Nonlinear potential theory of degenerate elliptic equations
Heinonen, Juha; Martio, Olli
2006-01-01
A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions.Starting with the theory of weighted Sobolev spaces, this treatment advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and ch
Nonlinear theory of scattering by localized potentials in metals
Energy Technology Data Exchange (ETDEWEB)
Howard, I A [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); March, N H [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); Oxford University, Oxford (United Kingdom); Echenique, P M [Donostia International Physics Center (DIPC), 20018 San Sebastian, Basque Country (Spain); Departamento de Fisica de Materiales and Centro Mixto CSIC-UPV/EHU, Facultad de Quimicas, UPV/EHU, Apartado 1072, 20080, San Sebastian (Spain)
2003-11-14
In early work, March and Murray gave a perturbation theory of the Dirac density matrix {gamma}(r, r') generated by a localized potential V(r) embedded in an initially uniform Fermi gas to all orders in V(r). For potentials sufficiently slowly varying in space, they summed the resulting series for r' = r to regain the Thomas-Fermi density {rho}(r) {proportional_to} [{mu} - V(r)]{sup 3/2}, with {mu} the chemical potential of the Fermi gas. For an admittedly simplistic repulsive central potential V(r) = vertical bar A vertical bar exp(-cr), it is first shown here that what amounts to the sum of the March-Murray series for the s-wave (only) contribution to the density, namely {rho}{sub s}(r, {mu}), can be obtained in closed form. Furthermore, for specific numerical values of A and c in this exponential potential, the long-range behaviour of {rho}{sub s}(r, {mu}) is related to the zero-potential form of March and Murray, which merely suffers a {mu}-dependent phase shift. This result is interpreted in relation to the recent high density screening theorem of Zaremba, Nagy and Echenique. A brief discussion of excess electrical resistivity caused by nonlinear scattering in a Fermi gas is added; this now involves an off-diagonal local density of states. Finally, for periodic lattices, contact is made with the quantum-mechanical defect centre models of Koster and Slater (1954 Phys. Rev. 96 1208) and of Beeby (1967 Proc. R. Soc. A 302 113), and also with the semiclassical approximation of Friedel (1954 Adv. Phys. 3 446). In appendices, solvable low-dimensional models are briefly summarized.
Lukeš, Jaroslav; Netuka, Ivan; Veselý, Jiří
1988-01-01
Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The Conference was organized by the Faculty of Mathematics and Physics, Charles University, with the collaboration of the Institute of Mathematics, Czechoslovak Academy of Sciences, the Department of Mathematics, Czech University of Technology, the Union of Czechoslovak Mathematicians and Physicists, the Czechoslovak Scientific and Technical Society, and supported by IMU. During the Conference, 69 scientific communications from different branches of potential theory were presented; the majority of them are in cluded in the present volume. (Papers based on survey lectures delivered at the Conference, its program as well as a collection of problems from potential theory will appear in a special volume of the Lecture Notes Series published by Springer-Verlag). Topics of these communications truly reflect the vast scope of contemporary potential theory. Some contributions deal...
Nonlinear theory of elastic shells
International Nuclear Information System (INIS)
Costa Junior, J.A.
1979-08-01
Nonlinear theory of elastic shells is developed which incorporates both geometric and physical nonlinearities and which does not make use of the well known Love-Kirchhoff hypothesis. The resulting equations are formulated in tensorial notation and are reduced to the ones of common use when simplifying assumptions encountered in the especific litterature are taken. (Author) [pt
Helms, Lester L
2014-01-01
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In ...
Nonlinear theory of drift instability
International Nuclear Information System (INIS)
Hatori, T.
1981-01-01
In this chapter, we review recent works on the analytical and numerical analysis for the nonlinear evolution of drift instabilities. Only the case of a coherent wave is considered. Contributions to the turbulence theory for drift instabilities are already presented in Chapter 4. (author)
Dimensional Reduction of Nonlinear Gauge Theories
Ikeda, Noriaki; Izawa, K.-I.
2004-09-01
We extend 2D nonlinear gauge theory from the Poisson sigma model based on Lie algebroid to a model with additional two-form gauge fields. Dimensional reduction of 3D nonlinear gauge theory yields an example of such a model, which provides a realization of Courant algebroid by 2D nonlinear gauge theory. We see that the reduction of the base structure generically results in a modification of the target (algebroid) structure.
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 ...... nonlinear media show the rich varieties of phenomena interpolating between these two limiting cases. Related problems are the existence of partially coherent nonlinear wave packets in nonlinear media. These aspects have attracted a lot of attention in recent years due to investigations...
Spectral theory and nonlinear functional analysis
Lopez-Gomez, Julian
2001-01-01
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.
Schürmann, Michael
2008-01-01
This volume contains the revised and completed notes of lectures given at the school "Quantum Potential Theory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007. Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory, concentrating on probabilistic potential theory and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented.
Theory for nonlinear dynamic force spectroscopy.
Björnham, Oscar; Andersson, Magnus
2017-04-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information on the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear manner. For example, bacterial adhesion pili and polymers with worm-like chain properties are structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work, we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory, we modeled a bio-complex expressed on a stiff, an elastic, and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found that the nonlinear DFS (NLDFS) theory correctly predicted the numerical results. We also present a protocol suggesting an experimental approach and analysis method of the data to estimate the bond length and the thermal off-rate.
Nonlinear theory of electroelastic and magnetoelastic interactions
Dorfmann, Luis
2014-01-01
This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable...
Nonlinear theory of transverse beam echoes
Energy Technology Data Exchange (ETDEWEB)
Sen, Tanaji; Li, Yuan Shen
2017-10-04
Transverse beam echoes can be excited with a single dipole kick followed by a single quadrupole kick. They have been used to measure diffusion in hadron beams and have other diagnostic capabilities. Here we develop theories of the transverse echo nonlinear in both the dipole and quadrupole kick strengths. The theories predict the maximum echo amplitudes and the optimum strength parameters. We find that the echo amplitude increases with smaller beam emittance and the asymptotic echo amplitude can exceed half the initial dipole kick amplitude. We show that multiple echoes can be observed provided the dipole kick is large enough. The spectrum of the echo pulse can be used to determine the nonlinear detuning parameter with small amplitude dipole kicks. Simulations are performed to check the theoretical predictions. In the useful ranges of dipole and quadrupole strengths, they are shown to be in reasonable agreement.
Nonlinear analysis approximation theory, optimization and applications
2014-01-01
Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Nonlinear gravitons and curved twistor theory
International Nuclear Information System (INIS)
Penrose, R.
1976-01-01
A new approach to the quantization of general relativity is suggested in which a state consisting of just one graviton can be described, but in a way which involves both the curvature and nonlinearities of Einstein's theory. It is felt that this approach can be justified solely on its own merits but it also receives striking encouragement from another direction: a surprising mathematical result enables one to construct the general such nonlinear gravitation state from a curved twistor space, the construction being given in terms of one arbitrary holomorphic function of three complex variables. In this way, the approach fits naturally into the general twistor program for the description of quantized fields. (U.K.)
Nonlinear closed-loop control theory
International Nuclear Information System (INIS)
Perez, R.B.; Otaduy, P.J.; Abdalla, M.
1992-01-01
Traditionally, the control of nuclear power plants has been implemented by the use of proportional-integral (PI) control systems. PI controllers are both simple and, within their calibration range, highly reliable. However, PIs provide little performance information that could be used to diagnose out-of-range events or the nature of unanticipated transients that may occur in the plant. To go beyond the PI controller, the new control algorithms must deal with the physical system nonlinearities and with the reality of uncertain dynamics terms in its mathematical model. The tool to develop a new kind of control algorithm is provided by Optimal Control Theory. In this theory, a norm is minimized which incorporates the constraint that the model equations should be satisfied at all times by means of the Lagrange multipliers. Optimal control algorithms consist of two sets of coupled equations: (1) the model equations, integrated forward in time; and (2) the equations for the Lagrange multipliers (adjoints), integrated backwards in time. There are two challenges: dealing with large sets of coupled nonlinear equations and with a two-point boundary value problem that must be solved iteratively. In this paper, the rigorous conversion of the two-point boundary value problem into an initial value problem is presented. In addition, the incorporation into the control algorithm of ''real world'' constraints such as sensors and actuators, dynamic response functions and time lags introduced by the digitalization of analog signals is presented. (Author)
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
On the nonlinear theory of Fabry–Perot semiconductor lasers
International Nuclear Information System (INIS)
Noppe, Michael G
2016-01-01
Fundamentals of the nonlinear theory of Fabry–Perot semiconductor lasers have been developed, an integral part of which is natural linewidth theory. The formula for gain depending on the energy flux specifies the basic nonlinear effect in a laser. Necessary conditions for stimulated emission of the first and second kind are presented. Maxwell’s equations in the gain medium are applied to obtain equations for energy flux and for the description of non-linear phase effect. Based on the nonlinear theory, a number of experiments have been simulated; it indicates that the nonlinear theory is a new paradigm in laser theory. The nonlinear theory has provided recommendations for the development of lasers with improved properties, such as lasers with increased power and lasers with reduced natural linewidth. (paper)
Spectral theory and nonlinear analysis with applications to spatial ecology
Cano-Casanova, S; Mora-Corral , C
2005-01-01
This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.
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
Rigorous theory of molecular orientational nonlinear optics
Directory of Open Access Journals (Sweden)
Chong Hoon Kwak
2015-01-01
Full Text Available 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.
Nonlinear responses of chiral fluids from kinetic theory
Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun
2018-01-01
The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.
On nonlinear inner systems and connections with control theory
Petersen, Mark A.; van der Schaft, Arjan
2002-01-01
This paper extends some results involving linear inner systems to the nonlinear case. In thsi regard, the arithmetic of nonlinear inner systems is developed further and some new connections with nonlinear spectral and all-pass factorization and control theory are discussed. In particular, explicit
Lectures in nonlinear mechanics and chaos theory
Stetz, Albert W
2016-01-01
This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...
Perturbation Theory for Open Two-Level Nonlinear Quantum Systems
International Nuclear Information System (INIS)
Zhang Zhijie; Jiang Dongguang; Wang Wei
2011-01-01
Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)
Nonlinear structural mechanics theory, dynamical phenomena and modeling
Lacarbonara, Walter
2013-01-01
Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...
Nonlinear solar cycle forecasting: theory and perspectives
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 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 electroelasticity: material properties, continuum theory and applications.
Dorfmann, Luis; Ogden, Ray W
2017-08-01
In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.
DEFF Research Database (Denmark)
Norman, Patrick; Schimmelpfennig, Bernd; Ruud, Kenneth
2002-01-01
A systematic investigation of a hierarchy of methods for including relativistic effects in the calculation of linear and nonlinear optical properties was carried out. The simple ECP method and the more involved spin-averaged Douglas-Kroll approximation were compared to benchmark results obtained ...... with the time-dependent Dirac-Hartree-Fock method. It was found that in many cases, the performance of the ECP method exceeds its rank....
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
On nonequilibrium many-body systems III: nonlinear transport theory
International Nuclear Information System (INIS)
Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.
1986-01-01
A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt
Mathematical Systems Theory : from Behaviors to Nonlinear Control
Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien
2015-01-01
This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...
Energy flow theory of nonlinear dynamical systems with applications
Xing, Jing Tang
2015-01-01
This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...
Potential Theory Surveys and Problems
Lukeš, Jaroslav; Netuka, Ivan; Veselý, Jiří
1988-01-01
The volume comprises eleven survey papers based on survey lectures delivered at the Conference in Prague in July 1987, which covered various facets of potential theory, including its applications in other areas. The survey papers deal with both classical and abstract potential theory and its relations to partial differential equations, stochastic processes and other branches such as numerical analysis and topology. A collection of problems from potential theory, compiled on the occasion of the conference, is included, with additional commentaries, in the second part of this volume.
Nonlinear theory of a plasma Cherenkov maser
Energy Technology Data Exchange (ETDEWEB)
Choi, J.S. [Dongshin Univ., Chonnam (Korea, Democratic People`s Republic of); Heo, E.G.; Choi, D.I. [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Democratic People`s Republic of)] [and others
1995-12-31
The nonlinear saturation state in a plasma Cherenkov maser (PCM) propagating the intense relativistic electron beam through a circular waveguide partially filled with a dense annular plasma, is analyzed from the nonlinear formulation based on the cold fluid-Maxwell equations. We obtain the nonlinear efficiency and the final operation frequency under consideration of the effects of the beam current, the beam energy and the slow wave structure. We show that the saturation mechanism of a PCM instablity is a close correspondence in that of the relativistic two stream instability by the coherent trapping of electrons in a single most-ustable wave. And the optimal conditions in PCM operation are also obtained from performing our nonliear analysis together with computer simulations.
Applicability of linear and non-linear potential flow models on a Wavestar float
DEFF Research Database (Denmark)
Bozonnet, Pauline; Dupin, Victor; Tona, Paolino
2017-01-01
Numerical models based on potential flow theory, including different types of nonlinearities are compared and validated against experimental data for the Wavestar wave energy converter technology. Exact resolution of the rotational motion, non-linear hydrostatic and Froude-Krylov forces as well...... control action, limited to small amplitude motion with a single float, is well predicted by the numerical models, including the linear one. Still, float velocity is better predicted by accounting for non-linear hydrostatic and Froude-Krylov forces....
A Survey of Nonlinear Dynamics (Chaos Theory)
1991-04-01
example of an n = 1 Hamiltonian system does have separatrices. This is the 1D pendulum (Fig. 4.2): 9=p, p=-asin9;H(9,p) =p2 /2- acosO . (4-5) Phase space...method. There is no substitute for the actual labor of applying the nonlinear operator to a sum of normal modes, producing a general Galerkin vector
Introduction to the theory of nonlinear optimization
Jahn, Johannes
2007-01-01
This book serves as an introductory text to optimization theory in normed spaces. The topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a ba
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
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
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
Potential Theory of Multicomponent Adsorption
DEFF Research Database (Denmark)
Shapiro, Alexander; Stenby, Erling Halfdan
1998-01-01
We developed a theory of multicomponent adsorption on the basis of the potential concept originally suggested by Polanyi. The mixture is considered as a heterogeneous substance segregated in the external field emitted by the adsorbent. The same standard equation of state, with no additional fitting...... parameters, is used for the segregated and for the bulk phases. With this approach, few parameters are needed to correlate pure component adsorption isotherms. These parameters may be used to predict adsorption equilibria of multicomponent mixtures without additional adjustment. A connection between...... the potential theory and the spreading pressure concept is established, and problems of the theory consistency are studied. Numerical algorithms are suggested for evaluation of the segregated state of the mixture in the potential field of adsorption forces. Comparison with experimental data shows good agreement...
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
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)
The Inverted Pendulum Benchmark in Nonlinear Control Theory: A Survey
Directory of Open Access Journals (Sweden)
Olfa Boubaker
2013-05-01
Full Text Available Abstract For at least fifty years, the inverted pendulum has been the most popular benchmark, among others, in nonlinear control theory. The fundamental focus of this work is to enhance the wealth of this robotic benchmark and provide an overall picture of historical and current trend developments in nonlinear control theory, based on its simple structure and its rich nonlinear model. In this review, we will try to explain the high popularity of such a robotic benchmark, which is frequently used to realize experimental models, validate the efficiency of emerging control techniques and verify their implementation. We also attempt to provide details on how many standard techniques in control theory fail when tested on such a benchmark. More than 100 references in the open literature, dating back to 1960, are compiled to provide a survey of emerging ideas and challenging problems in nonlinear control theory accomplished and verified using this robotic system. Possible future trends that we can envision based on the review of this area are also presented.
Existence theory for nonlinear functional boundary value problems
Directory of Open Access Journals (Sweden)
Bapurao Dhage
2004-01-01
Full Text Available In this paper the existence of a solution of a general nonlinear functional two point boundary value problem is proved under mixed generalized Lipschitz and Carath\\'eodory conditions. An existence theorem for extremal solutions is also proved under certain monotonicity and weaker continuity conditions. Examples are provided to illustrate the theory developed in this paper.
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...
Backward stochastic differential equations from linear to fully nonlinear theory
Zhang, Jianfeng
2017-01-01
This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
Analysis of reactor power oscillation based on nonlinear dynamic theory
International Nuclear Information System (INIS)
Suzudo, Tomoaki
1994-07-01
Reactor power oscillations are discussed based on nonlinear dynamic theory with reference to stability problem of boiling water reactors (BWRs). The reactor noise from an actual plant is, firstly, analyzed by a method originally used for the analysis of chaotic phenomenon. The results show that this method gives better dynamic descriptor of oscillatory motion than those from previous methods, and that it is applicable to real-time monitoring system of the reactor core. Next, the low-dimensional phenomenological model of BWR power oscillation is analytically studied using bifurcation theory, a branch of nonlinear dynamic theory. From this analysis are derived explicit expressions for the steady state's linear stability and weak stability not given by numerical analyses, and the qualitative properties of the power oscillation can be better understood. (author)
Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.
Meair, Jonathan; Jacquod, Philippe
2013-02-27
We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.
SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-09-01
This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.
Properties of some nonlinear Schroedinger equations motivated through information theory
International Nuclear Information System (INIS)
Yuan, Liew Ding; Parwani, Rajesh R
2009-01-01
We update our understanding of nonlinear Schroedinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q = 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value η = 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, η might be encoding relativistic effects.
Mathematical theory of potential scattering
International Nuclear Information System (INIS)
Regge, T.
1963-01-01
Before we go into a detailed discussion of the potential scattering we would like to spend a few words on the reason potential scattering is interesting. We think that one of the main reasons of success of the potential model is that we can discuss it quite rigorously and that at the same time it gives a fairly intuitive picture of the scattering process and it provides in a way the language for a fully relativistic theory. We do not think that the potential model has been particularly satisfactory in explaining quantitatively the known experimental data, for instance the nucleon-nucleon scattering; yet we have good reasons to believe that at low energy any field theory will ultimately yield some sort of spin-dependent potential, containing spin orbit coupling and exchange terms. How this can be done and how far one has gone in this direction has nothing to do with the subject of these lectures which are merely concerned with the discussion of the solutions of the Schroedinger equation for a given class of potentials. That is,we assume from the very beginning that a potential exists although we do not know it or we know only broad features like the range and its analytic properties as function of the distance. For simplicity we do not deal with spin or exchange terms although they can be taken care of with little modifications. We just want to find those features of potential scattering which are to a large extent independent of the particular selection of the potential.
Diatomic interaction potential theory applications
Goodisman, Jerry
2013-01-01
Diatomic Interaction Potential Theory, Volume 2: Applications discusses the variety of applicable theoretical material and approaches in the calculations for diatomic systems in their ground states. The volume covers the descriptions and illustrations of modern calculations. Chapter I discusses the calculation of the interaction potential for large and small values of the internuclear distance R (separated and united atom limits). Chapter II covers the methods used for intermediate values of R, which in principle means any values of R. The Hartree-Fock and configuration interaction schemes des
Nonlinear Gyrokinetic Theory With Polarization Drift
International Nuclear Information System (INIS)
Wang, L.; Hahm, T.S.
2010-01-01
A set of the electrostatic toroidal gyrokinetic Vlasov equation and the Poisson equation, which explicitly includes the polarization drift, is derived systematically by using Lie-transform method. The polarization drift is introduced in the gyrocenter equations of motion, and the corresponding polarization density is derived. Contrary to the wide-spread expectation, the inclusion of the polarization drift in the gyrocenter equations of motion does not affect the expression for the polarization density significantly. This is due to modification of the gyrocenter phase-space volume caused by the electrostatic potential [T. S. Hahm, Phys. Plasmas 3, 4658 (1996)].
International Nuclear Information System (INIS)
Pang Xiaofeng
2010-01-01
When the Schroedinger equation in quantum mechanics is replaced by the nonlinear Schroedinger equation to describe microscopic particles in nonlinear quantum systems, it has been verified that the nature of the particles differs considerably from those in quantum mechanics, where they are localized and have also wave-corpuscle duality due to the nonlinear interactions. In this case the influences of externally applied potentials in the nonlinear Schroedinger equation on the natures of the microscopic particles have been studied by a perturbation theory. The studied results show that the external potential can change the states of the microscopic particles, such as the positions, amplitude and wave forms, but cannot change the wave-corpuscle duality. In the meanwhile, we find further that the relationship between the external potential and change of positions of the particle satisfies the rule of motion of classical particles. Thus we know from this study that the kinetic energy term, (h 2 /2m)∇ 2 φ, in the nonlinear Schroedinger equation can only make the microscopic particles have a wave feature, but the nonlinear interaction b|φ| 2 φ determines its corpuscle feature, their combination makes the microscopic particles have a wave-corpuscle duality, and the potential V(r → ,t)φ changes only the positions, amplitude and wave form of the particles. Therefore the nonlinear interaction plays an important role in determination of the wave-corpuscle duality of microscopic particles in quantum theory.
Potential theory for directed networks.
Directory of Open Access Journals (Sweden)
Qian-Ming Zhang
Full Text Available Uncovering factors underlying the network formation is a long-standing challenge for data mining and network analysis. In particular, the microscopic organizing principles of directed networks are less understood than those of undirected networks. This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks. Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. In summary, our main contribution is twofold: (i We propose a new mechanism for the local organization of directed networks; (ii We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find out direct applications in missing link prediction and friendship recommendation.
Potential Theory for Directed Networks
Zhang, Qian-Ming; Lü, Linyuan; Wang, Wen-Qiang; Zhou, Tao
2013-01-01
Uncovering factors underlying the network formation is a long-standing challenge for data mining and network analysis. In particular, the microscopic organizing principles of directed networks are less understood than those of undirected networks. This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks. Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. In summary, our main contribution is twofold: (i) We propose a new mechanism for the local organization of directed networks; (ii) We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find out direct applications in missing link prediction and friendship recommendation. PMID:23408979
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 electrodynamics coupled to teleparallel theory of gravity
Gamal, G. L. Nashed
2011-02-01
Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy—momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy—momentum we obtain the value of energy.
Information theory and stochastics for multiscale nonlinear systems
Majda, Andrew J; Grote, Marcus J
2005-01-01
This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...
Application of nonlinear feedback control theory to supermaneuverable aircraft
Garrard, William L.; Enns, Dale F.
1991-01-01
Controlled flight at extremely high angles of attack, far exceeding the stall angle, and/or at high angular rates is sometimes referred to as supermaneuvering flight. The objective was to examine methods for design of control laws for aircraft performing supermaneuvers. Since the equations which govern the motion of aircraft during supermaneuvers are nonlinear, this study concentrated on nonlinear control law design procedures. The two nonlinear techniques considered were Nonlinear Quadratic Regulator (NLQR) theory and nonlinear dynamic inversion. A conventional gain scheduled proportional plus integral (P + I) controller was also developed to serve as a baseline design typical of current control laws used in aircraft. A mathematical model of a generic supermaneuverable aircraft was developed from data obtained from the literature. A detailed computer simulation of the aircraft was also developed. This simulation allowed the flying of proposed supermaneuvers and was used to evaluate the performance of the control law designs and to generate linearized models of the aircraft at different flight conditions.
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
Composite Beam Theory with Material Nonlinearities and Progressive Damage
Jiang, Fang
Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping
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
Synthesis of robust nonlinear autopilots using differential game theory
Menon, P. K. A.
1991-01-01
A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.
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
Nonlinear dynamical systems for theory and research in ergonomics.
Guastello, Stephen J
2017-02-01
Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Calvo, Gabriel F.
2009-01-01
In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions
Chandra Shekhara Shetty, T.; Chidan Kumar, C. S.; Gagan Patel, K. N.; Chia, Tze Shyang; Dharmaprakash, S. M.; Ramasami, Ponnadurai; Umar, Yunusa; Chandraju, Siddegowda; Quah, Ching Kheng
2017-09-01
Two new chalcones namely, (2E)-1-(3-fluoro-4-methoxyphenyl)-3-(4-methoxyphenyl) prop-2-en-1-one and (2E)-3-(4-chlorophenyl)-1-(3-fluoro-4-methoxyphenyl)prop-2-en-1-one were synthesized and grown as single crystals by slow evaporation technique in methanol. The FTIR spectrum recorded confirms the presence of functional groups in these materials. The molecular conformation of the compounds was achieved by single crystal X-ray diffraction studies. The thermal stability of the crystals was determined from TGA/DSC curve. The third order optical nonlinearity of the chalcone compounds in DMF solution has been carried out using an Nd:YAG laser at 532 nm as the source of excitation. The nonlinear optical response was characterized by measuring the intensity dependent refractive index n2 of the medium using Z-scan technique. It is seen that the molecules exhibit a negative (defocusing) nonlinearity and large nonlinear refractive index of the order of -1.8 × 10-11 esu. The third-order nonlinearity of the studied chalcones is dominated by nonlinear refraction, which leads to strong optical limiting of laser. The result reveals that these two new chalcone molecules would be a promising material for optical limiting applications. In addition, the optimized molecular geometry, vibrational frequencies in gas, and the Molecular Electrostatic Potential (MEP) surface parameters of the two molecules were calculated using DFT/B3LYP method with 6-311++G(d,p) basis set in ground state. All the theoretical calculations were found in good agreement with experimental data.
Dissipative double-well potential: Nonlinear stationary and pulsating modes
International Nuclear Information System (INIS)
Zezyulin, Dmitry A.; Konotop, Vladimir V.; Alfimov, Georgy L.
2010-01-01
The analysis of nonlinear modes in a complex absorbing double-well potential supported by linear gain is presented. Families of the nonlinear modes and their bifurcations are found numerically by means of the properly modified 'shooting' method. Linear stability and dynamics of the modes are studied. It is shown that no stable modes exist in the case of attractive nonlinearity, while stable modes, including nonsymmetric ones, are found when the nonlinearity is repulsive. Varying a control parameter (e.g., the height of barrier between the wells) results in switching from one mode to another. Apart from stationary modes we have found pulsating solutions emergent from unstable modes.
Untangling the drivers of nonlinear systems with information theory
Wing, S.; Johnson, J.
2017-12-01
Many systems found in nature are nonlinear. The drivers of the system are often nonlinearly correlated with one another, which makes it a challenge to understand the effects of an individual driver. For example, solar wind velocity (Vsw) and density (nsw) are both found to correlate well with radiation belt fluxes and are thought to be drivers of the magnetospheric dynamics; however, the Vsw is anti-correlated with nsw, which can potentially confuse interpretation of these relationships as causal or coincidental. Information theory can untangle the drivers of these systems, describe the underlying dynamics, and offer constraints to modelers and theorists, leading to better understanding of the systems. Two examples are presented. In the first example, the solar wind drivers of geosynchronous electrons with energy range of 1.8-3.5 MeV are investigated using mutual information (MI), conditional mutual information (CMI), and transfer entropy (TE). The information transfer from Vsw to geosynchronous MeV electron flux (Je) peaks with a lag time (t) of 2 days. As previously reported, Je is anticorrelated with nsw with a lag of 1 day. However, this lag time and anticorrelation can be attributed mainly to the Je(t + 2 days) correlation with Vsw(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time operating in 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 days) vs. Vsw(t). In the second example, the previously identified causal parameters of the solar cycle such as the solar polar field, meridional flow, polar faculae (proxy for polar field), dipole axis strength
Multiple outflows, spatial components, and nonlinearities in age theory
Calabrese, Salvatore; Porporato, Amilcare
2017-01-01
Water age has become an important variable for the characterization of hydrologic systems. The goal of this paper is to analyze the role of multiple outflows, spatial components, and nonlinearities in age theory. We first extend the theory to linear systems with multiple outflows, including the relationship between age distribution at death and survival time distribution at birth. We further show that for each outflow there is a survival time distribution at birth, which normalized corresponds to the impulse-response function for the specific outflow. We also analyze how the impulse-response function affects both the amplitude gain and time delay of the outflow and the long-term average partitioning. With regard to linear spatially extended systems, we link the impulse-response function to the Green's function. This allows us to easily compute the loss function and the age distribution for the system. Finally, we focus on nonlinear systems to analyze the effects of storage-dependent and age distribution-dependent loss functions. By considering the Burgers' equation, we show how the relationships between spatial dynamics and the age distribution are complicated by nonlinearities.
On the non-linear scale of cosmological perturbation theory
International Nuclear Information System (INIS)
Blas, Diego; Garny, Mathias; Konstandin, Thomas
2013-04-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Theories of quantum dissipation and nonlinear coupling bath descriptors
Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing
2018-03-01
The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.
Non-linear second-order periodic systems with non-smooth potential
Indian Academy of Sciences (India)
In this paper we study second order non-linear periodic systems driven by the ordinary vector -Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on ...
Non-linear second-order periodic systems with non-smooth potential
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. In this paper we study second order non-linear periodic systems driven by the ordinary vector p-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth ...
Yeo, Joonhyun
2009-11-01
We study a zero-dimensional version of the fluctuating nonlinear hydrodynamics (FNH) of supercooled liquids originally investigated by Das and Mazenko (DM) [Shankar P. Das and Gene F. Mazenko Phys. Rev. A 34, 2265 (1986)]. The time-dependent density-like and momentum-like variables are introduced with no spatial degrees of freedom in this toy model. The structure of nonlinearities takes the similar form to the original FNH, which allows one to study in a simpler setting the issues raised recently regarding the field theoretical approaches to glass forming liquids. We study the effects of density nonlinearities on the time evolution of correlation and response functions by developing field theoretic formulations in two different ways: first by following the original prescription of DM and then by constructing a dynamical action which possesses a linear time-reversal symmetry as proposed recently. We show explicitly that, at the one-loop order of the perturbation theory, the DM-type field theory does not support a sharp ergodic-nonergodic transition, while the other admits one. The simple nature of the toy model in the DM formulation allows us to develop numerical solutions to a complete set of coupled dynamical equations for the correlation and response functions at the one-loop order.
Silva, Walter A.
1993-01-01
The presentation begins with a brief description of the motivation and approach that has been taken for this research. This will be followed by a description of the Volterra Theory of Nonlinear Systems and the CAP-TSD code which is an aeroelastic, transonic CFD (Computational Fluid Dynamics) code. The application of the Volterra theory to a CFD model and, more specifically, to a CAP-TSD model of a rectangular wing with a NACA 0012 airfoil section will be presented.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
Analytic theory of the nonlinear M = 1 tearing mode
International Nuclear Information System (INIS)
Hazeltine, R.D.; Meiss, J.D.; Morrison, P.J.
1985-09-01
Numerical studies show that the m = 1 tearing mode continues to grow exponentially well into the nonlinear regime, in contrast with the slow, ''Rutherford,'' growth of m > 1 modes. We present a single helicity calculation which generalizes that of Rutherford to the case when the constant-psi approximation is invalid. As in that theory, the parallel current becomes an approximate flux function when the island size, W, exceeds the linear tearing layer width. However for the m = 1 mode, W becomes proportional to deltaB, rather than (deltaB)/sup 1/2/ above this critical amplitude. This implies that the convective nonlinearity in Ohm's law, which couples the m = 0 component to the m = 1 component, dominates the resistive diffusion term. The balance between the inductive electric field and this convective nonlinearity results in exponential growth. Assuming the form of the perturbed fields to be like that of the linear mode, we find that the growth occurs at 71% of the linear rate
Nonlinear magnetotransport theory and Hall induced resistance oscillations in graphene.
Gutiérrez-Jáuregui, R; Torres, M
2014-06-11
The quantum oscillations of nonlinear magnetoresistance in graphene that occur in response to a dc current bias are investigated. We present a theoretical model for the nonlinear magnetotransport of graphene carriers. The model is based on the exact solution of the effective Dirac equation in crossed electric and magnetic fields, while the effects of randomly distributed impurities are perturbatively added. To compute the nonlinear current effects, we develop a covariant formulation of the migration center theory. The current is calculated for short- and large-range scatterers. The analysis of the differential resistivity in the large magnetic field region, shows that the extrema of the Shubnikov de Hass oscillations invert when the dc currents exceed a threshold value. These results are in good agreement with experimental observations. In the small magnetic field regime, corresponding to large filling factors, the existence of Hall induced resistance oscillations are predicted for ultra clean graphene samples. These oscillations originate from Landau-Zener tunneling between Landau levels, that are tilted by the strong electric Hall field.
Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory
Wang, Liming; Zheng, Shijie
2018-02-01
In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.
Nonlinear mean field theory for nuclear matter and surface properties
International Nuclear Information System (INIS)
Boguta, J.; Moszkowski, S.A.
1983-01-01
Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)
A non-linear theory of strong interactions
International Nuclear Information System (INIS)
Skyrme, T.H.R.
1994-01-01
A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs
Quantum theory from a nonlinear perspective Riccati equations in fundamental physics
Schuch, Dieter
2018-01-01
This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in ...
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
Nonlinear polarization of ionic liquids: theory, simulations, experiments
Kornyshev, Alexei
2010-03-01
Room temperature ionic liquids (RTILs) composed of large, often asymmetric, organic cations and simple or complex inorganic or organic anions do not freeze at ambient temperatures. Their rediscovery some 15 years ago is widely accepted as a ``green revolution'' in chemistry, offering an unlimited number of ``designer'' solvents for chemical and photochemical reactions, homogeneous catalysis, lubrication, and solvent-free electrolytes for energy generation and storage. As electrolytes they are non-volatile, some can sustain without decomposition up to 6 times higher voltages than aqueous electrolytes, and many are environmentally friendly. The studies of RTILs and their applications have reached a critical stage. So many of them can be synthesized - about a thousand are known already - their mixtures can further provide ``unlimited'' number of combinations! Thus, establishing some general laws that could direct the best choice of a RTIL for a given application became crucial; guidance is expected from theory and modelling. But for a physical theory, RTILs comprise a peculiar and complex class of media, the description of which lies at the frontier line of condensed matter theoretical physics: dense room temperature ionic plasmas with ``super-strong'' Coulomb correlations, which behave like glasses at short time-scale, but like viscous liquids at long-time scale. This talk will introduce RTILs to physicists and overview the current understanding of the nonlinear response of RTILs to electric field. It will focus on the theory, simulations, and experimental characterisation of the structure and nonlinear capacitance of the electrical double layer at a charged electrode. It will also discuss pros and contras of supercapacitor applications of RTILs.
Nonlinear dynamics of semiclassical coherent states in periodic potentials
International Nuclear Information System (INIS)
Carles, Rémi; Sparber, Christof
2012-01-01
We consider nonlinear Schrödinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding semiclassical scaling regime, we construct asymptotic solutions, which are concentrated both in space and in frequency around the effective semiclassical phase-space flow induced by Bloch’s spectral problem. The dynamics of these generalized coherent states is governed by a nonlinear Schrödinger model with effective mass. In the case of nonlocal nonlinearities, we establish a novel averaging-type result in the critical case. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
Theory of weakly nonlinear self-sustained detonations
Faria, Luiz
2015-11-03
We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations.
