Zeng, An-Ping; Modak, Jayant; Deckwer, Wolf-Dieter
2002-01-01
Pyruvate conversion to acetyl-CoA by the pyruvate dehydrogenase (PDH) multienzyme complex is known as a key node in affecting the metabolic fluxes of animal cell culture. However, its possible role in causing possible nonlinear dynamic behavior such as oscillations and multiplicity of animal cells has received little attention. In this work, the kinetic and dynamic behavior of PDH of eucaryotic cells has been analyzed by using both in vitro and simplified in vivo models. With the in vitro model the overall reaction rate (nu(1)) of PDH is shown to be a nonlinear function of pyruvate concentration, leading to oscillations under certain conditions. All enzyme components affect nu(1) and the nonlinearity of PDH significantly, the protein X and the core enzyme dihydrolipoamide acyltransferase (E2) being mostly predominant. By considering the synthesis rates of pyruvate and PDH components the in vitro model is expanded to emulate in vivo conditions. Analysis using the in vivo model reveals another interesting kinetic feature of the PDH system, namely, multiple steady states. Depending on the pyruvate and enzyme levels or the operation mode, either a steady state with high pyruvate decarboxylation rate or a steady state with significantly lower decarboxylation rate can be achieved under otherwise identical conditions. In general, the more efficient steady state is associated with a lower pyruvate concentration. A possible time delay in the substrate supply and enzyme synthesis can also affect the steady state to be achieved and leads to oscillations under certain conditions. Overall, the predictions of multiplicity for the PDH system agree qualitatively well with recent experimental observations in animal cell cultures. The model analysis gives some hints for improving pyruvate metabolism in animal cell culture.
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.
Oscillations in nonlinear systems
Hale, Jack K
2015-01-01
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa
Nonlinear (Anharmonic Casimir Oscillator
Directory of Open Access Journals (Sweden)
Habibollah Razmi
2011-01-01
Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.
Linearization of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E; Pascual, I [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-03-11
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for the complete range of oscillation amplitudes. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of the technique.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Cubication of Conservative Nonlinear Oscillators
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Modeling nonlinearities in MEMS oscillators.
Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A
2013-08-01
We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Abstract. Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable- coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota's bilinear method. The bilinear forms and analytic soliton solutions are derived, and the ...
Linearization of Conservative Nonlinear Oscillators
Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.
2009-01-01
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…
Cubication of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-09-15
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
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....
Analytical Solutions to Non-linear Mechanical Oscillation Problems
DEFF Research Database (Denmark)
Kaliji, H. D.; Ghadimi, M.; Barari, Amin
2011-01-01
In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated...... problems as indicated in the following cases....
On the nonlinear modeling of ring oscillators
Elwakil, Ahmed S.
2009-06-01
We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
Chaos in nonlinear oscillations controlling and synchronization
Lakshamanan, M
1996-01-01
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
Nonlinear analysis of ring oscillator circuits
Ge, Xiaoqing
2010-06-01
Using nonlinear systems techniques, we analyze the stability properties and synchronization conditions for ring oscillator circuits, which are essential building blocks in digital systems. By making use of its cyclic structure, we investigate local and global stability properties of an n-stage ring oscillator. We present a sufficient condition for global asymptotic stability of the origin and obtain necessity if the ring oscillator consists of identical inverter elements. We then give a synchronization condition for identical interconnected ring oscillators.
Nonlinear nanomechanical oscillators for ultrasensitive inertial detection
Datskos, Panagiotis George; Lavrik, Nickolay V
2013-08-13
A system for ultrasensitive mass and/or force detection of this invention includes a mechanical oscillator driven to oscillate in a nonlinear regime. The mechanical oscillator includes a piezoelectric base with at least one cantilever resonator etched into the piezoelectric base. The cantilever resonator is preferably a nonlinear resonator which is driven to oscillate with a frequency and an amplitude. The system of this invention detects an amplitude collapse of the cantilever resonator at a bifurcation frequency as the cantilever resonator stimulated over a frequency range. As mass and/or force is introduced to the cantilever resonator, the bifurcation frequency shifts along a frequency axis in proportion to the added mass.
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation
Fiori, Simone
2017-06-01
Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of complex nonlinear phenomena, as well as in engineering, being able to generate repeating (i.e., periodic) or non-repeating (i.e., chaotic) reference signals. The state of the classical oscillators known from the literature evolves in the space Rn , typically with n = 1 (e.g., the famous van der Pol vacuum-tube model), n = 2 (e.g., the FitzHugh-Nagumo model of spiking neurons) or n = 3 (e.g., the Lorenz simplified model of turbulence). The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.
Nonlinear oscillations in coriolis based gyroscopes
Directory of Open Access Journals (Sweden)
Dag Kristiansen
1999-01-01
Full Text Available In this paper we model and analyze nonlinear oscillations which are known to exist in some Coriolis based gyroscopes due to large amplitude excitation in the drive loop. A detailed derivation of a dynamic model for a cylinder gyroscope which includes geometric nonlinearities is given, and energy transfer between the system's modes are analyzed using perturbation theory and by proposing a simplified model. The model is also simulated, and the results are shown to give an accurate description of the experimental results. This work is done in order to gain a better understanding of the gyroscope's dynamics, and is intended to be a starting point for designing nonlinear observers and vibration controllers for the gyroscope in order to increase the performance.
Simulating Nonlinear Oscillations of Viscoelastically Damped Mechanical Systems
National Research Council Canada - National Science Library
M. D. Monsia; Y. J. F. Kpomahou
2014-01-01
... viscoelastic system experiencing large deformations response. The model is represented with the use of a mechanical oscillator consisting of an inertial body attached to a nonlinear viscoelastic spring...
Periodic Solutions for Highly Nonlinear Oscillation Systems
DEFF Research Database (Denmark)
Ghadimi, M; Barari, Amin; Kaliji, H.D
2012-01-01
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams. The r...
Variable order variable stepsize algorithm for solving nonlinear Duffing oscillator
Fadly Nurullah Rasedee, Ahmad; Ishak, Norizarina; Raihana Hamzah, Siti; Ijam, Hazizah Mohd; Suleiman, Mohamed; Bibi Ibrahim, Zarina; Sathar, Mohammad Hasan Abdul; Ainna Ramli, Nur; Shuhada Kamaruddin, Nur
2017-09-01
Nonlinear phenomena in science and engineering such as a periodically forced oscillator with nonlinear elasticity are often modeled by the Duffing oscillator (Duffing equation). The Duffling oscillator is a type of nonlinear higher order differential equation. In this research, a numerical approximation for solving the Duffing oscillator directly is introduced using a variable order stepsize (VOS) algorithm coupled with a backward difference formulation. By selecting the appropriate restrictions, the VOS algorithm provides a cost efficient computational code without affecting its accuracy. Numerical results have demonstrated the advantages of a variable order stepsize algorithm over conventional methods in terms of total steps and accuracy.
Solution branches for nonlinear problems with an asymptotic oscillation property
Directory of Open Access Journals (Sweden)
Lin Gong
2015-10-01
Full Text Available In this article we employ an oscillatory condition on the nonlinear term, to prove the existence of a connected component of solutions of a nonlinear problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions to the nonlinear problem for all parameter values in that interval.
Nonlinear Oscillations in Biology and Chemistry
1986-01-01
This volume contains the proceedings of a meeting entitled 'Nonlinear Oscillations in Biology and Chemistry', which was held at the University of Utah May 9-11,1985. The papers fall into four major categories: (i) those that deal with biological problems, particularly problems arising in cell biology, (ii) those that deal with chemical systems, (iii) those that treat problems which arise in neurophysiology, and (iv), those whose primary emphasis is on more general models and the mathematical techniques involved in their analysis. Except for the paper by Auchmuty, all are based on talks given at the meeting. The diversity of papers gives some indication of the scope of the meeting, but the printed word conveys neither the degree of interaction between the participants nor the intellectual sparks generated by that interaction. The meeting was made possible by the financial support of the Department of Mathe matics of the University of Utah. I am indebted to Ms. Toni Bunker of the Department of Mathematics for...
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Scleronomic Holonomic Constraints and Conservative Nonlinear Oscillators
Munoz, R.; Gonzalez-Garcia, G.; Izquierdo-De La Cruz, E.; Fernandez-Anaya, G.
2011-01-01
A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present…
Scleronomic holonomic constraints and conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Munoz, R; Gonzalez-Garcia, G; Izquierdo-De La Cruz, E Izquierdo-De La [Universidad Autonoma de la Ciudad de Mexico, Centro Historico, Fray Servando Teresa de Mier 92, Col Centro, Del Cuauhtemoc, Mexico DF, CP 06080 (Mexico); Fernandez-Anaya, G, E-mail: rodrigo.munoz@uacm.edu.mx, E-mail: gggharper@gmail.com, E-mail: erickidc@gmail.com, E-mail: guillermo.fernandez@uia.mx [Universidad Iberoamericana, Departamento de Fisica y Matematicas, Prolongacon Paseo de de la Reforma 880, Col Lomas de Santa Fe, Del Alvaro Obregn, Mexico DF, CP 01219 (Mexico)
2011-05-15
A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present cases in which the effective potential acting on the bead is not analytical around a minimum. The small oscillation approximation cannot be applied to such pathological cases. Nonetheless, these latter instances are studied with other standard techniques.
An Analytical Approximation Method for Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Wang Shimin
2012-01-01
Full Text Available An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Chou, Chia-Chun
2016-10-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton-Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Electromagnetic radiation due to nonlinear oscillations of a charged drop
Shiryaeva, S. O.; Grigor'ev, A. N.; Kolbneva, N. Yu.
2016-03-01
The nonlinear oscillations of a spherical charged drop are asymptotically analyzed under the conditions of a multimode initial deformation of its equilibrium shape. It is found that if the spectrum of initially excited modes contains two adjacent modes, the translation mode of oscillations is excited among others. In this case, the center of the drop's charge oscillates about the equilibrium position, generating a dipole electromagnetic radiation. It is shown that the intensity of this radiation is many orders of magnitude higher than the intensity of the drop's radiation, which arises in calculations of the first order of smallness and is related to the drop's charged surface oscillations.
Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation
Moon, Songky; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon
2015-01-01
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of $0.41\\dot{6}\\eta^2$ for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of $\\eta$ much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained...
Some heuristic procedures for analyzing random vibration of nonlinear oscillators.
Crandall, S. H.
1971-01-01
The stationary response of a lightly damped nonlinear oscillator subjected to wideband random excitation can be examined as an example of thermal equilibrium. It may be assumed that the response consists of a series of free-vibration cycles with small random fluctuations in phase and amplitude. Certain statistical properties of the response can be estimated by averaging corresponding properties of the free vibration with respect to cycle amplitude distributions. Such heuristic procedures for determining the expected frequency and the autocorrelation function of the stationary response are outlined. Some additional results concerning first-passage problems for nonlinear oscillators are included.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...... in the coupling transconductances, in conjunction with a finite amplitude relaxation time and de-tuning of the individual oscillators, cause close-to-carrier AM-to-PM noise conversion. A discussion is presented of how the theoretic results translate into design rules for quadrature oscillator ICs. SPECTRE RF...
Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach
Directory of Open Access Journals (Sweden)
Ricardo Aguilar-López
2014-01-01
Full Text Available The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-09-22
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities.
Nonlinear oscillation system of mass with serial linear and nonlinear springs
DEFF Research Database (Denmark)
Seyedalizadeh Ganji,, S.R; Barari, Amin; Karimpour, S
2013-01-01
In this paper, two powerful methods called Max–Min and parameter expansion have been applied for the determination of the periodic solutions of the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities. It is found that these methods introduce two...
Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
Santo, Daniele; Lannes, David
2017-01-01
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...... increases with the coupling strength. The results are compared with SPECTRE RF simulations....
Oscillation criteria for first-order forced nonlinear difference equations
Grace Said R; Agarwal Ravi P.; Smith Tim
2006-01-01
Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form Δx(n)+q1(n)xμ(n+1) = q2(n)xλ(n+1)+e(n), where λ, μ are the ratios of positive odd integers 0 <μ < 1 and λ > 1, are established.
Chaotic Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...
African Journals Online (AJOL)
With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...
PT-symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
2015-10-22
Oct 22, 2015 ... We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry, i.e., one of them has gain and the other an equal and opposite amount of loss. We first discuss various symmetries of the model. We show that both the linear system as well as a special case of the ...
Comparison of alternative improved perturbative methods for nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico)]. E-mail: paolo@ucol.mx; Raya, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2005-06-06
We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt-Poincare technique. As illustrative examples we choose one-dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.
Oscillation criteria for second order nonlinear perturbed differential equations
Directory of Open Access Journals (Sweden)
Moussadek Remili
2010-05-01
Full Text Available Sufficient conditions for the oscillation of the nonlinear second order differential equation $(a(tx^{\\prime }^{\\prime }+Q(t,x^{\\prime}=P(t,x,x^{\\prime }$ are established where the coefficients are continuous and $a(t$ is nonnegative.
Semiclassical approximation for a nonlinear oscillator with dissipation
Iomin, A.
2003-01-01
An $S$--matrix approach is developed for the chaotic dynamics of a nonlinear oscillator with dissipation. The quantum--classical crossover is studied in the framework of the semiclassical expansion for the $S$--matrix. Analytical expressions for the braking time and the $S$--matrix are obtained.
Coherence in Complex Networks of Oscillators
Lind, Pedro G.; Gallas, Jason A. C.; Herrmann, Hans J.
We study fully synchronized (coherent) states in complex networks of chaotic oscillators, reviewing the analytical approach of determining the stability conditions for synchronizability and comparing them with numerical criteria. As an example, we present detailed results for networks of chaotic logistic maps having three different scale-free topologies: random scale-free topology, deterministic pseudo-fractal scale-free network and Apollonian network. For random scale-free topology we find that the lower boundary of the synchronizability region scales approximately as k-μ, where k is the outgoing connectivity and μ depends on the local nonlinearity. For deterministic scale-free networks coherence is observed only when the coupling is heterogeneous, namely when it is proportional to some power of the neighbour connectivity. In all cases, stability conditions are determined from the eigenvalue spectrum of the Laplacian matrix and agree well with numerical results based on histograms of coherent states in parameter space. Additionally, we show that almost everywhere in the synchronizability region the basin of attraction of the coherent states fills the entire phase space, and that the transition to coherence is of first-order.
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.
Nonlinear oscillations of TM-mode gyrotrons
Chang, Tsun-Hsu; Yao, Hsin-Yu; Su, Bo-Yuan; Huang, Wei-Chen; Wei, Bo-Yuan
2017-12-01
This study investigates the interaction between the relativistic electrons and the waves in cavities with fixed field profiles. Both the transverse electric (TE) and the transverse magnetic (TM) cavity modes are examined, including three first-axial modes, TE011, TM011, and TM111, and two zero-axial modes, TM010 and TM110. The first-axial modes have the same resonant frequency, so a direct comparison can be made. By sweeping the electron pitch factor (α) and the electron transit angle (Θ), the optimal converting efficiency of TM modes occurs at α = 1.5 and Θ = 1.5π, unlike the TE mode of α = 2.0 and Θ = 1.0π. The converting efficiencies of both the first-axial TM modes are much lower than that of TE011 mode. The starting currents of TM011 and TM111 modes are four times higher than that of TE011 mode, indicating that these two TM modes are very difficult to oscillate. This evidences that under the traditional operating conditions, the TM-mode gyrotrons are insignificant. However, the two unique, zero-axial TM modes have relatively high converting efficiency. The highest converting efficiency of TM110 is 27.4%, the same value as that of TE011 mode. The starting currents of TM110 mode and TE011 mode are at the same level. The results suggest that some TM-mode gyrotron oscillators are feasible and deserve further theoretical and experimental studies.
Simulating Nonlinear Oscillations of Viscoelastically Damped Mechanical Systems
Directory of Open Access Journals (Sweden)
M. D. Monsia
2014-12-01
Full Text Available The aim of this work is to propose a mathematical model in terms of an exact analytical solution that may be used in numerical simulation and prediction of oscillatory dynamics of a one-dimensional viscoelastic system experiencing large deformations response. The model is represented with the use of a mechanical oscillator consisting of an inertial body attached to a nonlinear viscoelastic spring. As a result, a second-order first-degree Painlevé equation has been obtained as a law, governing the nonlinear oscillatory dynamics of the viscoelastic system. Analytical resolution of the evolution equation predicts the existence of three solutions and hence three damping modes of free vibration well known in dynamics of viscoelastically damped oscillating systems. Following the specific values of damping strength, over-damped, critically-damped and under-damped solutions have been obtained. It is observed that the rate of decay is not only governed by the damping degree but, also by the magnitude of the stiffness nonlinearity controlling parameter. Computational simulations demonstrated that numerical solutions match analytical results very well. It is found that the developed mathematical model includes a nonlinear extension of the classical damped linear harmonic oscillator and incorporates the Lambert nonlinear oscillatory equation with well-known solutions as special case. Finally, the three damped responses of the current mathematical model devoted for representing mechanical systems undergoing large deformations and viscoelastic behavior are found to be asymptotically stable.
First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators
Directory of Open Access Journals (Sweden)
R. Naz
2011-01-01
Full Text Available We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations. The difference arises in the gauge terms due to Lagrangians being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian. We have illustrated it here for nonlinear Duffing oscillators.
Analysis of highly nonlinear oscillation systems using He's max–min ...
Indian Academy of Sciences (India)
max method; nonlinear oscillation; duffing equation; homo- topy analysis method; He's energy balance method. 1. Introduction. Most of engineering problems, especially some oscillation equations are nonlinear, and in most cases it is difficult to ...
Discrete oscillator design linear, nonlinear, transient, and noise domains
Rhea, Randall W
2014-01-01
Oscillators are an essential part of all spread spectrum, RF, and wireless systems, and today's engineers in the field need to have a firm grasp on how they are designed. Presenting an easy-to-understand, unified view of the subject, this authoritative resource covers the practical design of high-frequency oscillators with lumped, distributed, dielectric and piezoelectric resonators. Including numerous examples, the book details important linear, nonlinear harmonic balance, transient and noise analysis techniques. Moreover, the book shows you how to apply these techniques to a wide range of os
The Duffing Equation Nonlinear Oscillators and their Behaviour
Kovacic, Ivana
2011-01-01
The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical
Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity
DEFF Research Database (Denmark)
Sfahania, M. G.; Ganji, S. S.; Barari, Amin
2010-01-01
This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...
Nonlinear dynamics in micromechanical and nanomechanical resonators and oscillators
Dunn, Tyler
dynamics in passive resonators, self-sustained MEMS are becoming increasingly prevalent in both research and technology for crucial objectives, such as measurement of time. Despite some effort, much work remains in order to understand phase noise and stability for an oscillator based upon a nonlinear resonator. With the eventual goal of making comprehensive measurements of such a nonlinear oscillator with controlled amplitude and phase, this work describes the realization of a micromechanical phase feedback oscillator.
A benevolent nonlinear system: The dynamically shifted oscillator
Thomsen, John. S.
1988-02-01
Hartmann has given an analysis of the dynamically shifted oscillator; this system is characterized by a restoring force k[x+x0 sign(x)], where sign(x)=x/‖x‖. He obtained an exact solution for free oscillations in terms of a Fourier series. This problem is reexamined and an alternative exact (piecewise) solution is given. The analysis is then extended to include a cosinusoidal forcing term. Exact solutions are given for three cases: (a) ω>ω0; (b) ω<ω0; (c) ω=ω0, where ω0 is the linear resonant frequency. Response curves are plotted and compared with those for the ``hard spring'' Duffing equation. While the system is simple enough to permit exact solutions in terms of elementary functions, it exhibits a number of characteristically nonlinear features; these include multiple-valued solutions, hysteresis effects, and amplitude jumps.
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Pikovsky, Arkady [Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Potsdam (Germany); Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Nonlinear oscillations in a muscle pacemaker cell model
González-Miranda, J. M.
2017-02-01
This article presents a numerical simulation study of the nonlinear oscillations displayed by the Morris-Lecar model [Biophys. J. 35 (1981) 193] for the oscillations experimentally observed in the transmembrane potential of a muscle fiber subject to an external electrical stimulus. We consider the model in the case when there is no external stimulation, aiming to establish the ability of the model to display biophysically reasonable pacemaker dynamics. We obtain 2D bifurcation diagrams showing that indeed the model presents oscillatory dynamics, displaying the two main types of action potentials that are observed in muscle fibers. The results obtained are shown to be structurally stable; that is, robust against changes in the values of system parameters. Moreover, it is demonstrated how the model is appropriate to analyze the action potentials observed in terms of the transmembrane currents creating them.
Infinite invariant densities due to intermittency in a nonlinear oscillator
Meyer, Philipp; Kantz, Holger
2017-08-01
Dynamical intermittency is known to generate anomalous statistical behavior of dynamical systems, a prominent example being the Pomeau-Manneville map. We present a nonlinear oscillator, i.e., a physical model in continuous time, whose properties in terms of weak ergodity breaking and aging have a one-to-one correspondence to the properties of the Pomeau-Manneville map. So for both systems in a wide range of parameters no physical invariant density exists. We show how this regime can be characterized quantitatively using the techniques of infinite invariant densities and the Thaler-Dynkin limit theorem. We see how expectation values exhibit aging in terms of scaling in time.
Infinite invariant densities due to intermittency in a nonlinear oscillator.
Meyer, Philipp; Kantz, Holger
2017-08-01
Dynamical intermittency is known to generate anomalous statistical behavior of dynamical systems, a prominent example being the Pomeau-Manneville map. We present a nonlinear oscillator, i.e., a physical model in continuous time, whose properties in terms of weak ergodity breaking and aging have a one-to-one correspondence to the properties of the Pomeau-Manneville map. So for both systems in a wide range of parameters no physical invariant density exists. We show how this regime can be characterized quantitatively using the techniques of infinite invariant densities and the Thaler-Dynkin limit theorem. We see how expectation values exhibit aging in terms of scaling in time.
Generalized quantum isotonic nonlinear oscillator in d dimensions
Energy Technology Data Exchange (ETDEWEB)
Hall, Richard L [Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec H3G 1M8 (Canada); Saad, Nasser [Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, PEI C1A 4P3 (Canada); Yesiltas, Oezlem, E-mail: rhall@mathstat.concordia.c, E-mail: nsaad@upei.c, E-mail: yesiltas@gazi.edu.t [Department of Physics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara (Turkey)
2010-11-19
We present a supersymmetric analysis for the d-dimensional Schroedinger equation with the generalized isotonic nonlinear-oscillator potential V(r) = B{sup 2}/r{sup 2} + {omega}{sup 2}r{sup 2} + 2g(r{sup 2} - a{sup 2})/(r{sup 2} + a{sup 2}){sup 2}, B {>=} 0. We show that the eigenequation for this potential is exactly solvable provided g = 2 and ({omega}a{sup 2}){sup 2} = B{sup 2} + (l + (d - 2)/2){sup 2}. Under these conditions, we obtain explicit formulae for all the energies and normalized bound-state wavefunctions.
Oscillations in the spectrum of nonlinear Thomson-backscattered radiation
Directory of Open Access Journals (Sweden)
C. A. Brau
2004-02-01
Full Text Available When an electron beam collides with a high-intensity laser beam, the spectrum of the nonlinear Thomson scattering in the backward direction shows strong oscillations like those in the spectrum of an optical klystron. Laser gain on the backward Thomson scattering is estimated using the Madey theorem, and the results suggest that Thomson-backscatter free-electron lasers are possible at wavelengths extending to the far uv using a terawatt laser beam from a chirped-pulse amplifier and a high-brightness electron beam from a needle cathode.
Synchronization in Complex Oscillator Networks and Smart Grids
Energy Technology Data Exchange (ETDEWEB)
Dorfler, Florian [Los Alamos National Laboratory; Chertkov, Michael [Los Alamos National Laboratory; Bullo, Francesco [Center for Control, Dynamical Systems and Computation, University of California at Santa Babara, Santa Barbara CA
2012-07-24
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing the interaction among them. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here we present a novel, concise, and closed-form condition for synchronization of the fully nonlinear, non-equilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters, or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters, they are statistically correct for almost all networks, and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks such as electric power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex networks scenarios and in smart grid applications.
Synchronization in complex oscillator networks and smart grids.
Dörfler, Florian; Chertkov, Michael; Bullo, Francesco
2013-02-05
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.
Modeling of a bipedal locomotor using coupled nonlinear oscillators of Van der Pol.
Dutra, Max S; De Pina Filho, Armando C; Romano, Vitor F
2003-04-01
Research to date points to an understanding of human biped locomotion that has been primarily experimental in nature largely due to the complexity of the process. In view of the new, exciting possibilities of programmed electrostimulation of artificial muscles to generate motion (locomotion), a critical study at the theoretical level is greatly warranted. There is strong evidence that many biological clocks consist of a population of mutually coupled oscillators [Pavlidis T (1973) Biological oscillators, Academic; Johnsson A (1978) Zur Biophysik biologischer Oszillatoren. In: Biophisik, Springer]. In this work, a form of bipedal locomotion is simulated by using mutually coupled nonlinear oscillators. A planar model, which includes three out of the six determinants of gait that characterize the human locomotion, was adopted.
Directory of Open Access Journals (Sweden)
Najeeb Alam Khan
2011-01-01
Full Text Available We applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u. We employed this method for higher-order approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. Many numerical results are given to prove the efficiency of the suggested technique.
Energy Technology Data Exchange (ETDEWEB)
Emenheiser, Jeffrey [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Chapman, Airlie; Mesbahi, Mehran [William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States); Pósfai, Márton [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Crutchfield, James P. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); D' Souza, Raissa M. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States)
2016-09-15
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.
National Research Council Canada - National Science Library
Krantz, Philip; Reshitnyk, Yarema; Wustmann, Waltraut; Bylander, Jonas; Gustavsson, Simon; Oliver, William D; Duty, Tim; Shumeiko, Vitaly; Delsing, Per
2013-01-01
.... The Duffing nonlinearity is determined from the probe-power dependent frequency shift of the oscillator, and the nonlinearity related to the parametric flux pumping, is determined from the pump...
Modified semi-classical methods for nonlinear quantum oscillations problems
Energy Technology Data Exchange (ETDEWEB)
Moncrief, Vincent [Department of Physics and Department of Mathematics, Yale University, P.O. Box 208120, New Haven, Connecticut 06520 (United States); Marini, Antonella [Department of Mathematics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA and Department of Mathematics, University of L' Aquila, Via Vetoio, 67010 L' Aquila, AQ (Italy); Maitra, Rachel [Department of Physics, Albion College, 611 E. Porter Street, Albion, Michigan 49224 (United States)
2012-10-15
We develop a modified semi-classical approach to the approximate solution of Schroedinger's equation for certain nonlinear quantum oscillations problems. In our approach, at lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. With suitable smoothness, convexity and coercivity properties imposed on its potential energy function, we prove, using methods drawn from the calculus of variations together with the (Banach space) implicit function theorem, the existence of a global, smooth 'fundamental solution' to this equation. Higher order quantum corrections thereto, for both ground and excited states, can then be computed through the integration of associated systems of linear transport equations, derived from Schroedinger's equation, and formal expansions for the corresponding energy eigenvalues obtained therefrom by imposing the natural demand for smoothness on the (successively computed) quantum corrections to the eigenfunctions. For the special case of linear oscillators our expansions naturally truncate, reproducing the well-known exact solutions for the energy eigenfunctions and eigenvalues. As an explicit application of our methods to computable nonlinear problems, we calculate a number of terms in the corresponding expansions for the one-dimensional anharmonic oscillators of quartic, sectic, octic, and dectic types and compare the results obtained with those of conventional Rayleigh/Schroedinger perturbation theory. To the orders considered (and, conjecturally, to all orders) our eigenvalue expansions agree with those of Rayleigh/Schroedinger theory whereas our wave functions more accurately capture the more-rapid-than-gaussian decay known to hold for the exact solutions to these problems. For the quartic oscillator in particular our results strongly suggest that both the ground state energy eigenvalue expansion and its associated wave
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-02-22
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
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...
Aeroelastic Limit-Cycle Oscillations resulting from Aerodynamic Non-Linearities
van Rooij, A.C.L.M.
2017-01-01
Aerodynamic non-linearities, such as shock waves, boundary layer separation or boundary layer transition, may cause an amplitude limitation of the oscillations induced by the fluid flow around a structure. These aeroelastic limit-cycle oscillations (LCOs) resulting from aerodynamic non-linearities
Discontinuity and complexity in nonlinear physical systems
Baleanu, Dumitru; Luo, Albert
2014-01-01
This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit
Energy Technology Data Exchange (ETDEWEB)
Kengne, Jacques [Laboratoire d' Automatique et Informatique Apliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Bandjoun (Cameroon); Kenmogne, Fabien [Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototype, University of Yaoundé 1, Yaoundé (Cameroon)
2014-12-15
The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by using time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Energy Technology Data Exchange (ETDEWEB)
Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Directory of Open Access Journals (Sweden)
Dzhinchvelashvili Guram Avtandilovich
2014-06-01
Full Text Available To estimate the influence of physical and geometric nonlinearity under seismic oscillations the authors used the model of 44-storied building calculation scheme. As a result the following tasks were solved: elastic dynamic analysis; consideration of geometric nonlinearity; physical nonlinearity modeling; spectral method calculation. The authors present the main research results and their practical importance.
A Closed Form Solution for Nonlinear Oscillators Frequencies Using Amplitude-Frequency Formulation
Directory of Open Access Journals (Sweden)
A. Barari
2012-01-01
Full Text Available Many nonlinear systems in industry including oscillators can be simulated as a mass-spring system. In reality, all kinds of oscillators are nonlinear due to the nonlinear nature of springs. Due to this nonlinearity, most of the studies on oscillation systems are numerically carried out while an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude-Frequency Formulation (AFF approach is applied to analyze some periodic problems arising in classical dynamics. Results are compared with another approximate analytical technique called Energy Balance Method developed by the authors (EBM and also numerical solutions. Close agreement of the obtained results reveal the accuracy of the employed method for several practical problems in engineering.
The numerical modelling of a driven nonlinear oscillator
Energy Technology Data Exchange (ETDEWEB)
Shew, C.
1995-11-01
The torsional oscillator in the Earth Sciences Division was developed at Lawrence Livermore National Laboratory and is the only one of its kind. It was developed to study the way rocks damp vibrations. Small rock samples are tested to determine the seismic properties of rocks, but unlike other traditional methods that propagate high frequency waves through small samples, this machine forces the sample to vibrate at low frequencies, which better models real-life properties of large masses. In this particular case, the rock sample is tested with a small crack in its middle. This forces the rock to twist against itself, causing a {open_quotes}stick-slip{close_quotes} friction, known as stiction. A numerical model that simulates the forced torsional osillations of the machine is currently being developed. The computer simulation implements the graphical language LabVIEW, and is looking at the nonlinear spring effects, the frictional forces, and the changes in amplitude and frequency of the forced vibration. Using LabVIEW allows for quick prototyping and greatly reduces the {open_quotes}time to product{close_quotes} factor. LabVIEW`s graphical environment allows scientists and engineers to use familiar terminology and icons (e.g. knobs, switches, graphs, etc.). Unlike other programming systems that use text-based languages, such as C and Basic, LabVIEW uses a graphical programming language to create programs in block diagram form.
Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators
Talukdar, Abdul Hafiz
2011-05-01
Exceptional behaviours of Memristor are illustrated in Memristor based second order (Wien oscillator) and third order (phase shift oscillator) oscillator systems in this Thesis. Conventional concepts about sustained oscillation have been argued by demonstrating the possibility of sustained oscillation with oscillating resistance and dynamic poles. Mathematical models are also proposed for analysis and simulations have been presented to support the surprising characteristics of the Memristor based oscillator systems. This thesis also describes a comparative study among the Wien family oscillators with one Memristor. In case of phase shift oscillator, one Memristor and three Memristors systems are illustrated and compared to generalize the nonlinear dynamics observed for both 2nd order and 3rd order system. Detail explanations are provided with analytical models to simplify the unconventional properties of Memristor based oscillatory systems.
Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink
Zang, Jian; Chen, Li-Qun
2017-08-01
Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass, a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra, and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed. The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity.
Frequency stabilization in nonlinear MEMS and NEMS oscillators
Lopez, Omar Daniel; Antonio, Dario
2014-09-16
An illustrative system includes an amplifier operably connected to a phase shifter. The amplifier is configured to amplify a voltage from an oscillator. The phase shifter is operably connected to a driving amplitude control, wherein the phase shifter is configured to phase shift the amplified voltage and is configured to set an amplitude of the phase shifted voltage. The oscillator is operably connected to the driving amplitude control. The phase shifted voltage drives the oscillator. The oscillator is at an internal resonance condition, based at least on the amplitude of the phase shifted voltage, that stabilizes frequency oscillations in the oscillator.
Ontology of Earth's nonlinear dynamic complex systems
Babaie, Hassan; Davarpanah, Armita
2017-04-01
As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.
Workshop on Nonlinear Phenomena in Complex Systems
1989-01-01
This book contains a thorough treatment of neural networks, cellular-automata and synergetics, in an attempt to provide three different approaches to nonlinear phenomena in complex systems. These topics are of major interest to physicists active in the fields of statistical mechanics and dynamical systems. They have been developed with a high degree of sophistication and include the refinements necessary to work with the complexity of real systems as well as the more recent research developments in these areas.
Oscillation Criteria for Second-Order Nonlinear Dynamic Equations on Time Scales
Directory of Open Access Journals (Sweden)
Shao-Yan Zhang
2012-01-01
Full Text Available This paper is concerned with oscillation of second-order nonlinear dynamic equations of the form on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria.
Complex dynamics of a particle in an oscillating potential field
Pal, Barnali; Dutta, Debjit; Poria, Swarup
2017-08-01
In this paper, the classical problem of the motion of a particle in one dimension with an external time-dependent field is studied from the point of view of the dynamical system. The dynamical equations of motion of the particle are formulated. Equilibrium points of the non-oscillating systems are found and their local stability natures are analysed. Effect of oscillating potential barrier is analysed through numerical simulations. Phase diagrams, bifurcation diagrams and variations of largest Lyapunov exponents are presented to show the existence of a wide range of nonlinear phenomena such as limit cycle, quasiperiodic and chaotic oscillations in the system. Effects of nonlinear damping in the model are also reported. Analysis of the physically interesting cases where damping is proportional to higher powers of velocity are presented for the sake of generalizing our findings and establishing firm conclusion.
Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions
Indian Academy of Sciences (India)
2015-10-13
Oct 13, 2015 ... In this paper, we briefly present an overview of the recent developments made in identifying/generating systems of Liénard-type nonlinear oscillators ... 097, India; Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401, India ...
Directory of Open Access Journals (Sweden)
H. M. Abdelhafez
2016-03-01
Full Text Available The modified differential transform method (MDTM, Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obtained using the fourth-order Runge-Kutta numerical solution method. A comparison of the result by the numerical Runge-Kutta fourth-order accuracy method is compared with the result by the MDTM and plotted in a long time domain.
Combination-Combination Hyperchaos Synchronization of Complex Memristor Oscillator System
Directory of Open Access Journals (Sweden)
Zhang Jin-E
2014-01-01
Full Text Available The combination-combination synchronization scheme is based on combination of multidrive systems and combination of multiresponse systems. In this paper, we investigate combination-combination synchronization of hyperchaotic complex memristor oscillator system. Several sufficient conditions are provided to ascertain the combination of two drive hyperchaotic complex memristor oscillator systems to synchronize the combination of two response hyperchaotic complex memristor oscillator systems. These new conditions improve and extend the existing synchronization results for memristive systems. A numerical example is given to show the feasibility of theoretical results.
