Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction
Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.
2005-03-01
We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.
The cardiorespiratory interaction: a nonlinear stochastic model and its synchronization properties
Bahraminasab, A.; Kenwright, D.; Stefanovska, A.; McClintock, P. V. E.
2007-06-01
We address the problem of interactions between the phase of cardiac and respiration oscillatory components. The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian processes. The so-called Markov analysis allows us to derive nonlinear stochastic equations for the reconstruction of the cardiorespiratory signals. The properties of these equations provide interesting new insights into the strength and direction of coupling which enable us to divide the couplings to two parts: deterministic and stochastic. It is shown that the synchronization behaviors of the reconstructed signals are statistically identical with original one.
Identification of stochastic interactions in nonlinear models of structural mechanics
Kala, Zdeněk
2017-07-01
In the paper, the polynomial approximation is presented by which the Sobol sensitivity analysis can be evaluated with all sensitivity indices. The nonlinear FEM model is approximated. The input area is mapped using simulations runs of Latin Hypercube Sampling method. The domain of the approximation polynomial is chosen so that it were possible to apply large number of simulation runs of Latin Hypercube Sampling method. The method presented also makes possible to evaluate higher-order sensitivity indices, which could not be identified in case of nonlinear FEM.
Zhang, Wei; Wang, Jun
2018-05-01
A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.
Stochastic nonlinear beam equations
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Stochastic inflation and nonlinear gravity
Salopek, D.S.; Bond, J.R.
1991-01-01
We show how nonlinear effects of the metric and scalar fields may be included in stochastic inflation. Our formalism can be applied to non-Gaussian fluctuation models for galaxy formation. Fluctuations with wavelengths larger than the horizon length are governed by a network of Langevin equations for the physical fields. Stochastic noise terms arise from quantum fluctuations that are assumed to become classical at horizon crossing and that then contribute to the background. Using Hamilton-Jacobi methods, we solve the Arnowitt-Deser-Misner constraint equations which allows us to separate the growing modes from the decaying ones in the drift phase following each stochastic impulse. We argue that the most reasonable choice of time hypersurfaces for the Langevin system during inflation is T=ln(Ha), where H and a are the local values of the Hubble parameter and the scale factor, since T is the natural time for evolving the short-wavelength scalar field fluctuations in an inhomogeneous background
Non-linear stochastic response of a shallow cable
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...
Research on nonlinear stochastic dynamical price model
Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng
2008-01-01
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies
Stochastic effects on the nonlinear Schroedinger equation
Flessas, G P; Leach, P G L; Yannacopoulos, A N
2004-01-01
The aim of this article is to provide a brief review of recent advances in the field of stochastic effects on the nonlinear Schroedinger equation. The article reviews rigorous and perturbative results. (review article)
Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.
Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua
2016-11-14
In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.
Stochastic Dominance under the Nonlinear Expected Utilities
Xinling Xiao
2014-01-01
Full Text Available In 1947, von Neumann and Morgenstern introduced the well-known expected utility and the related axiomatic system (see von Neumann and Morgenstern (1953. It is widely used in economics, for example, financial economics. But the well-known Allais paradox (see Allais (1979 shows that the linear expected utility has some limitations sometimes. Because of this, Peng proposed a concept of nonlinear expected utility (see Peng (2005. In this paper we propose a concept of stochastic dominance under the nonlinear expected utilities. We give sufficient conditions on which a random choice X stochastically dominates a random choice Y under the nonlinear expected utilities. We also provide sufficient conditions on which a random choice X strictly stochastically dominates a random choice Y under the sublinear expected utilities.
Nonlinear and stochastic dynamics of coherent structures
Rasmussen, Kim
1997-01-01
This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree of nonli......This Thesis deals with nonlinear and stochastic dynamics in systems which can be described by nonlinear Schrödinger models. Basically three different models are investigated. The first is the continuum nonlinear Schröndinger model in one and two dimensions generalized by a tunable degree...... introduces the nonlinear Schrödinger model in one and two dimensions, discussing the soliton solutions in one dimension and the collapse phenomenon in two dimensions. Also various analytical methods are described. Then a derivation of the nonlinear Schrödinger equation is given, based on a Davydov like...... system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...
Information theory and stochastics for multiscale nonlinear systems
Majda, Andrew J; Grote, Marcus J
2005-01-01
This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...
New travelling wave solutions for nonlinear stochastic evolution
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...
Distributed Fault Detection for a Class of Nonlinear Stochastic Systems
Bingyong Yan
2014-01-01
Full Text Available A novel distributed fault detection strategy for a class of nonlinear stochastic systems is presented. Different from the existing design procedures for fault detection, a novel fault detection observer, which consists of a nonlinear fault detection filter and a consensus filter, is proposed to detect the nonlinear stochastic systems faults. Firstly, the outputs of the nonlinear stochastic systems act as inputs of a consensus filter. Secondly, a nonlinear fault detection filter is constructed to provide estimation of unmeasurable system states and residual signals using outputs of the consensus filter. Stability analysis of the consensus filter is rigorously investigated. Meanwhile, the design procedures of the nonlinear fault detection filter are given in terms of linear matrix inequalities (LMIs. Taking the influence of the system stochastic noises into consideration, an outstanding feature of the proposed scheme is that false alarms can be reduced dramatically. Finally, simulation results are provided to show the feasibility and effectiveness of the proposed fault detection approach.
Nonlinear and Stochastic Dynamics in the Heart
Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.
2014-01-01
In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems. PMID:25267872
Nonlinear and stochastic dynamics in the heart
Qu, Zhilin, E-mail: zqu@mednet.ucla.edu [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Hu, Gang [Department of Physics, Beijing Normal University, Beijing 100875 (China); Garfinkel, Alan [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Integrative Biology and Physiology, University of California, Los Angeles, CA 90095 (United States); Weiss, James N. [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States)
2014-10-10
In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.
Nonlinear and stochastic dynamics in the heart
Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.
2014-01-01
In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems
Jacobian elliptic function expansion solutions of nonlinear stochastic equations
Wei Caimin; Xia Zunquan; Tian Naishuo
2005-01-01
Jacobian elliptic function expansion method is extended and applied to construct the exact solutions of the nonlinear Wick-type stochastic partial differential equations (SPDEs) and some new exact solutions are obtained via this method and Hermite transformation
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Stochastic hyperfine interactions modeling library
Zacate, Matthew O.; Evenson, William E.
2011-04-01
The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When
Backward stochastic differential equations from linear to fully nonlinear theory
Zhang, Jianfeng
2017-01-01
This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks
Chengrong Xie
2013-01-01
Full Text Available We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.
Stochastic development regression on non-linear manifolds
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...
On the Stochastic Wave Equation with Nonlinear Damping
Kim, Jong Uhn
2008-01-01
We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping
Probabilistic DHP adaptive critic for nonlinear stochastic control systems.
Herzallah, Randa
2013-06-01
Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.
Stability of Nonlinear Neutral Stochastic Functional Differential Equations
Minggao Xue
2010-01-01
Full Text Available Neutral stochastic functional differential equations (NSFDEs have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper is to remove the linear growth condition and establish a Khasminskii-type test for nonlinear NSFDEs. New criteria not only cover a wide class of highly nonlinear NSFDEs but they can also be verified much more easily than the classical criteria. Finally, several examples are given to illustrate main results.
Comparison of stochastic resonance in static and dynamical nonlinearities
Ma, Yumei; Duan, Fabing
2014-01-01
We compare the stochastic resonance (SR) effects in parallel arrays of static and dynamical nonlinearities via the measure of output signal-to-noise ratio (SNR). For a received noisy periodic signal, parallel arrays of both static and dynamical nonlinearities can enhance the output SNR by optimizing the internal noise level. The static nonlinearity is easily implementable, while the dynamical nonlinearity has more parameters to be tuned, at the risk of not exploiting the beneficial role of internal noise components. It is of interest to note that, for an input signal buried in the external Laplacian noise, we show that the dynamical nonlinearity is superior to the static nonlinearity in obtaining a better output SNR. This characteristic is assumed to be closely associated with the kurtosis of noise distribution. - Highlights: • Comparison of SR effects in arrays of both static and dynamical nonlinearities. • Static nonlinearity is easily implementable for the SNR enhancement. • Dynamical nonlinearity yields a better output SNR for external Laplacian noise
Stochastic interaction between TAE and alpha particles
Krlin, L.; Pavlo, P.; Malijevsky, I.
1996-01-01
The interaction of toroidicity-induced Alfven eigenmodes with thermonuclear alpha particles in the intrinsic stochasticity regime was investigated based on the numerical integration of the equation of motion of alpha particles in the tokamak. The first results obtained for the ITER parameters and moderate wave amplitudes indicate that the stochasticity is highest in the trapped/passing boundary region, where the alpha particles jump stochastically between the two regimes with an appreciable radial excursion (about 0.5 m amplitudes). A similar chaotic behavior was also found for substantially lower energies (about 350 keV). 7 figs., 15 refs
Quantitative Sociodynamics Stochastic Methods and Models of Social Interaction Processes
Helbing, Dirk
2010-01-01
This new edition of Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioral changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics and mathematics, but they have very often proven their explanatory power in chemistry, biology, economics and the social sciences as well. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces important concepts from nonlinear dynamics (e.g. synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches, a fundamental dynamic model is obtained, which opens new perspectives in the social sciences. It includes many established models a...
Quantitative sociodynamics stochastic methods and models of social interaction processes
Helbing, Dirk
1995-01-01
Quantitative Sociodynamics presents a general strategy for interdisciplinary model building and its application to a quantitative description of behavioural changes based on social interaction processes. Originally, the crucial methods for the modeling of complex systems (stochastic methods and nonlinear dynamics) were developed in physics but they have very often proved their explanatory power in chemistry, biology, economics and the social sciences. Quantitative Sociodynamics provides a unified and comprehensive overview of the different stochastic methods, their interrelations and properties. In addition, it introduces the most important concepts from nonlinear dynamics (synergetics, chaos theory). The applicability of these fascinating concepts to social phenomena is carefully discussed. By incorporating decision-theoretical approaches a very fundamental dynamic model is obtained which seems to open new perspectives in the social sciences. It includes many established models as special cases, e.g. the log...
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
S. L. Han
2012-01-01
Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.
Bonus algorithm for large scale stochastic nonlinear programming problems
Diwekar, Urmila
2015-01-01
This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...
Stochastic development regression on non-linear manifolds
Kühnel, Line; Sommer, Stefan Horst
2017-01-01
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...... in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes....
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.
Nonlinear Stochastic Analysis of Subharmonic Response of a Shallow Cable
Zhou, Q.; Stærdahl, Jesper Winther; Nielsen, Søren R.K.
2007-01-01
and stochastic subharmonic response is demonstrated upon comparison with a more involved model based on a spatial finite difference discretization of the full nonlinear partial differential equations of the cable. Since the stochastic response quantities are obtained by Monte Carlo simulation, which is extremely...... time-consuming for the finite difference model, most of the results are next based on the reduced model. Under harmonical varying support point motions the stable subharmonic motion consists of a harmonically varying component in the equilibrium plane and a large subharmonic out-of-plane component...... subharmonic response component is also present in the static equilibrium plane. Further, the time variation of the envelope process of the narrow-banded chordwise elongation process tends to enhance chaotic behaviour of the subharmonic response, which is detectable via extreme sensitivity on the initial...
Stochastic Fixed Points and Nonlinear Perron-Frobenius Theorem
Babaei, E.; Evstigneev, I. V.; Pirogov, S. A.
2016-01-01
We provide conditions for the existence of measurable solutions to the equation $\\xi(T\\omega)=f(\\omega,\\xi(\\omega))$, where $T:\\Omega \\rightarrow\\Omega$ is an automorphism of the probability space $\\Omega$ and $f(\\omega,\\cdot)$ is a strictly non-expansive mapping. We use results of this kind to establish a stochastic nonlinear analogue of the Perron-Frobenius theorem on eigenvalues and eigenvectors of a positive matrix. We consider a random mapping $D(\\omega)$ of a random closed cone $K(\\omeg...
Simple Planar Truss (Linear, Nonlinear and Stochastic Approach
Frydrýšek Karel
2016-11-01
Full Text Available This article deals with a simple planar and statically determinate pin-connected truss. It demonstrates the processes and methods of derivations and solutions according to 1st and 2nd order theories. The article applies linear and nonlinear approaches and their simplifications via a Maclaurin series. Programming connected with the stochastic Simulation-Based Reliability Method (i.e. the direct Monte Carlo approach is used to conduct a probabilistic reliability assessment (i.e. a calculation of the probability that plastic deformation will occur in members of the truss.
Hitting probabilities for nonlinear systems of stochastic waves
Dalang, Robert C
2015-01-01
The authors consider a d-dimensional random field u = \\{u(t,x)\\} that solves a non-linear system of stochastic wave equations in spatial dimensions k \\in \\{1,2,3\\}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent \\beta. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of \\mathbb{R}^d, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that ap
Stochastic modeling of mode interactions via linear parabolized stability equations
Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo
2017-11-01
Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.
Nonlinear stochastic systems with incomplete information filtering and control
Shen, Bo; Shu, Huisheng
2013-01-01
Nonlinear Stochastic Processes addresses the frequently-encountered problem of incomplete information. The causes of this problem considered here include: missing measurements; sensor delays and saturation; quantization effects; and signal sampling. Divided into three parts, the text begins with a focus on H∞ filtering and control problems associated with general classes of nonlinear stochastic discrete-time systems. Filtering problems are considered in the second part, and in the third the theory and techniques previously developed are applied to the solution of issues arising in complex networks with the design of sampled-data-based controllers and filters. Among its highlights, the text provides: · a unified framework for handling filtering and control problems in complex communication networks with limited bandwidth; · new concepts such as random sensor and signal saturations for more realistic modeling; and · demonstration of the use of techniques such...
Interactive Nonlinear Multiobjective Optimization Methods
Miettinen, Kaisa; Hakanen, Jussi; Podkopaev, Dmitry
2016-01-01
An overview of interactive methods for solving nonlinear multiobjective optimization problems is given. In interactive methods, the decision maker progressively provides preference information so that the most satisfactory Pareto optimal solution can be found for her or his. The basic features of several methods are introduced and some theoretical results are provided. In addition, references to modifications and applications as well as to other methods are indicated. As the...
Heterogeneous recurrence monitoring and control of nonlinear stochastic processes
Yang, Hui, E-mail: huiyang@usf.edu; Chen, Yun [Complex Systems Monitoring, Modeling and Analysis Laboratory, University of South Florida, Tampa, Florida 33620 (United States)
2014-03-15
Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.
Ge, Gen; Li, ZePeng
2016-01-01
A modified stochastic averaging method on single-degree-of-freedom (SDOF) oscillators under white noise excitations with strongly nonlinearity was proposed. Considering the existing approach dealing with strongly nonlinear SDOFs derived by Zhu and Huang [14, 15] is quite time consuming in calculating the drift coefficient and diffusion coefficients and the expressions of them are considerable long, the so-called He's energy balance method was applied to overcome the minor defect of the Zhu and Huang's method. The modified method can offer more concise approximate expressions of the drift and diffusion coefficients without weakening the accuracy of predicting the responses of the systems too much by giving an averaged frequency beforehand. Three examples, a cubic and quadratic nonlinearity coexisting oscillator, a quadratic nonlinear oscillator under external white noise excitations and an externally excited Duffing–Rayleigh oscillator, were given to illustrate the approach we proposed. The three examples were excited by the Gaussian white noise and the Gaussian colored noise separately. The stationary responses of probability density of amplitudes and energy, together with joint probability density of displacement and velocity are studied to verify the presented approach. The reliability of the systems were also investigated to offer further support. Digital simulations were carried out and the output of that are coincide with the theoretical approximations well.
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
Information Dynamics of a Nonlinear Stochastic Nanopore System
Claire Gilpin
2018-03-01
Full Text Available Nanopores have become a subject of interest in the scientific community due to their potential uses in nanometer-scale laboratory and research applications, including infectious disease diagnostics and DNA sequencing. Additionally, they display behavioral similarity to molecular and cellular scale physiological processes. Recent advances in information theory have made it possible to probe the information dynamics of nonlinear stochastic dynamical systems, such as autonomously fluctuating nanopore systems, which has enhanced our understanding of the physical systems they model. We present the results of local (LER and specific entropy rate (SER computations from a simulation study of an autonomously fluctuating nanopore system. We learn that both metrics show increases that correspond to fluctuations in the nanopore current, indicating fundamental changes in information generation surrounding these fluctuations.
Online prediction and control in nonlinear stochastic systems
Nielsen, Torben Skov
2002-01-01
speed and the relationship between (primarily) wind speed and wind power (the power curve). In paper G the model parameters are estimated using a RLS algorithm and any systematic time-variation of the model parameters is disregarded. Two di erent parameterizations of the power curve is considered...... are estimated using the algorithm proposed in paper C. The power curve and the diurnal variation of wind speed is estimated separately using the local polynomial regression procedure described in paper A . In paper J the parameters of the prediction model is assumed to be smooth functions of wind direction (and......The present thesis consists of a summary report and ten research papers. The subject of the thesis is on-line prediction and control of non-linear and non-stationary systems based on stochastic modelling. The thesis consists of three parts where the rst part deals with on-line estimation in linear...
Nonlinear laser-plasma interactions
Kaw, P. K.
2017-12-01
Soon after lasers were invented, there was tremendous curiosity on the nonlinear phenomena which would result in their interaction with a fully ionized plasma. Apart from the basic interest, it was realized that it could be used for the achievement of nuclear fusion in the laboratory. This led us to a paper on the propagation of a laser beam into an inhomogeneous fusion plasma, where it was first demonstrated that light would go up to the critical layer (where the frequency matches the plasma frequency) and get reflected from there with a reflection coefficient of order unity. The reflection coefficient was determined by collisional effects. Since the wave was expected to slow down to near zero group speed at the reflection point, the dominant collision frequency determining the reflection coefficient was the collision frequency at the reflection point. It turned out that the absorption of light was rather small for fusion temperatures. This placed a premium on investigation of nonlinear phenomena which might contribute to the absorption and penetration of the light into high-density plasma. An early investigation showed that electron jitter with respect to ions would be responsible for the excitation of decay instabilities which convert light waves into electrostatic plasma waves and ion waves near the critical frequency. These electrostatic waves would then get absorbed into the plasma even in the collisionless case and lead to plasma heating which is nonlinear. Detailed estimates of this heating were made. Similar nonlinear processes which could lead to stimulated scattering of light in the underdense region (ω >ω _p) were investigated together with a number of other workers. All these nonlinear processes need a critical threshold power for excitation. Another important process which was discovered around the same time had to do with filamentation and trapping of light when certain thresholds were exceeded. All of this work has been extensively verified in
Hu, Jun; Gao, Huijun
2014-01-01
This monograph introduces methods for handling filtering and control problems in nonlinear stochastic systems arising from network-induced phenomena consequent on limited communication capacity. Such phenomena include communication delay, packet dropout, signal quantization or saturation, randomly occurring nonlinearities and randomly occurring uncertainties.The text is self-contained, beginning with an introduction to nonlinear stochastic systems, network-induced phenomena and filtering and control, moving through a collection of the latest research results which focuses on the three aspects
Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations
Kushner, Harold J.
2012-01-01
This two-part paper deals with “foundational” issues that have not been previously considered in the modeling and numerical optimization of nonlinear stochastic delay systems. There are new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. There are two basic and interconnected themes for these models. The first, dealt with in this part, concerns the definition of admissible control. The classical definition of an admissible control as a nonanticipative relaxed control is inadequate for these models and needs to be extended. This is needed for the convergence proofs of numerical approximations for optimal controls as well as to have a well-defined model. It is shown that the new classes of admissible controls do not enlarge the range of the value functions, is closed (together with the associated paths) under weak convergence, and is approximatable by ordinary controls. The second theme, dealt with in Part II, concerns transportation equation representations, and their role in the development of numerical algorithms with much reduced memory and computational requirements.
A Volterra series approach to the approximation of stochastic nonlinear dynamics
Wouw, van de N.; Nijmeijer, H.; Campen, van D.H.
2002-01-01
A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system isapproximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this
Nonlinear stochastic heat equations with cubic nonlinearities and additive Q-regular noise in R^1
Henri Schurz
2010-09-01
Full Text Available Semilinear stochastic heat equations perturbed by cubic-type nonlinearities and additive space-time noise with homogeneous boundary conditions are discussed in R^1. The space-time noise is supposed to be Gaussian in time and possesses a Fourier expansion in space along the eigenfunctions of underlying Lapace operators. We follow the concept of approximate strong (classical Fourier solutions. The existence of unique continuous L^2-bounded solutions is proved. Furthermore, we present a procedure for its numerical approximation based on nonstandard methods (linear-implicit and justify their stability and consistency. The behavior of related total energy functional turns out to be crucial in the presented analysis.
Nonlinear dynamics of mushy layers induced by external stochastic fluctuations.
Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B
2018-02-28
The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the 'solid phase-mushy layer' and 'mushy layer-liquid phase' phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'. © 2018 The Author(s).
Ding, Bo; Fang, Huajing
2017-05-01
This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Nonlinear signaling on biological networks: The role of stochasticity and spectral clustering
Hernandez-Hernandez, Gonzalo; Myers, Jesse; Alvarez-Lacalle, Enrique; Shiferaw, Yohannes
2017-03-01
Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different conformational states. Signaling is typically a cooperative process which requires the occurrence of multiple binding events so that reaction rates have a nonlinear dependence on the amount of signaling molecule. It is this nonlinearity that endows biological signaling networks with robust switchlike properties which are critical to their biological function. In this study we investigate how the properties of these signaling systems depend on the network architecture. Our main result is that these nonlinear networks exhibit bistability where the network activity can switch between states that correspond to a low and high activity level. We show that this bistable regime emerges at a critical coupling strength that is determined by the spectral structure of the network. In particular, the set of nodes that correspond to large components of the leading eigenvector of the adjacency matrix determines the onset of bistability. Above this transition the eigenvectors of the adjacency matrix determine a hierarchy of clusters, defined by its spectral properties, which are activated sequentially with increasing network activity. We argue further that the onset of bistability occurs either continuously or discontinuously depending upon whether the leading eigenvector is localized or delocalized. Finally, we show that at low network coupling stochastic transitions to the active branch are also driven by the set of nodes that contribute more strongly to the leading eigenvector. However, at high coupling, transitions are insensitive to network structure since the network can be activated by stochastic transitions of a few nodes. Thus this work identifies important features of biological signaling networks that may underlie their biological
EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY
无
2010-01-01
This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.
Role of statistical linearization in the solution of nonlinear stochastic equations
Budgor, A.B.
1977-01-01
The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables
The development of the deterministic nonlinear PDEs in particle physics to stochastic case
Abdelrahman, Mahmoud A. E.; Sohaly, M. A.
2018-06-01
In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution.
Invariant measures for stochastic nonlinear beam and wave equations
Brzezniak, Z.; Ondreját, Martin; Seidler, Jan
2016-01-01
Roč. 260, č. 5 (2016), s. 4157-4179 ISSN 0022-0396 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic partial differential equation * stochastic beam equation * stochastic wave equation * invariant measure Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/ondrejat-0453412.pdf
Mourad Kerboua
2014-12-01
Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.
Qian, Hong
2011-01-01
The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)
A Non-linear Stochastic Model for an Office Building with Air Infiltration
Thavlov, Anders; Madsen, Henrik
2015-01-01
This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model...
El-Tawil, M A; Al-Jihany, A S
2008-01-01
In this paper, nonlinear oscillators under quadratic nonlinearity with stochastic inputs are considered. Different methods are used to obtain first order approximations, namely, the WHEP technique, the perturbation method, the Pickard approximations, the Adomian decompositions and the homotopy perturbation method (HPM). Some statistical moments are computed for the different methods using mathematica 5. Comparisons are illustrated through figures for different case-studies
Chen, Po-Wei; Chen, Bor-Sen
2011-08-01
Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods. Copyright © 2011 Elsevier Inc. All rights reserved.
Background field method for nonlinear σ-model in stochastic quantization
Nakazawa, Naohito; Ennyu, Daiji
1988-01-01
We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model. (orig.)
Bouard, Anne de; Debussche, Arnaud
2006-01-01
In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1
Effects of error feedback on a nonlinear bistable system with stochastic resonance
Li Jian-Long; Zhou Hui
2012-01-01
In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
Stability analysis for stochastic BAM nonlinear neural network with delays
Lv, Z. W.; Shu, H. S.; Wei, G. L.
2008-02-01
In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria.
Stability analysis for stochastic BAM nonlinear neural network with delays
Lv, Z W; Shu, H S; Wei, G L
2008-01-01
In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria
Interactive macroeconomics stochastic aggregate dynamics with heterogeneous and interacting agents
Di Guilmi, Corrado
2017-01-01
One of the major problems of macroeconomic theory is the way in which the people exchange goods in decentralized market economies. There are major disagreements among macroeconomists regarding tools to influence required outcomes. Since the mainstream efficient market theory fails to provide an internal coherent framework, there is a need for an alternative theory. The book provides an innovative approach for the analysis of agent based models, populated by the heterogeneous and interacting agents in the field of financial fragility. The text is divided in two parts; the first presents analytical developments of stochastic aggregation and macro-dynamics inference methods. The second part introduces macroeconomic models of financial fragility for complex systems populated by heterogeneous and interacting agents. The concepts of financial fragility and macroeconomic dynamics are explained in detail in separate chapters. The statistical physics approach is applied to explain theories of macroeconomic modelling a...
Wen-Jer Chang
2014-01-01
Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
Iwankiewicz, R.; Nielsen, Søren R. K.
Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically-numerical tec......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...
Volchenkov, D.
2009-01-01
Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magnetohydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications. (author)
Volchenkov, D. [Bielefeld Univ., Center of Excellence Cognitive Interaction Technology (CITEC) (Germany)
2009-03-15
Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magnetohydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications. (author)
Nonlinear control of fixed-wing UAVs in presence of stochastic winds
Rubio Hervas, Jaime; Reyhanoglu, Mahmut; Tang, Hui; Kayacan, Erdal
2016-04-01
This paper studies the control of fixed-wing unmanned aerial vehicles (UAVs) in the presence of stochastic winds. A nonlinear controller is designed based on a full nonlinear mathematical model that includes the stochastic wind effects. The air velocity is controlled exclusively using the position of the throttle, and the rest of the dynamics are controlled with the aileron, elevator, and rudder deflections. The nonlinear control design is based on a smooth approximation of a sliding mode controller. An extended Kalman filter (EKF) is proposed for the state estimation and filtering. A case study is presented: landing control of a UAV on a ship deck in the presence of wind based exclusively on LADAR measurements. The effectiveness of the nonlinear control algorithm is illustrated through a simulation example.
