnection

International Nuclear Information System (INIS)

Jardin, S.; Sovinec, C.; Breslau, J.; Ferraro, N.; Hudson, S.; King, J.; Kruger, S.; Ramos, J.; Schnack, D.

2008-01-01

The NIMROD and M3D/M3D-C1 codes now each have both a resistive MHD and a two-fluid (2F) capability including gyroviscosity and Hall terms. We describe: (1) a nonlinear 3D verification test in the resistive MHD regime in which the two codes are in detailed agreement, (2) new studies that illuminate the effect of two-fluid physics on spontaneous rotation in tokamaks, (3) studies of nonlinear reconnection in regimes of relevance to fusion plasmas with peak nonlinear reconnection rates that are essentially independent of the resistivity, and (4) linear two-fluid tearing mode calculations including electron mass that agree with analytic studies over a wide range of parameter regimes

C-map for Born-Infeld theories

CERN Document Server

Andrianopoli, Laura; Ferrara, Sergio; Trigiante, Mario

2016-01-01

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

Some relations of parameters in quantum field theory

International Nuclear Information System (INIS)

Ishikawa, K.

1986-01-01

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

Foundations of the non-linear mechanics of continua

CERN Document Server

Sedov, L I

1966-01-01

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

Is there a relativistic nonlinear generalization of quantum mechanics?

Energy Technology Data Exchange (ETDEWEB)

Elze, Hans-Thomas [Dipartimento di Fisica ' Enrico Fermi' , Largo Pontecorvo 3, I-56127 Pisa (Italy)

2007-05-15

Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of a U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.

Untangling the drivers of nonlinear systems with information theory

Science.gov (United States)

Wing, S.; Johnson, J.

2017-12-01

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

Third Conference on nonlinear science and complexity (NSC)

CERN Document Server

Machado, José; Baleanu, Dumitru; Dynamical Systems and Methods

2012-01-01

Nonlinear Systems and Methods For Mechanical, Electrical and Biosystems presents topics observed at the 3rd Conference on Nonlinear Science and Complexity(NSC), focusing on energy transfer and synchronization in hybrid nonlinear systems. The studies focus on fundamental theories and principles,analytical and symbolic approaches, computational techniques in nonlinear physical science and mathematics. Broken into three parts, the text covers:\\ Parametrical excited pendulum, nonlinear dynamics in hybrid systems, dynamical system synchronization and (N+1) body dynamics as well as new views different from the existing results in nonlinear dynamics. Mathematical methods for dynamical systems including conservation laws, dynamical symmetry in nonlinear differential equations and invex energies. Nonlinear phenomena in physical problems such as solutions, complex flows, chemical kinetics, Toda lattices and parallel manipulator. This book is useful to scholars, researchers and advanced technical members of industrial l...

Nonlinear programming analysis and methods

CERN Document Server

Avriel, Mordecai

2012-01-01

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

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

Science.gov (United States)

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

1998-01-01

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

A study of anharmonic al and nonlinear behaviours of vibrations of atomic nuclei

International Nuclear Information System (INIS)

Volpe, M.C.

1997-01-01

Double Giant Resonances, vibrational states in which a Giant Resonance is excited on top of another Giant Resonance, have been in the last years the object of many theories and studies. Whereas the measured energies and widths of these states agree with a theoretical predictions, the measured excitation cross sections on the other hand are almost always larger than the calculated ones. The standard theoretical approaches are based both on a harmonic approximation for the collective motion on the nucleus and on its linear response to an external field. In this work the influence of anharmonicities and non-linearities in the external field on the excitation of Double Giant Resonances are studied. First, an oscillator model and an extension of the Lipkin-Meshkow-Glick model are used to study the effects of anharmonicities and non-linearities on the excitation probabilities. The results show that these terms can influence the excitation probability of the second excited state in a significant way. Secondly, these exactly soluble schematic models are used to study some of the approximations made in microscopic calculations based on boson expansion methods and also some aspects on the time-dependent mean field approach. Finally, a microscopic calculation of the Coulomb excitation cross sections of Double Giant Resonances is presented for several nuclei. It is found that, for 208 Pb, the inclusion of anharmonicities and non-linearities and the consideration of many states that play a role in the excitation process give a satisfactory agreement between calculated and observed cross sections. (author)

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)

Exact travelling wave solutions for some important nonlinear

Indian Academy of Sciences (India)

The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...

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

Receptor theory and biological constraints on value.

Science.gov (United States)

Berns, Gregory S; Capra, C Monica; Noussair, Charles

2007-05-01

Modern economic theories of value derive from expected utility theory. Behavioral evidence points strongly toward departures from linear value weighting, which has given rise to alternative formulations that include prospect theory and rank-dependent utility theory. Many of the nonlinear forms for value assumed by these theories can be derived from the assumption that value is signaled by neurotransmitters in the brain, which obey simple laws of molecular movement. From the laws of mass action and receptor occupancy, we show how behaviorally observed forms of nonlinear value functions can arise.

A finite element model for nonlinear shells of revolution

International Nuclear Information System (INIS)

Cook, W.A.

1979-01-01

A shell-of-revolution model was developed to analyze impact problems associated with the safety analysis of nuclear material shipping containers. The nonlinear shell theory presented by Eric Reissner in 1972 was used to develop our model. Reissner's approach includes transverse shear deformation and moments turning about the middle surface normal. With these features, this approach is valid for both thin and thick shells. His theory is formulated in terms of strain and stress resultants that refer to the undeformed geometry. This nonlinear shell model is developed using the virtual work principle associated with Reissner's equilibrium equations. First, the virtual work principle is modified for incremental loading; then it is linearized by assuming that the nonlinear portions of the strains are known. By iteration, equilibrium is then approximated for each increment. A benefit of this approach is that this iteration process makes it possible to use nonlinear material properties. (orig.)

Nonlinear quantum gravity on the constant mean curvature foliation

International Nuclear Information System (INIS)

Wang, Charles H-T

2005-01-01

A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analysed as nonlinear quantum minisuperspaces in the context of the proposed theory

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

Science.gov (United States)

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

Dynamic behaviors for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a non-Kerr medium

Science.gov (United States)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Liu, De-Yin

2017-04-01

Effects of quantic nonlinearity on the propagation of the ultrashort optical pulses in a non-Kerr medium, like an optical fiber, can be described by a perturbed nonlinear Schrödinger equation with the power law nonlinearity, which is studied in this paper from a planar-dynamic-system view point. We obtain the equivalent two-dimensional planar dynamic system of such an equation, for which, according to the bifurcation theory and qualitative theory, phase portraits are given. Through the analysis of those phase portraits, we present the relations among the Hamiltonian, orbits of the dynamic system and types of the analytic solutions. Analytic expressions of the periodic-wave solutions, kink- and bell-shaped solitary-wave solutions are derived, and we find that the periodic-wave solutions can be reduced to the kink- and bell-shaped solitary-wave solutions.