History of nonlinear oscillations theory in France (1880-1940)
Ginoux, Jean-Marc
2017-01-01
This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own...
International Nuclear Information System (INIS)
Hernandez-Tenorio, C.; Belyaeva, T.L.; Serkin, V.N.
2007-01-01
The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schroedinger equation model with time-dependent harmonic oscillator potential. The model allows one to analyse on general basis a variety of nonlinear phenomena appearing both in Bose-Einstein condensate, condensed matter physics, nonlinear optics, and biophysics. The soliton parametric resonance is investigated by using two complementary methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible denaturation of soliton bound states are also considered
On the optical potential theory
International Nuclear Information System (INIS)
Zubarev, A.L.
1978-01-01
For the nuclear reaction description a separable optical potential is constructed. Sop is optimal in view of the Schwinger variational principle. The green function is calculated with the Vsub(opt) potential. Equations of the method of strong channel coupling. A characteristic case of the three-body problem is considered, namely: elastic scattering of a particle on the bound state of second and third particles
Non-linearities in Theory-of-Mind Development
Blijd-Hoogewys, Els M. A.; van Geert, Paul L. C.
2017-01-01
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. PMID:28101065
Magnetic fields, special relativity and potential theory elementary electromagnetic theory
Chirgwin, B H; Kilmister, C W
1972-01-01
Magnetic Fields, Special Relativity and Potential Theory is an introduction to electromagnetism, special relativity, and potential theory, with emphasis on the magnetic field of steady currents (magnetostatics). Topics covered range from the origin of the magnetic field and the magnetostatic scalar potential to magnetization, electromagnetic induction and magnetic energy, and the displacement current and Maxwell's equations. This volume is comprised of five chapters and begins with an overview of magnetostatics, followed by a chapter on the methods of solving potential problems drawn from elec
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...... to the previous theory of two-wave mixing, the theory presented here is more general and the application of the theory to the photorefractive materials, Kerr media and semiconductor broad-area amplifiers are described....
Wavepacket scattering in potential theory
International Nuclear Information System (INIS)
Weber, T.A.; Hammer, C.L.
1977-01-01
A contour integration technique is developed which enforces the initial conditions for wavepacket-potential scattering. The expansion coefficients for the exact energy eigenstate expansion are automatically expressed in terms of the plane wave expansion coefficients of the initial wavepacket, thereby simplifying what is usually a tedious, mathematical process. The method is applicable regardless of the initial spatial separation of the wavepacket from the scattering center
Quantum theory of a one-dimensional laser with output coupling. 2. Nonlinear theory
International Nuclear Information System (INIS)
Penaforte, J.C.; Baseia, B.
1984-01-01
A previous paper describing the quantum theory of a laser in linear approximation is here extended to the nonlinear case. Instead of the approach of conventional theory - which deals with discrete 'cavity-modes' and includes artificial mechanisms to simulates radiation field losses due to beam extraction - a more realistic model of optical cavity having output coupling is used that works entirely within the continuous spectrum, allowing one to obtain the equations for the field both inside and outside the laser cavity. Besides the quantum noise due to spontaneous emission, a noise term of classical nature due to transmission losses automatically emerges from the present treatment. For single-collective-mode operation the equations for laser field are solved exactly, yielding the transient and steady-state solutions. Inside the laser cavity, the results of nonlinear analysis agree with those found in conventional theory once the conventional 'mode-amplitude' is reinterpreted as a collective variable. Outside the cavity - unaccessible region in the conventional treatment - the solution for the laser field is also exhibited. Further considerations as concerning the role played by the noise terms in the field buildup are discussed. (Author) [pt
Microscopic theory of linear and nonlinear terahertz spectroscopy of semiconductors
Energy Technology Data Exchange (ETDEWEB)
Steiner, Johannes
2008-12-09
This Thesis presents a fully microscopic theory to describe terahertz (THz)-induced processes in optically-excited semiconductors. The formation process of excitons and other quasi-particles after optical excitation has been studied in great detail for a variety of conditions. Here, the formation process is not modelled but a realistic initial many-body state is assumed. In particular, the linear THz response is reviewed and it is demonstrated that correlated quasi-particles such as excitons and plasmons can be unambiguously detected via THz spectroscopy. The focus of the investigations, however, is on situations where the optically-excited many-body state is excited by intense THz fields. While weak pulses detect the many-body state, strong THz pulses control and manipulate the quasi-particles in a way that is not accessible via conventional techniques. The nonlinear THz dynamics of exciton populations is especially interesting because similarities and differences to optics with atomic systems can be studied. (orig.)
Inhomogeneous critical nonlinear Schroedinger equations with a harmonic potential
International Nuclear Information System (INIS)
Cao Daomin; Han Pigong
2010-01-01
In this paper, we study the Cauchy problem of the inhomogeneous nonlinear Schroedinger equation with a harmonic potential: i∂ t u=-div(f(x)∇u)+|x| 2 u-k(x)|u| 4/N u, x is an element of R N , N≥1, which models the remarkable Bose-Einstein condensation. We discuss the existence and nonexistence results and investigate the limiting profile of blow-up solutions with critical mass.
Explicit Nonlinear Model Predictive Control Theory and Applications
Grancharova, Alexandra
2012-01-01
Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
Theory of Nonlinear Dispersive Waves and Selection of the Ground State
International Nuclear Information System (INIS)
Soffer, A.; Weinstein, M.I.
2005-01-01
A theory of time-dependent nonlinear dispersive equations of the Schroedinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, 'selection of the ground state', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides
Origin of soft limits from nonlinear supersymmetry in Volkov-Akulov theory
Energy Technology Data Exchange (ETDEWEB)
Kallosh, Renata; Karlsson, Anna; Murli, Divyanshu [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305 (United States)
2017-03-15
We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.
Supersymmetric construction of exactly solvable potentials and nonlinear algebras
International Nuclear Information System (INIS)
Junker, G.; Roy, P.
1998-01-01
Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and lowering operators of these harmonic oscillators and the SUSY operators we construct ladder operators for these new conditionally solvable systems. It is found that these ladder operators together with the Hamilton operator form a nonlinear algebra which is of quadratic and cubic type for the SUSY partners of the linear and radial harmonic oscillator
An asymptotic derivation of weakly nonlinear ray theory
Indian Academy of Sciences (India)
2.1) in the neighbourhood of the exact characteristic surface in space-time. Proper interpretation of transport equation along the nonlinear rays corresponding to leading order amplitude w has lead to physically realistic solutions [19, 13, 14, 18].
Fidler, Andrew F.; Engel, Gregory S.
2013-10-01
We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.
Tackling non-linearities with the effective field theory of dark energy and modified gravity
Frusciante, Noemi; Papadomanolakis, Georgios
2017-12-01
We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly non-linear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, non-linear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding non-linear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the non-linear effective field theory framework by considering a general action in the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we proceed to map the beyond-Horndeski theory and low-energy Hořava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the non-linear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly non-linear scales.
Nguyen, Nhan; Ting, Eric; Chaparro, Daniel
2017-01-01
This paper investigates the effect of nonlinear large deflection bending on the aerodynamic performance of a high aspect ratio flexible wing. A set of nonlinear static aeroelastic equations are derived for the large bending deflection of a high aspect ratio wing structure. An analysis is conducted to compare the nonlinear bending theory with the linear bending theory. The results show that the nonlinear bending theory is length-preserving whereas the linear bending theory causes a non-physical effect of lengthening the wing structure under the no axial load condition. A modified lifting line theory is developed to compute the lift and drag coefficients of a wing structure undergoing a large bending deflection. The lift and drag coefficients are more accurately estimated by the nonlinear bending theory due to its length-preserving property. The nonlinear bending theory yields lower lift and span efficiency than the linear bending theory. A coupled aerodynamic-nonlinear finite element model is developed to implement the nonlinear bending theory for a Common Research Model (CRM) flexible wing wind tunnel model to be tested in the University of Washington Aeronautical Laboratory (UWAL). The structural stiffness of the model is designed to give about 10% wing tip deflection which is large enough that could cause the nonlinear deflection effect to become significant. The computational results show that the nonlinear bending theory yields slightly less lift than the linear bending theory for this wind tunnel model. As a result, the linear bending theory is deemed adequate for the CRM wind tunnel model.
Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory
Gnutzmann, Sven; Waltner, Daniel
2016-03-01
In this paper we present a general framework for solving the stationary nonlinear Schrödinger equation (NLSE) on a network of one-dimensional wires modeled by a metric graph with suitable matching conditions at the vertices. A formal solution is given that expresses the wave function and its derivative at one end of an edge (wire) nonlinearly in terms of the values at the other end. For the cubic NLSE this nonlinear transfer operation can be expressed explicitly in terms of Jacobi elliptic functions. Its application reduces the problem of solving the corresponding set of coupled ordinary nonlinear differential equations to a finite set of nonlinear algebraic equations. For sufficiently small amplitudes we use canonical perturbation theory, which makes it possible to extract the leading nonlinear corrections over large distances.
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
Application of inertia-induced excitation theory for nonlinear acoustic ...
Indian Academy of Sciences (India)
nant excitation source channel of acoustic turbulence in the transonic domain of plasma flow. In bi-ion plasmas like ... Qualitative and quantitative modifications are introduced into its nonlinear counterpart [3] as ... into vacuum is modeled by the appropriate consideration of space charge separation effect on the expanding.
Symmetry properties of some nonlinear field theory models
International Nuclear Information System (INIS)
Shvachka, A.B.
1984-01-01
Various approaches towards the study of symmetry properties of some nonlinear evolution equations as well as possible ways of their computer implementation using the computer algebra systems langage are discussed. Special attention is paid to the method of pseudopotential investigation of formal integrability and isovector method for the equations of balance
A nonlinear theory for elastic plates with application to characterizing paper properties
M. W. Johnson; Thomas J. Urbanik
1984-03-01
A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...
A Thermodynamic Theory of Solid Viscoelasticity. Part II:; Nonlinear Thermo-viscoelasticity
Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)
2002-01-01
This paper, second in the series of three papers, develops a general, nonlinear, non-isothermal, compressible theory for finite rubber viscoelasticity and specifies it in a form convenient for solving problems important to the rubber, tire, automobile, and air-space industries, among others. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory of differential type has been developed for arbitrary non-isothermal deformations of viscoelastic solids. In this theory, the constitutive equations were presented as the sum of a rubber elastic (equilibrium) and a liquid type viscoelastic (non-equilibrium) terms. These equations have then been simplified using several modeling and simplicity arguments.
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 boundary value problems in quantum field theory
International Nuclear Information System (INIS)
Schrader, R.
1989-01-01
We discuss the general structure of a quantum field theory which is free in the interior of a bounded set B of R n . It is shown how to recover the field theory in the interior of B from a certain quantum field theory on the boundary. With an application to string theory in mind, we discuss the example where B equals an interval and the boundary value problem is given in terms of a euclidean functional integral with a P(var phi) interaction restricted to the boundary. copyright 1989 Academic Press, Inc
Stabilization of solitons under competing nonlinearities by external potentials
Energy Technology Data Exchange (ETDEWEB)
Zegadlo, Krzysztof B., E-mail: zegadlo@if.pw.edu.pl; Karpierz, Miroslaw A. [Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa (Poland); Wasak, Tomasz; Trippenbach, Marek [Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa (Poland); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-12-15
We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.
Stamovlasis, Dimitrios
2011-04-01
In this study, an attempt is made to integrate Nonlinear Dynamical Systems theory and neo-Piagetian theories applied to creative mental processes, such as problem solving. A catastrophe theory model is proposed, which implements three neo-Piagetian constructs as controls: the functional M-capacity as asymmetry and logical thinking and the degree of field dependence independence as bifurcation. Data from achievement scores of students in tenth grade physics were analyzed using dynamic difference equations and statistical regression techniques. The cusp catastrophe model proved superior comparing to the pre-post linear counterpart and demonstrated nonlinearity at the behavioral level. The nonlinear phenomenology, such as hysteresis effects and bifurcation, is explained by an analysis, which provides a causal interpretation via the mathematical theory of self-organization and thus building bridges between NDS-theory concepts and neo-Piagetian theories. The contribution to theory building is made, by also addressing the emerging philosophical, - ontological and epistemological- questions about the processes of problem solving and creativity.
Nonlinear theory of wakefield excitation in a rectangular multizone dielectric resonator
Directory of Open Access Journals (Sweden)
K. V. Galaydych
2011-01-01
Full Text Available A nonlinear self-consistent theory has been constructed and used to investigate numerically the wakefield excitation in multilayered dielectric resonators by relativistic electron bunches. Analytical expressions for solenoidal and potential components of an excited electromagnetic field have been derived. The excitation of a five-zone dielectric resonator by relativistic electron bunches was numerically investigated and comparison was made between the longitudinal distribution of an axial electric field and the results obtained previously for a corresponding problem in the waveguide formulation. The necessity of optimizing geometrical parameters of the resonator to reduce mode amplitudes nonresonant with a bunch, and to obtain a symmetric distribution of the longitudinal electric field component in the drive and accelerating channels, has been demonstrated.
Nonlinear gyrokinetic theory for finite-Β plasmas
International Nuclear Information System (INIS)
Hahm, T.S.; Lee, W.W.; Brizard, A.
1988-02-01
A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-β plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formation is valid for arbitrary values of k/perpendicular//rho//sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques. 31 refs
Design Wave Load Prediction by Non-Linear Strip Theories
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
1998-01-01
Some methods for predicting global stochastic wave load responses in ships are presented. The methods take into account the elastic behaviour of the ship and at least some of the non-linearities in the wave-induced loadings.Numerical rsults obtained for actual ships are reviewed with special...... emphasis on their usefulness in design procedures covering both extreme responses and fatigue damage predictions....
Nonlinear time series theory, methods and applications with R examples
Douc, Randal; Stoffer, David
2014-01-01
FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre
Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.
Levinson, Howard W; Markel, Vadim A
2016-10-01
We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.
Parametrization-dependence of nonlinear quantum field theories
International Nuclear Information System (INIS)
Tyutin, I.
1982-01-01
It is shown that in an arbitrary quantum field theory a change of variables (transition to a different parametrization) leads only to a change of the field variables in the renormalized action and in the generating functional for the vertex functions. As a consequence of this it is shown that the beta-functions in two-dimensional chiral theories do not depend on the choice of parametrization. A remark on the uniqueness of the renormalized action concludes the paper
Nonlinear Theory of Nonparaxial Laser Pulse Propagation in Plasma Channels
International Nuclear Information System (INIS)
Esarey, E.; Schroeder, C. B.; Shadwick, B. A.; Wurtele, J. S.; Leemans, W. P.
2000-01-01
Nonparaxial propagation of ultrashort, high-power laser pulses in plasma channels is examined. In the adiabatic limit, pulse energy conservation, nonlinear group velocity, damped betatron oscillations, self-steepening, self-phase modulation, and shock formation are analyzed. In the nonadiabatic limit, the coupling of forward Raman scattering (FRS) and the self-modulation instability (SMI) is analyzed and growth rates are derived, including regimes of reduced growth. The SMI is found to dominate FRS in most regimes of interest. (c) 2000 The American Physical Society
Quantization of a non-linearly realized supersymmetric theory
International Nuclear Information System (INIS)
Shima, Kazunari
1976-01-01
The two-dimensional version of the Volkov-Akulov's Lagrngian, where the super-symmetry is realized non-linearly by means of a single Majorana spinor psi(x), is quantized. The equal time anti-commutators for the field are not c-numbers but functions of the field itself. By the explicite calculation we shall show that supersymmetry charges of the model form the supersymmetry algebra(the graded Lie algebra) and the supersymmetry charges exactly generate a constant translation of psi(x) in the spinor space. In this work we restrict our investigation to the two-dimensional space-time for the sake of simplicity. (auth.)
Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory
Bridges, Thomas J.; Ratliff, Daniel J.
2018-04-01
The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.
Directory of Open Access Journals (Sweden)
Xia Liu
2017-02-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. In this article, we consider a class of discrete nonlinear Schrodinger equations with unbounded potentials. We obtain some new sufficient conditions on the multiplicity results of ground state solutions for the equations by using the symmetric mountain pass lemma. Recent results in the literature are greatly improved.
Nonlinear Dynamic Theory of Acute Cell Injuries and Brain Ischemia
Taha, Doaa; Anggraini, Fika; Degracia, Donald; Huang, Zhi-Feng
2015-03-01
Cerebral ischemia in the form of stroke and cardiac arrest brain damage affect over 1 million people per year in the USA alone. In spite of close to 200 clinical trials and decades of research, there are no treatments to stop post-ischemic neuron death. We have argued that a major weakness of current brain ischemia research is lack of a deductive theoretical framework of acute cell injury to guide empirical studies. A previously published autonomous model based on the concept of nonlinear dynamic network was shown to capture important facets of cell injury, linking the concept of therapeutic to bistable dynamics. Here we present an improved, non-autonomous formulation of the nonlinear dynamic model of cell injury that allows multiple acute injuries over time, thereby allowing simulations of both therapeutic treatment and preconditioning. Our results are connected to the experimental data of gene expression and proteomics of neuron cells. Importantly, this new model may be construed as a novel approach to pharmacodynamics of acute cell injury. The model makes explicit that any pro-survival therapy is always a form of sub-lethal injury. This insight is expected to widely influence treatment of acute injury conditions that have defied successful treatment to date. This work is supported by NIH NINDS (NS081347) and Wayne State University President's Research Enhancement Award.
Freed, Alan; Leonov, Arkady I.
2002-01-01
This paper, the last in the series, continues developing the nonlinear constitutive relations for non-isothermal, compressible, solid viscoelasticity. We initially discuss a single integral approach, more suitable for the glassy state of rubber-like materials, with basic functionals involved in the thermodynamic description for this type of viscoelasticity. Then we switch our attention to analyzing stability constraints, imposed on the general formulation of the nonlinear theory of solid viscoelasticity. Finally, we discuss specific (known from the literature or new) expressions for material functions that are involved in the constitutive formulations of both the rubber-like and glassy-like, complementary parts of the theory.
Linear and nonlinear theory study of Alpha Virginis
International Nuclear Information System (INIS)
Cox, A.N.; Hodson, S.W.; Clancy, S.P.
1981-01-01
Nonlinear radiation hydrodynamic calculations using a model for α Virginis, a β Cephei star, have been made to see if the cause of the recurrent radial pulsation epochs can be discovered. The basic observed characteristics of β Cephei variables are presented. A review of the various proposals to make these stars pulsate concludes that the excitation mechanism must be in the central convective core or variable composition regions. The envelope damps radial fundamental mode pulsations in 4 years and in even shorter periods for radial overtones. It is proposed here that the mixing of envelope hydrogen into the hydrogen depleted (or even exhausted) core can produce periodic pressure pulses which drive the pulsation amplitude up to the observed value. During the decay of the pulsations, evolution toward higher luminosities enables further episodes of mixing and driving to occur. We predict rapid amplitude increases when mixing occurs and a slow decay of radial (and nonradial modes for other β Cephei variables) between mixing episodes
Canonical problems in scattering and potential theory
Vinogradov, SS; Vinogradova, ED
2001-01-01
Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and uni...
Canonical problems in scattering and potential theory
Vinogradov, SS; Vinogradova, ED
2002-01-01
Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and uni...
Kinetic theory of nonlinear transport phenomena in complex plasmas
Energy Technology Data Exchange (ETDEWEB)
Mishra, S. K. [Institute for Plasma Research (IPR), Gandhinagar 382428 (India); Sodha, M. S. [Centre for Energy Studies (CES), Indian Institute of Technology Delhi (IITD), New Delhi 110016 (India)
2013-03-15
In contrast to the prevalent use of the phenomenological theory of transport phenomena, a number of transport properties of complex plasmas have been evaluated by using appropriate expressions, available from the kinetic theory, which are based on Boltzmann's transfer equation; in particular, the energy dependence of the electron collision frequency has been taken into account. Following the recent trend, the number and energy balance of all the constituents of the complex plasma and the charge balance on the particles is accounted for; the Ohmic loss has also been included in the energy balance of the electrons. The charging kinetics for the complex plasma comprising of uniformly dispersed dust particles, characterized by (i) uniform size and (ii) the Mathis, Rumpl, and Nordsieck power law of size distribution has been developed. Using appropriate expressions for the transport parameters based on the kinetic theory, the system of equations has been solved to investigate the parametric dependence of the complex plasma transport properties on the applied electric field and other plasma parameters; the results are graphically illustrated.
Benoit, Michel; Yates, Marissa L.; Raoult, Cécile
2017-04-01
bathymetric profile also compare well with the measured values. The statistical distributions of the free surface elevation and wave height, calculated from the simulated time series, are compared to those of the measurements, with particular attention paid to the extreme waves. To use this model for realistic cases with complex bathymetric variations and multidirectional wave fields, the model has been extended to two horizontal dimensions (2DH). The spectral approach in the vertical dimension is retained, while the horizontal plane is discretized with scattered nodes to maintain the model's flexibility. The horizontal derivatives are estimated with finite-difference type formulas using Radial Basis Functions (Wright and Fornberg, 2006). The 2DH version of the code is applied to simulate the propagation of regular waves over a semi-circular step, which acts as a focusing lens. The simulation results are compared to the experimental data set of Whalin (1971). The evolution of the higher harmonic amplitudes in the shallow-water zone demonstrates the ability of the model to simulate wave propagation over complex 2DH coastal bathymetries. References: Becq-Girard F., Forget P., Benoit M. (1999) Non-linear propagation of unidirectional wave fields over varying topography. Coastal Eng., 38, 91-113. Tian Y., Sato S. (2008) A numerical model on the interaction between nearshore nonlinear waves and strong currents. Coast. Eng. Journal, 50(4), 369-395. Whalin R.W. (1971) The limit of applicability of linear wave refraction theory in a convergence zone. Technical report, DTIC Documents. Wright G.B., Fornberg B. (2006) Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comp. Phys., 212, 99-123. Yates M.L., Benoit M. (2015) Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves. Int. J. Numer. Meth. Fluids, 77, 616-640. Zakharov V.E. (1968) Stability of periodic
Nucleon-nucleon scattering in the functional quantum theory of the nonlinear spinor field
International Nuclear Information System (INIS)
Haegele, G.
1979-01-01
The author calculates the S matrix for the elastic nucleon-nucleon scattering in the lowest approximation using the quantum theory of nonlinear spinor fields with special emphasis to the ghost configuration of this theory. Introducing a general scalar product a new functional channel calculus is considered. From the results the R and T matrix elements and the differential and integral cross sections are derived. (HSI)
On a theory of stability for nonlinear stochastic chemical reaction networks
Smadbeck, Patrick; Kaznessis, Yiannis N.
2015-01-01
We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms. PMID:25978877
Modeling Nonlinear Acoustic Standing Waves in Resonators: Theory and Experiments
Raman, Ganesh; Li, Xiaofan; Finkbeiner, Joshua
2004-01-01
The overall goal of the cooperative research with NASA Glenn is to fundamentally understand, computationally model, and experimentally validate non-linear acoustic waves in enclosures with the ultimate goal of developing a non-contact acoustic seal. The longer term goal is to transition the Glenn acoustic seal innovation to a prototype sealing device. Lucas and coworkers are credited with pioneering work in Resonant Macrosonic Synthesis (RMS). Several Patents and publications have successfully illustrated the concept of Resonant Macrosonic Synthesis. To utilize this concept in practical application one needs to have an understanding of the details of the phenomenon and a predictive tool that can examine the waveforms produced within resonators of complex shapes. With appropriately shaped resonators one can produce un-shocked waveforms of high amplitude that would result in very high pressures in certain regions. Our goal is to control the waveforms and exploit the high pressures to produce an acoustic seal. Note that shock formation critically limits peak-to-peak pressure amplitudes and also causes excessive energy dissipation. Proper shaping of the resonator is thus critical to the use of this innovation.
Theory of Linear and Nonlinear Gain in a Gyroamplifier using a Confocal Waveguide.
Soane, Alexander V; Shapiro, Michael A; Stephens, Jacob C; Temkin, Richard J
2017-09-01
The linear and nonlinear theory of a gyroamplifier using a confocal waveguide is presented. A quasi-optical approach to describing the modes of a confocal waveguide is derived. Both the equations of motion and the mode excitation equation are derived in detail. The confocal waveguide circuit has the advantage of reducing mode competition but the lack of azimuthal symmetry presents challenges in calculating the gain. In the linear regime, the gain calculated using the exact form factor for the confocal waveguide agrees with an azimuthally averaged form factor. A beamlet code including velocity spread effects has been written to calculate the linear and nonlinear (saturated) gain. It has been successfully benchmarked against the MAGY code for azimuthally symmetric cases. For the confocal waveguide, the beamlet code shows that the saturated gain is reduced when compared with results obtained using an azimuthally averaged form factor. The beamlet code derived here extends the capabilities of nonlinear gyroamplifier theory to configurations that lack azimuthal symmetry.
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.
The nonlinearity of the scalar field in a relativistic mean-field theory of the nucleus
International Nuclear Information System (INIS)
Reinhard, P.G.
1987-10-01
The form of the nonlinear selfcoupling of the scalar meson field in a nuclear relativistic mean-field theory is investigated. The conventional ansatz is shown to produce instabilities in critical applications. A modified selfcoupling is proposed which guarantees stability under all conditions. (orig.)
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1992-01-01
In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1994-01-01
In the existing `direct¿ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a `finitely additive¿ white noise is used to model the observation noise. We remove this asymmetry by modelling the
Non-linear 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...
Electron Correlations in Local Effective Potential Theory
Directory of Open Access Journals (Sweden)
Viraht Sahni
2016-08-01
Full Text Available Local effective potential theory, both stationary-state and time-dependent, constitutes the mapping from a system of electrons in an external field to one of the noninteracting fermions possessing the same basic variable such as the density, thereby enabling the determination of the energy and other properties of the electronic system. This paper is a description via Quantal Density Functional Theory (QDFT of the electron correlations that must be accounted for in such a mapping. It is proved through QDFT that independent of the form of external field, (a it is possible to map to a model system possessing all the basic variables; and that (b with the requirement that the model fermions are subject to the same external fields, the only correlations that must be considered are those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation–Kinetic effects. The cases of both a static and time-dependent electromagnetic field, for which the basic variables are the density and physical current density, are considered. The examples of solely an external electrostatic or time-dependent electric field constitute special cases. An efficacious unification in terms of electron correlations, independent of the type of external field, is thereby achieved. The mapping is explicated for the example of a quantum dot in a magnetostatic field, and for a quantum dot in a magnetostatic and time-dependent electric field.
Directory of Open Access Journals (Sweden)
Teffera M. Asfaw
2016-01-01
Full Text Available Let X be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space X⁎. Let T:X⊇DT→2X⁎ be maximal monotone of type Γdϕ (i.e., there exist d≥0 and a nondecreasing function ϕ:0,∞→0,∞ with ϕ(0=0 such that 〈v⁎,x-y〉≥-dx-ϕy for all x∈DT, v⁎∈Tx, and y∈X,L:X⊃D(L→X⁎ be linear, surjective, and closed such that L-1:X⁎→X is compact, and C:X→X⁎ be a bounded demicontinuous operator. A new degree theory is developed for operators of the type L+T+C. The surjectivity of L can be omitted provided that RL is closed, L is densely defined and self-adjoint, and X=H, a real Hilbert space. The theory improves the degree theory of Berkovits and Mustonen for L+C, where C is bounded demicontinuous pseudomonotone. New existence theorems are provided. In the case when L is monotone, a maximality result is included for L and L+T. The theory is applied to prove existence of weak solutions in X=L20,T;H01Ω of the nonlinear equation given by ∂u/∂t-∑i=1N(∂/∂xiAix,u,∇u+Hλx,u,∇u=fx,t, x,t∈QT; ux,t=0, x,t∈∂QT; and ux,0=ux,T, x∈Ω, where λ>0, QT=Ω×0,T, ∂QT=∂Ω×0,T, Aix,u,∇u=∂/∂xiρx,u,∇u+aix,u,∇u (i=1,2,…,N, Hλx,u,∇u=-λΔu+gx,u,∇u, Ω is a nonempty, bounded, and open subset of RN with smooth boundary, and ρ,ai,g:Ω¯×R×RN→R satisfy suitable growth conditions. In addition, a new existence result is given concerning existence of weak solutions for nonlinear wave equation with nonmonotone nonlinearity.
Classical and Quantum Nonlinear Integrable Systems: Theory and Application
International Nuclear Information System (INIS)
Brzezinski, Tomasz
2003-01-01
This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems such as the KdV equation, vertex models, RSOS and IRF models, spin chains, integrable differential equations, discrete systems, Ising, Potts and other lattice models and reaction--diffusion processes, as well as outlining major methods of solving integrable systems. These include Lax pairs, Baecklund and Miura transformations, the inverse scattering method, various types of the Bethe Ansatz, Painleve methods, the dbar method and fusion methods to mention just a few. The book is divided into two parts, each containing five chapters. The first part is devoted to classical integrable systems and introduces the subject through the KdV equation, and then proceeds through Painleve analysis, discrete systems and two-dimensional integrable partial differential equations, to culminate in the review of solvable lattice models in statistical physics, solved through the coordinate and algebraic Bethe Ansatz methods. The second part deals with quantum integrable systems, and begins with an outline of unifying approaches to quantum, statistical, ultralocal and non-ultralocal systems. The theory and methods of solving quantum integrable spin chains are then described. Recent developments in applying Bethe Ansatz methods in condensed matter physics, including superconductivity and nanoscale physics, are reviewed. The book concludes with an introduction to diffusion-reaction processes. Every chapter is devoted to a different subject and is self-contained, and thus can be read separately. A reader interesting in classical methods of solitons, such as the methods of solving the KdV equation, can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5, and so on. Thus the book should appeal and be useful to a wide range of theoretical
Theory of plasmonic effects in nonlinear optics: the case of graphene
Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration
The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).
Towards time-dependent current-density-functional theory in the non-linear regime.
Escartín, J M; Vincendon, M; Romaniello, P; Dinh, P M; Reinhard, P-G; Suraud, E
2015-02-28
Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na2. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.
Towards time-dependent current-density-functional theory in the non-linear regime
Energy Technology Data Exchange (ETDEWEB)
Escartín, J. M. [Université de Toulouse, UPS, Laboratoire de Physique Théorique, IRSAMC, F-31062 Toulouse Cedex (France); CNRS, UMR5152, F-31062 Toulouse Cedex (France); Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Vincendon, M.; Dinh, P. M.; Suraud, E. [Université de Toulouse, UPS, Laboratoire de Physique Théorique, IRSAMC, F-31062 Toulouse Cedex (France); CNRS, UMR5152, F-31062 Toulouse Cedex (France); Romaniello, P. [Laboratoire de Physique Théorique, CNRS, IRSAMC, Université Toulouse III - Paul Sabatier and European Theoretical Spectroscopy Facility, 118 Route de Narbonne, 31062 Toulouse Cedex (France); Reinhard, P.-G. [Institut für Theoretische Physik, Universität Erlangen, Staudtstraße 7, D-91058 Erlangen (Germany)
2015-02-28
Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na{sub 2}. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.
Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential
Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.
2018-03-01
We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p > 0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.
Theory and praxis of map analsys in CHEF part 2: Nonlinear normal form
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /FERMILAB
2009-04-01
This is the second of three memos describing how normal form map analysis is implemented in CHEF. The first [1] explained the manipulations required to assure that initial, linear transformations preserved Poincare invariants, thereby confirming correct normalization of action-angle coordinates. In this one, the transformation will be extended to nonlinear terms. The third, describing how the algorithms were implemented within the software of CHEF's libraries, most likely will never be written. The first section, Section 2, quickly lays out preliminary concepts and relationships. In Section 3, we shall review the perturbation theory - an iterative sequence of transformations that converts a nonlinear mapping into its normal form - and examine the equation which moves calculations from one step to the next. Following that is a section titled 'Interpretation', which identifies connections between the normalized mappings and idealized, integrable, fictitious Hamiltonian models. A final section contains closing comments, some of which may - but probably will not - preview work to be done later. My reasons for writing this memo and its predecessor have already been expressed. [1] To them can be added this: 'black box code' encourages users to proceed with little or no understanding of what it does or how it operates. So far, CHEF has avoided this trap admirably by failing to attract potential users. However, we reached a watershed last year: even I now have difficulty following the software through its maze of operations. Extensions to CHEF's physics functionalities, software upgrades, and even simple maintenance are becoming more difficult than they should. I hope these memos will mark parts of the maze for easier navigation in the future. Despite appearances to the contrary, I tried to include no (or very little) more than the minimum needed to understand what CHEF's nonlinear analysis modules do.1 As with the first memo, material
Effective field theory approaches for tensor potentials
Energy Technology Data Exchange (ETDEWEB)
Jansen, Maximilian
2016-11-14
Effective field theories are a widely used tool to study physical systems at low energies. We apply them to systematically analyze two and three particles interacting via tensor potentials. Two examples are addressed: pion interactions for anti D{sup 0}D{sup *0} scattering to dynamically generate the X(3872) and dipole interactions for two and three bosons at low energies. For the former, the one-pion exchange and for the latter, the long-range dipole force induce a tensor-like structure of the potential. We apply perturbative as well as non-perturbative methods to determine low-energy observables. The X(3872) is of major interest in modern high-energy physics. Its exotic characteristics require approaches outside the range of the quark model for baryons and mesons. Effective field theories represent such methods and provide access to its peculiar nature. We interpret the X(3872) as a hadronic molecule consisting of neutral D and D{sup *} mesons. It is possible to apply an effective field theory with perturbative pions. Within this framework, we address chiral as well as finite volume extrapolations for low-energy observables, such as the binding energy and the scattering length. We show that the two-point correlation function for the D{sup *0} meson has to be resummed to cure infrared divergences. Moreover, next-to-leading order coupling constants, which were introduced by power counting arguments, appear to be essential to renormalize the scattering amplitude. The binding energy as well as the scattering length display a moderate dependence on the light quark masses. The X(3872) is most likely deeper bound for large light quark masses. In a finite volume on the other hand, the binding energy significantly increases. The dependence on the light quark masses and the volume size can be simultaneously obtained. For bosonic dipoles we apply a non-perturbative, numerical approach. We solve the Lippmann-Schwinger equation for the two-dipole system and the Faddeev
Giant-spin nonlinear response theory of magnetic nanoparticle hyperthermia: A field dependence study
Carrião, M. S.; Aquino, V. R. R.; Landi, G. T.; Verde, E. L.; Sousa, M. H.; Bakuzis, A. F.
