An introduction to nonlinear analysis and fixed point theory

CERN Document Server

Pathak, Hemant Kumar

2018-01-01

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

Nonlinear optimal control theory

CERN Document Server

Berkovitz, Leonard David

2012-01-01

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

Nonlinearity and disorder: Theory and applications

DEFF Research Database (Denmark)

Bang, Ole; Sørensen, Mads Peter

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

Nonlinear theory of electroelastic and magnetoelastic interactions

CERN Document Server

Dorfmann, Luis

2014-01-01

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

Harnessing mode-selective nonlinear optics for on-chip multi-channel all-optical signal processing

Directory of Open Access Journals (Sweden)

Ming Ma

2016-11-01

Full Text Available All-optical signal processing based on nonlinear optical effects allows for the realization of important functions in telecommunications including wavelength conversion, optical multiplexing/demultiplexing, Fourier transformation, and regeneration, amongst others, on ultrafast time scales to support high data rate transmission. In integrated photonic subsystems, the majority of all-optical signal processing systems demonstrated to date typically process only a single channel at a time or perform a single processing function, which imposes a serious limitation on the functionality of integrated solutions. Here, we demonstrate how nonlinear optical effects can be harnessed in a mode-selective manner to perform simultaneous multi-channel (two and multi-functional optical signal processing (i.e., regenerative wavelength conversion in an integrated silicon photonic device. This approach, which can be scaled to a higher number of channels, opens up a new degree of freedom for performing a broad range of multi-channel nonlinear optical signal processing functions using a single integrated photonic device.

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)

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.

A non-linear theory for the bubble regime of plasma wake fields in tailored plasma channels

CERN Document Server

Thomas, Johannes

2016-01-01

We introduce a first full analytical bubble and blow-out model for a radially inhomogeneous plasma in a quasi-static approximation. For both cases we calculate the accelerating and the focusing fields. In our model we also assume a thin electron layer that surrounds the wake field and calculate the field configuration within. Our theory holds for arbitrary radial density profiles and reduces to known models in the limit of a homogeneous plasma. From a previous study of hollow plasma channels with smooth boundaries for laser-driven electron acceleration in the bubble regime we know that pancake-like laser pulses lead to highest electron energies [Pukhov et al, PRL 113, 245003 (2014)]. As it was shown, the bubble fields can be adjusted to balance the laser depletion and dephasing lengths by varying the plasma density profile inside a deep channel. Now we show why the radial fields in the vacuum part of a channel become defocussing.

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

Nonlinear transport theory in the metal with tunnel barrier

Science.gov (United States)

Zubov, E. E.

2018-02-01

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

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

Drag reduction in channel flow using nonlinear control

Science.gov (United States)

Keefe, Laurence R.

1993-01-01

Two nonlinear control schemes have been applied to the problem of drag reduction in channel flow. Both schemes have been tested using numerical simulations at a mass flux Reynolds numbers of 4408, utilizing 2D nonlinear neutral modes for goal dynamics. The OGY-method, which requires feedback, reduces drag to 60-80 percent of the turbulent value at the same Reynolds number, and employs forcing only within a thin region near the wall. The H-method, or model-based control, fails to achieve any drag reduction when starting from a fully turbulent initial condition, but shows potential for suppressing or retarding laminar-to-turbulent transition by imposing instead a transition to a low drag, nonlinear traveling wave solution to the Navier-Stokes equation. The drag in this state corresponds to that achieved by the OGY-method. Model-based control requires no feedback, but in experiments to date has required the forcing be imposed within a thicker layer than the OGY-method. Control energy expenditures in both methods are small, representing less than 0.1 percent of the uncontrolled flow's energy.

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....

Concept of spatial channel theory applied to reactor shielding analysis

International Nuclear Information System (INIS)

Williams, M.L.; Engle, W.W. Jr.

1977-01-01

The concept of channel theory is used to locate spatial regions that are important in contributing to a shielding response. The method is analogous to the channel-theory method developed for ascertaining important energy channels in cross-section analysis. The mathematical basis for the theory is shown to be the generalized reciprocity relation, and sample problems are given to exhibit and verify properties predicted by the mathematical equations. A practical example is cited from the shielding analysis of the Fast Flux Test Facility performed at Oak Ridge National Laboratory, in which a perspective plot of channel-theory results was found useful in locating streaming paths around the reactor cavity shield

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

Determination of the onset nonlinearity hydrodynamic characteristics at two-phase flow in parallel vertical channels

International Nuclear Information System (INIS)

Jovic, V.; Afgan, N.; Jovic, L.; Spasojevic, D.

1993-01-01

The paper presents results of the experimental and theoretical analyses of linear and nonlinear characteristics of adiabatic two-phase water-air flow in vertical parallel channels. Regime character changes and linear to nonlinear dynamic characteristics transfer conditions were defined. (author)

A general theory of two-wave mixing in nonlinear media

DEFF Research Database (Denmark)

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

2009-01-01

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

Nonlinear 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.

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...

Out-of-band and adjacent-channel interference reduction by analog nonlinear filters

Science.gov (United States)

Nikitin, Alexei V.; Davidchack, Ruslan L.; Smith, Jeffrey E.

2015-12-01

In a perfect world, we would have `brick wall' filters, no-distortion amplifiers and mixers, and well-coordinated spectrum operations. The real world, however, is prone to various types of unintentional and intentional interference of technogenic (man-made) origin that can disrupt critical communication systems. In this paper, we introduce a methodology for mitigating technogenic interference in communication channels by analog nonlinear filters, with an emphasis on the mitigation of out-of-band and adjacent-channel interference. Interference induced in a communications receiver by external transmitters can be viewed as wide-band non-Gaussian noise affecting a narrower-band signal of interest. This noise may contain a strong component within the receiver passband, which may dominate over the thermal noise. While the total wide-band interference seen by the receiver may or may not be impulsive, we demonstrate that the interfering component due to power emitted by the transmitter into the receiver channel is likely to appear impulsive under a wide range of conditions. We give an example of mechanisms of impulsive interference in digital communication systems resulting from the nonsmooth nature of any physically realizable modulation scheme for transmission of a digital (discontinuous) message. We show that impulsive interference can be effectively mitigated by nonlinear differential limiters (NDLs). An NDL can be configured to behave linearly when the input signal does not contain outliers. When outliers are encountered, the nonlinear response of the NDL limits the magnitude of the respective outliers in the output signal. The signal quality is improved in excess of that achievable by the respective linear filter, increasing the capacity of a communications channel. The behavior of an NDL, and its degree of nonlinearity, is controlled by a single parameter in a manner that enables significantly better overall suppression of the noise-containing impulsive components

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

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

16-channel DWDM based on 1D defect mode nonlinear photonic crystal

Science.gov (United States)

Kalhan, Abhishek; Sharma, Sanjeev; Kumar, Arun

2018-05-01

We propose a sixteen-channel Dense Wavelength Division Multiplexer (DWDM), using the 1-D defect mode nonlinear photonic crystal which is a function of intensity as well as wavelength. Here, we consider an alternate layer of two semiconductor materials in which we found the bandgap of materials when defect layer is introduced then 16-channel dense wavelength division multiplexer is obtained within bandgap. From the theoretical analysis, we can achieve average quality factor of 7800.4, the uniform spectral line-width of 0.2 nm, crosstalk of -31.4 dB, central wavelength changes 0.07 nm/(1GW/cm2) and 100% transmission efficiency. Thus, Sixteen-channel DWDM has very high quality factor, low crosstalk, near 100% power transmission efficiency and small channel spacing (1.44 nm).

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

Nonlinear drift-diffusion model of gating in K and nACh ion channels

Energy Technology Data Exchange (ETDEWEB)

Vaccaro, S.R. [Department of Physics, University of Adelaide, Adelaide, South Australia 5005 (Australia)], E-mail: svaccaro@physics.adelaide.edu.au

2007-09-03

The configuration of a sensor regulates the transition between the closed and open states of both voltage and ligand gated channels. The closed state dwell-time distribution f{sub c}(t) derived from a Fokker-Planck equation with a nonlinear diffusion coefficient is in good agreement with experimental data and can account for the power law approximation to f{sub c}(t) for a delayed rectifier K channel and a nicotinic acetylcholine (nACh) ion channel. The solution of a master equation which approximates the Fokker-Planck equation provides a better description of the small time behaviour of the dwell-time distribution and can account for the empirical rate-amplitude correlation for these ion channels.

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 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.

Non-dispersive traveling waves in inclined shallow water channels

International Nuclear Information System (INIS)

Didenkulova, Ira; Pelinovsky, Efim

2009-01-01

Existence of traveling waves propagating without internal reflection in inclined water channels of arbitrary slope is demonstrated. It is shown that traveling non-monochromatic waves exist in both linear and nonlinear shallow water theories in the case of a uniformly inclined channel with a parabolic cross-section. The properties of these waves are studied. It is shown that linear traveling waves should have a sign-variable shape. The amplitude of linear traveling waves in a channel satisfies the same Green's law, which is usually derived from the energy flux conservation for smoothly inhomogeneous media. Amplitudes of nonlinear traveling waves deviate from the linear Green's law, and the behavior of positive and negative amplitudes are different. Negative amplitude grows faster than positive amplitude in shallow water. The phase of nonlinear waves (travel time) is described well by the linear WKB approach. It is shown that nonlinear traveling waves of any amplitude always break near the shoreline if the boundary condition of the full absorption is applied.

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'.

Transitional inertialess instabilities in driven multilayer channel flows

Science.gov (United States)

Papaefthymiou, Evangelos; Papageorgiou, Demetrios

2016-11-01

We study the nonlinear stability of viscous, immiscible multilayer flows in channels driven both by a pressure gradient and/or gravity in a slightly inclined channel. Three fluid phases are present with two internal interfaces. Novel weakly nonlinear models of coupled evolution equations are derived and we concentrate on inertialess flows with stably stratified fluids, with and without surface tension. These are 2 × 2 systems of second-order semilinear parabolic PDEs that can exhibit inertialess instabilities due to resonances between the interfaces - mathematically this is manifested by a transition from hyperbolic to elliptic behavior of the nonlinear flux functions. We consider flows that are linearly stable (i.e the nonlinear fluxes are hyperbolic initially) and use the theory of nonlinear systems of conservation laws to obtain a criterion (which can be verified easily) that can predict nonlinear stability or instability (i.e. nonlinear fluxes encounter ellipticity as they evolve spatiotemporally) at large times. In the former case the solution decays asymptotically to its base state, and in the latter nonlinear traveling waves emerge. EPSRC Grant Numbers EP/K041134 and EP/L020564.

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

A fundamental study of ''contribution'' transport theory and channel theory applications

International Nuclear Information System (INIS)

Williams, M.L.

1992-01-01

The objective of this three-year study is to develop a technique called ''channel theory'' that can be used in interpreting particle transport analysis such as frequently required in radiation shielding design and assessment. Channel theory is a technique used to provide insight into the mechanisms by which particles emitted from a source are transported through a complex system and register a response on some detector. It is based on the behavior of a pseudo particle called a ''contributon,'' which is the response carrier through space and energy channels that connect the source and detector. ''Contributons'' are those particles among all the ones contained in the system which will eventually contribute some amount of response to the detector. The specific goals of this projects are to provide a more fundamental theoretical understanding of the method, and to develop computer programs to apply the techniques to practical problems encountered in radiation transport analysis. The overall project can be divided into three components to meet these objectives: (a) Theoretical Development, (b) Code Development, and (c) Sample Applications. During the present third year of this study, an application of contributon theory to the analysis of radiation heating in a nuclear rocket has been completed, and a paper on the assessment of radiation damage response of an LWR pressure vessel and analysis of radiation propagation through space and energy channels in air at the Hiroshima weapon burst was accepted for publication. A major effort was devoted to developing a new ''Contributon Monte Carlo'' method, which can improve the efficiency of Monte Carlo calculations of radiation transport by tracking only contributons. The theoretical basis for Contributon Monte Carlo has been completed, and the implementation and testing of the technique is presently being performed

Generic theory for channel sinuosity.

Science.gov (United States)

Lazarus, Eli D; Constantine, José Antonio

2013-05-21

Sinuous patterns traced by fluid flows are a ubiquitous feature of physical landscapes on Earth, Mars, the volcanic floodplains of the Moon and Venus, and other planetary bodies. Typically discussed as a consequence of migration processes in meandering rivers, sinuosity is also expressed in channel types that show little or no indication of meandering. Sinuosity is sometimes described as "inherited" from a preexisting morphology, which still does not explain where the inherited sinuosity came from. For a phenomenon so universal as sinuosity, existing models of channelized flows do not explain the occurrence of sinuosity in the full variety of settings in which it manifests, or how sinuosity may originate. Here we present a generic theory for sinuous flow patterns in landscapes. Using observations from nature and a numerical model of flow routing, we propose that flow resistance (representing landscape roughness attributable to topography or vegetation density) relative to surface slope exerts a fundamental control on channel sinuosity that is effectively independent of internal flow dynamics. Resistance-dominated surfaces produce channels with higher sinuosity than those of slope-dominated surfaces because increased resistance impedes downslope flow. Not limited to rivers, the hypothesis we explore pertains to sinuosity as a geomorphic pattern. The explanation we propose is inclusive enough to account for a wide variety of sinuous channel types in nature, and can serve as an analytical tool for determining the sinuosity a landscape might support.

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

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

International Nuclear Information System (INIS)

Penaforte, J.C.; Baseia, B.

1984-01-01

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

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.