Linear and nonlinear symmetrically loaded shells of revolution approximated with the finite element method

International Nuclear Information System (INIS)

Cook, W.A.

1978-10-01

Nuclear Material shipping containers have shells of revolution as a basic structural component. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Present models are limited to large displacements, small rotations, and nonlinear materials. This report discusses a first approach to developing a finite element nonlinear shell of revolution model that accounts for these nonlinear geometric effects. The approach uses incremental loads and a linear shell model with equilibrium iterations. Sixteen linear models are developed, eight using the potential energy variational principle and eight using a mixed variational principle. Four of these are suitable for extension to nonlinear shell theory. A nonlinear shell theory is derived, and a computational technique used in its solution is presented

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

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

Science.gov (United States)

Sasaki, Misao; Wands, David

2010-06-01

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

Parallel processors and nonlinear structural dynamics algorithms and software

Science.gov (United States)

Belytschko, Ted

1989-01-01

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Nonlinear analysis of flexible plates lying on elastic foundation

Directory of Open Access Journals (Sweden)

Trushin Sergey

2017-01-01

Full Text Available This article describes numerical procedures for analysis of flexible rectangular plates lying on elastic foundation. Computing models are based on the theory of plates with account of transverse shear deformations. The finite difference energy method of discretization is used for reducing the initial continuum problem to finite dimensional problem. Solution procedures for nonlinear problem are based on Newton-Raphson method. This theory of plates and numerical methods have been used for investigation of nonlinear behavior of flexible plates on elastic foundation with different properties.

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

A new approach to nonlinear constrained Tikhonov regularization

KAUST Repository

Ito, Kazufumi

2011-09-16

We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented. © 2011 IOP Publishing Ltd.

Nonlinear electrostatic solitary waves in electron-positron plasmas

Science.gov (United States)

Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.

2016-02-01

The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.

Nonlinear Control of Heartbeat Models

Directory of Open Access Journals (Sweden)

Witt Thanom

2011-02-01

Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.

Determining the magnetically nonlinear characteristics of a three phase core-type power transformer

International Nuclear Information System (INIS)

Dolinar, Matjaz; Stumberger, Gorazd; Polajzer, Bostjan; Dolinar, Drago

2006-01-01

This paper presents nonlinear iron core model of a three-phase, three-limb power transformer which is given by the current-dependant characteristics of flux linkages. The magnetically nonlinear characteristics are determined by controlled magnetic excitation of all three limbs which allows to take into account the variable magnetic-cross couplings between different coils placed on limbs, caused by saturation. The corresponding partial derivatives of measured flux linkage characteristics are used in the transformer circuit model as a magnetically nonlinear iron core model in order to analyze the behaviour of a nonsymmetrically excited transformer. Numerical results using transformer model with the determined iron core model agree very well with the measured results

Weakly nonlinear dispersion and stop-band effects for periodic structures

DEFF Research Database (Denmark)

Sorokin, Vladislav; Thomsen, Jon Juel

of frequency band-gaps, i.e. frequency ranges in which elastic waves cannot propagate. Most existing analytical methods in the field are based on Floquet theory [1]; e.g. this holds for the classical Hill’s method of infinite determinants [1,2], and themethod of space-harmonics [3]. However, application...... of these methods for studying nonlinear problems isimpossible or cumbersome, since Floquet theory is applicable only for linear systems. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applications may demand effects of nonlinearity on structural response...... to be accounted for.The paper deals with analytically predicting dynamic response for nonlinear elastic structures with a continuous periodic variation in structural properties. Specifically, for a Bernoulli-Euler beam with aspatially continuous modulation of structural properties in the axial direction...

Nonlinear dynamics aspects of modern storage rings

International Nuclear Information System (INIS)

Helleman, R.H.G.; Kheifets, S.A.

1986-01-01

It is argued that the nonlinearity of storage rings becomes an essential problem as the design parameters of each new machine are pushed further and further. Yet the familiar methods of classical mechanics do not allow determination of single particle orbits over reasonable lengths of time. It is also argued that the single particle dynamics of a storage ring is possibly one of the cleanest and simplest nonlinear dynamical systems available with very few degrees of freedom. Hence, reasons are found for accelerator physicists to be interested in nonlinear dynamics and for researchers in nonlinear dynamics to be interested in modern storage rings. The more familiar methods of treating nonlinear systems routinely used in acclerator theory are discussed, pointing out some of their limitations and pitfalls. 39 refs., 1 fig

E11 and the non-linear dual graviton

Science.gov (United States)

Tumanov, Alexander G.; West, Peter

2018-04-01

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

Verification and Validation of Heat Transfer Model of AGREE Code

Energy Technology Data Exchange (ETDEWEB)

Tak, N. I. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Seker, V.; Drzewiecki, T. J.; Downar, T. J. [Department of Nuclear Engineering and Radiological Sciences, Univ. of Michigan, Michigan (United States); Kelly, J. M. [US Nuclear Regulatory Commission, Washington (United States)

2013-05-15

The AGREE code was originally developed as a multi physics simulation code to perform design and safety analysis of Pebble Bed Reactors (PBR). Currently, additional capability for the analysis of Prismatic Modular Reactor (PMR) core is in progress. Newly implemented fluid model for a PMR core is based on a subchannel approach which has been widely used in the analyses of light water reactor (LWR) cores. A hexagonal fuel (or graphite block) is discretized into triangular prism nodes having effective conductivities. Then, a meso-scale heat transfer model is applied to the unit cell geometry of a prismatic fuel block. Both unit cell geometries of multi-hole and pin-in-hole types of prismatic fuel blocks are considered in AGREE. The main objective of this work is to verify and validate the heat transfer model newly implemented for a PMR core in the AGREE code. The measured data in the HENDEL experiment were used for the validation of the heat transfer model for a pin-in-hole fuel block. However, the HENDEL tests were limited to only steady-state conditions of pin-in-hole fuel blocks. There exist no available experimental data regarding a heat transfer in multi-hole fuel blocks. Therefore, numerical benchmarks using conceptual problems are considered to verify the heat transfer model of AGREE for multi-hole fuel blocks as well as transient conditions. The CORONA and GAMMA+ codes were used to compare the numerical results. In this work, the verification and validation study were performed for the heat transfer model of the AGREE code using the HENDEL experiment and the numerical benchmarks of selected conceptual problems. The results of the present work show that the heat transfer model of AGREE is accurate and reliable for prismatic fuel blocks. Further validation of AGREE is in progress for a whole reactor problem using the HTTR safety test data such as control rod withdrawal tests and loss-of-forced convection tests.