New travelling wave solutions for nonlinear stochastic evolution ...
expansion method to look for travelling wave solutions of nonlinear partial differential equations. It is interesting to mention that, in this method the sign of the parameters can be used to judge the numbers and types of travelling wave solutions.
Chekroun, Mickaël D; Wang, Shouhong
2015-01-01
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Numerical Solution of Stochastic Nonlinear Fractional Differential Equations
El-Beltagy, Mohamed A.; Al-Juhani, Amnah
2015-01-01
Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.
Numerical Solution of Stochastic Nonlinear Fractional Differential Equations
El-Beltagy, Mohamed A.
2015-01-07
Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.
Asymptotic analysis of a stochastic non-linear nuclear reactor model
Rodriguez, M.A.; Sancho, J.M.
1986-01-01
The asymptotic behaviour of a stochastic non-linear nuclear reactor modelled by a master equation is analysed in two different limits: the thermodynamic limit and the zero-neutron-source limit. In the first limit a finite steady neutron density is obtained. The second limit predicts the neutron extinction. The interplay between these two limits is studied for different situations. (author)
Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate
Qixing Han
2013-01-01
Full Text Available We investigate a stochastic SIS model with nonlinear incidence rate. We show that there exists a unique nonnegative solution to the system, and condition for the infectious individuals I(t to be extinct is given. Moreover, we prove that the system has ergodic property. Finally, computer simulations are carried out to verify our results.
Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun
2015-12-01
This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.
Chon, K H; Hoyer, D; Armoundas, A A
1999-01-01
In this study, we introduce a new approach for estimating linear and nonlinear stochastic autoregressive moving average (ARMA) model parameters, given a corrupt signal, using artificial recurrent neural networks. This new approach is a two-step approach in which the parameters of the deterministic...... part of the stochastic ARMA model are first estimated via a three-layer artificial neural network (deterministic estimation step) and then reestimated using the prediction error as one of the inputs to the artificial neural networks in an iterative algorithm (stochastic estimation step). The prediction...... error is obtained by subtracting the corrupt signal of the estimated ARMA model obtained via the deterministic estimation step from the system output response. We present computer simulation examples to show the efficacy of the proposed stochastic recurrent neural network approach in obtaining accurate...
Soil-structure interaction including nonlinear soil
Gicev, Vlado
2008-01-01
There are two types of models of soil-structure system depending upon the rigidity of foundation: models with rigid and models with flexible foundation. Main features of the soil-structure interaction phenomenon: -wave scattering, -radiation damping, -reduction of the system frequencies. In this presentation, the influence of interaction on the development of nonlinear zones in the soil is studied.
Structure Learning in Stochastic Non-linear Dynamical Systems
Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.
2005-12-01
A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.
Kushner, Harold J.
2012-01-01
This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.
Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia
Jung, P.; Cornell-Bell, A. H.
Astrocyte-signaling has been observed in cell cultures and brain slices in the form of Calcium waves. Their functional relevance for neuronal communication, brain functions and diseases is, however, not understood. In this paper, the propagation of intercellular calcium waves is modeled in terms of waves in excitable media on a stochastic support. We utilize a novel method to decompose the spatiotemporal patterns into space-time clusters (wave fragments). Based on this cluster decomposition, a statistical description of wave patterns is developed.
Advances in nonlinear partial differential equations and stochastics
Kawashima, S
1998-01-01
In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Tunable Resonators for Nonlinear Modal Interactions
Ramini, Abdallah
2016-10-04
Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.
Tunable Resonators for Nonlinear Modal Interactions
Ramini, Abdallah; Hajjaj, Amal Z.; Younis, Mohammad I.
2016-01-01
Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.
Nonlinear Stochastic Models for Water Level Dynamics in Closed Lakes
Mishchenko, A.S.; Zelikin, M.I.; Zelikina, L.F.
1995-01-01
This paper presents the results of investigation of nonlinear mathematical models of the behavior of closed lakes using the example of the Caspian Sea. Forecasting the level of the Caspian Sea is crucial both for the economy of the region and for the region's environment. The Caspian Sea is a closed reservoir; it is well known that its level changes considerably due to a variety of factors including global climate change. A series of forecasts exists based on different methods and taking...
A Weak Solution of a Stochastic Nonlinear Problem
M. L. Hadji
2015-01-01
Full Text Available We consider a problem modeling a porous medium with a random perturbation. This model occurs in many applications such as biology, medical sciences, oil exploitation, and chemical engineering. Many authors focused their study mostly on the deterministic case. The more classical one was due to Biot in the 50s, where he suggested to ignore everything that happens at the microscopic level, to apply the principles of the continuum mechanics at the macroscopic level. Here we consider a stochastic problem, that is, a problem with a random perturbation. First we prove a result on the existence and uniqueness of the solution, by making use of the weak formulation. Furthermore, we use a numerical scheme based on finite differences to present numerical results.
Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory
Xu, Yan; Hu, Bin; Wu, Jiang; Zhang, Jianhua
2014-04-01
The excitation intervention of strategic alliance may change with the changes in the parameters of circumstance (e.g., external alliance tasks). As a result, the stable cooperation between members may suffer a complete unplanned betrayal at last. However, current perspectives on strategic alliances cannot adequately explain this transition mechanism. This study is a first attempt to analyze this nonlinear phenomenon through stochastic catastrophe theory (SCT). A stochastic dynamics model is constructed based on the cooperation of strategic alliance from the perspective of evolutionary game theory. SCT explains the discontinuous changes caused by the changes in environmental parameters. Theoretically, we identify conditions where catastrophe can occur in the cooperation of alliance members.
Weak-periodic stochastic resonance in a parallel array of static nonlinearities.
Yumei Ma
Full Text Available This paper studies the output-input signal-to-noise ratio (SNR gain of an uncoupled parallel array of static, yet arbitrary, nonlinear elements for transmitting a weak periodic signal in additive white noise. In the small-signal limit, an explicit expression for the SNR gain is derived. It serves to prove that the SNR gain is always a monotonically increasing function of the array size for any given nonlinearity and noisy environment. It also determines the SNR gain maximized by the locally optimal nonlinearity as the upper bound of the SNR gain achieved by an array of static nonlinear elements. With locally optimal nonlinearity, it is demonstrated that stochastic resonance cannot occur, i.e. adding internal noise into the array never improves the SNR gain. However, in an array of suboptimal but easily implemented threshold nonlinearities, we show the feasibility of situations where stochastic resonance occurs, and also the possibility of the SNR gain exceeding unity for a wide range of input noise distributions.
Nonlinear theory of electroelastic and magnetoelastic interactions
Dorfmann, Luis
2014-01-01
This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.
Nonlinear dynamics of interacting populations
Bazykin, Alexander D
1998-01-01
This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative the
Doering, C.R.
1985-01-01
Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory
Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination
Lei Wang
2017-01-01
Full Text Available In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.
Han, Qun; Xu, Wei; Sun, Jian-Qiao
2016-09-01
The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.
Wang, Jianhui; Liu, Zhi; Chen, C L Philip; Zhang, Yun
2017-10-12
Hysteresis exists ubiquitously in physical actuators. Besides, actuator failures/faults may also occur in practice. Both effects would deteriorate the transient tracking performance, and even trigger instability. In this paper, we consider the problem of compensating for actuator failures and input hysteresis by proposing a fuzzy control scheme for stochastic nonlinear systems. Compared with the existing research on stochastic nonlinear uncertain systems, it is found that how to guarantee a prescribed transient tracking performance when taking into account actuator failures and hysteresis simultaneously also remains to be answered. Our proposed control scheme is designed on the basis of the fuzzy logic system and backstepping techniques for this purpose. It is proven that all the signals remain bounded and the tracking error is ensured to be within a preestablished bound with the failures of hysteretic actuator. Finally, simulations are provided to illustrate the effectiveness of the obtained theoretical results.
Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves
Eldeberky, Y.; Madsen, Per A.
1999-01-01
and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...
Nonlinear interactions of counter-travelling waves
Matsuuchi, Kazuo
1980-01-01
Nonlinear interactions between two waves travelling in opposite directions are investigated. When a nonlinear Klein-Gordon equation is adopted as a model equation, it is shown that such a wave system is governed by a simple set of equations for their complex amplitudes. Steady progressive waves governed by this set are investigated for various cases classified according to the signs of the coefficients. It is then found that one wave travelling in one direction appears from a certain point and the other travelling in the opposite direction has a constant amplitude from that point. This phenomenon may be regarded as a sort of reflection in spite of no rigid boundary. (author)
Tail estimates for stochastic fixed point equations via nonlinear renewal theory
Collamore, Jeffrey F.; Vidyashankar, Anand N.
2013-01-01
estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....
Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations
Khan, Junaid Ali; Raja, Muhammad Asif Zahoor; Qureshi, Ijaz Mansoor
2011-01-01
We present an evolutionary computational approach for the solution of nonlinear ordinary differential equations (NLODEs). The mathematical modeling is performed by a feed-forward artificial neural network that defines an unsupervised error. The training of these networks is achieved by a hybrid intelligent algorithm, a combination of global search with genetic algorithm and local search by pattern search technique. The applicability of this approach ranges from single order NLODEs, to systems of coupled differential equations. We illustrate the method by solving a variety of model problems and present comparisons with solutions obtained by exact methods and classical numerical methods. The solution is provided on a continuous finite time interval unlike the other numerical techniques with comparable accuracy. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed. (general)
Advanced models of neural networks nonlinear dynamics and stochasticity in biological neurons
Rigatos, Gerasimos G
2015-01-01
This book provides a complete study on neural structures exhibiting nonlinear and stochastic dynamics, elaborating on neural dynamics by introducing advanced models of neural networks. It overviews the main findings in the modelling of neural dynamics in terms of electrical circuits and examines their stability properties with the use of dynamical systems theory. It is suitable for researchers and postgraduate students engaged with neural networks and dynamical systems theory.
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
Non-linear soil-structure interaction
Wolf, J.P.
1984-01-01
The basic equation of motion to analyse the interaction of a non-linear structure and an irregular soil with the linear unbounded soil is formulated in the time domain. The contribution of the unbounded soil involves convolution integrals of the dynamic-stiffness coefficients in the time domain and the corresponding motions. As another possibility, a flexibility formulation fot the contribution of the unbounded soil using the dynamic-flexibility coefficients in the time domain, together with the direct-stiffness method for the structure and the irregular soil can be applied. As an example of a non-linear soil-structure-interaction analysis, the partial uplift of the basemat of a structure is examined. (Author) [pt
Si, Wenjie; Dong, Xunde; Yang, Feifei
2018-03-01
This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.
Stochastic heterogeneous interaction promotes cooperation in spatial prisoner's dilemma game.
Ping Zhu
Full Text Available Previous studies mostly investigate player's cooperative behavior as affected by game time-scale or individual diversity. In this paper, by involving both time-scale and diversity simultaneously, we explore the effect of stochastic heterogeneous interaction. In our model, the occurrence of game interaction between each pair of linked player obeys a random probability, which is further described by certain distributions. Simulations on a 4-neighbor square lattice show that the cooperation level is remarkably promoted when stochastic heterogeneous interaction is considered. The results are then explained by investigating the mean payoffs, the mean boundary payoffs and the transition probabilities between cooperators and defectors. We also show some typical snapshots and evolution time series of the system. Finally, the 8-neighbor square lattice and BA scale-free network results indicate that the stochastic heterogeneous interaction can be robust against different network topologies. Our work may sharpen the understanding of the joint effect of game time-scale and individual diversity on spatial games.
Stochastic foundations in nonlinear density-regulation growth
Méndez, Vicenç; Assaf, Michael; Horsthemke, Werner; Campos, Daniel
2017-08-01
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for population extinction and calculate the mean time to extinction. If the population does not become extinct, we obtain analytical expressions for the population abundance distribution. Our theoretical results are based on WKB theory and the probability generating function formalism and are verified by numerical simulations.
Sun Zhiyuan; Yu Xin; Liu Ying; Gao Yitian
2012-01-01
We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.
Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying
2012-12-01
We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.
Kunwar, Ambarish; Mogilner, Alexander
2010-01-01
Transport by processive molecular motors plays an important role in many cell biological phenomena. In many cases, motors work together to transport cargos in the cell, so it is important to understand the mechanics of the multiple motors. Based on earlier modeling efforts, here we study effects of nonlinear force–velocity relations and stochastic load sharing on multiple motor transport. We find that when two or three motors transport the cargo, then the nonlinear and stochastic effects compensate so that the mechanical properties of the transport are robust. Similarly, the transport is insensitive to compliance of the cargo-motor links. Furthermore, the rate of movement against moderate loads is not improved by increasing the small number of motors. When the motor number is greater than 4, correlations between the motors become negligible, and the earlier analytical mean-field theory of the multiple motor transport holds. We predict that the effective diffusion of the cargo driven by the multiple motors under load increases by an order of magnitude compared to that for the single motor. Finally, our simulations predict that the stochastic effects are responsible for a significant dispersion of velocities generated by the 'tug-of-war' of the multiple opposing motors
A unified nonlinear stochastic time series analysis for climate science.
Moon, Woosok; Wettlaufer, John S
2017-03-13
Earth's orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability.
Singh, B.N.; Lal, Achchhe
2010-01-01
This study deals with the stochastic post-buckling and nonlinear free vibration analysis of a laminated composite plate resting on a two parameters Pasternak foundation with Winkler cubic nonlinearity having uncertain system properties. The system properties are modeled as basic random variables. A C 0 nonlinear finite element formulation of the random problem based on higher-order shear deformation theory in the von Karman sense is presented. A direct iterative method in conjunction with a stochastic nonlinear finite element method proposed earlier by the authors is extended to analyze the effect of uncertainty in system properties on the post-buckling and nonlinear free vibration of the composite plates having Winler type of geometric nonlinearity. Mean as well as standard deviation of the responses have been obtained for various combinations of geometric parameters, foundation parameters, stacking sequences and boundary conditions and compared with those available in the literature and Monte Carlo simulation.
Empirical method to measure stochasticity and multifractality in nonlinear time series
Lin, Chih-Hao; Chang, Chia-Seng; Li, Sai-Ping
2013-12-01
An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm, and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.
Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl
2018-06-01
The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.
Nonlinear interaction model of subsonic jet noise.
Sandham, Neil D; Salgado, Adriana M
2008-08-13
Noise generation in a subsonic round jet is studied by a simplified model, in which nonlinear interactions of spatially evolving instability modes lead to the radiation of sound. The spatial mode evolution is computed using linear parabolized stability equations. Nonlinear interactions are found on a mode-by-mode basis and the sound radiation characteristics are determined by solution of the Lilley-Goldstein equation. Since mode interactions are computed explicitly, it is possible to find their relative importance for sound radiation. The method is applied to a single stream jet for which experimental data are available. The model gives Strouhal numbers of 0.45 for the most amplified waves in the jet and 0.19 for the dominant sound radiation. While in near field axisymmetric and the first azimuthal modes are both important, far-field sound is predominantly axisymmetric. These results are in close correspondence with experiment, suggesting that the simplified model is capturing at least some of the important mechanisms of subsonic jet noise.
Fan, Kuangang; Zhang, Yan; Gao, Shujing; Wei, Xiang
2017-09-01
A class of SIR epidemic model with generalized nonlinear incidence rate is presented in this paper. Temporary immunity and stochastic perturbation are also considered. The existence and uniqueness of the global positive solution is achieved. Sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established. Moreover, the threshold behavior is discussed, and the threshold value R0 is obtained. We show that if R0 extinct with probability one, whereas if R0 > 1, then the system remains permanent in the mean.
Teng, Zhidong; Wang, Lei
2016-06-01
In this paper, a class of stochastic SIS epidemic models with nonlinear incidence rate is investigated. It is shown that the extinction and persistence of the disease in probability are determined by a threshold value R˜0. That is, if R˜0 1 then disease is weak permanent with probability one. To obtain the permanence in the mean of the disease, a new quantity R̂0 is introduced, and it is proved that if R̂0 > 1 the disease is permanent in the mean with probability one. Furthermore, the numerical simulations are presented to illustrate some open problems given in Remarks 1-3 and 5 of this paper.
Application of fast orthogonal search to linear and nonlinear stochastic systems
Chon, K H; Korenberg, M J; Holstein-Rathlou, N H
1997-01-01
Standard deterministic autoregressive moving average (ARMA) models consider prediction errors to be unexplainable noise sources. The accuracy of the estimated ARMA model parameters depends on producing minimum prediction errors. In this study, an accurate algorithm is developed for estimating...... linear and nonlinear stochastic ARMA model parameters by using a method known as fast orthogonal search, with an extended model containing prediction errors as part of the model estimation process. The extended algorithm uses fast orthogonal search in a two-step procedure in which deterministic terms...
Bixiang Wang
2013-08-01
Full Text Available We prove the existence and uniqueness of random attractors for the p-Laplace equation driven simultaneously by non-autonomous deterministic and stochastic forcing. The nonlinearity of the equation is allowed to have a polynomial growth rate of any order which may be greater than p. We further establish the upper semicontinuity of random attractors as the intensity of noise approaches zero. In addition, we show the pathwise periodicity of random attractors when all non-autonomous deterministic forcing terms are time periodic.
Chirikov, B.V.; Shepelyansky, D.L.
1983-02-01
Motion in the stochastic layer around the separatrix of a nonlinear resonance was investigated. The integral distribution function F(tau) of trajectory recurrence times tau to the center of the layer was numerically determined. It was found that the distribution F(tau) = A tau - /sup p/ is a power function, the exponent assuming two different values: for tau less than or equal to tau 0 , p = 1/2 and for tau >> tau 0 , p = 3/2 (time tau 0 is determined by the characteristics of the layer)
Effective stochastic generator with site-dependent interactions
Khamehchi, Masoumeh; Jafarpour, Farhad H.
2017-11-01
It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these generators can include local interactions. In this paper, we investigate this possibility by considering systems of classical particles moving on a one-dimensional lattice with open boundaries. The particles might have hard-core interactions similar to the particles in an exclusion process, or there can be many arbitrary particles at a single site in a zero-range process. Assuming that the interactions in the original process are local and site-independent, we will show that under certain constraints on the microscopic reaction rules, the stochastic generator of an unconditioned process can be local but site-dependent. As two examples, the asymmetric zero-temperature Glauber model and the A-model with diffusion are presented and studied under the above-mentioned constraints.
Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders
El Beltagy, Mohamed
2016-01-06
In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.
Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders
El Beltagy, Mohamed
2016-01-01
In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.
Prescribed Performance Fuzzy Adaptive Output-Feedback Control for Nonlinear Stochastic Systems
Lili Zhang
2014-01-01
Full Text Available A prescribed performance fuzzy adaptive output-feedback control approach is proposed for a class of single-input and single-output nonlinear stochastic systems with unmeasured states. Fuzzy logic systems are used to identify the unknown nonlinear system, and a fuzzy state observer is designed for estimating the unmeasured states. Based on the backstepping recursive design technique and the predefined performance technique, a new fuzzy adaptive output-feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example is provided to show the effectiveness of the proposed approach.
Huang, Guanghui; Wan, Jianping; Chen, Hui
2013-02-01
Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error. Copyright © 2012 Elsevier Ltd. All rights reserved.
A non-linear dimension reduction methodology for generating data-driven stochastic input models
Ganapathysubramanian, Baskar; Zabaras, Nicholas
2008-06-01
Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low
A non-linear dimension reduction methodology for generating data-driven stochastic input models
Ganapathysubramanian, Baskar; Zabaras, Nicholas
2008-01-01
Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R n . An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R d (d<< n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology
Interaction of stochastic boundary layer with plasma facing components
Nguyen, F.; Ghendrih, P.; Grosman, A.
1997-01-01
To alleviate the plasma-wall interaction problems in magnetic confinement devices, a stochastic layer is used at the edge of the Tore Supra tokamak (ergodic divertor). A very important point is to determine the power deposition on the plasma facing components. Two different kinds of transport can be identified in such a configuration: Stochastic transport surrounding the confined plasma, with a random walk process, and scrape-off layer (SOL) like transport, a laminar transport, near the plasma facing components. The laminar regime is investigated in terms of a simple criterion, namely that the power deposition is proportional to the radial penetration of the laminar zone flux tubes over a finite parallel length. The magnetic connection properties of the first wall components are then determined. The connection lengths are quantified with two characteristic scales. The larger corresponds to one poloidal turn and appears to be the characteristic parallel length for laminar transport. A field line tracing code MASTOC (magnetic stochastic configuration) is used to computer the complex topology and the statistics of the connection in the real tokamak geometry. The numerical simulations are then compared with the experimental heat deposition on the modules and neutralizer plates of the Tore Supra ergodic divertor. Good agreement is found. Further evidence of laminar transport is also provided by the tangential view of such structures revealed from H α structures in detached plasma experiments. (author). 27 refs, 14 figs
Nonlinear interactions in magnetised piezoelectric semiconductor plasmas
Sharma, Giriraj; Ghosh, S.
2000-01-01
Based on hydrodynamics model of plasmas an analytical investigation of frequency modulational interaction between copropagating high frequency pump and acoustic mode and consequent amplification (steady-state and transient) of the modulated waves is carried out in a magnetised piezoelectric semiconductor medium. The phenomenon of modulation amplification is treated as four wave interaction process involving cubic nonlinearity of the medium. Gain constants, threshold-pump intensities and optimum-pulse duration for the onset of modulational instabilities are estimated. The analysis has been performed in non-dispersive regime of the acoustic mode, which is one of the preconditions for achieving an appreciable initial steady-state growth of the modulated signal wave. It is found that the transient gain diminishes very rapidly if one chooses the pump pulse duration beyond the maximum gain point. Moreover, the desired value of the gain can be obtained by adjusting intensity and pulse duration of the pump and doping concentration of the medium concerned. (author)
Reddy, L Ram Gopal; Kuntamalla, Srinivas
2011-01-01
Heart rate variability analysis is fast gaining acceptance as a potential non-invasive means of autonomic nervous system assessment in research as well as clinical domains. In this study, a new nonlinear analysis method is used to detect the degree of nonlinearity and stochastic nature of heart rate variability signals during two forms of meditation (Chi and Kundalini). The data obtained from an online and widely used public database (i.e., MIT/BIH physionet database), is used in this study. The method used is the delay vector variance (DVV) method, which is a unified method for detecting the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal. From the results it is clear that there is a significant change in the nonlinearity and stochastic nature of the signal before and during the meditation (p value > 0.01). During Chi meditation there is a increase in stochastic nature and decrease in nonlinear nature of the signal. There is a significant decrease in the degree of nonlinearity and stochastic nature during Kundalini meditation.
Stochastic simulation of ecohydrological interactions between vegetation and groundwater
Dwelle, M. C.; Ivanov, V. Y.; Sargsyan, K.
2017-12-01
The complex interactions between groundwater and vegetation in the Amazon rainforest may yield vital ecophysiological interactions in specific landscape niches such as buffering plant water stress during dry season or suppression of water uptake due to anoxic conditions. Representation of such processes is greatly impacted by both external and internal sources of uncertainty: inaccurate data and subjective choice of model representation. The models that can simulate these processes are complex and computationally expensive, and therefore make it difficult to address uncertainty using traditional methods. We use the ecohydrologic model tRIBS+VEGGIE and a novel uncertainty quantification framework applied to the ZF2 watershed near Manaus, Brazil. We showcase the capability of this framework for stochastic simulation of vegetation-hydrology dynamics. This framework is useful for simulation with internal and external stochasticity, but this work will focus on internal variability of groundwater depth distribution and model parameterizations. We demonstrate the capability of this framework to make inferences on uncertain states of groundwater depth from limited in situ data, and how the realizations of these inferences affect the ecohydrological interactions between groundwater dynamics and vegetation function. We place an emphasis on the probabilistic representation of quantities of interest and how this impacts the understanding and interpretation of the dynamics at the groundwater-vegetation interface.
Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling
Hackett-Jones, Emily J.
2012-04-17
Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations. © 2012 American Physical Society.
Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Zhou, Weien, E-mail: weienzhou@nudt.edu.cn [College of Science, National University of Defense Technology, Changsha 410073 (China)
2017-08-01
We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.
Cui, Jianbo; Hong, Jialin; Liu, Zhihui; Zhou, Weien
2017-01-01
We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.
Tsuchida, Satoshi; Kuratsuji, Hiroshi
2018-05-01
A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.
Nonlinear interaction of colliding beams in particle storage rings
Herrera, J.C.; Month, M.
1979-01-01
When two beams of high energy particles moving in opposite directions are brought into collision, a large amount of energy is available for the production of new particles. However to obtain a sufficiently high event rate for rare processes, such as the production of the intermediate vector boson (Z 0 and W +- ), large beam currents are also required. Under this circumstance, the high charge density of one beam results in a classical electromagnetic interaction on the particles in the other beam. This very nonlinear space charge force, caled the beam-beam force, limits the total circulating charge and, thereby, the ultimate performance of the colliding ring system. The basic nature of the beam-beam force is discussed, indicating how it is quite different in the case of continuous beams, which cross each other at an angle as compared to the case of bunched beams which collide head-on. Some experimental observations on the beam-beam interaction in proton-proton and electron-positron beams are then reviewed and interpreted. An important aspect of the beam-beam problem in storage rings is to determine at what point in the analysis of the particle dynamics is it relevant to bring in the concepts of stochasticity, slow diffusion, and resonance overlap. These ideas are briefly discussed
Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)
2014-07-04
To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.