Nonlinear State of Sausage-like Instability of Electron Current Channels in Fast Ignition Concept of Inertial Fusion

International Nuclear Information System (INIS)

Jain, Neeraj; Das, Amita; Kaw, Predhiman; Sengupta, Sudip

2003-01-01

This paper deals with a detailed fluid simulation study of linear and nonlinear aspects of the velocity shear modes in electron current channels in a two dimensional geometry. Simulation results clearly show the flattening of flow profile and the development of sausage like structures (kink structures, which are intrinsically three dimensional excitations, are ruled out in the present simulations) which grow linearly and eventually saturate by nonlinear effects. An analytic understanding of the nonlinear saturation mechanism is also provided

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

Studying the formation of non-linear bursts in fully turbulent channel flows

Science.gov (United States)

Encinar, Miguel P.; Jimenez, Javier

2017-11-01

Linear transient growth has been suggested as a possible explanation for the intermittent behaviour, or `bursting', in shear flows with a stable mean velocity profile. Analysing fully non-linear DNS databases yields a similar Orr+lift-up mechanism, but acting on spatially localised wave packets rather than on monochromatic infinite wavetrains. The Orr mechanism requires the presence of backwards-leaning wall-normal velocity perturbations as initial condition, but the linear theory fails to clarify how these perturbations are formed. We investigate the latter in a time-resolved wavelet-filtered turbulent channel database, which allows us to assign an amplitude and an inclination angle to a flow region of selected size. This yields regions that match the dynamics of linear Orr for short times. We find that a short streamwise velocity (u) perturbation (i.e. a streak meander) consistently appears before the burst, but disappears before the burst reaches its maximum amplitude. Lift-up then generates a longer streamwise velocity perturbation. The initial streamwise velocity is also found to be backwards-leaning, contrary to the averaged energy-containing scales, which are known to be tilted forward. Funded by the ERC COTURB project.

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.

A Calibration Method for Nonlinear Mismatches in M-Channel Time-Interleaved Analog-to-Digital Converters Based on Hadamard Sequences

Directory of Open Access Journals (Sweden)

Husheng Liu

2016-11-01

Full Text Available The time-interleaved analog-to-digital converter (TIADC is an architecture used to achieve a high sampling rate and high dynamic performance. However, estimation and compensation methods are required to maintain the dynamic performance of the constituent analog-to-digital converters (ADCs due to channel mismatches. This paper proposes a blind adaptive method to calibrate the nonlinear mismatches in M-channel TIADCs (M-TIADCs. The nonlinearity-induced error signal is reconstructed by the proposed multiplier Hadamard transform (MHT structure, and the nonlinear parameters are estimated by the filtered-X least-mean square (FxLMS algorithm. The performance of cascade calibration is also analyzed. The numerical simulation results show that the proposed method consumes much less hardware resources while maintaining the calibration performance.

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

Digital non-linear equalization for flexible capacity ultradense WDM channels for metro core networking

DEFF Research Database (Denmark)

Arlunno, Valeria; Zhang, Xu; Larsen, Knud J.

2011-01-01

carriers, we demonstrate that a digital non-linear equalization allow to mitigate inter-channel interference and improve overall system performance in terms of OSNR. Evaluation of the algorithm and comparison with an ultradense WDM system with coherent carriers generated from a single laser are also......An experimental demonstration of Ultradense WDM with advanced digital signal processing is presented. The scheme proposed allows the use of independent tunable DFB lasers spaced at 12.5 GHz for ultradense WDM PM-QPSK flexible capacity channels for metro core networking. To allocate extremely closed...

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)…

ACTIVITY THEORY APPLIED AT CHANNEL EXPANSIONS IN SMALL AND MEDIUM ENTERPRISES

Directory of Open Access Journals (Sweden)

Siw Lundqvist

2017-06-01

Full Text Available Today’s commonly carried out channel expansions of commerce could be both costly and problematic to manage. Especially for small and medium-sized enterprises (SMEs that often suffer from a lack of digital competence, time and monetary resources in generally. Still, these transitions would be necessary to carry out because of customer demands and expectations concerning 24/7 availability, and access to digital commerce alternatives. Scarce resources are important reasons to search for how to carry out channel expansions with minimized problems. Activity theory (AT focuses on the whole in order to detect problems that hinder successful outcomes. Hence, this theory was applied to prior findings, from a project about SME’s channel expansions, highlighting several problems that could appear during these activities. Implications for research foremost involve issues connected to the use of AT; implications for practice particularly concern if and how AT could be used to support channel broadening activities.

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

Attitude Control of a Single Tilt Tri-Rotor UAV System: Dynamic Modeling and Each Channel's Nonlinear Controllers Design

Directory of Open Access Journals (Sweden)

Juing-Shian Chiou

2013-01-01

Full Text Available This paper has implemented nonlinear control strategy for the single tilt tri-rotor aerial robot. Based on Newton-Euler’s laws, the linear and nonlinear mathematical models of tri-rotor UAVs are obtained. A numerical analysis using Newton-Raphson method is chosen for finding hovering equilibrium point. Back-stepping nonlinear controller design is based on constructing Lyapunov candidate function for closed-loop system. By imitating the linguistic logic of human thought, fuzzy logic controllers (FLCs are designed based on control rules and membership functions, which are much less rigid than the calculations computers generally perform. Effectiveness of the controllers design scheme is shown through nonlinear simulation model on each channel.

Testing the applicability of Nernst-Planck theory in ion channels: comparisons with Brownian dynamics simulations.

Directory of Open Access Journals (Sweden)

Chen Song

Full Text Available The macroscopic Nernst-Planck (NP theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex 'catenary' channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction.

Testing the applicability of Nernst-Planck theory in ion channels: comparisons with Brownian dynamics simulations.

Science.gov (United States)

Song, Chen; Corry, Ben

2011-01-01

The macroscopic Nernst-Planck (NP) theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD) simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex 'catenary' channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction.

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

Matching Theory for Channel Allocation in Cognitive Radio Networks

Directory of Open Access Journals (Sweden)

L. Cao

2016-12-01

Full Text Available For a cognitive radio network (CRN in which a set of secondary users (SUs competes for a limited number of channels (spectrum resources belonging to primary users (PUs, the channel allocation is a challenge and dominates the throughput and congestion of the network. In this paper, the channel allocation problem is first formulated as the 0-1 integer programming optimization, with considering the overall utility both of primary system and secondary system. Inspired by matching theory, a many-to-one matching game is used to remodel the channel allocation problem, and the corresponding PU proposing deferred acceptance (PPDA algorithm is also proposed to yield a stable matching. We compare the performance and computation complexity between these two solutions. Numerical results demonstrate the efficiency and obtain the communication overhead of the proposed scheme.

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...

Experimental Results and Issues on Equalization for Nonlinear Memory Channel: Pre-Cursor Enhanced Ram-DFE Canceler

Science.gov (United States)

Yuan, Lu; LeBlanc, James

1998-01-01

This thesis investigates the effects of the High Power Amplifier (HPA) and the filters over a satellite or telemetry channel. The Volterra series expression is presented for the nonlinear channel with memory, and the algorithm is based on the finite-state machine model. A RAM-based algorithm operating on the receiver side, Pre-cursor Enhanced RAM-FSE Canceler (PERC) is developed. A high order modulation scheme , 16-QAM is used for simulation, the results show that PERC provides an efficient and reliable method to transmit data on the bandlimited nonlinear channel. The contribution of PERC algorithm is that it includes both pre-cursors and post-cursors as the RAM address lines, and suggests a new way to make decision on the pre-addresses. Compared with the RAM-DFE structure that only includes post- addresses, the BER versus Eb/NO performance of PERC is substantially enhanced. Experiments are performed for PERC algorithms with different parameters on AWGN channels, and the results are compared and analyzed. The investigation of this thesis includes software simulation and hardware verification. Hardware is setup to collect actual TWT data. Simulation on both the software-generated data and the real-world data are performed. Practical limitations are considered for the hardware collected data. Simulation results verified the reliability of the PERC algorithm. This work was conducted at NMSU in the Center for Space Telemetering and Telecommunications Systems in the Klipsch School of Electrical and Computer Engineering Department.

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.

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.

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.

A nonlinear model of flow in meandering submarine and subaerial channels

Science.gov (United States)

Imran, Jasim; Parker, Gary; Pirmez, Carlos

1999-12-01

A generalized model of flow in meandering subaqueous and subaerial channels is developed. The conservation equations of mass and momentum are depth/layer integrated, normalized, and represented as deviations from a straight base state. This allows the determination of integrable forms which can be solved at both linear and nonlinear levels. The effects of various flow and geometric parameters on the flow dynamics are studied. Although the model is not limited to any specific planform, this study focuses on sine-generated curves. In analysing the flow patterns, the turbidity current of the subaqueous case is simplified to a conservative density flow with water entrainment from above neglected. The subaqueous model thus formally corresponds to a subcritical or only mildly supercritical mud-rich turbidity current. By extension, however the analysis can be applied to a depositional or erosional current carrying sand that is changing only slowly in the streamwise direction. By bringing the subaqueous and subaerial cases into a common form, flow behaviour in the two environments can be compared under similar geometric and boundary conditions. A major difference between the two cases is the degree of superelevation of channel flow around bends, which is modest in the subaerial case but substantial in the subaqueous case. Another difference concerns Coriolis effects: some of the largest subaqueous meandering systems are so large that Coriolis effects can become important. The model is applied to meander bends on the youngest channel in the mid-fan region of the Amazon Fan and a mildly sinuous bend of the North-West Atlantic Mid-Ocean Channel. In the absence of specific data on the turbid flows that created the channel, the model can be used to make inferences about the flow, and in particular the range of values of flow velocity and sediment concentration that would allow the growth and downfan migration of meander bends.

Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

International Nuclear Information System (INIS)

Sugahara, Y.; Toki, H.

1994-01-01

We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

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...

Siegert pseudostate formulation of scattering theory: two-channel case

CERN Document Server

Sitnikov, G V

2003-01-01

Siegert pseudostates (SPS) are a finite basis representation of Siegert states (SS) for finite-range potentials. This paper presents a generalization of the SPS formulation of scattering theory, originally developed by Tolstikhin, Ostrovsky, and Nakamura ÝPhys. Rev. A 58, 2077 (1998)¿ for s-wave scattering in the one-channel case, to s-wave scattering in the two-channel case. This includes the investigation of the properties of orthogonality and completeness of two-channel SPS and the derivation of the SPS expansions for the two- channel Green function, wave function, and scattering matrix. Similar to the one-channel case, two types of expansions for the scattering matrix are obtained: one has a form of a sum and requires the knowledge of both the SPS eigenvalues and eigenfunctions, while the other has a form of a product and involves the eigenvalues only. As the size of the basis tends to infinity, the product formulas obtained here in terms of SPS coincide with those given by Le Couteur ÝProc. R. Soc. Lo...

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.

Applying marketing channel theory to food marketing in developing countries: A vertical disintegration model for horticultural marketing channels in Kenya

NARCIS (Netherlands)

Dijkstra, T.; Meulenberg, M.T.G.; Tilburg, van A.

2001-01-01

This article shows that marketing channel theory, which has been extensively applied in developed countries, can also be of great value to the developing world. Notably, the channel approach makes it possible to explain the number of trade levels observed in food marketing systems. We propose here a

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

Sensitivity Analysis of Multicarrier Digital Pre-distortion/ Equalization Techniques for Non-linear Satellite Channels

OpenAIRE

Piazza, Roberto; Shankar, Bhavani; Zenteno, Efrain; Ronnow, Daniel; Liolis, Kostantinos; Zimmer, Frank; Grasslin, Michael; Berheide, Tobias; Cioni, Stefano

2013-01-01

On-board joint power amplification of multiple-carrier DVB-S2 signals using a single High-Power Amplifier (HPA) is an emerging configuration that aims to reduce flight hardware and weight. However, effects specific to such a scenario degrade power and spectral efficiencies with increased Adjacent Channel Interference caused by non-linear characteristic of the HPA and power efficiency loss due to the increased Peak to Average Power Ratio (PAPR). The paper studies signal processing techniques ...

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.

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

International Nuclear Information System (INIS)

Oberman, C.

1972-01-01

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

Falsification of the ionic channel theory of hair cell transduction.

Science.gov (United States)

Rossetto, Michelangelo

2013-11-01

The hair cell provides the transduction of mechanical vibrations in the balance and acoustic sense of all vertebrates that swim, walk, or fly. The current theory places hair cell transduction in a mechanically controlled ion channel. Although the theory of a mechanical input modulating the flow of ions through an ion pore has been a useful tool, it is falsified by experimental data in the literature and can be definitively falsified by a proposed experiment.

Nonlinear mean field theory for nuclear matter and surface properties

International Nuclear Information System (INIS)

Boguta, J.; Moszkowski, S.A.

1983-01-01

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

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.

Theory of free-bound transitions in channeling radiation

International Nuclear Information System (INIS)

Saenz, A.W.; Nagl, A.; Uberall, H.

1988-01-01

On the basis of a single-string model, we derive formulas for the transition strengths of free-bound transitions of axially channeled electrons. We illustrate the theory by numerical calculations of these strengths for 3.5-MeV electrons in Si. Experimental evidence for such transitions has been obtained previously [J.U. Andersen et al., Nucl. Instrum. Methods 194, 209 (1982)] and is in good qualitative agreement with our calculations

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.

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

Coupled channel theory of pion--deuteron reaction applied to threshold scattering

International Nuclear Information System (INIS)

Mizutani, T.; Koltun, D.S.

1977-01-01

Scattering and absorption of pions by a nuclear target are treated together in a coupled channel theory. The theory is developed explicitly for the problem of pion scattering and absorption by a deuteron. The equations are presented in terms of the integral equations of three-body scattering theory. The method is then applied in an approximate from to calculate the contribution of pion absorption to the scattering length for pion--deuteron scattering. The sensitivity of the calculated results to the model assumptions and approximations is investigated

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

Mothers "Google It Up:" Extending Communication Channel Behavior in Diffusion of Innovations Theory.

Science.gov (United States)

Sundstrom, Beth

2016-01-01

This study employed qualitative methods, conducting 44 in-depth interviews with biological mothers of newborns to understand women's perceptions and use of new media, mass media, and interpersonal communication channels in relation to health issues. Findings contribute to theoretical and practical understandings of the role of communication channels in diffusion of innovations theory. In particular, this study provides a foundation for the use of qualitative research to advance applications of diffusion of innovations theory. Results suggest that participants resisted mass media portrayals of women's health. When faced with a health question, participants uniformly started with the Internet to "Google it up." Findings suggest new media comprise a new communication channel with new rules, serving the functions of both personal and impersonal influence. In particular, pregnancy and the postpartum period emerged as a time when campaign planners can access women in new ways online. As a result, campaign planners could benefit from introducing new ideas online and capitalizing on the strength of weak ties favored in new media. Results expand the innovativeness/needs paradox in diffusion of innovations theory by elaborating on the role of new media to reach underserved populations. These findings provide an opportunity to better understand patient information seeking through the lens of diffusion of innovations theory.