Nonlinear dynamics of spin transfer nano-oscillators
Indian Academy of Sciences (India)
spin-polarized current gives a time-varying resistance to the magnetic structure thereby inducing magnetization oscillations of frequency ... on two counts: (1) low output power (∼ nW), (2) high signal-to-noise ratio. Both the issues can be ... and to reduce the signal-to-noise ratio of the oscillators. In this paper, we summarize ...
Coupled oscillators in identification of nonlinear damping of a real parametric pendulum
Olejnik, Paweł; Awrejcewicz, Jan
2018-01-01
A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.
Synchronization of oscillators in complex networks
Indian Academy of Sciences (India)
This being the most conservative assumption will cover the largest class of oscillators including those which have multiple, disjoint α regions of stability as can ..... intake of food and energy which will be fruitful only if the new networks are a great improvement and provide the organisms some evolutionary advantages. In.
Synchronization of oscillators in complex networks
Indian Academy of Sciences (India)
Theory of identical or complete synchronization of identical oscillators in arbitrary networks is introduced. In addition, several graph theory concepts and results that augment the synchronization theory and a tie in closely to random, semirandom, and regular networks are introduced. Combined theories are used to explore ...
New approach method for solving Duffing-type nonlinear oscillator
Directory of Open Access Journals (Sweden)
H. Mirgolbabaee
2016-06-01
Results are presented for different values of amplitude vibration of the problem parameters which would certainly illustrate that this method (AGM is efficient and has enough accuracy in comparison with other semi analytical and numerical methods. Moreover, results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore, convergence problems for solving nonlinear equations by using AGM appear small.
Nonlinear oscillations of laminated plates using an accurate four ...
Indian Academy of Sciences (India)
The element is found to be free of shear locking and does not exhibit any spurious modes. In orderto compute the nonlinearfrequencies, linear mode shape corresponding to the fundamental frequency is assumed as the spatial distribution and nonlinear finite element equations are reduced to a single nonlinear ...
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...... accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples....
Elwakil, Ahmed S.
2009-04-28
Two novel sinusoidal oscillator structures with an explicit tanh(x) nonlinearity are proposed. The oscillators have the attractive feature: the higher the operating frequency, the lower the necessary gain required to start oscillations. A nonlinear model for the two oscillators is derived and verified numerically. Spice simulations using AMS BiCMOS 0.35 μ model parameters and experimental results are shown. Copyright © 2009 John Wiley & Sons, Ltd.
Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.
2018-01-01
In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.
Revival of oscillations from deaths in diffusively coupled nonlinear systems: Theory and experiment
Zou, Wei; Sebek, Michael; Kiss, István Z.; Kurths, Jürgen
2017-06-01
Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.
Remote synchronization of amplitudes across an experimental ring of non-linear oscillators
Energy Technology Data Exchange (ETDEWEB)
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it [Center for Mind/Brain Science, University of Trento, 38123 Mattarello TN, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2015-12-15
In this paper, the emergence of remote synchronization in a ring of 32 unidirectionally coupled non-linear oscillators is reported. Each oscillator consists of 3 negative voltage gain stages connected in a loop to which two integrators are superimposed and receives input from its preceding neighbour via a “mixing” stage whose gains form the main system control parameters. Collective behaviour of the network is investigated numerically and experimentally, based on a custom-designed circuit board featuring 32 field-programmable analog arrays. A diverse set of synchronization patterns is observed depending on the control parameters. While phase synchronization ensues globally, albeit imperfectly, for certain control parameter values, amplitudes delineate subsets of non-adjacent but preferentially synchronized nodes; this cannot be trivially explained by synchronization paths along sequences of structurally connected nodes and is therefore interpreted as representing a form of remote synchronization. Complex topology of functional synchronization thus emerges from underlying elementary structural connectivity. In addition to the Kuramoto order parameter and cross-correlation coefficient, other synchronization measures are considered, and preliminary findings suggest that generalized synchronization may identify functional relationships across nodes otherwise not visible. Further work elucidating the mechanism underlying this observation of remote synchronization is necessary, to support which experimental data and board design materials have been made freely downloadable.
Remote synchronization of amplitudes across an experimental ring of non-linear oscillators.
Minati, Ludovico
2015-12-01
In this paper, the emergence of remote synchronization in a ring of 32 unidirectionally coupled non-linear oscillators is reported. Each oscillator consists of 3 negative voltage gain stages connected in a loop to which two integrators are superimposed and receives input from its preceding neighbour via a "mixing" stage whose gains form the main system control parameters. Collective behaviour of the network is investigated numerically and experimentally, based on a custom-designed circuit board featuring 32 field-programmable analog arrays. A diverse set of synchronization patterns is observed depending on the control parameters. While phase synchronization ensues globally, albeit imperfectly, for certain control parameter values, amplitudes delineate subsets of non-adjacent but preferentially synchronized nodes; this cannot be trivially explained by synchronization paths along sequences of structurally connected nodes and is therefore interpreted as representing a form of remote synchronization. Complex topology of functional synchronization thus emerges from underlying elementary structural connectivity. In addition to the Kuramoto order parameter and cross-correlation coefficient, other synchronization measures are considered, and preliminary findings suggest that generalized synchronization may identify functional relationships across nodes otherwise not visible. Further work elucidating the mechanism underlying this observation of remote synchronization is necessary, to support which experimental data and board design materials have been made freely downloadable.
Building better oscillators using nonlinear dynamics and pattern ...
Indian Academy of Sciences (India)
2015-02-18
Feb 18, 2015 ... Frequency and time references play an essential role in modern technology and in living systems. The precision of self-sustained oscillations is limited by the effects of noise, which becomes evermore important as the sizes of the devices become smaller. In this paper, we review our recent theoretical ...
Müller, P. C.; Gürgöze, M.
2007-09-01
Recently, Hu [A note on the frequency of nonlinear conservative oscillators, Journal of Sound and Vibration 286 (2005) 653-662] presented a superposition method for the approximate determination of frequencies of conservative oscillators when the nonlinear restoring force consists of a superposition of several individual characteristics. In this contribution, it is shown that the conjecture of Hu is not true in general, particularly for underlinear systems. Only for overlinear systems are there plausible reasons for the validity of the conjecture, but even for this case one has to use caution.
Energy Technology Data Exchange (ETDEWEB)
Mamode, Malik, E-mail: Malik.Mamode@univ-reunion.f [Department of Physics, Laboratoire PIMENT/Equipe MASC, University of La Reunion (France)
2010-12-17
This paper deals with the calculation of the period and action integral of second-order autonomous nonlinear oscillators. We show that the Laplace transform of these energy-dependent quantities can be simply expressed as a function of the potential function which makes it possible to obtain a number of new results in an analytical closed-form. In addition to their computational interest, these results allow us to revisit the characterization and properties of classical isoperiodic and isochronous potentials. Applications in quantum mechanics for the semiclassical Einstein-Brillouin-Keller quantization and in statistical mechanics for Gibbs ensembles of nonlinear oscillators are also proposed.
Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
Directory of Open Access Journals (Sweden)
A. Fereidoon
2012-01-01
Full Text Available In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF.The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragón, J. L.
2012-08-08
We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems. © 2012 American Physical Society.
Electromagnetic radiation from linearly and nonlinearly oscillating charge drops
Grigor'ev, A. I.; Shiryaeva, S. O.
2016-12-01
It has been shown that analytic calculations of the intensity of electromagnetic radiation from an oscillating charged drop in the approximation linear in the oscillation amplitude (small parameter is on the order of 0.1) give only the quadrupole component of the total radiation. The dipole component can only be obtained in calculations using higher-order approximations. Nevertheless, the intensity of the dipole radiation turns out to be substantially higher (by 14-15 orders of magnitude). This is because the decomposition of radiation from a system of charges into multipole components (differing even in the rates of decrease in the potential with the distance) is carried out using the expansion in a substantially smaller parameter, viz., the ratio of the size of the emitting system (in our case, a drop of radius 10 μm) to the distance to the point of observation in the wave zone of the emission of radiation (emitted wavelength) of 100-1000 m. As a result, this second small parameter is on the order of 10-7 to 10-8. On the other hand, in accordance with the field theory, the ratio of intensities of quadrupole and dipole radiations is proportional to the squared ratio of the hydrodynamic velocity of the oscillating surface of a charged drop to the velocity of propagation of an electromagnetic signal in vacuum (velocity of light), which yields a ratio of 10-14 to 10-15.
On approximations of first integrals for a system of weakly nonlinear, coupled harmonic oscillators
Waluya, S.B.; van Horssen, W.T.
2001-01-01
In this paper a system of weakly nonlinear, coupled harmonic oscillators will be studied. It will be shown that the recently developed perturbation method based on integrating vectors can be used to approximate rst integrals and periodic solutions. To show how this perturbation method works the
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
An Apparatus to Demonstrate Linear and Nonlinear Oscillations of a Pendulum
Mayer, V. V.; Varaksina, E. I.
2016-01-01
A physical pendulum with a magnetic load is proposed for comparison of linear and nonlinear oscillations. The magnetic load is repelled by permanent magnets which are disposed symmetrically relative to the load. It is established that positions of the pendulum and the magnets determine the dependence of restoring force on displacement of the load.…
Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.
Picot, T.; Lupa?cu, A.; Saito, S.; Harmans, C.J.P.M.; Mooij, J.E.
2008-01-01
We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum nondemolition type. Two successive readouts
Escape time from potential wells of strongly nonlinear oscillators with slowly varying parameters
Directory of Open Access Journals (Sweden)
Cai Jianping
2005-01-01
Full Text Available The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well of quadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear oscillators with slowly varying parameters, and secondly the character of modulus of Jacobian elliptic function is applied to derive the equations governing the escape time. The approximate potential method, instead of Taylor series expansion, is used to approximate the potential of an oscillation system such that the asymptotic solution can be expressed in terms of Jacobian elliptic function. Numerical examples verify the efficiency of the present method.
RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios.
Tang, Zhi-Ling; Li, Si-Min; Yu, Li-Juan
2016-06-09
Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC) to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unidirectionally coupled, overdamped nonlinear oscillator ring is proposed. First, the numerical model of such a system is established based on the circuit of the nonlinear oscillator. Through numerical analysis of the model, the critical condition of the system's starting oscillation is determined, and the simulation results of the system's response to Gaussian white noise and periodic signal are presented. The results show that once the radio signal is input into the system, it starts oscillating when in the critical region, and the oscillating frequency of each element is fo/N, where fo is the frequency of the radio signal and N is the number of elements in the ring. The oscillation indicates that the spectrum resources at fo are occupied. At the same time, the sampling rate required for an ADC is reduced to the original value, 1/N. A prototypical circuit to verify the functionality of the system is designed, and the sensing bandwidth of the system is measured.
Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity
Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad
2017-12-01
A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.
DEFF Research Database (Denmark)
Blekhman, I. I.; Sorokin, V. S.
2016-01-01
A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics equat.......g., the requirement for the involved nonlinearities to be weak. The approach is illustrated by several relevant examples from various fields of science, e.g., mechanics, physics, chemistry and biophysics.......A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics...
Sustained small oscillations in nonlinear control systems. [launch vehicle dynamics
George, J. H.; Gunderson, R. W.; Hahn, H.
1975-01-01
Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.
Measurements on a guitar string as an example of a physical nonlinear driven oscillator
Carlà, Marcello; Straulino, Samuele
2017-08-01
An experimental study is described to characterize the oscillation of a guitar string around resonance. A periodic force was applied to the string, generated by the electromagnetic interaction between an alternating current flowing in the string and a magnetic field. The oscillation was studied by measuring the voltage induced in the string itself, which is proportional to the velocity. Accurate quantitative data were obtained for the velocity, both modulus and phase, with a time resolution of 3 ms, corresponding to the oscillation period. The measuring instrument was a personal computer with its sound card and an electronic amplifier, both used to generate the excitation current and record the velocity signal, while performing the required frequency sweep. The study covered an excitation force range more than two and half decades wide (51 dB). The experimental results showed very good agreement with the theoretical behavior of a Duffing oscillator with nonlinear damping over about two decades.
Modelling the transition from simple to complex Ca oscillations in ...
Indian Academy of Sciences (India)
2014-04-29
Apr 29, 2014 ... 2Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand. *Corresponding author (Fax, +91-755-2670562; Email, mannumanhas@gmail.com). A mathematical model is proposed which systematically investigates complex calcium oscillations in pancreatic.
On the complex oscillation of differential polynomials generated by ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 120; Issue 4. On the Complex Oscillation of Differential Polynomials Generated by Meromorphic Solutions of Differential Equations in the Unit Disc. Ting-Bin Cao Hong-Yan Xu Chuan-Xi Zhu. Volume 120 Issue 4 September 2010 pp 481-493 ...
Third Conference on nonlinear science and complexity (NSC)
Machado, José; Baleanu, Dumitru; Dynamical Systems and Methods
2012-01-01
Nonlinear Systems and Methods For Mechanical, Electrical and Biosystems presents topics observed at the 3rd Conference on Nonlinear Science and Complexity(NSC), focusing on energy transfer and synchronization in hybrid nonlinear systems. The studies focus on fundamental theories and principles,analytical and symbolic approaches, computational techniques in nonlinear physical science and mathematics. Broken into three parts, the text covers:\\ Parametrical excited pendulum, nonlinear dynamics in hybrid systems, dynamical system synchronization and (N+1) body dynamics as well as new views different from the existing results in nonlinear dynamics. Mathematical methods for dynamical systems including conservation laws, dynamical symmetry in nonlinear differential equations and invex energies. Nonlinear phenomena in physical problems such as solutions, complex flows, chemical kinetics, Toda lattices and parallel manipulator. This book is useful to scholars, researchers and advanced technical members of industrial l...
Directory of Open Access Journals (Sweden)
Saul Hazledine
Full Text Available Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia, with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.
Vertical-probe-induced asymmetric dust oscillation in complex plasma.
Harris, B J; Matthews, L S; Hyde, T W
2013-05-01
A complex plasma vertical oscillation experiment which modifies the bulk is presented. Spherical, micron-sized particles within a Coulomb crystal levitated in the sheath above the powered lower electrode in a GEC reference cell are perturbed using a probe attached to a Zyvex S100 Nanomanipulator. By oscillating the probe potential sinusoidally, particle motion is found to be asymmetric, exhibiting superharmonic response in one case. Using a simple electric field model for the plasma sheath, including a nonzero electric field at the sheath edge, dust particle charges are found by employing a balance of relevant forces and emission analysis. Adjusting the parameters of the electric field model allowed the change predicted in the levitation height to be compared with experiment. A discrete oscillator Green's function is applied using the derived force, which accurately predicts the particle's motion and allows the determination of the electric field at the sheath edge.
The Optical Whistle Oscillation Frustrated Spatial Soliton Formation in Nonlinear Cavities
Boyce, J; Boyce, Jack; Chiao, Raymond Y.
1998-01-01
A new type of transverse instability in dispersively nonlinear optical cavities, called the optical whistle, is discussed. This instability occurs in the mean-field, soliton forming limit when the cavity is driven with a finite-width Gaussian beam, and gives rise to oscillation, period doubling, and chaos. It is also seen that bistability is strongly affected due to the oscillation within the upper transmission branch. The phenomenon is interpreted as a mode-mismatch in the soliton formation process and is believed to have broad applicability.
Nonlinear waves in bipolar complex viscous astroclouds
Karmakar, P. K.; Haloi, A.
2017-05-01
A theoretical evolutionary model to analyze the dynamics of strongly nonlinear waves in inhomogeneous complex astrophysical viscous clouds on the gravito-electrostatic scales of space and time is procedurally set up. It compositionally consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neutral hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method reduces the inter-coupled structure equations into a pair of intermixed forced Korteweg-de Vries-Burgers (f-KdVB) equations. The force-terms are self-consistently sourced by inhomogeneous gravito-electrostatic interplay. A numerical illustrative shape-analysis based on judicious astronomical parametric platform shows the electrostatic waves evolving as compressive dispersive shock-like eigen-modes. A unique transition from quasi-monotonic to non-monotonic oscillatory compressive shock-like patterns is found to exist. In contrast, the self-gravitational and effective perturbations grow purely as non-monotonic compressive oscillatory shock-like structures with no such transitory features. It is seen that the referral frame velocity acts as amplitude-reducing agent (stabilizing source) for the electrostatic fluctuations solely. A comparison in the prognostic light of various earlier satellite-based observations and in-situ measurements is presented. The paper ends up with synoptic highlights on the main implications and non-trivial applications in the interstellar space and cosmic plasma environments leading to bounded structure formation.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
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.
Uncovering Oscillations, Complexity, and Chaos in Chemical Kinetics Using Mathematica
Ferreira, M. M. C.; Ferreira, W. C., Jr.; Lino, A. C. S.; Porto, M. E. G.
1999-06-01
Unlike reactions with no peculiar temporal behavior, in oscillatory reactions concentrations can rise and fall spontaneously in a cyclic or disorganized fashion. In this article, the software Mathematica is used for a theoretical study of kinetic mechanisms of oscillating and chaotic reactions. A first simple example is introduced through a three-step reaction, called the Lotka model, which exhibits a temporal behavior characterized by damped oscillations. The phase plane method of dynamic systems theory is introduced for a geometric interpretation of the reaction kinetics without solving the differential rate equations. The equations are later numerically solved using the built-in routine NDSolve and the results are plotted. The next example, still with a very simple mechanism, is the Lotka-Volterra model reaction, which oscillates indefinitely. The kinetic process and rate equations are also represented by a three-step reaction mechanism. The most important difference between this and the former reaction is that the undamped oscillation has two autocatalytic steps instead of one. The periods of oscillations are obtained by using the discrete Fourier transform (DFT)-a well-known tool in spectroscopy, although not so common in this context. In the last section, it is shown how a simple model of biochemical interactions can be useful to understand the complex behavior of important biological systems. The model consists of two allosteric enzymes coupled in series and activated by its own products. This reaction scheme is important for explaining many metabolic mechanisms, such as the glycolytic oscillations in muscles, yeast glycolysis, and the periodic synthesis of cyclic AMP. A few of many possible dynamic behaviors are exemplified through a prototype glycolytic enzymatic reaction proposed by Decroly and Goldbeter. By simply modifying the initial concentrations, limit cycles, chaos, and birhythmicity are computationally obtained and visualized.
Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity
Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.
2017-11-01
Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.
Non-Linear Oscillation in Ionic Current Due to Size Effect in Glass Nanopipette
Takami, Tomohide; Deng, Xiao Long; Son, Jong Wan; Kang, Eun Ji; Kawai, Tomoji; Park, Bae Ho
2012-11-01
We studied the size effect of the ionic current in glass pipette, and found an interesting 2.7 mHz oscillation at 50 nm. In this study, we would like to discuss the mechanism of the non-linear oscillation. Cation-rich layer with its Debye length λ exists in nanopipette, and its conductivity σd is lower than that in the central bulk layer σb in this study. The pressure difference ΔP = ΔcRT where Δc is the difference in concentrations between in and out of the pipette. Then, the ionic current I can be estimated by using Hagen-Poiseuille equation; I =π/8 η ΔcRT/l {σdr4 + (σb -σd) (λ - r) 2 (r2 + 2 rλ -λ2) } . (r : inner radius, l: pipette length, η: viscosity) The last term indicates the non-linear oscillation. Moreover, we roughly estimated λ = 2.08 ×(2r) 1 / 2. Then, the bulk layer appears appropriately when 2 r 50 nm, which causes the effective ionic current oscillation. This work was supported by KOSEF NRL Program grant funded by the Korea Government MEST (Grant No. 2010-0024525 and R0A-2008-000-20052-0), and WCU Program through the KOSEF funded by the MEST (Grant No. R31-2008-000-10057-0).
Application of He's homotopy perturbation method to conservative truly nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Belendez, T.; Marquez, A.; Neipp, C. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-08-15
We apply He's homotopy perturbation method to find improved approximate solutions to conservative truly nonlinear oscillators. This approach gives us not only a truly periodic solution but also the period of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters in the case of the cubic oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second order approximation we have shown that the relative error in the analytical approximate frequency is approximately 0.03% for any parameter values involved. We also compared the analytical approximate solutions and the Fourier series expansion of the exact solution. This has allowed us to compare the coefficients for the different harmonic terms in these solutions. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems.
Directory of Open Access Journals (Sweden)
Cheng Liu
2017-05-01
Full Text Available In this paper, a novel nonlinear robust damping controller is proposed to suppress power oscillation in interconnected power systems. The proposed power oscillation damping controller exhibits good nonlinearity and robustness. It can consider the strong nonlinearity of power oscillation and uncertainty of its model. First, through differential homeomorphic mapping, a mathematical model of the system can be transformed into the Brunovsky standard. Next, an extended state observer (ESO estimated and compensated for model errors and external disturbances as well as uncertain factors to achieve dynamic linearization of the nonlinear model. A power oscillation damping controller for interconnected power systems was designed on a backstepping-fractional order sliding mode variable structure control theory (BFSMC. Compared with traditional methods, the controller exhibits good dynamic performance and strong robustness. Simulations involving a four-generator two-area and partial test system of Northeast China were conducted under various disturbances to prove the effectiveness and robustness of the proposed damping control method.
Rath, Biswanath; Mallick, P.
2014-01-01
A new method for generating analytical expression of quantum Hamiltonian from non-linear differential equation with stationary energy level has been formulated.Further calculation of energy levels have been carried out analytically using and numerically using matrix diagonalisation method.
Nonlinear coupling between cortical oscillations and muscle activity during isotonic wrist flexion
Directory of Open Access Journals (Sweden)
Yuan Yang
2016-12-01
Full Text Available Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e. the contralateral primary sensorimotor areas, supplementary motor area, prefrontal area and posterior parietal cortex. For all these areas, linear coupling between EEG and EMG is present with peaks in the beta band (15-35 Hz, while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4 and non-integer (2:3 harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (supplementary motor area, prefrontal area compared to the sensory association area (posterior parietal cortex; but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback.
Serebrennikov, Aleksey M.
2014-09-01
Here, we introduce a nonlinear continuum mechanical theoretical model of dissipative plasmonic oscillations relying on the principle of least action. The proposed theory has allowed obtaining the expression of a stress tensor for an “electron gas-ionic frame” system. In parallel, an initial boundary value problem for nonlinear integrodifferential equations constituting the model has been formulated. On the basis of a finite-difference approach the iterative solution method, algorithm and solver have been worked out. Thereby we have investigated the phenomena of harmonic multiples generation by a cluster of metal nanoparticles. Also by using these tools the estimate of the density function parameter satisfying the requirement of regular oscillations has been obtained numerically. On the ground of extensive numerical runs it was found that for a given set of parameters the system response turned out to be mainly linear, however the contributions of the closest odd harmonic multiples (third and fifth) were well resolved under quantitative analysis. This result allows the nonlinearity governable by the principal equation of motion to be associated with Kerr's type nonlinearity.
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
Analysis of the Non-Linearity of El Niño Southern Oscillation Teleconnections
Frauen, Claudia; Dommenget, Dietmar; Rezny, Michael; Wales, Scott
2014-05-01
The El Niño Southern Oscillation (ENSO) has significant variations and non-linearities in its pattern and strength. ENSO events are shifted along the equator, with some located in the central Pacific (CP) and others in the east Pacific (EP). To study how these variations are reflected in global ENSO teleconnections we analyze observations and idealized atmospheric general circulation model (AGCM) simulations. Clear non-linearities exist in observed teleconnections of sea level pressure (SLP) and precipitation. However, it is difficult to distinguish if these are caused by the different signs, strengths or spatial patterns of events (strong El Niño events mostly being EP events and strong La Niña events mostly being CP events) or by combinations of these. Therefore, sensitivity experiments are performed with an AGCM forced with idealized EP and CP ENSO sea surface temperature (SST) patterns with varying signs and strengths. It can be shown that in general the response is stronger for warm events than for cold events and the teleconnections shift following the SST anomaly patterns. EP events show stronger non-linearities than CP events. The non-linear responses to ENSO events can be explained as a combination of non-linear responses to a linear ENSO (fixed pattern but varying signs and strengths) and a linear response to a non-linear ENSO (varying patterns). Any observed event is a combination of these aspects. While in most tropical regions these add up leading to stronger non-linear responses than expected from the single components, in some regions they cancel each other resulting in little overall non-linearity. This leads to strong regional differences in ENSO teleconnections.
Phase-noise reduction in surface wave oscillators by using nonlinear sustaining amplifiers.
Avramov, Ivan D
2006-04-01
Nonlinear sustaining amplifier operation has been investigated and applied to high-power negative resistance oscillators (NRO), using single-port surface transverse wave (STW) resonators, and single-transistor sustaining amplifiers for feedback-loop STW oscillators (FLSO) stabilized with two-port STW devices. In all cases, self-limiting, silicon (Si)-bipolar sustaining amplifiers that operate in the highly nonlinear AB-, B-, or C-class modes are implemented. Phase-noise reduction is based on the assumption that a sustaining amplifier, operating in one of these modes, uses current limiting and remains cut off over a significant portion of the wave period. Therefore, it does not generate 1/f noise over the cut-off portion of the radio frequency (RF) cycle, and this reduces the close-in oscillator phase noise significantly. The proposed method has been found to provide phase-noise levels in the -111 to -119 dBc/Hz range at 1 KHz carrier offset in 915 MHz C-class power NRO and FLSO generating up to 23 dBm of RF-power at RF versus dc (RF/dc) efficiencies exceeding 40%. C-class amplifier design techniques are used for adequate matching and high RF/dc efficiency.
Variational problem with complex coefficient of a nonlinear ...
Indian Academy of Sciences (India)
Abstract. An optimal control problem governed by a nonlinear Schrödinger equation with complex coefficient is investigated. The paper studies existence, uniqueness and optimality conditions for the control problem.
Nonlinear Dynamics of the Perceived Pitch of Complex Sounds
Cartwright, Julyan H. E.; González, Diego L.; Piro, Oreste
1999-06-01
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.
Nonlinear Dynamics of the Perceived Pitch of Complex Sounds
Cartwright, J H E; Piro, O; Cartwright, Julyan H. E.; Gonzalez, Diego L.; Piro, Oreste
1999-01-01
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.
Ordu, M.; Guo, J.; Ng Pack, G.; Shah, P.; Ramachandran, S.; Hong, M. K.; Ziegler, L. D.; Basu, S. N.; Erramilli, S.
2017-09-01
Germanium optical fibers hold great promise in extending semiconductor photonics into the fundamentally important mid-infrared region of the electromagnetic spectrum. The demonstration of nonlinear response in fabricated Ge fiber samples is a key step in the development of mid-infrared fiber materials. Here we report the observation of detuning oscillations in a germanium fiber in the mid-infrared region using femtosecond dispersed pump-probe spectroscopy. Detuning oscillations are observed in the frequency-resolved response when mid-infrared pump and probe pulses are overlapped in a fiber segment. The oscillations arise from the nonlinear frequency resolved nonlinear (χ(3)) response in the germanium semiconductor. Our work represents the first observation of coherent oscillations in the emerging field of germanium mid-infrared fiber optics.
Directory of Open Access Journals (Sweden)
M. Ordu
2017-09-01
Full Text Available Germanium optical fibers hold great promise in extending semiconductor photonics into the fundamentally important mid-infrared region of the electromagnetic spectrum. The demonstration of nonlinear response in fabricated Ge fiber samples is a key step in the development of mid-infrared fiber materials. Here we report the observation of detuning oscillations in a germanium fiber in the mid-infrared region using femtosecond dispersed pump-probe spectroscopy. Detuning oscillations are observed in the frequency-resolved response when mid-infrared pump and probe pulses are overlapped in a fiber segment. The oscillations arise from the nonlinear frequency resolved nonlinear (χ(3 response in the germanium semiconductor. Our work represents the first observation of coherent oscillations in the emerging field of germanium mid-infrared fiber optics.
Rosas-Ortiz, Oscar; Zelaya, Kevin
2018-01-01
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a mathematical procedure to satisfy the superposition principle. In this form the non-Hermitian oscillators can be studied in much the same way as in the Hermitian approaches. Two different nonlinear algebras generated by properly constructed ladder operators are found and the corresponding generalized coherent states are obtained. The non-Hermitian oscillators can be steered to the conventional one by the appropriate selection of parameters. In such limit, the generators of the nonlinear algebras converge to generalized ladder operators that would represent either intensity-dependent interactions or multi-photon processes if the oscillator is associated with single mode photon fields in nonlinear media.
Directory of Open Access Journals (Sweden)
I. Khatami
2008-01-01
Full Text Available The objective of this paper is to present an analytical investigation to analyze the vibration of parametrically excited oscillator with strong cubic negative nonlinearity based on Mathieu-Duffing equation. The analytic investigation was conducted by using He's homotopy-perturbation method (HPM. In order to obtain the analytical solution of Mathieu-Duffing equation, homotopy-perturbation method has been utilized. The Runge-Kutta's (RK algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution. Afterward, the effects of variation of the parameters on the accuracy of the homotopy-perturbation method were studied.
Nonlinear Aeroelastic Study of Stall Induced Oscillation in a Symmetric Airfoil
Sarkar, S.; Bijl, H.
2006-01-01
In this paper the aeroelastic stability of a wind turbine rotor in the dynamic stall regime is investigated. Increased flexibility of modern turbine blades makes them more susceptible to aeroelastic instabilities. Complex oscillation modes like flap/lead-lag are of particular concern, which give way
Long-time fidelity and chaos for a kicked nonlinear oscillator system
Kowalewska-Kudłaszyk, A.; Kalaga, J. K.; Leoński, W.
2009-01-01
We deal with a system comprising a nonlinear (Kerr-like) oscillator excited by a series of ultra-short external pulses. We introduce the fidelity-based entropic parameter that can be used as an indicator of quantum chaos. Moreover, we propose to use the fidelity-like parameter comprising the information about the mean number of photons in the system. We shall concentrate on the long-time behaviour of the parameters discussed, showing that for deep chaos cases the quantum fidelities behave cha...
Double symbolic joint entropy in nonlinear dynamic complexity analysis
Yao, Wenpo; Wang, Jun
2017-07-01
Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.
Probing the non-linear transient response of a carbon nanotube mechanical oscillator
Willick, Kyle; Tang, Xiaowu Shirley; Baugh, Jonathan
2017-11-01
Carbon nanotube (CNT) electromechanical resonators have demonstrated unprecedented sensitivities for detecting small masses and forces. The detection speed in a cryogenic setup is usually limited by the CNT contact resistance and parasitic capacitance of cabling. We report the use of a cold heterojunction bipolar transistor amplifying circuit near the device to measure the mechanical amplitude at microsecond timescales. A Coulomb rectification scheme, in which the probe signal is at much lower frequency than the mechanical drive signal, allows investigation of the strongly non-linear regime. The behaviour of transients in both the linear and non-linear regimes is observed and modeled by including Duffing and non-linear damping terms in a harmonic oscillator equation. We show that the non-linear regime can result in faster mechanical response times, on the order of 10 μs for the device and circuit presented, potentially enabling the magnetic moments of single molecules to be measured within their spin relaxation and dephasing timescales.
Investigation of the nonlinear equation of the circular sector oscillator by Akbari-Ganjiâs method
Directory of Open Access Journals (Sweden)
Hadi Mirgolbabaee
2017-11-01
Full Text Available In this paper, a new and innovative semi-analytical method called Akbari-Ganjiâs method (AGM has been applied to solve nonlinear equations of the semicircular oscillator. The major concern is to achieve an accurate solution that has an efficient approximation according to the Runge-Kutta numerical method. The results are presented for different values of parameters to demonstrate the applicability of this method. It was found that the proposed solution is very accurate and efficient for the discussed problem. It is worthwhile to mention that not only do convergence problems for solving nonlinear equations by using AGM appear small, but the results also demonstrate that the AGM could be applied to nonlinear problems with high nonlinearity. Keywords: Akbari Ganji's Method (AGM, Angular frequency, Circular sector oscillation, Nonlinear equation, Numerical Method (Runge-Kutta 4th
Nonlinear viscoelasticity and shear localization at complex fluid interfaces.
Erni, Philipp; Parker, Alan
2012-05-22
Foams and emulsions are often exposed to strong external fields, resulting in large interface deformations far beyond the linear viscoelastic regime. Here, we investigate the nonlinear and transient interfacial rheology of adsorption layers in large-amplitude oscillatory shear flow. As a prototypical material forming soft-solid-type interfacial adsorption layers, we use Acacia gum (i.e., gum arabic), a protein/polysaccharide hybrid. We quantify its nonlinear flow properties at the oil/water interface using a biconical disk interfacial rheometer and analyze the nonlinear stress response under forced strain oscillations. From the resulting Lissajous curves, we access quantitative measures recently introduced for nonlinear viscoelasticity, including the intracycle moduli for both the maximum and zero strains and the degree of plastic energy dissipation upon interfacial yielding. We demonstrate using in situ flow visualization that the onset of nonlinear viscoelasticity coincides with shear localization at the interface. Finally, we address the nonperiodic character of this flow transition using an experimental procedure based on opposing stress pulses, allowing us to extract additional interfacial properties such as the critical interfacial stress upon yielding and the permanent deformation.
The mechanism of non-linear photochemical oscillations in the mesopause region
Directory of Open Access Journals (Sweden)
M. Yu. Kulikov
2012-09-01
Full Text Available The mechanism of generation of 2-day photochemical oscillations in the mesopause region (80–90 km has been studied analytically. The initial system of equations of chemical kinetics describing the temporal evolution of O, O_{3}, H, OH and HO_{2} concentrations with allowance for diurnal variations of solar radiation has been simplified successively to a system of two nonlinear first-order time equations with sinusoidal external forcing. The obtained system has a minimum number of terms needed for generation of 2-day oscillations. Linearization of this system near the period-doubling threshold permits separating explicitly a particular case of the Mathieu equation ẍ + α · sin ω t · x = 0, in which the first sub-harmonic (ω/2 of the exciting force starts to grow exponentially when the amplitude of external forcing (α exceeds its threshold value. Finally, a system of two simplest differential equations with power-law nonlinearity has been derived that allows analytical investigation of the effect of arising of reaction-diffusion waves in the mesospheric photochemical system.
Complex geometrical optics of inhomogeneous and nonlinear saturable media
Berczynski, Pawel
2013-05-01
The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing along curvilinear trajectory in smoothly inhomogeneous and nonlinear saturable media. CGO method reduces the problem of Gaussian beam propagation in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to the other methods of nonlinear optics such as: variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of the evolution of beam intensity and wave front cross-section along curvilinear central ray with torsion in weakly absorptive and nonlinear saturable graded-index fiber, where the effect of initial beam ellipticity is included into our description.
Complex dynamics and morphogenesis an introduction to nonlinear science
Misbah, Chaouqi
2017-01-01
This book offers an introduction to the physics of nonlinear phenomena through two complementary approaches: bifurcation theory and catastrophe theory. Readers will be gradually introduced to the language and formalisms of nonlinear sciences, which constitute the framework to describe complex systems. The difficulty with complex systems is that their evolution cannot be fully predicted because of the interdependence and interactions between their different components. Starting with simple examples and working toward an increasing level of universalization, the work explores diverse scenarios of bifurcations and elementary catastrophes which characterize the qualitative behavior of nonlinear systems. The study of temporal evolution is undertaken using the equations that characterize stationary or oscillatory solutions, while spatial analysis introduces the fascinating problem of morphogenesis. Accessible to undergraduate university students in any discipline concerned with nonlinear phenomena (physics, mathema...
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Tenorio, C. [Benemerita Universidad Autonoma de Puebla, 7200 Puebla (Mexico) and Universidad Autonoma del Estado de Mexico (Mexico)]. E-mail: celso1@hotmail.com; Belyaeva, T.L. [Universidad Autonoma del Estado de Mexico (Mexico); Serkin, V.N. [Benemerita Universidad Autonoma de Puebla, 7200 Puebla (Mexico)
2007-09-01
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.
Zhang, Songchuan; Xia, Youshen
2018-01-01
Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an -norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.
Coherent population oscillations and superluminal light in a protein complex.