Zhu, Zhi-Wen; Zhang, Qing-Xin; Xu, Jia
2014-01-01
A kind of shape memory alloy (SMA) hysteretic nonlinear model was developed, and the nonlinear dynamics and bifurcation characteristics of the SMA thin film subjected to in-plane stochastic excitation were investigated. Van der Pol difference item was introduced to describe the hysteretic phenomena of the SMA strain–stress curves, and the nonlinear dynamic model of the SMA thin film subjected to in-plane stochastic excitation was developed. The conditions of global stochastic stability of the system were determined in singular boundary theory, and the probability density function of the system response was obtained. Finally, the conditions of stochastic Hopf bifurcation were analyzed. The results of theoretical analysis and numerical simulation indicate that self-excited vibration is induced by the hysteretic nonlinear characteristics of SMA, and stochastic Hopf bifurcation appears when the bifurcation parameter was changed; there are two limit cycles in the stationary probability density of the dynamic response of the system in some cases, which means that there are two vibration amplitudes whose probabilities are both very high, and jumping phenomena between the two vibration amplitudes appear with the change in conditions. The results obtained in this current paper are helpful for the application of the SMA thin film in stochastic vibration fields. - Highlights: • Hysteretic nonlinear model of shape memory alloy was developed. • Van der Pol item was introduced to interpret hysteretic strain–stress curves. • Nonlinear dynamic characteristics of the shape memory alloy film were analyzed. • Jumping phenomena were observed in the change of the parameters
Liu, Yunlong; Wang, Aiping; Guo, Lei; Wang, Hong
2017-07-09
This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.
Li, Yongming; Ma, Zhiyao; Tong, Shaocheng
2017-09-01
The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.
Yang, Tao; Cao, Qingjie
2018-03-01
This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.
Patrick C. Tobin; Ottar N. Bjornstad
2005-01-01
Natural enemy-victim systems may exhibit a range of dynamic space-time patterns. We used a theoretical framework to study spatiotemporal structuring in a transient natural enemy-victim system subject to differential rates of dispersal, stochastic forcing, and nonlinear dynamics. Highly mobile natural enemies that attacked less mobile victims were locally spatially...
Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique
El-Beltagy, Mohamed A.; Al-Mulla, Noah
2014-01-01
Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.
Sun, Ying; Ding, Derui; Zhang, Sunjie; Wei, Guoliang; Liu, Hongjian
2018-07-01
In this paper, the non-fragile ?-? control problem is investigated for a class of discrete-time stochastic nonlinear systems under event-triggered communication protocols, which determine whether the measurement output should be transmitted to the controller or not. The main purpose of the addressed problem is to design an event-based output feedback controller subject to gain variations guaranteeing the prescribed disturbance attenuation level described by the ?-? performance index. By utilizing the Lyapunov stability theory combined with S-procedure, a sufficient condition is established to guarantee both the exponential mean-square stability and the ?-? performance for the closed-loop system. In addition, with the help of the orthogonal decomposition, the desired controller parameter is obtained in terms of the solution to certain linear matrix inequalities. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed event-based controller design scheme.
Grigoryeva, Lyudmila; Henriques, Julie; Larger, Laurent; Ortega, Juan-Pablo
2014-07-01
Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs. Copyright © 2014 Elsevier Ltd. All rights reserved.
Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique
El-Beltagy, Mohamed A.
2014-01-06
Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.
Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems
Mahdi Alavi, S. M.; Saif, Mehrdad
2013-12-01
This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.
Stochastic Description of Activated Surface Diffusion with Interacting Adsorbates
Martínez-Casado, Ruth; Vega, José Luis; Sanz, Ángel S.; Miret-Artés, Salvador
Activated surface diffusion on metal surfaces is receiving much attention both experimentally and theoretically. One of the main theoretical problems in this field is to explain the line-shape broadening observed when the surface coverage is increased. Recently, we have proposed a fully stochastic model, the interacting single adsorbate (ISA) model, aimed at explaining and understanding this type of experiments, which essentially consists of considering the classical Langevin formulation with two types of noise forces: (i) a Gaussian white noise accounting for the substrate friction, and (ii) a shot noise simulating the interacting adsorbates at different coverages. No interaction potential between adsorbates is included because any trace of microscopic interaction seems to be wiped out in a Markovian regime. This model describes in a good approximation, and at a very low computational cost, the line-shape broadening observed experimentally. Furthermore, its mathematical simplicity also allows to derive some analytical expressions which are of much help in the interpretation of the physics underlying surface diffusion processes.
Nonlinear optical interactions in silicon waveguides
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.
Vasta, M.; Roberts, J. B.
1998-06-01
Methods for using fourth order spectral quantities to estimate the unknown parameters in non-linear, randomly excited dynamic systems are developed. Attention is focused on the case where only the response is measurable and the excitation is unmeasurable and known only in terms of a stochastic process model. The approach is illustrated through application to a non-linear oscillator with both non-linear damping and stiffness and with excitation modelled as a stationary Gaussian white noise process. The methods have applications in studies of the response of structures to random environmental loads, such as wind and ocean wave forces.
Elsheikh, Ahmed H.
2013-06-01
We introduce a nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of subsurface flow models. Sparse calibration is a challenging problem as the unknowns are both the non-zero components of the solution and their associated weights. NOMP is a greedy algorithm that discovers at each iteration the most correlated basis function with the residual from a large pool of basis functions. The discovered basis (aka support) is augmented across the nonlinear iterations. Once a set of basis functions are selected, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on stochastically approximated gradient using an iterative stochastic ensemble method (ISEM). In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem. © 2013 Elsevier Ltd.
Nonlinear interaction of waves in an inhomogeneous plasma
Istomin, Ya.N.
1988-01-01
Nonlinear wave processes in a weakly inhomogeneous plasma are considered. A quasilinear equation is derived which takes into account the effect of the waves on resonance particles, provided that the inhomogeneity appreciably affects the nature of the resonance interaction. Three-wave interaction is investigated under the same conditions. As an example, the nonlinear interaction in a relativistic plasma moving along a strong curvilinear magnetic field is considered
Zhang, Wei; Wang, Jun
2017-09-01
In attempt to reproduce price dynamics of financial markets, a stochastic agent-based financial price model is proposed and investigated by stochastic exclusion process. The exclusion process, one of interacting particle systems, is usually thought of as modeling particle motion (with the conserved number of particles) in a continuous time Markov process. In this work, the process is utilized to imitate the trading interactions among the investing agents, in order to explain some stylized facts found in financial time series dynamics. To better understand the correlation behaviors of the proposed model, a new time-dependent intrinsic detrended cross-correlation (TDI-DCC) is introduced and performed, also, the autocorrelation analyses are applied in the empirical research. Furthermore, to verify the rationality of the financial price model, the actual return series are also considered to be comparatively studied with the simulation ones. The comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets.
Quilty, J.; Adamowski, J. F.
2015-12-01
Urban water supply systems are often stressed during seasonal outdoor water use as water demands related to the climate are variable in nature making it difficult to optimize the operation of the water supply system. Urban water demand forecasts (UWD) failing to include meteorological conditions as inputs to the forecast model may produce poor forecasts as they cannot account for the increase/decrease in demand related to meteorological conditions. Meteorological records stochastically simulated into the future can be used as inputs to data-driven UWD forecasts generally resulting in improved forecast accuracy. This study aims to produce data-driven UWD forecasts for two different Canadian water utilities (Montreal and Victoria) using machine learning methods by first selecting historical UWD and meteorological records derived from a stochastic weather generator using nonlinear input variable selection. The nonlinear input variable selection methods considered in this work are derived from the concept of conditional mutual information, a nonlinear dependency measure based on (multivariate) probability density functions and accounts for relevancy, conditional relevancy, and redundancy from a potential set of input variables. The results of our study indicate that stochastic weather inputs can improve UWD forecast accuracy for the two sites considered in this work. Nonlinear input variable selection is suggested as a means to identify which meteorological conditions should be utilized in the forecast.
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
Stochastic quantum inflation for a canonical scalar field with linear self-interaction potential
Panotopoulos, Grigoris [CENTRA, Instituto Superior Tecnico, Universidade de Lisboa, Lisboa (Portugal)
2017-10-15
We apply Starobinsky's formalism of stochastic inflation to the case of a massless minimally coupled scalar field with linear self-interaction potential. We solve the corresponding Fokker-Planck equation exactly, and we obtain analytical expressions for the stochastic expectation values. (orig.)
Tavakoli, Ali; Nikoo, Mohammad Reza; Kerachian, Reza; Soltani, Maryam
2015-04-01
In this paper, a new fuzzy methodology is developed to optimize water and waste load allocation (WWLA) in rivers under uncertainty. An interactive two-stage stochastic fuzzy programming (ITSFP) method is utilized to handle parameter uncertainties, which are expressed as fuzzy boundary intervals. An iterative linear programming (ILP) is also used for solving the nonlinear optimization model. To accurately consider the impacts of the water and waste load allocation strategies on the river water quality, a calibrated QUAL2Kw model is linked with the WWLA optimization model. The soil, water, atmosphere, and plant (SWAP) simulation model is utilized to determine the quantity and quality of each agricultural return flow. To control pollution loads of agricultural networks, it is assumed that a part of each agricultural return flow can be diverted to an evaporation pond and also another part of it can be stored in a detention pond. In detention ponds, contaminated water is exposed to solar radiation for disinfecting pathogens. Results of applying the proposed methodology to the Dez River system in the southwestern region of Iran illustrate its effectiveness and applicability for water and waste load allocation in rivers. In the planning phase, this methodology can be used for estimating the capacities of return flow diversion system and evaporation and detention ponds.
Gutierrez, Rafael M.; Useche, Gina M.; Buitrago, Elias
2007-01-01
We present a procedure developed to detect stochastic and deterministic information contained in empirical time series, useful to characterize and make models of different aspects of complex phenomena represented by such data. This procedure is applied to a seismological time series to obtain new information to study and understand geological phenomena. We use concepts and methods from nonlinear dynamics and maximum entropy. The mentioned method allows an optimal analysis of the available information
Quantization of O(N) non-linear sigma models as the stochastic motion on Ssup(N-1)
Aldazabal, G.; Parga, N.
1983-09-01
We obtain the Langevin equations for the stochastic quantization of the O(N) non-linear sigma model by studying the random (Gaussian) motion on the sphere Ssup(N-1). We prove the equivalence of this procedure with a different one where the random forces are elements of the O(N) algebra. A proof that our approach yields in the equilibrium regime the quantum field theory is also given. (author)
Fully probabilistic control for stochastic nonlinear control systems with input dependent noise.
Herzallah, Randa
2015-03-01
Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained. Copyright © 2014 Elsevier Ltd. All rights reserved.
Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models
Elsheikh, Ahmed H.
2013-06-01
A novel parameter estimation algorithm is proposed. The inverse problem is formulated as a sequential data integration problem in which Gaussian process regression (GPR) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative stochastic ensemble method (ISEM). ISEM employs directional derivatives within a Gauss-Newton iteration for efficient gradient estimation. The resulting update equation relies on the inverse of the output covariance matrix which is rank deficient.In the proposed algorithm we use an iterative regularization based on the ℓ2 Boosting algorithm. ℓ2 Boosting iteratively fits the residual and the amount of regularization is controlled by the number of iterations. A termination criteria based on Akaike information criterion (AIC) is utilized. This regularization method is very attractive in terms of performance and simplicity of implementation. The proposed algorithm combining ISEM and ℓ2 Boosting is evaluated on several nonlinear subsurface flow parameter estimation problems. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier B.V.
Symbolic computation of nonlinear wave interactions on MACSYMA
Bers, A.; Kulp, J.L.; Karney, C.F.F.
1976-01-01
In this paper the use of a large symbolic computation system - MACSYMA - in determining approximate analytic expressions for the nonlinear coupling of waves in an anisotropic plasma is described. MACSYMA was used to implement the solutions of a fluid plasma model nonlinear partial differential equations by perturbation expansions and subsequent iterative analytic computations. By interacting with the details of the symbolic computation, the physical processes responsible for particular nonlinear wave interactions could be uncovered and appropriate approximations introduced so as to simplify the final analytic result. Details of the MACSYMA system and its use are discussed and illustrated. (Auth.)
Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling
Hackett-Jones, Emily J.; Landman, Kerry A.; Fellner, Klemens
2012-01-01
both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach
El-Khoury, O.; Kim, C.; Shafieezadeh, A.; Hur, J. E.; Heo, G. H.
2015-06-01
This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion.
El-Khoury, O; Shafieezadeh, A; Hur, J E; Kim, C; Heo, G H
2015-01-01
This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion. (paper)
Non-linear diffusion of charged particles due to stochastic electromagnetic fields
Martins, A.M.; Balescu, R.; Mendonca, J.T.
1989-01-01
It is well known that the energy confinement times observed in tokamak cannot be explained by the classical or neo-classical transport theory. The alternative explanations are based on the existence of various kinds of micro-instabilities, or on the stochastic destruction of the magnetic surfaces, due to the interaction of magnetic islands of different helicities. In the absence of a well established theory of anomalous transport it is perhaps important to study in some detail the diffusion coefficient of single charged particles in the presence of electromagnetic fluctuation, because it can provide the physical grounds for more complete and self-consistent calculations. In the present work we derive a general expression for the transverse diffusion coefficient of electrons and ions in a constant magnetic field and in the presence of space and time dependent electromagnetic fluctuation. We neglect macroscopic drifts due to inhomogeneity and field curvatures, but retain finite Larmor radius effects. (author) 3 refs
Stochastic three-wave interaction in flaring solar loops
Vlahos, L.; Sharma, R. R.; Papadopoulos, K.
1983-01-01
A model is proposed for the dynamic structure of high-frequency microwave bursts. The dynamic component is attributed to beams of precipitating electrons which generate electrostatic waves in the upper hybrid branch. Coherent upconversion of the electrostatic waves to electromagnetic waves produces an intrinsically stochastic emission component which is superposed on the gyrosynchrotron continuum generated by stably trapped electron fluxes. The role of the density and temperature of the ambient plasma in the wave growth and the transition of the three wave upconversion to stochastic, despite the stationarity of the energy source, are discussed in detail. The model appears to reproduce the observational features for reasonable parameters of the solar flare plasma.
Stochastic three-wave interaction in flaring solar loops
Vlahos, L.; Sharma, R.R.; Papadopoulos, K.
1983-01-01
We propose a model for the dynamic structure of high-frequency microwave bursts. The dynamic component is attributed to beams of precipitating electrons which generate electrostatic waves in the upper hybrid branch. Coherent upconversion of the electrostatic waves to electromagnetic waves produces an intrinsically stochastic emission component which is superposed on the gyrosynchrotron continuum generated by stably trapped electron fluxes. The role of the density and temperature of the ambient plasma in the wave growth and the transition of the three wave upconversion to stochastic, despite the stationarity of the energy source are discussed in detail. The model appears to reproduce the observational features for reasonable parameters of the solar flare plasma
Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture
Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong
The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.
Nonlinear PCA: characterizing interactions between modes of brain activity.
Friston, K; Phillips, J; Chawla, D; Büchel, C
2000-01-01
This paper presents a nonlinear principal component analysis (PCA) that identifies underlying sources causing the expression of spatial modes or patterns of activity in neuroimaging time-series. The critical aspect of this technique is that, in relation to conventional PCA, the sources can interact to produce (second-order) spatial modes that represent the modulation of one (first-order) spatial mode by another. This nonlinear PCA uses a simple neural network architecture that embodies a spec...
Stochastic motion from a forced plasma-maser interaction
Honjo, Haruo; Nambu, Mitsuhiro
1986-01-01
A model of forced plasma-maser effects is examined numerically. The model represents a conservative system and reduces to the forced type of the original Lotka-Volterra equation. A stochastic motion is found to occur when the density of a cold ion beam becomes larger. (author)
Laboratory beam-plasma interactions: linear and nonlinear
Christiansen, P.J.; Jain, V.K.; Bond, J.W.
1982-01-01
The present investigation is concerned with the configuration of a cool plasma (often magnetized axially) penetrated by an injected electron beam. The attempt is made to demonstrate that despite unavoidable scaling limitations, laboratory experiments can illuminate, in a controlled fashion, details of beam plasma interaction processes in a way which will never be possible in the space plasma physics. In view of the increasing interest in high frequency instabilities in the auroral zone, the possibilities for interesting cross fertilizations of the two fields appear to be extensive. The linear theory is considered along with low frequency couplings and indirect effects. Attention is given to the evidence for the existence of exponentially growing instabilities in beam plasma interactions. The consequences of such instabilities are also explored and some processes of nonlinear processes are discussed, taking into account quasi-linear effects, trapping effects, nonlinear effects, trapping effects, nonlinear wave-wave interactions, and self-modulation and cavitation. 80 references
Zhang Jinhui [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: jinhuizhang82@gmail.com; Shi Peng [Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL (United Kingdom); ILSCM, School of Science and Engineering, Victoria University, Melbourne, Vic. 8001 (Australia); School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095 (Australia)], E-mail: pshi@glam.ac.uk; Yang Hongjiu [Department of Automatic Control, Beijing Institute of Technology, Beijing 100081 (China)], E-mail: yanghongjiu@gmail.com
2009-12-15
This paper deals with the problem of non-fragile robust stabilization and H{sub {infinity}} control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are real time-varying as well as norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions for the existence of such controllers are presented based on the linear matrix inequalities (LMIs) approach. Numerical example is given to illustrate the effectiveness of the developed techniques.
Tong, Shaocheng; Wang, Tong; Li, Yongming; Zhang, Huaguang
2014-06-01
This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.
Non-linear electromagnetic interactions in thermal QED
Brandt, F.T.; Frenkel, J.
1994-08-01
The behavior of the non-linear interactions between electromagnetic fields at high temperature is examined. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. It is argued that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T -> ∞. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action. (author). 12 refs, 1 fig
Dynamic nonlinear interaction of elastic plates on discrete supports
Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.
1984-01-01
A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt
Keanini, R.G.
2011-01-01
Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the
Krishnan, Venkatarama
2005-01-01
Most useful for graduate students in engineering and finance who have a basic knowledge of probability theory, this volume is designed to give a concise understanding of martingales, stochastic integrals, and estimation. It emphasizes applications. Many theorems feature heuristic proofs; others include rigorous proofs to reinforce physical understanding. Numerous end-of-chapter problems enhance the book's practical value.After introducing the basic measure-theoretic concepts of probability and stochastic processes, the text examines martingales, square integrable martingales, and stopping time
Huanqing Wang
2014-01-01
Full Text Available The problem of fuzzy-based direct adaptive tracking control is considered for a class of pure-feedback stochastic nonlinear systems. During the controller design, fuzzy logic systems are used to approximate the packaged unknown nonlinearities, and then a novel direct adaptive controller is constructed via backstepping technique. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error eventually converges to a small neighborhood around the origin in the sense of mean quartic value. The main advantages lie in that the proposed controller structure is simpler and only one adaptive parameter needs to be updated online. Simulation results are used to illustrate the effectiveness of the proposed approach.
Weiwei Sun
2015-01-01
Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.
Nonlinear interaction of the surface waves at a plasma boundary
Dolgopolov, V.V.; El-Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1976-01-01
Amplitudes of electromagnetic waves with combination frequencies, radiating from the plasma boundary due to nonlinear interaction of the surface waves, have been found. Previous papers on this subject did not take into account that the tangential components of the electric field of waves with combination frequencies were discontinuous at the plasma boundary. (Auth.)
Non-Linear Interactive Stories in Computer Games
Bangsø, Olav; Jensen, Ole Guttorm; Kocka, Tomas
2003-01-01
The paper introduces non-linear interactive stories (NOLIST) as a means to generate varied and interesting stories for computer games automatically. We give a compact representation of a NOLIST based on the specification of atomic stories, and show how to build an object-oriented Bayesian network...
NON-LINEAR MODELING OF THE RHIC INTERACTION REGIONS
TOMAS, R.; FISCHER, W.; JAIN, A.; LUO, Y.; PILAT, F.
2004-01-01
For RHIC's collision lattices the dominant sources of transverse non-linearities are located in the interaction regions. The field quality is available for most of the magnets in the interaction regions from the magnetic measurements, or from extrapolations of these measurements. We discuss the implementation of these measurements in the MADX models of the Blue and the Yellow rings and their impact on beam stability
Nonlinear light-matter interactions in engineered optical media
Litchinitser, Natalia
In this talk, we consider fundamental optical phenomena at the interface of nonlinear and singular optics in artificial media, including theoretical and experimental studies of linear and nonlinear light-matter interactions of vector and singular optical beams in metamaterials. We show that unique optical properties of metamaterials open unlimited prospects to ``engineer'' light itself. Thanks to their ability to manipulate both electric and magnetic field components, metamaterials open new degrees of freedom for tailoring complex polarization states and orbital angular momentum (OAM) of light. We will discuss several approaches to structured light manipulation on the nanoscale using metal-dielectric, all-dielectric and hyperbolic metamaterials. These new functionalities, including polarization and OAM conversion, beam magnification and de-magnification, and sub-wavelength imaging using novel non-resonant hyperlens are likely to enable a new generation of on-chip or all-fiber structured light applications. The emergence of metamaterials also has a strong potential to enable a plethora of novel nonlinear light-matter interactions and even new nonlinear materials. In particular, nonlinear focusing and defocusing effects are of paramount importance for manipulation of the minimum focusing spot size of structured light beams necessary for nanoscale trapping, manipulation, and fundamental spectroscopic studies. Colloidal suspensions offer as a promising platform for engineering polarizibilities and realization of large and tunable nonlinearities. We will present our recent studies of the phenomenon of spatial modulational instability leading to laser beam filamentation in an engineered soft-matter nonlinear medium. Finally, we introduce so-called virtual hyperbolic metamaterials formed by an array of plasma channels in air as a result of self-focusing of an intense laser pulse, and show that such structure can be used to manipulate microwave beams in a free space. This
Linear and nonlinear interactions in the dark sector
Chimento, Luis P.
2010-01-01
We investigate models of interacting dark matter and dark energy for the Universe in a spatially flat Friedmann-Robertson-Walker space-time. We find the 'source equation' for the total energy density and determine the energy density of each dark component. We introduce an effective one-fluid description to evidence that interacting and unified models are related to each other, analyze the effective model, and obtain the attractor solutions. We study linear and nonlinear interactions, the former comprises a linear combination of the dark matter and dark energy densities, their first derivatives, the total energy density, its first and second derivatives, and a function of the scale factor. The latter is a possible generalization of the linear interaction consisting of an aggregate of the above linear combination and a significant nonlinear term built with a rational function of the dark matter and dark energy densities homogeneous of degree 1. We solve the evolution equations of the dark components for both interactions and examine exhaustively several examples. There exist cases where the effective one-fluid description produces different alternatives to the ΛCDM model and cases where the problem of coincidence is alleviated. In addition, we find that some nonlinear interactions yield an effective one-fluid model with a Chaplygin gas equation of state, whereas others generate cosmological models with de Sitter and power-law expansions. We show that a generic nonlinear interaction induces an effective equation of state which depends on the scale factor in the same way as the variable modified Chaplygin gas model, giving rise to the 'relaxed Chaplygin gas model'.
Dynamical soil-structure interactions: influence of soil behaviour nonlinearities
Gandomzadeh, Ali
2011-01-01
The interaction of the soil with the structure has been largely explored the assumption of material and geometrical linearity of the soil. Nevertheless, for moderate or strong seismic events, the maximum shear strain can easily reach the elastic limit of the soil behavior. Considering soil-structure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and therefore energy dissipation into the soil. Consequently, ignoring the nonlinear characteristics of the dynamic soil-structure interaction (DSSI) this phenomenon could lead to erroneous predictions of structural response. The goal of this work is to implement a fully nonlinear constitutive model for soils into a numerical code in order to investigate the effect of soil nonlinearity on dynamic soil structure interaction. Moreover, different issues are taken into account such as the effect of confining stress on the shear modulus of the soil, initial static condition, contact elements in the soil-structure interface, etc. During this work, a simple absorbing layer method based on a Rayleigh/Caughey damping formulation, which is often already available in existing Finite Element softwares, is also presented. The stability conditions of the wave propagation problems are studied and it is shown that the linear and nonlinear behavior are very different when dealing with numerical dispersion. It is shown that the 10 points per wavelength rule, recommended in the literature for the elastic media is not sufficient for the nonlinear case. The implemented model is first numerically verified by comparing the results with other known numerical codes. Afterward, a parametric study is carried out for different types of structures and various soil profiles to characterize nonlinear effects. Different features of the DSSI are compared to the linear case: modification of the amplitude and frequency content of the waves propagated into the soil, fundamental frequency, energy dissipation in
LINEAR AND NONLINEAR CORRECTIONS IN THE RHIC INTERACTION REGIONS
PILAT, F.; CAMERON, P.; PTITSYN, V.; KOUTCHOUK, J.P.
2002-01-01
A method has been developed to measure operationally the linear and non-linear effects of the interaction region triplets, that gives access to the multipole content through the action kick, by applying closed orbit bumps and analyzing tune and orbit shifts. This technique has been extensively tested and used during the RHIC operations in 2001. Measurements were taken at 3 different interaction regions and for different focusing at the interaction point. Non-linear effects up to the dodecapole have been measured as well as the effects of linear, sextupolar and octupolar corrections. An analysis package for the data processing has been developed that through a precise fit of the experimental tune shift data (measured by a phase lock loop technique to better than 10 -5 resolution) determines the multipole content of an IR triplet
Nonlinear interaction of energetic ring current protons with magnetospheric hydromagnetic waves
Chan, A.A.; Chen, L.; White, R.B.
1989-01-01
In order to study nonlinear wave-particle interactions in the Earth's magnetosphere we have derived Hamiltonian equations for the gyrophase-averaged nonrelativistic motion of charged particles in a perturbed dipole magnetic field. We assume low frequency (less than the proton gyrofrequency) fully electromagnetic perturbations, and we retain finite Larmor radius effects. Analytic and numerical results for the stochastic threshold of energetic protons (approx-gt 100 keV) in compressional geomagnetic pulsations in the Pc 5 range of frequencies 150--600 seconds are presented. These protons undergo a drift-bounce resonance with the Pc 5 waves which breaks the second (longitudinal) and third (flux) adiabatic invariants, while the first invariant (the magnetic moment) and the proton energy are approximately conserved. The proton motion in the observed spectrum of waves is found to be strongly diffusive, due to the overlap of neighboring primary resonances. copyright American Geophysical Union 1989
Nonlinear interaction of energetic ring current protons with magnetospheric hydromagnetic waves
Chan, A.A.; Chen, Liu; White, R.B.