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...

A theory of burn-out in heated channels at low mass velocities

International Nuclear Information System (INIS)

Randles, J.

1963-01-01

At low coolant mass velocities the fraction by weight of vapour flowing out of heated channels can become extremely large (∼ 90%). Consequently, the dominating feature of burn-out at small flow rates is that it occurs at high vapour qualities. For such a high degree of evaporation, the induced turbulence is very strong and the liquid phase is dispersed into a spray of droplets. By the application of the first law of thermodynamics and some basic relationships of turbulence theory to this spray, it is shown how an expression for the critical heat flux can be derived. By comparing this expression with the data from burn-out measurements on uniformly heated channels, reasonably good agreement is obtained. It is demonstrated that eddy slip and channel geometry are extremely important in the determination of the level of turbulence in the droplet motion. Having thus established a reasonable degree of plausibility for the theory, it is applied to channels heated by a chopped cosine form of power distribution. The results indicate that the effect of the axial variation of the power on the burnout heat flux can be described in a simple manner. (author)

Linear stability analysis and nonlinear simulation of the channeling effect on viscous fingering instability in miscible displacement

Science.gov (United States)

Shahnazari, M. R.; Maleka Ashtiani, I.; Saberi, A.

2018-03-01

In this paper, the effect of channeling on viscous fingering instability of miscible displacement in porous media is studied. In fact, channeling is introduced as a solution to stabilize the viscous fingering instability. In this solution, narrow channels were placed next to the walls, and by considering an exponential function to model the channeling effect, a heterogeneous media is assumed. In linear stability analysis, the governing equations are transferred to Fourier space, and by introducing a novel numerical method, the transferred equations are analyzed. The growth rate based on the wave number diagram has been drawn up in three sections of the medium. It is found that the flow becomes more stable at the center and unstable along the walls when the permeability ratio is increased. Also when the permeability ratio is approximately equal to one, the channeling has no significant effect. In nonlinear simulations, by using stream function and vortices, new equations have been rewritten and it is shown that channeling has a profound effect on the growth of the fingers and mechanisms. In addition to the superposition of velocity vectors and concentration contours, the development of instability is investigated using the mixing length and sweep efficiency diagram. The results show that although channeling reduces instability, it increases the displacement process time.

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.

Analysis of Nonlinear Dispersion of a Pollutant Ejected by an External Source into a Channel Flow

Directory of Open Access Journals (Sweden)

T. Chinyoka

2010-01-01

Full Text Available This paper focuses on the transient analysis of nonlinear dispersion of a pollutant ejected by an external source into a laminar flow of an incompressible fluid in a channel. The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation, and the nonlinear governing equations of momentum and pollutant concentration are obtained. The problem is solved numerically using a semi-implicit finite difference method. Solutions are presented in graphical form and given in terms of fluid velocity, pollutant concentration, skin friction, and wall mass transfer rate for various parametric values. The model can be a useful tool for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water body.

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

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.

Channel-coupling theory of covalent bonding in H2: A further application of arrangement-channel quantum mechanics

International Nuclear Information System (INIS)

Levin, F.S.; Krueger, H.

1977-01-01

The dissociation energy D/sub e/ and the equilibrium proton-proton separation R/sub eq/ of H 2 are calculated using the methods of arrangement-channel quantum mechanics. This theory is the channel component version of the channel-coupling array approach to many-body scattering, applied to bound-state problems. In the approximation used herein, the wave function is identical to that of the classic Heitler-London-Sugiura valence-bond calculation, which gave D/sub e/ = 3.14 eV and R/sub eq/ = 1.65a 0 , values accurate to 34% and 17.8%, respectively. The present method yields D/sub e/ = 4.437 eV and R/sub eq/ approx. = 1.42a 0 , accurate to 6.5% and 1%, respectively. Some implications of these results are discussed

Random matrix theory of multi-antenna communications: the Ricean channel

International Nuclear Information System (INIS)

Moustakas, Aris L; Simon, Steven H

2005-01-01

The use of multi-antenna arrays in wireless communications through disordered media promises huge increases in the information transmission rate. It is therefore important to analyse the information capacity of such systems in realistic situations of microwave transmission, where the statistics of the transmission amplitudes (channel) may be coloured. Here, we present an approach that provides analytic expressions for the statistics, i.e. the moments of the distribution, of the mutual information for general Gaussian channel statistics. The mathematical method applies tools developed originally in the context of coherent wave propagation in disordered media, such as random matrix theory and replicas. Although it is valid formally for large antenna numbers, this approach produces extremely accurate results even for arrays with as few as two antennas. We also develop a method to analytically optimize over the input signal distribution, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel. The emphasis of this paper is on elucidating the novel mathematical methods used. We do this by analysing a specific case when the channel matrix is a complex Gaussian with arbitrary mean and unit covariance, which is usually called the Ricean channel

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

Electroosmotic flow in a rectangular channel with variable wall zeta-potential: comparison of numerical simulation with asymptotic theory.

Science.gov (United States)

Datta, Subhra; Ghosal, Sandip; Patankar, Neelesh A

2006-02-01

Electroosmotic flow in a straight micro-channel of rectangular cross-section is computed numerically for several situations where the wall zeta-potential is not constant but has a specified spatial variation. The results of the computation are compared with an earlier published asymptotic theory based on the lubrication approximation: the assumption that any axial variations take place on a long length scale compared to a characteristic channel width. The computational results are found to be in excellent agreement with the theory even when the scale of axial variations is comparable to the channel width. In the opposite limit when the wavelength of fluctuations is much shorter than the channel width, the lubrication theory fails to describe the solution either qualitatively or quantitatively. In this short wave limit the solution is well described by Ajdari's theory for electroosmotic flow between infinite parallel plates (Ajdari, A., Phys. Rev. E 1996, 53, 4996-5005.) The infinitely thin electric double layer limit is assumed in the theory as well as in the simulation.

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

Information transmission and recovery in neural communications channels

International Nuclear Information System (INIS)

Eguia, M. C.; Rabinovich, M. I.; Abarbanel, H. D. I.

2000-01-01

Biological neural communications channels transport environmental information from sensors through chains of active dynamical neurons to neural centers for decisions and actions to achieve required functions. These kinds of communications channels are able to create information and to transfer information from one time scale to the other because of the intrinsic nonlinear dynamics of the component neurons. We discuss a very simple neural information channel composed of sensory input in the form of a spike train that arrives at a model neuron, then moves through a realistic synapse to a second neuron where the information in the initial sensory signal is read. Our model neurons are four-dimensional generalizations of the Hindmarsh-Rose neuron, and we use a model of chemical synapse derived from first-order kinetics. The four-dimensional model neuron has a rich variety of dynamical behaviors, including periodic bursting, chaotic bursting, continuous spiking, and multistability. We show that, for many of these regimes, the parameters of the chemical synapse can be tuned so that information about the stimulus that is unreadable at the first neuron in the channel can be recovered by the dynamical activity of the synapse and the second neuron. Information creation by nonlinear dynamical systems that allow chaotic oscillations is familiar in their autonomous oscillations. It is associated with the instabilities that lead to positive Lyapunov exponents in their dynamical behavior. Our results indicate how nonlinear neurons acting as input/output systems along a communications channel can recover information apparently ''lost'' in earlier junctions on the channel. Our measure of information transmission is the average mutual information between elements, and because the channel is active and nonlinear, the average mutual information between the sensory source and the final neuron may be greater than the average mutual information at an earlier neuron in the channel. This

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...

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.

Developing and exploring a theory for the lateral erosion of bedrock channels for use in landscape evolution models

Directory of Open Access Journals (Sweden)

A. L. Langston

2018-01-01

Full Text Available Understanding how a bedrock river erodes its banks laterally is a frontier in geomorphology. Theories for the vertical incision of bedrock channels are widely implemented in the current generation of landscape evolution models. However, in general existing models do not seek to implement the lateral migration of bedrock channel walls. This is problematic, as modeling geomorphic processes such as terrace formation and hillslope–channel coupling depends on the accurate simulation of valley widening. We have developed and implemented a theory for the lateral migration of bedrock channel walls in a catchment-scale landscape evolution model. Two model formulations are presented, one representing the slow process of widening a bedrock canyon and the other representing undercutting, slumping, and rapid downstream sediment transport that occurs in softer bedrock. Model experiments were run with a range of values for bedrock erodibility and tendency towards transport- or detachment-limited behavior and varying magnitudes of sediment flux and water discharge in order to determine the role that each plays in the development of wide bedrock valleys. The results show that this simple, physics-based theory for the lateral erosion of bedrock channels produces bedrock valleys that are many times wider than the grid discretization scale. This theory for the lateral erosion of bedrock channel walls and the numerical implementation of the theory in a catchment-scale landscape evolution model is a significant first step towards understanding the factors that control the rates and spatial extent of wide bedrock valleys.

Developing and exploring a theory for the lateral erosion of bedrock channels for use in landscape evolution models

Science.gov (United States)

Langston, Abigail L.; Tucker, Gregory E.

2018-01-01

Understanding how a bedrock river erodes its banks laterally is a frontier in geomorphology. Theories for the vertical incision of bedrock channels are widely implemented in the current generation of landscape evolution models. However, in general existing models do not seek to implement the lateral migration of bedrock channel walls. This is problematic, as modeling geomorphic processes such as terrace formation and hillslope-channel coupling depends on the accurate simulation of valley widening. We have developed and implemented a theory for the lateral migration of bedrock channel walls in a catchment-scale landscape evolution model. Two model formulations are presented, one representing the slow process of widening a bedrock canyon and the other representing undercutting, slumping, and rapid downstream sediment transport that occurs in softer bedrock. Model experiments were run with a range of values for bedrock erodibility and tendency towards transport- or detachment-limited behavior and varying magnitudes of sediment flux and water discharge in order to determine the role that each plays in the development of wide bedrock valleys. The results show that this simple, physics-based theory for the lateral erosion of bedrock channels produces bedrock valleys that are many times wider than the grid discretization scale. This theory for the lateral erosion of bedrock channel walls and the numerical implementation of the theory in a catchment-scale landscape evolution model is a significant first step towards understanding the factors that control the rates and spatial extent of wide bedrock valleys.

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...

Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels

International Nuclear Information System (INIS)

Liu, Jinn-Liang; Eisenberg, Bob

2014-01-01

A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces between the particles, because they are both expensive and tricky to compute. We include the steric effect of ions and water molecules with nonuniform sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of water molecules in an inhomogeneous aqueous electrolyte. Including the finite volume of water and the voids between particles is an important new part of the theory presented here. Fermi like distributions of all particle species are derived from the volume exclusion of classical particles. Volume exclusion and the resulting saturation phenomena are especially important to describe the binding and permeation mechanisms of ions in a narrow channel pore. The Gibbs free energy of the Fermi distribution reduces to that of a Boltzmann distribution when these effects are not considered. The classical Gibbs entropy is extended to a new entropy form — called Gibbs-Fermi entropy — that describes mixing configurations of all finite size particles and voids in a thermodynamic system where microstates do not have equal probabilities. The PNPF model describes the dynamic flow of ions, water molecules, as well as voids with electric fields and protein charges. The model also provides a quantitative mean-field description of the charge/space competition mechanism of particles within the highly charged and crowded channel pore. The PNPF results are in good accord with experimental currents recorded in a 10 8 -fold range of Ca 2+ concentrations. The results illustrate the anomalous mole fraction effect, a signature of L-type calcium channels. Moreover, numerical results concerning water density, dielectric permittivity, void volume, and steric energy provide useful details to

Analysis of neutron cross sections using the coupled-channel theory

International Nuclear Information System (INIS)

Tanaka, Shigeya

1975-01-01

Fast neutron total and scattering cross sections calculated with the coupled-channel theory and the spherical optical model are compared with experimental data. The optical-potential parameters used in both the calculations were obtained from comparison of calculations with scattering data for 209 Bi. The calculations for total cross sections were made for thirty-five nuclides from 23 Na to 239 Pu in the energy range of 0.25 to 15 MeV, and good results were obtained with the coupled-channel calculations. The comparisons of the calculations with the elastic data for about twenty nuclides were made at incident energies of 8 and 14 MeV. In general, the coupled-channel calculations at 8 MeV have given better agreements with the experimental data than the spherical optical-model calculations. At 14 MeV, differences between both the calculations were small. The analysis was also made for the elastic and inelastic scattering by several nuclei such as Fe, Ni, 120 Sn, Pu in the low energy region, and good results have been given by the coupled-channel calculations. Thus, it is demonstrated that the coupled-channel calculations with one set of the optical parameters well reproduce the total and scattering cross sections over a wide energy and mass region. (auth.)

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.

More Than Flow: Revisiting the Theory of Four Channels of Flow

Directory of Open Access Journals (Sweden)

Ching-I Teng

2012-01-01

Full Text Available Flow (FCF theory has received considerable attention in recent decades. In addition to flow, FCF theory proposed three influential factors, that is, boredom, frustration, and apathy. While these factors have received relatively less attention than flow, Internet applications have grown exponentially, warranting a closer reexamination of the applicability of the FCF theory. Thus, this study tested the theory that high/low levels of skill and challenge lead to four channels of flow. The study sample included 253 online gamers who provided valid responses to an online survey. Analytical results support the FCF theory, although a few exceptions were noted. First, skill was insignificantly related to apathy, possibly because low-skill users can realize significant achievements to compensate for their apathy. Moreover, in contrast with the FCF theory, challenge was positively related to boredom, revealing that gamers become bored with difficult yet repetitive challenges. Two important findings suggest new directions for FCF theory.

Doublet channel neutron-deuteron scattering in leading order effective field theory

OpenAIRE

B. BlankleiderFlinders U.; J. Gegelia(INFN)

2015-01-01

The doublet channel neutron-deuteron scattering amplitude is calculated in leading order effective field theory (EFT). It is shown that this amplitude does not depend on a constant contact interaction three-body force. Satisfactory agreement with available data is obtained when only two-body forces are included.