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

Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.

Science.gov (United States)

Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang

2017-06-12

Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.

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

Science.gov (United States)

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

2017-02-01

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

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.

Linear and nonlinear verification of gyrokinetic microstability codes

Science.gov (United States)

Bravenec, R. V.; Candy, J.; Barnes, M.; Holland, C.

2011-12-01

Verification of nonlinear microstability codes is a necessary step before comparisons or predictions of turbulent transport in toroidal devices can be justified. By verification we mean demonstrating that a code correctly solves the mathematical model upon which it is based. Some degree of verification can be accomplished indirectly from analytical instability threshold conditions, nonlinear saturation estimates, etc., for relatively simple plasmas. However, verification for experimentally relevant plasma conditions and physics is beyond the realm of analytical treatment and must rely on code-to-code comparisons, i.e., benchmarking. The premise is that the codes are verified for a given problem or set of parameters if they all agree within a specified tolerance. True verification requires comparisons for a number of plasma conditions, e.g., different devices, discharges, times, and radii. Running the codes and keeping track of linear and nonlinear inputs and results for all conditions could be prohibitive unless there was some degree of automation. We have written software to do just this and have formulated a metric for assessing agreement of nonlinear simulations. We present comparisons, both linear and nonlinear, between the gyrokinetic codes GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and GS2 [W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. We do so at the mid-radius for the same discharge as in earlier work [C. Holland, A. E. White, G. R. McKee, M. W. Shafer, J. Candy, R. E. Waltz, L. Schmitz, and G. R. Tynan, Phys. Plasmas 16, 052301 (2009)]. The comparisons include electromagnetic fluctuations, passing and trapped electrons, plasma shaping, one kinetic impurity, and finite Debye-length effects. Results neglecting and including electron collisions (Lorentz model) are presented. We find that the linear frequencies with or without collisions agree well between codes, as do the time averages of

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

DEFF Research Database (Denmark)

Bozonnet, Pauline; Dupin, Victor; Tona, Paolino

2017-01-01

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

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.

Performance emulation and parameter estimation for nonlinear fibre-optic links

DEFF Research Database (Denmark)

Piels, Molly; Porto da Silva, Edson; Zibar, Darko

2016-01-01

Fibre-optic communication systems, especially when operating in the nonlinear regime, generally do not perform exactly as theory would predict. A number of methods for data-based evaluation of nonlinear fibre-optic link parameters, both for accurate performance emulation and optimization...

Perturbation theory

International Nuclear Information System (INIS)

Bartlett, R.; Kirtman, B.; Davidson, E.R.

1978-01-01

After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references

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

Introduction to the theory of nonlinear optimization

CERN Document Server

Jahn, Johannes

2007-01-01

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

An introduction to chaos theory in CFD

Science.gov (United States)

Pulliam, Thomas H.

1990-01-01

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

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

Solitons and theory of representations

International Nuclear Information System (INIS)

Kulish, P.P.

1985-01-01

Problems on the theory of group representations finding application in constructing the quantum variant of the inverse scattering problem are discussed. The multicomponent nonlinear Shroedinger equation is considered as a main example of nonlinear evolution equations (NEE)

Finite elements of nonlinear continua

CERN Document Server

Oden, John Tinsley

1972-01-01

Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s

Nonlinear PDEs a dynamical systems approach

CERN Document Server

Schneider, Guido

2017-01-01

This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced...

Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint

CERN Document Server

Martínez-Guerra, Rafael

2017-01-01

This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

Nonlinear surface impedance of YBCO thin films: Measurements, modeling, and effects in devices

International Nuclear Information System (INIS)

Oates, D.E.; Koren, G.; Polturak, E.

1995-01-01

High-T c thin films continue to be of interest for passive device applications at microwave frequencies, but nonlinear effects may limit the performance. To understand these effects we have measured the nonlinear effects may limit the performance. To understand these effects we have measured the nonlinear surface impedance Z s in a number of YBa 2 Cu 3 O 7-x thin films as a function of frequency from 1 to 18 GHz, rf surface magnetic field H rf to 1500 Oe, and temperature from 4 K to T c . The results at low H rf are shown to agree quantitatively with a modified coupled-grain model and at high H rf with hysteresis-loss calculations using the Bean critical-state model applied to a thin strip. The loss mechanisms are extrinsic properties resulting from defects in the films. We also report preliminary measurements of the nonlinear impedance of Josephson junctions, and the results are related to the models of nonlinear Z s . The implications of nonlinear Z s for devices are discussed using the example of a five-pole bandpass filter

Advance elements of optoisolation circuits nonlinearity applications in engineering

CERN Document Server

Aluf, Ofer

2017-01-01

This book on advanced optoisolation circuits for nonlinearity applications in engineering addresses two separate engineering and scientific areas, and presents advanced analysis methods for optoisolation circuits that cover a broad range of engineering applications. The book analyzes optoisolation circuits as linear and nonlinear dynamical systems and their limit cycles, bifurcation, and limit cycle stability by using Floquet theory. Further, it discusses a broad range of bifurcations related to optoisolation systems: cusp-catastrophe, Bautin bifurcation, Andronov-Hopf bifurcation, Bogdanov-Takens (BT) bifurcation, fold Hopf bifurcation, Hopf-Hopf bifurcation, Torus bifurcation (Neimark-Sacker bifurcation), and Saddle-loop or Homoclinic bifurcation. Floquet theory helps as to analyze advance optoisolation systems. Floquet theory is the study of the stability of linear periodic systems in continuous time. Another way to describe Floquet theory, it is the study of linear systems of differential equations with p...