2017-05-01
Understanding high-field amplitude electromagnetic heat loss phenomena is of great importance, in particular, in the biomedical field, because the heat-delivery treatment plans might rely on analytical models that are only valid at low field amplitudes. Here, we develop a nonlinear response model valid for single-domain nanoparticles of larger particle sizes and higher field amplitudes in comparison to the linear response theory. A nonlinear magnetization expression and a generalized heat loss power equation are obtained and compared with the exact solution of the stochastic Landau-Lifshitz-Gilbert equation assuming the giant-spin hypothesis. The model is valid within the hyperthermia therapeutic window and predicts a shift of optimum particle size and distinct heat loss field amplitude exponents, which is often obtained experimentally using a phenomenological allometric function. Experimental hyperthermia data with distinct ferrite-based nanoparticles and third harmonic magnetization data support the nonlinear model, which also has implications for magnetic particle imaging and magnetic thermometry.
Nonlinear scattering from a plasma column. I - Theory. II Special cases
Crawford, F. W.; Harker, K. J.
1983-01-01
The scattered signal excited by nonlinear mixing of two plane waves normally incident on an infinitely long column of plasma is investigated. A general solution is obtained for the polarization in which the electric field vectors of the waves are perpendicular to the column axis and the column is assumed to be radically inhomogeneous. This general theory is then applied to the special cases of the inhomogeneous column in the long-wavelength limit, and the homogeneous column both for the general case and in the long-wavelength limit. It is determined that dipole and quadrupole components should predominate in the polar radiation pattern for the long-wavelength case. The special case of second harmonic generation due to a single incident wave is analyzed in detail. Nonlinear scattering coefficients are computed, and the corresponding polar radiation patterns are determined. The findings of this study are employed to evaluate the feasibility of observing nonlinear scattering from meteor trails.
Theory of ionization potentials of nonmetallic solids
Kumagai, Yu; Butler, Keith T.; Walsh, Aron; Oba, Fumiyasu
2017-03-01
Since the ionization potential (IP) is one of the fundamental quantities in a solid, ruling the physical and chemical properties and electronic device performances, many researchers have quantified the IPs using first-principles calculations of slab models recently. However, the breakdown into bulk and surface contributions has remained a contentious issue. In this study, we discuss how to decompose the IP into the bulk and surface contributions by using the macroscopic average technique. Although this procedure quantifies well-defined macroscopic dipoles and corroborates with the continuous model, it is not consistent with the physical intuition. This is because the strong charge fluctuation inside solids significantly contributes to the macroscopic dipole potential. We also discuss the possibility of an alternative splitting procedure that can be consistent with the physical intuition, and conclude that it is possible only when both bulk and surface charge density is well decomposed into a superposition of spherical charges. In the latter part, we evaluate the IPs of typical semiconductors and insulators such as Si, diamond, GaAs, GaN, ZnO, and MgO, using atomic-charge and molecular-charge approximations, in which the charge density of a solid is described as a superposition of charge density of the constituent atoms and molecules, respectively. We find that the atomic-charge approximation also known as the model-solid theory can successfully reproduce the IPs of covalent materials, but works poorly for ionic materials. On the other hand, the molecular-charge approximation, which partly takes into account the charge transfer from cations to anions, shows better predictive performance overall.
Solitary heat waves in nonlinear lattices with squared on-site potential
Indian Academy of Sciences (India)
resulting nonlinear equation in its natural form is very difficult to solve because of its high nonlinearity and discreteness. Hence we analyse it numerically and in addition we go for the continuum limit. Since the on-site potential is sufficient to ensure the validity of Fourier's law, we analyse the nature of heat conduction in ...
Application of the Hori Method in the Theory of Nonlinear Oscillations
Directory of Open Access Journals (Sweden)
Sandro da Silva Fernandes
2012-01-01
Full Text Available Some remarks on the application of the Hori method in the theory of nonlinear oscillations are presented. Two simplified algorithms for determining the generating function and the new system of differential equations are derived from a general algorithm proposed by Sessin. The vector functions which define the generating function and the new system of differential equations are not uniquely determined, since the algorithms involve arbitrary functions of the constants of integration of the general solution of the new undisturbed system. Different choices of these arbitrary functions can be made in order to simplify the new system of differential equations and define appropriate near-identity transformations. These simplified algorithms are applied in determining second-order asymptotic solutions of two well-known equations in the theory of nonlinear oscillations: van der Pol equation and Duffing equation.
Qian, Hong
2011-06-01
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.
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
On the theory of weak turbulence for the nonlinear Schrödinger equation
Escobedo, M
2015-01-01
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this article we prove the existence and approximations of solutions of periodic boundary-value problems of second-order ordinary nonlinear hybrid differential equations. We rely our results on Dhage iteration principle or method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. Our resutls are proved under weaker continuity and Lipschitz conditions. An example illustrates the theory developed in this article.
Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory
Xu, Yan; Hu, Bin; Wu, Jiang; Zhang, Jianhua
2014-04-01
The excitation intervention of strategic alliance may change with the changes in the parameters of circumstance (e.g., external alliance tasks). As a result, the stable cooperation between members may suffer a complete unplanned betrayal at last. However, current perspectives on strategic alliances cannot adequately explain this transition mechanism. This study is a first attempt to analyze this nonlinear phenomenon through stochastic catastrophe theory (SCT). A stochastic dynamics model is constructed based on the cooperation of strategic alliance from the perspective of evolutionary game theory. SCT explains the discontinuous changes caused by the changes in environmental parameters. Theoretically, we identify conditions where catastrophe can occur in the cooperation of alliance members.
T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory
Takahashi, Wataru
1995-01-01
The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the ories. Although our special emphasis was laid upon "nonlinearity" and "con vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark able rapid growth of this dis...
Zhu, Hong-Ming; Yu, Yu; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2017-12-01
We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale (rδrδL>0.5 for k ≲1 h /Mpc ) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21 cm intensity mapping initiatives.
International Nuclear Information System (INIS)
Symanzik, K.
1983-04-01
The method of paper I of this series is applied to the O(N) nonlinear sigma model. Due to use of non-manifestly-invariant perturbation theory the improvement part of the action, computed explicitly to one-loop order, is not manifestly O(N) invariant. It can be brought into manifestly O(N) invariant form by use of linear identities among dimension-four operators, which follow from the field equations of the unimproved action. The adequacy of the resulting two-parameter family of manifestly O(N) invariant improved actions is verified to one-loop order. (orig.)
Potential-functional embedding theory for molecules and materials.
Huang, Chen; Carter, Emily A
2011-11-21
We introduce a potential-functional embedding theory by reformulating a recently proposed density-based embedding theory in terms of functionals of the embedding potential. This potential-functional based theory completes the dual problem in the context of embedding theory for which density-functional embedding theory has existed for two decades. With this potential-functional formalism, it is straightforward to solve for the unique embedding potential shared by all subsystems. We consider charge transfer between subsystems and discuss how to treat fractional numbers of electrons in subsystems. We show that one is able to employ different energy functionals for different subsystems in order to treat different regions with theories of different levels of accuracy, if desired. The embedding potential is solved for by directly minimizing the total energy functional, and we discuss how to efficiently calculate the gradient of the total energy functional with respect to the embedding potential. Forces are also derived, thereby making it possible to optimize structures and account for nuclear dynamics. We also extend the theory to spin-polarized cases. Numerical examples of the theory are given for some homo- and hetero-nuclear diatomic molecules and a more complicated test of a six-hydrogen-atom chain. We also test our theory in a periodic bulk environment with calculations of basic properties of bulk NaCl, by treating each atom as a subsystem. Finally, we demonstrate the theory for water adsorption on the MgO(001)surface.
φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations
Sornette, D.; Simonetti, P.; Andersen, J. V.
2000-08-01
Physics and finance are both fundamentally based on the theory of random walks (and their generalizations to higher dimensions) and on the collective behavior of large numbers of correlated variables. The archetype examplifying this situation in finance is the portfolio optimization problem in which one desires to diversify on a set of possibly dependent assets to optimize the return and minimize the risks. The standard mean-variance solution introduced by Markovitz and its subsequent developments is basically a mean-field Gaussian solution. It has severe limitations for practical applications due to the strongly non-Gaussian structure of distributions and the nonlinear dependence between assets. Here, we present in details a general analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto Gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a nonlinear covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good conditioning. The portfolio distribution is then obtained as the solution of a mapping to a so-called φq field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The interaction (non-mean field) structure in this field theory is a direct consequence of the non-Gaussian nature of the distribution of asset price returns. We find that minimizing the portfolio variance (i.e. the relatively “small” risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive
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.
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
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)
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-08
In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.
A self-consistent nonlinear theory of resistive-wall instability in a relativistic electron beam
International Nuclear Information System (INIS)
Uhm, H.S.
1994-01-01
A self-consistent nonlinear theory of resistive-wall instability is developed for a relativistic electron beam propagating through a grounded cylindrical resistive tube. The theory is based on the assumption that the frequency of the resistive-wall instability is lower than the cutoff frequency of the waveguide. The theory is concentrated on study of the beam current modulation directly related to the resistive-wall klystron, in which a relativistic electron beam is modulated at the first cavity and propagates downstream through the resistive wall. Because of the self-excitation of the space charge waves by the resistive-wall instability, a highly nonlinear current modulation of the electron beam is accomplished as the beam propagates downstream. A partial integrodifferential equation is obtained in terms of the initial energy modulation (ε), the self-field effects (h), and the resistive-wall effects (κ). Analytically investigating the partial integrodifferential equation, a scaling law of the propagation distance z m at which the maximum current modulation occurs is obtained. It is found in general that the self-field effects dominate over the resistive-wall effects at the beginning of the propagation. As the beam propagates farther downstream, the resistive-wall effects dominate. Because of a relatively large growth rate of the instability, the required tube length of the klystron is short for most applications
A normal form approach to the theory of nonlinear betatronic motion
International Nuclear Information System (INIS)
Bazzani, A.; Todesco, E.; Turchetti, G.; Servizi, G.
1994-01-01
The betatronic motion of a particle in a circular accelerator is analysed using the transfer map description of the magnetic lattice. In the linear case the transfer matrix approach is shown to be equivalent to the Courant-Snyder theory: In the normal coordinates' representation the transfer matrix is a pure rotation. When the nonlinear effects due to the multipolar components of the magnetic field are taken into account, a similar procedure is used: a nonlinear change of coordinates provides a normal form representation of the map, which exhibits explicit symmetry properties depending on the absence or presence of resonance relations among the linear tunes. The use of normal forms is illustrated in the simplest but significant model of a cell with a sextupolar nonlinearity which is described by the quadratic Henon map. After recalling the basic theoretical results in Hamiltonian dynamics, we show how the normal forms describe the different topological structures of phase space such as KAM tori, chains of islands and chaotic regions; a critical comparison with the usual perturbation theory for Hamilton equations is given. The normal form theory is applied to compute the tune shift and deformation of the orbits for the lattices of the SPS and LHC accelerators, and scaling laws are obtained. Finally, the correction procedure of the multipolar errors of the LHC, based on the analytic minimization of the tune shift computed via the normal forms, is described and the results for a model of the LHC are presented. This application, relevant for the lattice design, focuses on the advantages of normal forms with respect to tracking when parametric dependences have to be explored. (orig.)
Singularity Theory for W-Algebra Potentials
Gaite, J
1994-01-01
The Landau potentials of W3-algebra models are analyzed with algebraic-geometric methods. The number of ground states and the number of independent perturbations of every potential coincide and can be computed. This number agrees with the structure of ground states obtained in a previous paper,
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
A Nonlinear Evolution Equation in an Ordered Space, Arising from Kinetic Theory
Grünfeld, C P
2005-01-01
We investigate the Cauchy problem for a nonlinear evolution equation, formulated in an abstract Lebesgue space, as a generalization of various Boltzmann kinetic models. Our main result provides sufficient conditions for the existence, uniqueness, and positivity of global in time solutions. The proof is based on ideas behind a well-known monotonicity method, originally developed within the existence theory of the classical Boltzmann equation in $L^1$. Our application examples concern Smoluchowski's coagulation equation, a Povzner-like equation with dissipative collisions, and a Boltzmann model with chemical reactions.
Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential
Directory of Open Access Journals (Sweden)
Runzhang Xu
2012-11-01
Full Text Available This article studies a nonlinear Schodinger equation with harmonic potential by constructing different cross-constrained problems. By comparing the different cross-constrained problems, we derive different sharp criterion and different invariant manifolds that separate the global solutions and blowup solutions. Moreover, we conclude that some manifolds are empty due to the essence of the cross-constrained problems. Besides, we compare the three cross-constrained problems and the three depths of the potential wells. In this way, we explain the gaps in [J. Shu and J. Zhang, Nonlinear Shrodinger equation with harmonic potential, Journal of Mathematical Physics, 47, 063503 (2006], which was pointed out in [R. Xu and Y. Liu, Remarks on nonlinear Schrodinger equation with harmonic potential, Journal of Mathematical Physics, 49, 043512 (2008].
Directory of Open Access Journals (Sweden)
Rabil Ayazoglu (Mashiyev
2017-11-01
where the nonlinearity is sublinear. We present the existence of infinitely many solutions for the problem. The main tool used here is a variational method and Krasnoselskii's genus theory combined with the theory of variable exponent Sobolev spaces. We also establish a Bartsch–Wang type compact embedding theorem for the variable exponent spaces.
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.
Directory of Open Access Journals (Sweden)
Ryo Oizumi
Full Text Available Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.
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
Kramers Turnover Theory for a Triple Well Potential
International Nuclear Information System (INIS)
Pollak, E.; Talkner, P.
2001-01-01
Kramers turnover theory is solved for a particle in a symmetric triple well potential for temperatures above the crossover temperature between tunneling and activated barrier crossing. Comparison with the turnover theory for a double well potential shows that the presence of the intermediate well always leads to a decrease of the reaction rate. At most though, the rate is a factor of two smaller than in the case of a double well potential. (author)
Korteweg-de Vries and nonlinear Schrödinger equations qualitative theory
Zhidkov, Peter E
2001-01-01
The emphasis of this book is on questions typical of nonlinear analysis and qualitative theory of PDEs. The selection of the material is related to the author's attempt to illuminate those particularly interesting questions not yet covered in other monographs though they have been the subject of published articles. One chapter, for example, is devoted to the construction of invariant measures for dynamical systems generated by certain equations and a result from a recent paper on basic properties of a system of eigenfunctions of a stationary problem. Also considered is an application of the method of qualitative theory of ODes to proving the existence of radial solutions of stationary problems and stability of solutions of NLSE nonvanishing as the spatial variable tends to infinity. Finally a recent result on the existence of an infinite sequence of invariant measures for the inegrable KdV equation is presented.
Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory
Directory of Open Access Journals (Sweden)
M. Jakomin
2011-01-01
Full Text Available In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the large displacements theory. We numerically calculate the deformation curve and the snap-through temperature using the fourth-order Runge-Kutta method and a nonlinear shooting method. We show how the temperature of both snap-through depends on the point where one type of the rotational curve transforms into another.
Electrostatic potential profile and nonlinear current in an interacting ...
Indian Academy of Sciences (India)
Unknown
Abstract. We consider an interacting one-dimensional molecular wire attached to two metal electrodes on either side of it. The electrostatic potential profile across the wire-electrode interface has been deduced solving the Schrodinger and Poisson equations self-consistently. Since the Poisson distribution crucially depends ...
Potential theory and the Lorenz condition
DEFF Research Database (Denmark)
Appel-Hansen, Jørgen
1994-01-01
When potentials are used to calculate the electromagnetic field intensities choices may be made. The present study is carried out in order to outline the various possibilities. It looks like the types of choices and their number depend on the actual situation and the preferences of the researcher...
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
Tokatly, I. V.
2011-11-01
It is shown that the density-potential mapping and the V-representability problems in the time-dependent current density functional theory (TDCDFT) are reduced to the solution of a certain many-body nonlinear Schrödinger equation (NLSE). The derived NLSE for TDCDFT links the earlier NLSE-based formulations of the time-dependent deformation functional theory (TDDefFT) and the time-dependent density functional theory (TDDFT). We establish a close relation between the nonlinear many-body problems which control the existence of TDCDFT, TDDFT, and TDDefFT, and thus develop a unified point of view on the whole family of the TDDFT-type theories.
Solitary heat waves in nonlinear lattices with squared on-site potential
Indian Academy of Sciences (India)
Abstract. A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the prop- erties of heat transfer are examined ...
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.
Svalbonas, V.; Levine, H.
1975-01-01
The theoretical analysis background for the STARS-2P nonlinear inelastic program is discussed. The theory involved is amenable for the analysis of large deflection inelastic behavior in axisymmetric shells of revolution subjected to axisymmetric loadings. The analysis is capable of considering such effects as those involved in nonproportional and cyclic loading conditions. The following are also discussed: orthotropic nonlinear kinematic hardening theory; shell wall cross sections and discrete ring stiffeners; the coupled axisymmetric large deflection elasto-plastic torsion problem; and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions.
Lanning, R. Nicholas; Xiao, Zhihao; Zhang, Mi; Novikova, Irina; Mikhailov, Eugeniy E.; Dowling, Jonathan P.
2017-07-01
We present a general, Gaussian spatial-mode propagation formalism for describing the generation of higher-order multi-spatial-mode beams generated during nonlinear interactions. Furthermore, to implement the theory, we simulate optical angular momentum transfer interactions and show how one can optimize the interaction to reduce the undesired modes. Past theoretical treatments of this problem have often been phenomenological, at best. Here we present an exact solution for the single-pass no-cavity regime, in which the nonlinear interaction is not overly strong. We apply our theory to two experiments, with very good agreement, and give examples of several more configurations, easily tested in the laboratory.
Turning points in nonlinear business cycle theories, financial crisis and the 2007-2008 downturn.
Dore, Mohammed H I; Singh, Ragiv G
2009-10-01
This paper reviews three nonlinear dynamical business cycle theories of which only one (The Goodwin model) reflects the stylized facts of observed business cycles and has a plausible turning point mechanism. The paper then examines the US (and now global) financial crisis of 2008 and the accompanying downturn in the US. The paper argues that a skewed income distribution could not sustain effective demand and that over the 2001-2006 expansion demand was maintained through massive amounts of credit, with more than 50 percent of sales in the US being maintained through credit. A vector autoregression model confirms the crucial role played by credit. However legislative changes that dismantled the restrictions placed on the financial sector after the crash of 1929 and the consequent structural changes in the financial sector after 1980 enabled the growth of new debt instruments and credit. But overexpansion of credit when profits and house prices were declining in 2005/06 led to a nonlinear shift due to a new realization of the poor quality of some of this debt, namely mortgage backed securities. Bankruptcies, followed by retrenchment at the banks, then led to the bursting of the credit bubble, with the possibility of a severe recession.
International Nuclear Information System (INIS)
Qiu Chunrong; Ouyang Zhengbiao; Zhang Shichang; Zhang Huibo; Jin Jianbo; Lai Yingxin
2005-01-01
A self-consistent nonlinear theory for the outer-slotted-coaxial-waveguide cyclotron autoresonance maser (CARM) amplifier is presented, which includes the characteristic equation of the wave, coupling equation of the wave with the relativistic electron beam and the simulation model. The influences of the magnetic field, the slot depth and width are investigated. The interesting characteristic of the device is that the mode competition can be efficiently suppressed by slotting the outer wall of the coaxial waveguide. A typical example is given by the theoretical design of a 137 GHz outer-slotted-coaxial-waveguide CARM amplifier by utilizing an electron beam with a voltage of 90 kV, current of 50 A, velocity pitch angle of 0.85 and a magnetic field of 43.0 kG. The nonlinear simulation predicts a power of 467.9 kW, an electronic efficiency of 10.4% and a saturated gain of 46.7 dB, if the electron beam has no velocity spread. However, the axial velocity spread deteriorates the device; for example, if the axial velocity spread is 2%, the peak power decreases to 332.4 kW with an efficiency of 7.4% and a saturated gain of 45.22 dB. Simulation shows that the efficiency of the outer-slotted-coaxial-waveguide CARM amplifier may be increased from 10.4% to 29.6% by tapering the magnetic field
[Analysis of the heart sound with arrhythmia based on nonlinear chaos theory].
Ding, Xiaorong; Guo, Xingming; Zhong, Lisha; Xiao, Shouzhong
2012-10-01
In this paper, a new method based on the nonlinear chaos theory was proposed to study the arrhythmia with the combination of the correlation dimension and largest Lyapunov exponent, through computing and analyzing these two parameters of 30 cases normal heart sound and 30 cases with arrhythmia. The results showed that the two parameters of the heart sounds with arrhythmia were higher than those with the normal, and there was significant difference between these two kinds of heart sounds. That is probably due to the irregularity of the arrhythmia which causes the decrease of predictability, and it's more complex than the normal heart sound. Therefore, the correlation dimension and the largest Lyapunov exponent can be used to analyze the arrhythmia and for its feature extraction.
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...... of our methods to Markov-driven processes.......This paper presents precise large deviation estimates for solutions to stochastic fixed point equations of the type V =_D f(V), where f(v)=Av+g(v) for a random function g(v)=o(v) a.s. as v tends to infinity. Specifically, we provide an explicit characterization of the pair (C,r) in the tail...
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...... are outlined. The procedure is applied to a typical SDOF system and results are compared with NLTH analysis commonly used for design purposes. Secondly, by means of the Virtual Work Principle, the definition of the equation of motion of a desired collapse mechanism of a multi degree of freedom (MDOF) system...
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.
A density functional theory-based chemical potential equalisation ...
Indian Academy of Sciences (India)
Unknown
of the conceptual framework in this direction. Thus, a perturbation theory of chemical binding has been developed17–20 where the concept of chemical potential equalisation4,5 (CPE) has been generalised to include the concept of bond chemical potential,17,18 spin- polarised electronegativity19,20 etc., thereby incorpo-.
Effective potential in Lorentz-breaking field theory models
Energy Technology Data Exchange (ETDEWEB)
Baeta Scarpelli, A.P. [Centro Federal de Educacao Tecnologica, Nova Gameleira Belo Horizonte, MG (Brazil); Setor Tecnico-Cientifico, Departamento de Policia Federal, Belo Horizonte, MG (Brazil); Brito, L.C.T. [Universidade Federal de Lavras, Departamento de Fisica, Lavras, MG (Brazil); Felipe, J.C.C. [Universidade Federal de Lavras, Departamento de Fisica, Lavras, MG (Brazil); Universidade Federal dos Vales do Jequitinhonha e Mucuri, Instituto de Engenharia, Ciencia e Tecnologia, Veredas, Janauba, MG (Brazil); Nascimento, J.R.; Petrov, A.Yu. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil)
2017-12-15
We calculate explicitly the one-loop effective potential in different Lorentz-breaking field theory models. First, we consider a Yukawa-like theory and some examples of Lorentz-violating extensions of scalar QED. We observe, for the extended QED models, that the resulting effective potential converges to the known result in the limit in which Lorentz symmetry is restored. Besides, the one-loop corrections to the effective potential in all the cases we study depend on the background tensors responsible for the Lorentz-symmetry violation. This has consequences for physical quantities like, for example, in the induced mass due to the Coleman-Weinberg mechanism. (orig.)
Solitary waves under the competition of linear and nonlinear periodic potentials
International Nuclear Information System (INIS)
Rapti, Z; Kevrekidis, P G; Konotop, V V; Jones, C K R T
2007-01-01
In this paper, we study the competition of the linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian perturbation theory can be used to obtain information about the existence of solutions, and the same approach, as well as eigenvalue count considerations, can be used to obtain detailed conditions about their linear stability. We find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of such solutions. A particularly interesting result of these considerations is the existence of a tunable cancellation effect between the linear and nonlinear lattices that allows for increased mobility of the solitary wave
Potential game theory applications in radio resource allocation
Lã, Quang Duy; Soong, Boon-Hee
2016-01-01
This book offers a thorough examination of potential game theory and its applications in radio resource management for wireless communications systems and networking. The book addresses two major research goals: how to identify a given game as a potential game, and how to design the utility functions and the potential functions with certain special properties in order to formulate a potential game. After proposing a unifying mathematical framework for the identification of potential games, the text surveys existing applications of this technique within wireless communications and networking problems found in OFDMA 3G/4G/WiFi networks, as well as next-generation systems such as cognitive radios and dynamic spectrum access networks. Professionals interested in understanding the theoretical aspect of this specialized field will find Potential Game Theory a valuable resource, as will advanced-level engineering students. It paves the way for extensive and rigorous research exploration on a topic whose capacity for...
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.
Generalized Sagdeev potential theory for shock waves modeling
Akbari-Moghanjoughi, M.
2017-05-01
In this paper, we develop an innovative approach to study the shock wave propagation using the Sagdeev potential method. We also present an analytical solution for Korteweg de Vries Burgers (KdVB) and modified KdVB equation families with a generalized form of the nonlinearity term which agrees well with the numerical one. The novelty of the current approach is that it is based on a simple analogy of the particle in a classical potential with the variable particle energy providing one with a deeper physical insight into the problem and can easily be extended to more complex physical situations. We find that the current method well describes both monotonic and oscillatory natures of the dispersive-diffusive shock structures in different viscous fluid configurations. It is particularly important that all essential parameters of the shock structure can be deduced directly from the Sagdeev potential in small and large potential approximation regimes. Using the new method, we find that supercnoidal waves can decay into either compressive or rarefactive shock waves depending on the initial wave amplitude. Current investigation provides a general platform to study a wide range of phenomena related to nonlinear wave damping and interactions in diverse fluids including plasmas.
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.
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.
Control of the symmetry breaking in double-well potentials by the resonant nonlinearity management
International Nuclear Information System (INIS)
Nistazakis, H. E.; Frantzeskakis, D. J.; Malomed, B. A.; Kevrekidis, P. G.
2011-01-01
We introduce a one-dimensional model of Bose-Einstein condensates (BECs), combining the double-well potential, which is a usual setting for the onset of spontaneous-symmetry-breaking (SSB) effects, and time-periodic modulation of the nonlinearity, which may be implemented by means of the Feshbach-resonance-management (FRM) technique. Both cases of the nonlinearity that is repulsive or attractive on the average are considered. In the former case, the main effect produced by the application of the FRM is spontaneous self-trapping of the condensate in either of the two potential wells in parameter regimes where it would remain untrapped in the absence of the management. In the weakly nonlinear regime, the frequency of intrinsic oscillations in the FRM-induced trapped state is very close to half the FRM frequency, suggesting that the effect is accounted for by a parametric resonance. In the case of the attractive nonlinearity, the FRM-induced effect is the opposite, i.e., enforced detrapping of a state which is self-trapped in its unmanaged form. In the latter case, the frequency of oscillations of the untrapped mode is close to a quarter of the driving frequency, suggesting that a higher-order parametric resonance may account for this effect.
Scattering theory for one-dimensional step potentials
International Nuclear Information System (INIS)
Ruijsenaars, S.N.M.; Bongaarts, P.J.M.
1977-01-01
The scattering theory is treated for the one-dimensional Dirac equation with potentials that are bounded, measurable, real-valued functions on the real line, having constant values, not necessarily the same, on the left and on the right side of a compact interval. Such potentials appear in the Klein paradox. It is shown that appropriately modified wave operators exist and that the corresponding S-operator is unitary. The connection between time-dependent scattering theory and time-independent scattering theory in terms of incoming and outgoing plane wave solutions is established and some further properties are proved. All results and their proofs have a straightforward translation to the one-dimensional Schroedinger equation with the same class of step potentials
Predicting path from undulations for C. elegans using linear and nonlinear resistive force theory
Keaveny, Eric E.; Brown, André E. X.
2017-04-01
A basic issue in the physics of behaviour is the mechanical relationship between an animal and its surroundings. The model nematode C. elegans provides an excellent platform to explore this relationship due to its anatomical simplicity. Nonetheless, the physics of nematode crawling, in which the worm undulates its body to move on a wet surface, is not completely understood and the mathematical models often used to describe this phenomenon are empirical. We confirm that linear resistive force theory, one such empirical model, is effective at predicting a worm’s path from its sequence of body postures for forward crawling, reversing, and turning and for a broad range of different behavioural phenotypes observed in mutant worms. Worms recently isolated from the wild have a higher effective drag anisotropy than the laboratory-adapted strain N2 and most mutant strains. This means the wild isolates crawl with less surface slip, perhaps reflecting more efficient gaits. The drag anisotropies required to fit the observed locomotion data (70 ± 28 for the wild isolates) are significantly larger than the values measured by directly dragging worms along agar surfaces (3-10 in Rabets et al (2014 Biophys. J. 107 1980-7)). A proposed nonlinear extension of the resistive force theory model also provides accurate predictions, but does not resolve the discrepancy between the parameters required to achieve good path prediction and the experimentally measured parameters. We confirm that linear resistive force theory provides a good effective model of worm crawling that can be used in applications such as whole-animal simulations and advanced tracking algorithms, but that the nature of the physical interaction between worms and their most commonly studied laboratory substrate remains unresolved.
Perdigão, Rui A. P.; Hall, Julia; Pires, Carlos A. L.; Blöschl, Günter
2017-04-01
Classical and stochastic dynamical system theories assume structural coherence and dynamic recurrence with invariants of motion that are not necessarily so. These are grounded on the unproven assumption of universality in the dynamic laws derived from statistical kinematic evaluation of non-representative empirical records. As a consequence, the associated formulations revolve around a restrictive set of configurations and intermittencies e.g. in an ergodic setting, beyond which any predictability is essentially elusive. Moreover, dynamical systems are fundamentally framed around dynamic codependence among intervening processes, i.e. entail essentially redundant interactions such as couplings and feedbacks. That precludes synergistic cooperation among processes that, whilst independent from each other, jointly produce emerging dynamic behaviour not present in any of the intervening parties. In order to overcome these fundamental limitations, we introduce a broad class of non-recursive dynamical systems that formulate dynamic emergence of unprecedented states in a fundamental synergistic manner, with fundamental principles in mind. The overall theory enables innovations to be predicted from the internal system dynamics before any a priori information is provided about the associated dynamical properties. The theory is then illustrated to anticipate, from non-emergent records, the spatiotemporal emergence of multiscale hyper chaotic regimes, critical transitions and structural coevolutionary changes in synthetic and real-world complex systems. Example applications are provided within the hydro-climatic context, formulating and dynamically forecasting evolving hydro-climatic distributions, including the emergence of extreme precipitation and flooding in a structurally changing hydro-climate system. Validation is then conducted with a posteriori verification of the simulated dynamics against observational records. Agreement between simulations and observations is
Chen, Weijie; Metz, Charles E; Giger, Maryellen L; Drukker, Karen
2010-02-01
Classifier design for a given classification task needs to take into consideration both the complexity of the classifier and the size of the dataset that is available for training the classifier. With limited training data, as often is the situation in computer-aided diagnosis of medical images, a classifier with simple structure (e.g., a linear classifier) is more robust and therefore preferred. We propose a novel two-class classifier, which we call a hybrid linear/nonlinear classifier (HLNLC), that involves two stages: the input features are linearly combined to form a scalar variable in the first stage and then the likelihood ratio of the scalar variable is used as the decision variable for classification. We first develop the theory of HLNLC by assuming that the feature data follow normal distributions. We show that the commonly used Fisher's linear discriminant function is generally not the optimal linear function in the first stage of the HLNLC. We formulate an optimization problem to solve for the optimal linear function in the first stage of the HLNLC, i.e., the linear function that maximizes the area under the receiver operating characteristic (ROC) curve of the HLNLC. For practical applications, we propose a robust implementation of the HLNLC by making a loose assumption that the two-class feature data arise from a pair of latent (rather than explicit) multivariate normal distributions. The novel hybrid classifier fills a gap between linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA) in the sense that both its theoretical performance and its complexity lie between those of the LDA and those of the QDA. Simulation studies show that the hybrid linear/nonlinear classifier performs better than LDA without increasing the classifier complexity accordingly. With a finite number of training samples, the HLNLC can perform better than that of the ideal observer due to its simplicity. Finally, we demonstrate the application of the HLNLC in
Existence, Stability and Dynamics of Nonlinear Modes in a 2D PartiallyPT Symmetric Potential
Directory of Open Access Journals (Sweden)
Jennie D’Ambroise
2017-02-01
Full Text Available It is known that multidimensional complex potentials obeying parity-time(PTsymmetry may possess all real spectra and continuous families of solitons. Recently, it was shown that for multi-dimensional systems, these features can persist when the parity symmetry condition is relaxed so that the potential is invariant under reﬂection in only a single spatial direction. We examine the existence, stability and dynamical properties of localized modes within the cubic nonlinear Schrödinger equation in such a scenario of partiallyPT-symmetric potential.
Phase-space description of plasma waves. Linear and nonlinear theory
International Nuclear Information System (INIS)
Biro, T.
1992-11-01
We develop an (r,k) phase space description of waves in plasmas by introducing Gaussian window functions to separate short scale oscillations from long scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation also in an inhomogeneous and time varying background plasma, we first discuss the proper form of the current response function. On the analogy of the particle distribution function f(v,r,t), we introduce a wave density N(k,r,t) on phase space. This function is proven to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density' along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible. Within the phase space representation, we obtain a very general formula for the second order nonlinear current in terms of the vector potential. This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasma, including the effects of inhomogeneous turbulence, wave convection and refraction. (author)
International Nuclear Information System (INIS)
El Kinani, A.H; Daoud, M.
2001-10-01
This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states a la Gazeau-Klauder and those a la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways. (author)
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.
Phase transitions at finite chemical potential in grand unified theories
International Nuclear Information System (INIS)
Bailin, D.; Love, A.
1984-01-01
We discuss the circumstances in which non-zero chemical potentials might prevent symmetry restoration in phase transitions in the early universe at grand unification or partial unification scales. The general arguments are illustrated by consideration of SO(10) and SU(5) grand unified theories. (orig.)
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.
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.
THE HEURISTIC POTENTIAL OF ANOMIE THEORY IN MODERN CRIMINOLOGY
Directory of Open Access Journals (Sweden)
Alexander Vladislavovich Pletnev
2015-01-01
Full Text Available This article deals with modern English theories of anomie. They can be used in Russian criminology. The main goal of article consists in detection of actual theories of anomie and definition of prospects of their use. As modern theories of anomie are poorly submitted in the Russian sociological and criminological literature, the subject of research is actual. This work contains the analysis of opportunities for adoption of modern conceptions of anomie of individual in Russian practice. During research development of the theory of anomie in the history of sociology was considered. The problem of anomie was admitted actual antique Greece. Anomie which is today concerned with normlessness and related to alienation is associated primarily with the works of Durkheim and Merton. Anomia developed in research by MacIver and Srole as a characteristic of individuals and related to the breakdown of the individual’s sense of attachment to society. Results of theoretical research show that theories of anomie of the personality have the greatest heuristic potential for modern Russian science. Other important conclusion of research is one that the anomie can have some sources of emergence. Further studying of this subject is necessary because English-language theories of anomie contain a set of theoretical and empirical results which can be used in the Russian criminology.