Yelleswarapu, Chandra S; Laoui, Samir; Philip, Reji; Rao, D V G L N
2008-03-17
We observed superluminal light in aqueous solution of the protein complex bacteriorhodopsin (bR) at 647.1 nm wavelength where it exhibits reverse saturable behavior, exploiting the technique of coherent population oscillations (CPO). With a modulation frequency of 10 Hz, the signal pulse through a 1 cm path cell is ahead by 3 msec relative to the reference pulse, corresponding to a group velocity of -3.3 m/sec. Following our early work on slow light in the same sample at the saturable wavelength 568.2 nm, we now explicitly observed the narrow spectral hole in the absorption band of the stable B state and further, demonstrated a close correlation between the profile of the hole and the corresponding pulse delay for various modulation frequencies. A similar behavior is observed for superluminal light versus antihole blown in the absorption band.
Ordu, M.; Guo, J.; G. Ng Pack; Shah, P.; S. Ramachandran; Hong, M K; Ziegler, L. D.; S. N. Basu; Erramilli, S
2017-01-01
Germanium optical fibers hold great promise in extending semiconductor photonics into the fundamentally important mid-infrared region of the electromagnetic spectrum. The demonstration of nonlinear response in fabricated Ge fiber samples is a key step in the development of mid-infrared fiber materials. Here we report the observation of detuning oscillations in a germanium fiber in the mid-infrared region using femtosecond dispersed pump-probe spectroscopy. Detuning oscillations are observed i...
Koval'skaya, G. A.; Petrov, A. K.
2016-01-01
Nonlinear vibrations in a closed system of coupled nonlinear oscillators are studied using acetylene type molecules as an example. A criterion for the stable existence of long-lived vibrational states—local modes—in one of the oscillators is obtained. It is shown that the disappearance of a local mode, as well as its appearance, proceeds abruptly, and the mechanism of stabilization of these excitations is due to the presence or absence of internal resonances of an oscillatory system such as any polyatomic molecule. Energy values needed to excite vibrations in which local modes can appear are determined. It is shown that calculation results agree with experimental data.
Sapsis, T. P.; Vakakis, A. F.; Gendelman, O. V.; Bergman, L. A.; Kerschen, G.; Quinn, D. D.
2009-08-01
We study targeted energy transfer in a two degree-of-freedom damped system under the condition of 1:1 transient resonance capture. The system consists of a linear oscillator strongly coupled to an essentially nonlinear attachment or nonlinear energy sink. In a companion paper [Quinn et al., Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures: part I, Journal of Sound and Vibration 311 (2008) 1228-1248] we studied the underlying structure of the Hamiltonian dynamics of this system, and showed that for sufficiently small values of viscous damping, nonlinear damped transitions are strongly influenced by the underlying topological structure of periodic and quasiperiodic orbits of the Hamiltonian system. In this work direct analytical treatment of the governing strongly nonlinear damped equations of motion is performed through slow/fast partitions of the transient responses, in order to investigate analytically the parameter region of optimal targeted energy transfer. To this end, we determine the characteristic time scales of the dynamics that influence the capacity of the nonlinear attachment to passively absorb and locally dissipate broadband energy from the linear oscillator. Then, we prove that optimal targeted energy transfer is realized for initial energies close to the neighborhood of a homoclinic orbit of the underlying Hamiltonian system. We study analytically transient orbits resulting as perturbations of the homoclinic orbit in the weakly damped system, and show that this yields an additional slow-time scale in the averaged dynamics, and leads to optimal targeted energy transfer from the linear oscillator to the nonlinear energy sink in a single "super-slow" half-cycle. We show that at higher energies, this "super-slow" half-cycle is replaced by strong nonlinear beats, which lead to significant but suboptimal targeted energy transfer efficiency. Finally, we investigate numerically targeted energy
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Gimeno, E; Mendez, D I; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2008-06-15
A modified generalized, rational harmonic balance method is used to construct approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable. The procedure is used to solve the nonlinear differential equation approximately. The approximate frequency obtained using this procedure is more accurate than those obtained using other approximate methods and the discrepancy between the approximate frequency and the exact one is lower than 0.40%.
Design of micro-optical parametric oscillators based on third-order nonlinearity
Zeng, Xiaoge
2013-01-01
We propose optimal designs for optical parametric oscillators (OPOs) based on four-wave mixing (FWM) in microcavities. We show that optimal designs in general call for different external coupling for pump and signal/idler resonances, and we provide a number of normalized performance metrics including threshold pump power and maximum achievable conversion efficiency for OPOs with and without two-photon (TPA) and free-carrier absorption (FCA). We find that the maximum achievable conversion efficiency is bound to an upper limit by nonlinear and free-carrier losses independent of pump power, while linear losses only increase the pump power required to achieve a certain conversion efficiency. The results of this work suggest unique advantages in on-chip implementations that allow explicit engineering of resonances, mode field overlaps, dispersion, and wavelength- and mode-selective coupling. We provide universal design curves that yield optimum designs, and give example designs of microring-resonator-based OPOs in...
Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator
Mansingka, Abhinav S.
2012-07-29
This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.
Design of Voltage control Oscillator using Nonlinear Composite Right/Left-Handed Transmission Line
Directory of Open Access Journals (Sweden)
H. J. El-Khozondar
2016-03-01
Full Text Available In the present work, we propose a voltage control oscillator (VCO at high frequency consists of nonlinear composite right/left-handed transmission line (CRLH-TL loaded with Resonant Tunneling Diode (RTD. We designed three prototype device examples. The first one consists of one cell with short circuit at the beginning of the cell between ground and patch, and 50 Ω load resistance were added at the end of the cell between ground and patch. The second one is similar to the first prototype but with open circuit at the beginning of the cell instated of short circuit. The third prototype consists of one cell with two 50 Ω load resistances added between ground and patch at the beginning and at the end of the cell. The proposed VCO models are capable of generating oscillations at frequencies between 4.87- 14.9 GHz. In our simulations, we used OrCAD and ADS software to analyze the proposed circuit.
Energy Technology Data Exchange (ETDEWEB)
Macias-Diaz, J.E. [Departamento de Matematicas y Fisica, Universidad Autonoma de Aguascalientes, Aguascalientes, Ags. 20100 (Mexico) and Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)]. E-mail: jemacias@correo.uaa.mx; Puri, A. [Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)]. E-mail: apuri@uno.edu
2007-07-02
In the present Letter, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear supratransmission. Our numerical results-which are based on a brand-new computational technique with energy-invariant properties-show an efficient and reliable transmission of information.
Existence of periodic orbits in nonlinear oscillators of Emden–Fowler form
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C., E-mail: mancass@erau.edu [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, SLP (Mexico)
2016-01-28
The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden–Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also allows us to construct periodic solutions to them. Two other nonlinear equations, a zero-frequency Ermakov equation and a positive power Emden–Fowler equation, are discussed in the same context. - Highlights: • An invariant transformation is used to find periodic solution of EF equations. • Phase plane study of the EF autonomous two-dimensional ODE system is performed. • Three examples are presented from the standpoint of the phase plane analysis.
An introduction to complex systems society, ecology, and nonlinear dynamics
Fieguth, Paul
2017-01-01
This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or per...
Foundations of Complex Systems Nonlinear Dynamics, Statistical Physics, and Prediction
Nicolis, Gregoire
2007-01-01
Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, h
Synchronization in Complex Networks of Nonlinear Dynamical Systems
Wu, Chai Wah
2007-01-01
This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ide
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Rodes, J.J. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fuentes, R.; Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-02-16
The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed.
DEFF Research Database (Denmark)
Ibsen, Lars Bo; Barari, Amin; Kimiaeifar, Amin
2010-01-01
/approximate analytical solution to strong nonlinear oscillators. Furthermore, it is shown that a large class of linear or nonlinear differential equations can be solved without the tangible restriction of sensitivity to the degree of the nonlinear term, adding that the method is quite convenient due to reduction in size...
DEFF Research Database (Denmark)
Ibsen, Lars Bo; Barari, Amin; Kimiaeifar, Amin
2010-01-01
/approximate analytical solution to strong nonlinear oscillators. Furthermore, it is shown that a large class of linear or nonlinear differential equations can be solved without the tangible restriction of sensitivity to the degree of the nonlinear term, adding that the method is quite convenient due to reduction in size...
Reduced Complexity Volterra Models for Nonlinear System Identification
Directory of Open Access Journals (Sweden)
Hacıoğlu Rıfat
2001-01-01
Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.
Chae, Jongchul; Litvinenko, Yuri E.
2017-08-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D2 and Hα lines.
Energy Technology Data Exchange (ETDEWEB)
Chae, Jongchul [Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826 (Korea, Republic of); Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)
2017-08-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.
New exact travelling wave solutions of some complex nonlinear equations
Bekir, Ahmet
2009-04-01
In this paper, we establish exact solutions for complex nonlinear equations. The tanh-coth and the sine-cosine methods are used to construct exact periodic and soliton solutions of these equations. Many new families of exact travelling wave solutions of the coupled Higgs and Maccari equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems.
Cherumadanakadan Thelliyil, S.; Ravindran, A. M.; Giannakis, D.; Majda, A.
2016-12-01
An improved index for real time monitoring and forecast verification of monsoon intraseasonal oscillations (MISO) is introduced using the recently developed Nonlinear Laplacian Spectral Analysis (NLSA) algorithm. Previous studies has demonstrated the proficiency of NLSA in capturing low frequency variability and intermittency of a time series. Using NLSA a hierarchy of Laplace-Beltrami (LB) eigen functions are extracted from the unfiltered daily GPCP rainfall data over the south Asian monsoon region. Two modes representing the full life cycle of complex northeastward propagating boreal summer MISO are identified from the hierarchy of Laplace-Beltrami eigen functions. These two MISO modes have a number of advantages over the conventionally used Extended Empirical Orthogonal Function (EEOF) MISO modes including higher memory and better predictability, higher fractional variance over the western Pacific, Western Ghats and adjoining Arabian Sea regions and more realistic representation of regional heat sources associated with the MISO. The skill of NLSA based MISO indices in real time prediction of MISO is demonstrated using hindcasts of CFSv2 extended range prediction runs. It is shown that these indices yield a higher prediction skill than the other conventional indices supporting the use of NLSA in real time prediction of MISO. Real time monitoring and prediction of MISO finds its application in agriculture, construction and hydro-electric power sectors and hence an important component of monsoon prediction.
Popov, Pavel; Sideris, Athanasios; Sirignano, William
2014-11-01
We examine the non-linear dynamics of the transverse modes of combustion-driven acoustic instability in a liquid-propellant rocket engine. Triggering can occur, whereby small perturbations from mean conditions decay, while larger disturbances grow to a limit-cycle of amplitude that may compare to the mean pressure. For a deterministic perturbation, the system is also deterministic, computed by coupled finite-volume solvers at low computational cost for a single realization. The randomness of the triggering disturbance is captured by treating the injector flow rates, local pressure disturbances, and sudden acceleration of the entire combustion chamber as random variables. The combustor chamber with its many sub-fields resulting from many injector ports may be viewed as a multi-scale complex system wherein the developing acoustic oscillation is the emergent structure. Numerical simulation of the resulting stochastic PDE system is performed using the polynomial chaos expansion method. The overall probability of unstable growth is assessed in different regions of the parameter space. We address, in particular, the seven-injector, rectangular Purdue University experimental combustion chamber. In addition to the novel geometry, new features include disturbances caused by engine acceleration and unsteady thruster nozzle flow.
Directory of Open Access Journals (Sweden)
Ting-Bin Cao
2010-11-01
Full Text Available The main purpose of this paper is to consider the oscillation theory on meromorphic solutions of second order linear differential equations of the form $f^{''}+A(zf=0$ where $A$ is meromorphic in the complex plane. We improve and extend some oscillation results due to Bank and Laine, Kinnunen, Liang and Liu, and others.
A study of synchronization of nonlinear oscillators: Application to epileptic seizures
Takeshita, Daisuke
This dissertation focuses on several problems in neuroscience from the perspective of nonlinear dynamics and stochastic processes. The first part concerns a method to visualize the idea of the power spectrum of spike trains, which has an educational value to introductory students in biophysics. The next part consists of experimental and computational work on drug-induced epileptic seizures in the rat neocortex. In the experimental part, spatiotemporal patterns of electrical activities in the rat neocortex are measured using voltage-sensitive dye imaging. Epileptic regions show well-synchronized, in-phase activity during epileptic seizures. In the computational part, a network of a Hodgkin-Huxley type neocortical neural model is constructed. Phase reduction, which is a dimension reduction technique for a stable limit cycle, is applied to the system. The results propose a possible mechanism for the initiation of the drug-induced seizure as a result of a bifurcation. In the last part, a theoretical framework is developed to obtain the statistics for the period of oscillations of a stable limit cycle under stochastic perturbation. A stochastic version of phase reduction and first passage time analysis are utilized for this purpose. The method presented here shows a good agreement with numerical results for the weak noise regime.
Directory of Open Access Journals (Sweden)
Yongjun Wu
2011-01-01
Full Text Available We study the stochastic optimal bounded control for minimizing the stationary response of strongly nonlinear oscillators under combined harmonic and wide-band noise excitations. The stochastic averaging method and the dynamical programming principle are combined to obtain the fully averaged Itô stochastic differential equations which describe the original controlled strongly nonlinear system approximately. The stationary joint probability density of the amplitude and phase difference of the optimally controlled systems is obtained from solving the corresponding reduced Fokker-Planck-Kolmogorov (FPK equation. An example is given to illustrate the proposed procedure, and the theoretical results are verified by Monte Carlo simulation.
Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; D'Incerti, Ludovico; Jovicich, Jorge
2015-03-01
In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D2), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.
Energy Technology Data Exchange (ETDEWEB)
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it [Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy); Center for Mind/Brain Sciences, University of Trento, Trento (Italy); Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge [Center for Mind/Brain Sciences, University of Trento, Trento (Italy); D' Incerti, Ludovico [Neuroradiology Unit, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2015-03-15
In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D{sub 2}), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.
Information mining in weighted complex networks with nonlinear rating projection
Liao, Hao; Zeng, An; Zhou, Mingyang; Mao, Rui; Wang, Bing-Hong
2017-10-01
Weighted rating networks are commonly used by e-commerce providers nowadays. In order to generate an objective ranking of online items' quality according to users' ratings, many sophisticated algorithms have been proposed in the complex networks domain. In this paper, instead of proposing new algorithms we focus on a more fundamental problem: the nonlinear rating projection. The basic idea is that even though the rating values given by users are linearly separated, the real preference of users to items between the different given values is nonlinear. We thus design an approach to project the original ratings of users to more representative values. This approach can be regarded as a data pretreatment method. Simulation in both artificial and real networks shows that the performance of the ranking algorithms can be improved when the projected ratings are used.
Without bounds a scientific canvas of nonlinearity and complex dynamics
Ryazantsev, Yuri; Starov, Victor; Huang, Guo-Xiang; Chetverikov, Alexander; Arena, Paolo; Nepomnyashchy, Alex; Ferrus, Alberto; Morozov, Eugene
2013-01-01
Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.
Structure-based control of complex networks with nonlinear dynamics
Zañudo, Jorge G T; Albert, Réka
2016-01-01
Given the network of interactions underlying a complex system, what can we learn about controlling such a system solely from its structure? Over a century of research in control theory has given us tools to answer this question, which were widely applied in science and engineering. Yet the current tools do not always consider the inherently nonlinear dynamics of real systems and the naturally occurring system states in their definition of "control", a term whose interpretation varies across disciplines. Here we use a new mathematical framework for structure-based control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors and which are guaranteed to be effective regardless of the dynamic details and parameters of the underlying system. We use this framework on several real networks, compar...
Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas
2014-01-01
Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467
Directory of Open Access Journals (Sweden)
Paulius Palevicius
2014-01-01
Full Text Available Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.
Brandão, P. A.; Cavalcanti, S. B.
2017-10-01
Propagation of wide optical beams in transverse periodic lattices have been reported to induce power oscillations between Fourier modes related by the Bragg resonance condition, resulting from the coupling between the beam and the periodic structure. These oscillations have been referred to as Rabi optical oscillations due to the analogy with matter Rabi oscillations. In this work, we investigate the behavior of Bragg-induced Rabi-type oscillations of a multimode Gaussian beam in the presence of optical nonlinearity. We find a combination of oscillation and spectrum broadening under both self-focusing and self-defocusing nonlinearities, in the sense that the oscillations are maintained while the spectrum is broadened and therefore partially transferred to the twin frequency. For intense self-focusing nonlinearities a complete leak of the initial mode profile to other modes is rapidly attained so that no oscillation is observed. In contrast, for intense self-defocusing nonlinearities the redistribution rate is so dramatic that oscillations cease and power only fades away.
Shmaliy, Yuriy S.; Rosales, Juan
2004-09-01
Dynamics of the mean amplitude of oscillations of a crystal oscillator with a linear feedback is outlined for low drives when the losses (friction) of a resonator become large and nonlinear after a long storage. The drive-level-dependence (DLD) of the crystal resonator losses is assumed to change inversely to the piezoelectric current. A stochastic differential equation for the mean amplitude is derived and solved in a sense of Ito. The development and attenuation processes are learned and it is shown that attenuation finishes at some non-zero level associated with the effect termed "sleeping sickness." The critical value of the friction is calculated and the conditions are discussed to avoid attenuation. Based upon, we show in that (1) if the value of the DLD coefficient of the resonator losses ranges below the critical point, the effect occurs primarilly in a delay of self-excitation; (2) contrary, noise drives the crystal oscillator.
Decuyper, J.; De Troyer, T.; Runacres, M. C.; Tiels, K.; Schoukens, J.
2018-01-01
The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.
Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control
Valenza, Gaetano; Citi, Luca; Garcia, Ronald G.; Taylor, Jessica Noggle; Toschi, Nicola; Barbieri, Riccardo
2017-02-01
The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson’s Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity.
Directory of Open Access Journals (Sweden)
Gang Chen
2012-01-01
Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.
Tian, Yan; Zhong, Lin-Feng; He, Gui-Tian; Yu, Tao; Luo, Mao-Kang; Stanley, H. Eugene
2018-01-01
We study stochastic resonance (SR) in an oscillator with nonlinear noise, fractional-order external damping, and fractional-order intrinsic damping. Using a moment equation, we derive the exact analytical expression of the output amplitude and find that fluctuations in the output amplitude are non-monotonic. Using numerical simulations we verify the accuracy of this analytical result. We find (i) that nonlinear noise plays a key role in system behavior and that the resonance of the output amplitude is diverse when there is nonlinear noise, (ii) that the order of the fractional-order damping strongly impacts resonant intensity and that the impact on resonant intensity of fractional-order external damping is opposite that of fractional-order intrinsic damping, and (iii) that the evolution of the output amplitude versus the frequency of the external periodic force exhibits three behaviors: a resonance with one peak, a resonance with one peak and one valley, and a resonance with one valley.
Di Egidio, Angelo; Contento, Alessandro; Vestroni, Fabrizio
2015-12-01
An open-cross section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear open-cross section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.
Dumeige, Y.; Yacomotti, A. M.; Grinberg, P.; Bencheikh, K.; Le Cren, E.; Levenson, J. A.
2012-06-01
We analytically show that inserting a driven, two-level system inside a microcavity can improve its optical properties. In this approach, the strong dispersion induced by a pump via population oscillations increases the cavity lifetime experienced by a slightly detuned probe. We further predict that if the cavity is pumped through a resonant channel, optical absorptive or dispersive bistability can be combined with the population-oscillation-induced steep material dispersion to obtain a strong quality-factor enhancement. Moreover, differential amplification coming from the nonlinear feature of the pump transfer function can be used to drastically increase the probe transmission beyond intrinsic characteristics of the resonator. The Q-factor enhancement and the differential amplification can be advantageously combined with a frequency pulling effect to stabilize or readjust the microcavity resonance frequency.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-03-17
He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient.
Viscous decay of nonlinear oscillations of a spherical bubble at large Reynolds number
Smith, W. R.; Wang, Q. X.
2017-08-01
The long-time viscous decay of large-amplitude bubble oscillations is considered in an incompressible Newtonian fluid, based on the Rayleigh-Plesset equation. At large Reynolds numbers, this is a multi-scaled problem with a short time scale associated with inertial oscillation and a long time scale associated with viscous damping. A multi-scaled perturbation method is thus employed to solve the problem. The leading-order analytical solution of the bubble radius history is obtained to the Rayleigh-Plesset equation in a closed form including both viscous and surface tension effects. Some important formulae are derived including the following: the average energy loss rate of the bubble system during each cycle of oscillation, an explicit formula for the dependence of the oscillation frequency on the energy, and an implicit formula for the amplitude envelope of the bubble radius as a function of the energy. Our theory shows that the energy of the bubble system and the frequency of oscillation do not change on the inertial time scale at leading order, the energy loss rate on the long viscous time scale being inversely proportional to the Reynolds number. These asymptotic predictions remain valid during each cycle of oscillation whether or not compressibility effects are significant. A systematic parametric analysis is carried out using the above formula for the energy of the bubble system, frequency of oscillation, and minimum/maximum bubble radii in terms of the Reynolds number, the dimensionless initial pressure of the bubble gases, and the Weber number. Our results show that the frequency and the decay rate have substantial variations over the lifetime of a decaying oscillation. The results also reveal that large-amplitude bubble oscillations are very sensitive to small changes in the initial conditions through large changes in the phase shift.
Nonlinear coupling between cortical oscillations and muscle activity during isotonic wrist flexion
Yang, Y.; Solis Escalante, T.; van de Ruit, M.L.; van der Helm, F.C.T.; Schouten, A.C.
2016-01-01
Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been
Oscillation of second-order forced nonlinear dynamic equations on time scales
Directory of Open Access Journals (Sweden)
Samir Saker
2005-11-01
on a time scale ${\\mathbb{T}}$ when $a(t>0$. We establish some sufficient conditions which ensure that every solution oscillates or satisfies $\\lim \\inf_{t\\rightarrow \\infty }\\left\\vert x(t\\right\\vert =0.$ Our oscillation results when $r(t=0$ improve the oscillation results for dynamic equations on time scales that has been established by Erbe and Peterson [Proc. Amer. Math. Soc \\ 132 (2004, 735-744], Bohner, Erbe and Peterson [J. Math. Anal. Appl. 301 (2005, 491--507] since our results do not require $\\int_{t_{0}}^{\\infty }q(t\\Delta t>0$ and $\\int_{\\pm t_{0}}^{\\pm \\infty } \\frac{du}{f(u}<\\infty .$ Also, as a special case when ${\\mathbb{T=R}}$, and $r(t=0$ our results improve some oscillation results for differential equations. Some examples are given to illustrate the main results.
Nonlinear Dynamics of Complex Coevolutionary Systems in Historical Times
Perdigão, Rui A. P.
2016-04-01
A new theoretical paradigm for statistical-dynamical modeling of complex coevolutionary systems is introduced, with the aim to provide historical geoscientists with a practical tool to analyse historical data and its underlying phenomenology. Historical data is assumed to represent the history of dynamical processes of physical and socio-economic nature. If processes and their governing laws are well understood, they are often treated with traditional dynamical equations: deterministic approach. If the governing laws are unknown or impracticable, the process is often treated as if being random (even if it is not): statistical approach. Although single eventful details - such as the exact spatiotemporal structure of a particular hydro-meteorological incident - may often be elusive to a detailed analysis, the overall dynamics exhibit group properties summarized by a simple set of categories or dynamical regimes at multiple scales - from local short-lived convection patterns to large-scale hydro-climatic regimes. The overwhelming microscale complexity is thus conveniently wrapped into a manageable group entity, such as a statistical distribution. In a stationary setting whereby the distribution is assumed to be invariant, alternating regimes are approachable as dynamical intermittence. For instance, in the context of bimodal climatic oscillations such as NAO and ENSO, each mode corresponds to a dynamical regime or phase. However, given external forcings or longer-term internal variability and multiscale coevolution, the structural properties of the system may change. These changes in the dynamical structure bring about a new distribution and associated regimes. The modes of yesteryear may no longer exist as such in the new structural order of the system. In this context, aside from regime intermittence, the system exhibits structural regime change. New oscillations may emerge whilst others fade into the annals of history, e.g. particular climate fluctuations during
Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions
Indian Academy of Sciences (India)
1Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University,. Tiruchirapalli 620 024, India. 2Department of Physics, KCG College of Technology, Karapakkam, Chennai 600 097, India. 3Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering,. SASTRA University ...
Complex dynamics of a particle in an oscillating potential field
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 89; Issue 2. Complex dynamics of ... Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009, India; Department of Basic and Applied Science, National Institute of Technology, Arunachal Pradesh 791 112, India ...
Complex dynamics of a particle in an oscillating potential field
Indian Academy of Sciences (India)
Barnali Pal
2017-07-25
Jul 25, 2017 ... nelling, wave-particle duality, or interference in which classical analogies are quite incapable of giving ... ping that links a complex-valued wave function solution of the time-independent Schrödinger's equation ... can be used to model human brain EEG signal [30]. It is evident that the Van der Pol–Duffing ...
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Li Gang
2016-01-01
Full Text Available This investigation is to solve the power-level control issue of a nonlinear pressurized water reactor core with xenon oscillations. A nonlinear pressurized water reactor core is modeled using the lumped parameter method, and a linear model of the core is then obtained through the small perturbation linearization way. The H∞loop shapingcontrolis utilized to design a robust controller of the linearized core model.The calculated H∞loop shaping controller is applied to the nonlinear core model. The nonlinear core model and the H∞ loop shaping controller build the nonlinear core power-level H∞loop shaping control system.Finally, the nonlinear core power-level H∞loop shaping control system is simulatedconsidering two typical load processes that are a step load maneuver and a ramp load maneuver, and simulation results show that the nonlinear control system is effective.
DEFF Research Database (Denmark)
Lindberg, Erik
1997-01-01
In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear wit...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos.......In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear...
Comparison of complex moduli obtained from forced and free damped oscillations
Heller, R.A.; Nederveen, C.J.
1967-01-01
While the concept of the complex modulus is based on a forced vibration experiment it is a frequent practice to perform instead a much simpler free damped oscillation test from which an approximate value of the modulus is then evaluated. The validity of this approach and the ensuing errors are
Directory of Open Access Journals (Sweden)
Ikuhiro Yamaguchi
Full Text Available Time delay is known to induce sustained oscillations in many biological systems such as electroencephalogram (EEG activities and gene regulations. Furthermore, interactions among delay-induced oscillations can generate complex collective rhythms, which play important functional roles. However, due to their intrinsic infinite dimensionality, theoretical analysis of interacting delay-induced oscillations has been limited. Here, we show that the two primary methods for finite-dimensional limit cycles, namely, the center manifold reduction in the vicinity of the Hopf bifurcation and the phase reduction for weak interactions, can successfully be applied to interacting infinite-dimensional delay-induced oscillations. We systematically derive the complex Ginzburg-Landau equation and the phase equation without delay for general interaction networks. Based on the reduced low-dimensional equations, we demonstrate that diffusive (linearly attractive coupling between a pair of delay-induced oscillations can exhibit nontrivial amplitude death and multimodal phase locking. Our analysis provides unique insights into experimentally observed EEG activities such as sudden transitions among different phase-locked states and occurrence of epileptic seizures.
Prospects and limitations of mathematical methods for decision making in nonlinear complex systems
DEFF Research Database (Denmark)
Starke, Jens; Berkemer, Rainer
2007-01-01
of the workshop Decision making and uncertainty in nonlinear complex systems for their valuable input on topics like uncertainty, nonlinearity, and complex systems in general. Scientists with different research backgrounds from various fields discussed several aspects of mathematical methods for decision making...
Efficient computation of quasiperiodic oscillations in nonlinear systems with fast rotating parts
DEFF Research Database (Denmark)
Schilder, Frank; Rübel, Jan; Starke, Jens
2008-01-01
We present a numerical method for the investigation of quasiperiodic oscillations in applications modeled by systems of ordinary differential equations. We focus on systems with parts that have a significant rotational speed. An important element of our approach is that it allows us to verify...
Bachelard, Nicolas; Sebbah, Patrick; Vanneste, Christian
2014-01-01
We use time-domain numerical simulations of a two-dimensional (2D) scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a small electric field intensity, we observe the strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a larger intensity induces non-linear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in non-linear Rabi oscillations. The transition between both regimes is observed and an analytical model is proposed which accurately describes our numerical observations.
Nonlinear optical response of tetra and mono substituted zinc phthalocyanine complexes
Energy Technology Data Exchange (ETDEWEB)
Fashina, Adedayo; Nyokong, Tebello, E-mail: t.nyokong@ru.ac.za
2015-11-15
The nonlinear absorption properties of 6 mono-substituted and 3 symmetric zinc phthalocyanine complexes have been studied in dimethylsulfoxide (DMSO) using 10 ns pulses at 532 nm. The non linear absorption of the complexes has been studied using the Z-scan technique. The study showed that both the singlet and triplet excited states contribute to the non linear absorption behavior. The nonlinear third-order susceptibility and second-order hyperpolarizability values of the complexes are reported. It was observed that two of the symmetric phthalocyanine complexes (5-α substituted with aminophenoxy and 9-β substituted with carboxyphenoxy) showed better and promising optical nonlinearity when compared to the other complexes studied. - Highlights: • Nonlinear absorption properties of zinc phthalocyanine are reported • Singlet and triplet excited states contribute to the non linear absorption. • Symmetrically tetra substituted phthalocyanines showed better optical nonlinearity.
Log-periodic oscillations due to discrete effects in complex networks
Sienkiewicz, Julian; Fronczak, Piotr; Hołyst, Janusz A.
2007-06-01
We show how discretization affects two major characteristics in complex networks: internode distances (measured as the shortest number of edges between network sites) and average path length, and as a result there are log-periodic oscillations of the above quantities. The effect occurs both in numerical network models as well as in such real systems as coauthorship, language, food, and public transport networks. Analytical description of these oscillations fits well numerical simulations. We consider a simple case of the network optimization problem, arguing that discrete effects can lead to a nontrivial solution.
Discontinuous Spirals of Stable Periodic Oscillations
DEFF Research Database (Denmark)
Sack, Achim; Freire, Joana G.; Lindberg, Erik
2013-01-01
We report the experimental discovery of a remarkable organization of the set of self-generated periodic oscillations in the parameter space of a nonlinear electronic circuit. When control parameters are suitably tuned, the wave pattern complexity of the periodic oscillations is found to increase...
Nonlinear oscillations of a coupled autoparametrical system with ideal and nonideal sources of power
Directory of Open Access Journals (Sweden)
Sado Danuta
2006-01-01
Full Text Available An ideal and nonideal autoparametrical system excited by DC motor with unbalanced mass is presented in this work. The system consists of the body of mass M which is hung on a nonlinear spring with a nonlinear damper, and a pendulum of the length l and mass m mounted to the body of mass M. It is assumed that the motion of the pendulum is damped by nonlinear resistive forces. Vibrations of both models (ideal and nonideal are researched. Solutions for the system response are presented for specific values of the parameters of system and the energy transfer between modes of vibrations is studied. Next excited vibrations for both models have been examined analytically and numerically. Except different kinds of periodic vibrations, there may also appear chaotic vibrations.
Directory of Open Access Journals (Sweden)
Banan Maayah
2014-01-01
Full Text Available A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.
Non-linear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
DEFF Research Database (Denmark)
Fereidoon, A.; Ghadimi, M.; Barari, Amin
2012-01-01
In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifthorder nonlinearity for two examples using He’s Frequency Amplitude Formulation (HFAF).The effectiveness and convenience of the method is illustrated in these examples. It will be shown...... that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems....
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
Wimmer, Martin; Christodoulides, Demetrios; Peschel, Ulf
2016-01-01
Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals ...
Directory of Open Access Journals (Sweden)
Bo Shen
2012-01-01
measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.
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.)
Numerical Analysis of Strongly Nonlinear Oscillation Systems using He's Max-Min Method
DEFF Research Database (Denmark)
Babazadeh, H; Domairry, G; Barari, Amin
2011-01-01
Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method for pre...
Stefszky, Michael; Mow-Lowry, Conor M.; McKenzie, Kirk; Chua, Sheon; Buchler, Ben C.; Symul, Thomas; McClelland, David E.; Lam, Ping Koy
2011-01-01
A squeezed light source requires properties such as high squeezing amplitude, high bandwidth and stability over time, ideally using as few resources, such as laser power, as possible. We compare three nonlinear materials, two of which have not been well characterized for squeezed state production,
An assessment of a semi analytical AG method for solving nonlinear oscillators
Directory of Open Access Journals (Sweden)
Hadi Mirgolbabaee
2016-02-01
Based on the comparison between AGM and numerical methods, AGM can be successfully applied for a broad range of nonlinear equations. One of the important reasons of selecting AGM for solving differential equations in miscellaneous fields not only in vibrations but also in different fields of sciences for instance fluid mechanics, solid mechanics, chemical engineering, etc. The main benefit of this method in comparison with the other approaches are as follows: normally according to the order of differential equations, we need boundary conditions so in the case of the number of boundary conditions is less than the order of the differential equation, AGM can create additional new boundary conditions in regard to the own differential equation and its derivatives. Results illustrate that method is efficient and has enough accuracy in comparison with other semi analytical and numerical methods because of the simplicity of this method. Moreover results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore convergence problems for solving nonlinear equations by using AGM appear small.
Setare, M. R.; Majari, P.
2018-02-01
We study the nonlinearity for the zigzag graphene nanoribbons (ZGNRs) with zigzag triangular holes (ZTHs). We show that in the presence of an external uniform magnetic field, a two-dimensional f-deformed Dirac oscillator can be used to describe the dynamics of the electrons in the ZGNRs with ZTHs. It is shown for the first time that the magnetic field direction has effect on the chirality of charge carriers in the ZGNRs punched with triangular holes. We also obtain the Landau-level spectrum in the weak and strong magnetic field regimes. Additionally, we compare Landau-level spectrum of this graphene-based device in the f-deformed scenario and original one. Our results provide a general viewpoint for the development of the zigzag graphene nanoribbons.
Rojan, Katharina; Léger, Yoan; Morigi, Giovanna; Richard, Maxime; Minguzzi, Anna
2017-09-01
Semiconductor microcavities in the strong-coupling regime exhibit an energy scale in the terahertz (THz) frequency range, which is fixed by the Rabi splitting between the upper and lower exciton-polariton states. While this range can be tuned by several orders of magnitude using different excitonic media, the transition between both polaritonic states is dipole forbidden. In this work, we show that, in cadmium telluride microcavities, the Rabi-oscillation-driven THz radiation is actually active without the need for any change in the microcavity design. This feature results from the unique resonance condition which is achieved between the Rabi splitting and the phonon-polariton states and leads to a giant enhancement of the second-order nonlinearity.
Anomalous nonlinear attenuation of ultrasound in solid 4He in a torsional oscillator below 200 mK
Iwasa, I.; Goodkind, J. M.; Kojima, H.
2014-12-01
In order to elucidate the ultra-low temperature behavior of solid 4He, simultaneous measurements of longitudinal ultrasound (US) and torsional oscillation have been made. Changes in attenuation and velocity of US at 10 MHz have been measured in polycrystalline hcp 4He samples (0.3 or 20 ppm of 3He impurity) grown in a 1 kHz torsional oscillator (TO). In a 0.3 ppm 3He sample, the US attenuation and velocity were found to depend on the US drive voltage at temperatures below 70 mK where the anomalies in the TO frequency and dissipation were also observed. The US attenuation at low T (10 mK) decreased monotonically as the drive voltage was decreased but then remained small and constant as the drive voltage was increased again. The US velocity change at low T was negative with respect to the high-T (400 mK) value, contrary to the positive sign expected from the known variation in the shear modulus. In a 20 ppm 3He sample, both the US and TO anomalies shifted to 150 mK. The amplitude dependence and hysteresis of US attenuation were related to pinning of dislocations by 3He impurities, and nonlinear spatial variations of the amplitude of US pulses were derived.