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

Multi-channel conduction in redox-based resistive switch modelled using quantum point contact theory

Energy Technology Data Exchange (ETDEWEB)

Miranda, E., E-mail: enrique.miranda@uab.cat; Suñé, J. [Departament d' Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallés, Barcelona (Spain); Mehonic, A.; Kenyon, A. J. [Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE (United Kingdom)

2013-11-25

A simple analytic model for the electron transport through filamentary-type structures in Si-rich silica (SiO{sub x})-based resistive switches is proposed. The model is based on a mesoscopic description and is able to account for the linear and nonlinear components of conductance that arise from both fully and partially formed conductive channels spanning the dielectric film. Channels are represented by arrays of identical scatterers whose number and quantum transmission properties determine the current magnitude in the low and high resistance states. We show that the proposed model not only reproduces the experimental current-voltage (I-V) characteristics but also the normalized differential conductance (dln(I)/dln(V)-V) curves of devices under test.

Nonlinear concentration gradients regulated by the width of channels for observation of half maximal inhibitory concentration (IC50) of transporter proteins.

Science.gov (United States)

Abe, Yuta; Kamiya, Koki; Osaki, Toshihisa; Sasaki, Hirotaka; Kawano, Ryuji; Miki, Norihisa; Takeuchi, Shoji

2015-08-21

This paper describes a simple microfluidic device that can generate nonlinear concentration gradients. We changed the "width" of channels that can drastically shorten the total microfluidic channel length and simplify the microfluidic network design rather than the "length" of channels. The logarithmic concentration gradients generated by the device were in good agreement with those obtained by simulation. Using this device, we evaluated a probable IC50 value of the ABC transporter proteins by the competitive transport assays at five different logarithmic concentrations. This probable IC50 value was in good agreement with an IC50 value (0.92 μM) obtained at the diluted concentrations of seven points.

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.

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.

Agency Theory, Futures Markets and Risk Shifting in Commodity Marketing Channels

NARCIS (Netherlands)

Kuwornu, J.K.M.; Kuiper, W.E.; Pennings, J.M.E.; Meulenberg, M.T.G.

2004-01-01

This paper applies agency theory to access risk shifting between the principal (marketing firms) and the agent (farmers) in a food marketing channel. It compares the case in which there is a futures market available for the risk-averse agents with the case in which there is no futures trading. The

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.

Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium

Directory of Open Access Journals (Sweden)

Q. Hussain

2018-06-01

Full Text Available The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study. Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters. Keywords: Nonlinear thermal radiation, Variable viscosity, Porous medium, Soret and Dufour effects, Peristalsis

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.

ac electrokinetic micropumps: The effect of geometrical confinement, Faradaic current injection, and nonlinear surface capacitance

DEFF Research Database (Denmark)

Olesen, Laurits Højgaard; Bruus, Henrik; Ajdari, A.

2006-01-01

therefore extend the latter theories to account for three experimentally relevant effects: (i) vertical confinement of the pumping channel, (ii) Faradaic currents from electrochemical reactions at the electrodes, and (iii) nonlinear surface capacitance of the Debye layer. We report here that these effects......Recent experiments have demonstrated that ac electrokinetic micropumps permit integrable, local, and fast pumping (velocities similar to mm/s) with low driving voltage of a few volts only. However, they also displayed many quantitative and qualitative discrepancies with existing theories. We...

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.

Toward nonlinear magnonics: Intensity-dependent spin-wave switching in insulating side-coupled magnetic stripes

Science.gov (United States)

Sadovnikov, A. V.; Odintsov, S. A.; Beginin, E. N.; Sheshukova, S. E.; Sharaevskii, Yu. P.; Nikitov, S. A.

2017-10-01

We demonstrate that the nonlinear spin-wave transport in two laterally parallel magnetic stripes exhibit the intensity-dependent power exchange between the adjacent spin-wave channels. By the means of Brillouin light scattering technique, we investigate collective nonlinear spin-wave dynamics in the presence of magnetodipolar coupling. The nonlinear intensity-dependent effect reveals itself in the spin-wave mode transformation and differential nonlinear spin-wave phase shift in each adjacent magnetic stripe. The proposed analytical theory, based on the coupled Ginzburg-Landau equations, predicts the geometry design involving the reduction of power requirement to the all-magnonic switching. A very good agreement between calculation and experiment was found. In addition, a micromagnetic and finite-element approach has been independently used to study the nonlinear behavior of spin waves in adjacent stripes and the nonlinear transformation of spatial profiles of spin-wave modes. Our results show that the proposed spin-wave coupling mechanism provides the basis for nonlinear magnonic circuits and opens the perspectives for all-magnonic computing architecture.

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.

Spatial channel theory: A technique for determining the directional flow of radiation through reactor systems

International Nuclear Information System (INIS)

Williams, M.L.; Engle, W.W.

1977-01-01

A method is introduced for determining streaming paths through a non-multiplying medium. The concepts of a ''response continuum'' and a pseudo-particle called a contribution are developed to describe the spatial channels through which response flows from a source to a detector. An example application of channel theory to complex shield analysis is cited

Application of the pertubation theory to a two channels model for sensitivity calculations in PWR cores

International Nuclear Information System (INIS)

Oliveira, A.C.J.G. de; Andrade Lima, F.R. de

1989-01-01

The present work is an application of the perturbation theory (Matricial formalism) to a simplified two channels model, for sensitivity calculations in PWR cores. Expressions for some sensitivity coefficients of thermohydraulic interest were developed from the proposed model. The code CASNUR.FOR was written in FORTRAN to evaluate these sensitivity coefficients. The comparison between results obtained from the matrical formalism of pertubation theory with those obtained directly from the two channels model, makes evident the efficiency and potentiality of this perturbation method for nuclear reactor cores sensitivity calculations. (author) [pt

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

Science.gov (United States)

Yaylali, I; Koçak, H; Jayakar, P

1996-07-01

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

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…

Nonlocal theory of electromagnetic wave decay into two electromagnetic waves in a rippled density plasma channel

International Nuclear Information System (INIS)

Sati, Priti; Tripathi, V. K.

2012-01-01

Parametric decay of a large amplitude electromagnetic wave into two electromagnetic modes in a rippled density plasma channel is investigated. The channel is taken to possess step density profile besides a density ripple of axial wave vector. The density ripple accounts for the momentum mismatch between the interacting waves and facilitates nonlinear coupling. For a given pump wave frequency, the requisite ripple wave number varies only a little w.r.t. the frequency of the low frequency decay wave. The radial localization of electromagnetic wave reduces the growth rate of the parametric instability. The growth rate decreases with the frequency of low frequency electromagnetic wave.

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

Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium

Science.gov (United States)

Hussain, Q.; Latif, T.; Alvi, N.; Asghar, S.

2018-06-01

The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study). Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters.

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.

Resource theory of non-Gaussian operations

Science.gov (United States)

Zhuang, Quntao; Shor, Peter W.; Shapiro, Jeffrey H.

2018-05-01

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.

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...

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)

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.

Digital nonlinearity compensation in high-capacity optical communication systems considering signal spectral broadening effect.

Science.gov (United States)

Xu, Tianhua; Karanov, Boris; Shevchenko, Nikita A; Lavery, Domaniç; Liga, Gabriele; Killey, Robert I; Bayvel, Polina

2017-10-11

Nyquist-spaced transmission and digital signal processing have proved effective in maximising the spectral efficiency and reach of optical communication systems. In these systems, Kerr nonlinearity determines the performance limits, and leads to spectral broadening of the signals propagating in the fibre. Although digital nonlinearity compensation was validated to be promising for mitigating Kerr nonlinearities, the impact of spectral broadening on nonlinearity compensation has never been quantified. In this paper, the performance of multi-channel digital back-propagation (MC-DBP) for compensating fibre nonlinearities in Nyquist-spaced optical communication systems is investigated, when the effect of signal spectral broadening is considered. It is found that accounting for the spectral broadening effect is crucial for achieving the best performance of DBP in both single-channel and multi-channel communication systems, independent of modulation formats used. For multi-channel systems, the degradation of DBP performance due to neglecting the spectral broadening effect in the compensation is more significant for outer channels. Our work also quantified the minimum bandwidths of optical receivers and signal processing devices to ensure the optimal compensation of deterministic nonlinear distortions.

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; �...

Correlation functions with fusion-channel multiplicity in W3 Toda field theory

International Nuclear Information System (INIS)

Belavin, Vladimir; Estienne, Benoit; Foda, Omar; Santachiara, Raoul

2016-01-01

Current studies of W N Toda field theory focus on correlation functions such that the W N highest-weight representations in the fusion channels are multiplicity-free. In this work, we study W 3 Toda 4-point functions with multiplicity in the fusion channel. The conformal blocks of these 4-point functions involve matrix elements of a fully-degenerate primary field with a highest-weight in the adjoint representation of sl 3 , and a fully-degenerate primary field with a highest-weight in the fundamental representation of sl 3 . We show that, when the fusion rules do not involve multiplicities, the matrix elements of the fully-degenerate adjoint field, between two arbitrary descendant states, can be computed explicitly, on equal footing with the matrix elements of the semi-degenerate fundamental field. Using null-state conditions, we obtain a fourth-order Fuchsian differential equation for the conformal blocks. Using Okubo theory, we show that, due to the presence of multiplicities, this differential equation belongs to a class of Fuchsian equations that is different from those that have appeared so far in W N theories. We solve this equation, compute its monodromy group, and construct the monodromy-invariant correlation functions. This computation shows in detail how the ambiguities that are caused by the presence of multiplicities are fixed by requiring monodromy-invariance.

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...

Nonlinear dynamic range transformation in visual communication channels.

Science.gov (United States)

Alter-Gartenberg, R

1996-01-01

The article evaluates nonlinear dynamic range transformation in the context of the end-to-end continuous-input/discrete processing/continuous-display imaging process. Dynamic range transformation is required when we have the following: (i) the wide dynamic range encountered in nature is compressed into the relatively narrow dynamic range of the display, particularly for spatially varying irradiance (e.g., shadow); (ii) coarse quantization is expanded to the wider dynamic range of the display; and (iii) nonlinear tone scale transformation compensates for the correction in the camera amplifier.

Dynamic statistical information theory

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel

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.

Theory, analysis and design of RF interferometric sensors

CERN Document Server

Nguyen, Cam

2012-01-01

Theory, Analysis and Design of RF Interferometric Sensors presents the theory, analysis and design of RF interferometric sensors. RF interferometric sensors are attractive for various sensing applications that require every fine resolution and accuracy as well as fast speed. The book also presents two millimeter-wave interferometric sensors realized using RF integrated circuits. The developed millimeter-wave homodyne sensor shows sub-millimeter resolution in the order of 0.05 mm without correction for the non-linear phase response of the sensor's quadrature mixer. The designed millimeter-wave double-channel homodyne sensor provides a resolution of only 0.01 mm, or 1/840th of the operating wavelength, and can inherently suppress the non-linearity of the sensor's quadrature mixer. The experimental results of displacement and velocity measurement are presented as a way to demonstrate the sensing ability of the RF interferometry and to illustrate its many possible applications in sensing. The book is succinct, ye...

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

Theory of the ion-channel laser

International Nuclear Information System (INIS)

Whittum, D.H.

1990-09-01

A relativistic electron beam propagating through a plasma in the ion-focussed regime exhibits an electromagnetic instability with peak growth rate near a resonant frequency ω∼2 γ 2 ωβ, where γ is the Lorentz factor and ωβ is the betatron frequency. The physical basis for this instability is that an ensemble of relativistic simple harmonic oscillators, weakly driven by an electromagnetic wave, will lose energy to the wave through axial bunching. This ''bunching'' corresponds to the development of an rf component in the beam current, and a coherent centroid oscillation. The subject of this thesis is the theory of a laser capitalizing on this electromagnetic instability. A historical perspective is offered. The basic features of relativistic electron beam propagation in the ion-focussed regime are reviewed. The ion-channel laser (ICL) instability is explored theoretically through an eikonal formalism, analgous to the ''KMR'' formalism for the free-electron laser (FEL). The dispersion relation is derived, and the dependence of growth rate on three key parameters is explored. Finite temperature effects are assessed. From this work it is found that the typical gain length for amplification is longer than the Rayleigh length and we go on to consider three mechanisms which will tend to guide waveguide. First, we consider the effect of the ion channel as a dielectric waveguide. We consider next the use of a conducting waveguide, appropriate for a microwave amplifier. Finally, we examine a form of ''optical guiding'' analgous to that found in the FEL. The eikonal formalism is used to model numerically the instability through and beyond saturation. Results are compared with the numerical simulation of the full equations of motion, and with the analytic scalings. The analytical requirement on detuning spread is confirmed

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.

Mapping nonlinear shallow-water tides: a look at the past and future

DEFF Research Database (Denmark)

Andersen, Ole Baltazar; Egbert, G.D.; Erofeeva, S.Y.

2006-01-01

advanced by the pioneering researches of Christian Le Provost who employed analytical theory, physical modeling, and numerical modeling in many extensive studies, especially of the tides of the English Channel. Le Provost's complementary work with satellite altimetry motivates our attempts to merge...... these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M-4 tide over the northwest European Shelf. Future applications of altimetry...

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 ...

The Importance of Non-Linearity on Turbulent Fluxes

DEFF Research Database (Denmark)

Rokni, Masoud

2007-01-01

Two new non-linear models for the turbulent heat fluxes are derived and developed from the transport equation of the scalar passive flux. These models are called as non-linear eddy diffusivity and non-linear scalar flux. The structure of these models is compared with the exact solution which...... is derived from the Cayley-Hamilton theorem and contains a three term-basis plus a non-linear term due to scalar fluxes. In order to study the performance of the model itself, all other turbulent quantities are taken from a DNS channel flow data-base and thus the error source has been minimized. The results...... are compared with the DNS channel flow and good agreement is achieved. It has been shown that the non-linearity parts of the models are important to capture the true path of the streamwise scalar fluxes. It has also been shown that one of model constant should have negative sign rather than positive, which had...