1989-09-01
In order to study nonlinear wave-particle interactions in the earth's magnetosphere we have derived Hamiltonian equations for the gyrophase-averaged nonrealistic motion of charged particles in a perturbed dipole magnetic field. We assume low frequency (less than the proton gyrofrequency) fully electromagnetic perturbations, and we retain finite Larmor radius effects. Analytic and numerical results for the stochastic threshold of energetic protons (approx gt 100 keV) in compressional geomagnetic pulsations in the Pc 5 range of frequencies (150--600 seconds) are presented. These protons undergo a drift-bounce resonance with the Pc 5 waves which breaks the second (longitudinal) and third (flux) adiabatic invariants, while the first invariant (the magnetic moment) and the proton energy are approximately conserved. The proton motion in the observed spectrum of waves is found to be strongly diffusive, due to the overlap of neighboring primary resonances. 17 refs., 2 figs
Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations
Atzberger, Paul J.
2011-01-01
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid-structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid-structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid-structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations.
Laboratory beam-plasma interactions linear and nonlinear
Christiansen, P.J.; Bond, J.W.; Jain, V.K.
1982-01-01
This chapter attempts to demonstrate that despite unavoidable scaling limitations, laboratory experiments can uncover details of beam plasma interaction processes which could never be revealed through space plasma physics. Topics covered include linear theory, low frequency couplings, indirect effects, nonlinear effects, quasi-linear effects, trapping effects, nonlinear wave-wave interactions, and self modulation and cavitation. Unstable electrostatic waves arising from an exchange of energy with the ''free energy'' beam features are considered as kinetic and as hydrodynamic, or fluid, instabilities. The consequences of such instabilities (e.g. when the waves have grown to a finite level) are examined and some studies are reviewed which have attempted to understand how the free energy originally available in the beam is redistributed to produce a final state of equilibrium turbulence
Yang, Y.; Solis Escalante, T.; van der Helm, F.C.T.; Schouten, A.C.
2016-01-01
Objective: This paper introduces a generalized coherence framework for detecting and characterizing nonlinear interactions in the nervous system, namely cross-spectral coherence (CSC). CSC can detect different types of nonlinear interactions including harmonic and intermodulation coupling as present
Nonlinear degenerate cross-diffusion systems with nonlocal interaction
Di Francesco, M.; Esposito, A.; Fagioli, S.
2017-01-01
We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform "coerciveness" assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove g...
Interaction of electromagnetic and acoustic waves in a stochastic atmosphere
Bhatnagar, N.; Peterson, A. M.
1979-01-01
In the Stanford radio acoustic sounding system (RASS) an electromagnetic signal is made to scatter from a moving acoustic pulse train. Under a Bragg-scatter condition maximum electromagnetic scattering occurs. The scattered radio signal contains temperature and wind information as a function of the acoustic-pulse position. In this investigation RASS performance is assessed in an atmosphere characterized by the presence of turbulence and mean atmospheric parameters. The only assumption made is that the electromagnetic wave is not affected by stochastic perturbations in the atmosphere. It is concluded that the received radio signal depends strongly on the intensity of turbulence for altitudes of the acoustic pulse greater than the coherence length of propagation. The effect of mean vertical wind and mean temperature on the strength of the received signal is also demonstrated to be insignificant. Mean horizontal winds, however, shift the focus of the reflected electromagnetic energy from its origin, resulting in a decrease in received signal level when a monostatic radio-frequency (RF) system is used. For a bistatic radar configuration with space diversified receiving antennas, the shifting of the acoustic pulse makes possible the remote measurement of the horizontal wind component.
Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves
Tobita, Miwa; Omura, Yoshiharu
2018-03-01
We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.
Albert, Carlo; Ulzega, Simone; Stoop, Ruedi
2016-04-01
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.
Dan Ye
2013-01-01
Full Text Available This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.
Zhaohui Chen
2013-01-01
Full Text Available The delay-dependent exponential L2-L∞ performance analysis and filter design are investigated for stochastic systems with mixed delays and nonlinear perturbations. Based on the delay partitioning and integral partitioning technique, an improved delay-dependent sufficient condition for the existence of the L2-L∞ filter is established, by choosing an appropriate Lyapunov-Krasovskii functional and constructing a new integral inequality. The full-order filter design approaches are obtained in terms of linear matrix inequalities (LMIs. By solving the LMIs and using matrix decomposition, the desired filter gains can be obtained, which ensure that the filter error system is exponentially stable with a prescribed L2-L∞ performance γ. Numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.
Kaulakys, B.; Alaburda, M.; Ruseckas, J.
2016-05-01
A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.
Guo, Yongfeng; Shen, Yajun; Tan, Jianguo
2016-09-01
The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.
Stochastic Coulomb interactions in space charge limited electron emission
Nijkerk, M.D.; Kruit, P.
2004-01-01
Emission models that form the basis of self-consistent field computations make use of the approximation that emitted electrons form a smooth space charge jelly. In reality, electrons are discrete particles that are subject to statistical Coulomb interactions. A Monte Carlo simulation tool is used to evaluate the influence of discrete space charge effects on self-consistent calculations of cathode-ray tube optics. We find that interactions in the space charge cloud affect the electron trajectories such that the velocity distribution is Maxwellian, regardless of the current density. Interactions near the emitter effectively conserve the Maxwellian distribution. The surprising result is that the width of the distribution of transversal velocities does not change. The distribution of longitudinal velocities does broaden, as expected from existing theories
J.A. Krommes
2009-05-19
Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.
Krommes, J.A.
2009-01-01
Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-? theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.
Fluid transport due to nonlinear fluid-structure interaction
Jensen, Jakob Søndergaard
1997-01-01
This work considers nonlinear fluid-structure interaction for a vibrating pipe containing fluid. Transverse pipe vibrations will force the fluid to move relative to the pipe creating unidirectional fluid flow towards the pipe end. The fluid flow induced affects the damping and the stiffness...... of the pipe. The behavior of the system in response to lateral resonant base excitation is analysed numerically and by the use of a perturbation method (multiple scales). Exciting the pipe in the fundamental mode of vibration seems to be most effective for transferring energy from the shaker to the fluid......, whereas higher modes of vibration can be used to transport fluid with pipe vibrations of smaller amplitude. The effect of the nonlinear geometrical terms is analysed and these terms are shown to affect the response for higher modes of vibration. Experimental investigations show good agreement...
Optimising stochastic trajectories in exact quantum jump approaches of interacting systems
Lacroix, D.
2004-11-01
The standard methods used to substitute the quantum dynamics of two interacting systems by a quantum jump approach based on the Stochastic Schroedinger Equation (SSE) are described. It turns out that for a given situation, there exists an infinite number of SSE reformulation. This fact is used to propose general strategies to optimise the stochastic paths in order to reduce the statistical fluctuations. In this procedure, called the 'adaptative noise method', a specific SSE is obtained for which the noise depends explicitly on both the initial state and on the properties of the interaction Hamiltonian. It is also shown that this method can be further improved by the introduction of a mean-field dynamics. The different optimisation procedures are illustrated quantitatively in the case of interacting spins. A significant reduction of the statistical fluctuations is obtained. Consequently, a much smaller number of trajectories is needed to accurately reproduce the exact dynamics as compared to the standard SSE method. (author)
Stochastic Coulomb interactions in space charge limited electron emission
Nijkerk, M.D.; Kruit, P.
2004-01-01
A Monte Carlo simulation tool, which was used to evaluate the influence of discrete space charge effects on self-consistent calculations of cathode-ray tube optics, was discussed. It was found that interactions in the space charge cloud affect the electron trajectories such that the velocity
Kanjilal, Oindrila; Manohar, C. S.
2017-07-01
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.
Dynamic Response of Non-Linear Inelsatic Systems to Poisson-Driven Stochastic Excitations
Nielsen, Søren R. K.; Iwankiewicz, R.
of an equivalent linearization techni que and substituting the non-analytical non-linearity in the original system by the cubic form in the pertinent state variables. The response moments are evaluated for the equivalent systems with the help of a generalized Ito's differential rule. The analytical results...
Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory
Frier, Christian; Sørensen, John Dalsgaard
2003-01-01
A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...
Kinematics of Nonlinearly Interacting MHD Instabilities in a Plasma
Hansen, Alexander K.
2000-01-01
Plasmas play host to a wide variety of instabilities. For example, tearing instabilities use finite plasma resistivity to exploit the free energy provided by plasma currents parallel to the magnetic field to alter the magnetic topology of the plasma through a process known as reconnection. These instabilities frequently make themselves known in magnetic confinement experiments such as tokamaks and reversed field pinches (RFPs). In RFP plasmas, in fact, several tearing instabilities (modes) are simultaneously active, and are of large amplitude. Theory predicts that in addition to interacting linearly with magnetic perturbations from outside the plasma, such as field errors or as resistive wall, the modes in the RFP can interact nonlinearly with each other through a three-wave interaction. In the current work investigations of both the linear (external) and nonlinear contributions to the kinematics of the tearing modes in the Madison Symmetric Torus (MST) RFP are reported Theory predicts that tearing modes will respond only to magnetic perturbations that are spatially resonant with them, and was supported by experimental work done on tokamak devices. The results in this work verified that the theory is still applicable to the RFP, in spite of its more complicated magnetic mode structure, involving perturbations of a single poloidal mode number
Nonlinear instability and chaos in plasma wave-wave interactions
Kueny, C.S.
1993-01-01
Conventional linear stability analysis may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipitation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, which leads to explosive growth. In the dissipationaless case, it is conjectured that intrinsic chaotic behavior may allow initially non-resonant systems to reach resonance by diffusion in phase space. This is illustrated for a simple equilibrium involving cold counter-streaming ions. The system is described in the fluid approximation by a Hamilitonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamilitonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, which occur generically for long enough wavelengths. Three-wave interactions which occur in isolated, but numerous, regions of parameter space can drive either decay instability or explosive instability. When the resonance for explosive growth is detuned, a stable region exists around the equilibrium point in phase space, while explosive growth occurs outside of a separatrix. These interactions may be described exactly if only one resonance is considered, while multiple nonlinear terms make the Hamiltonian nonintegradable. Simple Hamiltonians of two and three degrees of freedom are studied numerically using symplectic integration algorithms, including an explicit algorithm derived using Lie algebraic methods
Ryo Oizumi
Full Text Available Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.
Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.
2010-01-01
Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions were produced by all the three methods. The variation in the weight calculated by the methods was modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliabilitytraced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.
Nonlinear wave particle interaction in the Earth's foreshock
Mazelle, C.; LeQueau, D.; Meziane, K.; Lin, R. P.; Parks, G.; Reme, H.; Sanderson, T.; Lepping, R. P.
1997-01-01
The possibility that ion beams could provide a free energy source for driving an ion/ion instability responsible for the ULF wave occurrence is investigated. For this, the wave dispersion relation with the observed parameters is solved. Secondly, it is shown that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered around a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions with the observations are compared.
Non-linear effective Lagrangian treatment of 'Penguin' interaction
Pham, T.N.
1984-01-01
Using the non-linear effective lagrangian technique, we show explicitly that only derivative coupling is allowed for the K - π, K -> 2 π and K -> 3 π transitions induced by the ΔS = 1 Penguin operator of SVZ in agreement with chiral symmetry requirements. From a derivative coupling (3, anti 3) mass term and the SU(3) breaking effect for fsub(K)/fsub(π), we estimate the strength of the Penguin interactions and find it too small to account for the ΔI = 1/2 amplitude. (orig.)
Earthquake analysis with nonlinear soil-structure interaction and nonlinear supports of components
Hansson, V.
1990-01-01
For the determination of the seismic response of a structure the soil-structure interaction in most cases is modelled by a mass-spring-damper-system. Normally design concepts for components and piping are based on linear calculations and stress limitations. A concept for a reactor building for the HTR 100 consisted of a relatively high structure compared with the dimensions of the foundation. The structure was comparatively deep embedded in the soil, so here the embedment influences significantly the soil-structure interaction. The assembly of reactor vessel, heat exchanger and circulators has a height of about 37 m. Supports are arranged at different levels. Due to temperature deformations of the vessel and of the support constructions small gaps at the supports may only be avoided by complicated constructions of the supports. Nonlinear analyses were performed for soil, building and component with all supports. The finite element analyses used time histories. In order to describe the radiation damping the hysteresis of the soil with 1 percent material damping was considered. Nonlinearities in the interface of soil and foundation and due to gaps and friction at the supports were taken into account. The stiffness of the support constructions influences reactions and accelerations to a high extent. Properly chosen stiffnesses of the support constructions lead to a behaviour similar to linear elastic behaviour. 13 figs
MANFREDI, P.
2014-11-01
Full Text Available This paper extends recent literature results concerning the statistical simulation of circuits affected by random electrical parameters by means of the polynomial chaos framework. With respect to previous implementations, based on the generation and simulation of augmented and deterministic circuit equivalents, the modeling is extended to generic and ?black-box? multi-terminal nonlinear subcircuits describing complex devices, like those found in integrated circuits. Moreover, based on recently-published works in this field, a more effective approach to generate the deterministic circuit equivalents is implemented, thus yielding more compact and efficient models for nonlinear components. The approach is fully compatible with commercial (e.g., SPICE-type circuit simulators and is thoroughly validated through the statistical analysis of a realistic interconnect structure with a 16-bit memory chip. The accuracy and the comparison against previous approaches are also carefully established.
Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps
Ge, Qing; Ji, Guilin; Xu, Jiabo; Fan, Xiaolin
2016-11-01
In this paper, Brownian motion and L e ´ vy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0 ,R¯0 are showed. We find that if R˜0 1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.
Solution of Stochastic Nonlinear PDEs Using Automated Wiener-Hermite Expansion
Al-Juhani, Amnah
2014-01-06
The solution of the stochastic differential equations (SDEs) using Wiener-Hermite expansion (WHE) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In WHE approach, there is no randomness directly involved in the computations. One does not have to rely on pseudo random number generators, and there is no need to solve the SDEs repeatedly for many realizations. Instead, the deterministic system is solved only once. For previous research efforts see [2, 4].
Nonlinear interactions of focused resonance cone fields with plasmas
Stenzel, R.L.; Gekelman, W.
1977-01-01
A simple yet novel rf exciter structure has been developed for generating remotely intense rf fields in a magnetoplasma. It is a circular line source of radius R in a plane perpendicularB 0 driven with an rf signal at ω 0 E/sub rf/ 2 /nkT/sub e/>0.2, a strong density depression in the focal region (deltan/n>40%) is observed. The density perturbation modifies the cone angle and field distribution. This nonlinear interaction leads to a rapid growth of ion acoustic wave turbulence and a corresponding random rf field distribution in a broadened focal region. The development of the interaction is mapped in space and time
A non-linear theory of strong interactions
Skyrme, T.H.R.
1994-01-01
A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
Parsakhoo, Zahra; Shao, Yaping
2017-04-01
Near-surface turbulent mixing has considerable effect on surface fluxes, cloud formation and convection in the atmospheric boundary layer (ABL). Its quantifications is however a modeling and computational challenge since the small eddies are not fully resolved in Eulerian models directly. We have developed a Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer based on the Ito Stochastic Differential Equation (SDE) for air parcels (particles). Due to the complexity of the mixing in the ABL, we find that linear Ito SDE cannot represent convections properly. Three strategies have been tested to solve the problem: 1) to make the deterministic term in the Ito equation non-linear; 2) to change the random term in the Ito equation fractional, and 3) to modify the Ito equation by including Levy flights. We focus on the third strategy and interpret mixing as interaction between at least two stochastic processes with different Lagrangian time scales. The model is in progress to include the collisions among the particles with different characteristic and to apply the 3D model for real cases. One application of the model is emphasized: some land surface patterns are generated and then coupled with the Large Eddy Simulation (LES).
Non-parametric system identification from non-linear stochastic response
Rüdinger, Finn; Krenk, Steen
2001-01-01
An estimation method is proposed for identification of non-linear stiffness and damping of single-degree-of-freedom systems under stationary white noise excitation. Non-parametric estimates of the stiffness and damping along with an estimate of the white noise intensity are obtained by suitable...... of the energy at mean-level crossings, which yields the damping relative to white noise intensity. Finally, an estimate of the noise intensity is extracted by estimating the absolute damping from the autocovariance functions of a set of modified phase plane variables at different energy levels. The method...
Yun, Hae-Bum; Masri, Sami F
2009-01-01
A reliable structural health monitoring methodology (SHM) is proposed to detect relatively small changes in uncertain nonlinear systems. A total of 4000 physical tests were performed using a complex nonlinear magneto-rheological (MR) damper. With the effective (or 'genuine') changes and uncertainties in the system characteristics of the semi-active MR damper, which were precisely controlled with known means and standard deviation of the input current, the tested MR damper was identified with the restoring force method (RFM), a non-parametric system identification method involving two-dimensional orthogonal polynomials. Using the identified RFM coefficients, both supervised and unsupervised pattern recognition techniques (including support vector classification and k-means clustering) were employed to detect system changes in the MR damper. The classification results showed that the identified coefficients with orthogonal basis function can be used as reliable indicators for detecting (small) changes, interpreting the physical meaning of the detected changes without a priori knowledge of the monitored system and quantifying the uncertainty bounds of the detected changes. The classification errors were analyzed using the standard detection theory to evaluate the performance of the developed SHM methodology. An optimal classifier design procedure was also proposed and evaluated to minimize type II (or 'missed') errors
A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems
Taverniers, Søren; Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu
2017-02-01
Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.
Nonlinear dynamic soil-structure interaction in earthquake engineering
Nieto-Ferro, Alex
2013-01-01
The present work addresses a computational methodology to solve dynamic problems coupling time and Laplace domain discretizations within a domain decomposition approach. In particular, the proposed methodology aims at meeting the industrial need of performing more accurate seismic risk assessments by accounting for three-dimensional dynamic soil-structure interaction (DSSI) in nonlinear analysis. Two subdomains are considered in this problem. On the one hand, the linear and unbounded domain of soil which is modelled by an impedance operator computed in the Laplace domain using a Boundary Element (BE) method; and, on the other hand, the superstructure which refers not only to the structure and its foundations but also to a region of soil that possibly exhibits nonlinear behaviour. The latter sub-domain is formulated in the time domain and discretized using a Finite Element (FE) method. In this framework, the DSSI forces are expressed as a time convolution integral whose kernel is the inverse Laplace transform of the soil impedance matrix. In order to evaluate this convolution in the time domain by means of the soil impedance matrix (available in the Laplace domain), a Convolution Quadrature-based approach called the Hybrid Laplace-Time domain Approach (HLTA), is thus introduced. Its numerical stability when coupled to Newmark time integration schemes is subsequently investigated through several numerical examples of DSSI applications in linear and nonlinear analyses. The HLTA is finally tested on a more complex numerical model, closer to that of an industrial seismic application, and good results are obtained when compared to the reference solutions. (author)
Theoretical studies of some nonlinear laser-plasma interactions
Cohen, B.I.
1975-01-01
The nonlinear coupling of intense, monochromatic, electromagnetic radiation with plasma is considered in a number of special cases. The first part of the thesis serves as an introduction to three-wave interactions. A general formulation of the stimulated scattering of transverse waves by longitudinal modes in a warm, unmagnetized, uniform plasma is constructed. A general dispersion relation is derived that describes Raman and Brillouin scattering, modulational instability, and induced Thomson scattering. Raman scattering (the scattering of a photon into another photon and an electron plasma wave) is investigated as a possible plasma heating scheme. Analytic theory complemented by computer simulation is presented describing the nonlinear mode coupling of laser light with small and large amplitude, resonantly excited electron plasma waves. The simulated scattering of a coherent electromagnetic wave by low frequency density perturbations in homogeneous plasma is discussed. A composite picture of the linear dispersion relations for filamentation and Brillouin scattering is constructed. The absolute instability of Brillouin weak and strong coupling by analytic and numerical means is described
Asymptotic approach for the nonlinear equatorial long wave interactions
Ramirez Gutierrez, Enver; Silva Dias, Pedro L; Raupp, Carlos
2011-01-01
In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are discussed. In particular, we discuss the implications of the results for El Nino and the Madden-Julian in connection with other scales of time and spatial variability.
Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle
Giorgio Kaniadakis
2018-06-01
Full Text Available Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker–Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker–Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker–Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker–Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker–Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP that governs the particle kinetics of many body systems, introduced in G. Kaniadakis, Physica A 296, 405 (2001, univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker–Planck equation in its most general form.
Nonlinear threshold Boolean automata networks and phase transitions
Demongeot, Jacques; Sené, Sylvain
2010-01-01
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on the basis of classical stochastic threshold Boolean automata networks in which specific interaction potentials of neighbourhood coalition are taken into account. More precisely, specific nonlinear terms compose local transition functions that define locally t...
Nonlinear Stochastic stability analysis of Wind Turbine Wings by Monte Carlo Simulations
Larsen, Jesper Winther; Iwankiewiczb, R.; Nielsen, Søren R.K.
2007-01-01
and inertial contributions. A reduced two-degrees-of-freedom modal expansion is used specifying the modal coordinate of the fundamental blade and edgewise fixed base eigenmodes of the beam. The rotating beam is subjected to harmonic and narrow-banded support point motion from the nacelle displacement...... under narrow-banded excitation, and it is shown that the qualitative behaviour of the strange attractor is very similar for the periodic and almost periodic responses, whereas the strange attractor for the chaotic case loses structure as the excitation becomes narrow-banded. Furthermore......, the characteristic behaviour of the strange attractor is shown to be identifiable by the so-called information dimension. Due to the complexity of the coupled nonlinear structural system all analyses are carried out via Monte Carlo simulations....
Interaction between two point-like charges in nonlinear electrostatics
Breev, A.I. [Tomsk State University, Tomsk (Russian Federation); Tomsk Polytechnic University, Tomsk (Russian Federation); Shabad, A.E. [P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State University, Tomsk (Russian Federation)
2018-01-15
We consider two point-like charges in electrostatic interaction within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We find the common field of the two charges in a dipole-like approximation, where the separation between them R is much smaller than the observation distance r: with the linear accuracy with respect to the ratio R/r, and in the opposite approximation, where R >> r, up to the term quadratic in the ratio r/R. The consideration proposes the law a + bR{sup 1/3} for the energy, when the charges are close to one another, R → 0. This leads to the singularity of the force between them to be R{sup -2/3}, which is weaker than the Coulomb law, R{sup -2}. (orig.)
Interaction between two point-like charges in nonlinear electrostatics
Breev, A. I.; Shabad, A. E.
2018-01-01
We consider two point-like charges in electrostatic interaction within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We find the common field of the two charges in a dipole-like approximation, where the separation between them R is much smaller than the observation distance r : with the linear accuracy with respect to the ratio R / r, and in the opposite approximation, where R≫ r, up to the term quadratic in the ratio r / R. The consideration proposes the law a+b R^{1/3} for the energy, when the charges are close to one another, R→ 0. This leads to the singularity of the force between them to be R^{-2/3}, which is weaker than the Coulomb law, R^{-2}.
Nonlinear interaction and wave breaking with a submerged porous structure
Hsieh, Chih-Min; Sau, Amalendu; Hwang, Robert R.; Yang, W. C.
2016-12-01
Numerical simulations are performed to investigate interactive velocity, streamline, turbulent kinetic energy, and vorticity perturbations in the near-field of a submerged offshore porous triangular structure, as Stokes waves of different heights pass through. The wave-structure interaction and free-surface breaking for the investigated flow situations are established based on solutions of 2D Reynolds Averaged Navier-Stokes equations in a Cartesian grid in combination with K-ɛ turbulent closure and the volume of fluid methodology. The accuracy and stability of the adopted model are ascertained by extensive comparisons of computed data with the existing experimental and theoretical findings and through efficient predictions of the internal physical kinetics. Simulations unfold "clockwise" and "anticlockwise" rotation of fluid below the trough and the crest of the viscous waves, and the penetrated wave energy creates systematic flow perturbation in the porous body. The interfacial growths of the turbulent kinetic energy and the vorticity appear phenomenal, around the apex of the immersed structure, and enhanced significantly following wave breaking. Different values of porosity parameter and two non-porous cases have been examined in combination with varied incident wave height to reveal/analyze the nonlinear flow behavior in regard to local spectral amplification and phase-plane signatures. The evolution of leading harmonics of the undulating free-surface and the vertical velocity exhibits dominating roles of the first and the second modes in inducing the nonlinearity in the post-breaking near-field that penetrates well below the surface layer. The study further suggests the existence of a critical porosity that can substantially enhance the wave-shoaling and interface breaking.
Barber, Jared; Tanase, Roxana; Yotov, Ivan
2016-06-01
Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.
Cairns, Iver H.; Robinson, P. A.
1998-01-01
Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for
Katsoulakis, Markos A.; Vlachos, Dionisios G.
2003-11-01
We derive a hierarchy of successively coarse-grained stochastic processes and associated coarse-grained Monte Carlo (CGMC) algorithms directly from the microscopic processes as approximations in larger length scales for the case of diffusion of interacting particles on a lattice. This hierarchy of models spans length scales between microscopic and mesoscopic, satisfies a detailed balance, and gives self-consistent fluctuation mechanisms whose noise is asymptotically identical to the microscopic MC. Rigorous, detailed asymptotics justify and clarify these connections. Gradient continuous time microscopic MC and CGMC simulations are compared under far from equilibrium conditions to illustrate the validity of our theory and delineate the errors obtained by rigorous asymptotics. Information theory estimates are employed for the first time to provide rigorous error estimates between the solutions of microscopic MC and CGMC, describing the loss of information during the coarse-graining process. Simulations under periodic boundary conditions are used to verify the information theory error estimates. It is shown that coarse-graining in space leads also to coarse-graining in time by q2, where q is the level of coarse-graining, and overcomes in part the hydrodynamic slowdown. Operation counting and CGMC simulations demonstrate significant CPU savings in continuous time MC simulations that vary from q3 for short potentials to q4 for long potentials. Finally, connections of the new coarse-grained stochastic processes to stochastic mesoscopic and Cahn-Hilliard-Cook models are made.
On the stochastic interaction of monochromatic Alfven waves with toroidally trapped particles
Krlin, L.; Pavlo, P.; Tluchor, Z.; Gasek, Z.