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Elsayed M.E. Zayed
2016-02-01
Full Text Available In this article, the modified extended tanh-function method is employed to solve fractional partial differential equations in the sense of the modified Riemann–Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into nonlinear ordinary differential equations of integer orders. For illustrating the validity of this method, we apply it to four nonlinear equations namely, the space–time fractional generalized nonlinear Hirota–Satsuma coupled KdV equations, the space–time fractional nonlinear Whitham–Broer–Kaup equations, the space–time fractional nonlinear coupled Burgers equations and the space–time fractional nonlinear coupled mKdV equations.
Murrell, J K J
2001-01-01
previously unexplored regions of parameter space. We show that these calculations predict a range of previously unreported dynamical I-V characterises for SQUID rings in the strongly hysteretic regime. Finally, we present the successful realisation of a novel experimental technique that permits the weak link of a SQUID to be probed independently of the associated ring structure by mechanically opening and closing the ring. We demonstrate that this process can be completed during the same experimental run without the need for warming and re-cooling of the sample. This thesis is concerned with the investigation of the non-linear behaviour of a Superconducting Quantum Interference Device (SQUID) coupled to a RF tank circuit. We consider two regimes, one where the underlying SQUID behaviour is non-hysteretic with respect to an externally applied magnetic flux, and the other where hysteretic (dissipative) behaviour is observed. We show that, by following non-linearities induced in the tank circuit response, the un...
Nourifar, Mostafa; Sani, Ahmad Aftabi; Keyhani, Ali
2017-12-01
In this paper, we suggest an efficient method, based on the well-known multi-step differential transform method to considerably reduce the number of arithmetic operations of differential transform method. The proposed method is heavily depended on the solution of two nonlinear systems which are exactly solved and the closed-form expressions are derived, fortunately. The present method is suitable for solving the governing equations of oscillatory systems. This fact is thoroughly shown by several nonlinear numerical examples. Moreover, the number of arithmetic operations is calculated for all methods implemented in the article, i.e., the proposed method and two previous methods, and it is clearly illustrated that the present method is really efficient.
Donoso, Guillermo; Ladera, Celso L.
2012-01-01
We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…
Zayed, Elsayed M.E.; Amer, Yasser A.; Shohib, Reham M.A.
2016-01-01
In this article, the modified extended tanh-function method is employed to solve fractional partial differential equations in the sense of the modified Riemann–Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into nonlinear ordinary differential equations of integer orders. For illustrating the validity of this method, we apply it to four nonlinear equations namely, the space–time fractional generaliz...
An Acoustic Levitation Technique for the Study of Nonlinear Oscillations of Gas Bubbles in Liquids.
1983-08-15
a small bubble. On occasion, a hypodermic needle was used. The introduction of objects into the liquid required care to avoid disturbing the fluid...pressure gradient to the acoustic pressure gradient. These values’were then compared to a nonlinear theory . Results were very much * I in agreement except...for the region near the’ n=2 harmonic. An explanation -- for the discrepancy between theory and experiment appears to lie in the polytropic exponent
Płociniczak, Łukasz; Świtała, Mateusz
2018-01-01
In this paper we analyse a singular second-order nonlinear ODE which models the capillary rise of a fluid inside a tubular column. We prove global existence, uniqueness and find several approximations along with the asymptotic behaviour of the solution. Moreover, we are able to find a critical value of the nondimensional parameter for which the solution exhibits a transition in its behaviour: from being monotone to oscillatory. This is an analytical rigorous proof of the experimentally and numerically confirmed phenomenon.
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seyd ghasem enayati
2017-01-01
Full Text Available In this paper, two powerful analytical methods known as modified homotopy perturbation method and Amplitude Frequency Formulation called respectively MHPM and AFF, are introduced to derive approximate solutions of a system of ordinary differential equations appear in mechanical applications. These methods convert a difficult problem into a simple one, which can be easily handled. The obtained solutions are compared with numerical fourth order runge-kutta method to show the applicability and accuracy of both MHPM and AFF in solving this sample problem. The results attained in this paper confirm the idea that MHPM and AFF are powerful mathematical tools and they can be applied to linear and nonlinear problems.
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Janaina A. M. Pereira
2007-06-01
Full Text Available Simulations have been carried out on the bromate - oxalic acid - Ce(IV - acetone oscillating reaction, under flow conditions, using Field and Boyd's model (J. Phys. Chem. 1985, 89, 3707. Many different complex dynamic behaviors were found, including simple periodic oscillations, complex periodic oscillations, quasiperiodicity and chaos. Some of these complex oscillations can be understood as belonging to a Farey sequence. The many different behaviors were systematized in a phase diagram which shows that some regions of complex patterns were nested with one inside the other. The existence of almost all known dynamic behavior for this system allows the suggestion that it can be used as a model for some very complex phenomena that occur in biological systems.
An acoustic levitation technique for the study of nonlinear oscillations of gas bubbles in liquids
Young, D. A.; Crum, L. A.
1983-08-01
A technique of acoustic levitation was developed for the study of individual gas bubbles in a liquid. Isopropyl alcohol and a mixture of glycerine and water (33-1/3% glycerine by volume) were the two liquids used in this research. Bubbles were levitated near the acoustic pressure antinode of an acoustic wave in the range of 20-22 kHz. Measurements were made of the levitation number as a function of the normalized radius of the bubbles. The levitation number is the ratio of the hydrostatic pressure gradient to the acoustic pressure gradient. These values were then compared to a nonlinear theory. Results were very much in agreement except for the region near the n=2 harmonic. An explanation for the discrepancy between theory and experiment appears to lie in the polytropic exponent associated with the gas in the interior of the bubble.
Malfense Fierro, Gian Piero; Meo, Michele
2017-02-01
Recently, there has been high interest in the capabilities of nonlinear ultrasound techniques for damage/defect detection as these techniques have been shown to be quite accurate in imaging some particular type of damage. This paper presents a Constructive Nonlinear Array (CNA) method, for the detection and imaging of material defects/damage in a complex composite stiffened panel. CNA requires the construction of an ultrasound array in a similar manner to standard phased arrays systems, which require multiple transmitting and receiving elements. The method constructively phase-match multiple captured signals at a particular position given multiple transmit positions, similar to the total focusing method (TFM) method. Unlike most of the ultrasonic linear techniques, a longer excitation signal was used to achieve a steady-state excitation at each capturing position, so that compressive and tensile stress at defect/crack locations increases the likelihood of the generation of nonlinear elastic waves. Moreover, the technique allows the reduction of instrumentation nonlinear wave generation by relying on signal attenuation to naturally filter these errors. Experimental tests were carried out on a stiffened panel with manufacturing defects. Standard industrial linear ultrasonic test were carried out for comparison. The proposed new method allows to image damages/defects in a reliable and reproducible manner and overcomes some of the main limitations of nonlinear ultrasound techniques. In particular, the effectiveness and robustness of CNA and the advantages over linear ultrasonic were clearly demonstrated allowing a better resolution and imaging of complex and realistic flaws. Copyright Â© 2016 Elsevier B.V. All rights reserved.
2012-01-01
Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with
Chen, Bor-Sen; Hsu, Chih-Yuan
2012-10-26
Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI
Directory of Open Access Journals (Sweden)
Chen Bor-Sen
2012-10-01
Full Text Available Abstract Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI. We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI-based design problem
Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.
2017-11-01
An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜3 weeks.
Oscillating potential well in the complex plane and the adiabatic theorem
Longhi, Stefano
2017-10-01
A quantum particle in a slowly changing potential well V (x ,t ) =V ( x -x0(ɛ t ) ) , periodically shaken in time at a slow frequency ɛ , provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than ˜1 /ɛ . Specifically, we consider a double-well potential V (x ) sustaining two bound states spaced in frequency by ω0 and periodically shaken in a complex plane. Two different spatial displacements x0(t ) are assumed: the real spatial displacement x0(ɛ t ) =A sin(ɛ t ) , corresponding to ordinary Hermitian shaking, and the complex one x0(ɛ t ) =A -A exp(-i ɛ t ) , corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency ɛ is close to an odd resonance of ω0. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasienergies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasienergy crossing.
Energy Technology Data Exchange (ETDEWEB)
Zhang Huiqun [College of Mathematical Science, Qingdao University, Qingdao, Shandong 266071 (China)], E-mail: hellozhq@yahoo.com.cn
2009-02-15
By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.
Directory of Open Access Journals (Sweden)
Parovik Roman I.
2016-09-01
Full Text Available The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.
Cole-Hopf-like transformation for Schroedinger equations containing complex nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Kaniadakis, G.; Scarfone, A.M. [Dipartimento di Fisica, Politecnico di Torino, Torino (Italy) and Istituto Nazionale di Fisica della Materia, Unita del Politecnico di Torino, Torino (Italy)]. E-mails: kaniadakis@polito.it; scarfone@polito.it
2002-03-01
We consider systems which conserve the particle number and are described by Schroedinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf-like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature. (author)
Berczynski, Pawel
2013-12-01
In this paper complex geometrical optics (CGO) is applied to spatiotemporal evolution of 2D Gaussian wavepackets in nonlinear media of Kerr type. Instead of solving the commonly accepted nonlinear Schrödinger equation (NLS), we propose equations of geometrical optics: a complex eikonal equation and a complex transport equation. The eikonal equation lets us derive immediately the ordinary differential equations for spatial and temporal widths, omitting in this way the complicated variational process used in nonlinear optics. Moreover, the obtained CGO equations for actual spatial and temporal widths happen to be identical to those obtained by the variational method approach. From the transport equation we obtain the first order ordinary differential equation for complex amplitude evolution and the conservation principle for energy flux in the packet cross-section. For the combined effect of diffraction, anomalous dispersion and nonlinear refraction, we observe three types of solution for temporal and spatial widths of the packet propagating in a nonlinear medium of Kerr type: the diffraction/dispersion widening, the stationary solution and the solution under the effect of the spatiotemporal collapse. Moreover, we discuss the evolution of the 2D Gaussian wavepacket in a nonlinear inhomogeneous waveguide and we present conditions for stable propagation without the collapse effect. Under these conditions the wavepacket asymptotically approaches stationary solutions when the parameters of the waveguide change over the propagation distance. The paper also discusses the influence of initial spatial and temporal chirps on Gaussian wavepacket evolution in nonlinear media of Kerr type and in nonlinear inhomogeneous waveguides. Moreover, we notice that the equations for temporal and spatial widths of the 2D wavepacket have the same structure as the equations for the evolution of the elliptical Gaussian beam. Thus, the description of the 2D spatiotemporal wavepacket can be
Maccari, Attilio
2000-10-01
A weakly nonlinear Lorentz invariant complex field model in 3+1 dimensions is studied by an asymptotic perturbation method, based on Fourier expansion and spatio-temporal rescaling. It is shown that a nonlinear system of partial differential equations describes oscillation amplitudes of Fourier modes. This system is C-integrable, i.e., can be linearized through a suitable transformation of the dependent and independent variables. We resolve the Cauchy problem and demonstrate that localized nondispersive waves (envelope solitons) with finite energy exist under appropriate initial conditions. These particle-like solutions propagate with the group velocity of their carrier wave. During a collision solitons maintain their shape, because the only change is a phase shift. Energy E and momentum p of solitons are identical to those of a relativistic particle. If the Planck constant is connected to the spatial dimension of the envelope soliton, then we obtain at the lowest order of approximation the quantum relations E=ℏ ω, λ= h/ p, where λ and ω are wavelength and frequency of the carrier wave. This work represents a possible way to achieve the Einstein-de Broglie soliton-particle concept.
Nonlinear Phenomena in Complex Systems: From Nano to Macro Scale
Stanley, H
2014-01-01
Topics of complex system physics and their interdisciplinary applications to different problems in seismology, biology, economy, sociology, energy and nanotechnology are covered in this new work from renowned experts in their fields. In particular, contributed papers contain original results on network science, earthquake dynamics, econophysics, sociophysics, nanoscience and biological physics. Most of the papers use interdisciplinary approaches based on statistical physics, quantum physics and other topics of complex system physics. Papers on econophysics and sociophysics are focussed on societal aspects of physics such as, opinion dynamics, public debates and financial and economic stability. This work will be of interest to statistical physicists, economists, biologists, seismologists and all scientists working in interdisciplinary topics of complexity.
Siu-Siu, Guo; Qingxuan, Shi
2017-03-01
In this paper, single-degree-of-freedom (SDOF) systems combined to Gaussian white noise and Gaussian/non-Gaussian colored noise excitations are investigated. By expressing colored noise excitation as a second-order filtered white noise process and introducing colored noise as an additional state variable, the equation of motion for SDOF system under colored noise is then transferred artificially to multi-degree-of-freedom (MDOF) system under white noise excitations with four-coupled first-order differential equations. As a consequence, corresponding Fokker-Planck-Kolmogorov (FPK) equation governing the joint probabilistic density function (PDF) of state variables increases to 4-dimension (4-D). Solution procedure and computer programme become much more sophisticated. The exponential-polynomial closure (EPC) method, widely applied for cases of SDOF systems under white noise excitations, is developed and improved for cases of systems under colored noise excitations and for solving the complex 4-D FPK equation. On the other hand, Monte Carlo simulation (MCS) method is performed to test the approximate EPC solutions. Two examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Corresponding band-limited power spectral densities (PSDs) for colored noise excitations are separately given. Numerical studies show that the developed EPC method provides relatively accurate estimates of the stationary probabilistic solutions, especially the ones in the tail regions of the PDFs. Moreover, statistical parameter of mean-up crossing rate (MCR) is taken into account, which is important for reliability and failure analysis. Hopefully, our present work could provide insights into the investigation of structures under random loadings.
Nonlinear mapping methods with adjustable computational complexity for hyperspectral image analysis
Myasnikov, E. V.
2015-12-01
Nonlinear mapping (Sammon mapping) is a well-known dimensionality reduction technique. Recently several nonlinear mapping methods with reduced computational complexity have been proposed but they do not provide a flexible control over a computational complexity. In this paper a nonlinear mapping method with adjustable computational complexity is proposed. The proposed method is based on the hierarchical decomposition of the multidimensional space, priority queues, and simple optimization procedure to provide fast and flexible dimensionality reduction process. The proposed method is compared to an alternative one based on stochastic optimization. The experiments are carried out on well-known hyperspectral images. Studied methods are evaluated in terms of the data mapping error and runtime. Experimental results for both two- and three-dimensional output spaces are presented.
Hu, Eric Y; Bouteiller, Jean-Marie C; Song, Dong; Baudry, Michel; Berger, Theodore W
2015-01-01
Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.
Liao, Fuyuan; O'Brien, William D.; Jan, Yih-Kuen
2013-10-01
The objective of this study was to investigate the effects of local heating on the complexity of skin blood flow oscillations (BFO) under prolonged surface pressure in rats. Eleven Sprague-Dawley rats were studied: 7 rats underwent surface pressure with local heating (△t=10 °C) and 4 rats underwent pressure without heating. A pressure of 700 mmHg was applied to the right trochanter area of rats for 3 h. Skin blood flow was measured using laser Doppler flowmetry. The loading period was divided into nonoverlapping 30 min epochs. For each epoch, multifractal detrended fluctuation analysis (MDFA) was utilized to compute DFA coefficients and complexity of endothelial related metabolic, neurogenic, and myogenic frequencies of BFO. The results showed that under surface pressure, local heating led to a significant decrease in DFA coefficients of myogenic frequency during the initial epoch of loading period, a sustained decrease in complexity of myogenic frequency, and a significantly higher degree of complexity of metabolic frequency during the later phase of loading period. Surrogate tests showed that the reduction in complexity of myogenic frequency was associated with a loss of nonlinearity whereas increased complexity of metabolic frequency was associated with enhanced nonlinearity. Our results indicate that increased metabolic activity and decreased myogenic response due to local heating manifest themselves not only in magnitudes of metabolic and myogenic frequencies but also in their structural complexity. This study demonstrates the feasibility of using complexity analysis of BFO to monitor the ischemic status of weight-bearing skin and risk of pressure ulcers.
Complex hyperbolic-function method and its applications to nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Bai Chenglin [School of Physics Science and Information Engineering, Liaocheng University, Shandong 252059 (China); Zhao Hong [School of Physics Science and Information Engineering, Liaocheng University, Shandong 252059 (China)]. E-mail: lcced_bcl@hotmail.com
2006-06-19
Based on computerized symbolic computation, a complex hyperbolic-function method is proposed for the general nonlinear equations of mathematical physics in a unified way. In this method, we assume that exact solutions for a given general nonlinear equations be the superposition of different powers of the sech-function, tanh-function and/or their combinations. After finishing some direct calculations, we can finally obtain the exact solutions expressed by the complex hyperbolic function. The characteristic feature of this method is that we can derive exact solutions to the general nonlinear equations directly without transformation. Some illustrative equations, such as the (1+1)-dimensional coupled Schrodinger-KdV equation (2+1)-dimensional Davey-Stewartson equation and Hirota-Maccari equation, are investigated by this means and new exact solutions are found.
Complex hyperbolic-function method and its applications to nonlinear equations
Bai, Cheng-Lin; Zhao, Hong
2006-06-01
Based on computerized symbolic computation, a complex hyperbolic-function method is proposed for the general nonlinear equations of mathematical physics in a unified way. In this method, we assume that exact solutions for a given general nonlinear equations be the superposition of different powers of the sech-function, tanh-function and/or their combinations. After finishing some direct calculations, we can finally obtain the exact solutions expressed by the complex hyperbolic function. The characteristic feature of this method is that we can derive exact solutions to the general nonlinear equations directly without transformation. Some illustrative equations, such as the (1+1)-dimensional coupled Schrödinger KdV equation, (2+1)-dimensional Davey Stewartson equation and Hirota Maccari equation, are investigated by this means and new exact solutions are found.
Bifurcation and Nonlinear Oscillations.
1980-09-28
Structural stability and bifurcation theory. pp. 549-560 in Dinamical Systems (Ed. MI. Peixoto), Academic Press, 1973. [211 J. Sotomayor, Generic one...the specific structure of the bifurcation near the homo- clinic orbit. Near the Hopf bifurcation, our results could also be obtained from known...on U which maps orbits of f onto orbits of g preserving the sense of time. An f E9 is structurally stable if there is a neighborhood U of f such that
Colpitts Chaotic Oscillator Coupling with a Generalized Memristor
Directory of Open Access Journals (Sweden)
Ling Lu
2015-01-01
Full Text Available By introducing a generalized memristor into a fourth-order Colpitts chaotic oscillator, a new memristive Colpitts chaotic oscillator is proposed in this paper. The generalized memristor is equivalent to a diode bridge cascaded with a first-order parallel RC filter. Chaotic attractors of the oscillator are numerically revealed from the mathematical model and experimentally captured from the physical circuit. The dynamics of the memristive Colpitts chaotic oscillator is investigated both theoretically and numerically, from which it can be found that the oscillator has a unique equilibrium point and displays complex nonlinear phenomena.
Donges, Jonathan F; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V; Marwan, Norbert; Dijkstra, Henk A; Kurths, Jürgen
2015-01-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence qua...
Molz, F. J.; Faybishenko, B.; Jenkins, E. W.
2012-12-01
Mass and energy fluxes within the soil-plant-atmosphere continuum are highly coupled and inherently nonlinear. The main focus of this presentation is to demonstrate the results of numerical modeling of a system of 4 coupled, nonlinear ordinary differential equations (ODEs), which are used to describe the long-term, rhizosphere processes of soil microbial dynamics, including the competition between nitrogen-fixing bacteria and those unable to fix nitrogen, along with substrate concentration (nutrient supply) and oxygen concentration. Modeling results demonstrate the synchronized patterns of temporal oscillations of competing microbial populations, which are affected by carbon and oxygen concentrations. The temporal dynamics and amplitude of the root exudation process serve as a driving force for microbial and geochemical phenomena, and lead to the development of the Gompetzian dynamics, synchronized oscillations, and phase-space attractors of microbial populations and carbon and oxygen concentrations. The nonlinear dynamic analysis of time series concentrations from the solution of the ODEs was used to identify several types of phase-space attractors, which appear to be dependent on the parameters of the exudation function and Monod kinetic parameters. This phase space analysis was conducted by means of assessing the global and local embedding dimensions, correlation time, capacity and correlation dimensions, and Lyapunov exponents of the calculated model variables defining the phase space. Such results can be used for planning experimental and theoretical studies of biogeochemical processes in the fields of plant nutrition, phyto- and bio-remediation, and other ecological areas.
Data based identification and prediction of nonlinear and complex dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Wang, Wen-Xu [School of Systems Science, Beijing Normal University, Beijing, 100875 (China); Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Lai, Ying-Cheng, E-mail: Ying-Cheng.Lai@asu.edu [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States); Department of Physics, Arizona State University, Tempe, AZ 85287 (United States); Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom); Grebogi, Celso [Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom)
2016-07-12
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear
Data based identification and prediction of nonlinear and complex dynamical systems
Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso
2016-07-01
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical
Energy Technology Data Exchange (ETDEWEB)
Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)] [Instituto Universitario de Fisica Aplicada a las Ciencias y las Tecnologias, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Rodes, J.J. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fuentes, R.; Pascual, I. [Instituto Universitario de Fisica Aplicada a las Ciencias y las Tecnologias, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)] [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-11-09
In a previous short communication [A. Belendez, E. Fernandez, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.
A memristor-based third-order oscillator: beyond oscillation
Talukdar, A.; Radwan, A. G.; Salama, K. N.
2011-09-01
This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.
A memristor-based third-order oscillator: beyond oscillation
Talukdar, Abdul Hafiz Ibne
2012-10-06
This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.
CIME school “Fully Nonlinear PDEs in Real and Complex Geometry and Optics”
Capogna, Luca; Gutiérrez, Cristian E; Montanari, Annamaria
2014-01-01
The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari.
Complex {PT}-symmetric extensions of the nonlinear ultra-short light pulse model
Yan, Zhenya
2012-11-01
The short pulse equation u_{xt}=u+\\frac{1}{2}(u^2u_x)_x is PT symmetric, which arises in nonlinear optics for the ultra-short pulse case. We present a family of new complex PT-symmetric extensions of the short pulse equation, i[(iu_x)^{\\sigma }]_t=au+bu^m+ic[u^n(iu_x)^{\\epsilon }]_x \\,\\, (\\sigma ,\\, \\epsilon ,\\,a,\\,b,\\,c,\\,m,\\,n \\in {R}), based on the complex PT-symmetric extension principle. Some properties of these equations with some chosen parameters are studied including the Hamiltonian structures and exact solutions such as solitary wave solutions, doubly periodic wave solutions and compacton solutions. Our results may be useful to understand complex PT-symmetric nonlinear physical models. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Norris, G; McConnell, G
2010-03-01
A novel bi-directional pump geometry that nonlinearly increases the nonlinear optical conversion efficiency of a synchronously pumped optical parametric oscillator (OPO) is reported. This bi-directional pumping method synchronizes the circulating signal pulse with two counter-propagating pump pulses within a linear OPO resonator. Through this pump scheme, an increase in nonlinear optical conversion efficiency of 22% was achieved at the signal wavelength, corresponding to a 95% overall increase in average power. Given an almost unchanged measured pulse duration of 260 fs under optimal performance conditions, this related to a signal wavelength peak power output of 18.8 kW, compared with 10 kW using the traditional single-pass geometry. In this study, a total effective peak intensity pump-field of 7.11 GW/cm(2) (corresponding to 3.55 GW/cm(2) from each pump beam) was applied to a 3 mm long periodically poled lithium niobate crystal, which had a damage threshold intensity of 4 GW/cm(2), without impairing crystal integrity. We therefore prove the application of this novel pump geometry provides opportunities for power-scaling of synchronously pumped OPO systems together with enhanced nonlinear conversion efficiency through relaxed damage threshold intensity conditions.
Manjunatha, K. B.; Rajarao, Ravindra; Umesh, G.; Ramachandra Bhat, B.; Poornesh, P.
2017-10-01
We report the nonlinear optical properties of Ruthenium metal complex a promising organic material for use in scientific and technological applications. The thin films of newly synthesized ruthenium metal-organic complex were fabricated using spin coating technique. Z-scan and degenerate four wave mixing (DFWM) techniques used to extract the third-order nonlinear optical (NLO) parameters. The data reveals the investigated material exhibited relatively large NLO properties. The pump-probe experiments shows that the switch-on and off times of the material were in the order of μs at different pump intensities and the energy dependent transmission studies reveal good limiting property of the material in nanosecond regime.
The colpitts oscillator family
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
A tutorial study of the Colpitts oscillator family defined as all oscillators based on a nonlinear amplifier and a three- terminal linear resonance circuit with one coil and two capacitors. The original patents are investigated. The eigenvalues of the linearized Jacobian for oscillators based...
Blaise, Paul
2011-01-01
An invaluable reference for an overall but simple approach to the complexity of quantum mechanics viewed through quantum oscillators Quantum oscillators play a fundamental role in many areas of physics; for instance, in chemical physics with molecular normal modes, in solid state physics with phonons, and in quantum theory of light with photons. Quantum Oscillators is a timely and visionary book which presents these intricate topics, broadly covering the properties of quantum oscillators which are usually dispersed in the literature at varying levels of detail and often combined with other p
Non-linear dynamic complexity of the human EEG during meditation.
Aftanas, L I; Golocheikine, S A
2002-09-20
We used non-linear analysis to investigate the dynamical properties underlying the EEG in the model of Sahaja Yoga meditation. Non-linear dimensional complexity (DCx) estimates, indicating complexity of neuronal computations, were analyzed in 20 experienced meditators during rest and meditation using 62-channel EEG. When compared to rest, the meditation was accompanied by a focused decrease of DCx estimates over midline frontal and central regions. By contrast, additionally computed linear measures exhibited the opposite direction of changes: power in the theta-1 (4-6 Hz), theta-2 (6-8 Hz) and alpha-1 (8-10 Hz) frequency bands was increased over these regions. The DCx estimates negatively correlated with theta-2 and alpha-1 and positively with beta-3 (22-30 Hz) band power. It is suggested that meditative experience, characterized by less complex dynamics of the EEG, involves 'switching off' irrelevant networks for the maintenance of focused internalized attention and inhibition of inappropriate information. Overall, the results point to the idea that dynamically changing inner experience during meditation is better indexed by a combination of non-linear and linear EEG variables.
Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators
Directory of Open Access Journals (Sweden)
Gerold Baier
1997-01-01
Full Text Available We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. The systems involved are: (a a two-variable oscillator with two consecutive autocatalytic reactions derived from the Lotka–Volterra scheme; (b a minimal two-variable oscillator with one first-order autocatalytic reaction; (c a three-variable oscillator with first-order feedback lacking autocatalysis. The dynamics of a finite number of coupled biochemical oscillators may account for complex patterns in compartmentalized living systems like cells or tissue, and may be tested experimentally in coupled microreactors.
Directory of Open Access Journals (Sweden)
Zhe Zhang
2014-06-01
Full Text Available Purpose: The aim of this paper is to deal with the supply chain management (SCM with quantity discount policy under the complex fuzzy environment, which is characterized as the bi-fuzzy variables. By taking into account the strategy and the process of decision making, a bi-fuzzy nonlinear multiple objective decision making (MODM model is presented to solve the proposed problem.Design/methodology/approach: The bi-fuzzy variables in the MODM model are transformed into the trapezoidal fuzzy variables by the DMs's degree of optimism ?1 and ?2, which are de-fuzzified by the expected value index subsequently. For solving the complex nonlinear model, a multi-objective adaptive particle swarm optimization algorithm (MO-APSO is designed as the solution method.Findings: The proposed model and algorithm are applied to a typical example of SCM problem to illustrate the effectiveness. Based on the sensitivity analysis of the results, the bi-fuzzy nonlinear MODM SCM model is proved to be sensitive to the possibility level ?1.Practical implications: The study focuses on the SCM under complex fuzzy environment in SCM, which has a great practical significance. Therefore, the bi-fuzzy MODM model and MO-APSO can be further applied in SCM problem with quantity discount policy.Originality/value: The bi-fuzzy variable is employed in the nonlinear MODM model of SCM to characterize the hybrid uncertain environment, and this work is original. In addition, the hybrid crisp approach is proposed to transferred to model to an equivalent crisp one by the DMs's degree of optimism and the expected value index. Since the MODM model consider the bi-fuzzy environment and quantity discount policy, so this paper has a great practical significance.
Donges, Jonathan; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik; Marwan, Norbert; Dijkstra, Henk; Kurths, Jürgen
2016-04-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. pyunicorn is available online at https://github.com/pik-copan/pyunicorn. Reference: J.F. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q.-Y. Feng, L. Tupikina, V. Stolbova, R.V. Donner, N. Marwan, H.A. Dijkstra, and J. Kurths, Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos 25, 113101 (2015), DOI: 10.1063/1.4934554, Preprint: arxiv.org:1507.01571 [physics.data-an].
Nonlinear complexity behaviors of agent-based 3D Potts financial dynamics with random environments
Xing, Yani; Wang, Jun
2018-02-01
A new microscopic 3D Potts interaction financial price model is established in this work, to investigate the nonlinear complexity behaviors of stock markets. 3D Potts model, which extends the 2D Potts model to three-dimensional, is a cubic lattice model to explain the interaction behavior among the agents. In order to explore the complexity of real financial markets and the 3D Potts financial model, a new random coarse-grained Lempel-Ziv complexity is proposed to certain series, such as the price returns, the price volatilities, and the random time d-returns. Then the composite multiscale entropy (CMSE) method is applied to the intrinsic mode functions (IMFs) and the corresponding shuffled data to study the complexity behaviors. The empirical results indicate that the 3D financial model is feasible.
GPU simulation of nonlinear propagation of dual band ultrasound pulse complexes
Energy Technology Data Exchange (ETDEWEB)
Kvam, Johannes, E-mail: johannes.kvam@ntnu.no; Angelsen, Bjørn A. J., E-mail: bjorn.angelsen@ntnu.no [NTNU, Department of Circulation and Medical Imaging, 7491 Trondheim (Norway); Elster, Anne C., E-mail: elster@ntnu.no [NTNU, Department of Computer and Information Science, 7491 Trondheim (Norway)
2015-10-28
In a new method of ultrasound imaging, called SURF imaging, dual band pulse complexes composed of overlapping low frequency (LF) and high frequency (HF) pulses are transmitted, where the frequency ratio LF:HF ∼ 1 : 20, and the relative bandwidth of both pulses are ∼ 50 − 70%. The LF pulse length is hence ∼ 20 times the HF pulse length. The LF pulse is used to nonlinearly manipulate the material elasticity observed by the co-propagating HF pulse. This produces nonlinear interaction effects that give more information on the propagation of the pulse complex. Due to the large difference in frequency and pulse length between the LF and the HF pulses, we have developed a dual level simulation where the LF pulse propagation is first simulated independent of the HF pulse, using a temporal sampling frequency matched to the LF pulse. A separate equation for the HF pulse is developed, where the the presimulated LF pulse modifies the propagation velocity. The equations are adapted to parallel processing in a GPU, where nonlinear simulations of a typical HF beam of 10 MHz down to 40 mm is done in ∼ 2 secs in a standard GPU. This simulation is hence very useful for studying the manipulation effect of the LF pulse on the HF pulse.
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 ...
Directory of Open Access Journals (Sweden)
Qinming Liu
2012-01-01
Full Text Available Health management for a complex nonlinear system is becoming more important for condition-based maintenance and minimizing the related risks and costs over its entire life. However, a complex nonlinear system often operates under dynamically operational and environmental conditions, and it subjects to high levels of uncertainty and unpredictability so that effective methods for online health management are still few now. This paper combines hidden semi-Markov model (HSMM with sequential Monte Carlo (SMC methods. HSMM is used to obtain the transition probabilities among health states and health state durations of a complex nonlinear system, while the SMC method is adopted to decrease the computational and space complexity, and describe the probability relationships between multiple health states and monitored observations of a complex nonlinear system. This paper proposes a novel method of multisteps ahead health recognition based on joint probability distribution for health management of a complex nonlinear system. Moreover, a new online health prognostic method is developed. A real case study is used to demonstrate the implementation and potential applications of the proposed methods for online health management of complex nonlinear systems.
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
Directory of Open Access Journals (Sweden)
José F. Cariñena
2007-02-01
Full Text Available Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant curvature, the deformation parameter being related with the curvature. In this sense these systems are to be considered as a harmonic oscillator and a Smorodinsky-Winternitz system in such bi-dimensional spaces of constant curvature. The quantization of the first system will be carried out and it is shown that it is super-solvable in the sense that the Schrödinger equation reduces, in three different coordinate systems, to two separate equations involving only one degree of freedom.
Liu, Yang; Wang, Chao; Luo, Daping; Yang, Chao; Li, Jiang; Ge, Lin; Pan, Yubai; Li, Wenxue
2017-12-01
We demonstrate the passively mode-locked laser performances of bulk Yb:YAG ceramic prepared by non-aqueous tape casting, which generates initial pulses in temporal width of 3 ps and spectrum width of 3 nm without intra-cavity dispersion management. The ceramic laser is further used as seeding oscillator in a fiber nonlinear amplification system, where ultrashort pulses in maximum output power of ∼100 W and pulse duration of 70 fs are achieved. Moreover, the laser spectrum is broadened to be ∼41 nm due to self-phase modulation effects in the gain fiber, overcoming the narrow spectrum limitations of ceramic materials. Our approach opens a new avenue for power-scaling and spectrum-expanding of femtosecond ceramic lasers.
NATO Advanced Research Workshop on Recent advances in Nonlinear Dynamics and Complex System Physics
Casati, Giulio; Complex Phenomena in Nanoscale Systems
2009-01-01
Nanoscale physics has become one of the rapidly developing areas of contemporary physics because of its direct relevance to newly emerging area, nanotechnologies. Nanoscale devices and quantum functional materials are usually constructed based on the results of fundamental studies on nanoscale physics. Therefore studying physical phenomena in nanosized systems is of importance for progressive development of nanotechnologies. In this context study of complex phenomena in such systems and using them for controlling purposes is of great practical importance. Namely, such studies are brought together in this book, which contains 27 papers on various aspects of nanoscale physics and nonlinear dynamics.
Fan, Yuanpeng; Zhao, Jingyi; Yan, Qifan; Chen, Peng R; Zhao, Dahui
2014-03-12
Two water-soluble triscyclometalated organoiridium complexes, 1 and 2, with polar side chains that form nanoparticles emitting bright-red phosphorescence in water were synthesized. The optimal emitting properties are related to both the triscyclometalated structure and nanoparticle-forming ability in aqueous solution. Nonlinear optical properties are also observed with the nanoparticles. Because of their proper cellular uptake in addition to high emission brightness and effective two-photon absorbing ability, cell imaging can be achieved with nanoparticles of 2 bearing quaternary ammonium side chains at ultra-low effective concentrations using NIR incident light via the multiphoton excitation phosphorescence process.
Nonlinearity, coherence and complexity: Biophysical aspects related to health and disease.
Foletti, Alberto; Brizhik, Larissa
2017-01-01
Biological organisms are complex open dissipative systems whose dynamical stability is sustained due to the exchange of matter, energy and information. Dynamical stability occurs through a number of mechanisms that sustain efficient adaptive dynamics. Such properties of living matter can be the consequence of a self-consistent state of matter and electromagnetic field (EMF). Based on the soliton model of charge transport in redox processes, we describe a possible mechanism of the origin of endogenous EMF and coherence. Solitons are formed in polypeptides due to electron-lattice interaction. Solitons experience periodical potential barrier, as a result of which their velocity oscillates in time, and, hence, they emit electromagnetic radiation (EMR). Under the effect of such radiation from all other solitons, the synchronization of their dynamics takes place, which significantly increases the intensity of the general EMF. The complex structure of biological molecules, such as helical structure, is not only important for "structure-function" relations, but also the source of the stability of biophysical processes, e.g. effectiveness of energy and charge transport on macroscopic distances. Such a complex structure also provides the framework for the spatiotemporal structure of the endogenous EMF. The highly hierarchical organization of living organisms is a manifestation of their complexity, even at the level of simple unicellular organisms. This complexity increases the dynamical stability of open systems and enhances the possibility of information storage and processing. Our findings provide a qualitative overview of a possible biophysical mechanism that supports health and disease adaptive dynamics.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, C.; Gallego, S.; Ortuno, M.; Neipp, C. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-11-26
A modified He's homotopy perturbation method (HHPM) is used to calculate the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x{sup 1/3}. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified HHPM works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 0.6% for small and large values of oscillation amplitude, while this relative error is 0.17% for the second iteration and as low as 0.024% when the third approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that the former is very effective and convenient.