Correlation functions with fusion-channel multiplicity in W{sub 3} Toda field theory

Energy Technology Data Exchange (ETDEWEB)

Belavin, Vladimir [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky Avenue 53, 119991 Moscow (Russian Federation); Department of Quantum Physics, Institute for Information Transmission Problems,Bolshoy Karetny per. 19, 127994 Moscow (Russian Federation); Estienne, Benoit [LPTHE, CNRS and Université Pierre et Marie Curie,Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Foda, Omar [School of Mathematics and Statistics, University of Melbourne,Parkville, Victoria 3010 (Australia); Santachiara, Raoul [LPTMS, CNRS (UMR 8626), Université Paris-Saclay,15 rue Georges Clémenceau, 91405 Orsay (France)

2016-06-22

Current studies of W{sub N} Toda field theory focus on correlation functions such that the W{sub N} highest-weight representations in the fusion channels are multiplicity-free. In this work, we study W{sub 3} Toda 4-point functions with multiplicity in the fusion channel. The conformal blocks of these 4-point functions involve matrix elements of a fully-degenerate primary field with a highest-weight in the adjoint representation of sl{sub 3}, and a fully-degenerate primary field with a highest-weight in the fundamental representation of sl{sub 3}. We show that, when the fusion rules do not involve multiplicities, the matrix elements of the fully-degenerate adjoint field, between two arbitrary descendant states, can be computed explicitly, on equal footing with the matrix elements of the semi-degenerate fundamental field. Using null-state conditions, we obtain a fourth-order Fuchsian differential equation for the conformal blocks. Using Okubo theory, we show that, due to the presence of multiplicities, this differential equation belongs to a class of Fuchsian equations that is different from those that have appeared so far in W{sub N} theories. We solve this equation, compute its monodromy group, and construct the monodromy-invariant correlation functions. This computation shows in detail how the ambiguities that are caused by the presence of multiplicities are fixed by requiring monodromy-invariance.

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)

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Science.gov (United States)

Clark, S. E.; Oishi, Jeffrey S.

2017-05-01

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg-Landau equation. We further find that the Ginzburg-Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Energy Technology Data Exchange (ETDEWEB)

Clark, S. E. [Department of Astronomy, Columbia University, New York, NY 10027 (United States); Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu [Department of Physics and Astronomy, Bates College, Lewiston, ME 04240 (United States)

2017-05-20

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg–Landau equation. We further find that the Ginzburg–Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg–Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

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.

The role of different linear and non-linear channels of relaxation in scintillator non-proportionality

Energy Technology Data Exchange (ETDEWEB)

Bizarri, G.; Moses, W.W. [Lawrence Berkeley Laboratory, Berkeley, CA 94720-8119 (United States); Singh, J. [Faculty of EHS, B-41, Charles Darwin University, Darwin NT 0909 (Australia); Vasil' ev, A.N., E-mail: anvasiliev@rambler.r [Institute of Nuclear Physics, Moscow State University, Moscow 119991 (Russian Federation); Williams, R.T. [Department of Physics, Wake Forest University, Winston-Salem, NC 27109 (United States)

2009-12-15

The non-proportional dependence of a scintillator's light yield on primary particle energy is believed to be influenced crucially by the interplay of non-linear kinetic terms in the radiative and non-radiative decay of excitations versus locally deposited excitation density. A calculation of energy deposition, -dE/dx, along the electron track for NaI is presented for an energy range from several electron-volt to 1 MeV. Such results can be used to specify an initial excitation distribution, if diffusion is neglected. An exactly solvable two-channel (exciton and hole(electron)) model containing 1st and 2nd order kinetic terms is constructed and used to illustrate important features seen in non-proportional light-yield curves, including a dependence on pulse shaping (detection gate width).

The role of different linear and non-linear channels of relaxation in scintillator non-proportionality

International Nuclear Information System (INIS)

Bizarri, G.; Moses, W.W.; Singh, J.; Vasil'ev, A.N.; Williams, R.T.

2009-01-01

The non-proportional dependence of a scintillator's light yield on primary particle energy is believed to be influenced crucially by the interplay of non-linear kinetic terms in the radiative and non-radiative decay of excitations versus locally deposited excitation density. A calculation of energy deposition, -dE/dx, along the electron track for NaI is presented for an energy range from several electron-volt to 1 MeV. Such results can be used to specify an initial excitation distribution, if diffusion is neglected. An exactly solvable two-channel (exciton and hole(electron)) model containing 1st and 2nd order kinetic terms is constructed and used to illustrate important features seen in non-proportional light-yield curves, including a dependence on pulse shaping (detection gate width).

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.

Siegert pseudostate formulation of scattering theory: Nonzero angular momenta in the one-channel case

International Nuclear Information System (INIS)

Batishchev, Pavel A.; Tolstikhin, Oleg I.

2007-01-01

The Siegert pseudostate (SPS) formulation of scattering theory, originally developed by Tolstikhin, Ostrovsky, and Nakamura [Phys. Rev. A, 58, 2077 (1998)] for s-wave scattering in a spherically symmetric finite-range potential, is generalized to nonzero angular momenta. The orthogonality and completeness properties of SPSs are established and SPS expansions for the outgoing-wave Green's function, physical states, and scattering matrix are obtained. The present formulation completes the theory of SPSs in the one-channel case, making its application to three-dimensional problems possible. The results are illustrated by calculations for several model potentials

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.

Shear and shearless Lagrangian structures in compound channels

Science.gov (United States)

Enrile, F.; Besio, G.; Stocchino, A.

2018-03-01

Transport processes in a physical model of a natural stream with a composite cross-section (compound channel) are investigated by means of a Lagrangian analysis based on nonlinear dynamical system theory. Two-dimensional free surface Eulerian experimental velocity fields of a uniform flow in a compound channel form the basis for the identification of the so-called Lagrangian Coherent Structures. Lagrangian structures are recognized as the key features that govern particle trajectories. We seek for two particular class of Lagrangian structures: Shear and shearless structures. The former are generated whenever the shear dominates the flow whereas the latter behave as jet-cores. These two type of structures are detected as ridges and trenches of the Finite-Time Lyapunov Exponents fields, respectively. Besides, shearlines computed applying the geodesic theory of transport barriers mark Shear Lagrangian Coherent Structures. So far, the detection of these structures in real experimental flows has not been deeply investigated. Indeed, the present results obtained in a wide range of the controlling parameters clearly show a different behaviour depending on the shallowness of the flow. Shear and Shearless Lagrangian Structures detected from laboratory experiments clearly appear as the flow develops in shallow conditions. The presence of these Lagrangian Structures tends to fade in deep flow conditions.

Gravity currents in rotating channels. Part 1. Steady-state theory

Science.gov (United States)

Hacker, J. N.; Linden, P. F.

2002-04-01

A theory is developed for the speed and structure of steady-state non-dissipative gravity currents in rotating channels. The theory is an extension of that of Benjamin (1968) for non-rotating gravity currents, and in a similar way makes use of the steady-state and perfect-fluid (incompressible, inviscid and immiscible) approximations, and supposes the existence of a hydrostatic ‘control point’ in the current some distance away from the nose. The model allows for fully non-hydrostatic and ageostrophic motion in a control volume V ahead of the control point, with the solution being determined by the requirements, consistent with the perfect-fluid approximation, of energy and momentum conservation in V, as expressed by Bernoulli's theorem and a generalized flow-force balance. The governing parameter in the problem, which expresses the strength of the background rotation, is the ratio W = B/R, where B is the channel width and R = (g[prime prime or minute]H)1/2/f is the internal Rossby radius of deformation based on the total depth of the ambient fluid H. Analytic solutions are determined for the particular case of zero front-relative flow within the gravity current. For each value of W there is a unique non-dissipative two-layer solution, and a non-dissipative one-layer solution which is specified by the value of the wall-depth h0. In the two-layer case, the non-dimensional propagation speed c = cf(g[prime prime or minute]H)[minus sign]1/2 increases smoothly from the non-rotating value of 0.5 as W increases, asymptoting to unity for W [rightward arrow] [infty infinity]. The gravity current separates from the left-hand wall of the channel at W = 0.67 and thereafter has decreasing width. The depth of the current at the right-hand wall, h0, increases, reaching the full depth at W = 1.90, after which point the interface outcrops on both the upper and lower boundaries, with the distance over which the interface slopes being 0.881R. In the one-layer case, the wall

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

Science.gov (United States)

Schmidt, Patrick; Ó Náraigh, Lennon; Lucquiaud, Mathieu; Valluri, Prashant

2016-04-01

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

International Nuclear Information System (INIS)

Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant; Ó Náraigh, Lennon

2016-01-01

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the

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...

Non-linear osmosis

Science.gov (United States)

Diamond, Jared M.

1966-01-01

1. The relation between osmotic gradient and rate of osmotic water flow has been measured in rabbit gall-bladder by a gravimetric procedure and by a rapid method based on streaming potentials. Streaming potentials were directly proportional to gravimetrically measured water fluxes. 2. As in many other tissues, water flow was found to vary with gradient in a markedly non-linear fashion. There was no consistent relation between the water permeability and either the direction or the rate of water flow. 3. Water flow in response to a given gradient decreased at higher osmolarities. The resistance to water flow increased linearly with osmolarity over the range 186-825 m-osM. 4. The resistance to water flow was the same when the gall-bladder separated any two bathing solutions with the same average osmolarity, regardless of the magnitude of the gradient. In other words, the rate of water flow is given by the expression (Om — Os)/[Ro′ + ½k′ (Om + Os)], where Ro′ and k′ are constants and Om and Os are the bathing solution osmolarities. 5. Of the theories advanced to explain non-linear osmosis in other tissues, flow-induced membrane deformations, unstirred layers, asymmetrical series-membrane effects, and non-osmotic effects of solutes could not explain the results. However, experimental measurements of water permeability as a function of osmolarity permitted quantitative reconstruction of the observed water flow—osmotic gradient curves. Hence non-linear osmosis in rabbit gall-bladder is due to a decrease in water permeability with increasing osmolarity. 6. The results suggest that aqueous channels in the cell membrane behave as osmometers, shrinking in concentrated solutions of impermeant molecules and thereby increasing membrane resistance to water flow. A mathematical formulation of such a membrane structure is offered. PMID:5945254

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...

Flow rate-pressure drop relation for deformable shallow microfluidic channels

Science.gov (United States)

Christov, Ivan C.; Cognet, Vincent; Shidhore, Tanmay C.; Stone, Howard A.

2018-04-01

Laminar flow in devices fabricated from soft materials causes deformation of the passage geometry, which affects the flow rate--pressure drop relation. For a given pressure drop, in channels with narrow rectangular cross-section, the flow rate varies as the cube of the channel height, so deformation can produce significant quantitative effects, including nonlinear dependence on the pressure drop [{Gervais, T., El-Ali, J., G\\"unther, A. \\& Jensen, K.\\ F.}\\ 2006 Flow-induced deformation of shallow microfluidic channels.\\ \\textit{Lab Chip} \\textbf{6}, 500--507]. Gervais et. al. proposed a successful model of the deformation-induced change in the flow rate by heuristically coupling a Hookean elastic response with the lubrication approximation for Stokes flow. However, their model contains a fitting parameter that must be found for each channel shape by performing an experiment. We present a perturbation approach for the flow rate--pressure drop relation in a shallow deformable microchannel using the theory of isotropic quasi-static plate bending and the Stokes equations under a lubrication approximation (specifically, the ratio of the channel's height to its width and of the channel's height to its length are both assumed small). Our result contains no free parameters and confirms Gervais et. al.'s observation that the flow rate is a quartic polynomial of the pressure drop. The derived flow rate--pressure drop relation compares favorably with experimental measurements.

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...

Nonlinear dynamic effects in a two-wave CO2 laser

International Nuclear Information System (INIS)

Gorobets, V A; Kozlov, K V; Kuntsevich, B F; Petukhov, V O

1999-01-01

Theoretical and experimental investigations were made of nonlinear dynamic regimes of the operation of a two-wave CO 2 laser with cw excitation in an electric discharge and loss modulation in one of the channels. Nonlinear amplitude - frequency characteristics of each of the laser channels have two low-frequency resonance spikes, associated with forced linear oscillations of two coupled oscillators, and high-frequency spikes, corresponding to doubling of the period of the output radiation oscillations. At low loss-modulation frequencies the intensity oscillations of the output radiation in the coupled channels are in antiphase, whereas at high modulation frequencies the dynamics is cophasal. Nonlinear dynamic effects, such as doubling of the period and of the repetition frequency of the pulses and chaotic oscillations of the output radiation intensity, are observed for certain system parameters. (control of laser radiation parameters)

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...

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

Stage-discharge relationship in tidal channels

Science.gov (United States)

Kearney, W. S.; Mariotti, G.; Deegan, L.; Fagherazzi, S.

2016-12-01

Long-term records of the flow of water through tidal channels are essential to constrain the budgets of sediments and biogeochemical compounds in salt marshes. Statistical models which relate discharge to water level allow the estimation of such records from more easily obtained records of water stage in the channel. While there is clearly structure in the stage-discharge relationship, nonlinearity and nonstationarity of the relationship complicates the construction of statistical stage-discharge models with adequate performance for discharge estimation and uncertainty quantification. Here we compare four different types of stage-discharge models, each of which is designed to capture different characteristics of the stage-discharge relationship. We estimate and validate each of these models on a two-month long time series of stage and discharge obtained with an Acoustic Doppler Current Profiler in a salt marsh channel. We find that the best performance is obtained by models which account for the nonlinear and time-varying nature of the stage-discharge relationship. Good performance can also be obtained from a simplified version of these models which approximates the fully nonlinear and time-varying models with a piecewise linear formulation.

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.

Applicability of cable theory to vascular conducted responses.