Perturbation theory calculations of model pair potential systems
Energy Technology Data Exchange (ETDEWEB)
Gong, Jianwu [Iowa State Univ., Ames, IA (United States)
2016-01-01
Helmholtz free energy is one of the most important thermodynamic properties for condensed matter systems. It is closely related to other thermodynamic properties such as chemical potential and compressibility. It is also the starting point for studies of interfacial properties and phase coexistence if free energies of different phases can be obtained. In this thesis, we will use an approach based on the Weeks-Chandler-Anderson (WCA) perturbation theory to calculate the free energy of both solid and liquid phases of Lennard-Jones pair potential systems and the free energy of liquid states of Yukawa pair potentials. Our results indicate that the perturbation theory provides an accurate approach to the free energy calculations of liquid and solid phases based upon comparisons with results from molecular dynamics (MD) and Monte Carlo (MC) simulations.
Time-dependent density functional theory for nonlinear properties of open-shell systems.
Rinkevicius, Zilvinas; Jha, Prakash Chandra; Oprea, Corneliu I; Vahtras, Olav; Agren, Hans
2007-09-21
This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials
Matouš, Karel; Geers, Marc G. D.; Kouznetsova, Varvara G.; Gillman, Andrew
2017-02-01
Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials
International Nuclear Information System (INIS)
Matouš, Karel; Geers, Marc G.D.; Kouznetsova, Varvara G.; Gillman, Andrew
2017-01-01
Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials
Energy Technology Data Exchange (ETDEWEB)
Matouš, Karel, E-mail: kmatous@nd.edu [Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556 (United States); Geers, Marc G.D.; Kouznetsova, Varvara G. [Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven (Netherlands); Gillman, Andrew [Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556 (United States)
2017-02-01
Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.
Generalizing a nonlinear geophysical flood theory to medium-sized river networks
Gupta, Vijay K.; Mantilla, Ricardo; Troutman, Brent M.; Dawdy, David; Krajewski, Witold F.
2010-01-01
The central hypothesis of a nonlinear geophysical flood theory postulates that, given space-time rainfall intensity for a rainfall-runoff event, solutions of coupled mass and momentum conservation differential equations governing runoff generation and transport in a self-similar river network produce spatial scaling, or a power law, relation between peak discharge and drainage area in the limit of large area. The excellent fit of a power law for the destructive flood event of June 2008 in the 32,400-km2 Iowa River basin over four orders of magnitude variation in drainage areas supports the central hypothesis. The challenge of predicting observed scaling exponent and intercept from physical processes is explained. We show scaling in mean annual peak discharges, and briefly discuss that it is physically connected with scaling in multiple rainfall-runoff events. Scaling in peak discharges would hold in a non-stationary climate due to global warming but its slope and intercept would change.
Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials
Shiroky, I. B.; Gendelman, O. V.
2018-02-01
We address the problem of transition front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For generic nonlinear coupling, one encounters a special regime of transitions, characterized by extremely narrow fronts, far supersonic velocities of the front propagation, and long waves in the oscillatory tail. This regime can be qualitatively associated with a shock wave. The front propagation can be described with the help of a simple reduced-order model; the latter delivers a kinetic law, which is almost not sensitive to the fine details of the on-site potential. Besides, it is possible to predict all main characteristics of the transition front, including its velocity, as well as the frequency and the amplitude of the oscillatory tail. Numerical results are in good agreement with the analytical predictions. The suggested approach allows one to consider the effects of an external pre-load, the next-nearest-neighbor coupling and the on-site damping. When the damping is moderate, it is possible to consider the shock propagation in the damped chain as a perturbation of the undamped dynamics. This approach yields reasonable predictions. When the damping is high, the transition front enters a completely different asymptotic regime of a subsonic kink. The gradient nonlinearity generically turns negligible, and the propagating front converges to the regime described by a simple exact solution for a continuous model with linear coupling.
Remarks on a Class of Nonlinear Schrödinger Equations with Potential Vanishing at Infinity
Directory of Open Access Journals (Sweden)
Hongbo Zhu
2013-01-01
Full Text Available We study the following nonlinear Schrödinger equation −Δu+V(xu=K(xf(u, x∈ℝN, u∈H1(ℝN, where the potential V(x vanishes at infinity. Working in weighted Sobolev space, we obtain the ground states of problem ( under a Nahari type condition. Furthermore, if V(x,K(x are radically symmetric with respect to x∈ℝN, it is shown that problem ( has a positive solution with some more general growth conditions of the nonlinearity. Particularly, if f(u=up, then the growth restriction σ≤p≤N+2/N-2 in Ambrosetti et al. (2005 can be relaxed to σ~≤p≤N+2/N-2, where σ~<σ if 0<β<α<2.
Hao, Y. X.; Zhang, W.
2010-05-01
The present investigation focuses on the research of the nonlinear vibration of a cantilevered FGMs rectangular plate subjected to the transversal excitation. Materials properties of the constituents are graded in the thickness direction according to a power law distribution and are assumed to be temperature-dependent and vary along the thickness direction. In the framework of the Reddy's Third-order shear deformation plate theory, the governing equations of motion for the cantilever FGMs rectangular plate are derived by using the Hamilton's principle. The thermal effect due to one-dimensional temperature gradient is included in the analysis. The equations of motion can be reduced two-degree-of-freedom nonlinear system under the external excitations using the Galerkin's method. Using numerical method, the control equations are analyzed to obtain the response curves. A detailed parametric study is conducted to show the influences of the material properties on dynamic responses of the nonlinear vibration of the cantilever FGM plate.
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...
Theory of Nonlinear Guided Electromagnetic Waves in a Plane Two-Layered Dielectric Waveguide
Directory of Open Access Journals (Sweden)
Valeria Yu. Kurseeva
2017-01-01
Full Text Available Propagation of transverse electric electromagnetic waves in a homogeneous plane two-layered dielectric waveguide filled with a nonlinear medium is considered. The original wave propagation problem is reduced to a nonlinear eigenvalue problem for an equation with discontinuous coefficients. The eigenvalues are propagation constants (PCs of the guided waves that the waveguide supports. The existence of PCs that do not have linear counterparts and therefore cannot be found with any perturbation method is proven. PCs without linear counterparts correspond to a novel propagation regime that arises due to the nonlinearity. Numerical results are also presented; the comparison between linear and nonlinear cases is made.
Time-dependent potential-functional embedding theory
International Nuclear Information System (INIS)
Huang, Chen; Libisch, Florian; Peng, Qing; Carter, Emily A.
2014-01-01
We introduce a time-dependent potential-functional embedding theory (TD-PFET), in which atoms are grouped into subsystems. In TD-PFET, subsystems can be propagated by different suitable time-dependent quantum mechanical methods and their interactions can be treated in a seamless, first-principles manner. TD-PFET is formulated based on the time-dependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the time-dependent embedding potential, i.e., a potential-functional formulation. By exploiting the Runge-Gross theorem, we prove the uniqueness of the time-dependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proof-of-principle, we demonstrate TD-PFET for a Na 4 cluster, in which each Na atom is treated as one subsystem and propagated by time-dependent Kohn-Sham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na 4 cluster using ALDA. We envision that TD-PFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate time-dependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods
McNeish, Daniel; Dumas, Denis
2017-01-01
Recent methodological work has highlighted the promise of nonlinear growth models for addressing substantive questions in the behavioral sciences. In this article, we outline a second-order nonlinear growth model in order to measure a critical notion in development and education: potential. Here, potential is conceptualized as having three components-ability, capacity, and availability-where ability is the amount of skill a student is estimated to have at a given timepoint, capacity is the maximum amount of ability a student is predicted to be able to develop asymptotically, and availability is the difference between capacity and ability at any particular timepoint. We argue that single timepoint measures are typically insufficient for discerning information about potential, and we therefore describe a general framework that incorporates a growth model into the measurement model to capture these three components. Then, we provide an illustrative example using the public-use Early Childhood Longitudinal Study-Kindergarten data set using a Michaelis-Menten growth function (reparameterized from its common application in biochemistry) to demonstrate our proposed model as applied to measuring potential within an educational context. The advantage of this approach compared to currently utilized methods is discussed as are future directions and limitations.
On Fermion Masses, Gradient Flows and Potential in Supersymmetric Theories
D'Auria, R
2001-01-01
In any low energy effective supergravity theory general formulae exist which allow one to discuss fermion masses, the scalar potential and breaking of symmetries in a model independent set up. A particular role in this discussion is played by Killing vectors and Killing prepotentials. We outline these relations in general and specify then in the context of N=1 and N=2 supergravities in four dimensions. Useful relations of gauged quaternionic geometry underlying hypermultiplets dynamics are discussed.
Directory of Open Access Journals (Sweden)
Kamel Filali
2017-10-01
Full Text Available This paper estimated the liquefaction potential of a saturated soil deposit subjected to a horizontal seismic excitation at its base using the total stress approach. A comparative analysis between the simplified and the nonlinear dynamic methods was used to verify to what extent the simplified method could be reliable. In order to generalise the reliability of the simplified method for any value of the maximum acceleration for the used earthquakes, a correction for the maximum acceleration less than 0.3g was proposed based on the comparison of safety factor values determined by the dynamic method illustrated by the equivalent linear model with lumped masses and the simplified method for a given profile of soil subjected to 38 earthquakes. The nonlinear behaviour of soil was represented by two hyperbolic models: Hardin and Drnevich, and Masing. To determine the cyclic resistance ratio (CRR, the cone penetration test (CPT based method, the standard penetration test (SPT based method, and the shear wave velocity based method were used. The safety factor was calculated as the ratio of CRR/CSR, where CSR represents the cyclic stress ratio. The results of the proposed correction have given smaller values of the safety factor compared to the nonlinear dynamic methods for the maximum acceleration less than 0.3g. In other words, by considering this correction, the most unfavourable case is always given by the modified simplified method.
Cosmological solutions in string theory with dilaton self interaction potential
Mora, C
2003-01-01
In this work we present homogeneous and isotropic cosmological solutions for the low energy limit of string theory with a self interacting potential for the scalar field. For a potential that is a linear combination of two exponential, a family of exact solutions are found for the different spatial curvatures. Among this family a non singular accelerating solution for positive curvature is singled out and the violation of the energy conditions for that solution is studied, and also its astrophysical consequences. The string coupling for this solution is finite. (Author)
Comparison of potential models through heavy quark effective theory
International Nuclear Information System (INIS)
Amundson, J.F.
1995-01-01
I calculate heavy-light decay constants in a nonrelativistic potential model. The resulting estimate of heavy quark symmetry breaking conflicts with similar estimates from lattice QCD. I show that a semirelativistic potential model eliminates the conflict. Using the results of heavy quark effective theory allows me to identify and compensate for shortcomings in the model calculations in addition to isolating the source of the differences in the two models. The results lead to a rule as to where the nonrelativistic quark model gives misleading predictions
SL(2,Z) duality of Born-Infeld theory from non-linear self-dual electrodynamics in 6 dimensions
Berman, David
1997-01-01
We reformulate the Born-Infeld action, coupled to an axion and a dilaton in a duality manifest way. This action is the generalization of the Schwarz-Sen action for non-linear electrodynamics. We show that this action may be obtained by dimensional reduction on a torus of a self-dual theory in 6 dimensions. The dilaton-axion being identified with the complex structure of the torus. Applications to M-theory and the self-dual IIB three brane are investigated.
International Nuclear Information System (INIS)
Krishan, S.
2007-01-01
The Stieltjes transform has been used in place of a more common Laplace transform to determine the time evolution of the self-consistent field (SCF) of an unmagnetized semi-infinite plasma, where the plasma electrons together with a primary and a low-density secondary electron beam move perpendicular to the boundary surface. The secondary beam is produced when the primary beam strikes the grid. Such a plasma system has been investigated by Griskey and Stanzel [M. C. Grisky and R. L. Stenzel, Phys. Rev. Lett. 82, 556 (1999)]. The physical phenomenon, observed in their experiment, has been named by them as ''secondary beam instability.'' The character of the instability observed in the experiment is not the same as predicted by the conventional treatments--the field amplitude does not grow with time. In the frequency spectrum, the theory predicts peak values in the amplitude of SCF at the plasma frequency of plasma and secondary beam electrons, decreasing above and below it. The Stieltjes transform for functions, growing exponentially in the long time limit, does not exist, while the Laplace transform technique gives only exponentially growing solutions. Therefore, it should be interesting to know the kind of solutions that an otherwise physically unstable plasma will yield. In the high-frequency limit, the plasma has been found to respond to any arbitrary frequency of the initial field differentiated only by the strength of the resulting SCF. The condition required for exponential growth in the conventional treatments, and the condition for maximum amplitude (with respect to frequency) in the present treatment, have been found to be the same. Nonlinear mode coupling between the modes excited by the plasma electrons and the low-density secondary beam gives rise to two frequency-dependent peaks in the field amplitude, symmetrically located about the much stronger peak due to the plasma electrons, as predicted by the experiment
Modified potentials in many-body perturbation theory
International Nuclear Information System (INIS)
Silver, D.M.; Bartlett, R.J.
1976-01-01
Many-body perturbation-theory calculations of the pair-correlation energy within the regime of various finite expansions in two-center Slater-type basis sets are performed using a wide variety of modified potentials for the determination of unoccupied orbitals. To achieve meaningful convergence, it appears that the perturbation series must be carried through third order, using shifted denominators to include contributions from various higher-order diagrams. Moreover, certain denominator shifts are found necessary to ensure that a negative-definite resolvent accompanies the perturbation scheme when an arbitrary modified potential is employed. Through third order with denominator shifts, well-behaved modified potentials are found to give results that are equivalent, within 1 kcal/mole, to those obtained for pair-correlation energies with the standard self-consistent-field-V/sup N/ potential
International Nuclear Information System (INIS)
Klimachkov, D. A.; Petrosyan, A. S.
2016-01-01
Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the
Iizuka, S.
1998-02-01
Potential Modification Due to C60- Production * Modifications of the Floating Potential and the Plasma Potential in a C60 Plasma * Properties of Strongly Electronegative Plasma Produced at Afterglow of Electron Cyclotron Resonance Chlorine Plasma * 2.2 Particle Accelerations * Potential Structures Due to an Electron Beam-Excited Localized HF-Discharge (Invited) * Experiments and Computer Simulations of Electric Field Spikes in Electron Beam-Plasma Interaction * Magnetosonic Waves in Multi-Ion-Species Plasmas: Nonlinear Evolution and Ion Acceleration * Observation of Repetitive Electric Field Pulses Accompanying a Short Wave Train Near the Lower Hybrid Frequency in a High-Voltage Linear Plasma Discharge * Control of Potential Profile and Energy Transport to Machine Ends along Open Magnetic Field Lines in a Tandem Mirror * Observation of Ion Acceleration in Picosecond Laser Produced Plasma Expanding across a Magnetic Field * Pellet Ablation Characteristics and the Effect on the Potential in Toroidal Plasmas (Invited) * CHAPTER 3: CROSS-FIELD ELECTRIC FIELDS, VELOCITY SHEAR, AND VORTEX FORMATION * 3.1 Cross-Field Potential Structures * Laboratory Simulation of Transverse Magnetic Field Effects on Dynamics of Plasma Streams in Magnetosphere * Double-Layer-like and Sheath-like Potential Structures across Magnetic Field Lines * Relaxation of Virtual Cathode Oscillations due to Transverse Effects in a Crossed-Field Diode * Control of Radial Potential Profile and Related Low-Frequency Fluctuations in an ECR-Produced Plasma * Potential Formation in Magnetized Dusty Plasma * Potential Measurement Using Electrostatic Probe in Tokamak Boundary Plasma * Studies on Radial Electric Field and Confinement in Toroidal Plasmas (Invited) * 3.2 Velocity Shear * Space Chamber Investigations of Transverse Velocity Shear Driven Plasma Waves * Observations of the Velocity-Shear-Driven Instability in a Sodium Plasma (Invited) * The Effect of Negative Ions and Neutral Particle Collisions on the
Generating functionals for quantum field theories with random potentials
International Nuclear Information System (INIS)
Jain, Mudit; Vanchurin, Vitaly
2016-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.
DEFF Research Database (Denmark)
Stroescu, Ionut Emanuel; Sørensen, Lasse; Frigaard, Peter Bak
2016-01-01
A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good...
Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1
International Nuclear Information System (INIS)
Krivitsky, V.S.; Vladimirov, S.V.
1991-01-01
An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a 'direct' nonlinear interaction of particles and waves, and the influence of the non-stationary of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one. (author)
Topics in electromagnetic, acoustic, and potential scattering theory
Nuntaplook, Umaporn
With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves --- is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering in radially symmetric media is sufficient to gain insight into scattering in more complex media. Meeting the challenge of variable refractive indices and possibly complicated boundary conditions therefore requires accurate and efficient numerical methods, and where possible, analytic solutions to the radial equations from the governing scalar and vector wave equations (in acoustics and electromagnetic theory, respectively). Until relatively recently, researchers assumed a constant refractive index throughout the medium of interest. However, the most interesting and increasingly useful cases are those with non-constant refractive index profiles. In the majority of this dissertation the focus is on media with piecewise constant refractive indices in radially symmetric media. The method discussed is based on the solution of Maxwell's equations for scattering of plane electromagnetic waves from a dielectric (or "transparent") sphere in terms of the related Helmholtz equation. The main body of the dissertation (Chapters 2 and 3) is concerned with scattering from (i) a uniform spherical inhomogeneity embedded in an external medium with different properties, and (ii) a piecewise-uniform central inhomogeneity in the external medium. The latter results contain a natural generalization of
The Potential and Flux Landscape Theory of Ecology
Zhang, Kun; Wang, Erkang; Wang, Jin
2014-01-01
The species in ecosystems are mutually interacting and self sustainable stable for a certain period. Stability and dynamics are crucial for understanding the structure and the function of ecosystems. We developed a potential and flux landscape theory of ecosystems to address these issues. We show that the driving force of the ecological dynamics can be decomposed to the gradient of the potential landscape and the curl probability flux measuring the degree of the breaking down of the detailed balance (due to in or out flow of the energy to the ecosystems). We found that the underlying intrinsic potential landscape is a global Lyapunov function monotonically going down in time and the topology of the landscape provides a quantitative measure for the global stability of the ecosystems. We also quantified the intrinsic energy, the entropy, the free energy and constructed the non-equilibrium thermodynamics for the ecosystems. We studied several typical and important ecological systems: the predation, competition, mutualism and a realistic lynx-snowshoe hare model. Single attractor, multiple attractors and limit cycle attractors emerge from these studies. We studied the stability and robustness of the ecosystems against the perturbations in parameters and the environmental fluctuations. We also found that the kinetic paths between the multiple attractors do not follow the gradient paths of the underlying landscape and are irreversible because of the non-zero flux. This theory provides a novel way for exploring the global stability, function and the robustness of ecosystems. PMID:24497975
Theory and analysis of nonlinear dynamics and stability in storage rings: A working group summary
International Nuclear Information System (INIS)
Chattopadhyay, S.; Audy, P.; Courant, E.D.
1988-07-01
A summary and commentary of the available theoretical and analytical tools and recent advances in the nonlinear dynamics, stability and aperture issues in storage rings are presented. 11 refs., 4 figs
Stability analysis of nonlinear autonomous systems - General theory and application to flutter
Smith, L. L.; Morino, L.
1975-01-01
The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).
Density nonlinearities and a field theory for the dynamics of simple fluids
Mazenko, Gene F.; Yeo, Joonhyun
1994-01-01
We study the role of the Jacobian arising from a constraint enforcing the nonlinear relation: ${\\bf g}=\\rho{\\bf V}$, where $\\rho,\\: {\\bf g}$ and ${\\bf V}$ are the mass density, the momentum density and the local velocity field, respectively, in the field theoretic formulation of the nonlinear fluctuating hydrodynamics of simple fluids. By investigating the Jacobian directly and by developing a field theoretic formulation without the constraint, we find that no changes in dynamics result as co...
Bourdieu's theory of practice and its potential in nursing research.
Rhynas, Sarah J
2005-04-01
This paper seeks to consider the utility of Bourdieu's "Theory of Practice" in nursing, and considers specifically its use as a framework for research exploring nurses' conceptualizations of illness and the patients in their care. Bourdieu's work uses the concepts of field, capital and habitus to explain interactions within the social world. This paper describes these concepts and their relationship with nursing is discussed using dementia care as an example. The work of French scholar Pierre Bourdieu has contributed to debates throughout the social sciences, but has had relatively little attention in the nursing literature. Pierre Bourdieu's work developed against a backdrop of change in the academic world. The emergence of the social sciences and the debate around objective and subjective styles of research were influential in the development of his "Theory of Practice". The importance of the conceptualization process is discussed, and the considerable potential influence of conceptualization on patient care is highlighted. Reflexivity is a cornerstone of Bourdieu's work, and is an important feature of nursing research. Examples of health care research using his work as a framework are discussed, and some of the challenges of the approach are outlined. The use of Bourdieu's "Theory of Practice" as a research framework could allow nurse researchers to explore the interactions of nurses with the structures, agents and symbols of illness within the field of care. This work could enhance understanding of how nurses view and react to patients in their care, and promote the development of practice innovations and policy change. The theory may, therefore, have much to offer future nursing research.
The potential and flux landscape theory of evolution.
Zhang, Feng; Xu, Li; Zhang, Kun; Wang, Erkang; Wang, Jin
2012-08-14
We established the potential and flux landscape theory for evolution. We found explicitly the conventional Wright's gradient adaptive landscape based on the mean fitness is inadequate to describe the general evolutionary dynamics. We show the intrinsic potential as being Lyapunov function(monotonically decreasing in time) does exist and can define the adaptive landscape for general evolution dynamics for studying global stability. The driving force determining the dynamics can be decomposed into gradient of potential landscape and curl probability flux. Non-zero flux causes detailed balance breaking and measures how far the evolution from equilibrium state. The gradient of intrinsic potential and curl flux are perpendicular to each other in zero fluctuation limit resembling electric and magnetic forces on electrons. We quantified intrinsic energy, entropy and free energy of evolution and constructed non-equilibrium thermodynamics. The intrinsic non-equilibrium free energy is a Lyapunov function. Both intrinsic potential and free energy can be used to quantify the global stability and robustness of evolution. We investigated an example of three allele evolutionary dynamics with frequency dependent selection (detailed balance broken). We uncovered the underlying single, triple, and limit cycle attractor landscapes. We found quantitative criterions for stability through landscape topography. We also quantified evolution pathways and found paths do not follow potential gradient and are irreversible due to non-zero flux. We generalized the original Fisher's fundamental theorem to the general (i.e., frequency dependent selection) regime of evolution by linking the adaptive rate with not only genetic variance related to the potential but also the flux. We show there is an optimum potential where curl flux resulting from biotic interactions of individuals within a species or between species can sustain an endless evolution even if the physical environment is unchanged. We
Potential theory of adsorption for associating mixtures: possibilities and limitations
DEFF Research Database (Denmark)
Bjørner, Martin Gamel; Shapiro, Alexander; Kontogeorgis, Georgios
2013-01-01
The applicability of the Multicomponent Potential Theory of Adsorption (MPTA) for prediction of the adsorption equilibrium of several associating binary mixtures on different industrial adsorbents is investigated. In the MPTA the adsorbates are considered to be distributed fluids subject...... to describe the solid-fluid interactions. The potential is extended to include adsorbate-absorbent specific capacities rather than an adsorbent specific capacity. Correlations of pure component isotherms are generally excellent with individual capacities, although adsorption on silicas at different...... temperatures still poses a challenge. The quality of the correlations is usually independent on the applied EoS. Predictions for binary mixtures indicate that the MPTA+SRK is superior when adsorption occurs on non-polar or slightly polar adsorbents, while MPTA+CPA performs better for polar adsorbents, or when...
Stationary localized modes of the quintic nonlinear Schroedinger equation with a periodic potential
International Nuclear Information System (INIS)
Alfimov, G. L.; Konotop, V. V.; Pacciani, P.
2007-01-01
We consider localized modes (bright solitons) of the one-dimensional quintic nonlinear Schroedinger equation with a periodic potential, describing several mean-field models of low-dimensional condensed gases. In the case of attractive nonlinearity we deduce sufficient conditions for collapse. We show that there exist spatially localized modes with arbitrarily large numbers of particles. We study such solutions in the semi-infinite gap (attractive case) and in the first gap (attractive and repulsive cases), and show that a nonzero minimum value of the number of particles is necessary for a localized mode to be created. In the limit of large negative frequencies (attractive case) we observe quantization of the number of particles of the stationary modes. Such solutions can be interpreted as coupled Townes solitons and appear to be stable. The modes in the first gap have numbers of particles infinitely growing with frequencies approaching one of the gap edges, which is explained by the power decay of the modes. Stability of the localized modes is discussed
SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-08-01
This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.
Directory of Open Access Journals (Sweden)
Wang Guodong
2014-07-01
Full Text Available Earthquake disasters have brought great harm to people's life safety and economic property. Its effect on fabric mainly focus on random effects currently, the general pseudo excitation method could solve the inefficiency calculation problem of linear random earthquake. However it could not take the nonlinear problem factors into account for calculation. In this paper, we suggest that a nonlinear structural incentive method should be improved based on statistical linearity to calculate and solve absolute displacement value. Through the analysis and research for cases, we calculate the displacement, speed, random vibration spectrum of bridge’s accelerated speed, as well as the influencing situation of axial force. The results indicate that such perfect incentive method could not only perform nonlinear structure analysis, but also to be very accurate and high effective. Such method could reasonably avoid the displacement decomposition and solution of the pseudostatic model，thus it will be widely applied in common software.
On the non-linear dynamics of potential relaxation oscillations in bounded plasmas
International Nuclear Information System (INIS)
Krssak, M.; Skalny, J.D.; Gyergyek, T.; Cercek, M.
2007-01-01
Plasma in a 1-dimensional diode is studied theoretically and the computer simulations are used for verification of the theoretical model. When collector in the diode is biased positively, a double-layer is created in the system and consequently, we are able to observe oscillations of the potential, density and other plasma parameters. When external periodic forcing is applied, spectra of these oscillations are changed and effects of synchronisation and periodic pulling can be observed. Both of these effects are of non-linear nature and a good explanation is found using the analogy with Van der Pol oscillators. Following [1] and [2] approximate analytical solutions are found and then compared with computer simulations obtained using a 1-dimensional particle-in-cell code XPDP1. (author)
(2 + 1)-dimensional dynamical black holes in Einstein-nonlinear Maxwell theory
Gurtug, O.; Mazharimousavi, S. Habib; Halilsoy, M.
2018-02-01
Radiative extensions of BTZ metric in 2 + 1 dimensions are found which are sourced by nonlinear Maxwell fields and a null current. This may be considered as generalization of the problem formulated long go by Vaidya and Bonnor. The mass and charge are functions of retarded/advanced null coordinate apt for decay/inflation. The new solutions are constructed through a Theorem that works remarkably well for any nonlinear electrodynamic model. Hawking temperature is analyzed for the case of the Born-Infeld electrodynamics.
DEFF Research Database (Denmark)
leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2004-01-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...
Relation between linear and nonlinear N=3,4 supergravity theories
International Nuclear Information System (INIS)
Sevrin, A.; Thielemans, K.; Troost, W.
1993-01-01
The effective actions for d=2, N=3,4 chiral supergravities with a linear and a nonlinear gauge algebra are related to each other by a quantum reduction; the latter is obtained from the former by putting quantum currents equal to zero. This implies that the renormalization factors for the quantum actions are identical
Knoester, Jasper; Mukamel, Shaul
1990-01-01
A general scheme is presented for calculating the nonlinear optical response in condensed phases that provides a unified picture of excitons, polaritons, retardation, and local-field effects in crystals and in disordered systems. A fully microscopic starting point is taken by considering the
Potential evapotranspiration viewed from the perspective of constructal theory
Ciobanas, A. I.; Rousseau, A. N.
2007-12-01
In this study we investigated the evapotranspiration phenomena from the point of view of the thermodynamic constructal theory. When applied to the vegetation cover at the surface of the ground, the constructal law states that plants are adapting to gain maximum access to available resources and at the same time to minimize the internal irreversibilities of the system, that is the entropy generation rate. The analysis of plants under heat constraints showed that the optimal state of plant given potential conditions can be achieved if the optimal plant temperature defining the maximum productivity state is equal to the average air temperature which in turn has to be equal to the average vegetation temperature. To test this hypothesis, we modeled the vegetation cover as a thermodynamic system exchanging heat and mass with the atmosphere. The input data for the model were provided by the FLUXNET network. For 32 sites around the globe, we investigated the variation of the vegetation state with respect to the stomatal resistance rs. We showed that plants can thermoregulate their temperature by means of the stomatal resistance and that there is a critical stomatal resistance, rsmin, corresponding to a minimum entropy generation rate. We showed that, for sites characterized with highly evolved plants, the optimal thermodynamic state defined by rsmin is indeed selected by plants when potential condtions are met. When potential conditions are not met, plants will adapt such that the average state of vegetation will be as close as possible (given external constraints) to the optimal state defined by rsmin.
Critical points and nonlinear variational problems
International Nuclear Information System (INIS)
Ambrosetti, A.
1992-01-01
This monograph deals with critical point theory and its applications to some classes of nonlinear variational problems. The abstract setting includes the Lusternik-Schnirelman theory and minimax methods for unbounded functionals. Applications to elliptic boundary value problems, Vortex theory, homoclinic orbits and conservative systems with singular potentials are discussed. (author). refs
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.
Goldman, Benjamin D.; Scott, Robert C,; Dowell, Earl H.
2014-01-01
The purpose of this work is to develop a set of theoretical and experimental techniques to characterize the aeroelasticity of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A square TPS coupon experiences trailing edge oscillatory behavior during experimental testing in the 8' High Temperature Tunnel (HTT), which may indicate the presence of aeroelastic flutter. Several theoretical aeroelastic models have been developed, each corresponding to a different experimental test configuration. Von Karman large deflection theory is used for the plate-like components of the TPS, along with piston theory for the aerodynamics. The constraints between the individual TPS layers and the presence of a unidirectional foundation at the back of the coupon are included by developing the necessary energy expressions and using the Rayleigh Ritz method to derive the nonlinear equations of motion. Free vibrations and limit cycle oscillations are computed and the frequencies and amplitudes are compared with accelerometer and photogrammetry data from the experiments.
Evaluation of specific heat for superfluid helium between 0 - 2.1 K based on nonlinear theory
International Nuclear Information System (INIS)
Sasaki, Shosuke
2009-01-01
The specific heat of liquid helium was calculated theoretically in the Landau theory. The results deviate from experimental data in the temperature region of 1.3 - 2.1 K. Many theorists subsequently improved the results of the Landau theory by applying temperature dependence of the elementary excitation energy. As well known, many-body system has a total energy of Galilean covariant form. Therefore, the total energy of liquid helium has a nonlinear form for the number distribution function. The function form can be determined using the excitation energy at zero temperature and the latent heat per helium atom at zero temperature. The nonlinear form produces new temperature dependence for the excitation energy from Bose condensate. We evaluate the specific heat using iteration method. The calculation results of the second iteration show good agreement with the experimental data in the temperature region of 0 - 2.1 K, where we have only used the elementary excitation energy at 1.1 K.
International Nuclear Information System (INIS)
Holland, C.; Kim, E.J.; Champeaux, S.; Gurcan, O.; Rosenbluth, M.N.; Diamond, P.H.; Tynan, G.R.; Nevins, W.; Candy, J.
2003-01-01
Understanding the physics of shear flow and structure formation in plasmas is a central problem for the advancement of magnetic fusion because of the roles such flows are believed to play in regulating turbulence and transport levels. In this paper, we report on integrated experimental, computational, and theoretical studies of sheared zonal flows and radially extended convective cells, with the aim of assessing the results of theory experiment and theory-simulation comparisons. In particular, simulations are used as test beds for verifying analytical predictions and demonstrating the suitability of techniques such as bispectral analysis for isolating nonlinear couplings in data. Based on intriguing initial results suggesting increased levels of nonlinear coupling occur during L-H transitions, we have undertaken a comprehensive study of bispectral quantities in fluid and gyrokinetic simulations, and compared these results with theoretical expectations. Topics of study include locality and directionality of energy transfer, amplitude scaling, and parameter dependences. Techniques for inferring nonlinear coupling coefficients from data are discussed, and initial results from experimental data are presented. Future experimental studies are motivated. We also present work investigating the role of structures in transport. Analysis of simulation data indicates that the turbulent heat flux can be represented as an ensemble of 'heat pulses' of varying sizes, with a power law distribution. The slope of the power law is shown to determine global transport scaling (i.e. Bohm or gyro-Bohm). Theoretical work studying the dynamics of the largest cells (termed 'streamers') is presented, as well as results from ongoing analysis studying connections between heat pulse distribution and bispectral quantities. (author)
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
Fuchs, Armin
2013-01-01
With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz ...
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Energy Technology Data Exchange (ETDEWEB)
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-08-01
Full Text Available In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional diﬀerential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid ﬁxed point theorems of Dhage (2014 in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional diﬀerential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.
A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials
Li, Chen; Liao, Yufei
2018-03-01
Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.
Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory
2017-03-01
scale dynamics systems. Perhaps the most far reaching impact of this DRI will be a contribution that was not planned in the original proposal. This... contribution has to do with the generalization of Koopman decompositions using a fractional calculus perspective on complexity. By using a combination of... influenced by an external environment in which long-term memory is introduced. 15. SUBJECT TERMS nonlinear dynamics, spectral decompositions, fractional
Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics
Daniel W.F. Alves; Carlos Hoyos; Horatiu Nastase; Jacob Sonnenschein
2017-01-01
We examine knotted solutions, the most simple of which is the "Hopfion", from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. ...
Aklan, Nor Amirah Busul; Umarov, Bakhram
2015-10-01
The Cubic-Quintic Nonlinear Schrödinger Equation (CQNLSE) is one of the universal mathematical models constituting many interesting problems in physics such as plasma physics, condensed matter physics, Bose-Einstein condensates, nonlinear optics, etc. This paper studies the scattering of the soliton of the CQNLSE on the localized external potential namely Gaussian potential. The approximate analytical method, also known as variational method has been applied in order to derive the equations for soliton parameters evolution during the scattering process. The validity of approximations was tested by direct numerical simulations of CQNLSE with soliton initially located far from potential. It was shown, in case of the potential in the form of Gaussian function, that depending on initial velocity of the soliton, the soliton may be reflected by potential or transmitted through it. The critical values of the velocity separating these two scenarios have been identified.
DEFF Research Database (Denmark)
Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John-Josef
2014-01-01
In this work the stability properties of a nonlinear partial differential equation (PDE) with state–dependent parameters is investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (Potential) Burgers’ Equation. We show that for certain forms of coe...