1987-07-01
Monochromatic Alfven wave interaction with toroidaly trapped particles in the intrinsic stochasticity regime is discussed. Both the diffusion in velocities and in the radial position of bananas is studied. Using a suitable Hamiltonian formalism, the effect of wave parallel components E-tilde paral and B-tilde paral is investigated. The stochasticity threshold is estimated for plasma electrons and for thermonuclear alpha-particles (neglecting the effect of B-tilde paral ) by means of direct numerical integration of the corresponding canonical equations. Stochasticity causes transfer between trapped and untrapped regimes and the induced radial diffusion of bananas. The latter effect can considerably exceed neoclassical diffusion. The effect of B-tilde paral was only estimated analytically. It consisted in frequency modulation of the banana periodic motion coupled with a possible Mathieu instability. Nevertheless, for B-tilde paral corresponding to E-tilde paral , the effect seems to be weaker than the effect of E-tilde paral when the thermonuclear regime is considered. (author). 14 figs., 36 refs
A stochastic model for the interaction of plasticity and creep in metals
Steck, E.
1987-01-01
Describing the basic mechanisms for plastic deformations in crystalline materials by transition probabilities of a stochastic matrix over the state space of the internal barriers, results in a stochastic model which has the properties of a Markov-chain. It is possible to include in this model properties of the internal structure of the material and their changes during macroscopic deformation processes, such as hardening and recovery, or the influence of temperature on thermal activation. This description can be based on findings from metal physics and metallurgy, so that the stochastic model can be used as an intermediate model between the microscopic and the macroscopic description of the processes during plastic deformations. Inelastic deformations of crystalline materials (plasticity, creep, relaxation) are caused by slip processes in the crystal-lattice which are supported by movements of dislocations. The dislocation movements are opposed by internal barriers which have to be overcome by activation of the dislocations. This activation can be performed by stresses, which are in equilibrium with external forces, or by thermal energy. With the movements of dislocations and the connected slip processes, production of new dislocations occurs. The dislocations interact. This can result either in a reduction of their mobility or in annihilation. These processes are partially responsible for hardening or recovery. (orig./GL)
Venugopal, M.; Roy, D.; Rajendran, K.; Guillas, S.; Dias, F.
2017-01-01
Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra–Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems. PMID:28989311
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
Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao
2018-04-01
We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.
Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson
2017-02-01
Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a
The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process
Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko
2012-06-01
A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.
A test to evaluation non-linear soil structure interaction
Hagiwara, T.; Kitada, Y.
2005-01-01
JNES is planning a new project to study non-linear soil-structure interaction (SSI) effect under large earthquake ground motions equivalent to and/or over a design earthquake ground motion of S2. Concerning the SSI test, it is pointed out that handling of the scale effect of the specimen taking into account the surrounding soil on the earthquake response evaluation to the actual structure is essential issue for the scaled model test. Thus, for the test, the largest specimen possible and the biggest input motion possible are necessary. Taking into account the above issues, new test methodology, which utilizes artificial earthquake ground motion, is considered desirable if it can be performed at a realistic cost. With this motivation, we have studied the test methodology which applying blasting power as for a big earthquake ground motion. The information from a coalmine company in the U.S.A. indicates that the works performed in the surface coalmine to blast a rock covering a coal layer generates a big artificial ground motion, which is similar to earthquake ground motion. Application of this artificial earthquake ground motion for the SSI test is considered very promising because the blasting work is carried out periodically for mining coal so that we can apply artificial motions generated by the work if we construct a building model at a closed point to the blasting work area. The major purposes of the test are to understand (a) basic earthquake response characteristics of a Nuclear Power Plant (NPP) reactor building when a large earthquake strikes the NPP site and (b) nonlinear characteristics of SSI phenomenon during a big earthquake. In the paper of ICONE-13, we will introduce the test method and basic characteristics of measured artificial ground motions generated by the blasting works on an actual site. (authors)
Nonlinear interactions of electromagnetic waves with the auroral ionosphere
Wong, Alfred Y.
1999-09-01
The ionosphere provides us with an opportunity to perform plasma experiments in an environment with long confinement times, very large-scale lengths, and no confining walls. The auroral ionosphere with its nearly vertical magnetic field geometry is uniquely endowed with large amount of free energy from electron and ion precipitation along the magnetic field and mega-ampere current across the magnetic field. To take advantage of this giant outdoor laboratory, two facilities HAARP and HIPAS, with frequencies ranging from the radio to optical bands, are now available for active probing of and interaction with this interesting region. The ponderomotive pressures from the self-consistent wave fields have produced significant local perturbations of density and particle distributions at heights where the incident EM frequency matches a plasma resonance. This paper will review theory and experiments covering the nonlinear phenomena of parametric decay instability to wave collapse processes. At HF frequencies plasma lenses can be created by preconditioning pulses to focus what is a normally divergent beam into a high-intensity spot to further enhance nonlinear phenomena. At optical wavelengths a large rotating liquid metal mirror is used to focus laser pulses up to a given height. Such laser pulses are tuned to the same wavelengths of selected atomic and molecular resonances, with resulting large scattering cross sections. Ongoing experiments on dual-site experiments and excitation of ELF waves will be presented. The connection of such basic studies to environmental applications will be discussed. Such applications include the global communication using ELF waves, the ozone depletion and remediation and the control of atmospheric CO2 through the use of ion cyclotron resonant heating.
Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu
2016-03-01
The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.
Hua, Changchun; Zhang, Liuliu; Guan, Xinping
2017-01-01
This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.
Robust Numerical Methods for Nonlinear Wave-Structure Interaction in a Moving Frame of Reference
Kontos, Stavros; Lindberg, Ole
This project is focused on improving the state of the art for predicting the interaction between nonlinear ocean waves and marine structures. To achieve this goal, a flexible order finite difference potential flow solver has been extended to calculate for fully nonlinear wave-structure interaction...
Lu, Yunfan; Wang, Jun; Niu, Hongli
2015-01-01
An agent-based financial stock price model is developed and investigated by a stochastic interacting epidemic system, which is one of the statistical physics systems and has been used to model the spread of an epidemic or a forest fire. Numerical and statistical analysis are performed on the simulated returns of the proposed financial model. Complexity properties of the financial time series are explored by calculating the correlation dimension and using the modified multiscale entropy method. In order to verify the rationality of the financial model, the real stock market indexes, Shanghai Composite Index and Shenzhen Component Index, are studied in comparison with the simulation data of the proposed model for the different infectiousness parameters. The empirical research reveals that this financial model can reproduce some important features of the real stock markets. - Highlights: • A new agent-based financial price model is developed by stochastic interacting epidemic system. • The structure of the proposed model allows to simulate the financial dynamics. • Correlation dimension and MMSE are applied to complexity analysis of financial time series. • Empirical results show the rationality of the proposed financial model
Lu, Yunfan, E-mail: yunfanlu@yeah.net; Wang, Jun; Niu, Hongli
2015-06-12
An agent-based financial stock price model is developed and investigated by a stochastic interacting epidemic system, which is one of the statistical physics systems and has been used to model the spread of an epidemic or a forest fire. Numerical and statistical analysis are performed on the simulated returns of the proposed financial model. Complexity properties of the financial time series are explored by calculating the correlation dimension and using the modified multiscale entropy method. In order to verify the rationality of the financial model, the real stock market indexes, Shanghai Composite Index and Shenzhen Component Index, are studied in comparison with the simulation data of the proposed model for the different infectiousness parameters. The empirical research reveals that this financial model can reproduce some important features of the real stock markets. - Highlights: • A new agent-based financial price model is developed by stochastic interacting epidemic system. • The structure of the proposed model allows to simulate the financial dynamics. • Correlation dimension and MMSE are applied to complexity analysis of financial time series. • Empirical results show the rationality of the proposed financial model.
Realization of consensus of multi-agent systems with stochastically mixed interactions
Sun, Yongzheng, E-mail: yzsung@gmail.com; Li, Wang [School of Science, China University of Mining and Technology, Xuzhou 221008 (China); Zhao, Donghua [School of Mathematical Sciences, Fudan University, Shanghai 200433 (China)
2016-07-15
In this paper, we propose a new consensus model in which the interactions among agents stochastically switch between attraction and repulsion. Such a positive-and-negative mechanism is described by the white-noise-based coupling. Analytic criteria for the consensus and non-consensus in terms of the eigenvalues of the noise intensity matrix are derived, which provide a better understanding of the constructive roles of random interactions. Specifically, we discover a positive role of noise coupling that noise can accelerate the emergence of consensus. We find that the converging speed of the multi-agent network depends on the square of the second smallest eigenvalue of its graph Laplacian. The influence of network topologies on the consensus time is also investigated.
Turbulent response in a stochastic regime
Molvig, K.; Freidberg, J.P.; Potok, R.; Hirshman, S.P.; Whitson, J.C.; Tajima, T.
1981-06-01
The theory for the non-linear, turbulent response in a system with intrinsic stochasticity is considered. It is argued that perturbative Eulerian theories, such as the Direct Interaction Approximation (DIA), are inherently unsuited to describe such a system. The exponentiation property that characterizes stochasticity appears in the Lagrangian picture and cannot even be defined in the Eulerian representation. An approximation for stochastic systems - the Normal Stochastic Approximation - is developed and states that the perturbed orbit functions (Lagrangian fluctuations) behave as normally distributed random variables. This is independent of the Eulerian statistics and, in fact, we treat the Eulerian fluctuations as fixed. A simple model problem (appropriate for the electron response in the drift wave) is subjected to a series of computer experiments. To within numerical noise the results are in agreement with the Normal Stochastic Approximation. The predictions of the DIA for this mode show substantial qualitative and quantitative departures from the observations
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-01-01
Purpose: Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the “five Rs” (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider “stem-like cancer cells” (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. Methods: The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. Results: In sample calculations with linear quadratic parameters α = 0.3 per Gy, α/β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. Conclusions: The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-12-01
Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the "five Rs" (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider "stem-like cancer cells" (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. In sample calculations with linear quadratic parameters α = 0.3 per Gy, α∕β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are the ones appropriate for individualized
Control strategies for a stochastic model of host-parasite interaction in a seasonal environment.
Gómez-Corral, A; López García, M
2014-08-07
We examine a nonlinear stochastic model for the parasite load of a single host over a predetermined time interval. We use nonhomogeneous Poisson processes to model the acquisition of parasites, the parasite-induced host mortality, the natural (no parasite-induced) host mortality, and the reproduction and death of parasites within the host. Algebraic results are first obtained on the age-dependent distribution of the number of parasites infesting the host at an arbitrary time t. The interest is in control strategies based on isolation of the host and the use of an anthelmintic at a certain intervention instant t0. This means that the host is free living in a seasonal environment, and it is transferred to a uninfected area at age t0. In the uninfected area, the host does not acquire new parasites, undergoes a treatment to decrease the parasite load, and its natural and parasite-induced mortality are altered. For a suitable selection of t0, we present two control criteria that appropriately balance effectiveness and cost of intervention. Our approach is based on simple probabilistic principles, and it allows us to examine seasonal fluctuations of gastrointestinal nematode burden in growing lambs. Copyright © 2014 Elsevier Ltd. All rights reserved.
Nonlinear theory of surface-wave--particle interactions in a cylindrical plasma
Dengra, A.; Palop, J.I.F.
1994-01-01
This work is an application of the specular reflection hypothesis to the study of the nonlinear surface-wave--particle interactions in a cylindrical plasma. The model is based on nonlinear resolution of the Vlasov equation by the method of characteristics. The expression obtained for the rate of increase of kinetic energy per electron has permitted us to investigate the temporal behavior of nonlinear collisionless damping for different situations as a function of the critical parameters
Stochastic Nonlinear Aeroelasticity
2009-01-01
ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION Design and Analysis Methods Branch (AFRL/RBSD) Structures Division, Air Force... coff U∞ cs ea lw cw Figure 6: Wing and store geometry (left), wing box structural model (middle), flutter distribution (right
Model-free inference of direct network interactions from nonlinear collective dynamics.
Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc
2017-12-19
The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.
Stochastic interactions of two Brownian hard spheres in the presence of depletants
Karzar-Jeddi, Mehdi; Fan, Tai-Hsi; Tuinier, Remco; Taniguchi, Takashi
2014-01-01
A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the long-time correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions
Tucker, C. J.; Garratt, M. W.
1977-01-01
A stochastic leaf radiation model based upon physical and physiological properties of dicot leaves has been developed. The model accurately predicts the absorbed, reflected, and transmitted radiation of normal incidence as a function of wavelength resulting from the leaf-irradiance interaction over the spectral interval of 0.40-2.50 micron. The leaf optical system has been represented as Markov process with a unique transition matrix at each 0.01-micron increment between 0.40 micron and 2.50 micron. Probabilities are calculated at every wavelength interval from leaf thickness, structure, pigment composition, and water content. Simulation results indicate that this approach gives accurate estimations of actual measured values for dicot leaf absorption, reflection, and transmission as a function of wavelength.
Nonlinear infragravity–wave interactions on a gently sloping laboratory beach
De Bakker, A.T.M.; Herbers, T.H.C.; Smit, P.B.; Tissier, M.F.S.; Ruessink, B.G.
2015-01-01
A high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy
Beach steepness effects on nonlinear infragravity-wave interactions : A numerical study
De Bakker, A. T M; Tissier, M.F.S.; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to
Beach steepness effects on nonlinear infragravity-wave interactions : A numerical study
de Bakker, A. T M; Tissier, M. F S; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to
Nonlinear infragravity-wave interactions on a gently sloping laboratory beach
de Bakker, A. T M; Herbers, T. H C; Smit, P. B.; Tissier, M. F S; Ruessink, B. G.
2015-01-01
A high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy
Zhao, J. S.; Voitenko, Y.; De Keyser, J.; Wu, D. J.
2018-04-01
We study the decay of Alfvén waves in the solar wind, accounting for the joint operation of two-dimensional (2D) scalar and three-dimensional (3D) vector nonlinear interactions between Alfvén and slow waves. These interactions have previously been studied separately in long- and short-wavelength limits where they lead to 2D scalar and 3D vector decays, correspondingly. The joined action of the scalar and vector interactions shifts the transition between 2D and 3D decays to significantly smaller wavenumbers than was predicted by Zhao et al. who compared separate scalar and vector decays. In application to the broadband Alfvén waves in the solar wind, this means that the vector nonlinear coupling dominates in the extended wavenumber range 5 × 10‑4 ≲ ρ i k 0⊥ ≲ 1, where the decay is essentially 3D and nonlocal, generating product Alfvén and slow waves around the ion gyroscale. Here ρ i is the ion gyroradius, and k 0⊥ is the pump Alfvén wavenumber. It appears that, except for the smallest wavenumbers at and below {ρ }i{k}0\\perp ∼ {10}-4 in Channel I, the nonlinear decay of magnetohydrodynamic Alfvén waves propagating from the Sun is nonlocal and cannot generate counter-propagating Alfvén waves with similar scales needed for the turbulent cascade. Evaluation of the nonlinear frequency shift shows that product Alfvén waves can still be approximately described as normal Alfvénic eigenmodes. On the contrary, nonlinearly driven slow waves deviate considerably from normal modes and are therefore difficult to identify on the basis of their phase velocities and/or polarization.
Electrostatic potential profile and nonlinear current in an interacting ...
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Since the Poisson distribution crucially depends on charge densities ... formedon a large number of systems using semi-empirical to first-principles ... known by now that the current in these systems is a nonlinear function of the voltage and ..... the middle of the molecule and the potential drop is smaller near the interfaces.
Advanced Seismic Fragility Modeling using Nonlinear Soil-Structure Interaction Analysis
Bolisetti, Chandu [Idaho National Lab. (INL), Idaho Falls, ID (United States); Coleman, Justin [Idaho National Lab. (INL), Idaho Falls, ID (United States); Talaat, Mohamed [Simpson-Gupertz & Heger, Waltham, MA (United States); Hashimoto, Philip [Simpson-Gupertz & Heger, Waltham, MA (United States)
2015-09-01
The goal of this effort is to compare the seismic fragilities of a nuclear power plant system obtained by a traditional seismic probabilistic risk assessment (SPRA) and an advanced SPRA that utilizes Nonlinear Soil-Structure Interaction (NLSSI) analysis. Soil-structure interaction (SSI) response analysis for a traditional SPRA involves the linear analysis, which ignores geometric nonlinearities (i.e., soil and structure are glued together and the soil material undergoes tension when the structure uplifts). The NLSSI analysis will consider geometric nonlinearities.
Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment
Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.; Obayashi, T.
1986-01-01
A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction Experiment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. 4 figures.
Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment
Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.
A rocket-borne experiment called 'MINIX' was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction eXperiment and was carried out on August 29, 1983. The objective of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere, such as the ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no ohmic heating effects were detected.
Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment
Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.; Obayashi, T.
1986-01-01
A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction Experiment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. 4 figures
Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1
Krivitsky, V.S.; Vladimirov, S.V.
1991-01-01
An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a 'direct' nonlinear interaction of particles and waves, and the influence of the non-stationary of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one. (author)
Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas
2016-01-01
Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments.
The Impact of Dam-Reservoir-Foundation Interaction on Nonlinear Response of Concrete Gravity Dams
Amini, Ali Reza; Motamedi, Mohammad Hossein; Ghaemian, Mohsen
2008-01-01
To study the impact of dam-reservoir-foundation interaction on nonlinear response of concrete gravity dams, a two-dimensional finite element model of a concrete gravity dam including the dam body, a part of its foundation and a part of the reservoir was made. In addition, the proper boundary conditions were used in both reservoir and foundation in order to absorb the energy of outgoing waves at the far end boundaries. Using the finite element method and smeared crack approach, some different seismic nonlinear analyses were done and finally, we came to a conclusion that the consideration of dam-reservoir-foundation interaction in nonlinear analysis of concrete dams is of great importance, because from the performance point of view, this interaction significantly improves the nonlinear response of concrete dams
Interaction of few-cycle laser pulses in an isotropic nonlinear medium
Oganesyan, D L; Vardanyan, A O
2007-01-01
The interaction of few-cycle laser pulses propagating in an isotropic nonlinear medium is studied theoretically. A system of nonlinear Maxwell's equations is integrated numerically with respect to time by the finite difference method. The interaction of mutually orthogonal linearly polarised 0.81-μm, 10-fs pulses is considered. Both the instant Kerr polarisation response and Raman inertial response of the medium in the nonlinear part of the medium are taken into account. The spectral shift of the probe pulse caused by the cross-action of the reference pulse is studied. The spectra of the interacting pulses are studied for different time delays between them and the shifts of these spectra are obtained as a function of the time delay. (nonlinear optical phenomena)
Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction
Upadrashta, Deepesh; Yang, Yaowen
2015-01-01
Piezoelectric energy harvesting from ambient vibrations is a potential technology for powering wireless sensors and low power electronic devices. The conventional linear harvesters suffer from narrow operational bandwidth. Many attempts have been made especially using the magnetic interaction to broaden the bandwidth of harvesters. The finite element (FE) modeling has been used only for analyzing the linear harvesters in the literature. The main difficulties in extending the FE modeling to analyze the nonlinear harvesters involving magnetic interaction are developing the mesh needed for magnetic interaction in dynamic problems and the high demand on computational resource needed for solving the coupled electrical–mechanical–magnetic problem. In this paper, an innovative method is proposed to model the magnetic interaction without inclusion of the magnetic module. The magnetic force is modeled using the nonlinear spring element available in ANSYS finite element analysis (FEA) package, thus simplifying the simulation of nonlinear piezoelectric energy harvesters as an electromechanically coupled problem. Firstly, an FE model of a monostable nonlinear harvester with cantilever configuration is developed and the results are validated with predictions from the theoretical model. Later, the proposed technique of FE modeling is extended to a complex 2-degree of freedom nonlinear energy harvester for which an accurate analytical model is difficult to derive. The performance predictions from FEA are compared with the experimental results. It is concluded that the proposed modeling technique is able to accurately analyze the behavior of nonlinear harvesters with magnetic interaction. (paper)
Coherent nonlinear backscattering by laser-plasma interactions
Anderson, D.; Wilhelmsson, H.
1974-01-01
A theoretical analysis is carried out for the problem of coherent nonlinear backscattering of laser radiation by a high density plasma. A number of effects of direct interest to the DT-pellet fusion research is investigated. A simple physical description is introduced, which relies on a nonlinear potential formulation of the scattering equations. The simplicity and the unified nature of the approach enables one to evaluate and compare the influence on the radiation reflectivity of different effects, such as e.g. inhomogeneities, blow-off velocities, temperature gradients, laser band width and relativistic oscillatory velocities. The understanding of the role played by the various phenomena has consequently improved and it is thought that this approach should be useful for the interpretation of laser-plasma data obtained by computer simulation or laboratory experiments. The results may also be utilized to estimate how and to what extent one may avoid undesired anomalous reflection when planning new laser-plasma devices. (Auth.)
Soliton interaction in the coupled mixed derivative nonlinear Schroedinger equations
Zhang Haiqiang; Tian Bo; Lue Xing; Li He; Meng Xianghua
2009-01-01
The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schroedinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.
Huang, K.M. [Wuhan Univ. (China). School of Electronic Information; Chinese Academey of Sciences, Hefei (China). Key Lab. of Geospace Environment; Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China); Liu, A.Z.; Li, Z. [Embry Riddle Aeronautical Univ., Daytona Beach, FL (United States). Dept. of Physical Science; Zhang, S.D.; Yi, F. [Wuhan Univ. (China). School of Electronic Information; Ministry of Education, Wuhan (China). Key Lab. of Geospace Environment and Geodesy; State Observatory for Atmospheric Remote Sensing, Wuhan (China)
2012-07-01
Nonlinear interactions of gravity waves are studied with a two-dimensional, fully nonlinear model. The energy exchanges among resonant and near-resonant triads are examined in order to understand the spectral energy transfer through interactions. The results show that in both resonant and near-resonant interactions, the energy exchange between two high frequency waves is strong, but the energy transfer from large to small vertical scale waves is rather weak. This suggests that the energy cascade toward large vertical wavenumbers through nonlinear interaction is inefficient, which is different from the rapid turbulence cascade. Because of considerable energy exchange, nonlinear interactions can effectively spread high frequency spectrum, and play a significant role in limiting wave amplitude growth and transferring energy into higher altitudes. In resonant interaction, the interacting waves obey the resonant matching conditions, and resonant excitation is reversible, while near-resonant excitation is not so. Although near-resonant interaction shows the complexity of match relation, numerical experiments show an interesting result that when sum and difference near-resonant interactions occur between high and low frequency waves, the wave vectors tend to approximately match in horizontal direction, and the frequency of the excited waves is also close to the matching value. (orig.)
Venturi, D.; Karniadakis, G. E.
2012-08-01
By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection-reaction equation. By using a Fourier-Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.
S. I. Samsudin
2014-01-01
Full Text Available The wastewater treatment plant (WWTP is highly known with the nonlinearity of the control parameters, thus it is difficult to be controlled. In this paper, the enhancement of nonlinear PI controller (ENon-PI to compensate the nonlinearity of the activated sludge WWTP is proposed. The ENon-PI controller is designed by cascading a sector-bounded nonlinear gain to linear PI controller. The rate variation of the nonlinear gain kn is automatically updated based on adaptive interaction algorithm. Initiative to simplify the ENon-PI control structure by adapting kn has been proved by significant improvement under various dynamic influents. More than 30% of integral square error and 14% of integral absolute error are reduced compared to benchmark PI for DO control and nitrate in nitrogen removal control. Better average effluent qualities, less number of effluent violations, and lower aeration energy consumption resulted.
Modeling and complexity of stochastic interacting Lévy type financial price dynamics
Wang, Yiduan; Zheng, Shenzhou; Zhang, Wei; Wang, Jun; Wang, Guochao
2018-06-01
In attempt to reproduce and investigate nonlinear dynamics of security markets, a novel nonlinear random interacting price dynamics, which is considered as a Lévy type process, is developed and investigated by the combination of lattice oriented percolation and Potts dynamics, which concerns with the instinctive random fluctuation and the fluctuation caused by the spread of the investors' trading attitudes, respectively. To better understand the fluctuation complexity properties of the proposed model, the complexity analyses of random logarithmic price return and corresponding volatility series are preformed, including power-law distribution, Lempel-Ziv complexity and fractional sample entropy. In order to verify the rationality of the proposed model, the corresponding studies of actual security market datasets are also implemented for comparison. The empirical results reveal that this financial price model can reproduce some important complexity features of actual security markets to some extent. The complexity of returns decreases with the increase of parameters γ1 and β respectively, furthermore, the volatility series exhibit lower complexity than the return series
The dynamics of interacting nonlinearities governing long wavelength driftwave turbulence
Newman, D.E.
1993-09-01
Because of the ubiquitous nature of turbulence and the vast array of different systems which have turbulent solutions, the study of turbulence is an area of active research. Much present day understanding of turbulence is rooted in the well established properties of homogeneous Navier-Stokes turbulence, which, due to its relative simplicity, allows for approximate analytic solutions. This work examines a group of turbulent systems with marked differences from Navier-Stokes turbulence, and attempts to quantify some of their properties. This group of systems represents a variety of drift wave fluctuations believed to be of fundamental importance in laboratory fusion devices. From extensive simulation of simple local fluid models of long wavelength drift wave turbulence in tokamaks, a reasonably complete picture of the basic properties of spectral transfer and saturation has emerged. These studies indicate that many conventional notions concerning directions of cascades, locality and isotropy of transfer, frequencies of fluctuations, and stationarity of saturation are not valid for moderate to long wavelengths. In particular, spectral energy transfer at long wavelengths is dominated by the E x B nonlinearity, which carries energy to short scale in a manner that is highly nonlocal and anisotropic. In marked contrast to the canonical self-similar cascade dynamics of Kolmogorov, energy is efficiently passed between modes separated by the entire spectrum range in a correlation time. At short wavelengths, transfer is dominated by the polarization drift nonlinearity. While the standard dual cascade applies in this subrange, it is found that finite spectrum size can produce cascades that are reverse directed and are nonconservative in enstrophy and energy similarity ranges. In regions where both nonlinearities are important, cross-coupling between the nolinearities gives rise to large no frequency shifts as well as changes in the spectral dynamics
Dynamical interactions between solute and solvent studied by nonlinear infrared spectroscopy
Ohta, K.; Tominaga, K.