Nature's Autonomous Oscillators
Mayr, H. G.; Yee, J.-H.; Mayr, M.; Schnetzler, R.
2012-01-01
Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.
Nonlinear analysis of gas-water/oil-water two-phase flow in complex networks
Gao, Zhong-Ke; Wang, Wen-Xu
2014-01-01
Understanding the dynamics of multi-phase flows has been a challenge in the fields of nonlinear dynamics and fluid mechanics. This chapter reviews our work on two-phase flow dynamics in combination with complex network theory. We systematically carried out gas-water/oil-water two-phase flow experiments for measuring the time series of flow signals which is studied in terms of the mapping from time series to complex networks. Three network mapping methods were proposed for the analysis and identification of flow patterns, i.e. Flow Pattern Complex Network (FPCN), Fluid Dynamic Complex Network (FDCN) and Fluid Structure Complex Network (FSCN). Through detecting the community structure of FPCN based on K-means clustering, distinct flow patterns can be successfully distinguished and identified. A number of FDCN’s under different flow conditions were constructed in order to reveal the dynamical characteristics of two-phase flows. The FDCNs exhibit universal power-law degree distributions. The power-law exponent ...
Manjunatha, K. B.; Rajarao, Ravindra; Umesh, G.; Ramachandra Bhat, B.; Poornesh, P.
2017-08-01
A salen-based ruthenium (Ru) (II) complex was synthesized for possible use in nonlinear optical device applications. The Ru complex was doped in a polymer matrix to fabricate films using a low-cost spin-coating technique. The third-order nonlinear optical parameters of the complex were investigated by Z-scan and degenerate four-wave mixing techniques. The study reveals two-order enhancement of third-order optical susceptibility χ (3) and exhibits superior limiting capability due to a reverse saturable absorption process. All-optical switching action for the films indicates that the sample can function as an optical inverter or a NOT gate. Hence, the Ru (II) Schiff-base complex materializes as a possible candidate for use in nonlinear optical devices.
Modelling of Oscillations in Two-Dimensional Echo-Spectra of the Fenna-Matthews-Olson Complex
Hein, Birgit; Kramer, Tobias; Rodríguez, Mirta
2011-01-01
Recent experimental observations of time-dependent beatings in the two-dimensional echo-spectra of light-harvesting complexes at ambient temperatures have opened up the question whether coherence and wave-like behaviour plays a significant role in photosynthesis. We perform a numerical study of the absorption and echo-spectra of the Fenna-Matthews-Olson (FMO) complex in chlorobium tepidum and analyse the requirements in the theoretical model needed to reproduce beatings in the calculated spectra. The energy transfer in the FMO pigment-protein complex is theoretically described by an exciton Hamiltonian coupled to a phonon bath which account for the pigments electronic and vibrational excitations respectively. We use the hierarchical equations of motions method to treat the strong couplings in a non-perturbative way. We show that the oscillations in the two-dimensional echo-spectra persist in the presence of thermal noise and static disorder.
Directory of Open Access Journals (Sweden)
Pinar Deniz Tosun
2017-12-01
Full Text Available Specific patterns of brain activity during sleep and waking are recorded in the electroencephalogram (EEG. Time-frequency analysis methods have been widely used to analyse the EEG and identified characteristic oscillations for each vigilance state (VS, i.e., wakefulness, rapid-eye movement (REM and non-rapid-eye movement (NREM sleep. However, other aspects such as change of patterns associated with brain dynamics may not be captured unless a non-linear-based analysis method is used. In this pilot study, Permutation Lempel–Ziv complexity (PLZC, a novel symbolic dynamics analysis method, was used to characterise the changes in the EEG in sleep and wakefulness during baseline and recovery from sleep deprivation (SD. The results obtained with PLZC were contrasted with a related non-linear method, Lempel–Ziv complexity (LZC. Both measure the emergence of new patterns. However, LZC is dependent on the absolute amplitude of the EEG, while PLZC is only dependent on the relative amplitude due to symbolisation procedure and thus, more resistant to noise. We showed that PLZC discriminates activated brain states associated with wakefulness and REM sleep, which both displayed higher complexity, compared to NREM sleep. Additionally, significantly lower PLZC values were measured in NREM sleep during the recovery period following SD compared to baseline, suggesting a reduced emergence of new activity patterns in the EEG. These findings were validated using PLZC on surrogate data. By contrast, LZC was merely reflecting changes in the spectral composition of the EEG. Overall, this study implies that PLZC is a robust non-linear complexity measure, which is not dependent on amplitude variations in the signal, and which may be useful to further assess EEG alterations induced by environmental or pharmacological manipulations.
Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank.
Directory of Open Access Journals (Sweden)
Marco Bardoscia
Full Text Available We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013.
DEFF Research Database (Denmark)
Hjorth, Poul G.
2008-01-01
We discuss nonlinear mechanical systems containing several oscillators whose frequecies are all much higher than frequencies associated with the remaining degrees of freedom. In this situation a near constant of the motion, an adiabatic invariant, exists which is the sum of all the oscillator...
Fanti, Luciano; Gori, Luca; Mammana, Cristiana; Michetti, Elisabetta
2016-09-01
In this article, we investigate the local and global dynamics of a nonlinear duopoly model with price-setting firms and managerial delegation contracts (relative profits). Our study aims at clarifying the effects of the interaction between the degree of product differentiation and the weight of manager's bonus on long-term outcomes in two different states: managers behave more aggressively with the rival (competition) under product complementarity and less aggressively with the rival (cooperation) under product substitutability. We combine analytical tools and numerical techniques to reach interesting results such as synchronisation and on-off intermittency of the state variables (in the case of homogeneous attitude of managers) and the existence of chaotic attractors, complex basins of attraction, and multistability (in the case of heterogeneous attitudes of managers). We also give policy insights.
Low-Complexity Tracking of Laser and Nonlinear Phase Noise in WDM Optical Fiber Systems
DEFF Research Database (Denmark)
Yankov, Metodi Plamenov; Fehenberger, Tobias; Barletta, Luca
2015-01-01
In this paper, the wavelength division multiplexed (WDM) fiber optic channel is considered. It is shown that for ideal distributed Raman amplification (IDRA), the Wiener process model is suitable for the non-linear phase noise due to cross phase modulation from neighboring channels. Based...... on this model, a phase noise tracking algorithm is presented. We approximate the distribution of the phase noise at each time instant by a mixture of Tikhonov distributions, and derive a closed form expression for the posterior probabilities of the input symbols. This reduces the complexity dramatically...... compared to previous trellis-based approaches, which require numerical integration. Further, the proposed method performs very well in low-to-moderate signal-to-noise ratio (SNR), where standard decision directed (DD) methods, especially for high-order modulation, fail. The proposed algorithm does not rely...
Pesenson, M.; Pesenson, I.; McCollum, B.; Byalsky, M.
2010-07-01
Data is now produced faster than it can be meaningfully analyzed. Many modern data sets present unprecedented analytical challenges, not merely because of their size but by their inherent complexity and information richness. Large numbers of astronomical objects now have dozens or hundreds of useful parameters describing each one. Traditional color-color plots using a limited number of symbols and some color-coding are clearly inadequate for finding all useful correlations given such large numbers of parameters. To capitalize on the opportunities provided by these data sets one needs to be able to organize, analyze and visualize them in fundamentally new ways. The identification and extraction of useful information in multiparametric, high-dimensional data sets - data mining - is greatly facilitated by finding simpler, that is, lower-dimensional abstract mathematical representations of the data sets that are more amenable to analysis. Dimensionality reduction consists of finding a lower-dimensional representation of high-dimensional data by constructing a set of basis functions that capture patterns intrinsic to a particular state space. Traditional methods of dimension reduction and pattern recognition often fail to work well when performed upon data sets as complex as those that now confront astronomy. We present here our developments of data compression, sampling, nonlinear dimensionality reduction, and clustering, which are important steps in the analysis of large-scale, complex datasets.
Directory of Open Access Journals (Sweden)
Syed Tauseef Mohyud-Din
2015-01-01
Full Text Available This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in Jumarie’s sense. The accuracy, efficiency, and convergence of the proposed technique are demonstrated through the numerical examples. It is observed that the presented coupling is an alternative approach to overcome the demerit of complex calculation of fractional differential equations. The proposed technique is independent of complexities arising in the calculation of Lagrange multipliers, Adomian’s polynomials, linearization, discretization, perturbation, and unrealistic assumptions and hence gives the solution in the form of convergent power series with elegantly computed components. All the examples show that the proposed combination is a powerful mathematical tool to solve other nonlinear equations also.
Directory of Open Access Journals (Sweden)
Eric eHu
2015-09-01
Full Text Available Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.
Multiple Coexisting Attractors and Hysteresis in the Generalized Ueda Oscillator
Directory of Open Access Journals (Sweden)
Kehui Sun
2013-01-01
Full Text Available A periodically forced nonlinear oscillator called the generalized Ueda oscillator is proposed. The restoring force term of this equation consists of a nonlinear function sgn(x and an absolute function with a variant power. Dynamics is investigated by detailed numerical analysis as well as dynamic simulation, including the largest Lyapunov exponent, phase diagrams, and bifurcation diagrams. Multiple coexisting attractors and complex hysteresis phenomenon are observed. The results show that this system has rich dynamical behaviors, and it has a promising application in the fields of science and engineering.
Banerjee R Control of partial synchronization in chaotic oscillators ...
Indian Academy of Sciences (India)
see Laha U. 555. Bose Indrani. Early signatures of regime shifts in complex dynamical systems. 193. Cari˜nena José F. Generalized virial theorem for the Liénard- type systems. 373. Carmel Vigila Bai G M ... On symmetry groups of a 2D nonlinear diffu- sion equation with source. 543. Cross M C. Building better oscillators ...
Energy Technology Data Exchange (ETDEWEB)
George Neil
2003-05-12
FEL Oscillators have been around since 1977 providing not only a test bed for the physics of Free Electron Lasers and electron/photon interactions but as a workhorse of scientific research. More than 30 FEL oscillators are presently operating around the world spanning a wavelength range from the mm region to the ultraviolet using DC and rf linear accelerators and storage rings as electron sources. The characteristics that have driven the development of these sources are the desire for high peak and average power, high micropulse energies, wavelength tunability, timing flexibility, and wavelengths that are unavailable from more conventional laser sources. Substantial user programs have been performed using such sources encompassing medicine, biology, solid state research, atomic and molecular physics, effects of non-linear fields, surface science, polymer science, pulsed laser vapor deposition, to name just a few.
Guo, Bin; Chen, Zhongsheng; Guo, Jinyun; Liu, Feng; Chen, Chuanfa; Liu, Kangli
2016-01-01
Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960–2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD). Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years) and inter-decadal scale (quasi-12 and quasi-23 years). Moreover, the 2–3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements. PMID:27007388
Guo, Bin; Chen, Zhongsheng; Guo, Jinyun; Liu, Feng; Chen, Chuanfa; Liu, Kangli
2016-03-21
Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960-2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD). Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years) and inter-decadal scale (quasi-12 and quasi-23 years). Moreover, the 2-3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements.
Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem
DEFF Research Database (Denmark)
Delbary, Fabrice; Knudsen, Kim
2014-01-01
The Calderon problem is the mathematical formulation of the inverse problem in Electrical Impedance Tomography and asks for the uniqueness and reconstruction of an electrical conductivity distribution in a bounded domain from the knowledge of the Dirichlet-to-Neumann map associated to the general......The Calderon problem is the mathematical formulation of the inverse problem in Electrical Impedance Tomography and asks for the uniqueness and reconstruction of an electrical conductivity distribution in a bounded domain from the knowledge of the Dirichlet-to-Neumann map associated...... to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...
Energy Technology Data Exchange (ETDEWEB)
Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México DF (Mexico); Schuch, Dieter [Institut für Theoretische Physik, JW Goethe-Universität Frankfurt am Main, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México DF (Mexico); Rosas-Ortiz, Oscar [Physics Department, Cinvestav, A. P. 14-740, 07000 México D. F. (Mexico)
2015-09-15
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
Directory of Open Access Journals (Sweden)
Jenson Lim
Full Text Available Gene delivery technologies to introduce foreign genes into highly differentiated mammalian cells have improved significantly over the last few decades. Relatively new techniques such as magnetic nanoparticle-based gene transfection technology are showing great promise in terms of its high transfection efficiency and wide-ranging research applications. We have developed a novel gene delivery technique, which uses magnetic nanoparticles moving under the influence of an oscillating magnetic array. Herein we successfully introduced short interfering RNA (siRNA against green fluorescent protein (GFP or actin into stably-transfected GFP-HeLa cells or wild-type HeLa and rat aortic smooth muscle cells, respectively. This gene silencing technique occurred in a dose- and cell density- dependent manner, as reflected using fluorescence intensity and adhesion assays. Furthermore, using endocytosis inhibitors, we established that these magnetic nanoparticle-nucleic acid complexes, moving across the cell surface under the influence of an oscillating magnet array, enters into the cells via the caveolae-mediated endocytic pathway.
Fakhri, H.; Sayyah-Fard, M.
2017-12-01
The q-coherent states associated with the noncommutative complex plane Cq2 for the Biedenharn-Macfarlane q-oscillator are constructed by using a q-generalization of the Glauber's unitary displacement operator. The q-deformed counterpart of the eigenvalue equation of undeformed harmonic oscillator coherent states is obtained. Some properties of the q-coherent states are considered. It is shown that super-Poissonian statistics and saturation of the uncertainty relation occur simultaneously with the nonclassical behaviors including antibunching effects with nonnegative values less than unity and the negative values, for the second-order intensity q-correlation function in the case of q > 1. Furthermore, the nonclassical sub-Poissonian statistics is demonstrated simultaneously with bunching and antibunching effects such that in some regions of the coherence parameter the uncertainty inequality is satisfied, and violated elsewhere. We show that another nonclassical effect, the so-called strong squeezing effect, is exhibited by both quadrature variances in the latter issue.
Nonlinear Complex Dynamics of Carbon Emission Reduction Cournot Game with Bounded Rationality
Directory of Open Access Journals (Sweden)
LiuWei Zhao
2017-01-01
Full Text Available Based on the hypothesis of participant’s bounded rationality, our study formulated a novel Cournot duopoly game model of carbon emission reduction and, subsequently, analyzed the dynamic adjustment mechanism of emission reduction for enterprises. The existence and stability of the equilibrium solution of game are further discussed by the nonlinear dynamics theory. Our findings revealed that the parameters have key significance on the dynamic properties of the system. However, when the adjustment speed gets too large, the system loses the original stability and vividly demonstrates complex chaos phenomenon. Higher market prices in carbon trading have an outstanding impact on the stability of the system, which easily leads to system instability. Our study further controlled the chaos behavior of the power system by the delay feedback control. The results of the numerical analysis depict that the unstable behavior of the dynamic system can be controlled efficiently and quickly, in the quest to restore back a stable and orderly market. Our novel method is proved to have provided decision makers with effective solution to market instability.
Energy Technology Data Exchange (ETDEWEB)
Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: francesco.romeo@uniromal.it; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: giuseppe.rega@uniromal.it
2006-02-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.
Zhang, Chuan; Wang, Xingyuan; Luo, Chao; Li, Junqiu; Wang, Chunpeng
2018-03-01
In this paper, we focus on the robust outer synchronization problem between two nonlinear complex networks with parametric disturbances and mixed time-varying delays. Firstly, a general complex network model is proposed. Besides the nonlinear couplings, the network model in this paper can possess parametric disturbances, internal time-varying delay, discrete time-varying delay and distributed time-varying delay. Then, according to the robust control strategy, linear matrix inequality and Lyapunov stability theory, several outer synchronization protocols are strictly derived. Simple linear matrix controllers are designed to driver the response network synchronize to the drive network. Additionally, our results can be applied on the complex networks without parametric disturbances. Finally, by utilizing the delayed Lorenz chaotic system as the dynamics of all nodes, simulation examples are given to demonstrate the effectiveness of our theoretical results.
Complexity of free energy landscapes of peptides revealed by nonlinear principal component analysis.
Nguyen, Phuong H
2006-12-01
Employing the recently developed hierarchical nonlinear principal component analysis (NLPCA) method of Saegusa et al. (Neurocomputing 2004;61:57-70 and IEICE Trans Inf Syst 2005;E88-D:2242-2248), the complexities of the free energy landscapes of several peptides, including triglycine, hexaalanine, and the C-terminal beta-hairpin of protein G, were studied. First, the performance of this NLPCA method was compared with the standard linear principal component analysis (PCA). In particular, we compared two methods according to (1) the ability of the dimensionality reduction and (2) the efficient representation of peptide conformations in low-dimensional spaces spanned by the first few principal components. The study revealed that NLPCA reduces the dimensionality of the considered systems much better, than did PCA. For example, in order to get the similar error, which is due to representation of the original data of beta-hairpin in low dimensional space, one needs 4 and 21 principal components of NLPCA and PCA, respectively. Second, by representing the free energy landscapes of the considered systems as a function of the first two principal components obtained from PCA, we obtained the relatively well-structured free energy landscapes. In contrast, the free energy landscapes of NLPCA are much more complicated, exhibiting many states which are hidden in the PCA maps, especially in the unfolded regions. Furthermore, the study also showed that many states in the PCA maps are mixed up by several peptide conformations, while those of the NLPCA maps are more pure. This finding suggests that the NLPCA should be used to capture the essential features of the systems. (c) 2006 Wiley-Liss, Inc.
Extracting quantitative measures from finite length nonlinear timeseries- complex systems approaches
Wicks, R.; Chapman, S. C.; Kiyani, K.; Hnat, B.; Dendy, R. O.
2006-12-01
We consider two complex systems approaches to obtaining quantitative measures from `real world' timeseries, such as in situ solar wind observations and geomagnetic indices, where information about the process in not known a priori. The first is statistical- we discuss the problem of obtaining the scaling exponents from the PDF of fluctuations (differenced variables) via PDF collapse and structure functions. If the probability density is heavy tailed, outliers strongly influence the scaling behaviour of the moments. From an operational point of view, we wish to recover the scaling exponents of the underlying process by excluding a minimal population of these outliers. We test these ideas on a synthetically generated symmetric alpha-stable Lèvy process and show that the Lèvy exponent is recovered in up to the 6th order moment after ~0.1-0.5% of the data are excluded. The scaling properties of the excluded outliers can then be tested to provide additional information about the system. We highlight application of this technique to in- situ spacecraft observation of the turbulent solar wind and to geomagnetic indices. The second of these is dynamical- we explore the use of Mutual Information (MI) as a method to determine order- disorder transitions and test this idea on the Viscek `boid' model for flocking. We compare MI with the full system susceptibility we demonstrate that MI can pinpoint the phase transition with reasonable accuracy. We also consider the MI as a tool for detecting nonlinear correlation between different systems with application to `space weather', that is, solar wind triggering of geomagnetic activity on the earth.
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
Liu, Haimiao; Horváth, Attila K; Zhao, Yuemin; Lv, Xiaoli; Yang, Li; Gao, Qingyu
2012-01-28
In a continuous flow stirred tank reactor (CSTR), the reaction of thiourea-iodate-sulfite (TuIS) exhibits a rich variety of complex oscillations in pH. The transitions from 1(n) type oscillations to 1(3), 1(2) type and simple oscillations were observed on decreasing the flow rate gradually in small steps at 30.2 °C and 20.5 °C, respectively. The transitions from 1(n) type oscillations to 1(0)1(4), 1(0)1(3) type and simple oscillations were observed as well on increasing the temperature in small steps at a given flow rate. Based on the analogous iodate-sulfite-thiosulfate system a simple empirical rate law model is suggested to give a sound agreement between the experimental and simulated results on the complex oscillatory behaviour. A possible explanation of the emergence of the simple empirical rate law model from the mechanism of the individual reactions of the TuIS system is also discussed.
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Author Affiliations. Lin Xiao-Gang1 Liu Wen-Jun2 Lei Ming2. Key Laboratory of Optoelectronic Technology & Systems (Chongqing University), Ministry of Education, Chongqing, China; School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876, China ...
Non-linear Synthesis of Complex Laser Waveforms at Remote Distances
Berti, Nicolas; Hermelin, Sylvain; Kasparian, Jérôme; Wolf, Jean-Pierre
2015-01-01
Strong deformation of ultrashort laser pulse shapes is unavoidable when delivering high intensities at remote distances due to non-linear effects taking place while propagating. Relying on the reversibility of laser filamentation, we propose to explicitly design laser pulse shapes so that propagation serves as a non-linear field synthesizer at a remote target location. Such an approach allows, for instance, coherent control of molecules at a remote distance, in the context of standoff detection of pathogens or explosives.
Dalton, Gulliver T; Cifuentes, Marie P; Watson, Laurance A; Petrie, Simon; Stranger, Robert; Samoc, Marek; Humphrey, Mark G
2009-07-20
A combination of UV-vis-NIR spectroscopy, femtosecond Z-scan measurements, and time-dependent density functional theory (TD-DFT) calculations have been used to comprehensively investigate the linear optical and nonlinear optical (NLO) properties of pi-delocalizable metal-functionalized oligo(phenyleneethynylene)s. A range of unsymmetrically or symmetrically end-functionalized mono-, di-, tri-, penta-, hepta-, and nona(phenyleneethynylene)s were synthesized, with larger examples bearing varying numbers of 2,5-di(hexyloxy)phenyl groups to ensure sufficient solubility of the metal complex derivatives. The effect of incorporating varying numbers of solubilizing substituents in the OPE bridge, peripheral group modification, OPE lengthening, coligand variation, and metal location in the OPE on the linear optical properties has been established, with the first three molecular modifications resulting in significant changes in the optical absorption maxima. TD-DFT calculations reveal that the most intense transition in the linear optical spectra is localized on the OPE bridge and involves excitation from acetylenic to cumulenic molecular orbitals that are not greatly spatially separated from one another. The nonlinear optical properties are dominated by two-photon absorption, which for all but 1,4-{trans-[RuCl(dppm)(2)]C[triple bond]C}(2)C(6)H(4) appears as a band around 11,400 cm(-1) and a sharp increase of nonlinear absorption at frequencies >17,000 cm(-1). Surprisingly, there is relatively little influence of the length of the OPE bridge on the magnitude of the two-photon absorption cross sections, which are in the range 300-1000 GM.
Okanishi, Tohru; Akiyama, Tomoyuki; Tanaka, Shin-Ichi; Mayo, Ellen; Mitsutake, Ayu; Boelman, Cyrus; Go, Cristina; Snead, O Carter; Drake, James; Rutka, James; Ochi, Ayako; Otsubo, Hiroshi
2014-10-01
Multiple tubers in patients with tuberous sclerosis complex (TSC) often are responsible for drug-resistant epilepsy. The complexity of the epileptic network formed by multiple tubers complicates localization of the epileptogenic zone that is needed to design a surgical treatment strategy. High frequency oscillations (HFOs) on intracranial video-electroencephalography (IVEEG) may be a valuable surrogate marker for the localization of the epileptogenic zone. The purpose of this study was to test the hypothesis that high occurrence rate (OR) of interictal HFOs can guide the localization of the epileptogenic zone. We analyzed the OR of interictal HFOs at 80-200 Hz (ripples) and >200 Hz (fast ripples, FRs). We divided OR of interictal HFOs between high and low rates by thresholding. We analyzed the correlation between seizure outcomes using Engel classification and the resection ratio of the seizure onset zone (SOZ), and high-OR HFOs using ordinal logistic regression analysis. We collected 10 patients. The seizure outcomes resulted in Engel classification I in three patients, II in four, III in one, and IV in two. High-OR ripples (5-57 [mean 29] channels, 1-4 [2.8] lobes) and high-OR FRs (9-66 [mean 27] channels, 1-4 [2.6] lobes) were widely distributed. The resection ratio of SOZ did not show statistically significant correlation with the seizure outcome. The resection ratio of high-OR ripples showed statistically significant correlation with the seizure outcome (p = 0.038). The resection ratio of high-OR FRs showed statistically significant correlation with the seizure outcome (p = 0.048). The multiple extensive zones with high-OR HFOs suggest a complex and widespread epileptic network in patients with TSC. In a subset of TSC patients with drug-resistant epilepsy, resection of cortex with both interictal high-OR FRs and ripples on IVEEG correlated with a good seizure outcome. Wiley Periodicals, Inc. © 2014 International League Against Epilepsy.
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.
Parsons-Wingerter, Patricia
2010-01-01
When analyzed by VESsel GENeration Analysis (VESGEN) software, vascular patterns provide useful integrative read-outs of complex, interacting molecular signaling pathways. Using VESGEN, we recently discovered and published our innovative, surprising findings that angiogenesis oscillated with vascular dropout throughout progression of diabetic retinopathy, a blinding vascular disease. Our findings provide a potential paradigm shift in the current prevailing view on progression and treatment of this disease, and a new early-stage window of regenerative therapeutic opportunities. The findings also suggest that angiogenesis may oscillate with vascular disease in a homeostatic-like manner during early stages of other inflammatory progressive diseases such as cancer and coronary vascular disease.
Directory of Open Access Journals (Sweden)
Md. Shahjahan Ali
2015-01-01
Full Text Available The standard k-ε model has the deficiency of predicting swirling and vortical flows due to its isotropic assumption of eddy viscosity. In this study, a second-order nonlinear k-ε model is developed incorporating some new functions for the model coefficients to explore the models applicability to complex turbulent flows. Considering the realizability principle, the coefficient of eddy viscosity (cμ is derived as a function of strain and rotation parameters. The coefficients of nonlinear quadratic term are estimated considering the anisotropy of turbulence in a simple shear layer. Analytical solutions for the fundamental properties of swirl jet are derived based on the nonlinear k-ε model, and the values of model constants are determined by tuning their values for the best-fitted comparison with the experiments. The model performance is examined for two test cases: (i for an ideal vortex (Stuart vortex, the basic equations are solved numerically to predict the turbulent structures at the vortex center and the (ii unsteady 3D simulation is carried out to calculate the flow field of a compound channel. It is observed that the proposed nonlinear k-ε model can successfully predict the turbulent structures at vortex center, while the standard k-ε model fails. The model is found to be capable of accounting the effect of transverse momentum transfer in the compound channel through generating the horizontal vortices at the interface.
Model of stochastic self-oscillation in Gunn diode oscillators
Energy Technology Data Exchange (ETDEWEB)
Bocharov, E.P.; Korostelev, G.N.; Khripunov, M.V.
1987-07-01
The applicability of the two-mode nonlinear model of decay stochasticity for explanation of the transition from monochromatic self-oscillation to developed stochasticity in the Gunn diode oscillator is demonstrated. Numerical realizations of the basic regimes corresponding to various cases of consideration of the weak nonlinearity of the falling portion of the current-voltage characteristic are presented. A comparative analysis of calculation results of time realizations and experimentally observed oscillograms of stochastic regimes is performed.
Directory of Open Access Journals (Sweden)
R.A. Zait
2016-07-01
Full Text Available In this paper, the stochastic Wiener Hermite expansion (WHE is used to find the statistical measures (mean and variance of the first order stochastic approximation (Gaussian part of the stochastic solution processes related to the nonlinear damped Duffing oscillator model which is excited randomly by white noise process. Under the application of WHE, a deterministic model is generated to simulate the statistical measures. In next stages, smi-analytical treatments are performed under applying multi-step differential transformed method (Ms-DTM and some cases study are illustrated related to the statistical properties using Mathematica10 software.
Baxt, W G
1994-03-15
Background is presented to suggest that a great many biologic processes are chaotic. It is well known that chaotic processes can be accurately characterized by non-linear technologies. Evidence is presented that an artificial neural network, which is a known method for the application of non-linear statistics, is able to perform more accurately in identifying patients with and without myocardial infarction than either physicians or other computer paradigms. It is suggested that the improved performance may be due to the network's better ability to characterize what is a chaotic process imbedded in the problem of the clinical diagnosis of this entity.
DEFF Research Database (Denmark)
Lindgaard, Esben; Lund, Erik
2012-01-01
This paper presents a novel FEM-based approach for fiber angle optimal design of laminated composite structures exhibiting complicated nonlinear buckling behavior, thus enabling design of lighter and more cost-effective structures. The approach accounts for the geometrically nonlinear behavior...... of the structure by utilizing path tracing response analysis up until the buckling point. The method simultaneously includes loss of stability due to bifurcation and limiting behavior and thereby avoids problems related to mode or stability type switching during optimization. The optimization formulation...
Peri-implantitis: a complex condition with non-linear characteristics
Papantonopoulos, G.H.; Gogos, C.; Housos, E.; Bountis, T.; Loos, B.G.
2015-01-01
Aim To cluster peri-implantitis patients and explore non-linear patterns in peri-implant bone levels. Materials and Methods Clinical and radiographic variables were retrieved from 94 implant-treated patients (340 implants, mean 7.1 ± 4.1 years in function). Kernel probability density estimations on
Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks.
Gao, Zhongke; Jin, Ningde
2009-06-01
The identification of flow pattern is a basic and important issue in multiphase systems. Because of the complexity of phase interaction in gas-liquid two-phase flow, it is difficult to discern its flow pattern objectively. In this paper, we make a systematic study on the vertical upward gas-liquid two-phase flow using complex network. Three unique network construction methods are proposed to build three types of networks, i.e., flow pattern complex network (FPCN), fluid dynamic complex network (FDCN), and fluid structure complex network (FSCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K -mean clustering, useful and interesting results are found which can be used for identifying five vertical upward gas-liquid two-phase flow patterns. To investigate the dynamic characteristics of gas-liquid two-phase flow, we construct 50 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of gas-liquid two-phase flow. Furthermore, we construct FSCN and demonstrate how network statistic can be used to reveal the fluid structure of gas-liquid two-phase flow. In this paper, from a different perspective, we not only introduce complex network theory to the study of gas-liquid two-phase flow but also indicate that complex network may be a powerful tool for exploring nonlinear time series in practice.
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
Wei, Kun; Gao, Shilong; Zhong, Suchuan; Ma, Hong
2012-01-01
In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models – the Goodwin oscillator and the Rössler oscillator. By constructing a “dual memory” oscillator – the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically. PMID:22679500
Directory of Open Access Journals (Sweden)
Kun Wei
Full Text Available In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE. Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.
Wei, Kun; Gao, Shilong; Zhong, Suchuan; Ma, Hong
2012-01-01
In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.
Hyperchaotic system with unstable oscillators
DEFF Research Database (Denmark)
Murali, K.; Tamasevicius, A.; Mykolaitis, G.
2000-01-01
A simple electronic system exhibiting hyperchaotic behaviour is described. The system includes two nonlinearly coupled 2nd order unstable oscillators, each composed of an LC resonance loop and an amplifier. The system is investigated by means of numerical integration of appropriate differential...... equations, PSPICE simulations and hardware experiments. The Lyapunov exponents are presented to confirm hyperchaotic mode of the oscillations....
Energy Conservative Limit Cycle Oscillations
Stramigioli, Stefano; van Dijk, Michel
This paper shows how globally attractive limit cycle oscillations can be induced in a system with a nonlinear feedback element. Based on the same principle as the Van der Pol oscillator, the feedback behaves as a negative damping for low velocities but as an ordinary damper for high velocities. This
Dudinets, I. V.; Man’ko, V. I.; Marmo, G.; Zaccaria, F.
2017-11-01
Symplectic tomographies of classical and quantum states are shortly reviewed. The concept of nonlinear f-oscillators and their properties are recalled. The tomographic probability representations of oscillator coherent states and the problem of entanglement are then discussed. The entanglement of even and odd f-coherent states is evaluated by the linear entropy.
Directory of Open Access Journals (Sweden)
J.-J. Sinou
2017-01-01
Full Text Available During the past decades, the problem of friction-induced vibration and noise has been the subject of a huge amount of works. Various numerical simulations with finite elements models have been largely investigated to predict squeal events. Although a nonlinear analysis is more predictive than Complex Eigenvalues Analysis, one of the main drawbacks of the time analysis is the need of large computational efforts. In view of the complexity of the subject, this approach appears still computationally too expensive to be used in industry for finite element models. In this study, the potential of a new reduced model based on a double modal synthesis (i.e., a classical modal reduction via Craig and Bampton plus a condensation at the frictional interface based on complex modes for the prediction of self-excited vibrations of brake squeal is discussed. The effectiveness of the proposed modal reduction is tested on a finite element model of a simplified brake system. It will be shown that numerical results of times analysis by applying the proposed reduction correlate well with those of the nonlinear analysis based on a reference model, hence demonstrating the potential of using adapted modal reductions to predict the squeal propensity and to estimate self-excited vibrations and noise.
Praveen, P A; Ramesh Babu, R; Jothivenkatachalam, K; Ramamurthi, K
2015-11-05
Metal organic materials are widely investigated to find their suitability for nonlinear optical applications due to the advantage of combined organic and inorganic properties. In this work benzimidazole based metal organic thin films of dichlorobis (1H-Benzimidazole) Co(II) and dichlorobis (1H-Benzimidazole) Cu(II) were deposited by chemical bath deposition method. The deposited films were annealed at 100, 150 and 200 °C to investigate the effect of annealing on the properties of thin films. Surface homogeneity of the films was increased with the annealing temperature due to the surface diffusion of the films and the same was evidently shown by Raman spectroscopy and Atomic Force Microscopy studies. But annealing the films at 200 °C yielded bulk patches on the surface due to the distortion of molecules. Linear and nonlinear optical properties of the films annealed at 150 °C showed relatively higher transmittance and improved nonlinear optical properties than the other as prepared and annealed samples. Copyright © 2015 Elsevier B.V. All rights reserved.
Nonlinear amplitude dynamics in flagellar beating
Oriola, David; Casademunt, Jaume
2016-01-01
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive crosslinkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatiotemporal dynamics of dynein populations and flagell...
Nonlinear Dynamics Analysis of the Semiactive Suspension System with Magneto-Rheological Damper
Directory of Open Access Journals (Sweden)
Hailong Zhang
2015-01-01
Full Text Available This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The magneto-rheological (MR suspension system has been established, by employing the modified Bouc-Wen force-velocity (F-v model of magneto-rheological damper (MRD. The possibility of chaotic motions in MR suspension is discovered by employing the method of nonlinear stability analysis. With the bifurcation diagrams and corresponding Lyapunov exponent (LE spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasiperiodic oscillations, and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolutions to chaos through period-doubling bifurcations, saddle-node bifurcations, and reverse period-doubling bifurcations.
Zhang, Yali; Wang, Jun
2017-09-01
In an attempt to investigate the nonlinear complex evolution of financial dynamics, a new financial price model - the multitype range-intensity contact (MRIC) financial model, is developed based on the multitype range-intensity interacting contact system, in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading. Two new random visibility graph (VG) based analyses and Lempel-Ziv complexity (LZC) are applied to study the complex behaviors of return time series and the corresponding random sorted series. The VG method is the complex network theory, and the LZC is a non-parametric measure of complexity reflecting the rate of new pattern generation of a series. In this work, the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, the numerical empirical study shows the similar complexity behaviors between the model and the real markets, the research confirms that the financial model is reasonable to some extent.