Science.gov (United States)

Hald, Bjørn Olav; Jensen, Lars Jørn; Sørensen, Preben Graae; Holstein-Rathlou, Niels-Henrik; Jacobsen, Jens Christian Brings

2012-03-21

Conduction processes in the vasculature have traditionally been described using cable theory, i.e., locally induced signals decaying passively along the arteriolar wall. The decay is typically quantified using the steady-state length-constant, λ, derived from cable theory. However, the applicability of cable theory to blood vessels depends on assumptions that are not necessarily fulfilled in small arteries and arterioles. We have employed a morphologically and electrophysiologically detailed mathematical model of a rat mesenteric arteriole to investigate if the assumptions hold and whether λ adequately describes simulated conduction profiles. We find that several important cable theory assumptions are violated when applied to small blood vessels. However, the phenomenological use of a length-constant from a single exponential function is a good measure of conduction length. Hence, λ should be interpreted as a descriptive measure and not in light of cable theory. Determination of λ using cable theory assumes steady-state conditions. In contrast, using the model it is possible to probe how conduction behaves before steady state is achieved. As ion channels have time-dependent activation and inactivation, the conduction profile changes considerably during this dynamic period with an initially longer spread of current. This may have implications in relation to explaining why different agonists have different conduction properties. Also, it illustrates the necessity of using and developing models that handle the nonlinearity of ion channels. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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

A Vertical Channel Model of Molecular Communication based on Alcohol Molecules

Directory of Open Access Journals (Sweden)

Pengfei Lu

2016-05-01

Full Text Available The study of Molecular Communication(MC is more and more prevalence, and channel model of MC plays an important role in the MC System. Since different propagation environment and modulation techniques produce different channel model, most of the research about MC are in horizontal direction,but in nature the communications between nano machines are in short range and some of the information transportation are in the vertical direction, such as transpiration of plants, biological pump in ocean, and blood transportation from heart to brain. Therefore, this paper we propose a vertical channel model which nano-machines communicate with each other in the vertical direction based on pure diffusion. We rst propose a vertical molecular communication model, we mainly considered the gravity as the factor, though the channel model is also affected by other main factors, such as the ow of the medium, the distance between the transmitter and the receiver, the delay or sensitivity of the transmitter and the receiver. Secondly, we set up a test-bed for this vertical channel model, in order to verify the difference between the theory result and the experiment data. At last, we use the data we get from the experiment and the non-linear least squares method to get the parameters to make our channel model more accurate.

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 Ballistic Transport in an Atomically Thin Material.

Science.gov (United States)

Boland, Mathias J; Sundararajan, Abhishek; Farrokhi, M Javad; Strachan, Douglas R

2016-01-26

Ultrashort devices that incorporate atomically thin components have the potential to be the smallest electronics. Such extremely scaled atomically thin devices are expected to show ballistic nonlinear behavior that could make them tremendously useful for ultrafast applications. While nonlinear diffusive electron transport has been widely reported, clear evidence for intrinsic nonlinear ballistic transport in the growing array of atomically thin conductors has so far been elusive. Here we report nonlinear electron transport of an ultrashort single-layer graphene channel that shows quantitative agreement with intrinsic ballistic transport. This behavior is shown to be distinctly different than that observed in similarly prepared ultrashort devices consisting, instead, of bilayer graphene channels. These results suggest that the addition of only one extra layer of an atomically thin material can make a significant impact on the nonlinear ballistic behavior of ultrashort devices, which is possibly due to the very different chiral tunneling of their charge carriers. The fact that we observe the nonlinear ballistic response at room temperature, with zero applied magnetic field, in non-ultrahigh vacuum conditions and directly on a readily accessible oxide substrate makes the nanogap technology we utilize of great potential for achieving extremely scaled high-speed atomically thin devices.

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.

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.

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.

SYN3D: a single-channel, spatial flux synthesis code for diffusion theory calculations

Energy Technology Data Exchange (ETDEWEB)

Adams, C. H.

1976-07-01

This report is a user's manual for SYN3D, a computer code which uses single-channel, spatial flux synthesis to calculate approximate solutions to two- and three-dimensional, finite-difference, multigroup neutron diffusion theory equations. SYN3D is designed to run in conjunction with any one of several one- and two-dimensional, finite-difference codes (required to generate the synthesis expansion functions) currently being used in the fast reactor community. The report describes the theory and equations, the use of the code, and the implementation on the IBM 370/195 and CDC 7600 of the version of SYN3D available through the Argonne Code Center.

SYN3D: a single-channel, spatial flux synthesis code for diffusion theory calculations

International Nuclear Information System (INIS)

Adams, C.H.

1976-07-01

This report is a user's manual for SYN3D, a computer code which uses single-channel, spatial flux synthesis to calculate approximate solutions to two- and three-dimensional, finite-difference, multigroup neutron diffusion theory equations. SYN3D is designed to run in conjunction with any one of several one- and two-dimensional, finite-difference codes (required to generate the synthesis expansion functions) currently being used in the fast reactor community. The report describes the theory and equations, the use of the code, and the implementation on the IBM 370/195 and CDC 7600 of the version of SYN3D available through the Argonne Code Center

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 Algorithms for Channel Equalization and Map Symbol Detection.

Science.gov (United States)

Giridhar, K.

The transfer of information through a communication medium invariably results in various kinds of distortion to the transmitted signal. In this dissertation, a feed -forward neural network-based equalizer, and a family of maximum a posteriori (MAP) symbol detectors are proposed for signal recovery in the presence of intersymbol interference (ISI) and additive white Gaussian noise. The proposed neural network-based equalizer employs a novel bit-mapping strategy to handle multilevel data signals in an equivalent bipolar representation. It uses a training procedure to learn the channel characteristics, and at the end of training, the multilevel symbols are recovered from the corresponding inverse bit-mapping. When the channel characteristics are unknown and no training sequences are available, blind estimation of the channel (or its inverse) and simultaneous data recovery is required. Convergence properties of several existing Bussgang-type blind equalization algorithms are studied through computer simulations, and a unique gain independent approach is used to obtain a fair comparison of their rates of convergence. Although simple to implement, the slow convergence of these Bussgang-type blind equalizers make them unsuitable for many high data-rate applications. Rapidly converging blind algorithms based on the principle of MAP symbol-by -symbol detection are proposed, which adaptively estimate the channel impulse response (CIR) and simultaneously decode the received data sequence. Assuming a linear and Gaussian measurement model, the near-optimal blind MAP symbol detector (MAPSD) consists of a parallel bank of conditional Kalman channel estimators, where the conditioning is done on each possible data subsequence that can convolve with the CIR. This algorithm is also extended to the recovery of convolutionally encoded waveforms in the presence of ISI. Since the complexity of the MAPSD algorithm increases exponentially with the length of the assumed CIR, a suboptimal

Channel perceptions and usage: beyond media richness factors

NARCIS (Netherlands)

Pieterson, Willem Jan; Teerling, Marije; Ebbers, Wolfgang E.; Wimmer, Maria A.; Scholl, Hans J.; Ferro, Enrico

2008-01-01

In this paper, we asses how service channel perceptions affect channel choice and channel usage. Building on communication theories, such as the Media Richness Theory, we explore how different channel characteristics are perceived by citizens in a Dutch governmental service chain. The results of our

Channel Capacity Calculation at Large SNR and Small Dispersion within Path-Integral Approach

Science.gov (United States)

Reznichenko, A. V.; Terekhov, I. S.

2018-04-01

We consider the optical fiber channel modelled by the nonlinear Shrödinger equation with additive white Gaussian noise. Using Feynman path-integral approach for the model with small dispersion we find the first nonzero corrections to the conditional probability density function and the channel capacity estimations at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity in small dimensionless dispersion parameter is quadratic and positive therefore increasing the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region. Also for small dispersion case we find the analytical expressions for simple correlators of the output signals in our noisy channel.

Nonlinear dynamics of two-phase flow

International Nuclear Information System (INIS)

Rizwan-uddin

1986-01-01

Unstable flow conditions can occur in a wide variety of laboratory and industry equipment that involve two-phase flow. Instabilities in industrial equipment, which include boiling water reactor (BWR) cores, steam generators, heated channels, cryogenic fluid heaters, heat exchangers, etc., are related to their nonlinear dynamics. These instabilities can be of static (Ledinegg instability) or dynamic (density wave oscillations) type. Determination of regions in parameters space where these instabilities can occur and knowledge of system dynamics in or near these regions is essential for the safe operation of such equipment. Many two-phase flow engineering components can be modeled as heated channels. The set of partial differential equations that describes the dynamics of single- and two-phase flow, for the special case of uniform heat flux along the length of the channel, can be reduced to a set of two coupled ordinary differential equations [in inlet velocity v/sub i/(t) and two-phase residence time tau(t)] involving history integrals: a nonlinear ordinary functional differential equation and an integral equation. Hence, to solve these equations, the dependent variables must be specified for -(nu + tau) ≤ t ≤ 0, where nu is the single-phase residence time. This system of nonlinear equations has been solved analytically using asymptotic expansion series for finite but small perturbations and numerically using finite difference techniques

A special device used for measuring waste gas flow rate in the vent channel of Qinshan Nuclear Power Plant

International Nuclear Information System (INIS)

Zhang Yingjun; Zong Guifang; Shi Huaming; Yang Huimin; Jiang Yuana.

1988-01-01

A special Venturi-Pitot complex device is discribed which is used for measuring waste gas flow rate in the vent channel of Qinshan nuclear power plant. The device is located at the center of the channel. It can produce enlarged differential pressure signal under the condition of low gas velocity. And the flow resistance of this device is negligible. Experiments to determine the ratio of the velocity at the center of the channel to the average velocity were performed on a 1:12 test model. The special device was calibrated in a closed wind tunnel and its discharge coefficient was obtained. The uncertainty is ±3.5% and the nonlinearity is ±1.3%. The enlargement ratio and the discharge coefficient of the device are also deduced analytically on the basis of hydrodynamics theory

Improvement of Nonlinearity Correction for BESIII ETOF Upgrade

Science.gov (United States)

Sun, Weijia; Cao, Ping; Ji, Xiaolu; Fan, Huanhuan; Dai, Hongliang; Zhang, Jie; Liu, Shubin; An, Qi

2015-08-01

An improved scheme to implement integral non-linearity (INL) correction of time measurements in the Beijing Spectrometer III Endcap Time-of-Flight (BESIII ETOF) upgrade system is presented in this paper. During upgrade, multi-gap resistive plate chambers (MRPC) are introduced as ETOF detectors which increases the total number of time measurement channels to 1728. The INL correction method adopted in BESIII TOF proved to be of limited use, because the sharply increased number of electronic channels required for reading out the detector strips degrade the system configuration efficiency severely. Furthermore, once installed into the spectrometer, BESIII TOF electronics do not support the TDCs' nonlinearity evaluation online. In this proposed method, INL data used for the correction algorithm are automatically imported from a non-volatile read-only memory (ROM) instead of from data acquisition software. This guarantees the real-time performance and system efficiency of the INL correction, especially for the ETOF upgrades with massive number of channels. Besides, a signal that is not synchronized to the system 41.65 MHz clock from BEPCII is sent to the frontend electronics (FEE) to simulate pseudo-random test pulses for the purpose of online nonlinearity evaluation. Test results show that the time measuring INL errors in one module with 72 channels can be corrected online and in real time.

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

Conductance of Ion Channels - Theory vs. Experiment

Science.gov (United States)

Pohorille, Andrew; Wilson, Michael; Mijajlovic, Milan

2013-01-01

Transmembrane ion channels mediate a number of essential physiological processes in a cell ranging from regulating osmotic pressure to transmission of neural signals. Kinetics and selectivity of ion transport is of critical importance to a cell and, not surprisingly, it is a subject of numerous experimental and theoretical studies. In this presentation we will analyze in detail computer simulations of two simple channels from fungi - antiamoebin and trichotoxin. Each of these channels is made of an alpha-helical bundle of small, nongenomically synthesized peptides containing a number of rare amino acids and exhibits strong antimicrobial activity. We will focus on calculating ionic conductance defined as the ratio of ionic current through the channel to applied voltage. From molecular dynamics simulations, conductance can be calculated in at least two ways, each involving different approximations. Specifically, the current, given as the number of charges transferred through the channel per unit of time, can be obtained from the number of events in which ions cross the channel during the simulation. This method works well for large currents (high conductance values and/or applied voltages). If the number of crossing events is small, reliable estimates of current are difficult to achieve. Alternatively, conductance can be estimated assuming that ion transport can be well approximated as diffusion in the external potential given by the free energy profile. Then, the current can be calculated by solving the one-dimensional diffusion equation in this external potential and applied voltage (the generalized Nernst-Planck equation). To do so three ingredients are needed: the free energy profile, the position-dependent diffusion coefficient and the diffusive flux of ions into the channel. All these quantities can be obtained from molecular dynamics simulations. An important advantage of this method is that it can be used equally well to estimating large and small currents

Passive impedance-based second-order sliding mode control for non-linear teleoperators

Directory of Open Access Journals (Sweden)

Luis G García-Valdovinos

2017-02-01

Full Text Available Bilateral teleoperation systems have attracted significant attention in the last decade mainly because of technological advancements in both the communication channel and computers performance. In addition, non-linear multi-degree-of-freedom bilateral teleoperators along with state observers have become an open research area. In this article, a model-free exact differentiator is used to estimate the full state along with a chattering-free second-order sliding mode controller to guarantee a robust impedance tracking under both constant and an unknown time delay of non-linear multi-degree-of-freedom robots. The robustness of the proposed controller is improved by introducing a change of coordinates in terms of a new nominal reference similar to that used in adaptive control theory. Experimental results that validate the predicted behaviour are presented and discussed using a Phantom Premium 1.0 as the master robot and a Catalyst-5 virtual model as the slave robot. The dynamics of the Catalyst-5 system is solved online.

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)

Nonlinear bias analysis and correction of microwave temperature sounder observations for FY-3C meteorological satellite

Science.gov (United States)

Hu, Taiyang; Lv, Rongchuan; Jin, Xu; Li, Hao; Chen, Wenxin

2018-01-01

The nonlinear bias analysis and correction of receiving channels in Chinese FY-3C meteorological satellite Microwave Temperature Sounder (MWTS) is a key technology of data assimilation for satellite radiance data. The thermal-vacuum chamber calibration data acquired from the MWTS can be analyzed to evaluate the instrument performance, including radiometric temperature sensitivity, channel nonlinearity and calibration accuracy. Especially, the nonlinearity parameters due to imperfect square-law detectors will be calculated from calibration data and further used to correct the nonlinear bias contributions of microwave receiving channels. Based upon the operational principles and thermalvacuum chamber calibration procedures of MWTS, this paper mainly focuses on the nonlinear bias analysis and correction methods for improving the calibration accuracy of the important instrument onboard FY-3C meteorological satellite, from the perspective of theoretical and experimental studies. Furthermore, a series of original results are presented to demonstrate the feasibility and significance of the methods.