Nonlinear behavior of capacitive micro-beams based on strain gradient theory
International Nuclear Information System (INIS)
Fathalilou, Mohammad; Sadeghi, Morteza; Rezazadeh, Ghader
2014-01-01
This paper studies the size dependent behavior of materials in MEMS structures. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter and is insignificant for the high ratio of the characteristic size to the length-scale parameter, which is the case of the silicon base micro-beams. However, in some types of micro-beams like gold or nickel bases, the size dependent effect cannot be overlooked. In such cases, ignoring this behavior in modeling will lead to incorrect results. Some previous researchers have applied classic beam theory on their models and imposed a considerable hypothetical value of residual stress to match their theoretical results with the experimental ones. The equilibrium positions or fixed points of the gold and nickel micro-beams are obtained and shown that for a given DC voltage, there is a considerable difference between the obtained fixed points using classic beam theory, modified couple stress theory, and modified strain gradient theory. In addition, it is shown that the calculated static and dynamic pull-in voltages using higher order theories are much closer to the experimental results and are higher several times than those obtained by classic beam theory.
On the theory of nonlinear Cherenkov effect in the beams moving through the channel in dielectric
International Nuclear Information System (INIS)
Sapelkin, S.A.; Khizhnyak, N.A.
1974-01-01
A study was made of the Cherenkov effect in a beam moving through a channel in a dielectric. A system of two equations was derived describing the non-linear self-consistent Cherenkov effect. The initial linear stage of the process was considered in detail for the case where fields and currents in the system are determined exclusively by the initial conditions at the entrance to the interaction space. Radiation conditions, the power flux of Cherenkov radiation in the region containing the dielectric and the angle of emergence of the Cherenkov radiation were defined. Limit transitions to cases studied earlier are specified
Theory of heart biomechanics, biophysics, and nonlinear dynamics of cardiac function
Hunter, Peter; McCulloch, Andrew
1991-01-01
In recent years there has been a growth in interest in studying the heart from the perspective of the physical sciences: mechanics, fluid flow, electromechanics. This volume is the result of a workshop held in July 1989 at the Institute for Nonlinear Sciences at the University of California at San Diego that brought together scientists and clinicians with graduate students and postdoctoral fellows who shared an interest in the heart. The chapters were prepared by the invited speakers as didactic reviews of their subjects but also include the structure, mechanical properties, and function of the heart and the myocardium, electrical activity of the heart and myocardium, and mathematical models of heart function.
Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory
DEFF Research Database (Denmark)
Frier, Christian; Sørensen, John Dalsgaard
2003-01-01
to estimate the probability of exceeding a critical event, defined by a so-called limit state function. The limit state function is obtained implicitly by non-linear FEM analysis from a realization of random material properties. As the latter can be modeled as random fields varying continuously over...... the structure, a discretisation into random elements/variables is introduced. To this purpose, both the Midpoint (MP) and the Spatial Average (SA) approach are considered. The failure probability is obtained iteratively based on a first order Taylor series expansion of the limit state function. Thus...
THE HEURISTIC POTENTIAL OF ANOMIE THEORY IN MODERN CRIMINOLOGY
Alexander Vladislavovich Pletnev
2015-01-01
This article deals with modern English theories of anomie. They can be used in Russian criminology. The main goal of article consists in detection of actual theories of anomie and definition of prospects of their use. As modern theories of anomie are poorly submitted in the Russian sociological and criminological literature, the subject of research is actual. This work contains the analysis of opportunities for adoption of modern conceptions of anomie of individual in Russian practice. Durin...
Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential
Gizzi, A.; Loppini, A.; Ruiz-Baier, R.; Ippolito, A.; Camassa, A.; La Camera, A.; Emmi, E.; Di Perna, L.; Garofalo, V.; Cherubini, C.; Filippi, S.
2017-09-01
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.
The potential of speech act theory for New Testament exegesis ...
African Journals Online (AJOL)
Speech act theory as well offers New Testament exegesis some additional ways and means of approaching the text of the New Testament. This first in a series of two articles making a plea for the continued utilisation and application of this theory to the text of the New Testament, offers a brief discussion of the basic ...
National Research Council Canada - National Science Library
Wright, J
2000-01-01
...) agents at contaminated sites. Reported herein are theoretical ionization potentials for CW agents and their related compounds calculated using density functional theory at the B3LYP/6-311+G(2d,p) level of theory...
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.
1993-01-01
The computational capability of efficiently and accurately evaluate reactor core attributes (i.e., k eff and power distributions as a function of cycle burnup) utilizing a second-order accurate advanced nodal Generalized Perturbation Theory (GPT) model has been developed. The GPT model is derived from the forward non-linear iterative Nodal Expansion Method (NEM) strategy, thereby extending its inherent savings in memory storage and high computational efficiency to also encompass GPT via the preservation of the finite-difference matrix structure. The above development was easily implemented into the existing coarse-mesh finite-difference GPT-based in-core fuel management optimization code FORMOSA-P, thus combining the proven robustness of its adaptive Simulated Annealing (SA) multiple-objective optimization algorithm with a high-fidelity NEM GPT neutronics model to produce a powerful computational tool used to generate families of near-optimum loading patterns for PWRs. (orig.)
Phantom solution in a non-linear Israel-Stewart theory
Cruz, Miguel; Cruz, Norman; Lepe, Samuel
2017-06-01
In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p = ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than -1 and constant in time.
Nonlinear theory of stable, efficient operation of a gyrotron at cyclotron harmonics
International Nuclear Information System (INIS)
Saraph, G.P.; Antonsen, T.M. Jr.; Nusinovich, G.S.; Levush, B.
1993-01-01
One of the main obstacles in achieving stable, efficient operation at the cyclotron harmonics in a gyrotron is mode competition with parasitic modes at the fundamental frequency. In this article, the nonlinear dynamics of mode interactions in such a system are studied using a multifrequency, time-dependent model. The results of numerical simulations for a second harmonic gyrotron are presented by considering two starting scenarios: (a) fast voltage rise or an instant turn-on case, and (b) slow voltage rise case. For the first case, it is demonstrated that for a certain range of operating parameters, the presence of a parasitic mode at the fundamental can be helpful in the excitation of the second harmonic operating mode. In the second case, it is found that the unstable operating region increases with the value of the rise time constant of the electrode voltages. Stable, efficient gyrotron operation at the second harmonic is demonstrated using the numerical study
Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics
Directory of Open Access Journals (Sweden)
Daniel W.F. Alves
2017-10-01
Full Text Available We examine knotted solutions, the most simple of which is the “Hopfion”, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.
Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics
Alves, Daniel W. F.; Hoyos, Carlos; Nastase, Horatiu; Sonnenschein, Jacob
2017-10-01
We examine knotted solutions, the most simple of which is the ;Hopfion;, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.
Multiple Solutions for a Nonlinear Fractional Boundary Value Problem via Critical Point Theory
Directory of Open Access Journals (Sweden)
Yang Wang
2017-01-01
Full Text Available This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: DT-αaxD0+αux=fx,ux, x∈0,T, u0=uT=0, where α∈1/2,1, ax∈L∞0,T with a0=ess infx∈0,Tax>0, DT-α and D0+α stand for the left and right Riemann-Liouville fractional derivatives of order α, respectively, and f:0,T×R→R is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems.
Yang, Linlin; Li, Nianbei; Li, Baowen
2014-12-01
The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.
Directory of Open Access Journals (Sweden)
Jairo A. Paredes
2016-01-01
Full Text Available Ferrocement thin walls are the structural elements that comprise the earthquake resistant system of dwellings built with this material. This article presents the results drawn from an experimental campaign carried out over full-scale precast ferrocement thin walls that were assessed under lateral static loading conditions. The tests allowed the identification of structural parameters and the evaluation of the performance of the walls under static loading conditions. Additionally, an isotropic damage model for modelling the mortar was applied, as well as the classic elasto-plastic theory for modelling the meshes and reinforcing bars. The ferrocement is considered as a composite material, thus the serial/parallel mix theory is used for modelling its mechanical behavior. In this work a methodology for the numerical analysis that allows modeling the nonlinear behavior exhibited by ferrocement walls under static loading conditions, as well as their potential use in earthquake resistant design, is proposed.
Potential sources for nonlinear sorption of organic compounds to soils and natural solids
Chiou, C. T.
2003-04-01
The sorption isotherms of ethylene dibromide (EDB), diuron (DUN), and 3,5-dichlorophenol (DCP) from water to the humic acid and humin fractions of a peat soil have been measured. The data were compared with those of the same solutes on whole peat from which the humic acid (HA) and humin (HM) fractions were derived and on which the sorption of solutes exhibited varying extents of nonlinear capacities at low relative concentrations (Ce/Sw). The HA fraction as prepared by a density-fractionated method is relatively pure and presumably free of high-surface-area carbonaceous material (HSACM) that is considered to be responsible for the observed nonlinear sorption for nonpolar solutes (e.g., EDB) on the peat; conversely, the base-insoluble HM fraction as prepared is presumably enriched with HSACM, as manifested by the greatly higher BET-(N2) surface area than that of the whole peat. The sorption of EDB on HA exhibits no visible nonlinear effect, whereas the sorption on HM shows an enhanced nonlinearity over that on the whole peat. The sorption of polar DUN and DCP on HA and HM display nonlinear effects comparable with those on the whole peat; the effects are much more significant than those with nonpolar EDB. These results conform to the hypothesis that adsorption onto a small amount of strongly adsorbing HSACM is largely responsible for the nonlinear sorption of nonpolar solutes on soils and that additional specific interactions with the active groups of soil organic matter are responsible for the generally higher nonlinear sorption of the polar solutes.
Directory of Open Access Journals (Sweden)
Kyoung-Rok Lee
2013-12-01
Full Text Available A floating Oscillating Water Column (OWC wave energy converter, a Backward Bent Duct Buoy (BBDB, was simulated using a state-of-the-art, two-dimensional, fully-nonlinear Numerical Wave Tank (NWT technique. The hydrodynamic performance of the floating OWC device was evaluated in the time domain. The acceleration potential method, with a full-updated kernel matrix calculation associated with a mode decomposition scheme, was implemented to obtain accurate estimates of the hydrodynamic force and displacement of a freely floating BBDB. The developed NWT was based on the potential theory and the boundary element method with constant panels on the boundaries. The mixed Eulerian-Lagrangian (MEL approach was employed to capture the nonlinear free surfaces inside the chamber that interacted with a pneumatic pressure, induced by the time-varying airflow velocity at the air duct. A special viscous damping was applied to the chamber free surface to represent the viscous energy loss due to the BBDB's shape and motions. The viscous damping coefficient was properly selected using a comparison of the experimental data. The calculated surface elevation, inside and outside the chamber, with a tuned viscous damping correlated reasonably well with the experimental data for various incident wave conditions. The conservation of the total wave energy in the computational domain was confirmed over the entire range of wave frequencies.
On the use of contraction theory for the design of nonlinear observers for ocean vehicles
DEFF Research Database (Denmark)
Jouffroy, Jerome; Lottin, Jacques
Guaranteeing that traditional concepts of stability like uniform global exponential or asymptotic stability (UGES or UGAS) are veri ed when using design tools based on new concepts of stability may be of signicant importance. It is especially so when attempting to bridge the gap between theory...... and practice. This paper addresses the question of the applicability of contraction theory to the design of UGES observers for ocean vehicles. A relation between the concept of exponential convergence of a contracting system and uniform global exponential stability (UGES) is rst given. Then two contraction......-based GES observers, respectively for unmanned underwater vehicles (UUV) and a class of ships, are constructed, and simulation results are provided....
On the use of contraction theory for the design of nonlinear observers for ocean vehicles
DEFF Research Database (Denmark)
Jouffroy, Jerome; Lottin, Jacques
Guaranteeing that traditional concepts of stability like uniform global exponential or asymptotic stability (UGES or UGAS) are veri ed when using design tools based on new concepts of stability may be of signicant importance. It is especially so when attempting to bridge the gap between theory an......-based GES observers, respectively for unmanned underwater vehicles (UUV) and a class of ships, are constructed, and simulation results are provided....... and practice. This paper addresses the question of the applicability of contraction theory to the design of UGES observers for ocean vehicles. A relation between the concept of exponential convergence of a contracting system and uniform global exponential stability (UGES) is rst given. Then two contraction...
1989-01-01
LIEBERSTEIN, H. M.: " On the Hodgkin - Huxley Partial Differential Equation ", Math. Blosci., .1 (1967) p. 45-69. [253 ENGELBRECHT, J.: " On Theory... Y ., Kubota, H., Ishiguro, T., Ogawa, S.: Fully implicit high-resolution scheme for chemically reacting compressible flows ....................... 648...ks2 and with: either (4,,7) = (z, y ) or (,?) = (direction of the local gradient, its orthogonal). (23) This approach is very robust but rather
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...
Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm
Chen, C.; Xia, J.; Liu, J.; Feng, G.
2006-01-01
Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant
Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation
Directory of Open Access Journals (Sweden)
V. O. Vakhnenko
2016-01-01
Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Hamilton-Ostrogradsky principle in the theory of nonlinear elasticity with the combined approach
International Nuclear Information System (INIS)
Sporykhin, A.N.
1995-01-01
The assignment of a portion of the edge conditions in the deformed state and a portion of them in the initial state so that the initial and deformed states of the body are unknowns is a characteristic feature of the statement of a number of technological problems. Haber and Haber and Abel have performed studies in this direction, where constitutive relationships have been constructed within the framework of a linearly elastic material. Use of the displacements of individual particles as variable parameters in these relationships has required additional conditions that do not follow from the formulated problem. Use of familiar variational principles described in Euler coordinates is rendered difficult by the complexity of edge-condition formulation in the special case when the initial state is unknown. The latter is governed by the fact that variational principles are derived from the initial formulations open-quotes in Lagrangian coordinates,close quotes by recalculating the operation functional. Using Lagrange's principle, Novikov and Sporykhin constructed constitutive equations in the general case of a nonlinearly elastic body with edge conditions assigned in different configurations. An analogous problem is solved in this paper using the Hamilton-Ostrogradsky principle
Nonlinear dynamics of a pseudoelastic shape memory alloy system—theory and experiment
International Nuclear Information System (INIS)
Enemark, S; F Santos, I; A Savi, M
2014-01-01
In this work, a helical spring made from a pseudoelastic shape memory alloy was embedded in a dynamic system also composed of a mass, a linear spring and an excitation system. The mechanical behaviour of shape memory alloys is highly complex, involving hysteresis, which leads to damping capabilities and varying stiffness. Besides, these properties depend on the temperature and pretension conditions. Because of these capabilities, shape memory alloys are interesting in relation to engineering design of dynamic systems. A theoretical model based on a modification of the 1D Brinson model was established. Basically, the hardening and the sub-loop behaviour were altered. The model parameters were extracted from force–displacement tests of the spring at different constant temperatures as well as from differential scanning calorimetry. Model predictions were compared with experimental results of free and forced vibrations of the system setup under different temperature conditions. The experiments give a thorough insight into dynamic systems involving pseudoelastic shape memory alloys. Comparison between experimental results and the proposed model shows that the model is able to explain and predict the overall nonlinear behaviour of the system. (paper)
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...
Harker, K. J.
1972-01-01
Two basic high-frequency ionospheric instabilities are discussed - i.e., the three-wave parametric interaction, and the oscillating two-stream instability. In the parametric instability, the ion-acoustic wave has a complex frequency, whereas in the oscillating two-stream instability the ion-acoustic frequency is purely imaginary. The parametric instability is shown to be the only one whose threshold depends on the ion collision frequency. A coupled-mode theory is proposed which permits study and classification of high-frequency instabilities on a unified basis.
Theory of nonlinear acoustic forces acting on fluids and particles in microsystems
DEFF Research Database (Denmark)
Karlsen, Jonas Tobias
as well as experiments with aqueous solutions in an acoustofluidic glass-silicon microchip. The ability of the acoustic force density to stabilize fluid inhomogeneities makes possible the development of a microfluidic analog to density-gradient centrifugation, called iso-acoustic focusing, which...... is demonstrated for acousto-mechanical phenotyping of single white blood cells and cancer cells in continuous flow. The theory of the acoustic force density furthermore leads to the prediction of the possibility of using acoustic tweezers to actively manipulate miscible-fluid interfaces and concentration fields...
Zheligovsky, Vladislav
2011-01-01
New developments for hydrodynamical dynamo theory have been spurred by recent evidence of self-sustained dynamo activity in laboratory experiments with liquid metals. The emphasis in the present volume is on the introduction of powerful mathematical techniques required to tackle modern multiscale analysis of continous systems and there application to a number of realistic model geometries of increasing complexity. This introductory and self-contained research monograph summarizes the theoretical state-of-the-art to which the author has made pioneering contributions.
Exact solutions to nonlinear symmetron theory: One- and two-mirror systems
Brax, Philippe; Pitschmann, Mario
2018-03-01
We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one- or two-mirror system. The one-dimensional equations of motion are integrated exactly for both systems and their solutions can be expressed in terms of Jacobi elliptic functions. Surprisingly, in the case of two parallel mirrors, the equations of motion generically provide not a unique solution but a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to q BOUNCE experiments, neutron interferometry and for the calculation of the symmetron-field-induced "Casimir force" in the CANNEX experiment.
DEFF Research Database (Denmark)
Bendtsen, Claus; Nielsen, Ole Holm; Hansen, Lars Bruno
2001-01-01
The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...... works well on both serial and parallel computers, and good scalability of the algorithm is obtained. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.......The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...... propose a new algorithm of this kind which is well suited for the SCF method, since the accuracy of the eigensolution is gradually improved along with the outer SCF-iterations. Best efficiency is obtained for small-block-size iterations, and the algorithm is highly memory efficient. The implementation...
Activity theory as a potential framework for technology research in ...
African Journals Online (AJOL)
of the activity system leads to shifts at all levels of the system. I conclude by arguing that the strength of Activity Theory lies in its ability to enable one to understand learning as the complex result of tool mediated interactions, rather than as something opaque, which happens in a student's mind. South African Journal of ...
Directory of Open Access Journals (Sweden)
Edward A. Startsev
2003-08-01
Full Text Available In plasmas with strongly anisotropic distribution functions (T_{∥b}/T_{⊥b}≪1 a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9, 3138 (2002] of the stability properties of intense non-neutral charged particle beams with large temperature anisotropy (T_{⊥b}≫T_{∥b} to allow for nonaxisymmetric perturbations with ∂/∂θ≠0. The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined. The simulation results clearly show that moderately intense beams with s_{b}=ω[over ^]_{pb}^{2}/2γ_{b}^{2}ω_{β⊥}^{2}≳0.5 are linearly unstable to short-wavelength perturbations with k_{z}^{2}r_{b}^{2}≳1, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ω[over ^]_{pb}^{2}=4πn[over ^]_{b}e_{b}^{2}/γ_{b}m_{b} is the relativistic plasma frequency squared, and ω_{β⊥} is the betatron frequency associated with the applied smooth-focusing field. A theoretical model is developed based on the Vlasov-Maxwell equations which describes the essential features of the linear stages of instability. Both the simulations and the analytical theory predict that the dipole mode (azimuthal mode number m=1 is the most unstable mode. In the nonlinear stage, tails develop in the longitudinal momentum distribution function, and the kinetic instability saturates due to resonant wave-particle interactions.
Non-linear second-order periodic systems with non-smooth potential
Indian Academy of Sciences (India)
Our theorem appears to be the first such result (even for smooth problems) for systems monitored by the -Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a generalized Landesman–Lazer type condition which generalizes previous ones used in the ...
Superfield approach to calculation of effective potential in supersymmetric field theories
International Nuclear Information System (INIS)
Bukhbinder, I.L.; Kuzenko, S.M.; Yarevskaya, Zh.V.
1993-01-01
Superfield method of computing effective potential in supersymmetric field theories is suggested. The one-loop effective potential of the Wess-Zumino model is found. The prescription for obtaining multi-loop corrections is described
Nian, Jun
2017-01-01
The duality between the N-particle sector of quantum nonlinear Schrödinger equation and the 2D N = (2, 2) * U(N) topological Yang-Mills-Higgs theory was found by Gerasimov and Shatashvili some time ago. At the large N and large ’t Hooft coupling limit, the gravity dual of the 2D N = (2, 2) * U(N) topological Yang-Mills-Higgs theory can be constructed. Consequently, as a first example, one can formulate a triangle relation between integrable model, gauge theory and gravity. We present the results of the gravity dual in this paper, and make some checks at classical level between the gravity dual and the nonlinear Schrödinger equation. This paper is based on the talk given by the author at the 24th International Conference on Integrable Systems and Quantum Symmetries, and more details can be found in Ref. [1].
Chapter 8. Elementary notions on the quantum theory of potential scattering
International Nuclear Information System (INIS)
Anon.
1977-01-01
Elementary notions in quantum theory of potential scattering are exposed: stationary states of scattering, calculus of cross section, scattering by central potential, phase shift method. In complement, these questions are studied: free particle (stationary states of well defined kinetic momentum); phenomenological description of collisions with absorption; elementary examples of application of the scattering theory [fr
Directory of Open Access Journals (Sweden)
Nguyen Dinh Duc
2015-12-01
Full Text Available This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of thick functionally graded material (FGM plates using both of the first-order shear deformation plate theory and stress function with full motion equations (not using Volmir’s assumptions. The FGM plate is assumed to rest on elastic foundation and subjected to mechanical, thermal, and damping loads. Numerical results for dynamic response of the FGM plate are obtained by Runge–Kutta method. The results show the material properties, the elastic foundations, mechanical and thermal loads on the nonlinear dynamic response of functionally graded plates.
International Nuclear Information System (INIS)
Liu Guanghui; Guo Kangxian; Wang Chao
2012-01-01
The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.
Potential Performance Theory (PPT): A General Theory of Task Performance Applied to Morality
Trafimow, David; Rice, Stephen
2008-01-01
People can use a variety of different strategies to perform tasks and these strategies all have two characteristics in common. First, they can be evaluated in comparison with either an absolute or a relative standard. Second, they can be used at varying levels of consistency. In the present article, the authors develop a general theory of task…
On low energy scattering theory with Coulomb potentials
International Nuclear Information System (INIS)
Gibson, A.G.
1985-09-01
The scattering length is a very useful characteristic of the scattering phenomena. But in the presence of a combined potential (e.g. in nuclear physics, when Coulomb, the polarization and the strong potentials are to be added), the analytical definition of the scattering length in not unambigous and strictly defined. This problem is discussed in detail, the various alternatives are examined and compared. A practical suggestion is given for the proper choice of the definition and for the calculation of scattering length. Numerical solutions of the Schroedinger equation are compared with the results of different definitions. Some questions of application to nuclear physics are discussed. (D.Gy.)
A density functional theory-based chemical potential equalisation ...
Indian Academy of Sciences (India)
The electron density changes in molecular systems in the presence of external electric fields are modeled for simplicity in terms of the induced charges and dipole moments at the individual atomic sites. A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole ...
L2-gain and passivity techniques in nonlinear control
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...
Prychynenko, Diana; Sitte, Matthias; Litzius, Kai; Krüger, Benjamin; Bourianoff, George; Kläui, Mathias; Sinova, Jairo; Everschor-Sitte, Karin
2018-01-01
Inspired by the human brain, there is a strong effort to find alternative models of information processing capable of imitating the high energy efficiency of neuromorphic information processing. One possible realization of cognitive computing involves reservoir computing networks. These networks are built out of nonlinear resistive elements which are recursively connected. We propose that a Skyrmion network embedded in magnetic films may provide a suitable physical implementation for reservoir computing applications. The significant key ingredient of such a network is a two-terminal device with nonlinear voltage characteristics originating from magnetoresistive effects, such as the anisotropic magnetoresistance or the recently discovered noncollinear magnetoresistance. The most basic element for a reservoir computing network built from "Skyrmion fabrics" is a single Skyrmion embedded in a ferromagnetic ribbon. In order to pave the way towards reservoir computing systems based on Skyrmion fabrics, we simulate and analyze (i) the current flow through a single magnetic Skyrmion due to the anisotropic magnetoresistive effect and (ii) the combined physics of local pinning and the anisotropic magnetoresistive effect.
Nguyen Dinh Duc; Pham Hong Cong
2015-01-01
This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of thick functionally graded material (FGM) plates using both of the first-order shear deformation plate theory and stress function with full motion equations (not using Volmir’s assumptions). The FGM plate is assumed to rest on elastic foundation and subjected to mechanical, thermal, and damping loads. Numerical results for dynamic response of the FGM plate are obtained by Runge–Kutta metho...
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.
International Nuclear Information System (INIS)
Okabe, Y.; Nagi, A.D.S.
1983-01-01
The Shiba-Rusinov theory of magnetic impurities in a superconductor is investigated, with special attention paid to the role of the potential scattering term in the electron-impurity interaction. The meaning of Anderson's theorem in the Shiba-Rusinov theory is discussed
Note on the evolution of the gravitational potential in Rastall scalar field theories
International Nuclear Information System (INIS)
Fabris, J.C.; Hamani Daouda, M.; Piattella, O.F.
2012-01-01
We investigate the evolution of the gravitational potential in Rastall scalar field theories. In a single component model a consistent perturbation theory, formulated in the Newtonian gauge, is possible only for γ=1, which is the General Relativity limit. On the other hand, the addition of another canonical fluid component allows to consider the case γ≠1.
Kinetic theory for dilute cohesive granular gases with a square well potential
Takada, Satoshi; Saitoh, K.; Hayakawa, Hisao
2016-01-01
We develop the kinetic theory of dilute cohesive granular gases in which the attractive part is described by a square well potential. We derive the hydrodynamic equations from the kinetic theory with the microscopic expressions for the dissipation rate and the transport coefficients. We check the
A density functional theory-based chemical potential equalisation ...
Indian Academy of Sciences (India)
Unknown
2 r r r r r rr. ′....... ′. ′. + ∫∫ v v δ δρ δ δρ ρ δ E. (7). Analogously the change in chemical potential µ(=. µ0 + ∆µ) is given up to first order change in δρ(r) by,. ∆µ = µ – µ0. = δv(r) + ∫ dr′η(r, r′)δρ(r′),. (8) .... point charge dipole approximation and hence the po- tential and the field generated at site α due to ...
Energy Technology Data Exchange (ETDEWEB)
Charles R. Tolle; Mark Pengitore
2009-08-01
This paper explores the overlaps between the Control community’s work on System Identification (SysID) and the Physics, Mathematics, Chaos, and Complexity communities’ work on phase-space reconstruction via time-delay embedding. There are numerous overlaps between the goals of each community. Nevertheless, the Controls community can gain new insight as well as some new very powerful tools for SysID from the latest developments within the Physics, Mathematics, Chaos, and Complexity communities. These insights are gained via the work on phase-space reconstruction of non-linear dynamics. New methods for discovering non-linear differential based equations that evolved from embedding operations can shed new light on hybrid-systems theory, Nyquest-Shannon’s Theories, and network based control theory. This paper strives to guide the Controls community towards a closer inspection of the tools and additional insights being developed within the Physics, Mathematics, Chaos, and Complexity communities for discovery of system dynamics, the first step in control system development. The paper introduces the concepts of phase-space reconstruction via time-delay embedding (made famous byWhitney, Takens, and Sauer’s Thoreoms), intergrate-and-fire embedding, and non-linear differential equation discovery based on Perona’s method.
Nonlinear theory of a free electron laser with a helical wiggler and an axial guide magnetic field
Directory of Open Access Journals (Sweden)
N. S. Ginzburg
2013-09-01
Full Text Available A 1D nonlinear theory of a free electron laser (FEL with a helical wiggler and an axial guide magnetic field is developed based on averaged equations of the electron motion. By averaging we separated two different cases of the e-beam/rf-wave interaction. The first one corresponds to the traditional wiggler synchronism (resonance of rf wave with the electrons moving along stationary helical trajectories. The second one corresponds to combination resonances distinguishing by excitation of oscillation of the electrons near the stationary helical trajectory. Comparative analysis of the FEL operation in different regimes has been studied under the traditional wiggler synchronism condition. It was shown that FELs operated far from cyclotron resonance (including a reversed guide field orientation possess low sensitivity to the initial velocity spread in the driving beam resulting in high electron efficiency. In contrast, under the weak guide field (the gyrofrequency is less than the bounce frequency of a conventional orientation, the FEL efficiency is restricted by a significant increase in the transverse velocity of the electrons during the interaction with the rf wave that results in violation of the synchronism conditions and is accompanied by electron current losses. An additional mechanism of FEL efficiency enhancement under the conventional guide field orientation in the conditions when the gyrofrequency is higher than the bounce frequency, based on the dependence of the effective mass of the oscillating electrons on their energy, was demonstrated. Results of the theoretical analysis are compared with the results of experimental studies of FEL oscillators. The specific features of energy extraction from the electron beam under condition of an abnormal Doppler effect in the case of the combination resonance are described. This regime is beneficial to increase radiation frequency keeping wiggler period and electron energies.
One-loop effective potential in nonlocal supersymmetric theories
de Mello, E. R. Bezerra; Gama, F. S.; Nascimento, J. R.; Petrov, A. Yu.
2017-01-01
Within the superfield approach, we consider the nonlocal generalization of the Wess-Zumino model and calculate the one-loop low-energy contributions to the effective action. Four different nonlocal models are considered, among which only the first model does not reduce to the standard Wess-Zumino model when we take the parameter of nonlocality of the model, Λ , much greater than any energy scale; in addition, this model also depends on an extra parameter ξ . As to the other three models, the result looks like the renormalized effective potential for the usual Wess-Zumino model, where the normalization scale μ is replaced by the Λ . Moreover, the fourth model displays a divergence which can be eliminated through the appropriate wave function renormalization.
Nonlinear composite beam theory
National Research Council Canada - National Science Library
Hodges, Dewey H
2006-01-01
.... Reproduction or translation of any part of this work beyond that permitted by Sections 107 and 108 of the U.S. Copyright Law without the permission of the copyright owner is unlawful. The code following this statement indicates the copyright owner's consent that copies of articles in this volume may be made for personal or internal use, on condit...
Finite Temperature Effective Potential for Spontaneously Broken $\\lambda \\Phi^4$ Theory
Nachbagauer, Herbert
1994-01-01
We present a self-consistent calculation of the finite temperature effective potential for $\\lambda \\Phi^4$ theory in four dimensions using a composite operator effective action. We find that in a spontaneously broken theory not only the so-called daisy and superdaisy graphs contribute to the next-to-leading order thermal mass, but also resummed non-local diagrams are of the same order, thus altering the effective potential at small effective mass.
A quantum model of exaptation: incorporating potentiality into evolutionary theory.
Gabora, Liane; Scott, Eric O; Kauffman, Stuart
2013-09-01
The phenomenon of preadaptation, or exaptation (wherein a trait that originally evolved to solve one problem is co-opted to solve a new problem) presents a formidable challenge to efforts to describe biological phenomena using a classical (Kolmogorovian) mathematical framework. We develop a quantum framework for exaptation with examples from both biological and cultural evolution. The state of a trait is written as a linear superposition of a set of basis states, or possible forms the trait could evolve into, in a complex Hilbert space. These basis states are represented by mutually orthogonal unit vectors, each weighted by an amplitude term. The choice of possible forms (basis states) depends on the adaptive function of interest (e.g., ability to metabolize lactose or thermoregulate), which plays the role of the observable. Observables are represented by self-adjoint operators on the Hilbert space. The possible forms (basis states) corresponding to this adaptive function (observable) are called eigenstates. The framework incorporates key features of exaptation: potentiality, contextuality, nonseparability, and emergence of new features. However, since it requires that one enumerate all possible contexts, its predictive value is limited, consistent with the assertion that there exists no biological equivalent to "laws of motion" by which we can predict the evolution of the biosphere. Copyright © 2013 Elsevier Ltd. All rights reserved.
Indirect recoil implantation following nuclear reactions: Theory and potential applications
International Nuclear Information System (INIS)
Conlon, T.W.
1980-01-01
A general treatment of indirect recoil implantation following nuclear reactions is given for the first time. This method allows implantation into any substrate of a wide range of species produced by nuclear reactions either in a thin sacrificial target or from a solid target. It is demonstrated that this can be done whilst avoiding primary beam damage to the substrate. Two cases are considered, the general one in which non-elastic nuclear reactions produce the recoil species of interest and secondly the special case of elastic recoils. In both cases a number of novel features of the process not previously described are outlined. For example, by controlling the angular acceptance of the substrate for recoil products the method can be tailored to give well controlled implantation profiles very similar to direct implantation (i.e., approximately Gaussian in range) or more extensive depth distributions whose profiles are simply determined by the centre of mass angular distribution of the reaction product. The flux of particles available for implantation is approximately 10 -4 smaller than from direct implantation facilities, but is comparable to the useful implantation dose achieved by the established technique of direct elastic recoil implantation. The radiation damage is little more than that associated with the indirect implant itself in contrast to direct elastic recoil implantation where the potential damage produced often mediates against the use of that technique. The main advantage of this relatively new method over the conventional methods is the wider range of species which can be implanted with minimum damage to the substrate. These include elements which cannot be conveniently produced from ion sources as well as exotic species which cannot be produced other than by nuclear reactions; radioactive species are good examples of both cases. (orig.)
On the theory of interaction potentials in ionic crystals
Energy Technology Data Exchange (ETDEWEB)
Acevedo, Roberto [Departamento de Ciencia de los Materiales, Facultad de Ciencias Fisicas y Matematicas, Beauchef 850, Santiago (Chile); Soto-Bubert, Andres [Instituto de Ciencias Basicas, Facultad de Ingenieria, Universidad Diego Portales, Avenida Ejercito 441, Santiago (Chile)], E-mail: roberto.acevedo@umayor.cl
2008-11-01
The aim of this research work is to report a more comprehensive and detailed study of both, the intermolecular and intramolecular potencial functions with reference to the various families of the elpasolite type crystals. The cohesive energy has been thought as a sum of three terms; the long range (Coulombic), the Born and the van der Waals contributions to the total energy. The Born-Mayer-Buckingham potential{sup 1} has been employed in all of these current studies and a number of convergence tests are analyzed from a formal viewpoint. Our work has been focused to the following systems: Cs{sub 2}NaLnF{sub 6}, Cs{sub 2}NaLnCl{sub 6}, Cs{sub 2}NaLnBr{sub 6}, Rb{sub 2}NaLnF{sub 6} and Cs{sub 2}KLnF{sub 6} in the Fm3m space group. A substantial amount of theoretical models have been analyzed and several computing simulations have been undertaken to estimate the reticular energies and the corresponding heat of formation for these crystals. To achieve this goal, a Born-Haber thermodynamic cycle has been introduced in our model. It is shown that the calculated energy values are reasonable and follow the expected trend along the lanthanide series in the periodic chart. We also discuss the advantages and disadvantages of the current and proposed generalized model. The most likely sources for improvement are discussed in detail. New convergence tests as well as some master equations have been introduced to study the various diagonal contributions to the total energy.
DEFF Research Database (Denmark)
Enemark, Søren; Santos, Ilmar F.