Gauthier, Nicolas; Argouarch, Gilles; Paul, Frédéric; Toupet, Loic; Ladjarafi, Abdelkader; Costuas, Karine; Halet, Jean-François; Samoc, Marek; Cifuentes, Marie P; Corkery, T Christopher; Humphrey, Mark G
2011-05-09
The new [(η(2)-dppe)(η(5)-C(5)Me(5))Fe(C≡C-1,4-C(6)H(4)C≡C)Ru(η(2) -dppe)(2) C≡C(C(6)H(5))] complex (3-H) and its hexanuclear relative [{(η(2)-dppe)(η(5)-C(5) Me(5))Fe(C≡C-1,4-C(6)H(4)-C≡C)Ru(η(2)-dppe)(2)(C≡C-1,4-C(6)H(4)C≡C)(3)(1,3,5-C(6)H(3))] (4) have been synthesized and characterized. The linear and cubic nonlinear optical properties of these compounds in their various redox states have been studied along with those of the analogous complexes [(η(2)-dppe)(η(5)-C(5)Me(5))Fe(C≡C-1,4-C(6)H(4)C≡C)Ru(η(2)-dppe)(2)R][PF(6)](n) (n=0-2; R=Cl, 2-Cl; R=C≡C(4-C(6)H(4)NO(2)),3-NO(2)). We show that molecules exhibiting large third-order nonlinearities can be obtained by assembling such dinuclear Fe/Ru units around a central 1,3,5-substituted C(6)H(3) core. These data are discussed with a particular emphasis on the large changes in their nonlinear (third-order) optical properties brought about by oxidation. Experimental and computational (DFT) evidence for the electronic structures of these compounds in their various redox states is presented using 3-H(n+) as a prototypical model. Single crystals of this complex in its mono-oxidized state (3-H[PF(6)]) provide the first structural data for such carbon-rich Fe(III) /Ru(II) heteronuclear mixed-valent (MV) systems. Although experimental evidence for the structure of the dioxidized states was more difficult to obtain, the theoretical study reveals that 3-H(2+) can be considered to have a biradical structure with two independent spins. The low-lying absorptions that appear in the near-infrared (NIR) range for all these compounds following oxidation correspond to intervalence charge-transfer (IVCT) bands for the mono-oxidized states and to ligand-to-metal charge-transfer (LMCT) transitions for the dioxidized states. These play a crucial role in the strong optical modulation achieved. The possibility of accessing additional states with distinct linear or nonlinear optical properties is also briefly
Directory of Open Access Journals (Sweden)
Lixiang Wang
2013-01-01
Full Text Available This study reports the GPU parallelization of complex three-dimensional software for nonlinear analysis of concrete structures. It focuses on coupled thermomechanical analysis of complex structures. A coupled FEM/DEM approach (CDEM is given from a fundamental theoretical viewpoint. As the modeling of a large structure by means of FEM/DEM may lead to prohibitive computation times, a parallelization strategy is required. With the substantial development of computer science, a GPU-based parallel procedure is implemented. A comparative study between the GPU and CPU computation results is presented, and the runtimes and speedups are analyzed. The results show that dramatic performance improvements are gained from GPU parallelization.
Jamali, A.; Khaleghi, E.; Gholaminezhad, I.; Nariman-zadeh, N.
2016-05-01
In this paper, a new multi-objective genetic programming (GP) with a diversity preserving mechanism and a real number alteration operator is presented and successfully used for Pareto optimal modelling of some complex non-linear systems using some input-output data. In this study, two different input-output data-sets of a non-linear mathematical model and of an explosive cutting process are considered separately in three-objective optimisation processes. The pertinent conflicting objective functions that have been considered for such Pareto optimisations are namely, training error (TE), prediction error (PE), and the length of tree (complexity of the network) (TL) of the GP models. Such three-objective optimisation implementations leads to some non-dominated choices of GP-type models for both cases representing the trade-offs among those objective functions. Therefore, optimal Pareto fronts of such GP models exhibit the trade-off among the corresponding conflicting objectives and, thus, provide different non-dominated optimal choices of GP-type models. Moreover, the results show that no significant optimality in TE and PE may occur when the TL of the corresponding GP model exceeds some values.
Tanaka, Gouhei; Aihara, Kazuyuki
2009-09-01
A widely used complex-valued activation function for complex-valued multistate Hopfield networks is revealed to be essentially based on a multilevel step function. By replacing the multilevel step function with other multilevel characteristics, we present two alternative complex-valued activation functions. One is based on a multilevel sigmoid function, while the other on a characteristic of a multistate bifurcating neuron. Numerical experiments show that both modifications to the complex-valued activation function bring about improvements in network performance for a multistate associative memory. The advantage of the proposed networks over the complex-valued Hopfield networks with the multilevel step function is more outstanding when a complex-valued neuron represents a larger number of multivalued states. Further, the performance of the proposed networks in reconstructing noisy 256 gray-level images is demonstrated in comparison with other recent associative memories to clarify their advantages and disadvantages.
Das, Papari; Karmakar, Pralay Kumar
2018-01-01
A nonextensive nonthermal magnetized viscoelastic astrofluid, compositionally containing nonthermal electrons and ions together with massive polarized dust micro-spherical grains of variable electric charge, is allowed to endure weakly nonlinear perturbation around its equilibrium. The nonextensivity originating from the large-scale non-local effects is included via the Tsallis thermo-statistical distribution laws describing the lighter species. Assuming the equilibrium as a homogeneous hydrostatic one, the dust polarization effects are incorporated via the conventional homogeneous polarization force law. The perturbed fluid model evolves as a unique conjugate pair of coupled extended Korteweg-de Vries (e-KdV) equations. A constructed numerical tapestry shows the collective excitations of a new pair of distinct classes of nonlinear mode structures in new parametric space. The first family indicates periodic electrostatic compressive eigenmodes in the form of soliton-chains. Likewise, the second one reveals gravitational rarefactive solitary patterns. Their microphysical multi-parametric dependencies of the eigen-patterns are illustratively analyzed and bolstered. The paper ends up with some promising implications and applications in the astro-cosmo-plasmic context of wave-induced accretive triggering processes responsible for gravitationally bounded (gravito-condensed) astro-structure formation, such as stellesimals, planetsimals, etc.
Directory of Open Access Journals (Sweden)
Papari Das
2018-01-01
Full Text Available A nonextensive nonthermal magnetized viscoelastic astrofluid, compositionally containing nonthermal electrons and ions together with massive polarized dust micro-spherical grains of variable electric charge, is allowed to endure weakly nonlinear perturbation around its equilibrium. The nonextensivity originating from the large-scale non-local effects is included via the Tsallis thermo-statistical distribution laws describing the lighter species. Assuming the equilibrium as a homogeneous hydrostatic one, the dust polarization effects are incorporated via the conventional homogeneous polarization force law. The perturbed fluid model evolves as a unique conjugate pair of coupled extended Korteweg-de Vries (e-KdV equations. A constructed numerical tapestry shows the collective excitations of a new pair of distinct classes of nonlinear mode structures in new parametric space. The first family indicates periodic electrostatic compressive eigenmodes in the form of soliton-chains. Likewise, the second one reveals gravitational rarefactive solitary patterns. Their microphysical multi-parametric dependencies of the eigen-patterns are illustratively analyzed and bolstered. The paper ends up with some promising implications and applications in the astro-cosmo-plasmic context of wave-induced accretive triggering processes responsible for gravitationally bounded (gravito-condensed astro-structure formation, such as stellesimals, planetsimals, etc.
Condorelli, Rosalia
2016-01-01
Can we share even today the same vision of modernity which Durkheim left us by its suicide analysis? or can society 'surprise us'? The answer to these questions can be inspired by several studies which found that beginning the second half of the twentieth century suicides in western countries more industrialized and modernized do not increase in a constant, linear way as modernization and social fragmentation process increases, as well as Durkheim's theory seems to lead us to predict. Despite continued modernizing process, they found stabilizing or falling overall suicide rate trends. Therefore, a gradual process of adaptation to the stress of modernization associated to low social integration levels seems to be activated in modern society. Assuming this perspective, the paper highlights as this tendency may be understood in the light of the new concept of social systems as complex adaptive systems, systems which are able to adapt to environmental perturbations and generate as a whole surprising, emergent effects due to nonlinear interactions among their components. So, in the frame of Nonlinear Dynamical System Modeling, we formalize the logic of suicide decision-making process responsible for changes at aggregate level in suicide growth rates by a nonlinear differential equation structured in a logistic way, and in so doing we attempt to capture the mechanism underlying the change process in suicide growth rate and to test the hypothesis that system's dynamics exhibits a restrained increase process as expression of an adaptation process to the liquidity of social ties in modern society. In particular, a Nonlinear Logistic Map is applied to suicide data in a modern society such as the Italian one from 1875 to 2010. The analytic results, seeming to confirm the idea of the activation of an adaptation process to the liquidity of social ties, constitutes an opportunity for a more general reflection on the current configuration of modern society, by relating the
Broadband hyperchaotic oscillator with delay line
DEFF Research Database (Denmark)
Cenys, Antanas; Lindberg, Erik; Anagnostopoulos, A. N.
2002-01-01
Dynamical systems with time delay can be employed as high dimensional hyperchaotic oscillators with multiple positive Lyapunov exponents. We describe an electronic circuit composed of a 3-stage amplifier and a delay line in the feedback loop. The 1st stage of the amplifier is a nonlinear one whil...... 20 dB. Mathematical models are presented. The oscillators are described either by a scalar nonlinear DDE or by a set combined of one nonlinear DDE and two linear ODEs....
The Duffing oscillator with damping
DEFF Research Database (Denmark)
Johannessen, Kim
2015-01-01
An analytical solution to the differential equation describing the Duffing oscillator with damping is presented. The damping term of the differential equation and the initial conditions satisfy an algebraic equation, and thus the solution is specific for this type of damping. The nonlinear term....... It is established that the period of oscillation is shorter compared to that of a linearized model but increasing with time and asymptotically approaching the period of oscillation of the linear damped model. An explicit expression for the period of oscillation has been derived, and it is found to be very accurate....
A unifying view of synchronization for data assimilation in complex nonlinear networks
Abarbanel, Henry D. I.; Shirman, Sasha; Breen, Daniel; Kadakia, Nirag; Rey, Daniel; Armstrong, Eve; Margoliash, Daniel
2017-12-01
Networks of nonlinear systems contain unknown parameters and dynamical degrees of freedom that may not be observable with existing instruments. From observable state variables, we want to estimate the connectivity of a model of such a network and determine the full state of the model at the termination of a temporal observation window during which measurements transfer information to a model of the network. The model state at the termination of a measurement window acts as an initial condition for predicting the future behavior of the network. This allows the validation (or invalidation) of the model as a representation of the dynamical processes producing the observations. Once the model has been tested against new data, it may be utilized as a predictor of responses to innovative stimuli or forcing. We describe a general framework for the tasks involved in the "inverse" problem of determining properties of a model built to represent measured output from physical, biological, or other processes when the measurements are noisy, the model has errors, and the state of the model is unknown when measurements begin. This framework is called statistical data assimilation and is the best one can do in estimating model properties through the use of the conditional probability distributions of the model state variables, conditioned on observations. There is a very broad arena of applications of the methods described. These include numerical weather prediction, properties of nonlinear electrical circuitry, and determining the biophysical properties of functional networks of neurons. Illustrative examples will be given of (1) estimating the connectivity among neurons with known dynamics in a network of unknown connectivity, and (2) estimating the biophysical properties of individual neurons in vitro taken from a functional network underlying vocalization in songbirds.
Energy Technology Data Exchange (ETDEWEB)
Theiler, J. [Los Alamos National Lab., NM (United States)]|[Santa Fe Inst., NM (United States); Nichols, S. [Georgia Inst. of Tech., Atlanta, GA (United States). School of Physics
1993-09-01
The sensitivity to noise of the coherent (or in-phase) attractor for a set of N globally coupled maps is studied; these discrete-time maps are associated with the continuous-time equations of motion for a series array of Josephson junction oscillators. We investigate both geometrical properties of the basin of attraction in the large N limit, and the implications of this geometry on the average time for the system to ``escape`` from the coherently oscillating mode. Our main results are that the attractor basin maintains a box-shaped ``core`` of finite radius even as N {yields} {infinity}, and that the in-phase attractor of a large N array is much less vulnerable to noise than are the out-of-phase attractors.
Resonance-Enhanced Nonlinear Optical Effects
Sun, Xuan
Nonlinear optical processes, which manifest as many interesting phenomena such as nonlinear wave mixing, optical rectification, intensity-dependent refractive index change, harmonic generation, etc., have found very broad applications. Unfortunately, most optical media exhibit rather weak optical nonlinearities and a majority of nonlinear optical processes have to rely on substantial optical powers to support nonlinear wave interactions, which becomes a major challenge for nonlinear photonic application. This thesis is devoted to exploring enhanced nonlinear optical phenomena, by taking advantage of a certain type of resonance to enhance the nonlinear wave interactions. For this purpose, we employed both natural atomic resonances via electron transition and engineered optical resonances in micro/nanophotonic device structures, for different applications. These two types of resonances, although distinctive in their physical natures, both are able to significantly increase the strength and elongate the time of optical wave interactions, thus leading to dramatic enhancement of nonlinear optical effects. On one hand, we utilized unique energy-level structures in alkali vapor plasmas to dramatically enhance the electron tunneling ionization process and to produce significant resonance-enhanced four-wave mixing for efficient terahertz (THz) wave generation that is crucial for long-wave application. On the other hand, we utilized the enhancement offered by high-Q optical resonances inside microresonators to produce significant photothermal backaction to dramatically suppress the fundamental temperature fluctuations of microresonators, which is essential for sensing and metrology applications. With such cavity-resonance enhancement, we revealed a new regime of nonlinear optical oscillation dynamics in lithium niobate microresonators that results from unique competition between the thermo-optic nonlinear effect and the photorefractive effect, which is inaccessible to
Insuasty, Braulio; Atienza, Carmen; Seoane, Carlos; Martín, Nazario; Garín, Javier; Orduna, Jesús; Alcalá, Rafael; Villacampa, Belén
2004-10-15
A novel D-pi-A system in which tetrathiafulvalene (TTF) and pi-extended TTFs as strong electron donors are covalently connected to a tricarbonyl (eta(6)-arene)chromium complex as the acceptor moiety through a systematically increased conjugated bridge of vinylene units (12a-c, 16a-c) have been synthesized by Wittig-Horner olefination reaction. The electronic spectra as well as the electrochemical data reveal a different behavior of TTF derivatives (12a-c) and of exTTF derivatives (16a-c). Cyclic voltammetry shows the influence of the tricarbonylchromium arene on the oxidation potentials in compounds 12a-c, and no remarkable effect is observed for exTTFs (16a-c). The nonlinear optical properties of 12a-c and 16a-c have been calculated by using the ab initio CPHF/6-31G//B3P86/6-31G model, and the time-dependent density functional theory (TD-DFT) method has been used for the calculation of the electronic transitions. The calculations reveal that an intraligand charge-transfer transition (ILCT) and the metal to ligand charge-transfer transition (MLCT) are responsible for the nonlinear response. In addition, the large angles formed by the ground-state dipole moment and the vectorial hyperpolarizability are responsible for the mubeta values determined experimentally by the EFISH technique.
Kuwahara, Jun; Miyata, Hajime; Konno, Hidetoshi
2017-09-01
Recently, complex dynamics of globally coupled oscillators have been attracting many researcher's attentions. In spite of their numerous studies, their features of nonlinear oscillator systems with global and local couplings in two-dimension (2D) are not understood fully. The paper focuses on 2D states of coherent, clustered and chaotic oscillation especially under the effect of negative global coupling (NGC) in 2D Alief-Panfilov model. It is found that the tuning NGC can cause various new coupling-parameter dependency on the features of oscillations. Then quantitative characterization of various states of oscillations (so called spiral wave turbulence) is examined by using the pragmatic information (PI) which have been utilized in analyzing multimode laser, solar activity and neuronal systems. It is demonstrated that the dynamics of the PI for various oscillations can be characterized successfully by the Hyper-Gamma stochastic process.
Simulations of oscillatory systems with award-winning software, physics of oscillations
Butikov, Eugene I
2015-01-01
Deepen Your Students' Understanding of Oscillations through Interactive Experiments Simulations of Oscillatory Systems: with Award-Winning Software, Physics of Oscillations provides a hands-on way of visualizing and understanding the fundamental concepts of the physics of oscillations. Both the textbook and software are designed as exploration-oriented supplements for courses in general physics and the theory of oscillations. The book is conveniently structured according to mathematical complexity. Each chapter in Part I contains activities, questions, exercises, and problems of varying levels of difficulty, from straightforward to quite challenging. Part II presents more sophisticated, highly mathematical material that delves into the serious theoretical background for the computer-aided study of oscillations. The software package allows students to observe the motion of linear and nonlinear mechanical oscillatory systems and to obtain plots of the variables that describe the systems along with phase diagram...
Mahmoud, Emad E.; Al-Adwani, Madeha A.
A novel chaotic model with complex variables and cubic non-linear terms was proposed. The new system is a six dimensional continuous real autonomous chaotic system. The characteristics of this system containing invariance, dissipation, equilibria and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams and chaotic achievement are studied. Converting and turning the system chaotic behavior to its unstable trivial fixed point via the Lyapunov stability theorem. An approach proposed to analyze the system chaos synchronization. Analytical expressions are derived for control functions. The chaos synchronization results were employed to develop a simple application in secure communication. Numerical effects computed to experiment the control forces scientific expressions gravity and to show the chaos synchronization of a chaotic system.
Gao, Qiong; Liao, Tian-he; Cui, Yuan-feng
2008-08-15
From the viewpoint of unconstrained optimization the phase-retrieval problem of a 1D complex signal in the fractional Fourier domain is formulated as a nonlinear least-squares problem. A definition of the discrete fractional Fourier transform (DFRFT) constructed by a discrete Hermite-Gaussian function is adopted here. The ill-posedness of the problem is stressed, and the Levenberg-Marquardt algorithm of Moré's form is used to solve it. In contrast to many published references, this method can reconstruct the phase accurately from the amplitude of the original signal and the one of its DFRFT at any order in the interval (0, 2). For amplitudes with low-level noise this method also works well.
The virial theorem for nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar
2009-09-15
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)
Tetko, Igor V; Solov'ev, Vitaly P; Antonov, Alexey V; Yao, Xiaojun; Doucet, Jean Pierre; Fan, Botao; Hoonakker, Frank; Fourches, Denis; Jost, Piere; Lachiche, Nicolas; Varnek, Alexandre
2006-01-01
A benchmark of several popular methods, Associative Neural Networks (ANN), Support Vector Machines (SVM), k Nearest Neighbors (kNN), Maximal Margin Linear Programming (MMLP), Radial Basis Function Neural Network (RBFNN), and Multiple Linear Regression (MLR), is reported for quantitative-structure property relationships (QSPR) of stability constants logK1 for the 1:1 (M:L) and logbeta2 for 1:2 complexes of metal cations Ag+ and Eu3+ with diverse sets of organic molecules in water at 298 K and ionic strength 0.1 M. The methods were tested on three types of descriptors: molecular descriptors including E-state values, counts of atoms determined for E-state atom types, and substructural molecular fragments (SMF). Comparison of the models was performed using a 5-fold external cross-validation procedure. Robust statistical tests (bootstrap and Kolmogorov-Smirnov statistics) were employed to evaluate the significance of calculated models. The Wilcoxon signed-rank test was used to compare the performance of methods. Individual structure-complexation property models obtained with nonlinear methods demonstrated a significantly better performance than the models built using multilinear regression analysis (MLRA). However, the averaging of several MLRA models based on SMF descriptors provided as good of a prediction as the most efficient nonlinear techniques. Support Vector Machines and Associative Neural Networks contributed in the largest number of significant models. Models based on fragments (SMF descriptors and E-state counts) had higher prediction ability than those based on E-state indices. The use of SMF descriptors and E-state counts provided similar results, whereas E-state indices lead to less significant models. The current study illustrates the difficulties of quantitative comparison of different methods: conclusions based only on one data set without appropriate statistical tests could be wrong.
An analytical formulation for phase noise in MEMS oscillators.
Agrawal, Deepak; Seshia, Ashwin
2014-12-01
In recent years, there has been much interest in the design of low-noise MEMS oscillators. This paper presents a new analytical formulation for noise in a MEMS oscillator encompassing essential resonator and amplifier nonlinearities. The analytical expression for oscillator noise is derived by solving a second-order nonlinear stochastic differential equation. This approach is applied to noise modeling of an electrostatically addressed MEMS resonator-based square-wave oscillator in which the resonator and oscillator circuit nonlinearities are integrated into a single modeling framework. By considering the resulting amplitude and phase relations, we derive additional noise terms resulting from resonator nonlinearities. The phase diffusion of an oscillator is studied and the phase diffusion coefficient is proposed as a metric for noise optimization. The proposed nonlinear phase noise model provides analytical insight into the underlying physics and a pathway toward the design optimization for low-noise MEMS oscillators.
Fractional dynamics of coupled oscillators with long-range interaction.
Tarasov, Vasily E; Zaslavsky, George M
2006-06-01
We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha, when 0coupled oscillators and show how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on alpha. The presence of a fractional derivative also leads to the occurrence of localized structures. Particular solutions for fractional time-dependent complex Ginzburg-Landau (or nonlinear Schrodinger) equation are derived. These solutions are interpreted as synchronized states and localized structures of the oscillatory medium.
Complex nonlinear behaviour of a fixed bed reactor with reactant recycle
DEFF Research Database (Denmark)
Recke, Bodil; Jørgensen, Sten Bay
1999-01-01
The fixed bed reactor with reactant recycle investigated in this paper can exhibit periodic solutions. These solutions bifurcate from the steady state in a Hopf bifurcation. The Hopf bifurcation encountered at the lowest value of the inlet concentration turns the steady state unstable and marks......,that the dynamic behaviour of a fixed bed reactor with reactant recycle is much more complex than previously reported....
Shih, Peter; Kaul, Brian C; Jagannathan, S; Drallmeier, James A
2008-08-01
A novel reinforcement-learning-based dual-control methodology adaptive neural network (NN) controller is developed to deliver a desired tracking performance for a class of complex feedback nonlinear discrete-time systems, which consists of a second-order nonlinear discrete-time system in nonstrict feedback form and an affine nonlinear discrete-time system, in the presence of bounded and unknown disturbances. For example, the exhaust gas recirculation (EGR) operation of a spark ignition (SI) engine is modeled by using such a complex nonlinear discrete-time system. A dual-controller approach is undertaken where primary adaptive critic NN controller is designed for the nonstrict feedback nonlinear discrete-time system whereas the secondary one for the affine nonlinear discrete-time system but the controllers together offer the desired performance. The primary adaptive critic NN controller includes an NN observer for estimating the states and output, an NN critic, and two action NNs for generating virtual control and actual control inputs for the nonstrict feedback nonlinear discrete-time system, whereas an additional critic NN and an action NN are included for the affine nonlinear discrete-time system by assuming the state availability. All NN weights adapt online towards minimization of a certain performance index, utilizing gradient-descent-based rule. Using Lyapunov theory, the uniformly ultimate boundedness (UUB) of the closed-loop tracking error, weight estimates, and observer estimates are shown. The adaptive critic NN controller performance is evaluated on an SI engine operating with high EGR levels where the controller objective is to reduce cyclic dispersion in heat release while minimizing fuel intake. Simulation and experimental results indicate that engine out emissions drop significantly at 20% EGR due to reduction in dispersion in heat release thus verifying the dual-control approach.
Control of coupled oscillator networks with application to microgrid technologies
Arenas, Alex
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable syn- chronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
Control of coupled oscillator networks with application to microgrid technologies.
Skardal, Per Sebastian; Arenas, Alex
2015-08-01
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
Cultrera, G.; Boore, D.M.; Joyner, W.B.; Dietel, C.M.
1999-01-01
Ground-motion recordings obtained at the Van Norman Complex from the 1994 Northridge, California, mainshock and its aftershocks constitute an excellent data set for the analysis of soil response as a function of ground-motion amplitude. We searched for nonlinear response by comparing the Fourier spectral ratios of two pairs of sites for ground motions of different levels, using data from permanent strong-motion recorders and from specially deployed portable instruments. We also compared the amplitude dependence of the observed ratios with the amplitude dependence of the theoretical ratios obtained from 1-D linear and 1-D equivalent-linear transfer functions, using recently published borehole velocity profiles at the sites to provide the low-strain material properties. One pair of sites was at the Jensen Filtration Plant (JFP); the other pair was the Rinaldi Receiving Station (RIN) and the Los Angeles Dam (LAD). Most of the analysis was concentrated on the motions at the Jensen sites. Portable seismometers were installed at the JFP to see if the motions inside the structures housing the strong-motion recorders differed from nearby free-field motions. We recorded seven small earthquakes and found that the high-frequency, low-amplitude motions in the administration building were about 0.3 of those outside the building. This means that the lack of high frequencies on the strong-motion recordings in the administration building relative to the generator building is not due solely to nonlinear soil effects. After taking into account the effects of the buildings, however, analysis of the suite of strong- and weak-motion recordings indicates that nonlinearity occurred at the JFP. As predicted by equivalent-linear analysis, the largest events (the mainshock and the 20 March 1994 aftershock) show a significant deamplification of the high-frequency motion relative to the weak motions from aftershocks occurring many months after the mainshock. The weak-motion aftershocks
Altürk, Sümeyye; Avcı, Davut; Tamer, Ömer; Atalay, Yusuf; Şahin, Onur
2016-11-01
A cobalt(II) complex of 6-methylpicolinic acid, [Co(6-Mepic)2(H2O)2]·2H2O, was prepared and fully determined by single crystal X-ray crystal structure analysis as well as FT-IR, FT-Raman. UV-vis spectra were recorded within different solvents, to illustrate electronic transitions and molecular charge transfer within complex 1. The coordination sphere of complex 1 is a distorted octahedron according to single crystal X-ray results. Moreover, DFT (density functional theory) calculations with HSEH1PBE/6-311 G(d,p) level were carried out to back up the experimental results, and form base for future work in advanced level. Hyperconjugative interactions, intramolecular charge transfer (ICT), molecular stability and bond strength were researched by the using natural bond orbital (NBO) analysis. X-ray and NBO analysis results demonsrate that O-H···O hydrogen bonds between the water molecules and carboxylate oxygen atoms form a 2D supramolecular network, and also adjacent 2D networks connected by C-H···π and π···π interactions to form a 3D supramolecular network. Additionally, the second- and third-order nonlinear optical parameters of complex 1 were computed at DFT/HSEH1PBE/6-311 G(d,p) level. The refractive index (n) was calculated by using the Lorentz-Lorenz equation in order to investigate polarization behavior of complex 1 in different solvent polarities. The first-order static hyperpolarizability (β) value is found to be lower than pNA value because of the inversion symmetry around Co (II). But the second-order static hyperpolarizability (γ) value is 2.45 times greater than pNA value (15×10-30 esu). According to these results, Co(II) complex can be considered as a candidate to NLO material. Lastly molecular electrostatic potential (MEP), frontier molecular orbital energies and related molecular parameters for complex 1 were evaluated.
The pseudoforce approach to fully nonlinear plasma excitations
Akbari-Moghanjoughi, M.
2017-08-01
In this paper, we develop a technique to study the dynamic structure of oscillations in plasmas. We consider the hydrodynamic model and reduce the system of closed equations to the system of differential equations with integrable Hamiltonian. Then, using the analogy of pseudoparticle oscillation in the pseudoforce field, we generalize the Hamiltonian to include the dissipation and external driving force effects. The developed method is used to study various features of electron-ion plasmas with different equations of state for ions. It is shown that this method can be used in the analysis of superposed fully nonlinear oscillations and even the sheath structure of plasmas. The generalized pseudoforce equation is then used to study the dynamics of damped periodically forced nonlinear ion acoustic oscillations in plasmas with adiabatic and isothermal ion fluids. We found striking differences in dynamics of oscillations in these plasmas. The fundamental difference in the dynamic character of oscillations between adiabatic and isothermal ion fluids is described based on the fast ion fluid response to external perturbations in the case of adiabatic ion fluid compression. The current approach may be easily extended to more complex situations with different species and in the presence of electromagnetic interactions.
Alahmadi, Adnan A S; Samson, Rebecca S; Gasston, David; Pardini, Matteo; Friston, Karl J; D'Angelo, Egidio; Toosy, Ahmed T; Wheeler-Kingshott, Claudia A M
2016-06-01
Previous studies have used fMRI to address the relationship between grip force (GF) applied to an object and BOLD response. However, whilst the majority of these studies showed a linear relationship between GF and neural activity in the contralateral M1 and ipsilateral cerebellum, animal studies have suggested the presence of non-linear components in the GF-neural activity relationship. Here, we present a methodology for assessing non-linearities in the BOLD response to different GF levels, within primary motor as well as sensory and cognitive areas and the cerebellum. To be sensitive to complex forms, we designed a feasible grip task with five GF targets using an event-related visually guided paradigm and studied a cohort of 13 healthy volunteers. Polynomial functions of increasing order were fitted to the data. (1) activated motor areas irrespective of GF; (2) positive higher-order responses in and outside M1, involving premotor, sensory and visual areas and cerebellum; (3) negative correlations with GF, predominantly involving the visual domain. Overall, our results suggest that there are physiologically consistent behaviour patterns in cerebral and cerebellar cortices; for example, we observed the presence of a second-order effect in sensorimotor areas, consistent with an optimum metabolic response at intermediate GF levels, while higher-order behaviour was found in associative and cognitive areas. At higher GF levels, sensory-related cortical areas showed reduced activation, interpretable as a redistribution of the neural activity for more demanding tasks. These results have the potential of opening new avenues for investigating pathological mechanisms of neurological diseases.
Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz
1995-01-01
Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.
Energy Technology Data Exchange (ETDEWEB)
Maccari, A. [Istituto Tecnico `G. Cardano`, Monterotondo, Rome (Italy)
1996-08-01
The most important characteristics of the non-local oscillator, an oscillator subjected to an additional non-local force, are extensively studied by means of a new asymptotic perturbation method that is able to furnish an approximate solution of weakly non-linear differential equations. The resulting motion is doubly periodic, because a second little frequency appears, in addition to the fundamental harmonic frequency. Comparison with the numerical solution obtained by the Runge-Kitta method confirms the validity of the asymptotic perturbation method and its importance for the study of non-linear dynamical systems.
State space modeling of Memristor-based Wien oscillator
Talukdar, Abdul Hafiz Ibne
2011-12-01
State space modeling of Memristor based Wien \\'A\\' oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.
Non-linear finite element model to assess the effect of tendon forces on the foot-ankle complex.
Morales-Orcajo, Enrique; Souza, Thales R; Bayod, Javier; Barbosa de Las Casas, Estevam
2017-11-01
A three-dimensional foot finite element model with actual geometry and non-linear behavior of tendons is presented. The model is intended for analysis of the lower limb tendon forces effect in the inner foot structure. The geometry of the model was obtained from computational tomographies and magnetic resonance images. Tendon tissue was characterized with the first order Ogden material model based on experimental data from human foot tendons. Kinetic data was employed to set the load conditions. After model validation, a force sensitivity study of the five major foot extrinsic tendons was conducted to evaluate the function of each tendon. A synergic work of the inversion-eversion tendons was predicted. Pulling from a peroneus or tibialis tendon stressed the antagonist tendons while reducing the stress in the agonist. Similar paired action was predicted for the Achilles tendon with the tibialis anterior. This behavior explains the complex control motion performed by the foot. Furthermore, the stress state at the plantar fascia, the talocrural joint cartilage, the plantar soft tissue and the tendons were estimated in the early and late midstance phase of walking. These estimations will help in the understanding of the functional role of the extrinsic muscle-tendon-units in foot pronation-supination. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.
Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong
2017-10-01
In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.
Indian Academy of Sciences (India)
processes at the cellular level like the glycolytic pathway, peroxi- dase-catalysed reaction or the biosynthesis of certain proteins. A systematic study of oscillating chemical reactions is of consider- able interest, since these oscillating reactions can be used as prototype examples of the behaviours possible in reactions gov-.
Phase-locked Josephson soliton oscillators
DEFF Research Database (Denmark)
Holst, T.; Hansen, Jørn Bindslev; Grønbech-Jensen, N.
1991-01-01
Detailed experimental characterization of the phase-locking at both DC and at microwave frequencies is presented for two closely spaced Josephson soliton (fluxon) oscillators. In the phase-locked state, the radiated microwave power exhibited an effective gain. With one common bias source......, a frequency tunability of the phase-locked oscillators up to 7% at 10 GHz was observed. The interacting soliton oscillators were modeled by two inductively coupled nonlinear transmission lines...
Zhang, Guowu; Zhang, Junwei; Hong, Xuezhi; He, Sailing
2017-02-20
A novel frequency domain nonlinear compensation method, FD-NC, is proposed for orthogonal frequency division multiplexing (OFDM) based visible light communication (VLC) system. By tackling the memory nonlinear impairments from light emitting diodes (LEDs) in the frequency domain rather than in the time domain, the proposed method has much lower computational complexity than the conventional time domain Volterra nonlinear compensation method (TD-NC). Both theoretical derivation and experimental investigation of the proposed method in OFDM based VLC systems with four types of commercial LEDs are presented. The results of experiments show that the proposed low-complexity FD-NC method with a moderate truncation factor achieves a performance comparable to that of the TD-NC. The application of FD-NC method in the bit-power loading OFDM VLC system is also experimentally demonstrated. Compared with the linear equalization case, at a bit error rate (BER) of 3.8 × 10-3 (a), the transmission distance of a 960 Mbps VLC system can be extended from 0.7 m to 1.8 m by the FD-NC, and (b) the achievable system capacity can be enhanced by 18.7%~36.5% for transmission distance in the range of 0.5 m~2 m with the FD-NC. The complexity analysis shows that the required number of real-valued multiplications (RNRM) of the FD-NC is independent of linear or nonlinear memory length. The reduction of RNRM achieved by the FD-NC over the TD-NC becomes more profound for a larger nonlinear memory length or a smaller truncation factor.
Prediction of pilot induced oscillations
Directory of Open Access Journals (Sweden)
Valentin PANĂ
2011-03-01
Full Text Available An important problem in the design of flight-control systems for aircraft under pilotedcontrol is the determination of handling qualities and pilot-induced oscillations (PIO tendencieswhen significant nonlinearities exist in the vehicle description. The paper presents a method to detectpossible pilot-induced oscillations of Category II (with rate and position limiting, a phenomenonusually due to a misadaptation between the pilot and the aircraft response during some tasks in whichtight closed loop control of the aircraft is required from the pilot. For the analysis of Pilot in the LoopOscillations an approach, based on robust stability analysis of a system subject to uncertainparameters, is proposed. In this analysis the nonlinear elements are substituted by linear uncertainparameters. This approach assumes that PIO are characterized by a limit cycle behavior.
Nonlinear dynamics of cardiovascular ageing
Energy Technology Data Exchange (ETDEWEB)
Shiogai, Y. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom); Stefanovska, A. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom); Faculty of Electrical Engineering, University of Ljubljana, Ljubljana (Slovenia); McClintock, P.V.E. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom)], E-mail: p.v.e.mcclintock@lancaster.ac.uk
2010-03-15
The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in
Nonlinear dynamics of cardiovascular ageing
Shiogai, Y.; Stefanovska, A.; McClintock, P. V. E.
2010-03-01
The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in
Misra, A P
2015-01-01
The nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma with a pair of trapped ions is investigated. Starting from a set of hydrodynamic equations for massive dust fluids as well as kinetic Vlasov equations for ions, and applying the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation with a complex coefficient of nonlinearity is derived, which governs the evolution of small-amplitude DA waves in plasmas. The complex coefficient arises due to vortex-like distributions of both positive and negative ions. An analytical as well as numerical solution of the KdV equation are obtained and analyzed with the effects of external magnetic field, the dust pressure as well as different mass and temperatures of positive and negative ions.