M theory on deformed superspace

Science.gov (United States)

Faizal, Mir

2011-11-01

In this paper we will analyze a noncommutative deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in N=1 superspace formalism. We will then analyze the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries for this deformed ABJM theory, and its linear as well as nonlinear gauges. We will show that the sum of the gauge fixing term and the ghost term for this deformed ABJM theory can be expressed as a combination of the total BRST and the total anti-BRST variation, in Landau and nonlinear gauges. We will show that in Landau and Curci-Ferrari gauges deformed ABJM theory is invariant under an additional set of symmetry transformations. We will also discuss the effect that the addition of a bare mass term has on this theory.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

Science.gov (United States)

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Discrete-time inverse optimal control for nonlinear systems

CERN Document Server

Sanchez, Edgar N

2013-01-01

Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

Halo Mitigation Using Nonlinear Lattices

CERN Document Server

Sonnad, Kiran G

2005-01-01

This work shows that halos in beams with space charge effects can be controlled by combining nonlinear focusing and collimation. The study relies on Particle-in-Cell (PIC) simulations for a one dimensional, continuous focusing model. The PIC simulation results show that nonlinear focusing leads to damping of the beam oscillations thereby reducing the mismatch. It is well established that reduced mismatch leads to reduced halo formation. However, the nonlinear damping is accompanied by emittance growth causing the beam to spread in phase space. As a result, inducing nonlinear damping alone cannot help mitigate the halo. To compensate for this expansion in phase space, the beam is collimated in the simulation and further evolution of the beam shows that the halo is not regenerated. The focusing model used in the PIC is analysed using the Lie Transform perturbation theory showing that by averaging over a lattice period, one can reuduce the focusing force to a form that is identical to that used in the PIC simula...

Non-gaussianity versus nonlinearity of cosmological perturbations.

Science.gov (United States)

Verde, L

2001-06-01

Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

Bound-Electron Nonlinearity Beyond the Ionization Threshold

Science.gov (United States)

Wahlstrand, J. K.; Zahedpour, S.; Bahl, A.; Kolesik, M.; Milchberg, H. M.

2018-05-01

We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

Nonlinear systems techniques for dynamical analysis and control

CERN Document Server

Lefeber, Erjen; Arteaga, Ines

2017-01-01

This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participan...

Spin and diamagnetism in linear and nonlinear optics

International Nuclear Information System (INIS)

Andersen, Torsten; Keller, Ole; Huebner, Wolfgang; Johansson, Boerje

2004-01-01

We present a local-field theory for spin and diamagnetism in linear and nonlinear optics. We examine all the processes contained in the Pauli Hamiltonian and its corresponding microscopic current density, including the terms depending on the electron spin. The resulting general real-space conductivities are presented and discussed. To quantify the implications of including the spin, we study the linear and nonlinear optical properties of free-electron metals, represented by the screened homogeneous electron gas. The real-space formalism is transformed into Fourier space, and the symmetries of the linear and nonlinear optical conductivities in a homogeneous electron gas are discussed. Numerical results are presented for the homogeneous electron gas, in which we treat ω and q as independent variables, thereby opening the theory to near-field optics and the study of evanescent waves. We show that in regions of the ω-q spectrum, the presence of diamagnetism and spin dynamics significantly alters the response in comparison to considering only the paramagnetic response. Additionally, we discuss the effects of screening, and we finish our treatment by a discussion of how to connect the present theory to existing methods in ab initio solid-state physics

Mathematical control theory

International Nuclear Information System (INIS)

Agrachev, A.A.

2002-01-01

This volume is based on the lecture notes of the minicourses given in the frame of the school on Mathematical Control Theory held at the Abdus Salam ICTP from 3 to 28 September 2001. Mathematical Control Theory is a rapidly growing field which provides strict theoretical and computational tools for dealing with problems arising in electrical and aerospace engineering, automatics, robotics, applied chemistry, and biology etc. Control methods are also involved in questions pertaining to the development of countries in the South, such as wastewater treatment, agronomy, epidemiology, population dynamics, control of industrial and natural bio-reactors. Since most of these natural processes are highly nonlinear, the tools of nonlinear control are essential for the modelling and control of such processes. At present regular courses in Mathematical Control Theory are rarely included in the curricula of universities, and very few researchers receive enough background in the field. Therefore it is important to organize specific activities in the form of schools to provide the necessary background for those embarking on research in this field. The school at the Abdus Salam ICTP consisted of several minicourses intended to provide an introduction to various topics of Mathematical Control Theory, including Linear Control Theory (finite and infinite-dimensional), Nonlinear Control, and Optimal Control. The last week of the school was concentrated on applications of Mathematical Control Theory, in particular, those which are important for the development of non-industrialized countries. The school was intended primarily for mathematicians and mathematically oriented engineers at the beginning of their career. The typical participant was expected to be a graduate student or young post-doctoral researcher interested in Mathematical Control Theory. It was assumed that participants have sufficient background in Ordinary Differential Equations and Advanced Calculus. The volume

Mathematical control theory

Energy Technology Data Exchange (ETDEWEB)

Agrachev, A A [Steklov Mathematical Institute, Moscow (Russian Federation); SISSA, Trieste [Italy; ed.

2002-07-15

This volume is based on the lecture notes of the minicourses given in the frame of the school on Mathematical Control Theory held at the Abdus Salam ICTP from 3 to 28 September 2001. Mathematical Control Theory is a rapidly growing field which provides strict theoretical and computational tools for dealing with problems arising in electrical and aerospace engineering, automatics, tics, applied chemistry, and biology etc. Control methods are also involved in questions pertaining to the development of countries in the South, such as wastewater treatment, agronomy, epidemiology, population dynamics, control of industrial and natural bio-reactors. Since most of these natural processes are highly nonlinear, the tools of nonlinear control are essential for the modelling and control of such processes. At present regular courses in Mathematical Control Theory are rarely included in the curricula of universities, and very few researchers receive enough background in the field. Therefore it is important to organize specific activities in the form of schools to provide the necessary background for those embarking on research in this field. The school at the Abdus Salam ICTP consisted of several minicourses intended to provide an introduction to various topics of Mathematical Control Theory, including Linear Control Theory (finite and infinite-dimensional), Nonlinear Control, and Optimal Control. The last week of the school was concentrated on applications of Mathematical Control Theory, in particular, those which are important for the development of non-industrialized countries. The school was intended primarily for mathematicians and mathematically oriented engineers at the beginning of their career. The typical participant was expected to be a graduate student or young post-doctoral researcher interested in Mathematical Control Theory. It was assumed that participants have sufficient background in Ordinary Differential Equations and Advanced Calculus. The volume contains

Importance theory for lumped-parameter systems

International Nuclear Information System (INIS)

Cady, K.B.; Kenton, M.A.; Ward, J.C.; Piepho, M.G.