2016-01-01
In this work, the nonlinear dynamic behaviour of a vertical rigid rotor interacting with a flexible foundation by means of two passive magnetic bearings is quantified and evaluated. The quantification is based on theoretical and experimental investigation of the non-uniformity (anisotropy......-coupling between the two orthogonal directions, especially during counter-phase motion between shaft and bearings. The clear nonlinear behaviour is facilitated by the lack of damping resulting in relatively large vibrations. The overall nonlinear dynamic behaviour is well captured by the theoretical model, thereby...
Long-term potential nonlinear predictability of El Niño-La Niña events
Astudillo, H. F.; Abarca-del-Río, R.; Borotto, F. A.
2017-07-01
We show that the monthly recorded history (1866-2014) of the Southern Oscillation Index (SOI), a descriptor of the El Niño Southern Oscillation (ENSO) phenomenon, can be correctly described as a dynamic system supporting a potential nonlinear predictability well beyond the spring barrier. Long-term predictability is strongly connected to a detailed knowledge about the topology of the attractor obtained by embedding the SOI index in a wavelet base state space. By utilizing the state orbits on the attractor, we show that the information contained in the SOI is sufficient to provide nonlinear attractor information, allowing the detection of predictability for longer than a year: 2, 3, and 4 years in advance throughout the record with an acceptable error. This is possible due to the fact that the lower-frequency variability of the SOI presents long-term positive autocorrelation. Thus, by using complementary methods, we confirm that the reconstructed attractor of the low-frequency part (lower than 1/year) of SOI time series cannot be attributed to stochastic influences. Furthermore, we establish its multifractality. As an example of the capabilities of the methodology, we investigate a few specific El Niño (1972-1973, 1982-1983, 1997-1998) and La Niña (1973-1973, 1988-1989 and 2010-2011) events. Our results indicate that each of these present several equivalent temporal structures over other eras of these 149 years (1866-2014). Accordingly, none of these cases, including extreme events, presents temporal singularity. We conclude that the methodology's simplicity of implementation and ease of use makes it suitable for studying nonlinear predictability in any area where observations are similar to those describing the ENSO phenomenon.
Donges, J. F.; Donner, R. V.; Marwan, N.; Breitenbach, S. F. M.; Rehfeld, K.; Kurths, J.
2015-05-01
The Asian monsoon system is an important tipping element in Earth's climate with a large impact on human societies in the past and present. In light of the potentially severe impacts of present and future anthropogenic climate change on Asian hydrology, it is vital to understand the forcing mechanisms of past climatic regime shifts in the Asian monsoon domain. Here we use novel recurrence network analysis techniques for detecting episodes with pronounced non-linear changes in Holocene Asian monsoon dynamics recorded in speleothems from caves distributed throughout the major branches of the Asian monsoon system. A newly developed multi-proxy methodology explicitly considers dating uncertainties with the COPRA (COnstructing Proxy Records from Age models) approach and allows for detection of continental-scale regime shifts in the complexity of monsoon dynamics. Several epochs are characterised by non-linear regime shifts in Asian monsoon variability, including the periods around 8.5-7.9, 5.7-5.0, 4.1-3.7, and 3.0-2.4 ka BP. The timing of these regime shifts is consistent with known episodes of Holocene rapid climate change (RCC) and high-latitude Bond events. Additionally, we observe a previously rarely reported non-linear regime shift around 7.3 ka BP, a timing that matches the typical 1.0-1.5 ky return intervals of Bond events. A detailed review of previously suggested links between Holocene climatic changes in the Asian monsoon domain and the archaeological record indicates that, in addition to previously considered longer-term changes in mean monsoon intensity and other climatic parameters, regime shifts in monsoon complexity might have played an important role as drivers of migration, pronounced cultural changes, and the collapse of ancient human societies.
Roussis, Panayiotis C.; Tsopelas, Panos C.; Constantinou, Michael C.
2010-03-01
The work presented in this paper serves as numerical verification of the analytical model developed in the companion paper for nonlinear dynamic analysis of multi-base seismically isolated structures. To this end, two numerical examples have been analyzed using the computational algorithm incorporated into program 3D-BASIS-ME-MB, developed on the basis of the newly-formulated analytical model. The first example concerns a seven-story model structure that was tested on the earthquake simulator at the University at Buffalo and was also used as a verification example for program SAP2000. The second example concerns a two-tower, multi-story structure with a split-level seismic-isolation system. For purposes of verification, key results produced by 3D-BASIS-ME-MB are compared to experimental results, or results obtained from other structural/finite element programs. In both examples, the analyzed structure is excited under conditions of bearing uplift, thus yielding a case of much interest in verifying the capabilities of the developed analysis tool.
Directory of Open Access Journals (Sweden)
Haicheng Yu
2018-01-01
Full Text Available A fully coupled nonlinear three-dimensional (3D hydroelastic method is developed to investigate vibrational responses of a large ship with a pronounced bow flare subjected to high seas. This numerical model consists of a 3D boundary element method, 1D Euler-Bernoulli beam model, and a 2D generalized Wagner model. Green water loads were considered. Experimental study was carried out in a towing tank on a self-propelled segmented model with nonuniform steel backbones. The ship model was tested in regular incident waves of large amplitude. Impact pressure and nonlinear vertical bending moments were measured and compared with numerical predictions. The proposed nonlinear model produced similar results to the experimental model. Furthermore, the effects of elastic modes and nonlinearities on the numerical results were analyzed.
Yi, Liang; Shi, Zhengguo; Tan, Liangcheng; Deng, Chenglong
2018-03-01
We conducted a statistical study to characterize the nonlinear response of the East Asian summer monsoon (EASM) to its potential forcing factors over the last 260 ka on orbital timescales. We find that both variation in solar insolation and global ice volume were responsible for the nonlinear forcing of orbital-scale monsoonal variations, accounting for 80% of the total variance. Specifically, EASM records with dominated precession variance exhibit a more sensitive response to changes in solar insolation during intervals of enhanced monsoon strength, but are less sensitive during intervals of reduced monsoon strength. In the case of global ice volume with 100-ka variance, this difference is not one of sensitivity but rather a difference in baseline conditions, such as the relative areas of land and sea which affected the land-sea thermal gradient. We therefore suggest that EASM records with dominated precession variance recorded the signal of a shift in the location of the Inter-tropical Convergence Zone, and the associated changes in the incidence of torrential rainfall; while for proxies with dominated 100-ka variance, it recorded changes in the land-sea thermal gradient via its effects on non-torrential precipitation.
Nonlinear elliptic differential equations with multivalued nonlinearities
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
Nonlinear elliptic differential equations with multivalued ... has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth .... A is upper semicontinuous (as a set-valued map) from every finite dimensional subspace of X into ...
Nonlinear chiral transport phenomena
Chen, Jiunn-Wei; Ishii, Takeaki; Pu, Shi; Yamamoto, Naoki
2016-06-01
We study the nonlinear responses of relativistic chiral matter to the external fields such as the electric field E , gradients of temperature and chemical potential, ∇T and ∇μ . Using the kinetic theory with Berry curvature corrections under the relaxation time approximation, we compute the transport coefficients of possible new electric currents that are forbidden in usual chirally symmetric matter but are allowed in chirally asymmetric matter by parity. In particular, we find a new type of electric current proportional to ∇μ ×E due to the interplay between the effects of the Berry curvature and collisions. We also derive an analog of the "Wiedemann-Franz" law specific for anomalous nonlinear transport in relativistic chiral matter.
Directory of Open Access Journals (Sweden)
Soren Ventegodt
2003-01-01
Full Text Available This review presents one of the eight theories of the quality of life (QOL used for making the SEQOL (self-evaluation of quality of life questionnaire or the quality of life as realizing life potential. This theory is strongly inspired by Maslow and the review furthermore serves as an example on how to fulfill the demand for an overall theory of life (or philosophy of life, which we believe is necessary for global and generic quality-of-life research.Whereas traditional medical science has often been inspired by mechanical models in its attempts to understand human beings, this theory takes an explicitly biological starting point. The purpose is to take a close view of life as a unique entity, which mechanical models are unable to do. This means that things considered to be beyond the individual's purely biological nature, notably the quality of life, meaning in life, and aspirations in life, are included under this wider, biological treatise. Our interpretation of the nature of all living matter is intended as an alternative to medical mechanism, which dates back to the beginning of the 20th century. New ideas such as the notions of the human being as nestled in an evolutionary and ecological context, the spontaneous tendency of self-organizing systems for realization and concord, and the central role of consciousness in interpreting, planning, and expressing human reality are unavoidable today in attempts to scientifically understand all living matter, including human life.
Li, H. M.; Zhao, J. Q.; You, L. Y.
2015-10-01
We investigate the explicit matter-wave soliton solutions of the cubic-quintic nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and potentials. With a systematic way, we construct some integrable systems with localized cubic-quintic nonlinearities and an infinite number of potentials, including optical lattice potential and combined time-dependent magnetic-optical potentials in the form of linear-lattice, harmonic-lattice and harmonic-linear-lattice ones. Also, corresponding analytical localized soliton solutions in terms of Mathieu and elliptic functions are studied, such as snake solitons, moving breathing solitons and oscillating solitons. Finally, some stable solitons are found by means of the stability analysis of the exact solutions with the split-step Fourier transform method.
Application of the theory of local potential to some hydrodynamics and heat transfer problems
International Nuclear Information System (INIS)
Delhaye, Jean-Marc
1970-04-01
This short research thesis addresses the field of thermodynamics of irreversible phenomena. The author first recalls the fundamentals of conservation laws, as well as initial postulates of thermodynamics of irreversible phenomena. He reports the study of the conditions of application of the principle of minimum entropy production, and presents the main characteristics of the theory of the local potential. He briefly presents some applications of this theory to hydrodynamics and heat transfer problems in fluid flows [fr
The relativistic two-body potentials of constraint theory from summation of Feynman diagrams
Jallouli, H.; Sazdjian, H.
1996-01-01
The relativistic two-body potentials of constraint theory for systems composed of two spin-0 or two spin-1/2 particles are calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates them to the scattering amplitude. The cases of scalar and vector interactions with massless photons are considered. The two-photon exchange contributions, calculated with covariant propagators,are globally free of spurious infra-red singularities and produce at leading order ...
von Lilienfeld, O Anatole; Tavernelli, Ivano; Rothlisberger, Ursula; Sebastiani, Daniel
2004-10-08
We add an effective atom-centered nonlocal term to the exchange-correlation potential in order to cure the lack of London dispersion forces in standard density functional theory. Calibration of this long-range correction is performed using density functional perturbation theory and an arbitrary reference. Without any prior assignment of types and structures of molecular fragments, our corrected generalized gradient approximation density functional theory calculations yield correct equilibrium geometries and dissociation energies of argon-argon, benzene-benzene, graphite-graphite, and argon-benzene complexes.
Traversa, Fabio L; Di Ventra, Massimiliano; Bonani, Fabrizio
2013-04-26
Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic coefficients. Here, we extend the theory by proving a theorem for the general class of systems including linear operators commuting with the period-shift operator. The present theorem greatly expands the range of applicability of Floquet theory to a multitude of phenomena that were previously inaccessible with this type of analysis, such as dynamical systems with memory. As an important extension, we also prove Bloch's theorem for nonlocal potentials.
Combined effects of changing-sign potential and critical nonlinearities in Kirchhoff type problems
Directory of Open Access Journals (Sweden)
Gao-Sheng Liu
2016-08-01
Full Text Available In this article, we study the existence and multiplicity of positive solutions for a class of Kirchhoff type problems involving changing-sign potential and critical growth terms. Using the concentration compactness principle and Nehari manifold, we obtain the existence and multiplicity of nonzero non-negative solutions.
Han, Guopeng; Wang, Ying; Su, Xin; Yang, Zhihua; Pan, Shilie
2017-05-15
Mid-Infrared nonlinear optical (Mid-IR NLO) crystals with excellent performances play a particularly important role for applications in areas such as telecommunications, laser guidance, and explosives detection. However, the design and growth of high performance Mid-IR NLO crystals with large NLO efficiency and high laser-damage threshold (LDT) still face numerous fundamental challenge. In this study, two potential Mid-IR NLO materials, Rb 2 LiVO 4 (RLVO) and Cs 2 LiVO 4 (CLVO) with noncentrosymmetric structures (Orthorhombic, Cmc2 1 ) were synthesized by high-temperature solution method. Thermal analysis and powder X-ray diffraction demonstrate that RLVO and CLVO melt congruently. Centimeter sized crystals of CLVO have been grown by the top-seeded solution growth method. RLVO and CLVO exhibit strong second harmonic generation (SHG) effects (about 4 and 5 times that of KH 2 PO 4 , respectively) with a phase-matching behavior at 1.064 μm, and a wide transparency range (0.33-6.0 μm for CLVO). More importantly, RLVO and CLVO possess a high LDT value (~28 × AgGaS 2 ). In addition, the density functional theory (DFT) and dipole moments studies indicate that the VO 4 anionic groups have a dominant contribution to the SHG effects in RLVO and CLVO. These results suggest that the title compounds are promising NLO candidate crystals applied in the Mid-IR region.
Energy Technology Data Exchange (ETDEWEB)
Rahmani, S.; Hassanabadi, H. [Shahrood University of Technology, Physics Department, Shahrood (Iran, Islamic Republic of)
2017-09-15
Employing generalized quantum isotonic oscillator potential we determine wave function for mesonic system in nonrelativistic formalism. Then we investigate branching ratios of leptonic decays for heavy-light mesons including a charm quark. Next, by applying the Isgur-Wise function we obtain branching ratios of semileptonic decays for mesons including a bottom quark. The weak decay of the B{sub c} meson is also analyzed to study the life time. Comparison with other available theoretical approaches is presented. (orig.)
One-Body Potential Theory of Molecules and Solids Modified Semiempirically for Electron Correlation
International Nuclear Information System (INIS)
March, N.H.
2010-08-01
The study of Cordero, March and Alonso (CMA) for four spherical atoms, Be,Ne,Mg and Ar, semiempirically fine-tunes the Hartree-Fock (HF) ground-state electron density by inserting the experimentally determined ionization potentials. The present Letter, first of all, relates this approach to the very recent work of Bartlett 'towards an exact correlated orbital theory for electrons'. Both methods relax the requirement of standard DFT that a one-body potential shall generate the exact ground-state density, though both work with high quality approximations. Unlike DFT, the CMA theory uses a modified HF non-local potential. It is finally stressed that this potential generates also an idempotent Dirac density matrix. The CMA approach is thereby demonstrated to relate, albeit approximately, to the DFT exchange-correlation potential. (author)
Correlated orbital theories with both local and non-local one-body potentials
Directory of Open Access Journals (Sweden)
Norman H. March
2010-10-01
Full Text Available After a brief survey of current density functional theory (DFT, based on an incompletely known one-body potential V(r, a method due to Cordero, March, and Alonso (CMA is summarized. This obtains the ground-state density n(r, for spherical atoms as yet, from a semi-empirical fine-tuning of Hartree-Fock (HF theory, which of course involves a non-local potential because of the presence of the Fock operator. This leads to n(r for spherical atoms of quantum Monte Carlo quality. A more recent proposal, related to CMA but different, by Bartlett, is also reviewed.
International Nuclear Information System (INIS)
Popov, V.N.
1990-01-01
The present set of articles is devoted to the theory of operators with random potential and a number of problems on statistical physics. Average wave operators and average scattering operator are calculated for the Schroedinger operator with potential randomly dependent on time. It is shown that the averaged dynamics behaves freely within the limits of infinite time. Results on application of functional integration method to some problems of statistical physics: theory of systems with model Hamiltonians and their dynamics, ferromagnetic systems of 1/2 spin, Coulomb and quantum crystals are presented
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Nonlinear electron acoustic structures generated on the high-potential side of a double layer
Directory of Open Access Journals (Sweden)
R. Pottelette
2009-04-01
Full Text Available High-time resolution measurements of the electron distribution function performed in the auroral upward current region reveals a large asymmetry between the low- and high-potential sides of a double-layer. The latter side is characterized by a large enhancement of a locally trapped electron population which corresponds to a significant part (~up to 30% of the total electron density. As compared to the background hot electron population, this trapped component has a very cold temperature in the direction parallel to the static magnetic field. Accordingly, the differential drift between the trapped and background hot electron populations generates high frequency electron acoustic waves in a direction quasi-parallel to the magnetic field. The density of the trapped electron population can be deduced from the frequency where the electron acoustic spectrum maximizes. In the auroral midcavity region, the electron acoustic waves may be modulated by an additional turbulence generated in the ion acoustic range thanks to the presence of a pre-accelerated ion beam located on the high-potential side of the double layer. Electron holes characterized by bipolar pulses in the electric field are sometimes detected in correlation with these electron acoustic wave packets.
International Nuclear Information System (INIS)
Dubrovsky, V.G.; Formusatik, I.B.
2003-01-01
The scheme for calculating via Zakharov-Manakov ∂-macron-dressing method of new rational solutions with constant asymptotic values at infinity of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear evolution equation and new exact rational potentials of two-dimensional stationary Schroedinger (2DSchr) equation with multiple pole wave functions is developed. As examples new lumps of VN nonlinear equation and new exact rational potentials of 2DSchr equation with multiple pole of order two wave functions are calculated. Among the constructed rational solutions are as nonsingular and also singular
DEFF Research Database (Denmark)
Larsen, Jon Steffen; Santos, Ilmar
2015-01-01
, hence accurate prediction of their response is important. This paper gives theoretical and experimental contributions by implementing and validating a new method to simulate the nonlinear steady-state response of a rotor supported by three pads segmented AFBs. The fluid film pressures, foil deflections...
Fulcher, Lewis P.
1979-01-01
Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)
International Nuclear Information System (INIS)
March, N.H.; Nagy, A.
2006-01-01
A formally exact integral equation theory for the exchange-only potential V x (r) in density functional theory was recently set up by Howard and March [I.A. Howard, N.H. March, J. Chem. Phys. 119 (2003) 5789]. It involved a 'closure' function P(r) satisfying the exact sum rule ∫P(r)dr=0. The simplest choice P(r)=0 recovers then the approximation proposed by Della Sala and Gorling [F. Della Sala, A. Gorling, J. Chem. Phys. 115 (2001) 5718] and by Gritsenko and Baerends [O.V. Gritsenko, E.J. Baerends, Phys. Rev. A 64 (2001) 042506]. Here, refined choices of P(r) are proposed, the most direct being based on the KLI (Krieger-Li-Iafrate) approximation. A further choice given some attention is where P(r) involves frontier orbital properties. In particular, the introduction of the LUMO (lowest unoccupied molecular) orbital, along with the energy separation between HOMO (highest occupied molecular orbital) and LUMO levels, should prove a significant step beyond current approximations to the optimized potential method, all of which involve only single-particle occupied orbitals
Copper-doped Al12N12 nano-cages: potential candidates for nonlinear optical materials
Gilani, Mazhar Amjad; Tabassum, Sobia; Gul, Urooj; Mahmood, Tariq; Alharthi, Abdulrahman I.; Alotaibi, Mshari A.; Geesi, Mohammed; Sheikh, Rizwan; Ayub, Khurshid
2018-01-01
DFT calculations have been performed to study geometric, electronic and NLO properties of copper-doped Al12N12 nano-cages. Doping of copper significantly reduces HOMO-LUMO gap of the nano-cages. The most prominent change in E g is observed for Cu@R6 (copper at the center of the six-membered ring), where E g is reduced by 52% of the original value. Total and partial densities of states have been plotted for all the structures revealing that a new HOMO has appeared between the original frontier molecular orbitals of Al12N12. Polarizabilities and hyperpolarizabilities show manifold increase ( α = 418 au and β 0 = 1.8 × 104 au for Cu@R6) than pure Al12N12. TD-DFT calculations have been performed to obtain crucial excited states to account for the high hyperpolarizability values. The hyperpolarizability trend estimated from the two-level method and DFT calculations correlates nicely. The hyperpolarizability trend is justified nicely from the decreased E g. These findings designate such doped nano-cages as excellent candidates for their potential applications in electronic devices.
Clerc, Daryl G
2016-07-21
An ab initio approach was used to study the molecular-level interactions that connect gene-mutation to changes in an organism׳s phenotype. The study provides new insights into the evolutionary process and presents a simplification whereby changes in phenotypic properties may be studied in terms of the binding affinities of the chemical interactions affected by mutation, rather than by correlation to the genes. The study also reports the role that nonlinear effects play in the progression of organs, and how those effects relate to the classical theory of evolution. Results indicate that the classical theory of evolution occurs as a special case within the ab initio model - a case having two attributes. The first attribute: proteins and promoter regions are not shared among organs. The second attribute: continuous limiting behavior exists in the physical properties of organs as well as in the binding affinity of the associated chemical interactions, with respect to displacements in the chemical properties of proteins and promoter regions induced by mutation. Outside of the special case, second-order coupling contributions are significant and nonlinear effects play an important role, a result corroborated by analyses of published activity levels in binding and transactivation assays. Further, gradations in the state of perfection of an organ may be small or large depending on the type of mutation, and not necessarily closely-separated as maintained by the classical theory. Results also indicate that organs progress with varying degrees of interdependence, the likelihood of successful mutation decreases with increasing complexity of the affected chemical system, and differences between the ab initio model and the classical theory increase with increasing complexity of the organism. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.
Higgs Potential of the SU(5) theory in the one-loop approximation
International Nuclear Information System (INIS)
Anselm, A.; Iogansen, A.
1981-01-01
We have calculated the effective potential of the 24-plet and 5-plet of Higgs bosons for the SU(5) theory of Georgi and Glashow in the one-loop approximation. We have taken into account the loops of the gauge bosons, quarks, and leptons. We have corrected numerical errors made in Ref. 3. The technique which we have developed can be used to calculate the effective potential also in the case of other groups
Computation of hybrid static potentials in SU(3 lattice gauge theory
Directory of Open Access Journals (Sweden)
Reisinger Christian
2018-01-01
Full Text Available We compute hybrid static potentials in SU(3 lattice gauge theory. We present a method to automatically generate a large set of suitable creation operators with defined quantum numbers from elementary building blocks. We show preliminary results for several channels and discuss, which structures of the gluonic flux tube seem to be realized by the ground states in these channels.
Scattering theory for the Klein-Gordon equation with nondecreasing potentials
International Nuclear Information System (INIS)
Cruz, Maximino; Arredondo R, Juan H.
2008-01-01
The Klein-Gordon equation is considered in the case of nondecreasing potentials. The energy inner product is nonpositive on a subspace of infinite dimension, not consisting entirely of eigenvectors of the associated operator. A scattering theory for this case is developed and asymptotic completeness for generalized Moeller operators is proven
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
Energy Technology Data Exchange (ETDEWEB)
Sethna, J.P.; Krumhansl, J.A.
1994-08-01
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.
Rivière, J.; Renaud, G.; Guyer, R. A.; Johnson, P. A.
2013-08-01
Standard nonlinear ultrasonic methods such as wave frequency mixing or resonance based measurements allow one to extract average, bulk variations of modulus and attenuation versus strain level. In contrast, dynamic acousto-elasticity (DAE) provides the elastic behavior over the entire dynamic cycle including hysteresis and memory effects, detailing the full nonlinear behavior under tension and compression. In this work, we address experimental difficulties and apply new processing methods, illustrating them with a Berea sandstone sample. A projection procedure is used to analyze the complex nonlinear signatures and extract the harmonic content. Amplitude dependences of the harmonic content are compared with existing models. We show that a combination of classical and hysteretic nonlinear models capture most of the observed phenomena. Some differences between existing models and experimental data are highlighted, however. A progressive decrease of the power-law amplitude dependence is found for harmonics larger than the second and for strains larger than 10-6. This observation is related to the phenomenon of acoustic conditioning that brings the material to a metastable state for each new excitation amplitude. Analysis of the steady-state regime provides additional information regarding acoustic conditioning, i.e., a progressive decrease of the amplitude of odd harmonics during excitation time with a log(t)-dependence. This observation confirms that the harmonic content is affected by the conditioning. Experimental challenges addressed include the fact that the compressional mode used for DAE can be affected by bending/torsion modes: their influence is evaluated, and guidances are given to minimize effects.
2014-09-01
The concept of nonlinear radar has been explored within the radio-frequency identification ( RFID ) community: associated applications range from...Proc. SPIE. 2003;5089. 3 Wang T, Sjahputera O, Keller JM. Landmine detection using forward-looking GPR with object tracking , Proc. SPIE...Comput. Electron. Agr. 2002;35:151–169. 7 Nikitin PV, Rao KVS. Harmonic scattering from passive UHF RFID tags. Proc. IEEE Antennas and Propagat. Soc
Prediction of adsorption from liquid mixtures in microporous media by the potential theory
DEFF Research Database (Denmark)
Monsalvo, Matias Alfonso; Shapiro, Alexander
2007-01-01
Despite its industrial importance, adsorption from the liquid phase has been studied much less extensively than adsorption from the gas phase. In this paper, we study the adsorption of liquid mixtures on the basis of the multicomponent potential theory of adsorption (MPTA). The MPTA is based...... on the potential concept originally developed by Polanyi. In this theory, the driving force for physical adsorption is measured by the adsorption potential that is a function of the distance from the solid surface. In this way, the adsorbate is considered as a heterogeneous substance segregated in the external......, obtaining relatively simple models useful for engineering applications. Comparison with experimental data shows good agreement and high degree of predictability. (C) 2007 Elsevier B.V. All rights reserved....
Study of high-pressure adsorption from supercritical fluids by the potential theory
DEFF Research Database (Denmark)
Monsalvo, Matias Alfonso; Shapiro, Alexander
2009-01-01
The multicomponent potential theory of adsorption (MPTA), which has been previously used to study low-pressure adsorption of subcritical fluids, is extended to adsorption equilibria from supercritical fluids up to high pressures. The MPTA describes an adsorbed phase as an inhomogeneous fluid...... with thermodynamic properties that depend on the distance from the solid surface (or position in the porous space). The description involves the two kinds of interactions present in the adsorbed fluid, i.e. the fluid-fluid and fluid-solid interactions. accounted for by means of an equation of state (Eo......S) and interaction potential functions, respectively. This makes it possible to generate the different MPTA models by combination of the relevant EoS/potentials. In the present work, the simplified perturbed-chain statistical associating fluid theory (sPC-SAFT) EoS is used for the thermodynamic description of both...
2013-01-01
filter, Bayesian decision theory, Generalized Likelihood Ratio Test (GLRT), and constant false alarm rate ( CFAR ) processing (31). Once the...Abbreviations, and Acronyms CFAR constant false alarm rate CNR cognitive nonlinear radar EM electromagnetic FCC Federal Communications Comission
Directory of Open Access Journals (Sweden)
Redrothu Hanumantharao
2013-01-01
Full Text Available A novel semiorganic nonlinear optical crystal bis (L-glutamine potassium nitrate (BGPN grown by slow evaporation technique at ambient temperature. The grown crystal surface has been analyzed by chemical etching and atomic force microscopy (AFM studies. Amplitude parameters like area roughness, roughness average, valley height, valley depth, peak height, and peak valley height were measured successfully from AFM studies. Etching studies were carried out by various solvents like water, methanol and ethanol. The etching study indicates the occurrence of different types of etch pit patterns like striations and steplike pattern. The laser damage threshold energy has been measured by irradiating laser beam using a Q-switched Nd: YAG laser (1064 nm. Second harmonic generation (SHG studies have been performed by famous Kurtz powder technique with reference to standard potassium dihydrogen phosphate single crystals (KDP. It is found from this technique that SHG efficiency of BGPN is in comparison to that of standard KDP crystals.
Cheng, Jin; Yu, Kuang; Libisch, Florian; Dieterich, Johannes M; Carter, Emily A
2017-03-14
Quantum mechanical embedding theories partition a complex system into multiple spatial regions that can use different electronic structure methods within each, to optimize trade-offs between accuracy and cost. The present work incorporates accurate but expensive correlated wave function (CW) methods for a subsystem containing the phenomenon or feature of greatest interest, while self-consistently capturing quantum effects of the surroundings using fast but less accurate density functional theory (DFT) approximations. We recently proposed two embedding methods [for a review, see: Acc. Chem. Res. 2014 , 47 , 2768 ]: density functional embedding theory (DFET) and potential functional embedding theory (PFET). DFET provides a fast but non-self-consistent density-based embedding scheme, whereas PFET offers a more rigorous theoretical framework to perform fully self-consistent, variational CW/DFT calculations [as defined in part 1, CW/DFT means subsystem 1(2) is treated with CW(DFT) methods]. When originally presented, PFET was only tested at the DFT/DFT level of theory as a proof of principle within a planewave (PW) basis. Part 1 of this two-part series demonstrated that PFET can be made to work well with mixed Gaussian type orbital (GTO)/PW bases, as long as optimized GTO bases and consistent electron-ion potentials are employed throughout. Here in part 2 we conduct the first PFET calculations at the CW/DFT level and compare them to DFET and full CW benchmarks. We test the performance of PFET at the CW/DFT level for a variety of types of interactions (hydrogen bonding, metallic, and ionic). By introducing an intermediate CW/DFT embedding scheme denoted DFET/PFET, we show how PFET remedies different types of errors in DFET, serving as a more robust type of embedding theory.
Xu, Hao; Pei, Yongmao; Li, Faxin; Fang, Daining
2018-05-01
The magnetic, electric and mechanical behaviors are strongly coupled in magnetoelectric (ME) materials, making them great promising in the application of functional devices. In this paper, the magneto-electro-mechanical fully coupled constitutive behaviors of ME laminates are systematically studied both theoretically and experimentally. A new probabilistic domain switching function considering the surface ferromagnetic anisotropy and the interface charge-mediated effect is proposed. Then a multi-scale multi-field coupling nonlinear constitutive model for layered ME composites is developed with physical measureable parameters. The experiments were performed to compare the theoretical predictions with the experimental data. The theoretical predictions have a good agreement with experimental results. The proposed constitutive relation can be used to describe the nonlinear multi-field coupling properties of both ME laminates and thin films. Several novel coupling experimental phenomena such as the electric-field control of magnetization, and the magnetic-field tuning of polarization are observed and analyzed. Furthermore, the size-effect of the electric tuning behavior of magnetization is predicted, which demonstrates a competition mechanism between the interface strain-mediated effect and the charge-driven effect. Our study offers deep insight into the coupling microscopic mechanism and macroscopic properties of ME layered composites, which is benefit for the design of electromagnetic functional devices.
Maitra, Rahul; Akinaga, Yoshinobu; Nakajima, Takahito
2017-08-21
A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.
Killing spinors for the bosonic string and Kaluza-Klein theory with scalar potentials
International Nuclear Information System (INIS)
Liu, Haishan; Lue, H.; Wang, Zhao-Long
2012-01-01
The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that Kaluza-Klein theory can be gauged so that the Killing spinors are charged under the Kaluza-Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories. (orig.)
Microscopic optical model potential based on Brueckner-Hartree-Fock theory
International Nuclear Information System (INIS)
Li Lulu; Zhao Enguang; Zhou Shangui; Li Zenghua; Zuo Wei; Bonaccorso, Angela; Lonbardo, Umberto
2010-01-01
The optical model is one of the most important models in the study of nuclear reactions. In the optical model, the elastic channel is considered to be dominant and the contributions of all other absorption channels are described by introducing an imaginary potential, Koning and Delaroche obtained empirically the so-called KDR optical potentials based on a best-fitting of massive experimental data on nucleon-nucleus scattering reactions. The volume part is found to be dominant in the real component of the OMP at low energies. Using the Bruckner-Hartree-Fock theory with Bonn B potential plus self consistent three body force, the nucleon-nucleus optical potential is studied in this thesis. In the Bruckner theory, the on-shell self energy, is corresponding to the depth of the volume part of the optical model potential (OMP) for nucleon-nucleus scattering. Using Bruckner-Hartree-Fock theory, the nucleon on-shell self energy is calculated based on Hughenoltz-Van Hove (HVH) theorem. The microscopic optical potentials thus obtained agree well with the volume part of the KDR potentials. Furthermore, the isospin splitting in the volume part of the OMP is also reproduced satisfactorily. The isospin effect in the volume part of the OMP is directly related to the isospin splitting of the effective mass of the nucleon. According to our results, the isospin splitting of neutron to proton effective mass is such that the neutron effective mass increases with isospin, whereas the proton effective mass decreases. The isovector potential U n (E) - U p (E) vanishes at energy E ≈ 200 MeV and then changes sign indicating a possible inversion in the effective mass isospin spitting. We also calculated from the Bruckner theory the imaginary part of the OMP, and the microscopic calculations predict that the isospin splitting exists also in the imaginary OMP whereas the empirical KDR potentials do not show this feature. The shape of the real component of the nucleon-nucleus OMP is
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
Gulans, Andris; Kontur, Stefan; Meisenbichler, Christian; Nabok, Dmitrii; Pavone, Pasquale; Rigamonti, Santiago; Sagmeister, Stephan; Werner, Ute; Draxl, Claudia
2014-09-10
Linearized augmented planewave methods are known as the most precise numerical schemes for solving the Kohn-Sham equations of density-functional theory (DFT). In this review, we describe how this method is realized in the all-electron full-potential computer package, exciting. We emphasize the variety of different related basis sets, subsumed as (linearized) augmented planewave plus local orbital methods, discussing their pros and cons and we show that extremely high accuracy (microhartrees) can be achieved if the basis is chosen carefully. As the name of the code suggests, exciting is not restricted to ground-state calculations, but has a major focus on excited-state properties. It includes time-dependent DFT in the linear-response regime with various static and dynamical exchange-correlation kernels. These are preferably used to compute optical and electron-loss spectra for metals, molecules and semiconductors with weak electron-hole interactions. exciting makes use of many-body perturbation theory for charged and neutral excitations. To obtain the quasi-particle band structure, the GW approach is implemented in the single-shot approximation, known as G(0)W(0). Optical absorption spectra for valence and core excitations are handled by the solution of the Bethe-Salpeter equation, which allows for the description of strongly bound excitons. Besides these aspects concerning methodology, we demonstrate the broad range of possible applications by prototypical examples, comprising elastic properties, phonons, thermal-expansion coefficients, dielectric tensors and loss functions, magneto-optical Kerr effect, core-level spectra and more.
Yang, Chen
2018-05-01
The transitions from classical theories to quantum theories have attracted many interests. This paper demonstrates the analogy between the electromagnetic potentials and wave-like dynamic variables with their connections to quantum theory for audiences at advanced undergraduate level and above. In the first part, the counterpart relations in the classical electrodynamics (e.g. gauge transform and Lorenz condition) and classical mechanics (e.g. Legendre transform and free particle condition) are presented. These relations lead to similar governing equations of the field variables and dynamic variables. The Lorenz gauge, scalar potential and vector potential manifest a one-to-one similarity to the action, Hamiltonian and momentum, respectively. In the second part, the connections between the classical pictures of electromagnetic field and particle to quantum picture are presented. By characterising the states of electromagnetic field and particle via their (corresponding) variables, their evolution pictures manifest the same algebraic structure (isomorphic). Subsequently, pictures of the electromagnetic field and particle are compared to the quantum picture and their interconnections are given. A brief summary of the obtained results are presented at the end of the paper.