National Research Council Canada - National Science Library
Sarah E Morgan; Daniel J Cole; Alex W Chin
2016-01-01
.... The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level in large protein structures, whilst incorporating anharmonicity in the inter-residue...
Oscillators - an approach for a better understanding
DEFF Research Database (Denmark)
Lindberg, Erik
2003-01-01
The aim of this tutorial is to provide an electronic engineer knowledge and insight for a better understanding of the mechanisms behind the behaviour of electronic oscillators. A linear oscillator is a mathematical fiction which can only be used as a starting point for the design of a real...... oscillator based on the Barkhausen criteria. Statements in textbooks and papers saying that the nonlinearities are bringing back the poles to the imaginary axis are wrong. The concept of "frozen eigenvalues" is introduced by means of piece-wise-linear modelling of the nonlinear components which are necessary...
The Wien Bridge Oscillator Family
DEFF Research Database (Denmark)
Lindberg, Erik
2006-01-01
A tutorial in which the Wien bridge family of oscillators is defined and investigated. Oscillators which do not fit into the Barkhausen criterion topology may be designed. A design procedure based on initial complex pole quality factor is reported. The dynamic transfer characteristic...
Energy Technology Data Exchange (ETDEWEB)
Arik, M. (Istanbul Technical Univ. (Turkey). Dept. of Mathematics Bogazici Univ., Istanbul (Turkey). Dept. of Physics); Demircan, E.; Turgut, T. (Texas Univ., Austin, TX (United States). Dept. of Physics); Ekinci, L.; Mungan, M. (Bogazici Univ., Istanbul (Turkey). Dept. of Physics)
1992-07-01
We discuss the properties of oscillators whose spectrum is given by a generalized Fibonacci sequence. The properties include: Invariance under the unitary quantum group, generalized angular momentum, coherent states and difference calculus, relativistic interpretation. (orig.).
Nonlinear mechanical resonators for ultra-sensitive mass detection
Energy Technology Data Exchange (ETDEWEB)
Datskos, Panos G [ORNL; Lavrik, Nickolay V [ORNL
2014-01-01
The fundamental sensitivity limit of an appropriately scaled down mechanical resonator can approach one atomic mass unit when only thermal noise is present in the system. However, operation of such nanoscale mechanical resonators is very challenging due to minuteness of their oscillation amplitudes and presence of multiple noise sources in real experimental environments. In order to surmount these challenges, we use microscale cantilever resonators driven to large amplitudes, far beyond their nonlinear instability onset. Our experiments show that such a nonlinear cantilever resonator, described analytically as a Duffing oscillator, has mass sensing performance comparable to that of much smaller resonators operating in a linear regime. We demonstrate femtogram level mass sensing that relies on a bifurcation point tracking that does not require any complex readout means. Our approaches enable straightforward detection of mass changes that are near the fundamental limit imposed by thermo-mechanical fluctuations.
Nonlinear amplitude dynamics in flagellar beating
Oriola, David; Gadêlha, Hermes; Casademunt, Jaume
2017-03-01
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.
Blume, Christine; Lechinger, Julia; del Giudice, Renata; Wislowska, Malgorzata; Heib, Dominik P J; Schabus, Manuel
2015-08-01
The ability to attribute independent mental states (e.g. opinions, perceptions, beliefs) to oneself and others is termed Theory of Mind (ToM). Previous studies investigating ToM usually employed verbal paradigms and functional neuroimaging methods. Here, we studied oscillatory responses in the electroencephalogram (EEG) in a non-verbal social cognition task. The aim of this study was twofold: First, we wanted to investigate differences in oscillatory responses to animations differing with regard to the complexity of social "interactions". Secondly, we intended to evaluate the basic cognitive processes underlying social cognition. To this end, we analyzed theta, alpha, beta and gamma task-related de-/synchronization (TRD/TRS) during presentation of six non-verbal videos differing in the complexity of (social) "interactions" between two geometric shapes. Videos were adopted from Castelli et al. (2000)and belonged to three conditions: Videos designed to evoke attributions of mental states (ToM), interaction descriptions (goal-directed, GD) and videos in which the shapes moved randomly (R). Analyses revealed that only theta activity consistently varied as a function of social "interaction" complexity. Results suggest that ToM/GD videos attract more attention and working-memory resources and may have activated related memory contents. Alpha and beta results were less consistent. While alpha effects suggest that observation of social "interactions" may benefit from inhibition of self-centered processing, oscillatory responses in the beta range could be related to action observation. In summary, the results provide insight into basic cognitive processes involved in social cognition and render the paradigm attractive for the investigation of social cognitive processes in non-verbal populations. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.
Generalized decomposition methods for singular oscillators
Energy Technology Data Exchange (ETDEWEB)
Ramos, J.I. [Room I-320-D, E. T. S. Ingenieros Industriales, Universidad de Malaga, Plaza El Ejido, s/n 29013 Malaga (Spain)], E-mail: jirs@lcc.uma.es
2009-10-30
Generalized decomposition methods based on a Volterra integral equation, the introduction of an ordering parameter and a power series expansion of the solution in terms of the ordering parameter are developed and used to determine the solution and the frequency of oscillation of a singular, nonlinear oscillator with an odd nonlinearity. It is shown that these techniques provide solutions which are free from secularities if the unknown frequency of oscillation is also expanded in power series of the ordering parameter, require that the nonlinearities be analytic functions of their arguments, and, at leading-order, provide the same frequency of oscillation as two-level iterative techniques, the homotopy perturbation method if the constants that appear in the governing equation are expanded in power series of the ordering parameter, and modified artificial parameter - Linstedt-Poincare procedures.
Strategy revealing phenotypic differences among synthetic oscillator designs.
Lomnitz, Jason G; Savageau, Michael A
2014-09-19
Considerable progress has been made in identifying and characterizing the component parts of genetic oscillators, which play central roles in all organisms. Nonlinear interaction among components is sufficiently complex that mathematical models are required to elucidate their elusive integrated behavior. Although natural and synthetic oscillators exhibit common architectures, there are numerous differences that are poorly understood. Utilizing synthetic biology to uncover basic principles of simpler circuits is a way to advance understanding of natural circadian clocks and rhythms. Following this strategy, we address the following questions: What are the implications of different architectures and molecular modes of transcriptional control for the phenotypic repertoire of genetic oscillators? Are there designs that are more realizable or robust? We compare synthetic oscillators involving one of three architectures and various combinations of the two modes of transcriptional control using a methodology that provides three innovations: a rigorous definition of phenotype, a procedure for deconstructing complex systems into qualitatively distinct phenotypes, and a graphical representation for illuminating the relationship between genotype, environment, and the qualitatively distinct phenotypes of a system. These methods provide a global perspective on the behavioral repertoire, facilitate comparisons of alternatives, and assist the rational design of synthetic gene circuitry. In particular, the results of their application here reveal distinctive phenotypes for several designs that have been studied experimentally as well as a best design among the alternatives that has yet to be constructed and tested.
Stable bubble oscillations beyond Blake's critical threshold.
Hegedűs, Ferenc
2014-04-01
The equilibrium radius of a single spherical bubble containing both non-condensable gas and vapor is determined by the mechanical balance at the bubble interface. This expression highlights the fact that decreasing the ambient pressure below the so called Blake's critical threshold, the bubble has no equilibrium state at all. In the last decade many authors have tried to find evidence for the existence of stable bubble oscillation under harmonic forcing in this regime, that is, they have tried to stabilize the bubble motion applying ultrasonic radiation on the bubble. The available numerical results provide only partial proof for the existence as they are usually based on linearized or weakly nonlinear (higher order approximation) bubble models. Here, based on numerical techniques of the modern nonlinear and bifurcation theory, the existence of stable bubble motion has been proven without any restrictions in nonlinearities. Although the model, applied in this paper, is the rather simple Rayleigh-Plesset equation, the presented technique can be extended to more complex bubble models easily. Copyright © 2014 Elsevier B.V. All rights reserved.
Nonlinear Hysteretic Torsional Waves.
Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V
2015-07-31
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Roles of protein ubiquitination and degradation kinetics in biological oscillations.
Directory of Open Access Journals (Sweden)
Lida Xu
Full Text Available Protein ubiquitination and degradation play important roles in many biological functions and are associated with many human diseases. It is well known that for biochemical oscillations to occur, proper degradation rates of the participating proteins are needed. In most mathematical models of biochemical reactions, linear degradation kinetics has been used. However, the degradation kinetics in real systems may be nonlinear, and how nonlinear degradation kinetics affects biological oscillations are not well understood. In this study, we first develop a biochemical reaction model of protein ubiquitination and degradation and calculate the degradation rate against the concentration of the free substrate. We show that the protein degradation kinetics mainly follows the Michaelis-Menten formulation with a time delay caused by ubiquitination and deubiquitination. We then study analytically how the Michaelis-Menten degradation kinetics affects the instabilities that lead to oscillations using three generic oscillation models: 1 a positive feedback mediated oscillator; 2 a positive-plus-negative feedback mediated oscillator; and 3 a negative feedback mediated oscillator. In all three cases, nonlinear degradation kinetics promotes oscillations, especially for the negative feedback mediated oscillator, resulting in much larger oscillation amplitudes and slower frequencies than those observed with linear kinetics. However, the time delay due to protein ubiquitination and deubiquitination generally suppresses oscillations, reducing the amplitude and increasing the frequency of the oscillations. These theoretical analyses provide mechanistic insights into the effects of specific proteins in the ubiquitination-proteasome system on biological oscillations.
New Look at Nonlinear Aerodynamics in Analysis of Hypersonic Panel Flutter
Directory of Open Access Journals (Sweden)
Dan Xie
2017-01-01
Full Text Available A simply supported plate fluttering in hypersonic flow is investigated considering both the airflow and structural nonlinearities. Third-order piston theory is used for nonlinear aerodynamic loading, and von Karman plate theory is used for modeling the nonlinear strain-displacement relation. The Galerkin method is applied to project the partial differential governing equations (PDEs into a set of ordinary differential equations (ODEs in time, which is then solved by numerical integration method. In observation of limit cycle oscillations (LCO and evolution of dynamic behaviors, nonlinear aerodynamic loading produces a smaller positive deflection peak and more complex bifurcation diagrams compared with linear aerodynamics. Moreover, a LCO obtained with the linear aerodynamics is mostly a nonsimple harmonic motion but when the aerodynamic nonlinearity is considered more complex motions are obtained, which is important in the evaluation of fatigue life. The parameters of Mach number, dynamic pressure, and in-plane thermal stresses all affect the aerodynamic nonlinearity. For a specific Mach number, there is a critical dynamic pressure beyond which the aerodynamic nonlinearity has to be considered. For a higher temperature, a lower critical dynamic pressure is required. Each nonlinear aerodynamic term in the full third-order piston theory is evaluated, based on which the nonlinear aerodynamic formulation has been simplified.
Directory of Open Access Journals (Sweden)
Iñigo Arregui
2012-04-01
Full Text Available Prominences are intriguing, but poorly understood, magnetic structures of the solar corona. The dynamics of solar prominences has been the subject of a large number of studies, and of particular interest is the study of prominence oscillations. Ground- and space-based observations have confirmed the presence of oscillatory motions in prominences and they have been interpreted in terms of magnetohydrodynamic (MHD waves. This interpretation opens the door to perform prominence seismology, whose main aim is to determine physical parameters in magnetic and plasma structures (prominences that are difficult to measure by direct means. Here, we review the observational information gathered about prominence oscillations as well as the theoretical models developed to interpret small amplitude oscillations and their temporal and spatial attenuation. Finally, several prominence seismology applications are presented.
Noisy Oscillations in the Actin Cytoskeleton of Chemotactic Amoeba
Negrete, Jose; Pumir, Alain; Hsu, Hsin-Fang; Westendorf, Christian; Tarantola, Marco; Beta, Carsten; Bodenschatz, Eberhard
2016-09-01
Biological systems with their complex biochemical networks are known to be intrinsically noisy. Here we investigate the dynamics of actin polymerization of amoeboid cells, which are close to the onset of oscillations. We show that the large phenotypic variability in the polymerization dynamics can be accurately captured by a generic nonlinear oscillator model in the presence of noise. We determine the relative role of the noise with a single dimensionless, experimentally accessible parameter, thus providing a quantitative description of the variability in a population of cells. Our approach, which rests on a generic description of a system close to a Hopf bifurcation and includes the effect of noise, can characterize the dynamics of a large class of noisy systems close to an oscillatory instability.
Flutter analysis of an airfoil with multiple nonlinearities and uncertainties
Directory of Open Access Journals (Sweden)
Haitao Liao
2013-09-01
Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.
Nonlinear absorption in discrete systems
Energy Technology Data Exchange (ETDEWEB)
Spire, A; Leon, J [Physique Mathematique et Theorique, CNRS-UMR5825, Universite Montpellier 2, 34095 Montpellier (France)
2004-10-01
In the context of nonlinear scattering, a continuous wave incident onto a nonlinear discrete molecular chain of coupled oscillators can be partially absorbed as a result of a three-wave resonant interaction that couples two HF-waves of frequencies close to the edge of the Brillouin zone. Hence both nonlinearity and discreteness are necessary for generating this new absorption process which manifests itself by soliton generation in the medium. As a paradigm of this nonlinear absorption we consider here the Davydov model that describes exciton-phonon coupling in hydrogen-bonded molecular chains.
Rutten, R.J.
1999-01-01
This review concentrates on the quiet-Sun chromosphere. Its internetwork areas are dynamically dominated by the so-called chromospheric three-minute oscillation. They are interpretationally dominated by the so-called Ca II K 2V and H 2V grains. The main points of this review are that the one
The landscape of nonlinear structural dynamics: an introduction.
Butlin, T; Woodhouse, J; Champneys, A R
2015-09-28
Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner's guide to what hitherto might seem like a vast and complex research landscape. © 2015 The Authors.
PT -symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
Note that there are two special cases (i.e. when q = −1, −1/3) when A2 only satisfies quadratic equation. 5.5 A novel exact solution of the RWA equations. In addition to the solutions just discussed, the coupled eqs (69) and (70) also have a novel exact solution φ1 = e(γ /2)t−(ia/γ ) sinh(γ t+φ)−ibt , φ2 = e−(γ /2)t−(ia/γ ) sinh(γ ...
Effect of boundary on controlled memristor-based oscillator
Fouda, Mohamed E.
2012-10-01
Recently, the applications of memristors have spread into many fields and especially in the circuit theory. Many models have been proposed for the HP-memristor based on the window functions. In this paper, we introduce a complete mathematical analysis of the controlled reactance-less oscillator for two different window functions of Joglekar\\'s model (linear and nonlinear dopant drift) to discuss the effect of changing the window function on the oscillator\\'s behavior. The generalized necessary and sufficient conditions based on the circuit elements and control voltages for both the linear and nonlinear models are introduced. Moreover, closed form expressions for the oscillation frequency and duty cycle are derived for these models and verified using PSPICE simulations showing an excellent matching. Finally a comparison between the linear and nonlinear models which shows their effect on the oscillation frequency and conditions of oscillation is introduced. © 2012 IEEE.
Oscillations-free PID control of anesthetic drug delivery in neuromuscular blockade.
Medvedev, Alexander; Zhusubaliyev, Zhanybai T; Rosén, Olov; Silva, Margarida M
2016-07-25
The PID-control of drug delivery or the neuromuscular blockade (NMB) in closed-loop anesthesia is considered. The NMB system dynamics portrayed by a Wiener model can exhibit sustained nonlinear oscillations under realistic PID gains and for physiologically feasible values of the model parameters. Such oscillations, also repeatedly observed in clinical trials, lead to under- and over-dosing of the administered drug and undermine patient safety. This paper proposes a tuning policy for the proportional PID gain that via bifurcation analysis ensures oscillations-free performance of the control loop. Online estimates of the Wiener model parameters are needed for the controller implementation and monitoring of the closed-loop proximity to oscillation. The nonlinear dynamics of the PID-controlled NMB system are studied by bifurcation analysis. A database of patient models estimated under PID-controlled neuromuscular blockade during general anesthesia is utilized, along with the corresponding clinical measurements. The performance of three recursive algorithms is compared in the application at hand: an extended Kalman filter, a conventional particle filter (PF), and a PF making use of an orthonormal basis to estimate the probability density function from the particle set. It is shown that with a time-varying proportional PID gain, the type of equilibria of the closed-loop system remains the same as in the case of constant controller gains. The recovery time and frequency of oscillations are also evaluated in simulation over the database of patient models. Nonlinear identification techniques based on model linearization yield biased parameter estimates and thus introduce superfluous uncertainty. The bias and variance of the estimated models are related to the computational complexity of the identification algorithms, highlighting the superiority of the PFs in this safety-critical application. The study demonstrates feasibility of the proposed oscillation-free control
Waves and Oscillations in Plasmas
Pecseli, Hans L
2012-01-01
The result of more than 15 years of lectures in plasma sciences presented at universities in Denmark, Norway, and the United States, Waves and Oscillations in Plasmas addresses central issues in modern plasma sciences. The book covers fluid models as well as kinetic plasma models, including a detailed discussion of, for instance, collisionless Landau damping. Offering a clear separation of linear and nonlinear models, the book can be tailored for readers of varying levels of expertise.Designed to provide basic training in linear as well as nonlinear plasma dynamics, and practical in areas as d
2013-01-01
This book offers a comprehensive picture of nonequilibrium phenomena in nanoscale systems. Written by internationally recognized experts in the field, this book strikes a balance between theory and experiment, and includes in-depth introductions to nonequilibrium fluctuation relations, nonlinear dynamics and transport, single molecule experiments, and molecular diffusion in nanopores. The authors explore the application of these concepts to nano- and biosystems by cross-linking key methods and ideas from nonequilibrium statistical physics, thermodynamics, stochastic theory, and dynamical s
Hydrodynamic Force on a Cylinder Oscillating at Low Frequency
Berg, Robert F.; Yao, Minwu; Panzarella, Charles H.
2007-01-01
The hydrodynamic force on a cylinder oscillating transversely to its axis is a nonlinear function of the displacement amplitude x0. We report measurements and numerical calculations of the force at frequencies low enough that delta > R, where delta is the viscous penetration length and R is the cylinder radius. For small amplitudes, the numerically calculated Fourier transform of the force per unit length, F(sub small), agrees with Stokes' analytical calculation. For larger amplitudes, the force per unit length found by both calculation and measurement is F = F(sub small)C (x(sub 0)/delta,R/delta). The complex function C depends only weakly on R/delta, indicating that x0/delta is more appropriate as a scaling variable than the Keulegan-Carpenter number KC = pi*x(sub 0)/R. The measurements used a torsion oscillator driven at frequencies from 1 to 12 Hz while immersed in dense xenon. The oscillator comprised cylinders with an effective radius of R = 13.4 micron and oscillation amplitudes as large as x(sub 0)/delta = 4 (corresponding to KC as large as 71). The calculations used similar conditions except that the amplitudes were as large as x0/delta = 28.
Nonlinearity and nonclassicality in a nanomechanical resonator
Energy Technology Data Exchange (ETDEWEB)
Teklu, Berihu [Clermont Universite, Blaise Pascal University, CNRS, PHOTON-N2, Institut Pascal, Aubiere Cedex (France); Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy); Ferraro, Alessandro; Paternostro, Mauro [Queen' s University, Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Belfast (United Kingdom); Paris, Matteo G.A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy)
2015-12-15
We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems. (orig.)
Advances in dynamics, patterns, cognition challenges in complexity
Pikovsky, Arkady; Rulkov, Nikolai; Tsimring, Lev
2017-01-01
This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Celebrating seminal contributions to the field by Prof. M. I. Rabinovich of the University of California at San Diego, this volume brings together perspectives on both the fundamental aspects of complexity studies, as well as in applications in different fields ranging from granular patterns to understanding of the cognitive brain and mind dynamics. The slate of world-class authors review recent achievements that together present a broad and coherent coverage of modern research in complexity greater than the sum of its parts. Presents the most up-to-date developments in the studies of complexity Combines basic and applied aspects Links background nonlinear theory of oscillations and waves with modern approaches Allows readers to recognize general dynamical principles across the applications fields.
OnWien Bridge Oscillators as Modified Multi-vibrators
DEFF Research Database (Denmark)
Lindberg, Erik
2014-01-01
A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals......A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals...
Friction and nonlinear dynamics
Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.
2016-01-01
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.
Graffi, Dario
2011-01-01
L. Cesari: Non-linear analysis.- J.K. Hale: Oscillations in neutral functional differential equations.- M. Jean: Elements de la theorie des equations differentielles avec commandes.- J. Mawhin: Un apercu des recherches belges en theorie des equations differentielles ordinaires dans le champ reel entre 1967 et 1972.- Yu A. Mitropol'skii: Certains aspects des progres de la methode de centrage.- Th. Vogel: Quelques problemes non lineaires en physique mathematique.
Rayleigh-type parametric chemical oscillation.
Ghosh, Shyamolina; Ray, Deb Shankar
2015-09-28
We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.
Minimal model for complex dynamics in cellular processes
Suguna, C.; Chowdhury, Kanchan K.; Sinha, Somdatta
1999-11-01
Cellular functions are controlled and coordinated by the complex circuitry of biochemical pathways regulated by genetic and metabolic feedback processes. This paper aims to show, with the help of a minimal model of a regulated biochemical pathway, that the common nonlinearities and control structures present in biomolecular interactions are capable of eliciting a variety of functional dynamics, such as homeostasis, periodic, complex, and chaotic oscillations, including transients, that are observed in various cellular processes.
Dynamics-Enabled Nanoelectromechanical Systems (NEMS) Oscillators
2014-06-01
AFRL-RY-WP-TR-2014-0144 DYNAMICS-ENABLED NANOELECTROMECHANICAL SYSTEMS ( NEMS ) OSCILLATORS Michael Roukes California Institute...SYSTEMS ( NEMS ) OSCILLATORS 5a. CONTRACT NUMBER FA8650-10-1-7029 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 61101E 6. AUTHOR(S) Michael Roukes...engineer, and demonstrate nonlinear-dynamics-enabled nanoelectromechanical system ( NEMS ) frequency-source technology. 15. SUBJECT TERMS
Energy Technology Data Exchange (ETDEWEB)
Márquez, Bicky A., E-mail: bmarquez@ivic.gob.ve; Suárez-Vargas, José J., E-mail: jjsuarez@ivic.gob.ve; Ramírez, Javier A. [Centro de Física, Instituto Venezolano de Investigaciones Científicas, km. 11 Carretera Panamericana, Caracas 1020-A (Venezuela, Bolivarian Republic of)
2014-09-01
Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.
Srivastava, Ambrish Kumar; Kumar, Abhishek; Misra, Neeraj
2017-08-01
We propose a new class of endofullerene complexes by encapsulating superalkali species (viz. FLi2, OLi3 and NLi4) within C60 and then interacting with superhalogens (viz. BF4, BCl4 and BBr4). Our DFT calculations reveal that all M@C60-BF4 (M = FLi2 < OLi3 < NLi4) endofullerene complexes are stable against complexation and deencapsulation. The first order mean hyperpolarizability (βo) values decrease with the increase in the size of encapsulated superalkalis but increase with the increase in the size of superhalogen. The trend of βo values has been explained by TDDFT calculated parameters for crucial electronic transitions of endofullerene complexes.
Graf, Rudolf F
1996-01-01
This series of circuits provides designers with a quick source for oscillator circuits. Why waste time paging through huge encyclopedias when you can choose the topic you need and select any of the specialized circuits sorted by application?This book in the series has 250-300 practical, ready-to-use circuit designs, with schematics and brief explanations of circuit operation. The original source for each circuit is listed in an appendix, making it easy to obtain additional information.Ready-to-use circuits.Grouped by application for easy look-up.Circuit source listing
Power oscillation damping controller
DEFF Research Database (Denmark)
2012-01-01
A power oscillation damping controller is provided for a power generation device such as a wind turbine device. The power oscillation damping controller receives an oscillation indicating signal indicative of a power oscillation in an electricity network and provides an oscillation damping control...... signal in response to the oscillation indicating signal, by processing the oscillation damping control signal in a signal processing chain. The signal processing chain includes a filter configured for passing only signals within a predetermined frequency range....
Monte Carlo filters for identification of nonlinear structural dynamical ...
Indian Academy of Sciences (India)
relevance in structural engineering has not yet been explored in the existing literature. Accord- ingly, in the present work, we apply three simulation-based filtering strategies to the problem of system parameter identification in two typical nonlinear oscillators, namely, the Duffing oscillator and the Coulomb oscillator.
Tamer, Ömer; Avcı, Davut; Atalay, Yusuf; Çoşut, Bünyemin; Zorlu, Yunus; Erkovan, Mustafa; Yerli, Yusuf
2016-02-01
A novel manganese (II) complex with picolinic acid (pyridine 2-carboxylic acid, Hpic), namely, [Mn(pic)2(H2O)2] was prepared and its crystal structure was fully characterized by using single crystal X-ray diffraction. Picolinate (pic) ligands were coordinated to the central manganese(II) ion as bidentate N,O-donors through the nitrogen atoms of pyridine rings and the oxygen atoms of carboxylate groups forming five-membered chelate rings. The spectroscopic characterization of Mn(II) complex was performed by the applications of FT-IR, Raman, UV-vis and EPR techniques. In order to support these studies, density functional theory (DFT) calculations were carried out by using B3LYP level. IR and Raman spectra were simulated at B3LYP level, and obtained results indicated that DFT calculations generally give compatible results to the experimental ones. The electronic structure of the Mn(II) complex was predicted using time dependent DFT (TD-DFT) method with polarizable continuum model (PCM). Molecular stability, hyperconjugative interactions, intramolecular charge transfer (ICT) and bond strength were investigated by applying natural bond orbital (NBO) analysis. Nonlinear optical properties of Mn(II) complex were investigated by the determining of molecular polarizability (α) and hyperpolarizability (β) parameters.
Is the quadrature oscillator a multivibrator?
DEFF Research Database (Denmark)
Lindberg, Erik
2004-01-01
The aim of this article is to give insight into the mechanisms behind the behavior of oscillators from a new angle, introducing the idea of "frozen eigenvalues". This approach is based on piecewise-linear modelling and a study of the eigenvalues of the time varying linearized Jacobian of the nonl......The aim of this article is to give insight into the mechanisms behind the behavior of oscillators from a new angle, introducing the idea of "frozen eigenvalues". This approach is based on piecewise-linear modelling and a study of the eigenvalues of the time varying linearized Jacobian...... of the nonlinear differential equations describing the oscillator. A multivibrator and a quadrature oscillator are used as test examples. The mechanisms behind the oscillations of the two circuits are compared....
Oscillation of first order neutral delay differential equations
Directory of Open Access Journals (Sweden)
John Graef
2004-08-01
Full Text Available In this paper, the authors established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.
Modified Legendre Wavelets Technique for Fractional Oscillation Equations
Directory of Open Access Journals (Sweden)
Syed Tauseef Mohyud-Din
2015-10-01
Full Text Available Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinear fractional order oscillation equation into a fractional order recurrence relation and then Legendre wavelets method is applied on the converted problem. In order to check the efficiency and accuracy of the suggested modification, we have considered three problems namely: fractional order force-free Duffing–van der Pol oscillator, forced Duffing–van der Pol oscillator and higher order fractional Duffing equations. The obtained results are compared with the results obtained via other techniques.
Energy Technology Data Exchange (ETDEWEB)
Bhattacharjee, Saurav, E-mail: sauravtsk.bhattacharjee@gmail.com; Das, Nilakshi [Department of Physics, Tezpur University, Assam 784028 (India)
2015-10-15
A systematic theoretical investigation has been carried out on the role of dust charging dynamics on the nature and stability of DIA (Dust Ion Acoustic) mode in complex plasma. The study has been made for both linear and non-linear scale regime of DIA mode. The observed results have been characterized in terms of background plasma responses towards dust surface responsible for dust charge fluctuation, invoking important dusty plasma parameters, especially the ion flow speed and dust size. The linear analyses confirm the nature of instability in DIA mode in presence of dust charge fluctuation. The instability shows a damping of DIA mode in subsonic flow regime followed by a gradual growth in instability in supersonic limit of ion flow. The strength of non-linearity and their existence domain is found to be driven by different dusty plasma parameters. As dust is ubiquitous in interstellar medium with plasma background, the study also addresses the possible effect of dust charging dynamics in gravito-electrostatic characterization and the stability of dust molecular clouds especially in proto-planetary disc. The observations are influential and interesting towards the understanding of dust settling mechanism and formation of dust environments in different regions in space.
Senthilkumar, Kabali; Thirumoorthy, Krishnan; Vinitha, G.; Soni, Kiran; Bhuvanesh, Nattamai S. P.; Palanisami, Nallasamy
2017-01-01
The d10 metal complexes based on 3-methyl-5-ferrocenyl-1H-pyrazole (L = 3-Me-5-FcPz) ligand [M(L)4(NO3)2] Zn=(1) and Cd=(2), [Hg(L)4(NO3)2].dmf (3) have been synthesized and characterized by FT-IR, NMR, UV-Vis and elemental analysis. The molecular structure of compound 2 and its crystal packing were determined by single crystal X-ray diffraction. The nitrate anions are also involved in intermolecular hydrogen bonding with adjacent ferrocene units and it forms zig-zag one-dimensional polymeric structure. UV-Vis investigations on the positive solvatochromic behavior of 1-3 revealed that the solvation of the push-pull character increases with increasing polarity. The third-order nonlinear optical (NLO) properties of 1-3 have been determined by Z-scan technique and the results indicate that compounds 1-3 exhibits the strong self-defocusing effect. The nonlinear susceptibility χ(3) values are calculated in the order of 10-6 esu.
The approach to investigation of the the regions of self-oscillations
Velieva, T. R.; Kulyabov, D. S.; Korolkova, A. V.; Zaryadov, I. S.
2017-12-01
Self-oscillating modes in control systems of computer networks quite negatively affect the characteristics of these networks. The problem of finding the areas of self-oscillations is actual and important as the study of parameters of self-oscillations. Due to the significant nonlinearity of control characteristics, the study of the self-oscillating modes presents certain difficulties. This paper describes the technique of research of self-oscillating modes.
Vecchiarelli, Anthony G.; Li, Min; Mizuuchi, Michiyo; Hwang, Ling Chin; Seol, Yeonee; Neuman, Keir C.; Mizuuchi, Kiyoshi
2016-01-01
The Escherichia coli Min system self-organizes into a cell-pole to cell-pole oscillator on the membrane to prevent divisions at the cell poles. Reconstituting the Min system on a lipid bilayer has contributed to elucidating the oscillatory mechanism. However, previous in vitro patterns were attained with protein densities on the bilayer far in excess of those in vivo and failed to recapitulate the standing wave oscillations observed in vivo. Here we studied Min protein patterning at limiting MinD concentrations reflecting the in vivo conditions. We identified “burst” patterns—radially expanding and imploding binding zones of MinD, accompanied by a peripheral ring of MinE. Bursts share several features with the in vivo dynamics of the Min system including standing wave oscillations. Our data support a patterning mechanism whereby the MinD-to-MinE ratio on the membrane acts as a toggle switch: recruiting and stabilizing MinD on the membrane when the ratio is high and releasing MinD from the membrane when the ratio is low. Coupling this toggle switch behavior with MinD depletion from the cytoplasm drives a self-organized standing wave oscillator. PMID:26884160
Leder, Ron S.
2002-08-01
Our example from nature is two groups of about 10,000 cells in the brain called Suprachiasmatic Nuclei (SCN) and how light can entrain free running endogenous periodic behavior via the retina's connection to the SCN. Our major question is how a complex behavior like this can arise in nature. Finally presented is a mathematical model and simulation showing how simple periodic signals can be coupled to produce spatio-temporal chaotic behavior and how two complex signals can combine to produce simple coherent behavior with a hypothetical analogy to phase resetting in biological circadian pacemakers.
Gündüzalp, Ayla Balaban; Özsen, İffet; Alyar, Hamit; Alyar, Saliha; Özbek, Neslihan
2016-09-01
Schiff bases; 1,8-bis(thiophene-2-carboxaldimine)-p-menthane (L1) and 1,8-bis(furan-2-carboxaldimine)-p-menthane (L2) have been synthesized and characterized by elemental analysis, 1Hsbnd 13C NMR, UV-vis, FT-IR and LC-MS methods. 1H and 13C shielding tensors for L1 and L2 were calculated with GIAO/DFT/B3LYP/6-311++G(d,p) methods in CDCl3. The vibrational band assignments, nonlinear optical (NLO) activities, frontier molecular orbitals (FMOs) and absorption spectrum have been investigated by the same basis set. Schiff base-copper(II) complexes have been synthesized and structurally characterized with spectroscopic methods, magnetic and conductivity measurements. The spectroscopic data suggest that Schiff base ligands coordinate through azomethine-N and thiophene-S/furan-O donors (as SNNS and ONNO chelating systems) to give a tetragonal geometry around the copper(II) ions. Schiff bases and Cu(II) complexes have been screened for their biological activities on different species of pathogenic bacteria, those are, Gram positive bacteria: Bacillus subtitilus, Yersinia enterotica, Bacillus cereus, Listeria monocytogenes, Micrococcus luteus and Gram negative bacteria: Escherichia coli, Pseudomonas aeroginosa, Shigella dysenteriae, Salmonella typhi, Klebsiella pseudomonas by using microdilution technique (MIC values in mM). Biological activity results show that Cu(II) complexes have higher activities than parent ligands and metal chelation may affect significantly the antibacterial behavior of the organic ligands.
Optical transitions and Rabi oscillations in waveguide arrays.
Makris, K G; Christodoulides, D N; Peleg, O; Segev, M; Kip, D
2008-07-07
It is theoretically demonstrated that Rabi interband oscillations are possible in waveguide arrays. Such transitions can take place in optical lattices when the unit-cell is periodically modulated along the propagation direction. Under phase-matching conditions, direct power transfer between two Floquet-Bloch modes can occur. In the nonlinear domain, periodic oscillations between two different lattice solitons are also possible.
Haar Wavelet Operational Matrix Method for Fractional Oscillation Equations
Directory of Open Access Journals (Sweden)
Umer Saeed
2014-01-01
Full Text Available We utilized the Haar wavelet operational matrix method for fractional order nonlinear oscillation equations and find the solutions of fractional order force-free and forced Duffing-Van der Pol oscillator and higher order fractional Duffing equation on large intervals. The results are compared with the results obtained by the other technique and with exact solution.
Porta, Alberto; De Maria, Beatrice; Bari, Vlasta; Marchi, Andrea; Faes, Luca
2017-06-01
We test the hypothesis that the linear model-based (MB) approach for the estimation of conditional entropy (CE) can be utilized to assess the complexity of the cardiac control in healthy individuals. An MB estimate of CE was tested in an experimental protocol (i.e., the graded head-up tilt) known to produce a gradual decrease of cardiac control complexity as a result of the progressive vagal withdrawal and concomitant sympathetic activation. The MB approach was compared with traditionally exploited nonlinear model-free (MF) techniques such as corrected approximate entropy, sample entropy, corrected CE, two k -nearest-neighbor CE procedures and permutation CE. Electrocardiogram was recorded in 17 healthy subjects at rest in supine position and during head-up tilt with table angles of 15°, 30°, 45°, 60°, and 75°. Heart period (HP) was derived as the temporal distance between two consecutive R-wave peaks and analysis was carried out over stationary sequences of 256 successive HPs. The performance of the MB method in following the progressive decrease of HP complexity with tilt table angles was in line with those of MF approaches and the MB index was remarkably correlated with the MF ones. The MB approach can be utilized to monitor the changes of the complexity of the cardiac control, thus speeding up dramatically the CE calculation. The remarkable performance of the MB approach challenges the notion, generally assumed in cardiac control complexity analysis based on CE, about the need of MF techniques and could allow real-time applications.