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

The effect of quintic nonlinearity on the propagation characteristics of dispersion managed optical solitons

International Nuclear Information System (INIS)

Konar, S.; Mishra, Manoj; Jana, S.

2006-01-01

The role of quintic nonlinearity on the propagation characteristics of optical solitons in dispersion managed optical communication systems has been presented in this paper. It has been shown that quintic nonlinearity has only marginal influence on single pulse propagation. However, numerical simulation has been undertaken to reveal that quintic nonlinearity reduces collision distance between neighbouring pulses of the same channel. It is found that for lower map strength the collapse distance between intra channel pulses is very much sensitive to the dispersion map strength

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....

Multiuser receiver for DS-CDMA signals in multipath channels: an enhanced multisurface method.

Science.gov (United States)

Mahendra, Chetan; Puthusserypady, Sadasivan

2006-11-01

This paper deals with the problem of multiuser detection in direct-sequence code-division multiple-access (DS-CDMA) systems in multipath environments. The existing multiuser detectors can be divided into two categories: (1) low-complexity poor-performance linear detectors and (2) high-complexity good-performance nonlinear detectors. In particular, in channels where the orthogonality of the code sequences is destroyed by multipath, detectors with linear complexity perform much worse than the nonlinear detectors. In this paper, we propose an enhanced multisurface method (EMSM) for multiuser detection in multipath channels. EMSM is an intermediate piecewise linear detection scheme with a run-time complexity linear in the number of users. Its bit error rate performance is compared with existing linear detectors, a nonlinear radial basis function detector trained by the new support vector learning algorithm, and Verdu's optimal detector. Simulations in multipath channels, for both synchronous and asynchronous cases, indicate that it always outperforms all other linear detectors, performing nearly as well as nonlinear detectors.

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

Secrecy Capacity Analysis over α−μ Fading Channels

KAUST Repository

Lei, Hongjiang

2017-02-15

In this work, we study the secrecy capacity of the classic Wyner’s model over the α − μ fading channels, where α and μ specify the nonlinearity and clustering of fading channels, respectively. The average secrecy capacity (ASC) is derived in closed-form by using the extended generalized bivariate Fox’s Hfunction (EGBFHF). Moreover, the asymptotic analysis of ASC in high signal-to-noise ratio (SNR) regime is conducted. The asymptotic results unveil that the ASC follows the scaling law of Θ(ln p), where p stands for the ratio between the average powers of main channels and eavesdropping channels. Moreover, the ASC can be enhanced by increasing the transmit SNR, while there exists a ceiling of ASC as the SNRs at both sides are improved simultaneously. The accuracy of the analytical results is validated by Monte-Carlo simulations. The numerical results show that rigorous fading channels are beneficial to the secrecy performance, that is, serious nonlinearity (small α) and sparse clustering (small μ) will lead to the improvement of ASC.

Secrecy Capacity Analysis over α−μ Fading Channels

KAUST Repository

Lei, Hongjiang; Ansari, Imran Shafique; Pan, Gaofeng; Alomair, Basel; Alouini, Mohamed-Slim

2017-01-01

In this work, we study the secrecy capacity of the classic Wyner’s model over the α − μ fading channels, where α and μ specify the nonlinearity and clustering of fading channels, respectively. The average secrecy capacity (ASC) is derived in closed-form by using the extended generalized bivariate Fox’s Hfunction (EGBFHF). Moreover, the asymptotic analysis of ASC in high signal-to-noise ratio (SNR) regime is conducted. The asymptotic results unveil that the ASC follows the scaling law of Θ(ln p), where p stands for the ratio between the average powers of main channels and eavesdropping channels. Moreover, the ASC can be enhanced by increasing the transmit SNR, while there exists a ceiling of ASC as the SNRs at both sides are improved simultaneously. The accuracy of the analytical results is validated by Monte-Carlo simulations. The numerical results show that rigorous fading channels are beneficial to the secrecy performance, that is, serious nonlinearity (small α) and sparse clustering (small μ) will lead to the improvement of ASC.

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

RBS cross-section of MeV ions channeling in crystals from quantum theory

International Nuclear Information System (INIS)

Den Besten, J.L.; Jamieson, D.N.; Spizzirri, P.G.; Allen, L.J.

1999-01-01

We present an alternative approach to describing Rutherford Backscattered (RBS) angular yield scans. The Bloch wave method to formulate the cross-section is a fundamental approach originating from Schrodinger's equation. This quantum formulation is often used when describing various aspects of electron diffraction including Backscattering, EDX and TEM but has seen little application to the very short wavelength regime of MeV ions. It offers several significant advantages. Great freedom is given to crystal properties and structure in the theory allowing a fundamental insight into the channeling phenomena and hence the crystal itself. We have calculated both planar and axial channeling scans and these maps are shown to be in good agreement to their experimental counterparts. There is excellent correlation between the theoretical and experimental results for both χ min and Ψ 1/2 . Further investigation is required into the area of absorption or dechanneling. This phenomenon requires different mechanisms for electron and ion scattering differ greatly

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.

Networked Predictive Control for Nonlinear Systems With Arbitrary Region Quantizers.

Science.gov (United States)

Yang, Hongjiu; Xu, Yang; Xia, Yuanqing; Zhang, Jinhui

2017-04-06

In this paper, networked predictive control is investigated for planar nonlinear systems with quantization by an extended state observer (ESO). The ESO is used not only to deal with nonlinear terms but also to generate predictive states for dealing with network-induced delays. Two arbitrary region quantizers are applied to take effective values of signals in forward channel and feedback channel, respectively. Based on a "zoom" strategy, sufficient conditions are given to guarantee stabilization of the closed-loop networked control system with quantization. A simulation example is proposed to exhibit advantages and availability of the results.

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.

Classical fluid aspects of nonlinear Schrödinger equations and solitons

Directory of Open Access Journals (Sweden)

James G. Gilson

1987-01-01

Full Text Available The author extends his alternative theory for Schrödinger quantum mechanics by introducing the idea of energy reference strata over configuration space. It is then shown that the view from various such strata defines, the content of the system of interest and enables a variety of different descriptions of events in the same space time region. Thus according to “the point of view” or energy stratum chosen so the type of Schrödinger equation, linear or otherwise, appropriate to describe the system is determined. A nonlinear information channel between two dimensional fluid action in hyperspace into two dimensional energy hyperspace is shown to exist generally as a background to nonlinear Schrödinger structures. In addition it is shown how soliton solutions of the one dimensional Schrödinger equation are related to two dimensional vortex fields in hyperspace.

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.

Many-body scattering theory methods as a means for solving bound-state problems: Applications of arrangement-channel quantum mechanics

International Nuclear Information System (INIS)

Levin, F.S.; Krueger, H.

1977-01-01

We propose in this article that the non-Hermitian equations typical of some many-body scattering theories be used to help solve many-body bound-state problems. The basic idea is to exploit the channel nature of many-body bound states that must exist because bound states are obvious negative-energy extensions of scattering states. Since atomic, molecular, and nuclear systems all display multichannel effects for E > 0, at least through Pauli-principle effects if not through mass-transfer reactions, this use of positive-energy methods for solving bound-state problems could have wide applicability. The development used here is based on the channel-component-state method of the channel-coupling-array theory, recently described in detail for the E > 0 case, and various aspects of the formalism are discussed. Detailed calculations using simple approximations are discussed for H 2 + , one of the simplest systems displaying channel structure. Comparison with the exact, Born-Oppenheimer results of Wind show that the non-Hermitian-equation, channel-component values of the equilibrium separation and total binding energy are accurate to within 2%, while the dissociation energy is accurate to 10%. The resulting wave function is identical to that arising from the simplest MO calculation, for which these numbers are less accurate than the preceding by at least a factor of 3. We also show that identical particle symmetry for the H 2 + case reduces the pair of coupled (two-channel) equations to a single equation with an exchange term. Similar reductions will occur for larger numbers of identical particles, thus suggesting application of the formalism to atomic structure problems. A detailed analysis of the present numerical results, their general implications, and possible applications is also given

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

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.

Equalization of Multiuser Wireless CDMA Downlink Considering Transmitter Nonlinearity Using Walsh Codes

Directory of Open Access Journals (Sweden)

Pinter Stephen Z

2007-01-01

Full Text Available Transmitter nonlinearity has been a major issue in many scenarios: cellular wireless systems have high power RF amplifier (HPA nonlinearity at the base station; satellite downlinks have nonlinear TWT amplifiers in the satellite transponder and multipath conditions in the ground station; and radio-over-fiber (ROF systems consist of a nonlinear optical link followed by a wireless channel. In many cases, the nonlinearity is simply ignored if there is no out-of-band emission. This results in poor BER performance. In this paper we propose a new technique to estimate the linear part of the wireless downlink in the presence of a nonlinearity using Walsh codes; Walsh codes are commonly used in CDMA downlinks. Furthermore, we show that equalizer performance is significantly improved by taking into account the presence of the nonlinearity during channel estimation. This is shown by using a regular decision feedback equalizer (DFE with both wireless and RF amplifier noise. We perform estimation in a multiuser CDMA communication system where all users transmit their signal simultaneously. Correlation analysis is applied to identify the channel impulse response (CIR and the derivation of key correlation relationships is shown. A difficulty with using Walsh codes in terms of their correlations (compared to PN sequences is then presented, as well as a discussion on how to overcome it. Numerical evaluations show a good estimation of the linear system with 54 users in the downlink and a signal-to-noise ratio (SNR of 25 dB. Bit error rate (BER simulations of the proposed identification and equalization algorithms show a BER of achieved at an SNR of dB.

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.

Quantum privacy and Schur product channels

Science.gov (United States)

Levick, Jeremy; Kribs, David W.; Pereira, Rajesh

2017-12-01

We investigate the quantum privacy properties of an important class of quantum channels, by making use of a connection with Schur product matrix operations and associated correlation matrix structures. For channels implemented by mutually commuting unitaries, which cannot privatise qubits encoded directly into subspaces, we nevertheless identify private algebras and subsystems that can be privatised by the channels. We also obtain further results by combining our analysis with tools from the theory of quasi-orthogonal operator algebras and graph theory.

Separation of irradiance and reflectance from observed color images by logarithmical nonlinear diffusion process

Science.gov (United States)

Saito, Takahiro; Takahashi, Hiromi; Komatsu, Takashi

2006-02-01

The Retinex theory was first proposed by Land, and deals with separation of irradiance from reflectance in an observed image. The separation problem is an ill-posed problem. Land and others proposed various Retinex separation algorithms. Recently, Kimmel and others proposed a variational framework that unifies the previous Retinex algorithms such as the Poisson-equation-type Retinex algorithms developed by Horn and others, and presented a Retinex separation algorithm with the time-evolution of a linear diffusion process. However, the Kimmel's separation algorithm cannot achieve physically rational separation, if true irradiance varies among color channels. To cope with this problem, we introduce a nonlinear diffusion process into the time-evolution. Moreover, as to its extension to color images, we present two approaches to treat color channels: the independent approach to treat each color channel separately and the collective approach to treat all color channels collectively. The latter approach outperforms the former. Furthermore, we apply our separation algorithm to a high quality chroma key in which before combining a foreground frame and a background frame into an output image a color of each pixel in the foreground frame are spatially adaptively corrected through transformation of the separated irradiance. Experiments demonstrate superiority of our separation algorithm over the Kimmel's separation algorithm.

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

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.

Study on the dissociative recombination of HeH+ by multi-channel quantum defect theory

Directory of Open Access Journals (Sweden)

Takagi Hidekazu

2015-01-01

Full Text Available The dissociative recombination of HeH+ is studied using multi-channel quantum defect theory. We investigated how the partial waves of incident electrons affect the DR cross section. The DR cross section depends on the position of the center of partial wave expansion for the adiabatic S-matrix of electron scattering. When the Rydberg states correlate with the Rydberg states of the hydrogen atom at large internuclear distances, the center should be on the hydrogen atom for a better convergence of the expansion.

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...

Influence of friction on buckling of a drill string in the circular channel of a bore hole

Directory of Open Access Journals (Sweden)

Valery Gulyayev

2016-10-01

Full Text Available Abstract Enhancement of technology and techniques for drilling deep directed oil and gas bore hole is one of the most important problems of the current petroleum industry. Not infrequently, the drilling of these bore holes is attended by occurrence of extraordinary situations associated with technical accidents. Among these is the Eulerian loss of stability of a drill string in the channel of a curvilinear bore hole. Methods of computer simulation should play a dominant role in prediction of these states. In this paper, a new statement of the problem of critical buckling of the drill strings in 3D curvilinear bore holes is proposed. It is based on combined use of the theory of curvilinear elastic rods, Eulerian theory of stability, theory of channel surfaces, and methods of classical mechanics of systems with nonlinear constraints. It is noted that the stated problem is singularly perturbed and its solutions have the shapes of localized harmonic wavelets. The calculation results showed that the friction effects lead to essential redistribution of internal axial forces, as well as changing the eigenmode shapes and sites of their localization. These features make the buckling phenomena less predictable and raise the role of computer simulation of these effects.

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.

Asymptotic Performance Analysis of the k-th Best Link Selection over Wireless Fading Channels: An Extreme Value Theory Approach

KAUST Repository

Al-Badarneh, Yazan Hussein

2018-01-25

We consider a general selection-diversity (SD) scheme in which the k-th best link is selected from a number of links. We use extreme value theory (EVT) to derive simple closed-form asymptotic expressions for the average throughput, effective throughput and average bit error probability (BEP) for the k-th best link over various channel models that are widely used to characterize fading in wireless communication systems. As an application example, we consider the Weibull fading channel model and verify the accuracy of the derived asymptotic expressions through Monte Carlo simulations.