1981-01-01

A general sensitivity theory has been developed for nonlinear lumped parameter system simulations. The point of departure is general perturbation theory for nonlinear systems. Importance theory as developed here allows the calculation of the sensitivity of a response function to any physical or design parameter; importance of any equation or term or physical effect in the system model on the response function; variance of the response function caused by the variances and covariances of all physical parameters; and approximate effect on the response function of missing physical phenomena or incorrect parameters

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.

Nonlinear dynamics in psychology

Directory of Open Access Journals (Sweden)

Stephen J. Guastello

2001-01-01

Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.

Canonical action-angle formalism for quantized nonlinear fields

International Nuclear Information System (INIS)

Garbaczewki, P.

1987-01-01

The canonical quantizations of field and action-angle coordinates which (locally) parameterize the phase manifold for the same nonlinear field theory model (e.g. sine-Gordon and nonlinear Schrodinger with the attractive coupling) are reconciled on the common for both cases state space. The classical-quantum relationship is maintained in the mean: coherent state expectation values of operators give rise to classical objects

Symmetries and discretizations of the O(3) nonlinear sigma model

Energy Technology Data Exchange (ETDEWEB)

Flore, Raphael [TPI, Universitaet Jena (Germany)

2011-07-01

Nonlinear sigma models possess many interesting properties like asymptotic freedom, confinement or dynamical mass generation, and hence serve as toy models for QCD and other theories. We derive a formulation of the N=2 supersymmetric extension of the O(3) nonlinear sigma model in terms of constrained field variables. Starting from this formulation, it is discussed how the model can be discretized in a way that maintains as many symmetries of the theory as possible. Finally, recent numerical results related to these discretizations are presented.

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

Science.gov (United States)

Pikichyan, H. V.

2017-07-01

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

Nonlinear Cyclotron absorption of a hole doppleron in cadmium

Energy Technology Data Exchange (ETDEWEB)

Voloshin, I.F.; Bugal' ter, G.A.; Demikhovskii, V.Y.; Fisher, L.M.; Yudin, V.A.

1977-10-01

We investigated experimentally the nonlinear behavior of the impedance of a cadmium plate in the region of existence of the hole doppleron. It is shown theoretically that this phenomenon can be attributed to nonlinear cyclotron absorption of the wave in the metal. A theory of nonlinear cyclotron absorption of a hole doppleron in cadmium is constructed. The nonlinearity is due to the influence of the wave magnetic field H that alters the trajectories of the resonant electrons responsible for the cyclotron asorption. The Lorentz force connected with the field H modulates the particle velocity along the magnetic field at a characteristic frequency ..omega../sub 0/ proportional to the square root of the wave amplitude. The modulation of the longitudinal particle velocity leads to violation of the condition of their resonant interaction with the wave, as a result of which the absorption coefficient decreases. The nonlinearity is significant when the frequency ..omega../sub 0/ is large compared with the electron-collision frequency. A decrease of the cyclotron absorption changes radically the picture of the surface-impedance oscillations of the plate in the magnetic field. We studied in the experiment the influence of the temperature, of the angle of inclination of the magnetic field, and of the frequency on the nonlinear-effect threshold field that separates the regions of linear and nonlinear behavior of the sample impedance. The measurement results are in qualitative agreement with the conclusions of the theory.

Outline of a nonlinear, relativistic quantum mechanics of extended particles

International Nuclear Information System (INIS)

Mielke, E.W.

1981-01-01

A quantum theory of intrinsically extended particles similar to de Broglie's theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)

Outline of a nonlinear, relativistic quantum mechanics of extended particles

International Nuclear Information System (INIS)

Mielke, E.W.

1981-01-01

A quantum theory of intrinsically extended particles similar to de Broglie's Theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)

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.

Inflation from Asymptotically Safe Theories

DEFF Research Database (Denmark)

Nielsen, Niklas Grønlund; Sannino, Francesco; Svendsen, Ole

2015-01-01

for inflation. In the minimal coupling case the theory requires large non-perturbative quantum corrections to the quantum potential for the theory to agree with data, while in the non- minimal coupling case the perturbative regime in the couplings of the theory is preferred. Requiring the theory to reproduce...... the observed amplitude of density perturbations constrain the geometric data of the theory such as the number of colors and flavors for generic values of the non-minimal coupling....

Perspectives of nonlinear dynamics

International Nuclear Information System (INIS)

Jackson, E.A.

1985-03-01

Four lectures were given weekly in October and November, 1984, and some of the ideas presented here will be of use in the future. First, a brief survey of the historical development of nonlinear dynamics since about 1890 was given, and then, a few topics were discussed in detail. The objective was to introduce some of many concepts and methods which are presently used for describing nonlinear dynamics. The symbiotic relationship between sciences of all types and mathematics, two main categories of the models describing nature, the method for describing the dynamics of a system, the idea of control parameters and topological dimension, the asymptotic properties of dynamics, abstract dynamics, the concept of embedding, singular perturbation theory, strange attractor, Fermi-Pasta-Ulam phenomena, an example of computer heuristics, the idea of elementary catastrophe theory and so on were explained. The logistic map is the simplest introduction to complex dynamics. The complicated dynamics is referred to as strange attractors. Two-dimensional maps are the highest dimensional maps commonly studied. These were discussed in detail. (Kako, I.)

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

OpenAIRE

Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.

2014-01-01

Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

Minimal theory of massive gravity

International Nuclear Information System (INIS)

De Felice, Antonio; Mukohyama, Shinji

2016-01-01

We propose a new theory of massive gravity with only two propagating degrees of freedom. While the homogeneous and isotropic background cosmology and the tensor linear perturbations around it are described by exactly the same equations as those in the de Rham–Gabadadze–Tolley (dRGT) massive gravity, the scalar and vector gravitational degrees of freedom are absent in the new theory at the fully nonlinear level. Hence the new theory provides a stable nonlinear completion of the self-accelerating cosmological solution that was originally found in the dRGT theory. The cosmological solution in the other branch, often called the normal branch, is also rendered stable in the new theory and, for the first time, makes it possible to realize an effective equation-of-state parameter different from (either larger or smaller than) −1 without introducing any extra degrees of freedom.

Portfolios with nonlinear constraints and spin glasses

Science.gov (United States)

Gábor, Adrienn; Kondor, I.

1999-12-01

In a recent paper Galluccio, Bouchaud and Potters demonstrated that a certain portfolio problem with a nonlinear constraint maps exactly onto finding the ground states of a long-range spin glass, with the concomitant nonuniqueness and instability of the optimal portfolios. Here we put forward geometric arguments that lead to qualitatively similar conclusions, without recourse to the methods of spin glass theory, and give two more examples of portfolio problems with convex nonlinear constraints.