2006-01-01
Interactions between solute and solvent play an important role in chemical reaction dynamics and in many relaxation processes in condensed phases. Recently third-order nonlinear infrared (IR) spectroscopy has shown to be useful to investigate solute-solvent interaction and dynamics of the vibrational transition. These studies provide detailed information on the energy relaxation of the vibrationally excited state, and the time scale and the magnitude of the time correlation functions of the vibrational frequency fluctuations. In this work we have studied vibrational energy relaxation (VER) of solutions and molecular complexes by nonlinear IR spectroscopy, especially IR pump-probe method, to understand the microscopic interactions in liquids. (authors)
Ulku, Huseyin Arda
2015-02-01
An explicit marching on-in-time (MOT) based time domain electric field volume integral equation (TDVIE) solver for characterizing electromagnetic wave interactions on scatterers with nonlinear material properties is proposed. Discretization of the unknown electric field intensity and flux density is carried out by half and full Schaubert-Wilton-Glisson basis functions, respectively. Coupled system of spatially discretized TDVIE and the nonlinear constitutive relation between the field intensity and the flux density is integrated in time to compute the samples of the unknowns. An explicit PE(CE)m scheme is used for this purpose. Explicitness allows for \\'easy\\' incorporation of the nonlinearity as a function only to be evaluated on the right hand side of the coupled system of equations. A numerical example that demonstrates the applicability of the proposed MOT scheme to analyzing electromagnetic interactions on Kerr-nonlinear scatterers is presented. © 2015 IEEE.
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...
Plasma heating by non-linear wave-Plasma interaction | Echi ...
We simulate the non-linear interaction of waves with magnetized tritium plasma with the aim of determining the parameter values that characterize the response of the plasma. The wave-plasma interaction has a non-conservative Hamiltonian description. The resulting system of Hamilton's equations is integrated numerically ...
Nonlinear interaction of Rayleigh--Taylor and shear instabilities
Finn, J.M.
1993-01-01
Results on the nonlinear behavior of the Rayleigh--Taylor instability and consequent development of shear flow by the shear instability [Phys. Fluids B 4, 488 (1992)] are presented. It is found that the shear flow is generated at sufficient amplitude to reduce greatly the convective transport. For high viscosity, the time-asymptotic state consists of an equilibrium with shear flow and vortex flow (with islands, or ''cat's eyes''), or a relaxation oscillation involving an interplay between the shear instability and the Rayleigh--Taylor instability in the presence of shear. For low viscosity, the dominant feature is a high-frequency nonlinear standing wave consisting of convective vortices localized near the top and bottom boundaries. The localization of these vortices is due to the smaller shear near the boundary regions. The convective transport is largest around these convective vortices near the boundary and there is a region of good confinement near the center. The possible relevance of this behavior to the H mode and edge-localized modes (ELM's) in the tokamak edge region is discussed
Elsheikh, Ahmed H.; Wheeler, Mary Fanett; Hoteit, Ibrahim
2013-01-01
is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem. © 2013 Elsevier Ltd.
Kuang-Leman; Wu Yong Shi
2003-01-01
We study linear and nonlinear optical properties of an electromagnetically induced transparency (EIT) medium interacting with two quantized laser fields in the adiabatic EIT case. We show that the EIT medium exhibits normal dispersion. Kerr and higher-order nonlinear refractive index coefficients are also calculated in a completely analytical form. It is indicated that the EIT medium exhibits giant resonantly enhanced nonlinearities. We discuss the response of the EIT medium to nonclassical light fields and find that the polarization vanishes when the probe laser is initially in a nonclassical state of no single-photon coherence.
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-01-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Chaotic saddles in nonlinear modulational interactions in a plasma
Miranda, Rodrigo A.; Rempel, Erico L.; Chian, Abraham C.-L.
2012-01-01
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Chaotic saddles in nonlinear modulational interactions in a plasma
Miranda, Rodrigo A. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); University of Brasilia (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Chian, Abraham C.-L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Observatoire de Paris, LESIA, CNRS, 92195 Meudon (France)
2012-11-15
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Nonlinear interaction of powerful short electromagnetic pulses with an electron plasma
Rao, N.N.; Yu, M.Y.; Shukla, P.K.
1990-01-01
The nonlinear interaction of powerful short electromagnetic pulses with a plasma consisting of two groups of electrons and immobile ions has been studied. It is shown that the interaction is governed by a nonlinear equation for the electromagnetic wave envelope and a driven nonlinear equation for the low-frequency electron fluctuations. The driver for the latter depends explicitly on the spatio-temporal evolution of the electromagnetic wave flux. It is found that, depending on the cold-to-hot electron density ratio, the localized pulse can propagate with sub- as well as supersonic velocities accompanied by compressional or rarefactional density perturbations. The conditions of existence for the different types of solitary pulses are obtained. The present investigation may be relevant to the study of wave-plasma interaction devices such as inertial fusion confinement as well as to ionospheric modification experiments. (author)
Khalil, Sh.M.; El-Sherif, N.; El-Siragy, N.M.; Tanta Univ.; El-Naggar, I.A.; Alexandria Univ.
1985-01-01
Investigation is made for nonlinear interaction between incident radiation and a surface wave in a magnetized plasma layer. Both interacting waves are of P polarization. The generated currents and fields at combination frequencies are obtained analytically. Unlike the S-polarized interacting waves, the magnetic field affects the fundamental waves and leads to an amplification of generated waves when their frequencies approach the cyclotron frequency. (author)
Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun
2018-01-01
In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.
Nonlinear interaction of fast particles with Alfven waves in toroidal plasmas
Candy, J.; Borba, D.; Huysmans, G.T.A.; Kerner, W.; Berk, H.L.
1996-01-01
A numerical algorithm to study the nonlinear, resonant interaction of fast particles with Alfven waves in tokamak geometry has been developed. The scope of the formalism is wide enough to describe the nonlinear evolution of fishbone modes, toroidicity-induced Alfven eigenmodes and ellipticity-induced Alfven eigenmodes, driven by both passing and trapped fast ions. When the instability is sufficiently weak, it is known that the wave-particle trapping nonlinearity will lead to mode saturation before wave-wave nonlinearities are appreciable. The spectrum of linear modes can thus be calculated using a magnetohydrodynamic normal-mode code, then nonlinearly evolved in time in an efficient way according to a two-time-scale Lagrangian dynamical wave model. The fast particle kinetic equation, including the effect of orbit nonlinearity arising from the mode perturbation, is simultaneously solved of the deviation, δf = f - f 0 , from an initial analytic distribution f 0 . High statistical resolution allows linear growth rates, frequency shifts, resonance broadening effects, and nonlinear saturation to be calculated quickly and precisely. The results have been applied to an ITER instability scenario. Results show that weakly-damped core-localized modes alone cause negligible alpha transport in ITER-like plasmas--even with growth rates one order of magnitude higher than expected values. However, the possibility of significant transport in reactor-type plasmas due to weakly unstable global modes remains an open question
Nonlinear disruption of ecological interactions in response to nitrogen deposition.
Ochoa-Hueso, Raúl
2016-10-01
Global environmental change (GEC) is affecting species interactions and causing a rapid decline in biodiversity. In this study, I present a new Ecosystem Disruption Index to quantify the impacts of simulated nitrogen (N) deposition (0, 10, 20, and 50 kg N·ha -1 ·yr -1 + 6-7 kg N·ha -1 ·yr -1 background) on abiotic and biotic ecological interactions. This comparative index is based on pairwise linear and quadratic regression matrices. These matrices, calculated at the N treatment level, were constructed using a range of abiotic and biotic ecosystem constituents: soil pH, shrub cover, and the first component of several separate principal component analyses using soil fertility data (total carbon and N) and community data (annual plants, microorganisms, biocrusts, edaphic fauna) for a total of seven ecosystem constituents. Four years of N fertilization in a semiarid shrubland completely disrupted the network of ecological interactions, with a greater proportional increase in ecosystem disruption at low N addition levels. Biotic interactions, particularly those involving microbes, shrubs, and edaphic fauna, were more prone to be lost in response to N, whereas interactions involving soil properties were more resilient. In contrast, edaphic fauna was the only group directly affected by N addition, with mites and collembolans increasing their abundance with up to 20 kg N·ha -1 ·yr -1 and then decreasing, which supports the idea of higher-trophic-level organisms being more sensitive to disturbance due to more complex links with other ecosystem constituents. Future experimental studies evaluating the impacts of N deposition, and possibly other GEC drivers, on biodiversity and biotic and abiotic interactions may be able to explain results more effectively in the context of ecological networks as a key feature of ecosystem sensitivity. © 2016 by the Ecological Society of America.
Nonlinear effects in interactions of swift ions with solids
Crawford, O.H.; Dorado, J.J.; Flores, F.
1994-01-01
The passage of a swift charged particle through a solid gives rise to a wake of induced electron density behind the particle. It is calculated for a proton penetrating an electron gas having the density of the valence electrons in gold, assuming linear response of the medium. The induced potential associated with the wake is responsible for the energy loss of the particle, and for many effects that have captured recent interest. These include, among others, vicinage effects on swift ion clusters, emission of electrons from bombarded solids, forces on swift ions near a surface, and energy shifts in electronic states of channeled ions. Furthermore, the wake has a determining influence on the spatial distribution, and character, of energy deposition in the medium. Previous theoretical studies of these phenomena have employed a linear wake, i.e., one that is proportional to the charge of the projectile, eZ. However, in most experiments that measure these effects, the conditions are such that the wake must include higher-order terms in Z. The purpose of this study is to analyze the nonlinear wake, to understand how the linear results must be revised
Topological charge algebra of optical vortices in nonlinear interactions.
Zhdanova, Alexandra A; Shutova, Mariia; Bahari, Aysan; Zhi, Miaochan; Sokolov, Alexei V
2015-12-28
We investigate the transfer of orbital angular momentum among multiple beams involved in a coherent Raman interaction. We use a liquid crystal light modulator to shape pump and Stokes beams into optical vortices with various integer values of topological charge, and cross them in a Raman-active crystal to produce multiple Stokes and anti-Stokes sidebands. We measure the resultant vortex charges using a tilted-lens technique. We verify that in every case the generated beams' topological charges obey a simple relationship, resulting from angular momentum conservation for created and annihilated photons, or equivalently, from phase-matching considerations for multiple interacting beams.
Current interactions from the one-form sector of nonlinear higher-spin equations
Gelfond, O. A.; Vasiliev, M. A.
2018-06-01
The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η = exp iφ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant η η bar . Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η = 0) η bar = 0.
Kanjilal, Oindrila, E-mail: oindrila@civil.iisc.ernet.in; Manohar, C.S., E-mail: manohar@civil.iisc.ernet.in
2017-07-15
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. - Highlights: • The distance minimizing control forces minimize a bound on the sampling variance. • Establishing Girsanov controls via solution of a two-point boundary value problem. • Girsanov controls via Volterra's series representation for the transfer functions.
Electron-lattice Interaction and Nonlinear Excitations in Cuprate Structures
Paulsen, J.; Eschrig, H.; Drechsler, S.L.; Malek, J.
1995-01-01
A low temperature lattice modulation of the chains of the YBa 2 Cu 3 O 7 is considered by deriving a Hamiltonian of electron-lattice interaction from density-functional calculations for deformed lattice and solving it for the groundstate. Hubbard-type Coulomb interaction is included. The obtained groundstate is a charge-density-wave state with a pereodicity of four lattice constants and a gap for one-electron excitations of about 1eV, sensitively depending on parameters of the Hamiltonian. There are lots of polaronic and solitonic excitations with formation energies deep in the gap, which can pin the Fermi level and thus produce again metallicity of the chain. They might also contribute to pairing of holes in adjacent CuO 2 -planes. (author)
Wang, Guochao; Wang, Jun
2017-01-01
We make an approach on investigating the fluctuation behaviors of financial volatility duration dynamics. A new concept of volatility two-component range intensity (VTRI) is developed, which constitutes the maximal variation range of volatility intensity and shortest passage time of duration, and can quantify the investment risk in financial markets. In an attempt to study and describe the nonlinear complex properties of VTRI, a random agent-based financial price model is developed by the finite-range interacting biased voter system. The autocorrelation behaviors and the power-law scaling behaviors of return time series and VTRI series are investigated. Then, the complexity of VTRI series of the real markets and the proposed model is analyzed by Fuzzy entropy (FuzzyEn) and Lempel-Ziv complexity. In this process, we apply the cross-Fuzzy entropy (C-FuzzyEn) to study the asynchrony of pairs of VTRI series. The empirical results reveal that the proposed model has the similar complex behaviors with the actual markets and indicate that the proposed stock VTRI series analysis and the financial model are meaningful and feasible to some extent.
Nonlinear interaction of an ion flux with plasma
Ivanov, A.A.; Krasheninnikov, S.I.; Pistunovich, V.I.; Soboleva, T.K.; Yushamanov, P.N.
The present report discusses the interaction of an ion beam, formed during the charge exchange of injected neutral atoms, with a plasma. Methods of analytical study by means of quasi-linear equations as well as two-dimensional numerical modelling are used. It is shown that at a beam velocity U 0 /C/sub s/ approximately less than 1 / 2 , the relaxation process may be described by using the theory of quasi-linear relaxation of electron beams, at U 0 /C/sub s/ approximately greater than 10; one can neglect the slowing down of the ion beam and consider only the angular spread. An analytical dependence of the spread angle on time was obtained. On the basis of the ion beam relaxation theory evolved, experiments on charge exchange of plasma fluxes on a gas target are analyzed. It is shown that the anomalous scattering of the plasma flux observed in a series of experiments may be explained by the interaction of ions of the flux with ion-acoustic oscillations of the target plasma. Consideration of damping of ion-acoustic noise by the plasma electrons and ions leads to a limitation of the relaxation of the angular distribution function. The relationships obtained are in good agreement with the experimental results
Benisti, D.
2011-01-01
This manuscript provides a theoretical description, sometimes illustrated by experimental results, of several examples of field-matter interaction in various domains of physics, showing how the same basic concepts and theoretical methods may be used in very different physics situations. The issues addressed here are nonlinear field-matter interaction in plasma physics within the framework of classical mechanics (with a particular emphasis on wave-particle interaction), the linear analysis of beam-plasma instabilities in the relativistic regime, and the quantum description of laser-atom interaction, including quantum electrodynamics. Novel methods are systematically introduced in order to solve some very old problems, like the nonlinear counterpart of the Landau damping rate in plasma physics, for example. Moreover, our results directly apply to inertial confinement fusion, laser propagation in an atomic vapor, ion acceleration in a magnetized plasma and the physics of the Reversed Field Pinch for magnetic fusion. (author)
Amein, W.H.; El-Siragy, N.M.; Nagy, O.Z.; Sayed, Y.A.
1981-01-01
Nonlinear interaction of S-Polarized surface waves at the boundary of a semibounded magnetized plasma is investigated. The expressions of the amplitudes of the generated waves are found. It is shown that, the generated waves with combined frequencies are equally radiated from the transient layer into plasma and vacuum
Rasmussen, Kim; Christiansen, Peter Leth; Johansson, Magnus
1998-01-01
A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exp...
Interaction-induced effects in the nonlinear coherent response of quantum-well excitons
Wagner, Hans Peter; Schätz, A.; Langbein, Wolfgang Werner
1999-01-01
Interaction-induced processes are studied using the third-order nonlinear polarization created in polarization-dependent four-wave-mixing experiments (FWM) on a ZnSe single quantum well. We discuss their influence by a comparison of the experimental FWM with calculations based on extended optical...
High-order finite difference solution for 3D nonlinear wave-structure interaction
Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter
2010-01-01
This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme O...
Interaction of Lyapunov vectors in the formulation of the nonlinear extension of the Kalman filter.
Palatella, Luigi; Trevisan, Anna
2015-04-01
When applied to strongly nonlinear chaotic dynamics the extended Kalman filter (EKF) is prone to divergence due to the difficulty of correctly forecasting the forecast error probability density function. In operational forecasting applications ensemble Kalman filters circumvent this problem with empirical procedures such as covariance inflation. This paper presents an extension of the EKF that includes nonlinear terms in the evolution of the forecast error estimate. This is achieved starting from a particular square-root implementation of the EKF with assimilation confined in the unstable subspace (EKF-AUS), that is, the span of the Lyapunov vectors with non-negative exponents. When the error evolution is nonlinear, the space where it is confined is no more restricted to the unstable and neutral subspace causing filter divergence. The algorithm presented here, denominated EKF-AUS-NL, includes the nonlinear terms in the error dynamics: These result from the nonlinear interaction among the leading Lyapunov vectors and account for all directions where the error growth may take place. Numerical results show that with the nonlinear terms included, filter divergence can be avoided. We test the algorithm on the Lorenz96 model, showing very promising results.
Study on concentration nonlinearity of interacting acoustic flows in cadmium sulfide and tellurium
Ilisavskij, Yu.V.; Kulakova, L.A.; Yakhkind, Eh.Z.
1976-01-01
The ratio of an one-mode (self-action of an external monochromatic sound wave) and a many-mode (interaction of an external wave with crystal thermal phonons) concentration nonlinearity has been experimentally investigated on sound amplification in cadmium sulphide and tellurium. It has been shown that in a strong piezoelectric the main part in the nonlinear limitation of the sound amplification in a drift field is played by the wave interaction, i.e., the transfer of the sound wave energy into the crystal sound modes starts before the nonlinear self-action of a wave. In Te characterized by a large value of the electromechanical coupling constant value at the sound frequency of about 250 MHz the threshold of many-mode nonlinearity is achieved in fields much below the critical one, and corresponds to the sound intensity as low as 10 -7 W/cm 2 , as compared with 10 -2 W/cm 2 -the threshold of the one-mode nonlinearity
Musammil, N. M.; Porsezian, K.; Nithyanandan, K.; Subha, P. A.; Tchofo Dinda, P.
2017-09-01
We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.
Sharp asymptotics for stochastic dynamics with parallel updating rule with self-interaction
Bovier, A.; Nardi, F.R.; Spitoni, C.
2011-01-01
In this paper we study metastability for a stochastic dynamics with a parallel updating rule in particular for a probabilistic cellular automata. The problem is addressed in the Freidlin Wentzel regime, i.e., finite volume, small magnetic field, and in the limit when temperature tends to zero. We
Avetissian, Hamlet
2006-01-01
This book covers a large class of fundamental investigations into Relativistic Nonlinear Electrodynamics. It explores the interaction between charged particles and strong laser fields, mainly concentrating on contemporary problems of x-ray lasers, new type small set-up high-energy accelerators of charged particles, as well as electron-positron pair production from super powerful laser fields of relativistic intensities. It will also discuss nonlinear phenomena of threshold nature that eliminate the concurrent inverse processes in the problems of Laser Accelerator and Free Electron Laser, thus creating new opportunities for solving these problems.
Shen, Yanfeng; Cesnik, Carlos E. S.
2016-04-01
This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.
Nonlinear Jaynes–Cummings model for two interacting two-level atoms
Santos-Sánchez, O de los; González-Gutiérrez, C; Récamier, J
2016-01-01
In this work we examine a nonlinear version of the Jaynes–Cummings model for two identical two-level atoms allowing for Ising-like and dipole–dipole interplays between them. The model is said to be nonlinear in the sense that it can incorporate both a general intensity-dependent interaction between the atomic system and the cavity field and/or the presence of a nonlinear medium inside the cavity. As an example, we consider a particular type of atom-field coupling based upon the so-called Buck–Sukumar model and a lossless Kerr-like cavity. We describe the possible effects of such features on the evolution of some quantities of current interest, such as atomic excitation, purity, concurrence, the entropy of the field and the evolution of the latter in phase space. (paper)
De Santis, Emilio; Marinelli, Carlo
2007-01-01
We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove 'fixation', i.e. players will adopt a constant strategy after a finite time. The resulting dynamics is related to zero-temperature Glauber dynamics on random graphs of possibly infinite volume
Bhaumik, Lopamudra; Raychowdhury, Prishati
2013-01-01
Highlights: • Seismic response analysis of an internal shearwall of a reactor is done. • Incremental dynamic analysis is performed with 30 recorded ground motions. • Equivalent viscous damping increases up to twice when nonlinear SSI is considered. • Roof drift demand increases up to 25% upon consideration of foundation nonlinearity. • Base shear, base moment and ductility reduce up to 62%, 40%, and 35%, respectively. - Abstract: This study focuses on the seismic response analysis of an internal shearwall of a typical Indian reactor resting on a medium dense sandy silty soil, incorporating the nonlinear behavior of the soil-foundation interface. The modeling is done in an open-source finite element framework, OpenSees, where the soil-structure interaction (SSI) is modeled using a Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach. Static pushover analysis and cyclic analysis are performed followed by an incremental dynamic analysis (IDA) with 30 recorded ground motions. For performing IDA, the spectral acceleration of each motion corresponding to the fundamental period, S a (T 1 )is incremented from 0.1 g to 1.0 g with an increment step of 0.1 g. It is observed from the cyclic analysis that the equivalent viscous damping of the system increases upto twice upon incorporation of inelastic SSI. The IDA results demonstrate that the average peak base shear, base moment and displacement ductility demand reduces as much as 62%, 40%, and 35%, respectively, whereas the roof drift demand increases up to 25% upon consideration of foundation nonlinearity for the highest intensity motion. These observations indicate the need of critical consideration of nonlinear soil-structure interaction as any deficient modeling of the same may lead to an inaccurate estimation of the seismic demands of the structure
Bhaumik, Lopamudra, E-mail: lbhaumi2@illinois.edu [University of Illinois at Urbana-Champaign (United States); Raychowdhury, Prishati, E-mail: prishati@iitk.ac.in [Indian Institute of Technology Kanpur (India)
2013-12-15
Highlights: • Seismic response analysis of an internal shearwall of a reactor is done. • Incremental dynamic analysis is performed with 30 recorded ground motions. • Equivalent viscous damping increases up to twice when nonlinear SSI is considered. • Roof drift demand increases up to 25% upon consideration of foundation nonlinearity. • Base shear, base moment and ductility reduce up to 62%, 40%, and 35%, respectively. - Abstract: This study focuses on the seismic response analysis of an internal shearwall of a typical Indian reactor resting on a medium dense sandy silty soil, incorporating the nonlinear behavior of the soil-foundation interface. The modeling is done in an open-source finite element framework, OpenSees, where the soil-structure interaction (SSI) is modeled using a Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach. Static pushover analysis and cyclic analysis are performed followed by an incremental dynamic analysis (IDA) with 30 recorded ground motions. For performing IDA, the spectral acceleration of each motion corresponding to the fundamental period, S{sub a}(T{sub 1})is incremented from 0.1 g to 1.0 g with an increment step of 0.1 g. It is observed from the cyclic analysis that the equivalent viscous damping of the system increases upto twice upon incorporation of inelastic SSI. The IDA results demonstrate that the average peak base shear, base moment and displacement ductility demand reduces as much as 62%, 40%, and 35%, respectively, whereas the roof drift demand increases up to 25% upon consideration of foundation nonlinearity for the highest intensity motion. These observations indicate the need of critical consideration of nonlinear soil-structure interaction as any deficient modeling of the same may lead to an inaccurate estimation of the seismic demands of the structure.
Three-wave interaction in two-component quadratic nonlinear lattices
Konotop, V. V.; Cunha, M. D.; Christiansen, Peter Leth
1999-01-01
We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that. energy conversion and pulse propagation known...... from three-wave interaction is reproduced in the lattice and that exact phase matching of parametric processes can be obtained in non-phase-matched lattices by tilting the interacting plane waves with respect to each other. [S1063-651X(99)15110-9]....
Bauer, J.
1980-01-01
Thesis dealing with the analysis of earthquake response of structures. In order to achieve a reliable risk assessment, the results of the seismic risk analysis have to be seen in an overall view together with the results of stochastic vibrational analyses, and the data on maximum supportable stresses of the structure. Taking into account stochastic seismic focus models and calculation methods is of special significance in this connection. Based upon well-known seismic risk assessment models, the calculation of the annual probability for exceeding the acceleration level is carried out also considering the length of the failure zone, assuming that the energy released during an earthquake is uniformly, distributed over this fracture zone. The strong influence of local parameters on the annual exceeding probability is shown by a sensitivity analysis. (orig./RW) [de
Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A
2003-06-01
Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.
Game Theory of Tumor–Stroma Interactions in Multiple Myeloma: Effect of Nonlinear Benefits
Javad Salimi Sartakhti
2018-05-01
Full Text Available Cancer cells and stromal cells often exchange growth factors with paracrine effects that promote cell growth: a form of cooperation that can be studied by evolutionary game theory. Previous models have assumed that interactions between cells are pairwise or that the benefit of a growth factor is a linear function of its concentration. Diffusible factors, however, affect multiple cells and generally have nonlinear effects, and these differences are known to have important consequences for evolutionary dynamics. Here, we study tumor–stroma paracrine signaling using a model with multiplayer collective interactions in which growth factors have nonlinear effects. We use multiple myeloma as an example, modelling interactions between malignant plasma cells, osteoblasts, and osteoclasts. Nonlinear benefits can lead to results not observed in linear models, including internal mixed stable equilibria and cyclical dynamics. Models with linear effects, therefore, do not lead to a meaningful characterization of the dynamics of tumor–stroma interactions. To understand the dynamics and the effect of therapies it is necessary to estimate the shape of the benefit functions experimentally and parametrize models based on these functions.
Lagrangian analysis of nonlinear wave-wave interactions in bounded plasmas
Carr, A.R.
1979-01-01
In a weakly turbulent nonlinear wave-supporting medium, one of the important nonlinear processes which may occur is resonant three-wave interaction. Whitham's averaged Lagrangian method provides a general formulation of wave evolution laws which is easily adapted to nonlinear dispersive media. In this thesis, the strength of nonlinear interactions between three coherent, axisymmetric, low frequency, magnetohydrodynamic (Alfven) waves propagating in resonance along a cold cylindrical magnetized plasma column is calculated. Both a uniform and a parabolic density distribution have been considered. To account for a non-zero plasma temperature, pressure effects have been included. Distinctive features of the work are the use of cylindrical geometry, the presence of a finite rather than an infinite axial magnetic field, the treatment of a parabolic density distribution, and the inclusion of both ion and electron contributions in all expressions. Two astrophysical applications of the presented theory have been considered. In the first, the possibility of resonant three-wave coupling between geomagnetic micropulsations, which propagate as Alfven or magnetosonic waves along the Earth's magnetic field lines, has been investigated. The second case is the theory of energy transport through the solar chromosphere by upward propagating magnetohydrodynamic waves, which may then couple to heavily damped waves in the corona, causing the observed excess heating in that region
Nonlinear soil-structure interaction analysis of SIMQUAKE II. Final report
Vaughan, D.K.; Isenberg, J.