Asymptotic Performance Analysis of the k-th Best Link Selection over Wireless Fading Channels: An Extreme Value Theory Approach

KAUST Repository

Al-Badarneh, Yazan Hussein; Georghiades, Costas; Alouini, Mohamed-Slim

2018-01-01

We consider a general selection-diversity (SD) scheme in which the k-th best link is selected from a number of links. We use extreme value theory (EVT) to derive simple closed-form asymptotic expressions for the average throughput, effective throughput and average bit error probability (BEP) for the k-th best link over various channel models that are widely used to characterize fading in wireless communication systems. As an application example, we consider the Weibull fading channel model and verify the accuracy of the derived asymptotic expressions through Monte Carlo simulations.

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...

Optimal beamforming in MIMO systems with HPA nonlinearity

KAUST Repository

Qi, Jian

2010-09-01

In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

Optimal beamforming in MIMO systems with HPA nonlinearity

KAUST Repository

Qi, Jian; Aissa, Sonia

2010-01-01

In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

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

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

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)

Two-way CSI-assisted AF relaying with HPA nonlinearity

KAUST Repository

Qi, Jian

2015-09-11

In this paper, we investigate half-duplex two-way dual-hop channel state information (CSI)-assisted amplify-andforward (AF) relaying in the presence of high-power amplifier (HPA) nonlinearity at relays. The expression for the end-toend signal-to-noise ratio (SNR) is derived as per the modified system model by taking into account the interference caused by relaying scheme and HPA nonlinearity. The system performance of the considered relaying network is evaluated in terms of average symbol error probability (SEP) in Nakagami-m fading channels, by making use of the moment-generating function (MGF) approach. Numerical results are provided and show the effects of several parameters, such as quadrature amplitude modulation (QAM) order, number of relays, HPA parameters, and Nakagami parameter, on performance. © 2015 IEEE.

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.

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

Large third-order optical nonlinearity in vertically oriented mesoporous silica thin films embedded with Ag nanoparticles

Energy Technology Data Exchange (ETDEWEB)

Tan, Min; Liu, Qiming, E-mail: qmliu@whu.edu.cn [Wuhan University, Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology (China)

2016-12-15

Taking advantage of the channel confinement of mesoporous films to prevent the agglomeration of Ag nanoparticles to achieve large third-order optical nonlinearity in amorphous materials, Ag-loaded composite mesoporous silica film was prepared by the electrochemical deposition method on ITO substrate. Ag ions were firstly transported into the channels of mesoporous film by the diffusion and binding force of channels, which were reduced to nanoparticles by applying suitable voltage. The existence and uniform distribution of Ag nanoparticles ranging in 1–10 nm in the mesoporous silica thin films were exhibited by UV spectrophotometer, X-ray powder diffraction (XRD), transmission electron microscopy (TEM), and X-ray photoelectron spectroscopy (XPS) measurements. The third-order optical nonlinearity induced by Ag nanoparticles was studied by the Z-scan technique. Due to the local field surface plasmon resonance, the maximum third-order nonlinear optical susceptibility of Ag-loaded composite mesoporous silica film is 1.53×10{sup −10} esu, which is 1000 times larger than that of the Ag-contained chalcogenide glasses which showed large nonlinearity in amorphous materials.

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

Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

Science.gov (United States)

Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

2018-04-01

We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

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

Sausage instabilities in electron current channels and the problem of fast ignition

International Nuclear Information System (INIS)

Das, A.

2002-01-01

In the fast ignition concept of laser fusion, an intense picosecond laser pulse incident on an overdense pellet is absorbed by nonlinear mechanisms and gets converted into inward propagating fast electron currents. PIC simulations show that the return shielding currents due to cold plasma interact with the incoming currents and intense Weibel, tearing and coalescence instabilities take place, which organize the current into a few current channels. The stability of these current channels is thus a topic of great interest. We have carried out linear and nonlinear studies of 2 - dimensional sausage instabilities of a slab model of the current channels in the framework of electron magnetohydrodynamic fluid approximation. The analytic calculations and numerical simulations for some simple velocity profiles show the presence of linear instability driven by velocity shear. Nonlinear studies on the saturation of instabilities and their reaction back on the relaxation of the velocity profile have also been made. A discussion of the consequences of such EMHD turbulence induced relaxation and stopping of fast electrons, for the fast ignition concept will be presented. (author)

Fiber Nonlinearity Post-Compensation by Optical Phase Conjugation for 40Gb/s CO-OFDM Systems

International Nuclear Information System (INIS)

Qiao Yao-Jun; Liu Xue-Jun; Ji Yue-Feng

2011-01-01

Fiber nonlinearity impairments in a 40-Gb/s coherent optical orthogonal frequency division multiplexing (COOFDM) system are post-compensated for by a new method of fiber nonlinearity post-compensation (FNPC). The FNPC located before the CO-OFDM receiver includes an optical phase conjugation (OPC) unit and a subsequent 80-km-high nonlinear fiber (HNLF) as a fiber nonlinearity compensator. The OPC unit is based on a four wave mixing effect in a semiconductor optical amplifier. The fiber nonlinearity impairments in the transmission link are post-compensated for after OPC by transmission through the HNLF with a large nonlinearity coefficient. Simulation results show that the nonlinear threshold (NLT) (for Q > 10 dB) can be increased by about 2.5 dB and the maximum Q factor is increased by about 1.2 dB for the single-channel 40-Gb/s CO-OFDM system with periodic dispersion maps. In the 50-GHz channel spacing wavelength-division-multiplexing system, the NLT increases by 1.1 dB, equating to a 0.7 dB improvement for the maximum Q factor. (fundamental areas of phenomenology(including applications))

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

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.

Multiplex multivariate recurrence network from multi-channel signals for revealing oil-water spatial flow behavior.

Science.gov (United States)

Gao, Zhong-Ke; Dang, Wei-Dong; Yang, Yu-Xuan; Cai, Qing

2017-03-01

The exploration of the spatial dynamical flow behaviors of oil-water flows has attracted increasing interests on account of its challenging complexity and great significance. We first technically design a double-layer distributed-sector conductance sensor and systematically carry out oil-water flow experiments to capture the spatial flow information. Based on the well-established recurrence network theory, we develop a novel multiplex multivariate recurrence network (MMRN) to fully and comprehensively fuse our double-layer multi-channel signals. Then we derive the projection networks from the inferred MMRNs and exploit the average clustering coefficient and the spectral radius to quantitatively characterize the nonlinear recurrent behaviors related to the distinct flow patterns. We find that these two network measures are very sensitive to the change of flow states and the distributions of network measures enable to uncover the spatial dynamical flow behaviors underlying different oil-water flow patterns. Our method paves the way for efficiently analyzing multi-channel signals from multi-layer sensor measurement system.

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)

The minimum yield in channeling

International Nuclear Information System (INIS)

Uguzzoni, A.; Gaertner, K.; Lulli, G.; Andersen, J.U.

2000-01-01

A first estimate of the minimum yield was obtained from Lindhard's theory, with the assumption of a statistical equilibrium in the transverse phase-space of channeled particles guided by a continuum axial potential. However, computer simulations have shown that this estimate should be corrected by a fairly large factor, C (approximately equal to 2.5), called the Barrett factor. We have shown earlier that the concept of a statistical equilibrium can be applied to understand this result, with the introduction of a constraint in phase-space due to planar channeling of axially channeled particles. Here we present an extended test of these ideas on the basis of computer simulation of the trajectories of 2 MeV α particles in Si. In particular, the gradual trend towards a full statistical equilibrium is studied. We also discuss the introduction of this modification of standard channeling theory into descriptions of the multiple scattering of channeled particles (dechanneling) by a master equation and show that the calculated minimum yields are in very good agreement with the results of a full computer simulation

Generalization of Spatial Channel Theory to Three-Dimensional x-y-z Transport Computations

International Nuclear Information System (INIS)

Abu-Shumays, I. K.; Hunter, M. A.; Martz, R. L.; Risner, J. M.

2002-01-01

Spatial channel theory, initially introduced in 1977 by M. L. Williams and colleagues at ORNL, is a powerful tool for shield design optimization. It focuses on so called ''contributon'' flux and current of particles (a fraction of the total of neutrons, photons, etc.) which contribute directly or through their progeny to a pre-specified response, such as a detector reading, dose rate, reaction rate, etc., at certain locations of interest. Particles that do not contribute directly or indirectly to the pre-specified response, such as particles that are absorbed or leak out, are ignored. Contributon fluxes and currents are computed based on combined forward and adjoint transport solutions. The initial concepts were considerably improved by Abu-Shumays, Selva, and Shure by introducing steam functions and response flow functions. Plots of such functions provide both qualitative and quantitative information on dominant particle flow paths and identify locations within a shield configuration that are important in contributing to the response of interest. Previous work was restricted to two dimensional (2-D) x-y rectangular and r-z cylindrical geometries. This paper generalizes previous work to three-dimensional x-y-z geometry, since it is now practical to solve realistic 3-D problems with multidimensional transport programs. As in previous work, new analytic expressions are provided for folding spherical harmonics representations of forward and adjoint transport flux solutions. As a result, the main integrals involve in spatial channel theory are computed exactly and more efficiently than by numerical quadrature. The analogy with incompressible fluid flow is also applied to obtain visual qualitative and quantitative measures of important streaming paths that could prove vital for shield design optimization. Illustrative examples are provided. The connection between the current paper and the excellent work completed by M. L. Williams in 1991 is also discussed

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

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

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.

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.

Two-way CSI-assisted AF relaying with HPA nonlinearity

KAUST Repository

Qi, Jian; Aissa, Sonia; Alouiniz, Mohamed-Slim

2015-01-01

In this paper, we investigate half-duplex two-way dual-hop channel state information (CSI)-assisted amplify-andforward (AF) relaying in the presence of high-power amplifier (HPA) nonlinearity at relays. The expression for the end-toend signal

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

Quantum channels and their entropic characteristics

International Nuclear Information System (INIS)

Holevo, A S; Giovannetti, V

2012-01-01

One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of a quantum channel which is a basic building block of any data-transmitting or data-processing system. This development resulted in an elaborated structural theory and was accompanied by the discovery of a whole spectrum of entropic quantities, notably the channel capacities, characterizing information-processing performance of the channels. This paper gives a survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite-dimensional quantum systems. We also touch upon the 'continuous-variables' case, which provides an arena for quantum Gaussian systems. Most of the practical realizations of quantum information processing were implemented in such systems, in particular based on principles of quantum optics. Several important entropic quantities are introduced and used to describe the basic channel capacity formulae. The remarkable role of specific quantum correlations—entanglement—as a novel communication resource is stressed.

Novel procedure for characterizing nonlinear systems with memory: 2017 update

Science.gov (United States)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2017-05-01

The present article discusses novel improvements in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra or 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] . The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order and alleviate the Curse of Dimensionality (COD) in order to realize practical nonlinear solutions of scientific and engineering interest.

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

Quantum-correlation breaking channels, quantum conditional probability and Perron-Frobenius theory

Science.gov (United States)

Chruściński, Dariusz

2013-03-01

Using the quantum analog of conditional probability and classical Bayes theorem we discuss some aspects of particular entanglement breaking channels: quantum-classical and classical-classical channels. Applying the quantum analog of Perron-Frobenius theorem we generalize the recent result of Korbicz et al. (2012) [8] on full and spectrum broadcasting from quantum-classical channels to arbitrary quantum channels.

Quantum-correlation breaking channels, quantum conditional probability and Perron–Frobenius theory

International Nuclear Information System (INIS)

Chruściński, Dariusz

2013-01-01

Using the quantum analog of conditional probability and classical Bayes theorem we discuss some aspects of particular entanglement breaking channels: quantum–classical and classical–classical channels. Applying the quantum analog of Perron–Frobenius theorem we generalize the recent result of Korbicz et al. (2012) [8] on full and spectrum broadcasting from quantum–classical channels to arbitrary quantum channels.

Defect Distributions in Channeling Experiments

DEFF Research Database (Denmark)

Andersen, Hans Henrik; Sigmund, P.

1965-01-01

A simple collision model allows to calculate energy losses of perfectly channeled particles. The maximum energy loss is related in a simple way to the displacement energy of lattice atoms perpendicular to the channel. From that, one obtains rather definite predictions on the possibility...... of radiation damage by channeled particles. As an application, one gets a necessary criterion for the occurence of super tails in channeling experiments. The theory involves some assumptions on the behaviour of Born-Mayer potentials which are verified by comparison to experimental displacement energies....

Wireless Energy Harvesting Using Signals from Multiple Fading Channels

KAUST Repository

Chen, Yunfei

2017-08-01

In this paper, we study the average, the probability density function and the cumulative distribution function of the harvested power. In the study, the signals are transmitted from multiple sources. The channels are assumed to be either Rician fading or Gamma-shadowed Rician fading. The received signals are then harvested by using either a single harvester for simultaneous transmissions or multiple harvesters for transmissions at different frequencies, antennas or time slots. Both linear and nonlinear models for the energy harvester at the receiver are examined. Numerical results are presented to show that, when a large amount of harvested power is required, a single harvester or the linear range of a practical nonlinear harvester are more efficient, to avoid power outage. Further, the power transfer strategy can be optimized for fixed total power. Specifically, for Rayleigh fading, the optimal strategy is to put the total power at the source with the best channel condition and switch off all other sources, while for general Rician fading, the optimum magnitudes and phases of the transmitting waveforms depend on the channel parameters.

Reduced Complexity Volterra Models for Nonlinear System Identification

Directory of Open Access Journals (Sweden)

Hacıoğlu Rıfat

2001-01-01

Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.

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.

Conduction channels of an InAs-Al nanowire Josephson weak link

International Nuclear Information System (INIS)

Goffman, M F; Urbina, C; Pothier, H; Nygård, J; Marcus, C M; Krogstrup, P

2017-01-01

We present a quantitative characterization of an electrically tunable Josephson junction defined in an InAs nanowire proximitized by an epitaxially-grown superconducting Al shell. The gate-dependence of the number of conduction channels and of the set of transmission coefficients are extracted from the highly nonlinear current–voltage characteristics. Although the transmissions evolve non-monotonically, the number of independent channels can be tuned, and configurations with a single quasi-ballistic channel achieved. (fast track communication)