Nonlinear optical interactions in silicon waveguides
Directory of Open Access Journals (Sweden)
Kuyken B.
2017-03-01
Full Text Available The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.
Dependence of synchronization frequency of Kuramoto oscillators ...
Indian Academy of Sciences (India)
matically by Wiener [7,8]. He realized the ubiquity of the phenomenon and speculated its involvement in the generation of alpha rhythms in the brain. ..... [6] Y Kuramoto, Chemical oscillations, waves, and turbulence (Dover Publications, Mineola,. New York, 2003). [7] N Wiener, Nonlinear problem in random theory edited by ...
Nigmatullin, Raul R.; Khramov, A.S.; Kiyamov, A.G.; Fatkhullin, B. F.; Machado, J. A. Tenreiro; Baleanu, Dumitru
2015-01-01
New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small ...
Mechano-chemical oscillations and waves in reactive gels
Yashin, Victor V.; Kuksenok, Olga; Dayal, Pratyush; Balazs, Anna C.
2012-06-01
We review advances in a new area of interdisciplinary research that concerns phenomena arising from inherent coupling between non-linear chemical dynamics and mechanics. This coupling provides a route for chemical-to-mechanical energy transduction, which enables materials to exhibit self-sustained oscillations and/or waves in both concentration and deformation fields. We focus on synthetic polymer gels, where the chemo-mechanical behavior can be engineered into the material. We provide a brief review of experimental observations on several types of chemo-mechanical oscillations in gels. Then, we discuss methods used to theoretically and computationally model self-oscillating polymer gels. The rest of the paper is devoted to describing results of theoretical and computational modeling of gels that undergo the oscillatory Belousov-Zhabotinsky (BZ) reaction. We discuss a remarkable form of mechano-chemical transduction in these materials, where the application of an applied force or mechanical contact can drive the system to switch between different dynamical behavior, or alter the mechanical properties of the material. Finally, we discuss ways in which photosensitive BZ gels could be used to fabricate biomimetic self-propelled objects. In particular, we describe how non-uniform illumination can be used to direct the movement of BZ gel ‘worms’ along complex paths, guiding them to bend, reorient and turn.
Linear stability analysis of collective neutrino oscillations without spurious modes
Morinaga, Taiki; Yamada, Shoichi
2018-01-01
Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.
International Conference on Applications in Nonlinear Dynamics
Longhini, Patrick; Palacios, Antonio
2017-01-01
This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.
Practical design of a nonlinear tuned vibration absorber
DEFF Research Database (Denmark)
Grappasonni, C.; Habib, G.; Detroux, T.
2014-01-01
The aim of the paper is to develop a new nonlinear tuned vibration absorber (NLTVA) capable of mitigating the vibrations of nonlinear systems which are known to exhibit frequency-energy-dependent oscillations. A nonlinear generalization of Den Hartog's equal-peak method is proposed to ensure equal...
Modeling microtubule oscillations
DEFF Research Database (Denmark)
Jobs, E.; Wolf, D.E.; Flyvbjerg, H.
1997-01-01
Synchronization of molecular reactions in a macroscopic volume may cause the volume's physical properties to change dynamically and thus reveal much about the reactions. As an example, experimental time series for so-called microtubule oscillations are analyzed in terms of a minimal model...... for this complex polymerization-depolymerization cycle. The model reproduces well the qualitatively different time series that result from different experimental conditions, and illuminates the role and importance of individual processes in the cycle. Simple experiments are suggested that can further test...... and define the model and the polymer's reaction cycle....
A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network
Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien
2017-03-01
With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices’ non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing.
Kiran, A. J.; Lee, H. W.; Sampath Kumar, H. C.; Rudresha, B. J.; Bhat, B. R.; Yeom, D.-I.; Kim, K.; Rotermund, F.
2010-03-01
A new coordination compound, chloro(1,10-phenanthroline-N, N')(triphenylphosphine)copper(I) dichloromethane, incorporated in poly(methyl methacrylate) exhibits superior nonlinear optical properties in the near-infrared spectral region. Its nonlinear response time and third-order nonlinear optical susceptibility at 800 nm are <= 90 fs and 1.8 × 10 - 10 esu, respectively. Considerable nonlinear absorption is observed with this sample, near 800 and 1250 nm. The contribution of the excited states to the total nonlinear absorption process is discussed. The results reveal the potential of this newly designed compound for multi-photon absorption-based photonic applications.
Directory of Open Access Journals (Sweden)
S.H. Chen
1996-01-01
Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.
Sustained oscillations in living cells
Danø, Sune; Sørensen, Preben Graae; Hynne, Finn
1999-11-01
Glycolytic oscillations in yeast have been studied for many years simply by adding a glucose pulse to a suspension of cells and measuring the resulting transient oscillations of NADH. Here we show, using a suspension of yeast cells, that living cells can be kept in a well defined oscillating state indefinitely when starved cells, glucose and cyanide are pumped into a cuvette with outflow of surplus liquid. Our results show that the transitions between stationary and oscillatory behaviour are uniquely described mathematically by the Hopf bifurcation. This result characterizes the dynamical properties close to the transition point. Our perturbation experiments show that the cells remain strongly coupled very close to the transition. Therefore, the transition takes place in each of the cells and is not a desynchronization phenomenon. With these two observations, a study of the kinetic details of glycolysis, as it actually takes place in a living cell, is possible using experiments designed in the framework of nonlinear dynamics. Acetaldehyde is known to synchronize the oscillations. Our results show that glucose is another messenger substance, as long as the glucose transporter is not saturated.
Harmonic oscillator in Snyder space: The classical case and the ...
Indian Academy of Sciences (India)
This modified parameters give us a modified energy spectrum also. Keywords. Harmonic oscillator ... time where the non-commutativity of space operators is proportional to non-linear combinations of phase ... in §4. 2. The classical case. Classical n dimensional Snyder space is characterized by its non-linear commutation.
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Oscillating fluorescence in an unstable colloidal dispersion of CdSe/ZnS core/shell quantum dots.
Komoto, Atsushi; Maenosono, Shinya; Yamaguchi, Yukio
2004-09-28
Fluorescence oscillation is observed in an ensemble of colloidal CdSe/ZnS core/shell quantum dots (QDs) dispersed in nonpolar solvent under continuous irradiation. The QDs dispersed in toluene gradually aggregate and change their fluorescence intensity, even in the dark. During the aggregation, the QD/toluene suspension is unstable, that is, overdispersed. The fluorescence oscillation is found only in this unstable state before the system reaches steady state. In addition, the aggregation rate is promoted by irradiation and strongly correlates with the oscillation amplitude. Our experimental results indicate that the dispersion instability plays an important role in both linear and nonlinear dynamics of the fluorescence. It is inferred from the experimental results and previous studies that the complex time evolution of fluorescence in the QD/toluene dispersion is possibly due to adsorption and desorption of surface ligand molecules over the course of QD aggregation.
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Zhao, De-Min; Zhang, Qi-Chang
2010-03-01
The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attention. The Poincaré mapping method and Floquet theory are adopted to analyse the limit cycle oscillation flutter and chaotic motion of this system. The result shows that the limit cycle oscillation flutter can be accurately predicted by the Floquet multiplier. The phase trajectories of both the pitch and plunge motion are obtained and the results show that the plunge motion is much more complex than the pitch motion. It is also proved that initial conditions have important influences on the dynamics character of the airfoil system. In a certain range of airspeed and with the same system parameters, the stable limit cycle oscillation, chaotic and multi-periodic motions can be detected under different initial conditions. The figure of the Poincaré section also approves the previous conclusion.
Introduction to classical and quantum harmonic oscillators
Bloch, Sylvan C
2013-01-01
From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con
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
Wave Physics Oscillations - Solitons - Chaos
Nettel, Stephen
2009-01-01
This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior.
Special Section on Synchronization in Nonlinear Science and Engineering
Ikeguchi, Tohru; Tokuda, Isao
Synchronization is a ubiquitous phenomenon of coupled nonlinear oscillators, commonly found in physics, engineering, biology, and other diverse disciplines. It has a long research history back to Christiaan Huygens, who discovered synchronized motion of two pendulum clocks in 1673. It is very easy to observe synchronization in our daily life: e.g., metronomes, candle fires, pet-bottle oscillators, saltwater oscillators, and so on(See, for example, experimental movies at http://www.youtube.com/user/IkeguchiLab?feature=watch). For the last few decades, significant development has been made from both theories and experiments on synchronization of coupled limit cycle oscillators as well as coupled chaotic oscillators. Applications have been also developed to communication technologies, controlling techniques, and data analysis. Combined with the idea from complex network theory, neuroscience, and systems biology, the research speed of synchronization has been even accelerated. This Special Section of NOLTA is primarily dedicated to the recent advanced development of basics and applications of synchronization in science and engineering. A number of qualified works is included, ranging from experimental study on synchronization of Huygens' system, analog circuits, and singing voice to applied study of synchronization in communication networks. One invited paper is devoted to comprehensive reviews on generalized synchronization of chaotic oscillators. On behalf of the editorial committee of the special section, the guest editors would like to express their sincere thanks to all the authors for their excellent contributions. In particular, they are grateful to Prof. Dr. Ulrich Parlitz for contributing his distinguished review article. They would also like to thank the reviewers and the members of the guest editorial committee, especially Prof. Hiroo Sekiya of Chiba University and the editorial staffs of the NOLTA journal, for their supports on publishing this Special
Sanchez-Vila, X.; Rubol, S.; Fernandez-Garcia, D.
2011-12-01
Despite the fact that the prognoses on the availability of resources related to different climate scenarios have been already formulated, the complex hydrological and biogeochemical reactions taking place in different compartments in natural environmental media are poorly understood, especially regarding the interactions between water bodies, and the reactions taking place at soil-water interfaces. Amongst them, the inter-relationship between hydrology, chemistry and biology has important implications in natural (rivers, lakes) and man-made water facilities (lagoons, artificial recharge pounds, reservoirs, slow infiltration systems, etc). The consequences involve environment, economic, social and health-risk aspects. At the current stage, only limited explanations are available to understand the implications of these relationships on ecosystem services, water quality and water quantity. Therefore, there is an urgent need to seek a full understanding of these physical-biogeochemical processes in water-bodies, sediments and biota and its implications in ecological and health risk. We present a soil column experiment and a mathematical model which aim to study the mutual interplay between water and bacteria activity in porous media, the corresponding dynamics and the feedback on nutrient cycling by using a multidisciplinary approach.
The Approximate Analysis of Nonlinear Behavior of Structure under Harmonic Loading
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2010-01-01
to the scientists in the field. Studying on nonlinear dynamics highlights the fact that essentially all dynamic systems encountered in the real world are nonlinear, meaning that their description as differential equations contains nonlinear terms. Such nonlinearities appear in different ways, such as through...... especially near fault regions, a part of the structure remains linear, but some part of it behaves nonlinearly; this is simulated by a damped nonlinear oscillator. In this paper, the nonlinear equation of oscillator with damping which is representative of the dynamic behavior of a structure has been solved...
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Energy Technology Data Exchange (ETDEWEB)
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
Dumur, Frédéric; Mayer, Cédric R; Hoang-Thi, Khuyen; Ledoux-Rak, Isabelle; Miomandre, Fabien; Clavier, Gilles; Dumas, Eddy; Méallet-Renault, Rachel; Frigoli, Michel; Zyss, Joseph; Sécheresse, Francis
2009-09-07
The synthesis, linear optical and nonlinear optical properties, as well as the electrochemical behavior of a series of pro-ligands containing the 4-(4-N,N-dimethylaminostyryl)-1-methyl pyridinium (DASP(+)) group as a push-pull moiety covalently linked to terpyridine or bipyridine as chelating ligands are reported in this full paper. The corresponding multifunctional Ru(II) and Zn(II) complexes were prepared and investigated. The structural, electronic, and optical properties of the pro-ligands and the ruthenium complexes were investigated using density functional theory (DFT) and time-dependent (TD) DFT calculations. A fairly good agreement was observed between the experimental and the calculated electronic spectra of the pro-ligands and their corresponding ruthenium complexes. A quenching of luminescence was evidenced in all ruthenium complexes compared with the free pro-ligands but even the terpyridine-functionalized metal complexes exhibited detectable luminescence at room temperature. Second order nonlinear optical (NLO) measurements were performed by Harmonic Light Scattering and the contribution of the DASP(+) moieties (and their relative ordering) and the metal-polypyridyl core need to be considered to explain the nonlinear optical properties of the metal complexes.
Global dynamics of a stochastic neuronal oscillator
Yamanobe, Takanobu
2013-11-01
Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.
Experimental study of the robust global synchronization of Brockett oscillators
Ahmed, Hafiz; Ushirobira, Rosane; Efimov, Denis
2017-12-01
This article studies the experimental synchronization of a family of a recently proposed oscillator model, i.e. the Brockett oscillator [R. Brockett, Synchronization without periodicity, in Mathematical Systems Theory, A Volume in Honor of U. Helmke, edited by K. Huper, J. Trumpf (CreateSpace, Seattle, USA, 2013), pp. 65-74]. Due to its structural property, Brockett oscillator can be considered as a promising benchmark nonlinear model for investigating synchronization and the consensus phenomena. Our experimental setup consists of analog circuit realizations of a network of Brockett oscillators. Experimental results obtained in this work correspond to the prior theoretical findings.
Kong, Ming; Liu, Yanqiu; Wang, Hui; Luo, Junshan; Li, Dandan; Zhang, Shengyi; Li, Shengli; Wu, Jieying; Tian, Yupeng
2015-01-25
Four novel Zn(II) terpyridine complexes (ZnLCl2, ZnLBr2, ZnLI2, ZnL(SCN)2) based on carbazole derivative group were designed, synthesized and fully characterized. Their photophysical properties including absorption and one-photon excited fluorescence, two-photon absorption (TPA) and optical power limiting (OPL) were further investigated systematically and interpreted on the basis of theoretical calculations (TD-DFT). The influences of different solvents on the absorption and One-Photon Excited Fluorescence (OPEF) spectral behavior, quantum yields and the lifetime of the chromophores have been investigated in detail. The third-order nonlinear optical (NLO) properties were investigated by open/closed aperture Z-scan measurements using femtosecond pulse laser in the range from 680 to 1080 nm. These results revealed that ZnLCl2 and ZnLBr2 exhibited strong two-photon absorption and ZnLCl2 showed superior optical power limiting property. Copyright © 2014 Elsevier B.V. All rights reserved.
Petnikova, V. M.; Shuvalov, Vladimir V.
2010-09-01
An approach based on the description of competition of quadratic processes of merging and decomposition of quanta resulting in the formation of cnoidal waves on an effective cascade cubic Kerr-type nonlinearity is used to optimise the scheme of a single-cavity optical parametric oscillator. It is shown that the use of a feedback circuit (cavity) decreases the period of cnoidal waves produced in a nonlinear crystal, while the optimisation procedure of the transfer constant of this circuit (reflectivity of the output mirror of the cavity) is reduced to matching this period with the nonlinear crystal length.
A synthesis theory for self-oscillating adaptive systems /SOAS/
Horowitz, I.; Smay, J.; Shapiro, A.
1974-01-01
A quantitative synthesis theory is presented for the Self-Oscillating Adaptive System (SOAS), whose nonlinear element has a static, odd character with hard saturation. The synthesis theory is based upon the quasilinear properties of the SOAS to forced inputs, which permits the extension of quantitative linear feedback theory to the SOAS. A reasonable definition of optimum design is shown to be the minimization of the limit cycle frequency. The great advantages of the SOAS is its zero sensitivity to pure gain changes. However, quasilinearity and control of the limit cycle amplitude at the system output, impose additional constraints which partially or completely cancel this advantage, depending on the numerical values of the design parameters. By means of narrow-band filtering, an additional factor is introduced which permits trade-off between filter complexity and limit cycle frequency minimization.
Robustness and period sensitivity analysis of minimal models for biochemical oscillators.
Caicedo-Casso, Angélica; Kang, Hye-Won; Lim, Sookkyung; Hong, Christian I
2015-08-12
Biological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.
Nonlinear effects of electrolyte diodes and transistors in a polymer gel medium.
Hegedus, Laszlo; Kirschner, Norbert; Wittmann, Maria; Simon, Peter; Noszticzius, Zoltan; Amemiya, Takashi; Ohmori, Takao; Yamaguchi, Tomohiko
1999-06-01
The polarization curve of an acid-base interface in a hydrogel medium has a diode characteristic. Two of each such electrolyte diodes can be combined to give an electrolyte transistor. When a salt is added to the alkaline or to the acidic part of a reverse biased electrolyte diode, the current response is highly nonlinear. If the salt is added to the acidic side, even bistability can be observed. This bistability can generate complex oscillations in a base-acid-base electrolyte transistor. These nonlinear effects are studied experimentally and theoretically. While the nonlinear salt effect can be explained with the Nernst-Planck equations, to understand the bistable behavior further investigations are necessary. (c) 1999 American Institute of Physics.
Oscillations in Mathematical Biology
1983-01-01
The papers in this volume are based on talks given at a one day conference held on the campus of Adelphi University in April 1982. The conference was organized with the title "Oscillations in Mathematical Biology;" however the speakers were allowed considerable latitutde in their choice of topics. In the event, the talks all concerned the dynamics of non-linear systems arising in biology so that the conference achieved a good measure of cohesion. Some of the speakers cho~e not to submit a manuscript for these proceedings, feeling that their material was too conjectural to be committed to print. Also the paper of Rinzel and Troy is a distillation of the two separate talks that the authors gave. Otherwise the material reproduces the conference proceedings. The conference was made possible by the generous support of the Office of the Dean of the College of Arts and Sciences at Adelphi. The bulk of the organization of the conference was carried out by Dr. Ronald Grisell whose energy was in large measure responsib...
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
Positive feedback promotes oscillations in negative feedback loops.
Ananthasubramaniam, Bharath; Herzel, Hanspeter
2014-01-01
A simple three-component negative feedback loop is a recurring motif in biochemical oscillators. This motif oscillates as it has the three necessary ingredients for oscillations: a three-step delay, negative feedback, and nonlinearity in the loop. However, to oscillate, this motif under the common Goodwin formulation requires a high degree of cooperativity (a measure of nonlinearity) in the feedback that is biologically "unlikely." Moreover, this recurring negative feedback motif is commonly observed augmented by positive feedback interactions. Here we show that these positive feedback interactions promote oscillation at lower degrees of cooperativity, and we can thus unify several common kinetic mechanisms that facilitate oscillations, such as self-activation and Michaelis-Menten degradation. The positive feedback loops are most beneficial when acting on the shortest lived component, where they function by balancing the lifetimes of the different components. The benefits of multiple positive feedback interactions are cumulative for a majority of situations considered, when benefits are measured by the reduction in the cooperativity required to oscillate. These positive feedback motifs also allow oscillations with longer periods than that determined by the lifetimes of the components alone. We can therefore conjecture that these positive feedback loops have evolved to facilitate oscillations at lower, kinetically achievable, degrees of cooperativity. Finally, we discuss the implications of our conclusions on the mammalian molecular clock, a system modeled extensively based on the three-component negative feedback loop.
Gotoda, Hiroshi; Amano, Masahito; Miyano, Takaya; Ikawa, Takuya; Maki, Koshiro; Tachibana, Shigeru
2012-12-01
We characterize complexities in combustion instability in a lean premixed gas-turbine model combustor by nonlinear time series analysis to evaluate permutation entropy, fractal dimensions, and short-term predictability. The dynamic behavior in combustion instability near lean blowout exhibits a self-affine structure and is ascribed to fractional Brownian motion. It undergoes chaos by the onset of combustion oscillations with slow amplitude modulation. Our results indicate that nonlinear time series analysis is capable of characterizing complexities in combustion instability close to lean blowout.
Phase locking between Josephson soliton oscillators
DEFF Research Database (Denmark)
Holst, T.; Hansen, Jørn Bindslev; Grønbech-Jensen, N.
1990-01-01
We report observations of phase-locking phenomena between two Josephson soliton (fluxon) oscillators biased in self-resonant modes. The locking strength was measured as a function of bias conditions. A frequency tunability of the phase-locked oscillators up to 7% at 10 GHz was observed. Two coupled...... perturbed sine-Gordon equations were derived from an equivalent circuit consisting of inductively coupled, nonlinear, lossy transmission lines. These equations were solved numerically to find the locking regions. Good qualitative agreement was found between the experimental results and the calculations...
Nonlinear dynamics in ventricular fibrillation.
Hastings, H M; Evans, S J; Quan, W; Chong, M L; Nwasokwa, O
1996-09-17
Electrogram recordings of ventricular fibrillation appear complex and possibly chaotic. However, sequences of beat-to-beat intervals obtained from these recordings are generally short, making it difficult to explicitly demonstrate nonlinear dynamics. Motivated by the work of Sugihara on atmospheric dynamics and the Durbin-Watson test for nonlinearity, we introduce a new statistical test that recovers significant dynamical patterns from smoothed lag plots. This test is used to show highly significant nonlinear dynamics in a stable canine model of ventricular fibrillation.
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...
Kleinberg, L. L.
1969-01-01
Microelectronic oscillator uses a bipolar transistor to circumvent the problem of developing suitable inductors for lower frequencies. The oscillator is fabricated by hybrid thin film techniques or by monolithic construction. Discrete microminiature components may also be employed.
Ma, Hongbin
2015-01-01
This book presents the fundamental fluid flow and heat transfer principles occurring in oscillating heat pipes and also provides updated developments and recent innovations in research and applications of heat pipes. Starting with fundamental presentation of heat pipes, the focus is on oscillating motions and its heat transfer enhancement in a two-phase heat transfer system. The book covers thermodynamic analysis, interfacial phenomenon, thin film evaporation, theoretical models of oscillating motion and heat transfer of single phase and two-phase flows, primary factors affecting oscillating motions and heat transfer, neutron imaging study of oscillating motions in an oscillating heat pipes, and nanofluid’s effect on the heat transfer performance in oscillating heat pipes. The importance of thermally-excited oscillating motion combined with phase change heat transfer to a wide variety of applications is emphasized. This book is an essential resource and learning tool for senior undergraduate, gradua...
Phenomenology of neutrino oscillations
Indian Academy of Sciences (India)
Abstract. The phenomenology of solar, atmospheric, supernova and laboratory neutrino oscillations is described. Analytical formulae for matter effects are reviewed. The results from oscillations are confronted with neutrinoless double beta decay.
Compactons in strongly nonlinear lattices
Ahnert, Karsten
2010-01-01
In the present work, we study wave phenomena in strongly nonlinear lattices. Such lattices are characterized by the absence of classical linear waves. We demonstrate that compactons – strongly localized solitary waves with tails decaying faster than exponential – exist and that they play a major role in the dynamics of the system under consideration. We investigate compactons in different physical setups. One part deals with lattices of dispersively coupled limit cycle oscillators which find ...
Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects
Directory of Open Access Journals (Sweden)
Jie-Yu Chen
2009-05-01
Full Text Available In Atomic force microscope (AFM examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale.
Traveling wave solutions of the nonlinear Schrödinger equation
Akbari-Moghanjoughi, M.
2017-10-01
In this paper, we investigate the traveling soliton and the periodic wave solutions of the nonlinear Schrödinger equation (NLSE) with generalized nonlinear functionality. We also explore the underlying close connection between the well-known KdV equation and the NLSE. It is remarked that both one-dimensional KdV and NLSE models share the same pseudoenergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlinear mathematical models, namely, the Helmholtz and the Duffing oscillators' potentials. It is found that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequency ratio for the Helmholtz potential between the nonlinear periodic carrier and the modulated sinusoidal waves is always in the range 0.5 ≤ Ω/ω ≤ 0.537285 regardless of the potential parameter values. The values of Ω/ω = {0.5, 0.537285} correspond to the cnoidal waves modulus of m = {0, 1} for soliton and sinusoidal limits and m = 0.5, respectively. Moreover, the current NLSE model is extended to fully NLSE (FNLSE) situation for Sagdeev oscillator pseudopotential which can be derived using a closed set of hydrodynamic fluid equations with a fully integrable Hamiltonian system. The generalized quasi-three-dimensional traveling wave solution is also derived. The current simple hydrodynamic plasma model may also be generalized to two dimensions and other complex situations including different charged species and cases with magnetic or gravitational field effects.
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Nico, V.; Frizzell, R.; Punch, J.
2017-04-01
Conventional vibration energy harvesters are generally based on linear mass-spring oscillator models. Major limitations with common designs are their narrow bandwidths and the increase of resonant frequency as the device is scaled down. To overcome these problems, a two-degree-of-freedom nonlinear velocity-amplified energy harvester has been developed. The device comprises two masses, oscillating one inside the other, between four sets of nonlinear magnetic springs. Impacts between the masses allow momentum transfer from the heavier mass to the lighter, providing velocity amplification. This paper studies the nonlinear effects introduced by the presence of magnetic springs, using high order spectral analysis techniques on experimental and simulated data obtained for a range of excitation levels and magnetic spring configurations, which enabled the effective spring constant to be varied. Standard power spectrum analysis only provide limited information on the response of nonlinear systems. Instead, bispectral analysis is used here to provide deeper insight of the complex dynamics of the nonlinear velocity-amplified energy harvester. The analysis allows identification of period-doubling and couplings between modes that could be used to choose geometrical parameters to enhance the bandwidth of the device.
Artificial Nonlinearity Generated from Electromagnetic Coupling Metamolecule
Wen, Yongzheng; Zhou, Ji
2017-04-01
A purely artificial mechanism for optical nonlinearity is proposed based on a metamaterial route. The mechanism is derived from classical electromagnetic interaction in a metamolecule consisting of a cut-wire meta-atom nested within a split-ring meta-atom. Induced by the localized magnetic field in the split-ring meta-atom, the magnetic force drives an anharmonic oscillation of free electrons in the cut-wire meta-atom, generating an intrinsically nonlinear electromagnetic response. An explicit physical process of a second-order nonlinear behavior is adequately described, which is perfectly demonstrated with a series of numerical simulations. Instead of "borrowing" from natural nonlinear materials, this novel mechanism of optical nonlinearity is artificially dominated by the metamolecule geometry and possesses unprecedented design freedom, offering fascinating possibilities to the research and application of nonlinear optics.
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
Indian Academy of Sciences (India)
Rahul Pandit
2008-10-31
Oct 31, 2008 ... ”The more complex a thing is, the more you can talk about it.” - attributed to Giorgio Parisi. ▻ ”C'est magnifique, mais ce n'est pas de la science.” (It is magnificent, but not all of it is science.) - attributed ... Earliest examples: theoretical computer science, algorithmic complexity, etc. ▻ Rapid progress after the ...
Complex spatiotemporal behavior in the photosensitive ferroin-bromate-4-nitrophenol reaction.
Bell, Jeffrey G; Wang, Jichang
2015-04-09
Investigation illustrates that the bromate-4-nitrophenol reaction in a stirred batch reactor undergoes spontaneous oscillations under very broad initial reactant concentrations. The addition of ferroin has subtle influences on the nonlinear behavior, in which the frequency and total number of oscillations were greatly reduced at a low or high ferroin concentration, as opposed to the significant increase at a moderate ferroin concentration. Temporal oscillations with a modulating frequency were also observed in the ferroin-bromate-4-nitrophenol system. In a capillary tube the ferroin-bromate-4-nitrophenol reaction generated propagating wave trains with various complex behaviors such as period-doubled intermittent propagation failure. Illumination was found to have a profound effect on the temporal oscillations in the bromate-4-nitrophenol reaction and on those long lasting wave activities. Spectroscopic studies were able to identify 1,4-benzoquinone, 2-bromo-1,4-benzoquinone, and 2-bromo-4-nitrophenol as major components during the reaction.
Oscillations and Waves in Sunspots
Directory of Open Access Journals (Sweden)
Elena Khomenko
2015-11-01
Full Text Available A magnetic field modifies the properties of waves in a complex way. Significant advances have been made recently in our understanding of the physics of sunspot waves with the help of high-resolution observations, analytical theories, as well as numerical simulations. We review the current ideas in the field, providing the most coherent picture of sunspot oscillations as by present understanding.
Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
Arroyo, Sebastián I
2014-01-01
We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, disclose new effects of nonlinearities on oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled -contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators -and, in particular, micromechanical oscillators- provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phase-shift control oscillations are stable over the whole resonance curve. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higher-harmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency whe...
Global Analysis of Nonlinear Dynamics
Luo, Albert
2012-01-01
Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.
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
Hierarchical Robust and Adaptive Nonlinear Control Design
National Research Council Canada - National Science Library
Haddad, Wassim
2003-01-01
The authors proposed the development of a general multiechelon hierarchical nonlinear switching control design framework that minimizes control law complexity subject to the achievement of control law robustness...
Phase Multistability in Coupled Oscillator Systems
DEFF Research Database (Denmark)
Mosekilde, Erik; Postnov, D.E.; Sosnovtseva, Olga
2003-01-01
The phenomenon of phase multistability arises in connection with the synchronization of coupled oscillator systems when the systems individually display complex wave forms associated, for instance, with the presence of subharmonic components or with significant variations of the phase velocity...... along the orbit of the individual oscillator. Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns. In particular we demonstrate the nested structure of synchronization regions for oscillations with multicrest wave forms...... and investigate how the number of spikes per train and the proximity of a neighboring equilibrium point can influence the formation of coexisting regimes in coupled bursters....
Nonlinear optics principles and applications
Rottwitt, Karsten
2014-01-01
IntroductionReview of linear opticsInduced polarizationHarmonic oscillator modelLocal field correctionsEstimated nonlinear responseSummaryTime-domain material responseThe polarization time-response functionThe Born-Oppenheimer approximationRaman scattering response function of silicaSummaryMaterial response in the frequency domain, susceptibility tensorsThe susceptibility tensorThe induced polarization in the frequency domainSum of monochromatic fieldsThe prefactor to the induced polarizationThird-order polarization in the Born-Oppenheimer approximation in the frequency domainKramers-Kronig relationsSummarySymmetries in nonlinear opticsSpatial symmetriesSecond-order materialsThird-order nonlinear materialsCyclic coordinate-systemContracted notation for second-order susceptibility tensorsSummaryThe nonlinear wave equationMono and quasi-monochromatic beamsPlane waves - the transverse problemWaveguidesVectorial approachNonlinear birefringenceSummarySecond-order nonlinear effectsGeneral theoryCoupled wave theoryP...
Chaos, Periodicity, and Quasiperiodicity in a Radio-Physical Oscillator
Wiggers, Vinícius; Rech, Paulo C.
2017-06-01
We report parameter planes displaying dynamical behaviors of a radio-physical oscillator system, which is modeled by a set of four-parameter three autonomous first-order nonlinear ordinary differential equations. Each parameter plane is numerically computed, and the dynamical behavior of each point is characterized by using the respective Lyapunov exponents spectrum. Chaotic, periodic, and quasiperiodic regions are therefore bounded in parameter planes of a radio-physical oscillator system.
Neurodynamics: nonlinear dynamics and neurobiology.
Abarbanel, H D; Rabinovich, M I
2001-08-01
The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.
Autonomous third-order duffing-holmes type chaotic oscillator
DEFF Research Database (Denmark)
Lindberg, Erik; Tamaseviciute, E; Mykolaitis, G
2009-01-01
A novel Duffing-Holmes type autonomous chaotic oscillator is described. In comparison with the well-known nonautonomous Duffing-Holmes circuit it lacks the external periodic drive, but includes two extra linear feedback subcircuits, namely a direct positive feedback loop, and an inertial negative...... feedback loop. In contrast to many other autonomous chaotic oscillators, including linear unstable resonators and nonlinear damping loops, the novel circuit is based on nonlinear resonator and linear damping loop in the negative feedback. SPICE simulation and hardware experimental investigations...
Non-linear stochastic response of a shallow cable
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2004-01-01
The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two...
Determination of Non-Linear Dynamic Aerodynamic Coefficients for Aircraft
1997-01-01
Representation - a Time Domain Perspective", AGARD CP-497, Nov. 1991. (10) Jenkins, J. E. and Haniff , E. S., "Non-Linear and Unsteady Aerodynamic Responses of a...8217 Delta Wing Oscillating in Roll", AIAA 94-3507. (12) Haniff , E., "Dynamic Nonlinear Airloads-Representation and Measurement", AGARD CP-386, May, 1985 (13
Curvature-induced symmetry breaking in nonlinear Schrodinger models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Mingaleev, S. F.; Christiansen, Peter Leth
2000-01-01
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states decrea...
Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method
Directory of Open Access Journals (Sweden)
A. M. El-Naggar
2015-11-01
Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.
Non-Linear Aeroelastic Analysis Using the Point Transformation Method, Part 1: Freeplay Model
LIU, L.; WONG, Y. S.; LEE, B. H. K.
2002-05-01
A point transformation technique is developed to investigate the non-linear behavior of a two-dimensional aeroelastic system with freeplay models. Two formulations of the point transformation method are presented, which can be applied to accurately predict the frequency and amplitude of limit cycle oscillations. Moreover, it is demonstrated that the developed formulations are capable of detecting complex aeroelastic responses such as periodic motions with harmonics, period doubling, chaotic motions and the coexistence of stable limit cycles. Applications of the point transformation method to several test examples are presented. It is concluded that the formulations developed in this paper are efficient and effective.
Kato, Shoji
2016-01-01
This book presents the current state of research on disk oscillation theory, focusing on relativistic disks and tidally deformed disks. Since the launch of the Rossi X-ray Timing Explorer (RXTE) in 1996, many high-frequency quasiperiodic oscillations (HFQPOs) have been observed in X-ray binaries. Subsequently, similar quasi-periodic oscillations have been found in such relativistic objects as microquasars, ultra-luminous X-ray sources, and galactic nuclei. One of the most promising explanations of their origin is based on oscillations in relativistic disks, and a new field called discoseismology is currently developing. After reviewing observational aspects, the book presents the basic characteristics of disk oscillations, especially focusing on those in relativistic disks. Relativistic disks are essentially different from Newtonian disks in terms of several basic characteristics of their disk oscillations, including the radial distributions of epicyclic frequencies. In order to understand the basic processes...
Nonlinear Farley-Buneman instability with Dust Impurities.
Atamaniuk, B.; Volokitin, A. S.
2009-04-01
The regimes of nonlinear stabilization of instability of low frequency waves in magnetized, weakly ionized and inhomogeneous ionospheric dusty plasma are considered. In the lower ionosphere in the E--region, a complex process transforms wind energy into currents creating the E--region electrojet. If these currents exceed a certain critical amplitude, a streaming instability called the Farley--Buneman or a collisional two-stream instability develops. When the number of cooperating waves remains small due to a competition of processes of their instability and attenuation, the turbulence appears in the result of their stochastic behavior. Then even system with finite number of interacting waves can realize a turbulent state in active media. At conditions when electrons are magnetized and characteristic time of density oscillations exceed the rate of electron ion collisions and electron dust collision the drift of electrons perpendicular to magnetic field is the main motion. Consequently, the main nonlinearity appears in result of convection of a density perturbation in one wave by another wave in the perpendicular to magnetic field and mathematically is expressed in a specific vector form The strong collisional damping of waves allow to assume that a typical perturbed state of plasma can be described as finite set of interacting waves. This allow to avoid difficulties of 3D simulations and to make full study of nonlinear stabilization and influence of the dust component in the conditions when the number of interacting waves keeps small by the strong competition of processes wave damping and instabilities Keywords: Dusty Plasmas, Farley-Buneman Instability, Nonlinear Stabilization. REFERENCES 1. M. Oppenheim and N. Otani, Geophysical Research Letters, 22, pp. 353-356, 1995. 2. A.V. Volosevich and C.V. Meister, Int. Journal of Geomagnetism and aeronomy, 3 pp.151-156, 2002 3. A. S. Volokitin and B. Atamaniuk, Reduced nonlinear description of Farley-Buneman instability