Hagedorn, Peter
1982-01-01
Thoroughly revised and updated, the second edition of this concise text provides an engineer's view of non-linear oscillations, explaining the most important phenomena and solution methods. Non-linear descriptions are important because under certain conditions there occur large deviations from the behaviors predicted by linear differential equations. In some cases, completely new phenomena arise that are not possible in purely linear systems. The theory of non-linear oscillations thus has important applications in classical mechanics, electronics, communications, biology, and many other branches of science. In addition to many other changes, this edition has a new section on bifurcation theory, including Hopf's theorem.
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.
Hu, Jinniu; Toki, Hiroshi; Shen, Hong
2016-10-18
We study the properties of nuclear matter with lattice nucleon-nucleon (NN) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice NN potential. Three mesons, pion, σ meson, and ω meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around -3 and -5 MeV at saturation density, while it becomes -8 and -12 MeV in relativistic framework with 1 S 0 , 3 S 1 , and 3 D 1 channels using our two parameter sets. For the pure neutron matter, the equations of state in non-relativistic and relativistic cases are very similar due to only consideration 1 S 0 channel with isospin T = 1 case.
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
The biopsychosocial model and its potential for a new theory of homeopathy.
Schmidt, Josef M
2012-04-01
Since the nineteenth century the theory of conventional medicine has been developed in close alignment with the mechanistic paradigm of natural sciences. Only in the twentieth century occasional attempts were made to (re)introduce the 'subject' into medical theory, as by Thure von Uexküll (1908-2004) who elaborated the so-called biopsychosocial model of the human being, trying to understand the patient as a unit of organic, mental, and social dimensions of life. Although widely neglected by conventional medicine, it is one of the most coherent, significant, and up-to-date models of medicine at present. Being torn between strict adherence to Hahnemann's original conceptualization and alienation caused by contemporary scientific criticism, homeopathy today still lacks a generally accepted, consistent, and definitive theory which would explain in scientific terms its strength, peculiarity, and principles without relapsing into biomedical reductionism. The biopsychosocial model of the human being implies great potential for a new theory of homeopathy, as may be demonstrated with some typical examples. Copyright © 2012. Published by Elsevier Ltd.
Fowler, Nicholas J; Blanford, Christopher F; Warwicker, Jim; de Visser, Sam P
2017-11-02
Blue copper proteins, such as azurin, show dramatic changes in Cu 2+ /Cu + reduction potential upon mutation over the full physiological range. Hence, they have important functions in electron transfer and oxidation chemistry and have applications in industrial biotechnology. The details of what determines these reduction potential changes upon mutation are still unclear. Moreover, it has been difficult to model and predict the reduction potential of azurin mutants and currently no unique procedure or workflow pattern exists. Furthermore, high-level computational methods can be accurate but are too time consuming for practical use. In this work, a novel approach for calculating reduction potentials of azurin mutants is shown, based on a combination of continuum electrostatics, density functional theory and empirical hydrophobicity factors. Our method accurately reproduces experimental reduction potential changes of 30 mutants with respect to wildtype within experimental error and highlights the factors contributing to the reduction potential change. Finally, reduction potentials are predicted for a series of 124 new mutants that have not yet been investigated experimentally. Several mutants are identified that are located well over 10 Å from the copper center that change the reduction potential by more than 85 mV. The work shows that secondary coordination sphere mutations mostly lead to long-range electrostatic changes and hence can be modeled accurately with continuum electrostatics. © 2017 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.
Chen, Yi-Xiang; Xu, Zhou-Xiang; Jiang, Yun-Feng; Shi, Jin; Xu, Fang-Qian
2015-07-01
We obtain exact spatial localized mode solutions of a (2+1)-dimensional nonlinear Schrödinger equation with constant diffraction and cubic-quintic nonlinearity in Script PScript T-symmetric potential, and study the linear stability of these solutions. Based on these results, we further derive exact spatial localized mode solutions in a cubic-quintic medium with harmonic and Script PScript T-symmetric potentials. Moreover, the dynamical behaviors of spatial localized modes in the exponential diffraction decreasing waveguide and the periodic distributed amplification system are investigated. Supported by the Project of Technology Office in Zhejiang Province under Grant No. 2014C32006, the Special Foundation for theoretical physics Research Program of China under Grant No. 11447124, National Natural Science Foundation of China under Grant No. 11374254 and the Higher School Visiting Scholar Development under Grant No. FX2013103
Potential function methods for approximately solving linear programming problems theory and practice
Bienstock, Daniel
2002-01-01
Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.
Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan; Aktürk, Tolga
2018-03-01
In this study, using the extended sinh-Gordon equation expansion method, we construct the dark, bright, combined dark-bright optical, singular, combined singular solitons and singular periodic waves solutions to the complex cubic nonlinear Schrödinger equation with δ-potential. The conditions for the existence of the obtained solutions are given. To present the physical feature of the acquired result, the 2D and 3D graphs are plotted under the choice of suitable values of the parameters.
Full-potential multiple scattering theory with space-filling cells for bound and continuum states.
Hatada, Keisuke; Hayakawa, Kuniko; Benfatto, Maurizio; Natoli, Calogero R
2010-05-12
We present a rigorous derivation of a real-space full-potential multiple scattering theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wavefunction. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach provides a straightforward extension of MST in the muffin-tin (MT) approximation, with only one truncation parameter given by the classical relation l(max) = kR(b), where k is the electron wavevector (either in the excited or ground state of the system under consideration) and R(b) is the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l(max) --> ∞ limit. Consequently, this feature provides a firm ground for the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.
Nonlinear Analysis and Variational Problems
Pardalos, Panos M
2010-01-01
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization. "Nonlinear Analysis and Variational Problems" is organized into two parts. Part I, Nonlinear Analysis, centers on stability issues for functional equations, fixed point
Nonlinear σ-model with non-compact symmetry group and the theory of nonideal bose gas
International Nuclear Information System (INIS)
Pashaev, O.K.
1985-01-01
A continuous classical model of the Heisenberg magnet is constructed on the non-compact SU(1, 1)/U(1) manifold which is gauge equivalent to the nonlinear Schroedinger equation (MLS) of the repulsive type. It is shown that the choice of gauge transformation function as the Jost solutions for the NLS linear problem allows one to obtain solutions of the appropriate Σ-model of the magnet. Spin-wave and soliton solutions are presented. Energy, momentum and magnetization integrals are calculated. Spin waves are determined by the Bogoluybov frequency and describe precession on the hyperboloid surface with a fixed Msub(z) value. Soliton solution describes the magnetization vector yield from the precession plane. When condensate density p → O, then the spectrum coincides with the result obtained for SU(2) Heisenberg ferromagnet and with an exact solution for Bethe spin complex. In the case corresponding to unlimited length of vector S, the soliton spectrum coincides with the hole spectrum of antiferromagnet. There magnetizations related to the upper and lower sheets of the hyperboloid compensate for each other
Perdigão, R. A. P.
2017-12-01
Predictability assessments are traditionally made on a case-by-case basis, often by running the particular model of interest with randomly perturbed initial/boundary conditions and parameters, producing computationally expensive ensembles. These approaches provide a lumped statistical view of uncertainty evolution, without eliciting the fundamental processes and interactions at play in the uncertainty dynamics. In order to address these limitations, we introduce a systematic dynamical framework for predictability assessment and forecast, by analytically deriving governing equations of predictability in terms of the fundamental architecture of dynamical systems, independent of any particular problem under consideration. The framework further relates multiple uncertainty sources along with their coevolutionary interplay, enabling a comprehensive and explicit treatment of uncertainty dynamics along time, without requiring the actual model to be run. In doing so, computational resources are freed and a quick and effective a-priori systematic dynamic evaluation is made of predictability evolution and its challenges, including aspects in the model architecture and intervening variables that may require optimization ahead of initiating any model runs. It further brings out universal dynamic features in the error dynamics elusive to any case specific treatment, ultimately shedding fundamental light on the challenging issue of predictability. The formulated approach, framed with broad mathematical physics generality in mind, is then implemented in dynamic models of nonlinear geophysical systems with various degrees of complexity, in order to evaluate their limitations and provide informed assistance on how to optimize their design and improve their predictability in fundamental dynamical terms.
Energy Technology Data Exchange (ETDEWEB)
Treder, H.J.
1975-08-01
For planetary motions the post-Newtonian approximations of classical, special-relativistic, and general-covariant theories are compared. It is shown that, in this approximation, the anisotropy terms, which occur in the effective interaction potential in classical and special-relativistic theories, suggest a retardation of gravitation. In the post-Newtonian approximation of general-covariant theories the fixation of a retardation velocity is equivalent to coordinate conditions. All post-Newtonian corrections are dipole-like ones, while, according to Gauss, the classical perturbation theory generally leads to quadrupole-like corrections of the perturbation potential. (auth)
Fahleson, Tobias; Norman, Patrick
2017-10-14
The second-order nonlinear (or cubic) response function is derived from the Ehrenfest theorem with inclusion made of the finite lifetimes of the excited states, representing the extension of the derivation of the quadratic response function in the same framework [P. Norman et al., J. Chem. Phys. 123, 194103 (2005)]. The resulting damped response functions are physically sound and converging also in near-resonance and resonance regions of the spectrum. Being an accurate approximation for small complex frequencies (defined as the sum of an optical frequency and an imaginary damping parameter), the polynomial expansion of the complex cubic response function in terms of the said frequencies is presented and used to validate the program implementation. In terms of approximate state theory, the computationally tractable expressions of the damped cubic response function are derived and implemented at the levels of Hartree-Fock and Kohn-Sham density functional theory. Numerical examples are provided in terms of studies of the intensity-dependent refractive index of para-nitroaniline and the two-photon absorption cross section of neon. For the latter property, a numerical comparison is made against calculations of the square of two-photon matrix elements that are identified from a residue analysis of the resonance-divergent quadratic response function.
Heiny, J A; Jong, D S
1990-01-01
Voltage-sensing dyes were used to examine the electrical behavior of the T-system under passive recording conditions similar to those commonly used to detect charge movement. These conditions are designed to eliminate all ionic currents and render the T-system potential linear with respect to the command potential applied at the surface membrane. However, we found an unexpected nonlinearity in the relationship between the dye signal from the T-system and the applied clamp potential. An additional voltage- and time-dependent optical signal appears over the same depolarizing range of potentials where change movement and mechanical activation occur. This nonlinearity is not associated with unblocked ionic currents and cannot be attributed to lack of voltage clamp control of the T-system, which appears to be good under these conditions. We propose that a local electrostatic potential change occurs in the T-system upon depolarization. An electrostatic potential would not be expected to extend beyond molecular distances of the membrane and therefore would be sensed by a charged dye in the membrane but not by the voltage clamp, which responds solely to the potential of the bulk solution. Results obtained with different dyes suggest that the location of the phenomena giving rise to the extra absorbance change is either intramembrane or at the inner surface of the T-system membrane.
Fully nonlinear elliptic equations
Caffarelli, Luis A
1995-01-01
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa
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
Tamilselvan, K.; Kanna, T.; Khare, Avinash
2017-10-01
We systematically construct a distinct class of complex potentials including parity-time (PT ) symmetric potentials for the stationary Schrödinger equation by using the soliton and periodic solutions of the four integrable real nonlinear evolution equations (NLEEs), namely the sine-Gordon (sG) equation, the modified Korteweg-de Vries (mKdV) equation, combined mKdV-sG equation and the Gardner equation. These potentials comprise of kink, breather, bion, elliptic bion, periodic and soliton potentials which are explicitly constructed from the various respective solutions of the NLEEs. We demonstrate the relevance between the identified complex potentials and the potential of the graphene model from an application point of view.
Scaling of the quark-antiquark potential and improved actions in SU(2) lattice gauge theory
International Nuclear Information System (INIS)
Montvay, I.; Gutbrod, F.
1983-11-01
The scaling behaviour of the quark-antiquark potential is investigated by a high statistics Monte Carlo calculation in SU(2) lattice gauge theory. Besides the standard one-plaquette action we also use Symanzik's tree-level improved action and Wilson's block-spin improved action. No significant differences between Symanzik's action and the standard action have been observed. For small β Wilson's action scales differently. The string tension value chi extracted from the data corresponds to Λsub(latt) = (0.018 +- 0.001) √chi for the one-plaquette action. (orig.)
On-the-Fly Machine Learning of Atomic Potential in Density Functional Theory Structure Optimization
Jacobsen, T. L.; Jørgensen, M. S.; Hammer, B.
2018-01-01
Machine learning (ML) is used to derive local stability information for density functional theory calculations of systems in relation to the recently discovered SnO2 (110 )-(4 ×1 ) reconstruction. The ML model is trained on (structure, total energy) relations collected during global minimum energy search runs with an evolutionary algorithm (EA). While being built, the ML model is used to guide the EA, thereby speeding up the overall rate by which the EA succeeds. Inspection of the local atomic potentials emerging from the model further shows chemically intuitive patterns.
Kengne, E; Lakhssassi, A; Liu, W M
2017-08-01
A lossless nonlinear LC transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear LC transmission networks.
THEORY OF GENERATIONS AS A TOOL FOR ANALYSIS, FORMATION AND DEVELOPMENT OF LABOUR POTENTIAL
Directory of Open Access Journals (Sweden)
I. M. Gurova
2016-01-01
Full Text Available The modern Strauss–Howe generational theory created at the intersection of economic, sociological, historical and psychological Sciences. She focuses primarily on difference of attitudes of generations, due to the specific social environment, corresponding to a certain period of time. Such a perspective on issues related to the human factor in the economy, has recently attracted interest not only from researchers, but also finds application for solving practical problems in some fields of business.Subject / theme. The article is devoted to one of the urgent contemporary socio-economic problems – the issue of the formation and development of labor potential. In this context, the theory of generations is offered by the authors as a tool for the study of qualitative parameters of human resources and the planning of future work opportunities in our country. In particular, the article considers the main aspects of the classical version of the Strauss–Howe generational theory and its Russian adaptation. Statistics describing the General demographics and working population of Russia from the point of view of generational groups. On this basis, a forecast is made of the labor potential of the country in the long term structure, review and compare the basic values and business characteristics of its constituent generations. Problem areas for which use of generational approach is rational are revealed and the corresponding recommendations are made.Objectives. The purpose of this article is justification of the possible application of provisions of modern theories of generations to identify and predict the dynamics of qualitative characteristics of the domestic workforce, as well as the prospects of its use in order to control the formation and development of labor potential.Methods. Methodological basis of the presented work make comparative and economic-statistical and socio-cultural methods of analysis.Results. In the framework of this article
Tamagawa, Hirohisa; Ikeda, Kota
2017-09-01
Donnan theory and Goldman-Hodgkin-Katz equation (GHK eq.) state that the nonzero membrane potential is generated by the asymmetric ion distribution between two solutions separated by a semipermeable membrane and/or by the continuous ion transport across the semipermeable membrane. However, there have been a number of reports of the membrane potential generation behaviors in conflict with those theories. The authors of this paper performed the experimental and theoretical investigation of membrane potential and found that (1) Donnan theory is valid only when the macroscopic electroneutrality is sufficed and (2) Potential behavior across a certain type of membrane appears to be inexplicable on the concept of GHK eq. Consequently, the authors derived a conclusion that the existing theories have some limitations for predicting the membrane potential behavior and we need to find a theory to overcome those limitations. The authors suggest that the ion adsorption theory named Ling's adsorption theory, which attributes the membrane potential generation to the mobile ion adsorption onto the adsorption sites, could overcome those problems.
A non-linear theory for the bubble regime of plasma wake fields in tailored plasma channels
Thomas, Johannes
2016-01-01
We introduce a first full analytical bubble and blow-out model for a radially inhomogeneous plasma in a quasi-static approximation. For both cases we calculate the accelerating and the focusing fields. In our model we also assume a thin electron layer that surrounds the wake field and calculate the field configuration within. Our theory holds for arbitrary radial density profiles and reduces to known models in the limit of a homogeneous plasma. From a previous study of hollow plasma channels with smooth boundaries for laser-driven electron acceleration in the bubble regime we know that pancake-like laser pulses lead to highest electron energies [Pukhov et al, PRL 113, 245003 (2014)]. As it was shown, the bubble fields can be adjusted to balance the laser depletion and dephasing lengths by varying the plasma density profile inside a deep channel. Now we show why the radial fields in the vacuum part of a channel become defocussing.
Size-dependent error of the density functional theory ionization potential in vacuum and solution
Energy Technology Data Exchange (ETDEWEB)
Sosa Vazquez, Xochitl A.; Isborn, Christine M., E-mail: cisborn@ucmerced.edu [Chemistry and Chemical Biology, School of Natural Sciences, University of California, Merced, 5200 North Lake Road, Merced, California 95343 (United States)
2015-12-28
Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.
Eigenvalues of Non-Linear Problems
Prodi, Giovanni
2011-01-01
H. Amann: Nonlinear eigenvalue problems in ordered Banach spaces.- P.C. Fife: Branching phenomena in fluid dynamics and chemical reaction-diffusion theory.- W. Klingenberg: The theory of closed geodesics.- P. Rabinowitz: Variational methods for nonlinear eigenvalue problems.- M. Reeken: Existence of solutions to the Hartree-Fock equations.- R. Turner: Positive solutions of nonlinear eigenvalue problems.
Singular Nonlinear H∞ Optimal Control Problem
Schaft, A.J. van der
1996-01-01
The theory of nonlinear H∞ optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for
2010-03-01
indeed studied the dynamics of our systems at impulses approaching speeds 750 m /s and preliminary analyses using state of the art hydrocodes17...These systems, now referred to as deco - rated TCs DTCs, represent a significant improvement and turn out to be strongly nonlinear in their...presented. Hard sphere approximations for both systems follow in Sec. III. Section IV outlines the numerical approach and results for the deco - rated chain
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Nonlinear integral operators and applications
Musielak, Julian; Bardaro, Carlo
2003-01-01
In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential equations. As regards the latter, applications were soon extended beyond linear operators. In approximation theory, however, applications were limited to linear operators mainly by the fact that the notion of singularity of an integral operator was closely connected with its linearity. This book represents the first attempt at a comprehensive treatment of approximation theory by means of nonlinear integral operators in function spaces. In particular, the fundamental notions of approximate identity for kernels of nonlinear operators and a general concept of modulus of continuity are developed in order to obtain consistent approximation results. Applications to nonlinear summability, nonlinear integral equations and ...
Regularization and the potential of effective field theory in nucleon-nucleon scattering
International Nuclear Information System (INIS)
Phillips, D.R.
1998-04-01
This paper examines the role that regularization plays in the definition of the potential used in effective field theory (EFT) treatments of the nucleon-nucleon interaction. The author considers N N scattering in S-wave channels at momenta well below the pion mass. In these channels (quasi-)bound states are present at energies well below the scale m π 2 /M expected from naturalness arguments. He asks whether, in the presence of such a shallow bound state, there is a regularization scheme which leads to an EFT potential that is both useful and systematic. In general, if a low-lying bound state is present then cutoff regularization leads to an EFT potential which is useful but not systematic, and dimensional regularization with minimal subtraction leads to one which is systematic but not useful. The recently-proposed technique of dimensional regularization with power-law divergence subtraction allows the definition of an EFT potential which is both useful and systematic
Potential landscape and flux field theory for turbulence and nonequilibrium fluid systems
Wu, Wei; Zhang, Feng; Wang, Jin
2018-02-01
Turbulence is a paradigm for far-from-equilibrium systems without time reversal symmetry. To capture the nonequilibrium irreversible nature of turbulence and investigate its implications, we develop a potential landscape and flux field theory for turbulent flow and more general nonequilibrium fluid systems governed by stochastic Navier-Stokes equations. We find that equilibrium fluid systems with time reversibility are characterized by a detailed balance constraint that quantifies the detailed balance condition. In nonequilibrium fluid systems with nonequilibrium steady states, detailed balance breaking leads directly to a pair of interconnected consequences, namely, the non-Gaussian potential landscape and the irreversible probability flux, forming a 'nonequilibrium trinity'. The nonequilibrium trinity characterizes the nonequilibrium irreversible essence of fluid systems with intrinsic time irreversibility and is manifested in various aspects of these systems. The nonequilibrium stochastic dynamics of fluid systems including turbulence with detailed balance breaking is shown to be driven by both the non-Gaussian potential landscape gradient and the irreversible probability flux, together with the reversible convective force and the stochastic stirring force. We reveal an underlying connection of the energy flux essential for turbulence energy cascade to the irreversible probability flux and the non-Gaussian potential landscape generated by detailed balance breaking. Using the energy flux as a center of connection, we demonstrate that the four-fifths law in fully developed turbulence is a consequence and reflection of the nonequilibrium trinity. We also show how the nonequilibrium trinity can affect the scaling laws in turbulence.
Including diverging electrostatic potential in 3D-RISM theory: The charged wall case
Vyalov, Ivan; Rocchia, Walter
2018-03-01
Although three-dimensional site-site molecular integral equations of liquids are a powerful tool of the modern theoretical chemistry, their applications to the problem of characterizing the electrical double layer originating at the solid-liquid interface with a macroscopic substrate are severely limited by the fact that an infinitely extended charged plane generates a divergent electrostatic potential. Such potentials cannot be treated within the standard 3D-Reference Interaction Site Model equation solution framework since it leads to functions that are not Fourier transformable. In this paper, we apply a renormalization procedure to overcome this obstacle. We then check the validity and numerical accuracy of the proposed computational scheme on the prototypical gold (111) surface in contact with water/alkali chloride solution. We observe that despite the proposed method requires, to achieve converged charge densities, a higher spatial resolution than that suited to the estimation of biomolecular solvation with either 3D-RISM or continuum electrostatics approaches, it still is computationally efficient. Introducing the electrostatic potential of an infinite wall, which is periodic in 2 dimensions, we avoid edge effects, permit a robust integration of Poisson's equation, and obtain the 3D electrostatic potential profile for the first time in such calculations. We show that the potential within the electrical double layer presents oscillations which are not grasped by the Debye-Hückel and Gouy-Chapman theories. This electrostatic potential deviates from its average of up to 1-2 V at small distances from the substrate along the lateral directions. Applications of this theoretical development are relevant, for example, for liquid scanning tunneling microscopy imaging.
A potential theory approach to an algorithm of conceptual space partitioning
Directory of Open Access Journals (Sweden)
Roman Urban
2017-12-01
Full Text Available A potential theory approach to an algorithm of conceptual space partitioning This paper proposes a new classification algorithm for the partitioning of a conceptual space. All the algorithms which have been used until now have mostly been based on the theory of Voronoi diagrams. This paper proposes an approach based on potential theory, with the criteria for measuring similarities between objects in the conceptual space being based on the Newtonian potential function. The notion of a fuzzy prototype, which generalizes the previous definition of a prototype, is introduced. Furthermore, the necessary conditions that a natural concept must meet are discussed. Instead of convexity, as proposed by Gärdenfors, the notion of geodesically convex sets is used. Thus, if a concept corresponds to a set which is geodesically convex, it is a natural concept. This definition applies, for example, if the conceptual space is an Euclidean space. As a by-product of the construction of the algorithm, an extension of the conceptual space to d-dimensional Riemannian manifolds is obtained. Algorytm podziału przestrzeni konceptualnych przy użyciu teorii potencjału W niniejszej pracy zaproponowany został nowy algorytm podziału przestrzeni konceptualnej. Dotąd podział taki zazwyczaj wykorzystywał teorię diagramów Voronoi. Nasze podejście do problemu oparte jest na teorii potencjału Miara podobieństwa pomiędzy elementami przestrzeni konceptualnej bazuje na Newtonowskiej funkcji potencjału. Definiujemy pojęcie rozmytego prototypu, który uogólnia dotychczas stosowane definicje prototypu. Ponadto zajmujemy się warunkiem koniecznym, który musi spełniać naturalny koncept. Zamiast wypukłości zaproponowanej przez Gärdenforsa, rozważamy linie geodezyjne w obszarze odpowiadającym danemu konceptowi naturalnemu, otrzymując warunek mówiący, że koncept jest konceptem naturalnym, jeżeli zbiór odpowiadający temu konceptowi jest geodezyjnie wypuk
Microscopic theory for nucleon-nucleus optical potential in intermediate energies
International Nuclear Information System (INIS)
He Guozhu; Cai Chonghai
1984-01-01
Based on the scattering theory of KMT and FGH we calculate the nucleon-nucleus optical potentials of 4 He, 16 O and 40 Ca from the Paris N-N potential given by M. Lacombe et al. The real part Vsub(R)(r) of our optential has the form of Woods-Saxon when the kinetic energy E of the incident nucleon is low. The depth of Vsub(R)(r) will decrease as E increases, and it turns into positive in the interior of nucleus when E approx.= 300 MeV. The repulsive effect in the interior of nucleus increases rapidly as E increases even more, butthere always exists some attractive effect at the surface of nucleus. Therefore, Vsub(R)(r) has generally the wine-bottle bottom shape. We also calculate the quatity Jv/N = (4π/N)∫sub(0)sub(infinity)Vsub(R)(r)r 2 dr. Our results are basically in acordance with those of M.Jaminon et al's relativistic Hatree calculation as well as the experimental results. In this work we also calculate the imaginary part of optical potential and its variation with the kinetic energy of the incident nucleon
The time-reversal- and parity-violating nuclear potential in chiral effective theory
Energy Technology Data Exchange (ETDEWEB)
Maekawa, C.M. [Instituto de Matematica, Estatistica e Fisica, Universidade Federal do Rio Grande, Campus Carreiros, PO Box 474, 96201-900 Rio Grande, RS (Brazil); Mereghetti, E., E-mail: emanuele@physics.arizona.edu [Department of Physics, University of Arizona, Tucson, AZ 85721 (United States); Vries, J. de [KVI, Theory Group, University of Groningen, 9747 AA Groningen (Netherlands); Kolck, U. van [Department of Physics, University of Arizona, Tucson, AZ 85721 (United States)
2011-12-15
We derive the parity- and time-reversal-violating nuclear interactions stemming from the QCD {theta}{sup Macron} term and quark/gluon operators of effective dimension 6: quark electric dipole moments, quark and gluon chromo-electric dipole moments, and two four-quark operators. We work in the framework of two-flavor chiral perturbation theory, where a systematic expansion is possible. The different chiral-transformation properties of the sources of time-reversal violation lead to different hadronic interactions. For all sources considered the leading-order potential involves known one-pion exchange, but its specific form and the relative importance of short-range interactions depend on the source. For the {theta}{sup Macron} term, the leading potential is solely given by one-pion exchange, which does not contribute to the deuteron electric dipole moment. In subleading order, a new two-pion-exchange potential is obtained. Its short-range component is indistinguishable from one of two undetermined contact interactions that appear at the same order and represent effects of heavier mesons and other short-range QCD dynamics. One-pion-exchange corrections at this order are discussed as well.
Enhancement of nonlinear optical properties of compounds of silica ...
Indian Academy of Sciences (India)
theory is exploited to replace the spherical nanoparticles with cylindrical and ellipsoidal ones, facil- itating the calculation of the third-order nonlinear effective ... associated with light scattering, whereby the electromagnetic potentials and fields are expanded by spherical harmonics [22,23]. Such solutions utilize the desirable ...
Pineda, Evan J.; Waas, Anthony M.
2012-01-01
A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, enhanced Schapery theory (EST), utilizes separate ISVs for modeling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening. It is assumed that matrix microdamage is the dominant damage mechanism in continuous fiber-reinforced polymer matrix laminates, and its evolution is controlled with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Typically, failure evolution (i.e., post-peak strain softening) results in pathologically mesh dependent solutions within a finite element method (FEM) setting. Therefore, consistent character element lengths are introduced into the formulation of the evolution of the three failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs is derived. The theory is implemented into commercial FEM software. Objectivity of total energy dissipated during the failure process, with regards to refinements in the FEM mesh, is demonstrated. The model is also verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared to the experiments.
International Nuclear Information System (INIS)
Levi, Michele; Steinhoff, Jan
2016-01-01
The next-to-next-to-leading order spin-squared interaction potential for generic compact binaries is derived for the first time via the effective field theory for gravitating spinning objects in the post-Newtonian scheme. The spin-squared sector is an intricate one, as it requires the consideration of the point particle action beyond minimal coupling, and mainly involves the spin-squared worldline couplings, which are quite complex, compared to the worldline couplings from the minimal coupling part of the action. This sector also involves the linear in spin couplings, as we go up in the nonlinearity of the interaction, and in the loop order. Hence, there is an excessive increase in the number of Feynman diagrams, of which more are higher loop ones. We provide all the Feynman diagrams and their values. The beneficial ''nonrelativistic gravitational'' fields are employed in the computation. This spin-squared correction, which enters at the fourth post-Newtonian order for rapidly rotating compact objects, completes the conservative sector up to the fourth post-Newtonian accuracy. The robustness of the effective field theory for gravitating spinning objects is shown here once again, as demonstrated in a recent series of papers by the authors, which obtained all spin dependent sectors, required up to the fourth post-Newtonian accuracy. The effective field theory of spinning objects allows to directly obtain the equations of motion, and the Hamiltonians, and these will be derived for the potential obtained here in a forthcoming paper
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory....... 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...
Energy Technology Data Exchange (ETDEWEB)
Mandal, Parikshit [Department of Chemistry, Physical Chemistry Section, Visva Bharati University, Santiniketan, Birbhum 731 235, West Bengal (India); Ghosh, Manas [Department of Chemistry, Physical Chemistry Section, Visva Bharati University, Santiniketan, Birbhum 731 235, West Bengal (India)], E-mail: pcmg77@rediffmail.com
2008-09-01
We explore the pattern of frequency-dependent linear and non-linear optical (NLO) response of one electron quantum dots harmonically confined in two dimensions. For some fixed values of transverse magnetic field strength ({omega}{sub c}), and harmonic confinement potential ({omega}{sub 0}), the influence of effective mass (m*) of the system and the symmetry breaking anharmonic interaction on the frequency-dependent linear ({alpha}), and the first ({beta}), and second ({gamma}) NLO responses of the dot is computed through linear variational route. The investigation reveals interesting roles played by the anharmonic interaction and effective mass in modulating the response properties.
International Nuclear Information System (INIS)
Qin Wenxin
2003-01-01
By using the method of symbolic dynamics, we study the bifurcations of steady states in a class of lattices of nonlinear discrete Klein-Gordon type with double-quadratic on-site potential. We derive by virtue of the admissible condition the critical value ε 0 of the coupling strength, below which the steady states persist without bifurcations. If the coupling coefficient ε passes through the critical value, some of the steady states disappear. Meanwhile there are no new steady states created as ε varies. We obtain bifurcation values of some lower-order spatially periodic steady states by introducing the concept 'characteristic polynomial' of periodic sequences
Islam, Nasarul; Niaz, Saba; Manzoor, Taniya; Pandith, Altaf Hussain
2014-10-01
The density functional theoretical (DFT) computations were performed at the B3LYP/6-311G++(d, p) level to calculate the equilibrium geometry, vibrational wave numbers, intensities, and various other molecular properties of brucine and strychnine, which were found in satisfactory agreement with the experimental data. The out-of-phase stretching modes of aromatic rings and carbonyl stretching modes in combination with CH stretching modes at stereogenic centers generate VCD signals, which are remarkably efficient configuration markers for these chiral molecular systems. NBOs analysis reveals that the large values of second order perturbation energy (47.24 kcal/mol for brucine and 46.93 kcal/mol for strychnine) confirms strong hyperconjugative interaction between the orbital containing the lone pair of electron of nitrogen and the neighboring Cdbnd O antibonding orbital. The molecular electrostatic potential map of strychnine molecule, with no polar groups other than the lone keto group, shows less polarization, which accounts for its lower susceptibility towards electrophilic attack as compared to brucine.
Improvements of Critical Heat Flux Models Based on the Viscous Potential Flow Theory
International Nuclear Information System (INIS)
Kim, Byoung Jae; Lee, Jong Hyuk; Kim, Kyung Doo
2014-01-01
Kelvin-Helmholtz instability is analyzed based on a potential flow of inviscid fluids. However, if the viscosity effect is taken into consideration, a nonuniform flow occurs due to the shear stress at the interface. The idea to incorporate the effects of fluid viscosities into the Kelvin-Helmholtz instability can be found in the viscous potential flow theory. Joseph and Liao showed that the potential (irrotational) flow of viscous fluids satisfies the Navier- Stokes equation. For the potential flow, since the vorticity is identically zero, the viscous term vanishes in the Navier-Stokes equation; the motion of fluid is governed by the Bernoulli equation. However, the viscous stresses do not vanish in general. Therefore, the viscous pressure is entered through the normal stress balance at the interface. In the viscous potential flow, the shear stress is neglected at the interface and wall, and thus there is a velocity slip at the interface. These treatments are consistent with the fact that the interface waves are induced more by pressure than by shear force. Funada and Joseph presented a viscous potential flow analysis of the Kelvin-Helmholtz instability. Funada et al. carried out a stability analysis of a circular fluid jet into another fluid. Funada and Joseph considered the capillary instability. The viscous potential flow analysis is more accurate than the inviscid flow analysis in terms of the growth rate. Therefore, the critical condition of the Kelvin-Helmholtz instability can be predicted more accurately than the inviscid flow analysis. In this study, the interfacial instabilities of viscous potential flows are applied to critical heat flux models for saturated pool boiling on infinite horizontal surfaces, with the aim of including the effects of fluid viscosities. The critical conditions of the circular jet and Kelvin- Helmholtz instabilities are incorporated into the hydrodynamic theory model and liquid macrolayer dryout model. Circular jet instabilities is
Energy Technology Data Exchange (ETDEWEB)
Rojas-Briseño, J.G.; Martínez-Orozco, J.C.; Rodríguez-Vargas, I. [Unidad Académica de Física, Universidad Autónoma de Zacatecas, Calzada Solidaridad esquina con Paseo la Bufa S/N, C.P. 98060, Zacatecas, Zac. (Mexico); Mora-Ramos, M.E. [Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, CP 62209, Cuernavaca, Morelos (Mexico); Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia)
2013-09-01
In this work we are reporting the energy level spectrum for a quantum system consisting of an n-type double δ-doped quantum well with a Schottky barrier potential in a Gallium Arsenide matrix. The calculated states are taken as the basis for the evaluation of the linear and third-order nonlinear contributions to the optical absorption coefficient and to the relative refractive index change, making particular use of the asymmetry of the potential profile. These optical properties are then reported as a function of the Schottky barrier height (SBH) and the separation distance between the δ-doped quantum wells. Also, the effects of the application of hydrostatic pressure are studied. The results show that the amplitudes of the resonant peaks are of the same order of magnitude of those obtained in the case of single δ-doped field effect transistors; but tailoring the asymmetry of the confining potential profile allows the control the resonant peak positions.