1982-04-01
This report describes an analytic method for modeling of soil-structure interaction (SSI) for nuclear power plants in earthquakes and discusses its application to SSI analyses of SIMQUAKE II. The method is general and can be used to simulate a three-dimensional structural geometry, nonlinear site characteristics and arbitrary input ground shaking. The analytic approach uses the soil island concept to reduce SSI models to manageable size and cost. Nonlinear constitutive behavior of the soil is represented by the nonlinear, kinematic cap model. In addition, a debonding-rebonding soil-structure interface model is utilized to represent nonlinear effects which singificantly alter structural response in the SIMQUAKE tests. STEALTH, an explicit finite difference code, is used to perform the dynamic, soil-structure interaction analyses. Several two-dimensional posttest SSI analyses of model containment structures in SIMQUAKE II are performed and results compared with measured data. These analyses qualify the analytic method. They also show the importance of including debonding-rebonding at the soil-structure interface. Sensitivity of structural response to compaction characteristics of backfill material is indicated
The role of nonlinear self-interaction in the dynamics of planetary-scale atmospheric fluctuations
Saffioti, C; Malguzzi, P; Speranza, A
2016-01-01
A central role in the general circulation of the atmosphere is played by planetary-scale inertial fluctuations with zonal wavenumber in the range k = 1–4. Geopotential variance in this range is markedly non-gaussian and a great fraction of it is non-propagating, in contrast with the normal distribution of amplitudes and the basically propagating character of fluctuations in the baroclinic range (3 < k < 15). While a wave dispersion relationship can be identified in the baroclinic range, no clear relationship between time and space scales emerges in the ultra-long regime ( k < 5, period >10 days). We investigate the hypothesis that nonlinear self-interaction of planetary waves influences the mobility (and, therefore, the dispersion) of ultra-long planetary fluctuations. By means of a perturbation expansion of the barotropic vorticity equation we derive a minimal analytic description of the impact of self-nonlinearity on mobility and we show that this is responsible for a correction term to phase speed, with the prevalent effect of slowing down the propagation of waves. The intensity of nonlinear self-interaction is shown to increase with the complexity of the flow, depending on both its zonal and meridional modulations. Reanalysis data of geopotential height and zonal wind are analysed in order to test the effect of self-nonlinearity on observed planetary flows. (paper)
Petrică Andreea-Cristina
2017-07-01
Full Text Available Modeling exchange rate volatility became an important topic for research debate starting with 1973, when many countries switched to floating exchange rate system. In this paper, we focus on the EUR/RON exchange rate both as an economic measure and present the implied economic links, and also as a financial investment and analyze its movements and fluctuations through two volatility stochastic processes: the Standard Generalized Autoregressive Conditionally Heteroscedastic Model (GARCH and the Exponential Generalized Autoregressive Conditionally Heteroscedastic Model (EGARCH. The objective of the conditional variance processes is to capture dependency in the return series of the EUR/RON exchange rate. On this account, analyzing exchange rates could be seen as the input for economic decisions regarding Romanian macroeconomics - the exchange rates being influenced by many factors such as: interest rates, inflation, trading relationships with other countries (imports and exports, or investments - portfolio optimization, risk management, asset pricing. Therefore, we talk about political stability and economic performance of a country that represents a link between the two types of inputs mentioned above and influences both the macroeconomics and the investments. Based on time-varying volatility, we examine implied volatility of daily returns of EUR/RON exchange rate using the standard GARCH model and the asymmetric EGARCH model, whose parameters are estimated through the maximum likelihood method and the error terms follow two distributions (Normal and Student’s t. The empirical results show EGARCH(2,1 with Asymmetric order 2 and Student’s t error terms distribution performs better than all the estimated standard GARCH models (GARCH(1,1, GARCH(1,2, GARCH(2,1 and GARCH(2,2. This conclusion is supported by the major advantage of the EGARCH model compared to the GARCH model which consists in allowing good and bad news having different impact on the
Li, Yunji; Peng, Li
2018-02-28
Wireless sensors have many new applications where remote estimation is essential. Considering that a remote estimator is located far away from the process and the wireless transmission distance of sensor nodes is limited, sensor nodes always forward data packets to the remote estimator through a series of relays over a multi-hop link. In this paper, we consider a network with sensor nodes and relay nodes where the relay nodes can forward the estimated values to the remote estimator. An event-triggered remote estimator of state and fault with the corresponding data-forwarding scheme is investigated for stochastic systems subject to both randomly occurring nonlinearity and randomly occurring packet dropouts governed by Bernoulli-distributed sequences to achieve a trade-off between estimation accuracy and energy consumption. Recursive Riccati-like matrix equations are established to calculate the estimator gain to minimize an upper bound of the estimator error covariance. Subsequently, a sufficient condition and data-forwarding scheme are presented under which the error covariance is mean-square bounded in the multi-hop links with random packet dropouts. Furthermore, implementation issues of the theoretical results are discussed where a new data-forwarding communication protocol is designed. Finally, the effectiveness of the proposed algorithms and communication protocol are extensively evaluated using an experimental platform that was established for performance evaluation with a sensor and two relay nodes.
Ulku, Huseyin Arda
2014-07-06
Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half
An explicit method in non-linear soil-structure interaction
Kunar, R.R.
1981-01-01
The explicit method of analysis in the time domain is ideally suited for the solution of transient dynamic non-linear problems. Though the method is not new, its application to seismic soil-structure interaction is relatively new and deserving of public discussion. This paper describes the principles of the explicit approach in soil-structure interaction and it presents a simple algorithm that can be used in the development of explicit computer codes. The paper also discusses some of the practical considerations like non-reflecting boundaries and time steps. The practicality of the method is demonstrated using a computer code, PRESS, which is used to compare the treatment of strain-dependent properties using average strain levels over the whole time history (the equivalent linear method) and using the actual strain levels at every time step to modify the soil properties (non-linear method). (orig.)
On the interaction of small-scale linear waves with nonlinear solitary waves
Xu, Chengzhu; Stastna, Marek
2017-04-01
In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow
El Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1992-09-01
Electromagnetic waves radiated with combination frequencies from a semi-bounded plasma due to nonlinear interaction of radiation with surface wave (both of P-polarization) has been investigated. Waves are radiated both into vacuum and plasma are found to be P-polarized. We take into consideration the continuity at the plasma boundary of the tangential components of the electric field of the waves. The case of normal incidence of radiation and rarefield plasma layer is also studied. (author). 7 refs
Stochastic quantization and gravity
Rumpf, H.
1984-01-01
We give a preliminary account of the application of stochastic quantization to the gravitational field. We start in Section I from Nelson's formulation of quantum mechanics as Newtonian stochastic mechanics and only then introduce the Parisi-Wu stochastic quantization scheme on which all the later discussion will be based. In Section II we present a generalization of the scheme that is applicable to fields in physical (i.e. Lorentzian) space-time and treat the free linearized gravitational field in this manner. The most remarkable result of this is the noncausal propagation of conformal gravitons. Moreover the concept of stochastic gauge-fixing is introduced and a complete discussion of all the covariant gauges is given. A special symmetry relating two classes of covariant gauges is exhibited. Finally Section III contains some preliminary remarks on full nonlinear gravity. In particular we argue that in contrast to gauge fields the stochastic gravitational field cannot be transformed to a Gaussian process. (Author)
Tewarie, P.; Bright, M.G.; Hillebrand, A.; Robson, S.E.; Gascoyne, L.E.; Morris, P.G.; Meier, J.; Van Mieghem, P.; Brookes, M.J.
2016-01-01
Understanding the electrophysiological basis of resting state networks (RSNs) in the human brain is a critical step towards elucidating how inter-areal connectivity supports healthy brain function. In recent years, the relationship between RSNs (typically measured using haemodynamic signals) and electrophysiology has been explored using functional Magnetic Resonance Imaging (fMRI) and magnetoencephalography (MEG). Significant progress has been made, with similar spatial structure observable in both modalities. However, there is a pressing need to understand this relationship beyond simple visual similarity of RSN patterns. Here, we introduce a mathematical model to predict fMRI-based RSNs using MEG. Our unique model, based upon a multivariate Taylor series, incorporates both phase and amplitude based MEG connectivity metrics, as well as linear and non-linear interactions within and between neural oscillations measured in multiple frequency bands. We show that including non-linear interactions, multiple frequency bands and cross-frequency terms significantly improves fMRI network prediction. This shows that fMRI connectivity is not only the result of direct electrophysiological connections, but is also driven by the overlap of connectivity profiles between separate regions. Our results indicate that a complete understanding of the electrophysiological basis of RSNs goes beyond simple frequency-specific analysis, and further exploration of non-linear and cross-frequency interactions will shed new light on distributed network connectivity, and its perturbation in pathology. PMID:26827811
Nonlinear instability and chaos in plasma wave-wave interactions, I., Introduction
Kueny, C.S.; Morrison, P.J.
1994-11-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper [submitted to Physics of Plasmas], this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various (integrable) systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper
Nonlinear instability and chaos in plasma wave--wave interactions. I. Introduction
Kueny, C.S.; Morrison, P.J.
1995-01-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free-energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave--wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper (submitted to Phys. Plasmas), this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various integrable systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper. copyright 1995 American Institute of Physics
Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan
2018-01-01
We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.
Soto-Crespo, J M; Grelu, Philippe; Akhmediev, Nail
2006-05-01
We demonstrate the existence of stable optical light bullets in nonlinear dissipative media for both cases of normal and anomalous chromatic dispersion. The prediction is based on direct numerical simulations of the (3+1)-dimensional complex cubic-quintic Ginzburg-Landau equation. We do not impose conditions of spherical or cylindrical symmetry. Regions of existence of stable bullets are determined in the parameter space. Beyond the domain of parameters where stable bullets are found, unstable bullets can be transformed into "rockets" i.e. bullets elongated in the temporal domain. A few examples of the interaction between two optical bullets are considered using spatial and temporal interaction planes.
Hoyer, Dirk; Leder, Uwe; Hoyer, Heike; Pompe, Bernd; Sommer, Michael; Zwiener, Ulrich
2002-01-01
The heart rate variability (HRV) is related to several mechanisms of the complex autonomic functioning such as respiratory heart rate modulation and phase dependencies between heart beat cycles and breathing cycles. The underlying processes are basically nonlinear. In order to understand and quantitatively assess those physiological interactions an adequate coupling analysis is necessary. We hypothesized that nonlinear measures of HRV and cardiorespiratory interdependencies are superior to the standard HRV measures in classifying patients after acute myocardial infarction. We introduced mutual information measures which provide access to nonlinear interdependencies as counterpart to the classically linear correlation analysis. The nonlinear statistical autodependencies of HRV were quantified by auto mutual information, the respiratory heart rate modulation by cardiorespiratory cross mutual information, respectively. The phase interdependencies between heart beat cycles and breathing cycles were assessed basing on the histograms of the frequency ratios of the instantaneous heart beat and respiratory cycles. Furthermore, the relative duration of phase synchronized intervals was acquired. We investigated 39 patients after acute myocardial infarction versus 24 controls. The discrimination of these groups was improved by cardiorespiratory cross mutual information measures and phase interdependencies measures in comparison to the linear standard HRV measures. This result was statistically confirmed by means of logistic regression models of particular variable subsets and their receiver operating characteristics.
Experimental investigation of gravity wave turbulence and of non-linear four wave interactions..
Berhanu, Michael
2017-04-01
Using the large basins of the Ecole Centrale de Nantes (France), non-linear interactions of gravity surface waves are experimentally investigated. In a first part we study statistical properties of a random wave field regarding the insights from the Wave Turbulence Theory. In particular freely decaying gravity wave turbulence is generated in a closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonl-inear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, non-linear and dissipative time scales to test the time scale separation. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant of the weak turbulence theory is evaluated. In a second part, resonant interactions of oblique surface gravity waves in a large basin are studied. We generate two oblique waves crossing at an acute angle. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory. L. Deike, B. Miquel, P. Gutiérrez, T. Jamin, B. Semin, M. Berhanu, E. Falcon and F. Bonnefoy, Role of the basin boundary conditions in gravity wave turbulence, Journal of Fluid Mechanics 781, 196 (2015) F. Bonnefoy, F. Haudin, G. Michel, B. Semin, T. Humbert, S. Aumaître, M. Berhanu and E. Falcon, Observation of resonant interactions among surface gravity waves, Journal of Fluid Mechanics (Rapids) 805, R3 (2016)
Nonlinear interaction of photons and phonons in electron-positron plasmas
Tajima, T.; Taniuti, T.
1990-03-01
Nonlinear interaction of electromagnetic waves and acoustic modes in an electron-positron plasma is investigated. The plasma of electrons and positrons is quite plastic so that the imposition of electromagnetic (EM) waves causes depression of the plasma and other structural imprints on it through either the nonresonant or resonant interaction. Our theory shows that the nonresonant interaction can lead to the coalescence of photons and collapse of plasma cavity in higher (≥ 2) dimensions. The resonant interaction, in which the group velocity of EM waves is equal to the phase velocity of acoustic waves, is analyzed and a set of basic equations of the system is derived via the reductive perturbation theory. We find new solutions of solitary types: bright solitons, kink solitons, and dark solitons as the solutions to these equations. Our computation hints their stability. An impact of the present theory on astrophysical plasma settings is expected, including the cosmological relativistically hot electron-positron plasma. 20 refs., 9 figs
Spears, Robert Edward; Coleman, Justin Leigh
2015-01-01
Currently the Department of Energy (DOE) and the nuclear industry perform seismic soil-structure interaction (SSI) analysis using equivalent linear numerical analysis tools. For lower levels of ground motion, these tools should produce reasonable in-structure response values for evaluation of existing and new facilities. For larger levels of ground motion these tools likely overestimate the in-structure response (and therefore structural demand) since they do not consider geometric nonlinearities (such as gaping and sliding between the soil and structure) and are limited in the ability to model nonlinear soil behavior. The current equivalent linear SSI (SASSI) analysis approach either joins the soil and structure together in both tension and compression or releases the soil from the structure for both tension and compression. It also makes linear approximations for material nonlinearities and generalizes energy absorption with viscous damping. This produces the potential for inaccurately establishing where the structural concerns exist and/or inaccurately establishing the amplitude of the in-structure responses. Seismic hazard curves at nuclear facilities have continued to increase over the years as more information has been developed on seismic sources (i.e. faults), additional information gathered on seismic events, and additional research performed to determine local site effects. Seismic hazard curves are used to develop design basis earthquakes (DBE) that are used to evaluate nuclear facility response. As the seismic hazard curves increase, the input ground motions (DBE's) used to numerically evaluation nuclear facility response increase causing larger in-structure response. As ground motions increase so does the importance of including nonlinear effects in numerical SSI models. To include material nonlinearity in the soil and geometric nonlinearity using contact (gaping and sliding) it is necessary to develop a nonlinear time domain methodology. This
F. Hossain
2004-01-01
Full Text Available This study presents a simple and efficient scheme for Bayesian estimation of uncertainty in soil moisture simulation by a Land Surface Model (LSM. The scheme is assessed within a Monte Carlo (MC simulation framework based on the Generalized Likelihood Uncertainty Estimation (GLUE methodology. A primary limitation of using the GLUE method is the prohibitive computational burden imposed by uniform random sampling of the model's parameter distributions. Sampling is improved in the proposed scheme by stochastic modeling of the parameters' response surface that recognizes the non-linear deterministic behavior between soil moisture and land surface parameters. Uncertainty in soil moisture simulation (model output is approximated through a Hermite polynomial chaos expansion of normal random variables that represent the model's parameter (model input uncertainty. The unknown coefficients of the polynomial are calculated using limited number of model simulation runs. The calibrated polynomial is then used as a fast-running proxy to the slower-running LSM to predict the degree of representativeness of a randomly sampled model parameter set. An evaluation of the scheme's efficiency in sampling is made through comparison with the fully random MC sampling (the norm for GLUE and the nearest-neighborhood sampling technique. The scheme was able to reduce computational burden of random MC sampling for GLUE in the ranges of 10%-70%. The scheme was also found to be about 10% more efficient than the nearest-neighborhood sampling method in predicting a sampled parameter set's degree of representativeness. The GLUE based on the proposed sampling scheme did not alter the essential features of the uncertainty structure in soil moisture simulation. The scheme can potentially make GLUE uncertainty estimation for any LSM more efficient as it does not impose any additional structural or distributional assumptions.
Antoci, Angelo; Galeotti, Marcello; Russu, Paolo; Luigi Sacco, Pier
2018-05-01
In this paper, we study a nonlinear model of the interaction between trait selection and population dynamics, building on previous work of Ghirlanda et al. [Theor. Popul. Biol. 77, 181-188 (2010)] and Antoci et al. [Commun. Nonlinear Sci. Numer. Simul. 58, 92-106 (2018)]. We establish some basic properties of the model dynamics and present some simulations of the fine-grained structure of alternative dynamic regimes for chosen combinations of parameters. The role of the parameters that govern the reinforcement/corruption of maladaptive vs. adaptive traits is of special importance in determining the model's dynamic evolution. The main implication of this result is the need to pay special attention to the structural forces that may favor the emergence and consolidation of maladaptive traits in contemporary socio-economies, as it is the case, for example, for the stimulation of dysfunctional consumption habits and lifestyles in the pursuit of short-term profits.
Antoci, Angelo; Galeotti, Marcello; Russu, Paolo; Luigi Sacco, Pier
2018-05-01
In this paper, we study a nonlinear model of the interaction between trait selection and population dynamics, building on previous work of Ghirlanda et al. [Theor. Popul. Biol. 77, 181-188 (2010)] and Antoci et al. [Commun. Nonlinear Sci. Numer. Simul. 58, 92-106 (2018)]. We establish some basic properties of the model dynamics and present some simulations of the fine-grained structure of alternative dynamic regimes for chosen combinations of parameters. The role of the parameters that govern the reinforcement/corruption of maladaptive vs. adaptive traits is of special importance in determining the model's dynamic evolution. The main implication of this result is the need to pay special attention to the structural forces that may favor the emergence and consolidation of maladaptive traits in contemporary socio-economies, as it is the case, for example, for the stimulation of dysfunctional consumption habits and lifestyles in the pursuit of short-term profits.
DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations
Engsig-Karup, Allan Peter; Hesthaven, Jan; Bingham, Harry B.
2008-01-01
equations in complex and curvilinear geometries which amends the application range of previous numerical models that have been based on structured Cartesian grids. The Boussinesq method provides the basis for the accurate description of fully nonlinear and dispersive water waves in both shallow and deep...... waters within the breaking limit. To demonstrate the current applicability of the model both linear and mildly nonlinear test cases are considered in two horizontal dimensions where the water waves interact with bottom-mounted fully reflecting structures. It is established that, by simple symmetry...... considerations combined with a mirror principle, it is possible to impose weak slip boundary conditions for both structured and general curvilinear wall boundaries while maintaining the accuracy of the scheme. As is standard for current high-order Boussinesq-type models, arbitrary waves can be generated...
Complete elimination of nonlinear light-matter interactions with broadband ultrafast laser pulses
Shu, Chuan-Cun; Dong, Daoyi; Petersen, Ian R.
2017-01-01
optical effects, however, the probability of pure single-photon absorption is usually very low, which is particularly pertinent in the case of strong ultrafast laser pulses with broad bandwidth. Here we demonstrate theoretically a counterintuitive coherent single-photon absorption scheme by eliminating...... nonlinear interactions of ultrafast laser pulses with quantum systems. That is, a completely linear response of the system with respect to the spectral energy density of the incident light at the transition frequency can be obtained for all transition probabilities between 0 and 100% in multilevel quantum...... systems. To that end, a multiobjective optimization algorithm is developed to find an optimal spectral phase of an ultrafast laser pulse, which is capable of eliminating all possible nonlinear optical responses while maximizing the probability of single-photon absorption between quantum states. This work...
Subagadis, Yohannes Hagos; Schütze, Niels; Grundmann, Jens
2014-05-01
An amplified interconnectedness between a hydro-environmental and socio-economic system brings about profound challenges of water management decision making. In this contribution, we present a fuzzy stochastic approach to solve a set of decision making problems, which involve hydrologically, environmentally, and socio-economically motivated criteria subjected to uncertainty and ambiguity. The proposed methodological framework combines objective and subjective criteria in a decision making procedure for obtaining an acceptable ranking in water resources management alternatives under different type of uncertainty (subjective/objective) and heterogeneous information (quantitative/qualitative) simultaneously. The first step of the proposed approach involves evaluating the performance of alternatives with respect to different types of criteria. The ratings of alternatives with respect to objective and subjective criteria are evaluated by simulation-based optimization and fuzzy linguistic quantifiers, respectively. Subjective and objective uncertainties related to the input information are handled through linking fuzziness and randomness together. Fuzzy decision making helps entail the linguistic uncertainty and a Monte Carlo simulation process is used to map stochastic uncertainty. With this framework, the overall performance of each alternative is calculated using an Order Weighted Averaging (OWA) aggregation operator accounting for decision makers' experience and opinions. Finally, ranking is achieved by conducting pair-wise comparison of management alternatives. This has been done on the basis of the risk defined by the probability of obtaining an acceptable ranking and mean difference in total performance for the pair of management alternatives. The proposed methodology is tested in a real-world hydrosystem, to find effective and robust intervention strategies for the management of a coastal aquifer system affected by saltwater intrusion due to excessive groundwater
2015-09-30
Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves...interaction of surface and internal gravity waves in the South China Sea. We will seek answers to the following questions: 1) How does the wind-wave
Quan Ji; Wang Xianjia
2013-01-01
Traditional evolutionary games assume uniform interaction rate, which means that the rate at which individuals meet and interact is independent of their strategies. But in some systems, especially biological systems, the players interact with each other discriminately. Taylor and Nowak (2006) were the first to establish the corresponding non-uniform interaction rate model by allowing the interaction rates to depend on strategies. Their model is based on replicator dynamics which assumes an infinite size population. But in reality, the number of individuals in the population is always finite, and there will be some random interference in the individuals' strategy selection process. Therefore, it is more practical to establish the corresponding stochastic evolutionary model in finite populations. In fact, the analysis of evolutionary games in a finite size population is more difficult. Just as Taylor and Nowak said in the outlook section of their paper, ''The analysis of non-uniform interaction rates should be extended to stochastic game dynamics of finite populations''. In this paper, we are exactly doing this work. We extend Taylor and Nowak's model from infinite to finite case, especially focusing on the infiuence of non-uniform connection characteristics on the evolutionary stable state of the system. We model the strategy evolutionary process of the population by a continuous ergodic Markov process. Based on the limit distribution of the process, we can give the evolutionary stable state of the system. We make a complete classification of the symmetric 2 × 2 games. For each case game, the corresponding limit distribution of the Markov-based process is given when noise intensity is small enough. In contrast with most literatures in evolutionary games using the simulation method, all our results obtained are analytical. Especially, in the dominant-case game, coexistence of the two strategies may become evolutionary stable states in our model. This result can be
Rabajante, Jomar Fajardo; Talaue, Cherryl Ortega
2015-01-01
Graphical abstract: Display Omitted -- Highlights: •Properties of n-dimensional decision model of competitive interaction networks. •Graphical technique for component-wise and steady state stability analysis. •Search for parameter conditions that control equilibrium switching. •Illustrations of multi-stable systems and repressilators. -- Abstract: Concurrent decision-making model (CDM) of interaction networks with more than two antagonistic components represents various biological systems, such as gene interaction, species competition and mental cognition. The CDM model assumes sigmoid kinetics where every component stimulates itself but concurrently represses the others. Here we prove generic mathematical properties (e.g., location and stability of steady states) of n-dimensional CDM with either symmetric or asymmetric reciprocal antagonism between components. Significant modifications in parameter values serve as biological regulators for inducing steady state switching by driving a temporal state to escape an undesirable equilibrium. Increasing the maximal growth rate and decreasing the decay rate can expand the basin of attraction of a steady state that contains the desired dominant component. Perpetually adding an external stimulus could shut down multi-stability of the system which increases the robustness of the system against stochastic noise. We further show that asymmetric interaction forming a repressilator-type network generates oscillatory behavior
Klinkusch, Stefan; Tremblay, Jean Christophe
2016-05-14
In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.
Klinkusch, Stefan; Tremblay, Jean Christophe [Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin (Germany)
2016-05-14
In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.
K. Hacıefendioğlu
2012-04-01
Full Text Available The deconvolution effect of the near-fault earthquake ground motions on the stochastic dynamic response of tunnel-soil deposit interaction systems are investigated by using the finite element method. Two different earthquake input mechanisms are used to consider the deconvolution effects in the analyses: the standard rigid-base input and the deconvolved-base-rock input model. The Bolu tunnel in Turkey is chosen as a numerical example. As near-fault ground motions, 1999 Kocaeli earthquake ground motion is selected. The interface finite elements are used between tunnel and soil deposit. The mean of maximum values of quasi-static, dynamic and total responses obtained from the two input models are compared with each other.
Matías A Goldin
Full Text Available The nature of telencephalic control over premotor and motor circuits is debated. Hypotheses range from complete usurping of downstream circuitry to highly interactive mechanisms of control. We show theoretically and experimentally, that telencephalic song motor control in canaries is consistent with a highly interactive strategy. As predicted from a theoretical model of respiratory control, mild cooling of a forebrain nucleus (HVC led to song stretching, but further cooling caused progressive restructuring of song, consistent with the hypothesis that respiratory gestures are subharmonic responses to a timescale present in the output of HVC. This interaction between a life-sustaining motor function (respiration and telencephalic song motor control suggests a more general mechanism of how nonlinear integration of evolutionarily new brain structures into existing circuitry gives rise to diverse, new behavior.
Simple computer model for the nonlinear beam--beam interaction in ISABELLE
Herrera, J.C.; Month, M.; Peierls, R.F.