Nonlinear switching dynamics in a photonic-crystal nanocavity

International Nuclear Information System (INIS)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel; Vukovic, Dragana; Peucheret, Christophe; Yvind, Kresten; Mork, Jesper

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching contrast.

Nonlinear switching dynamics in a photonic-crystal nanocavity

DEFF Research Database (Denmark)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...... the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms...

Coastal tomographic mapping of nonlinear tidal currents and residual currents

Science.gov (United States)

Zhu, Ze-Nan; Zhu, Xiao-Hua; Guo, Xinyu

2017-07-01

Depth-averaged current data, which were obtained by coastal acoustic tomography (CAT) July 12-13, 2009 in Zhitouyang Bay on the western side of the East China Sea, are used to estimate the semidiurnal tidal current (M2) as well as its first two overtide currents (M4 and M6). Spatial mean amplitude ratios M2:M4:M6 in the bay are 1.00:0.15:0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, where water depths are larger than 60 m, M4 velocity amplitudes measured by CAT agree well with those predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. In addition, dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents. This is the first ever nonlinear tidal current study by CAT.

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-05-14

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

Nonlinear transport processes in tokamak plasmas. I. The collisional regimes

International Nuclear Information System (INIS)

Sonnino, Giorgio; Peeters, Philippe

2008-01-01

An application of the thermodynamic field theory (TFT) to transport processes in L-mode tokamak plasmas is presented. The nonlinear corrections to the linear ('Onsager') transport coefficients in the collisional regimes are derived. A quite encouraging result is the appearance of an asymmetry between the Pfirsch-Schlueter (P-S) ion and electron transport coefficients: the latter presents a nonlinear correction, which is absent for the ions, and makes the radial electron coefficients much larger than the former. Explicit calculations and comparisons between the neoclassical results and the TFT predictions for Joint European Torus (JET) plasmas are also reported. It is found that the nonlinear electron P-S transport coefficients exceed the values provided by neoclassical theory by a factor that may be of the order 10 2 . The nonlinear classical coefficients exceed the neoclassical ones by a factor that may be of order 2. For JET, the discrepancy between experimental and theoretical results for the electron losses is therefore significantly reduced by a factor 10 2 when the nonlinear contributions are duly taken into account but, there is still a factor of 10 2 to be explained. This is most likely due to turbulence. The expressions of the ion transport coefficients, determined by the neoclassical theory in these two regimes, remain unaltered. The low-collisional regimes, i.e., the plateau and the banana regimes, are analyzed in the second part of this work

Nonperturbative theory of weak pre- and post-selected measurements

Energy Technology Data Exchange (ETDEWEB)

Kofman, Abraham G., E-mail: kofmana@gmail.com; Ashhab, Sahel; Nori, Franco

2012-11-01

This paper starts with a brief review of the topic of strong and weak pre- and post-selected (PPS) quantum measurements, as well as weak values, and afterwards presents original work. In particular, we develop a nonperturbative theory of weak PPS measurements of an arbitrary system with an arbitrary meter, for arbitrary initial states of the system and the meter. New and simple analytical formulas are obtained for the average and the distribution of the meter pointer variable. These formulas hold to all orders in the weak value. In the case of a mixed preselected state, in addition to the standard weak value, an associated weak value is required to describe weak PPS measurements. In the linear regime, the theory provides the generalized Aharonov–Albert–Vaidman formula. Moreover, we reveal two new regimes of weak PPS measurements: the strongly-nonlinear regime and the inverted region (the regime with a very large weak value), where the system-dependent contribution to the pointer deflection decreases with increasing the measurement strength. The optimal conditions for weak PPS measurements are obtained in the strongly-nonlinear regime, where the magnitude of the average pointer deflection is equal or close to the maximum. This maximum is independent of the measurement strength, being typically of the order of the pointer uncertainty. In the optimal regime, the small parameter of the theory is comparable to the overlap of the pre- and post-selected states. We show that the amplification coefficient in the weak PPS measurements is generally a product of two qualitatively different factors. The effects of the free system and meter Hamiltonians are discussed. We also estimate the size of the ensemble required for a measurement and identify optimal and efficient meters for weak measurements. Exact solutions are obtained for a certain class of the measured observables. These solutions are used for numerical calculations, the results of which agree with the theory

Nonperturbative theory of weak pre- and post-selected measurements

International Nuclear Information System (INIS)

Kofman, Abraham G.; Ashhab, Sahel; Nori, Franco

2012-01-01

This paper starts with a brief review of the topic of strong and weak pre- and post-selected (PPS) quantum measurements, as well as weak values, and afterwards presents original work. In particular, we develop a nonperturbative theory of weak PPS measurements of an arbitrary system with an arbitrary meter, for arbitrary initial states of the system and the meter. New and simple analytical formulas are obtained for the average and the distribution of the meter pointer variable. These formulas hold to all orders in the weak value. In the case of a mixed preselected state, in addition to the standard weak value, an associated weak value is required to describe weak PPS measurements. In the linear regime, the theory provides the generalized Aharonov–Albert–Vaidman formula. Moreover, we reveal two new regimes of weak PPS measurements: the strongly-nonlinear regime and the inverted region (the regime with a very large weak value), where the system-dependent contribution to the pointer deflection decreases with increasing the measurement strength. The optimal conditions for weak PPS measurements are obtained in the strongly-nonlinear regime, where the magnitude of the average pointer deflection is equal or close to the maximum. This maximum is independent of the measurement strength, being typically of the order of the pointer uncertainty. In the optimal regime, the small parameter of the theory is comparable to the overlap of the pre- and post-selected states. We show that the amplification coefficient in the weak PPS measurements is generally a product of two qualitatively different factors. The effects of the free system and meter Hamiltonians are discussed. We also estimate the size of the ensemble required for a measurement and identify optimal and efficient meters for weak measurements. Exact solutions are obtained for a certain class of the measured observables. These solutions are used for numerical calculations, the results of which agree with the theory

Periodicity of a class of nonlinear fuzzy systems with delays

International Nuclear Information System (INIS)

Yu Jiali; Yi Zhang; Zhang Lei

2009-01-01

The well known Takagi-Sugeno (T-S) model gives an effective method to combine some simple local systems with their linguistic description to represent complex nonlinear dynamic systems. By using the T-S method, a class of local nonlinear systems having nice dynamic properties can be employed to represent some global complex nonlinear systems. This paper proposes to study the periodicity of a class of global nonlinear fuzzy systems with delays by using T-S method. Conditions for guaranteeing periodicity are derived. Examples are employed to illustrate the theory.