Energy Technology Data Exchange (ETDEWEB)
Hobbs, M.L.
1997-12-01
Determination of product species, equations-of-state (EOS) and thermochemical properties of high explosives and pyrotechnics remains a major unsolved problem. Although, empirical EOS models may be calibrated to replicate detonation conditions within experimental variability (5--10%), different states, e.g. expansion, may produce significant discrepancy with data if the basic form of the EOS model is incorrect. A more physically realistic EOS model based on intermolecular potentials, such as the Jacobs Cowperthwaite Zwisler (JCZ3) EOS, is needed to predict detonation states as well as expanded states. Predictive capability for any EOS requires a large species data base composed of a wide variety of elements. Unfortunately, only 20 species have known JCZ3 molecular force constants. Of these 20 species, only 10 have been adequately compared to experimental data such as molecular scattering or shock Hugoniot data. Since data in the strongly repulsive region of the molecular potential is limited, alternative methods must be found to deduce force constants for a larger number of species. The objective of the present study is to determine JCZ3 product species force constants by using a corresponding states theory. Intermolecular potential parameters were obtained for a variety of gas species using a simple corresponding states technique with critical volume and critical temperature. A more complex, four parameter corresponding state method with shape and polarity corrections was also used to obtain intermolecular potential parameters. Both corresponding state methods were used to predict shock Hugoniot data obtained from pure liquids. The simple corresponding state method is shown to give adequate agreement with shock Hugoniot data.
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Caldwell, Kate; Harris, Sarah Parker; Renko, Maija
2012-12-01
Contemporary policy encourages self-employment and entrepreneurship as a vehicle for empowerment and self-sufficiency among people with disabilities. However, such encouragement raises important citizenship questions concerning the participation of people with intellectual and developmental disabilities (IDD). As an innovative strategy for addressing pressing social and economic problems, "social entrepreneurship" has become a phrase that is gaining momentum in the IDD community--one that carries with it a very distinct history. Although social entrepreneurship holds the potential to be an empowering source of job creation and social innovation, it also has the potential to be used to further disenfranchise this marginalized population. It is crucial that in moving forward society takes care not to perpetuate existing models of oppression, particularly in regard to the social and economic participation of people with IDD. The conceptual tools addressed in this article can inform the way that researchers, policymakers, and practitioners approach complex issues, such as social entrepreneurship, to improve communication among disciplines while retaining an integral focus on rights and social justice by framing this issue within citizenship theory.
Dynamical changes of the polar cap potential structure: an information theory approach
Directory of Open Access Journals (Sweden)
I. Coco
2011-10-01
Full Text Available Some features, such as vortex structures often observed through a wide spread of spatial scales, suggest that ionospheric convection is turbulent and complex in nature. Here, applying concepts from information theory and complex system physics, we firstly evaluate a pseudo Shannon entropy, H, associated with the polar cap potential obtained from the Super Dual Auroral Radar Network (SuperDARN and, then, estimate the degree of disorder and the degree of complexity of ionospheric convection under different Interplanetary Magnetic Field (IMF conditions. The aforementioned quantities are computed starting from time series of the coefficients of the 4th order spherical harmonics expansion of the polar cap potential for three periods, characterised by: (i steady IMF B_{z} > 0, (ii steady IMF B_{z} < 0 and (iii a double rotation from negative to positive and then positive to negative B_{z}. A neat dynamical topological transition is observed when the IMF B_{z} turns from negative to positive and vice versa, pointing toward the possible occurrence of an order/disorder phase transition, which is the counterpart of the large scale convection rearrangement and of the increase of the global coherence. This result has been confirmed by applying the same analysis to a larger data base of about twenty days of SuperDARN data, allowing to investigate the role of IMF B_{y} too.
Generalized solutions of nonlinear partial differential equations
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
Review of Hydroelasticity Theories
DEFF Research Database (Denmark)
Chen, Xu-jun; Wu, You-sheng; Cui, Wei-cheng
2006-01-01
Existing hydroelastic theories are reviewed. The theories are classified into different types: two-dimensional linear theory, two-dimensional nonlinear theory, three-dimensional linear theory and three-dimensional nonlinear theory. Applications to analysis of very large floating structures (VLFS)......) are reviewed and discussed in details. Special emphasis is placed on papers from China and Japan (in native languages) as these papers are not generally publicly known in the rest of the world....
Noncooperative Game Theory: A Review with Potential Applications to Agricultural Markets
Sexton, Richard J.
1993-01-01
This paper is a survey on noncooperative game theory relevant to agricultural markets. It is divided into two parts. Part I discussed types of noncooperative games and reviews important developments in noncooperative game theory solution concepts, including Nash equilibrium, subgame perfect equilibrium, and perfect Bayesian equilibrium. Strengths and weaknesses of game theory as a modelling tool are also assessed. Part II illustrates applications of the theory to agricultural markets. Game th...
[Business organization theory: its potential use in the organization of the operating room].
Bartz, H-J
2005-07-01
The paradigm of patient care in the German health system is changing. The introduction of German Diagnosis Related Groups (G-DRGs), a diagnosis-related coding system, has made process-oriented thinking increasingly important. The treatment process is viewed and managed as a whole from the admission to the discharge of the patient. The interfaces of departments and sectors are diminished. A main objective of these measures is to render patient care more cost efficient. Within the hospital, the operating room (OR) is the most expensive factor accounting for 25 - 50 % of the costs of a surgical patient and is also a bottleneck in the surgical patient care. Therefore, controlling of the perioperative treatment process is getting more and more important. Here, the business organisation theory can be a very useful tool. Especially the concepts of process organisation and process management can be applied to hospitals. Process-oriented thinking uncovers and solves typical organisational problems. Competences, responsibilities and tasks are reorganised by process orientation and the enterprise is gradually transformed to a process-oriented system. Process management includes objective-oriented controlling of the value chain of an enterprise with regard to quality, time, costs and customer satisfaction. The quality of the process is continuously improved using process-management techniques. The main advantage of process management is consistent customer orientation. Customer orientation means to be aware of the customer's needs at any time during the daily routine. The performance is therefore always directed towards current market requirements. This paper presents the basics of business organisation theory and to point out its potential use in the organisation of the OR.
Directory of Open Access Journals (Sweden)
Dregan Alex
2011-12-01
theory models to coded electronic patient records might potentially contribute to identifying medical codes that offer poor discrimination or low calibration. This might indicate the need for improved coding sets or a requirement for improved clinical coding practice. However, in this study estimates were only obtained for a small proportion of participants and there was some evidence of poor model fit. There was also evidence of variation in the utilisation of codes between family practices raising the possibility that, in practice, properties of codes may vary for different coders.
Recent topics in non-linear partial differential equations 4
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.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Anti-D3 branes and moduli in non-linear supergravity
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.
Nonlinear programming analysis and methods
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.
Sheela, N R; Muthu, S; Sampathkrishnan, S; Al-Saadi, Abdulaziz A
2015-03-15
The spectroscopic techniques and semi-empirical molecular calculations have been utilized to analyze the drug Tizanidine (5CDIBTA). The solid phase Fourier Transform Infrared (FTIR) and Fourier Transform Raman (FTR) spectral analysis of 5CDIBTA is carried out along with density functional theory (DFT) calculations (B3LYP) with the 6-311++G(d,p) basis set. Detailed interpretation of the vibrational spectra of the compound has been made on the basis of the calculated potential energy distribution (PED). The individual atomic charges by NPA using B3LYP method is studied. A study on the Mulliken atomic charges, frontier molecular orbitals (HOMO-LUMO), molecular electrostatic potential (MEP) and thermodynamic properties were performed. The electric dipole moment (μ) and the first hyperpolarizability (α) values of the investigated molecule were also computed. Copyright © 2014 Elsevier B.V. All rights reserved.
Giesbertz, K J H
2015-08-07
A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especially for time-dependent one-body reduced density matrix (1RDM) functional theory, this is an important step forward, since a solid foundation has currently been lacking. The theorem is equally valid for static response functions in the non-degenerate case, so can be used to characterize the uniqueness of the potential in the ground state version of the corresponding density-functional-like theory. Such a classification of the uniqueness of the non-local potential in ground state 1RDM functional theory has been lacking for decades. With the aid of presented invertibility theorem presented here, a complete classification of the non-uniqueness of the non-local potential in 1RDM functional theory can be given for the first time.
Person perception precedes theory of mind: an event related potential analysis.
Wang, Y W; Lin, C D; Yuan, B; Huang, L; Zhang, W X; Shen, D L
2010-09-29
Prior to developing an understanding of another person's mental state, an ability termed "theory of mind" (ToM), a perception of that person's appearance and actions is required. However the relationship between this "person perception" and ToM is unclear. To investigate the time course of ToM and person perception, event-related potentials (ERP) were recorded while 17 normal adults received three kinds of visual stimuli: cartoons involving people (person perception cartoons), cartoons involving people and also requiring ToM for comprehension (ToM cartoons), and scene cartoons. We hypothesized that the respective patterns of brain activation would be different under these three stimuli, at different stages in time. Our findings supported this proposal: the peak amplitudes of P200 for scene cartoons were significantly lower than for person perception or ToM cartoons, while there were no significant differences between the latter two for P200. During the 1000-1300 ms epoch, the mean amplitudes of the late positive components (LPC) for person perception were more positive than for scene representation, while the mean amplitudes of the LPC for ToM were more positive than for person perception. The present study provides preliminary evidence of the neural dynamic that underlies the dissociation between person perception and ToM. Copyright 2010 IBRO. Published by Elsevier Ltd. All rights reserved.
Van Strien, Jan W.; Isbell, Lynne A.
2017-01-01
Studies of event-related potentials in humans have established larger early posterior negativity (EPN) in response to pictures depicting snakes than to pictures depicting other creatures. Ethological research has recently shown that macaques and wild vervet monkeys respond strongly to partially exposed snake models and scale patterns on the snake skin. Here, we examined whether snake skin patterns and partially exposed snakes elicit a larger EPN in humans. In Task 1, we employed pictures with close-ups of snake skins, lizard skins, and bird plumage. In task 2, we employed pictures of partially exposed snakes, lizards, and birds. Participants watched a random rapid serial visual presentation of these pictures. The EPN was scored as the mean activity (225–300 ms after picture onset) at occipital and parieto-occipital electrodes. Consistent with previous studies, and with the Snake Detection Theory, the EPN was significantly larger for snake skin pictures than for lizard skin and bird plumage pictures, and for lizard skin pictures than for bird plumage pictures. Likewise, the EPN was larger for partially exposed snakes than for partially exposed lizards and birds. The results suggest that the EPN snake effect is partly driven by snake skin scale patterns which are otherwise rare in nature. PMID:28387376
The potential of speech act theory for New Testament exegesis: Some basic concepts
Directory of Open Access Journals (Sweden)
J. E. Botha
1991-01-01
Full Text Available Exegetes and biblical scholars are increasingly utilising the precepts of modern literary and linguistic theories in dealing with the text of the Bible. Speech act theory as well offers New Testament exegesis some additional ways and means of approaching the text of the New Testament. This first in a series of two articles making a plea for the continued utilisation and application of this theory to the text of the New Testament, offers a brief discussion of the basic principles of the theory.
Gogonea, Valentin
This article presents a theoretical investigation of the reaction mechanism of imidazole nitration by peroxynitrite using density functional theory calculations. Understanding this reaction mechanism will help in elucidating the mechanism of guanine nitration by peroxynitrite, which is one of the assumed chemical pathways for damaging DNA in cells. This work focuses on the analysis of the potential energy surface (PES) for this reaction in the gas phase. Calculations were carried out using Hartree-Fock (HF) and density functional theory (DFT) Hamiltonians with double-zeta basis sets ranging from 6-31G(d) to 6-31++G(d,p), and the triple-zeta basis set 6-311G(d). The computational results reveal that the reaction of imidazole with peroxynitrite in gas phase produces the following species: (i) hydroxide ion and 2-nitroimidazole, (ii) hydrogen superoxide ion and 2-nitrosoimidazole, and (iii) water and 2-nitroimidazolide. The rate-determining step is the formation of a short-lived intermediate in which the imidazole C2 carbon is covalently bonded to peroxynitrite nitrogen. Three short-lived intermediates were found in the reaction path. These intermediates are involved in a proton-hopping transport from C2 carbon to the terminal oxygen of the OO moiety of peroxynitrite via the nitroso (ON) oxygen. Both HF and DFT calculations (using the Becke3-Lee-Yang-Parr functional) lead to similar reaction paths for proton transport, but the landscape details of the PES for HF and DFT calculations differ. This investigation shows that the reaction of imidazole with peroxynitrite produces essentially the same types of products (nitro- and nitroso-) as observed experimentally in the reaction of guanine with peroxynitrite, which makes the former reaction a good model to study by computation the essential characteristics of the latter reaction. Nevertheless, the computationally determined activation energy for imidazole nitration by peroxynitrite in the gas phase is 84.1 kcal
Nonlinear Optics and Applications
Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)
2007-01-01
Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.
Doney, Robert L.; Agui, Juan H.; Sen, Surajit
2009-09-01
Rapid absorption of impulses using light-weight, small, reusable systems is a challenging problem. An axially aligned set of progressively shrinking elastic spheres, a "tapered chain," has been shown to be a versatile and scalable shock absorber in earlier simulational, theoretical, and experimental works by several authors. We have recently shown (see R. L. Doney and S. Sen, Phys. Rev. Lett. 97, 155502 (2006)) that the shock absorption ability of a tapered chain can be dramatically enhanced by placing small interstitial grains between the regular grains in the tapered chain systems. Here we focus on a detailed study of the problem introduced in the above mentioned letter, present extensive dynamical simulations using parameters for a titanium-aluminum-vanadium alloy Ti6Al4V, derive attendant hard-sphere analyses based formulae to describe energy dispersion, and finally discuss some preliminary experimental results using systems with chrome spheres and small Nitinol interstitial grains to present the underlying nonlinear dynamics of this so-called decorated tapered granular alignment. We are specifically interested in small systems, comprised of several grains. This is because in real applications, mass and volume occupied must inevitably be minimized. Our conclusion is that the decorated tapered chain offers enhanced energy dispersion by locking in much of the input energy in the grains of the tapered chain rather than in the small interstitial grains. Thus, the present study offers insights into how the shock absorption capabilities of these systems can be pushed even further by improving energy absorption capabilities of the larger grains in the tapered chains. We envision that these scalable, decorated tapered chains may be used as shock absorbing components in body armor, armored vehicles, building applications and in perhaps even in applications in rehabilitation science.
Kumar, Amit; Deval, Vipin; Tandon, Poonam; Gupta, Archana; Deepak D'silva, E
2014-09-15
A combined experimental and theoretical investigation on FT-IR, FT-Raman, NMR, UV-vis spectra of a chalcone derivative (2E)-3-[4-(methylsulfanyl) phenyl]-1-(4-nitrophenyl) prop-2-en-1-one (4N4MSP) has been reported. 4N4MSP has two planar rings connected through conjugated double bond and it provides a necessary configuration to show non-linear optical (NLO) response. The molecular structure, fundamental vibrational frequencies and intensity of the vibrational bands are interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) with B3LYP functional and 6-311++G(d,p) basis set combination. The analysis of the fundamental modes was made with the help of potential energy distribution (PED). Molecular electrostatic potential (MEP) surface was plotted over the geometry primarily for predicting sites and relative reactivities towards electrophilic and nucleophilic attack. The delocalization of electron density of various constituents of the molecule has been discussed with the aid of NBO analysis. The electronic properties, such as excitation energies, oscillator strength, wavelengths, HOMO and LUMO energies, were calculated by time-dependent density functional theory (TD-DFT) and the results complement the experimental findings. The recorded and calculated 1H chemical shifts in gas phase and MeOD solution are gathered for reliable calculations of magnetic properties. Thermodynamic properties like heat capacity (C°p,m), entropy (S°m), enthalpy (H°m) have been calculated for the molecule at the different temperatures. Based on the finite-field approach, the non-linear optical (NLO) parameters such as dipole moment, mean polarizability, anisotropy of polarizability and first order hyperpolarizability of 4N4MSP molecule are calculated. The predicted first hyperpolarizability shows that the molecule has a reasonably good nonlinear optical (NLO) behavior. Copyright © 2014 Elsevier B.V. All
Electrodynamics: a consequence of nonlinear realizations of the Lorentz group
International Nuclear Information System (INIS)
Dalton, B.
1981-01-01
Extensions from the representations of the Lorentz group to include local nonlinear diagonal transformations is sufficient to generate, via the covariant derivative, the interaction of minimal coupling. These diagonal realizations are characterized by six functions phisub(i) which must satisfy a system of transformation equations. Inequivalent categories of solutions for the phisub(i) give rise to different electromagnetic fields. The Dirac monopole and Coulomb potentials follow directly from two different categories of these nonlinear realizations. Within this theory, charge becomes simply the nonlinear counterpart of intrinsic spin for a particular nonlinear realization of the Lorentz group. Charge is thus placed on equal footing with intrinsic spin in the sense that both phenomena can be described as consequences of our space-time symmetry. Other solutions for the six phisub(i) exist, including a spinor. The possibility that with these other solutions, these realizations could represent some other basic properties of elementary particles is discussed. (author)
International Nuclear Information System (INIS)
Bartlett, R.; Kirtman, B.; Davidson, E.R.
1978-01-01
After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references
Theory of resistivity-gradient-driven turbulence
Energy Technology Data Exchange (ETDEWEB)
Garcia, L.; Diamond, P.H.; Carreras, B.A.; Callen, J.D.
1985-07-01
A theory of the nonlinear evolution and saturation of resistivity driven turbulence, which evolves from linear rippling instabilities, is presented. The nonlinear saturation mechanism is identified both analytically and numerically. Saturation occurs when the turbulent diffusion of the resistivity is large enough so that dissipation due to parallel electron thermal conduction balances the nonlinearly modified resistivity gradient driving term. The levels of potential, resistivity, and density fluctuations at saturation are calculated. A combination of computational modeling and analytic treatment is used in this investigation.
Pineda, Evan Jorge; Waas, Anthony M.
2013-01-01
A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, referred to as enhanced Schapery theory (EST), utilizes separate ISVs for modeling the effects of damage and failure. Consistent characteristic lengths are introduced into the formulation to govern the evolution of the failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs are derived. The theory is implemented into a commercial finite element code. The model is verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared against the experimental results.
Energy Technology Data Exchange (ETDEWEB)
Krivitsky, V.S.; Vladimirov, S.V. (Academy of Sciences of the USSR, Moscow (USSR). General Physics Institute. Theoretical Dept.)
1991-10-01
The evolution of the distribution function due to the simultaneous nonlinear interaction of plasma particles with resonant and non-resonant waves is studied. A stationary particle distribution resulting from a balance of the quasi-linear interaction and the nonlinear one is found. The temporal evolution of an initial {delta}-function-shaped distribution (like a 'beam') is examined in the one-dimensional case. General formulae are obtained for stochastic particle acceleration. (author).
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
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.
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
Li, Min; Xu, Tao
2015-03-01
Via the Nth Darboux transformation, a chain of nonsingular localized-wave solutions is derived for a nonlocal nonlinear Schrödinger equation with the self-induced parity-time (PT) -symmetric potential. It is found that the Nth iterated solution in general exhibits a variety of elastic interactions among 2N solitons on a continuous-wave background and each interacting soliton could be the dark or antidark type. The interactions with an arbitrary odd number of solitons can also be obtained under different degenerate conditions. With N=1 and 2, the two-soliton and four-soliton interactions and their various degenerate cases are discussed in the asymptotic analysis. Numerical simulations are performed to support the analytical results, and the stability analysis indicates that the PT-symmetry breaking can also destroy the stability of the soliton interactions.
International Nuclear Information System (INIS)
Sormann, H.
2001-01-01
The excessive sensitivity of the momentum densities of electron-positron annihilation pairs (MDAP) to crystal potentials found in this study severely deteriorates a possibility to use a comparison between theoretical and experimental MDAP results as a criterion for the legitimacy of electron-positron interaction theories. Illustrative examples are given. (orig.)
Model of the N-quark potential in SU(N gauge theory using gauge-string duality
Directory of Open Access Journals (Sweden)
Oleg Andreev
2016-05-01
Full Text Available We use gauge-string duality to model the N-quark potential in pure Yang–Mills theories. For SU(3, the result agrees remarkably well with lattice simulations. The model smoothly interpolates between almost the Δ-law at short distances and the Y-law at long distances.
On the chiral perturbation theory for two-flavor two-color QCD at finite chemical potential
Czech Academy of Sciences Publication Activity Database
Brauner, Tomáš
2006-01-01
Roč. 21, č. 7 (2006), s. 559-569 ISSN 0217-7323 R&D Projects: GA ČR(CZ) GD202/05/H003 Institutional research plan: CEZ:AV0Z10480505 Keywords : two-color QCD * chiral perturbation theory * chemical potential Subject RIV: BE - Theoretical Physics Impact factor: 1.564, year: 2006
Rasmus Karlsson
2012-01-01
While structural approaches to sustainability have remained unable to muster wider political support, green political theory has for some time taken a voluntarist turn, arguing that deep changes in attitudes and behaviour are necessary to reduce the ecological debt of the rich countries. Within environmental citizenship theory it is believed that justice requires each individual to start living within his or her 'ecological space'. Firmly rooted in the pollution paradigm, environmental citize...
Nonlinear drift tearing mode. Strong mode of excitation and stabilization mechanisms
International Nuclear Information System (INIS)
Galeev, A.A.; Zelenyj, L.M.; Kuznetsova, M.M.
1985-01-01
A nonlinear theory of magnetic disturbance development in collisionless configurations with magnetic field shear is considered. The instability evolution is investigated with account for the dynamics of ions and potential electric fields which determine the mode stabilization. It has been found that the drift tearing mode possesses metastable properties: in a nonlinear mode even the growth of linearly stable disturbances of the finite amplitude is possible
Cembran, Alessandro; Song, Lingchun; Mo, Yirong; Gao, Jiali
2010-01-01
A multistate density functional theory in the framework of the valence bond model is described. The method is based on a block-localized density functional theory (BLDFT) for the construction of valence-bond-like diabatic electronic states and is suitable for the study of electron transfer reactions and for the representation of reactive potential energy surfaces. The method is equivalent to a valence bond theory with the treatment of the localized configurations by using density functional theory (VBDFT). In VBDFT, the electron densities and energies of the valence bond states are determined by BLDFT. A functional estimate of the off-diagonal matrix elements of the VB Hamiltonian is proposed, making use of the overlap integral between Kohn–Sham determinants and the exchange-correlation functional for the ground state substituted with the transition (exchange) density. In addition, we describe an approximate approach, in which the off-diagonal matrix element is computed by wave function theory using block-localized Kohn–Sham orbitals. The key feature is that the electron density of the adiabatic ground state is not directly computed nor used to obtain the ground-state energy; the energy is determined by diagonalization of the multistate valence bond Hamiltonian. This represents a departure from the standard single-determinant Kohn–Sham density functional theory. The multistate VBDFT method is illustrated by the bond dissociation of H2+ and a set of three nucleophilic substitution reactions in the DBH24 database. In the dissociation of H2+, the VBDFT method yields the correct asymptotic behavior as the two protons stretch to infinity, whereas approximate functionals fail badly. For the SN2 nucleophilic substitution reactions, the hybrid functional B3LYP severely underestimates the barrier heights, while the approximate two-state VBDFT method overcomes the self-interaction error, and overestimates the barrier heights. Inclusion of the ionic state in a three
National Research Council Canada - National Science Library
Rassias, Themistocles M
1987-01-01
... known that nonlinear partial differential equations can not be treated in the same systematic way as linear ones and this volume provides, among other things, proofs of existence and uniqueness theorems for nonlinear differential equations of a global nature. However, the basic techniques which have proven to be efficient in dealing with li...
Directory of Open Access Journals (Sweden)
Hwang Sungmin
2017-01-01
Full Text Available We present our calculation of the non-relativistic corrections to the heavy quark-antiquark potential up to leading and next-to-leading order (NLO via the effective string theory (EST. Full systematics of effective field theory (EFT are discussed in order for including the NLO contribution that arises in the EST. We also show how the number of dimensionful parameters arising from the EST are reduced by the constraints between the Wilson coeffcients from non-relativistic EFTs for QCD.
Pure classical SU(2) Yang-Mills theory with potentials invariant under a U(1) gauge subgroup
International Nuclear Information System (INIS)
Bacry, H.
1978-07-01
The present article is devoted to pure SU(2) classical Yang-Mills theories whose potentials are invariant under a U(1) gauge subgroup. Such potentials are shown to be associated with classical Maxwell-like fields with magnetic sources as 't Hooft's monopole is associated with the Dirac magnetic monopole. Conversely, the authors give Yang-Mills potentials corresponding to some Maxwell-like fields, in particular static magnetic fields with emphasis on those with cylindrical symmetry (including the dipole and other multipoles) and the ephemerons corresponding to an instantaneous magnetic multipole
Trejos, Víctor M; Gil-Villegas, Alejandro
2012-05-14
Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.
[Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile
Achong, A.
1999-05-01
This paper presents a non-linear analysis of the dome-shaped notes on the steelpan under compressive and thermal stresses. Equations are derived for the static and dynamic response of symmetrically distorted notes. Analytical results are obtained for modal frequencies, non-linear coupling coefficients and the buckling parameter. Experimental results demonstrate the vibration characteristics and their dependence on temperature. Experimental results were also obtained for the effects of stress relaxation which follows the shaping and tuning process of these notes by hammer peening. The results of the analysis are applicable to other shell-like structures not necessarily designed for musical purposes.
Gripshover, Sarah J; Markman, Ellen M
2013-08-01
In two experiments, we used a novel approach to educating young children about nutrition. Instead of teaching simple facts, we provided a rich conceptual framework that helped children understand the need to eat a variety of healthy foods. Using the insight that children's knowledge can be organized into coherent belief systems, or intuitive theories, we (a) analyzed the incipient knowledge that guides young children's reasoning about the food-body relationship, (b) identified the prerequisites that children need to conceptualize food as a source of nutrition, and (c) devised a strategy for teaching young children a coherent theory of food as a source of diverse nutrients. In these two experiments, we showed that children can learn and generalize this conceptual framework. Moreover, this learning led children to eat more vegetables at snack time. Our findings demonstrate that young children can benefit from an intervention that capitalizes on their developing intuitive theories about nutrition.
Magnetic-field asymmetry of nonlinear thermoelectric and heat transport
International Nuclear Information System (INIS)
Hwang, Sun-Yong; Sánchez, David; López, Rosa; Lee, Minchul
2013-01-01
Nonlinear transport coefficients do not obey, in general, reciprocity relations. We here discuss the magnetic-field asymmetries that arise in thermoelectric and heat transport of mesoscopic systems. Based on a scattering theory of weakly nonlinear transport, we analyze the leading-order symmetry parameters in terms of the screening potential response to either voltage or temperature shifts. We apply our general results to a quantum Hall antidot system. Interestingly, we find that certain symmetry parameters show a dependence on the measurement configuration. (paper)
The biopsychosocial model and its potential for a new theory of homeopathy
Schmidt, Josef M.
2012-01-01
Since the nineteenth century the theory of conventional medicine has been developed in close alignment with the mechanistic paradigm of natural sciences. Only in the twentieth century occasional attempts were made to (re)introduce the ‘subject’ into medical theory, as by Thure von Uexküll (1908–2004) who elaborated the so-called biopsychosocial model of the human being, trying to understand the patient as a unit of organic, mental, and social dimensions of life. Although widely neglected by c...
Quasi-potential and Two-Scale Large Deviation Theory for Gillespie Dynamics
Li, Tiejun
2016-01-07
The construction of energy landscape for bio-dynamics is attracting more and more attention recent years. In this talk, I will introduce the strategy to construct the landscape from the connection to rare events, which relies on the large deviation theory for Gillespie-type jump dynamics. In the application to a typical genetic switching model, the two-scale large deviation theory is developed to take into account the fast switching of DNA states. The comparison with other proposals are also discussed. We demonstrate different diffusive limits arise when considering different regimes for genetic translation and switching processes.
Wu, Wei; Wang, Jin
2013-09-28
We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is
Directory of Open Access Journals (Sweden)
V. K. Karastathis
2010-11-01
Full Text Available We examine the possible non-linear behaviour of potentially liquefiable layers at selected sites located within the expansion area of the town of Nafplion, East Peloponnese, Greece. Input motion is computed for three scenario earthquakes, selected on the basis of historical seismicity data, using a stochastic strong ground motion simulation technique, which takes into account the finite dimensions of the earthquake sources. Site-specific ground acceleration synthetics and soil profiles are then used to evaluate the liquefaction potential at the sites of interest. The activation scenario of the Iria fault, which is the closest one to Nafplion (M=6.4, is found to be the most hazardous in terms of liquefaction initiation. In this scenario almost all the examined sites exhibit liquefaction features at depths of 6–12 m. For scenario earthquakes at two more distant seismic sources (Epidaurus fault – M6.3; Xylokastro fault – M6.7 strong ground motion amplification phenomena by the shallow soft soil layer are expected to be observed.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Directory of Open Access Journals (Sweden)
E.O. Ulloa-Dávila
2017-12-01
Full Text Available An approximate analytical solution to the fluctuation potential problem in the modified Poisson-Boltzmann theory of electrolyte solutions in the restricted primitive model is presented. The solution is valid for all inter-ionic distances, including contact values. The fluctuation potential solution is implemented in the theory to describe the structure of the electrolyte in terms of the radial distribution functions, and to calculate some aspects of thermodynamics, viz., configurational reduced energies, and osmotic coefficients. The calculations have been made for symmetric valence 1:1 systems at the physical parameters of ionic diameter 4.25·10^{-10} m, relative permittivity 78.5, absolute temperature 298 K, and molar concentrations 0.1038, 0.425, 1.00, and 1.968. Radial distribution functions are compared with the corresponding results from the symmetric Poisson-Boltzmann, and the conventional and modified Poisson-Boltzmann theories. Comparisons have also been done for the contact values of the radial distributions, reduced configurational energies, and osmotic coefficients as functions of electrolyte concentration. Some Monte Carlo simulation data from the literature are also included in the assessment of the thermodynamic predictions. Results show a very good agreement with the Monte Carlo results and some improvement for osmotic coefficients and radial distribution functions contact values relative to these theories. The reduced energy curve shows excellent agreement with Monte Carlo data for molarities up to 1 mol/dm^3.
Les, Tomasz
2017-01-01
In this article, I present the argument that educational theory has specific character, which distinguishes it from most scientific disciplines. It requires the application of not only strictly scientific methods, which essentially consist of descriptions and explanations, but also normative ones, which indicate how it is related to philosophy and…
Dissipative tunneling through a potential barrier in the Lindblad theory of open quantum systems
International Nuclear Information System (INIS)
Isar, A.
2000-01-01
In the Lindblad theory for open quantum systems, and analytical expression of the tunneling probability through an inverted parabola is obtained. This probability depends on the environment coefficient and increase with the dissipation and the temperature of the thermal bath. (author)
Heinz, Bettina
More than a decade after the provocative writings of French feminist writers Julie Kristeva, Luce Irigaray, Helene Cixous, and Monique Wittig first appeared, the exploration of sexual and gender differences continues to draw controversy. Their work has been considered mostly in regard to literature, philosophy, and feminist theory, but their…
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... that at resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
NONLINEAR TIDES IN CLOSE BINARY SYSTEMS
International Nuclear Information System (INIS)
Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh
2012-01-01
We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' ∼> 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P ∼ 3 [P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P ∼< a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing
Semi-classical analysis for nonlinear Schrödinger equations
Carles, Remi
2008-01-01
These lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger e
2016-07-01
architectures , practical nonlinearities, nonlinear dynamics 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT: SAR 8. NUMBER OF PAGES...performers from Mesodynamic Architectures (MESO) and uPNT all to include devices in these runs. This cost-sharing was planned, and is necessary for...contributions to the performance of MEMS gyroscopes. In particular, we have demonstrated for the first time that Parametric Amplification can improve the
DEFF Research Database (Denmark)
Chen, X.; Cui, W.; Jensen, Jørgen Juncher
2003-01-01
The theory and typical numerical results of a second order nonlinear hydroelastic analysis of floating bodies are presented in a series of papers in which only nonlinearity in fluids is considered. Under the assumption of linear fluid, the hydroelastic analysis methods of nonlinear structure are ...
Akemann, G; Bloch, J; Shifrin, L; Wettig, T
2008-01-25
We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.
Primordial fluctuations from nonlinear couplings
International Nuclear Information System (INIS)
Calzetta, E.A.; Gonorazky, S.
1997-01-01
We study the spectrum of primordial fluctuations in theories where the inflaton field is nonlinearly coupled to massless fields and/or to itself. Conformally invariant theories generically predict a scale-invariant spectrum. Scales entering the theory through infrared divergences cause logarithmic corrections to the spectrum, tilting it towards the blue. We discuss in some detail whether these fluctuations are quantum or classical in nature. copyright 1997 The American Physical Society
Singular nonlinear H-infinity optimal control problem
Maas, W.C.A.; Maas, W.C.A.; van der Schaft, Arjan
1996-01-01
The theory of nonlinear H∞ of optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for
Past and Potential Theory for Special Warfare Operational Art: People’s War and Contentious Politics
2015-03-04
the scientific method could be used to examine historical case studies.114 His examination of the English , American, French, and Russian Revolutions...its full evaluation as a grammar of revolutionary war. Finally, a translation of basic concepts from contentious politics into useful outlines and...be founded upon distinct and sound theories of war and warfare. This monograph argues that from 1952-1965, the US Army Special Forces developed two
4U 1820-30 as a potential test of the nonsymmetric gravitational theory of Moffat
Krisher, Timothy P.
1987-01-01
Recent observations of the X-ray burst source 4U 1820-30 have revealed a 685 s modulation of the luminosity. How this system could provide a stringent test of the nonsymmetric gravitational theory (NGT) of Moffat (1979), provided the observed periodicity is due to orbital motion of a binary system, is discussed. The possible orbital period change predicted by general relativity may be detectable in this system.
Device Applications of Nonlinear Dynamics
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.
On the gluonic operator effective potential in holographic Yang-Mills theory
Kiritsis, Elias; Li, Wenliang; Nitti, Francesco
2015-04-01
The holographic formalism is applied to the calculation of the effective potential for the scalar glueball operator. Three different versions of this operator are defined, and for each we compute the associated effective potential and discuss its properties and scheme ambiguities. For one of them, the trace of the stress tensor, the potential is fixed by scale covariance and the conformal anomaly. Contact is made to earlier attempts to guess this effective potential from the conformal anomaly. We apply our results to the Improved Holographic QCD model calculating the glueball condensate.