Applications of Nonlinear Dynamics Model and Design of Complex Systems

CERN Document Server

In, Visarath; Palacios, Antonio

2009-01-01

This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

Linear and non-linear optics of condensed matter

International Nuclear Information System (INIS)

McLean, T.P.

1977-01-01

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

High-order nonlinear susceptibilities of He

International Nuclear Information System (INIS)

Liu, W.C.; Clark, C.W.

1996-01-01

High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. The authors have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s, within the framework of Rayleigh=Schroedinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Ponte and Shakeshaft, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used; the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals

Nonlinear reflection of shock shear waves in soft elastic media.

Science.gov (United States)

Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

2010-02-01

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

Can Malin's gravitational-field equations be modified to obtain a viable theory of gravity to obtain a viable theory of gravity to obtain a viable theory of gravity

International Nuclear Information System (INIS)

Smalley, L.L.; Prestage, J.

1976-01-01

Malin's gravitational theory, which was recently shown by Lindblom and Nester to be incorrect, is modified by means of a recently proposed method for obtaining viable gravitational theories. The resulting self-consistent theory, which is in effect a Rastall-type modification of the Einstein theory, exhibits nonconservation of momentum, yet agrees with all experimental limits known to date within the PPN framework

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

Science.gov (United States)

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

2014-01-01

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

On the problem of the existence of the solutions of the nonlinear nonsingular equations of quantum field theory

International Nuclear Information System (INIS)

Nelipa, N.F.

1978-01-01

The existence of the solution of the nonlinear, singular equations of quantum field theory is discussed. By making use of the Banach's and Schauder's fixed point theorems, the condition of the existence of these equations is found. As some illustration, these methods were applied to the equations for the π-scattering on static nucleon. The investigations of the other equations of quantum field theory (Chew-Low, double dispersin relation, Green's function) lead to the similar result. The application of the Newton-Kantorovich method to the Chew-Low equations also gives the similar result. What are the causes of such situation[ The main suggestions which the author has used were that the Banach's, the Schauder's, and the Newton-Kantorovich methods were applied and the Hoelder space was choosen. It may be that the method are crude. It may be that the solutions do not belong to the Hoelder space. Now it is rather difficult to say which role each of these two suggestions plays. (Kobatake, H.)

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 ...

Nonlinear problems in theoretical physics

International Nuclear Information System (INIS)

Ranada, A.F.

1979-01-01

This volume contains the lecture notes and review talks delivered at the 9th GIFT international seminar on theoretical physics on the general subject 'Nonlinear Problems in Theoretical Physics'. Mist contributions deal with recent developments in the theory of the spectral transformation and solitons, but there are also articles from the field of transport theory and plasma physics and an unconventional view of classical and quantum electrodynamics. All contributions to this volume will appear under their corresponding subject categories. (HJ)

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

Science.gov (United States)

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

2007-09-21

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

Chaos control of third-order phase-locked loops using backstepping nonlinear controller

International Nuclear Information System (INIS)

Harb, Ahmad M.; Harb, Bassam A.

2004-01-01

Previous study showed that a third-order phase-locked loop (PLL) with sinusoidal phase detector characteristics experienced a Hopf bifurcation point as well as chaotic behavior. As a result, this behavior drives the PLL to the out-of-lock (unstable) state. The analysis was based on a modern nonlinear theory such as bifurcation and chaos. The main goal of this paper is to control this chaotic behavior. A nonlinear controller based on the theory of backstepping is designed. The study showed the effectiveness of the designed nonlinear controller in controlling the undesirable unstable behavior and pulling the PLL back to the in-lock state

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

Directory of Open Access Journals (Sweden)

Tieshan He

2011-01-01

Full Text Available This paper is concerned with the existence of nontrivial periodic solutions and positive periodic solutions to a nonlinear second-order difference equation. Under some conditions concerning the first positive eigenvalue of the linear equation corresponding to the nonlinear second-order equation, we establish the existence results by using the topological degree and fixed point index theories.

A Conic Sector-Based Methodology for Nonlinear Control Design

OpenAIRE

Doyle, Francis J., III; Morari, Manfred

1990-01-01

A design method is presented for the analysis and synthesis of robust nonlinear controllers for chemical engineering systems. The method rigorously treats the effect of unmeasured disturbances and unmodeled dynamics on the stability and performance properties of a nonlinear system. The results utilise new extensions of structured singular value theory for analysis and recent synthesis results for approximate linearisation.

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

International Nuclear Information System (INIS)

Yao, Jianyong; Jiao, Zongxia; Yao, Bin

2014-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-04-15

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

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.

Energy in the Einstein-aether theory

International Nuclear Information System (INIS)

Eling, Christopher

2006-01-01

We investigate the energy of a theory with a unit vector field (the aether) coupled to gravity. Both the Weinberg and Einstein type energy-momentum pseudotensors are employed. In the linearized theory we find expressions for the energy density of the 5 wave modes. The requirement that the modes have positive energy is then used to constrain the theory. In the fully nonlinear theory we compute the total energy of an asymptotically flat spacetime. The resulting energy expression is modified by the presence of the aether due to the nonzero value of the unit vector at infinity and its 1/r falloff. The question of nonlinear energy positivity is also discussed, but not resolved

Flutter analysis of an airfoil with multiple nonlinearities and uncertainties

Directory of Open Access Journals (Sweden)

Haitao Liao

2013-09-01

Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

Nonlinear effects in evolution - an ab initio study: A model in which the classical theory of evolution occurs as a special case.

Science.gov (United States)

Clerc, Daryl G

2016-07-21

An ab initio approach was used to study the molecular-level interactions that connect gene-mutation to changes in an organism׳s phenotype. The study provides new insights into the evolutionary process and presents a simplification whereby changes in phenotypic properties may be studied in terms of the binding affinities of the chemical interactions affected by mutation, rather than by correlation to the genes. The study also reports the role that nonlinear effects play in the progression of organs, and how those effects relate to the classical theory of evolution. Results indicate that the classical theory of evolution occurs as a special case within the ab initio model - a case having two attributes. The first attribute: proteins and promoter regions are not shared among organs. The second attribute: continuous limiting behavior exists in the physical properties of organs as well as in the binding affinity of the associated chemical interactions, with respect to displacements in the chemical properties of proteins and promoter regions induced by mutation. Outside of the special case, second-order coupling contributions are significant and nonlinear effects play an important role, a result corroborated by analyses of published activity levels in binding and transactivation assays. Further, gradations in the state of perfection of an organ may be small or large depending on the type of mutation, and not necessarily closely-separated as maintained by the classical theory. Results also indicate that organs progress with varying degrees of interdependence, the likelihood of successful mutation decreases with increasing complexity of the affected chemical system, and differences between the ab initio model and the classical theory increase with increasing complexity of the organism. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.

Fourier imaging of non-linear structure formation

Energy Technology Data Exchange (ETDEWEB)

Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)

2017-04-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

Fourier imaging of non-linear structure formation

International Nuclear Information System (INIS)

Brandbyge, Jacob; Hannestad, Steen

2017-01-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

Numerical study of surface plasmon enhanced nonlinear absorption and refraction.

Science.gov (United States)

Kohlgraf-Owens, Dana C; Kik, Pieter G

2008-07-07

Maxwell Garnett effective medium theory is used to study the influence of silver nanoparticle induced field enhancement on the nonlinear response of a Kerr-type nonlinear host. We show that the composite nonlinear absorption coefficient, beta(c), can be enhanced relative to the host nonlinear absorption coefficient near the surface plasmon resonance of silver nanoparticles. This enhancement is not due to a resonant enhancement of the host nonlinear absorption, but rather due to a phase shifted enhancement of the host nonlinear refractive response. The enhancement occurs at the expense of introducing linear absorption, alpha(c), which leads to an overall reduced figure of merit beta(c)/alpha(c) for nonlinear absorption. For thin (< 1 microm) composites, the use of surface plasmons is found to result in an increased nonlinear absorption response compared to that of the host material.

Nonlinear coupling of tearing fluctuations in the Madison Symmetric Torus

International Nuclear Information System (INIS)

Sarff, J.S.; Almagri, A.F.; Cekic, M.; Den Hartog, D.J.; Fiksel, G.; Hokin, S.A.; Ji, H.; Prager, S.C.; Shen, W.; Stoneking, M.R.; Assadi, S.; Sidikman, K.L.

1992-11-01

Three-wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed-field pinch (RFP) [Fusion Technol. 19, 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in ''k-space. The strength of nonlinear three-wave interactions satisfying the sum rules m 1 + m 2 = m 3 and n 1 + n 2 = n 3 is measured by the bicoherency. In the RFP, m=l, n∼2R/a (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two m=l modes coupled to an m=2 mode and the coupling of intermediate toroidal modes, e.g., n=6 and 7 coupled to n=13. These experimental bispectral features agree with predicted bispectral features derived from MHD computation. However, in the experiment, enhanced coupling occurs in the ''crash'' phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade

Nonlinear differential equations

Energy Technology Data Exchange (ETDEWEB)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

Nonlinear differential equations

International Nuclear Information System (INIS)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

Adaptive nonlinear control using input normalized neural networks

International Nuclear Information System (INIS)

Leeghim, Henzeh; Seo, In Ho; Bang, Hyo Choong

2008-01-01

An adaptive feedback linearization technique combined with the neural network is addressed to control uncertain nonlinear systems. The neural network-based adaptive control theory has been widely studied. However, the stability analysis of the closed-loop system with the neural network is rather complicated and difficult to understand, and sometimes unnecessary assumptions are involved. As a result, unnecessary assumptions for stability analysis are avoided by using the neural network with input normalization technique. The ultimate boundedness of the tracking error is simply proved by the Lyapunov stability theory. A new simple update law as an adaptive nonlinear control is derived by the simplification of the input normalized neural network assuming the variation of the uncertain term is sufficiently small

Nonlinear features of the electron temperature gradient mode and electron thermal transport in tokamaks

International Nuclear Information System (INIS)

Kaw, P.K.; Singh, R.; Weiland, J.G.

2001-01-01

Analytical investigations of several linear and nonlinear features of ETG turbulence are reported. The linear theory includes effects such as finite beta induced electromagnetic shielding, coupling to electron magnetohydrodynamic modes like whistlers etc. It is argued that nonlinearly, turbulence and transport are dominated by radially extended modes called 'streamers'. A nonlinear mechanism generating streamers based on a modulational instability theory of the ETG turbulence is also presented. The saturation levels of the streamers using a Kelvin Helmholtz secondary instability mechanism are calculated and levels of the electron thermal transport due to streamers are estimated. (author)

Nonlinear oscillations in coriolis based gyroscopes

Directory of Open Access Journals (Sweden)

Dag Kristiansen

1999-01-01

Full Text Available In this paper we model and analyze nonlinear oscillations which are known to exist in some Coriolis based gyroscopes due to large amplitude excitation in the drive loop. A detailed derivation of a dynamic model for a cylinder gyroscope which includes geometric nonlinearities is given, and energy transfer between the system's modes are analyzed using perturbation theory and by proposing a simplified model. The model is also simulated, and the results are shown to give an accurate description of the experimental results. This work is done in order to gain a better understanding of the gyroscope's dynamics, and is intended to be a starting point for designing nonlinear observers and vibration controllers for the gyroscope in order to increase the performance.

Macroscopic and non-linear quantum games

International Nuclear Information System (INIS)

Aerts, D.; D'Hooghe, A.; Posiewnik, A.; Pykacz, J.

2005-01-01

Full text: We consider two models of quantum games. The first one is Marinatto and Weber's 'restricted' quantum game in which only the identity and the spin-flip operators are used. We show that this quantum game allows macroscopic mechanistic realization with the use of a version of the 'macroscopic quantum machine' described by Aerts already in 1980s. In the second model we use non-linear quantum state transformations which operate on points of spin-1/2 on the Bloch sphere and which can be used to distinguish optimally between two non-orthogonal states. We show that efficiency of these non-linear strategies out-perform any linear ones. Some hints on the possible theory of non-linear quantum games are given. (author)

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS

Directory of Open Access Journals (Sweden)

Bazhenov V.A.

2014-06-01

Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

Propagation of flexural waves in inhomogeneous plates exhibiting hysteretic nonlinearity: Nonlinear acoustic black holes.

Science.gov (United States)

Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua

2015-08-01

Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.

Neoclassical transport including collisional nonlinearity.

Science.gov (United States)

Candy, J; Belli, E A

2011-06-10

In the standard δf theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction δf is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.