1979-03-01
The beam--beam interaction for two counter-rotating continuous proton beams crossing at an angle can be simulated by a 1-dimensional nonlinear force. The model is applicable to ISABELLE as well as to the ISR. Since the interaction length is short compared with the length of the beam orbit, the interaction region is taken to be a point. The problem is then treated as a mapping with the remainder of the system taken to be a rotation of phase given by the betatron tune of the storage ring. The evolution of the mean square amplitude of a given distribution of particles is shown for different beam--beam strengths. The effect of round-off error with resulting loss of accuracy for particle trajectories is discussed. 3 figures
Wu, Y. [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China); Institute of Applied Electronics, China Academy of Engineering Physics, Mianyang 621900 (China); Science and Technology on High Power Microwave Laboratory, Mianyang 621900 (China); Xu, Z.; Li, Z. H. [Institute of Applied Electronics, China Academy of Engineering Physics, Mianyang 621900 (China); Tang, C. X. [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China)
2012-07-15
In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.
Wu, Y.; Xu, Z.; Li, Z. H.; Tang, C. X.
2012-07-01
In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.
Itasse, Maxime; Brazier, Jean-Philippe; Léon, Olivier; Casalis, Grégoire
2015-01-01
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m 1 , n 1 ), (m 2 , n 2 ), such that the difference in azimuth and in frequency matches the desired “target” mode (m 1 − m 2 , n 1 − n 2 ). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes
Effect of bottom slope on the nonlinear triad interactions in shallow water
Chen, Hongzhou; Tang, Xiaocheng; Zhang, Ri; Gao, Junliang
2018-05-01
This paper aims at investigating the effect of bottom slope to the nonlinear triad interactions for irregular waves propagating in shallow water. The physical experiments are conducted in a wave flume with respect to the transformation of waves propagating on three bottom slopes ( β = 1/15, 1/30, and 1/45). Irregular waves with different type of breaking that are mechanically generated based on JONSWAP spectra are used for the test. The obviously different variations of spectra measured on each bottom reveal a crucial role of slope effect in the energy transfer between harmonics. The wavelet-based bispectrum were used to examine the bottom slope effect on the nonlinear triad interactions. Results show that the different bottom slopes which waves are propagated on will cause a significant discrepancy of triad interactions. Then, the discussions on the summed bicoherence which denote the distribution of phase coupling on each frequency further clarify the effect of bottom slope. Furthermore, the summed of the real and imaginary parts of bispectrum which could reflect the intensity of frequency components participating in the wave skewness and asymmetry were also investigated. Results indicate that the value of these parameters will increase as the bottom slope gets steeper.
Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr; Casalis, Grégoire, E-mail: Gregoire.Casalis@onera.fr [Onera - The French Aerospace Lab, F-31055 Toulouse (France)
2015-08-15
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.
Liss, Alexander
Extreme weather events, such as heat waves and cold spells, cause substantial excess mortality and morbidity in the vulnerable elderly population, and cost billions of dollars. The accurate and reliable assessment of adverse effects of extreme weather events on human health is crucial for environmental scientists, economists, and public health officials to ensure proper protection of vulnerable populations and efficient allocation of scarce resources. However, the methodology for the analysis of large national databases is yet to be developed. The overarching objective of this dissertation is to examine the effect of extreme weather on the elderly population of the Conterminous US (ConUS) with respect to seasonality in temperature in different climatic regions by utilizing heterogeneous high frequency and spatio-temporal resolution data. To achieve these goals the author: 1) incorporated dissimilar stochastic high frequency big data streams and distinct data types into the integrated data base for use in analytical and decision support frameworks; 2) created an automated climate regionalization system based on remote sensing and machine learning to define climate regions for the Conterminous US; 3) systematically surveyed the current state of the art and identified existing gaps in the scientific knowledge; 4) assessed the dose-response relationship of exposure to temperature extremes on human health in relatively homogeneous climate regions using different statistical models, such as parametric and non-parametric, contemporaneous and asynchronous, applied to the same data; 5) assessed seasonal peak timing and synchronization delay of the exposure and the disease within the framework of contemporaneous high frequency harmonic time series analysis and modification of the effect by the regional climate; 6) modeled using hyperbolic functional form non-linear properties of the effect of exposure to extreme temperature on human health. The proposed climate
Tang, H. T.; Hofmann, R.; Yee, G.; Vaughan, D. K.
1980-01-01
Transient, nonlinear soil-structure interaction simulations of an Electric Power Research Institute, SIMQUAKE experiment were performed using the large strain, time domain STEALTH 2D code and a cyclic, kinematically hardening cap soil model. Results from the STEALTH simulations were compared to identical simulations performed with the TRANAL code and indicate relatively good agreement between all the STEALTH and TRANAL calculations. The differences that are seen can probably be attributed to: (1) large (STEALTH) vs. small (TRANAL) strain formulation and/or (2) grid discretization differences.
Poterasu, V.F.
1984-01-01
It is presented a method and the phase resonance for damping characteristic identification of non-linear soil-structural interaction. The algorithm can be applied in case of any, not necessarily, damping characteristic of the system examined. For the identification, the system is harmonically excited and are considered the super-harmonic amplitudes for odd and even powers of the x. The response of shear beam system for different levels of base excitation and for different locations of the load is considered. (Author) [pt
Ganji, S. S.; Barari, Amin; Sfahani, M. G.
2011-01-01
of time. The differential equations were solved using the method of Homotopy Perturbation. The simplicity and accuracy of the approximation are compared with “exact” solution and illustrated numerically and graphically. The results reveal that the HPM is very effective and simple and provides highly...... accurate solutions for nonlinear differential equations.......The phenomenon of stream–aquifer interaction was investigated via mathematical modeling using the Boussinesq equation. A new approximate solution of the one-dimensional Boussinesq equation is presented for a semi-infinite aquifer when the hydraulic head at the source is an arbitrary function...
Higher order terms of the nonlinear forces in plasmas with collisions at laser interaction
Kentwell, G.W.; Hora, H.
1980-01-01
The evaluation of the general expression of the nonlinear force of laser-plasma interaction showed discrepancies depending on the assumptions of the phase and collisions in the expressions used for E and H. While the first order terms of the derivations are remaining unchanged, new third order terms are found for the case of perpendicular incidence without collisions. With collisions, the additional non-pondermotive terms are derived to be more general than known before. It is then possible to evaluate the forces for oblique incidence with collisions and find an absorption caused force in the plane of the plasma surface. (author)
Nonlinear interaction of instability waves and vortex-pairing noise in axisymmetric subsonic jets
Yang, Hai-Hua; Zhang, Xing-Chen; Wan, Zhen-Hua; Sun, De-Jun [Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027 (China); Zhou, Lin, E-mail: wanzh@ustc.edu.cn [Institute of Structural Mechanics, Chinese Academy of Engineering Physics, Mianyang 623100 (China)
2016-10-15
A direct simulation with selected inflow forcing is performed for an accurate description of the jet flow field and far-field noise. The effects of the Mach number and heating on the acoustic field are studied in detail. The beam patterns and acoustic intensities are both varied as the change of the Mach number and temperature. The decomposition of the source terms of the Lilley–Goldstein (L–G) equation shows that the momentum and thermodynamic components lead to distinctly different beam patterns. Significant cancellation is found between the momentum and thermodynamic components at low polar angles for the isothermal jet and large polar angles for the hot jet. The cancellation leads to the minimum values of the far-field sound. Based on linear parabolized stability equation solutions, the nonlinear interaction model for sound prediction is built in combination with the L–G equation. The dominant beam patterns and their original locations predicted by the nonlinear model are in good agreement with the direct simulation results, and the predictions of sound pressure level (SPL) by the nonlinear model are relatively reasonable. (paper)
Nonlinear interaction of instability waves and vortex-pairing noise in axisymmetric subsonic jets
Yang, Hai-Hua; Zhou, Lin; Zhang, Xing-Chen; Wan, Zhen-Hua; Sun, De-Jun
2016-10-01
A direct simulation with selected inflow forcing is performed for an accurate description of the jet flow field and far-field noise. The effects of the Mach number and heating on the acoustic field are studied in detail. The beam patterns and acoustic intensities are both varied as the change of the Mach number and temperature. The decomposition of the source terms of the Lilley-Goldstein (L-G) equation shows that the momentum and thermodynamic components lead to distinctly different beam patterns. Significant cancellation is found between the momentum and thermodynamic components at low polar angles for the isothermal jet and large polar angles for the hot jet. The cancellation leads to the minimum values of the far-field sound. Based on linear parabolized stability equation solutions, the nonlinear interaction model for sound prediction is built in combination with the L-G equation. The dominant beam patterns and their original locations predicted by the nonlinear model are in good agreement with the direct simulation results, and the predictions of sound pressure level (SPL) by the nonlinear model are relatively reasonable.
Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy
Cantrell, John H.; Cantrell, Sean A.
2010-01-01
The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.
Beam-beam interaction and Pacman effects in the SSC with random nonlinear multipoles
Goderre, G.P.; Ohnuma, S.
1988-01-01
In order to find the combined effects of beam-beam interaction (head-on and long-range) and random nonlinear multipoles in dipole magnets, transverse tunes and smears have been calculated as a function of oscillation amplitudes. Two types of particles, ''regular'' and ''Pacman,'' have been investigated using a modified version of tracking code TEAPOT. Regular particles experience beam-beam interactions in all four interaction regions (IR's), both head-on and long range, while pacman particles interact with bunches of the other beam in one medium-beta and one low-beta IR's only. The model for the beam-beam interaction is of weak-strong type and the strong beam is assumed to have a round Gaussian charge distribution. Furthermore, it is assumed that the vertical closed orbit deviation arising from the finite crossing angle of 70 μrad is perfectly compensated for regular particles. The same compensation applied to pacman particles creates a closed orbit distortion. Linear tunes are adjusted for regular particles to the design values but there are no nonlinear corrections except for chromaticity correcting sextupoles in two families. Results obtained in this study do not show any reduction of dynamic or linear aperture for pacman particles but some doubts exist regarding the validity of defining the linear aperture from the smear alone. Preliminary results are given for regular particles when (Δp/p) is modulated by the synchrotron oscillation. For these, fifty oscillations corresponding to 26,350 revolutions have been tracked. A very slow increase in the horizontal amplitude, /approximately/4 /times/ 10/sup /minus/4//oscillation (relative), is a possibility but this should be confirmed by trackings of larger number of revolutions. 11 refs., 18 figs., 2 tabs
Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality
Dai, Zhiping; Yang, Zhenjun; Ling, Xiaohui; Zhang, Shumin; Pang, Zhaoguang
2016-01-01
The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and the oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.
Hamilton, Mark F.
1990-12-01
This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.
Nonlinear evolution dynamics of holographic superconductor model with scalar self-interaction
Li, Ran; Zi, Tieguang; Zhang, Hongbao
2018-04-01
We investigate the holographic superconductor model that is described by the Einstein-Maxwell theory with the self-interaction term λ |Ψ |4 of complex scalar field in asymptotic anti-de Sitter (AdS) spacetime. Below critical temperature Tc, the planar Reissner-Nordström-AdS black hole is unstable due to the near-horizon scalar condensation instability. We study the full nonlinear development of this instability by numerically solving the gravitational dynamics in the asymptotic AdS spacetime, and observe a dynamical process from the perturbed Reissner-Nordström-AdS black hole to a hairy black hole when the initial black hole temperature T process is then holographically dual to the dynamical superconducting phase transition process in the boundary theory. Furthermore, we also study the effect of the scalar self-interaction on time evolution of superconducting condensate operator, event and apparent horizon areas of the final hairy black hole.
Chimera regimes in a ring of oscillators with local nonlinear interaction
Shepelev, Igor A.; Zakharova, Anna; Vadivasova, Tatiana E.
2017-03-01
One of important problems concerning chimera states is the conditions of their existence and stability. Until now, it was assumed that chimeras could arise only in ensembles with nonlocal character of interactions. However, this assumption is not exactly right. In some special cases chimeras can be realized for local type of coupling [1-3]. We propose a simple model of ensemble with local coupling when chimeras are realized. This model is a ring of linear oscillators with the local nonlinear unidirectional interaction. Chimera structures in the ring are found using computer simulations for wide area of values of parameters. Diagram of the regimes on plane of control parameters is plotted and scenario of chimera destruction are studied when the parameters are changed.
Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
Duong, M. H.; Muntean, A.; Richardson, O. M.
2017-07-01
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.
Nonlinear mode interaction in equal-leg angle struts susceptible to cellular buckling.
Bai, L; Wang, F; Wadee, M A; Yang, J
2017-11-01
A variational model that describes the interactive buckling of a thin-walled equal-leg angle strut under pure axial compression is presented. A formulation combining the Rayleigh-Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Solving the equations using numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weak-axis flexural buckling mode and the strong-axis flexural-torsional buckling mode for the first time-the resulting behaviour being highly unstable. Physical experiments conducted on 10 cold-formed steel specimens are presented and the results show good agreement with the variational model.
Ishizawa, A.; Nakajima, N.
2007-01-01
Micro-turbulence and macro-magnetohydrodynamic (macro-MHD) instabilities can appear in plasma at the same time and interact with each other in a plasma confinement. The multi-scale-nonlinear interaction among micro-turbulence, double tearing instability and zonal flow is investigated by numerically solving a reduced set of two-fluid equations. It is found that the double tearing instability, which is a macro-MHD instability, appears in an equilibrium formed by a balance between micro-turbulence and zonal flow when the double tearing mode is unstable. The roles of the nonlinear and linear terms of the equations in driving the zonal flow and coherent convective cell flow of the double tearing mode are examined. The Reynolds stress drives zonal flow and coherent convective cell flow, while the ion diamagnetic term and Maxwell stress oppose the Reynolds stress drive. When the double tearing mode grows, linear terms in the equations are dominant and they effectively release the free energy of the equilibrium current gradient
Nonlinear dynamic analysis of framed structures including soil-structure interaction effects
Mahmood, M.N.; Ahmed, S.Y.
2008-01-01
The role of oil-structure interaction on seismic behavior of reinforced concrete structures is investigated in this paper. A finite element approach has been adopted to model the interaction system that consists of the reinforced concrete plane frame, soil deposit and interface which represents the frictional between foundation of the structure and subsoil. The analysis is based on the elasto-plastic behavior of the frame members (beams and columns) that is defined by the ultimate axial force-bending moment interaction curve, while the cap model is adopted to govern the elasto-plastic behavior of the soil material. Mohr-Coulomb failure law is used to determine the initiation of slippage at the interface, while the separation is assumed to determine the initiation of slippage at the interface, while the separation is assumed to occur when the stresses at the interface becomes tension stresses. New-Mark's Predictor-Corrector algorithm is adopted for nonlinear dynamic analysis. The main aim of present work is to evaluate the sensitivity of structures to different behavior of the soil and interface layer when subjected to an earthquake excitation. Predicted results of the dynamic analysis of the interaction system indicate that the soil-structure interaction problem can have beneficial effects on the structural behavior when different soil models (elastic and elasto-plastic) and interface conditions (perfect bond and permitted slip)are considered. (author)
Stochastic volatility and stochastic leverage
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
The study on the non-linear soil structure interaction for nuclear power plants
Tetsuya Hagiwara; Yoshio Kitada
2005-01-01
1. Introduction: JNES is planning a new project to study non-linear soil-structure interaction (SSI) effect under large earthquake ground motions equivalent to and/or over a design earthquake ground motion of S2(The extreme design earthquake). Concerning the SSI test, it is pointed out that handling of the scale effect of the specimen together with the surrounding soil on the earthquake response evaluation of the actual structure is essential issue for the scaled model test. Thus, for the test, the largest specimen possible and the biggest input motion possible are necessary. Taking into account the above issues, new test methodology, which utilizes artificial earthquake ground motion, is considered desirable if it can be performed at a realistic cost. Under this motivation, we have studied the test methodology which applying blasting power as for a big earthquake ground motion. The information from a coal mine company in the U.S.A. indicates that the works performed in the surface coal mine to blast a rock covering a coal layer generates a big artificial ground motion, which is similar to earthquake ground motion. Application of this artificial earthquake ground motion for the SSI test is considered very promising because the blasting work is carried out periodically for mining coal so that we can apply artificial motions generated by the work if we construct a building model at a closed point to the blasting work area. The major purposes of the test will be to understand (a) basic earthquake response characteristics of a Nuclear Power Plant (NPP) reactor building when a large earthquake strikes the NPP site and (b) nonlinear characteristics of SSI phenomenon during a big earthquake. In the paper, we introduce the test method and basic characteristics of measured artificial ground motions generated by the blasting works on an actual site. 2. Conclusion: It was confirmed that the artificial ground motions generated by blasting works have enough acceleration level
Znojil, Miloslav; Růžička, František; Zloshchastiev, K. G.
2017-01-01
Roč. 9, č. 8 (2017), č. článku 165. ISSN 2073-8994 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : PT symmetry * nonlinear Schrodinger equations * logarithmic nonlinearities Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.457, year: 2016
C. M. Huang
2006-12-01
Full Text Available To quantitatively study the effects of nonlinear interactions on tide structure, a nonlinear numerical tidal model is developed, and the reliability and convergence of the adopted algorithm and coding are checked by numerical experiments. Under the same conditions as those employed by the GSWM-00 (Global Scale Wave Model 2000, our model provides the nonlinear quasi-steady solution of the migrating semidiurnal tide, which differs from the GSWM-00 result (the linear steady solution in the MLT region, especially above 100 km. Additionally, their amplitude difference displays a remarkable month-to-month variation, and its significant magnitudes occur during the month with strong semidiurnal tide. A quantitative analysis suggests that the main cause for the amplitude difference is that the initial migrating 12-h tide will interact with the mean flow as well as the nonlinearity-excited 6-h tide, and subsequently yield a new 12-h tidal part. Furthermore, our simulations also show that the mean flow/tidal interaction will significantly alter the background wind and temperature fields. The large magnitudes of the tidal amplitude difference and the background alteration indicate that the nonlinear processes involved in tidal propagations should be comprehensively considered in the description of global atmospheric dynamics in the MLT region. The comparisons among our simulations, the GSWMs and some observations of tides suggest that the nonlinearity-induced tidal structure variation could be a possible mechanism to account for some discrepancies between the GSWMs and the observations.
Suppression of stochastic pulsation in laser-plasma interaction by smoothing methods
Hora, H.; Aydin, M.
1992-01-01
The control of the very complex behavior of a plasma with laser interaction by smoothing with induced spatial incoherence or other methods was related to improving the lateral uniformity of the irradiation. While this is important, it is shown from numerical hydrodynamic studies that the very strong temporal pulsation (stuttering) will mostly be suppressed by these smoothing methods too
Nonlinear modulation of interacting between COMT and depression on brain function.
Gong, L; He, C; Yin, Y; Ye, Q; Bai, F; Yuan, Y; Zhang, H; Lv, L; Zhang, H; Zhang, Z; Xie, C
2017-09-01
The catechol-O-methyltransferase (COMT) gene is related to dopamine degradation and has been suggested to be involved in the pathogenesis of major depressive disorder (MDD). However, how this gene affects brain function properties in MDD is still unclear. Fifty patients with MDD and 35 cognitively normal participants underwent a resting-state functional magnetic resonance imaging scan. A voxelwise and data-drive global functional connectivity density (gFCD) analysis was used to investigate the main effects and the interactions of disease states and COMT rs4680 gene polymorphism on brain function. We found significant group differences of the gFCD in bilateral fusiform area (FFA), post-central and pre-central cortex, left superior temporal gyrus (STG), rectal and superior temporal gyrus and right ventrolateral prefrontal cortex (vlPFC); abnormal gFCDs in left STG were positively correlated with severity of depression in MDD group. Significant disease×COMT interaction effects were found in the bilateral calcarine gyrus, right vlPFC, hippocampus and thalamus, and left SFG and FFA. Further post-hoc tests showed a nonlinear modulation effect of COMT on gFCD in the development of MDD. Interestingly, an inverted U-shaped modulation was found in the prefrontal cortex (control system) but U-shaped modulations were found in the hippocampus, thalamus and occipital cortex (processing system). Our study demonstrated nonlinear modulation of the interaction between COMT and depression on brain function. These findings expand our understanding of the COMT effect underlying the pathophysiology of MDD. Copyright © 2017 Elsevier Masson SAS. All rights reserved.
Rate of non-linearity in DMS aerosol-cloud-climate interactions
M. A. Thomas
2011-11-01
Full Text Available The degree of non-linearity in DMS-cloud-climate interactions is assessed using the ECHAM5-HAMMOZ model by taking into account end-to-end aerosol chemistry-cloud microphysics link. The evaluation is made over the Southern oceans in austral summer, a region of minimal anthropogenic influence. In this study, we compare the DMS-derived changes in the aerosol and cloud microphysical properties between a baseline simulation with the ocean DMS emissions from a prescribed climatology, and a scenario where the DMS emissions are doubled. Our results show that doubling the DMS emissions in the current climate results in a non-linear response in atmospheric DMS burden and subsequently, in SO_{2} and H_{2}SO_{4} burdens due to inadequate OH oxidation. The aerosol optical depth increases by only ~20 % in the 30° S–75° S belt in the SH summer months. This increases the vertically integrated cloud droplet number concentrations (CDNC by 25 %. Since the vertically integrated liquid water vapor is constant in our model simulations, an increase in CDNC leads to a reduction in cloud droplet radius of 3.4 % over the Southern oceans in summer. The equivalent increase in cloud liquid water path is 10.7 %. The above changes in cloud microphysical properties result in a change in global annual mean radiative forcing at the TOA of −1.4 W m^{−2}. The results suggest that the DMS-cloud microphysics link is highly non-linear. This has implications for future studies investigating the DMS-cloud climate feedbacks in a warming world and for studies evaluating geoengineering options to counteract warming by modulating low level marine clouds.
Effect of nonlinear wave-particle interaction on electron-cyclotron absorption
Tsironis, C; Vlahos, L [Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece)
2006-09-15
We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the wave amplitude and frequency through the current response. This description allows for effects of the electron motions on the efficiency of the wave absorption, for example, the asynchrony between the wave phase and the gyroperiod. As an application, we study the absorption of an EC wave beam in a simplified tokamak geometry, for plasma parameters relevant to current and future fusion experiments. We conclude that, within the limits of our model, there are cases where the linear theory for the absorption of EC waves, used widely in the current literature, may overestimate the energy deposition. In such cases, nonlinear effects are essential for the accurate estimation of the plasma-wave coupling and their inclusion should be considered, especially when the wave power is dramatically increased as in the case of ITER.
Effect of nonlinear wave-particle interaction on electron-cyclotron absorption
Tsironis, C; Vlahos, L
2006-01-01
We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the wave amplitude and frequency through the current response. This description allows for effects of the electron motions on the efficiency of the wave absorption, for example, the asynchrony between the wave phase and the gyroperiod. As an application, we study the absorption of an EC wave beam in a simplified tokamak geometry, for plasma parameters relevant to current and future fusion experiments. We conclude that, within the limits of our model, there are cases where the linear theory for the absorption of EC waves, used widely in the current literature, may overestimate the energy deposition. In such cases, nonlinear effects are essential for the accurate estimation of the plasma-wave coupling and their inclusion should be considered, especially when the wave power is dramatically increased as in the case of ITER
Near-field soil-structure interaction analysis using nonlinear hybrid modeling
Katayama, I.; Chen, C.; Lee, Y.J.; Jean, W.Y.; Penzien, J.
1989-01-01
The hybrid modeling method (Gupta and Penzien 1980) and associated analysis procedure for solving a three-dimensional soil-structure interaction problem was developed by Gupta and Penzien (1981) and Gupta et al.(1982). Subsequently, successive modifications have been made to the original modeling method and analysis procedure allowing more general treatment of the SSI problem (Penzien, 1988). Through many correlation studies of field test data obtained under forced-vibration and earthquake-excitation conditions, it has been shown that the HASSI programs can effectively predict the dynamic response of a soil-structure system, if realistic soil parameters are adopted. In the above, the entire structure-foundation system is considered to respond in a linear fashion. Since the reflected three-dimensional waves at the soil-structure interface decays very rapidly with distance away from the structure (Katayama, 1987 (a)), the response of the soil close to the base of the structure may greatly affect its response; therefore, proper modeling of the non-linear soil behavior characteristic is essential. The nonlinear behavior of near-field soil has been taken into consideration in HASSI-7 by the standard equivalent linearization procedures used in programs SHAKE and FLUSH
Nonlinear plasma wave models in 3D fluid simulations of laser-plasma interaction
Chapman, Thomas; Berger, Richard; Arrighi, Bill; Langer, Steve; Banks, Jeffrey; Brunner, Stephan
2017-10-01
Simulations of laser-plasma interaction (LPI) in inertial confinement fusion (ICF) conditions require multi-mm spatial scales due to the typical laser beam size and durations of order 100 ps in order for numerical laser reflectivities to converge. To be computationally achievable, these scales necessitate a fluid-like treatment of light and plasma waves with a spatial grid size on the order of the light wave length. Plasma waves experience many nonlinear phenomena not naturally described by a fluid treatment, such as frequency shifts induced by trapping, a nonlinear (typically suppressed) Landau damping, and mode couplings leading to instabilities that can cause the plasma wave to decay rapidly. These processes affect the onset and saturation of stimulated Raman and Brillouin scattering, and are of direct interest to the modeling and prediction of deleterious LPI in ICF. It is not currently computationally feasible to simulate these Debye length-scale phenomena in 3D across experimental scales. Analytically-derived and/or numerically benchmarked models of processes occurring at scales finer than the fluid simulation grid offer a path forward. We demonstrate the impact of a range of kinetic processes on plasma reflectivity via models included in the LPI simulation code pF3D. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Towards modeling of nonlinear laser-plasma interactions with hydrocodes: The thick-ray approach
Colaïtis, A.; Duchateau, G.; Nicolaï, P.; Tikhonchuk, V.
2014-03-01
This paper deals with the computation of laser beam intensity in large-scale radiative hydrocodes applied to the modeling of nonlinear laser-plasma interactions (LPIs) in inertial confinement fusion (ICF). The paraxial complex geometrical optics (PCGO) is adapted for light waves in an inhomogeneous medium and modified to include the inverse bremsstrahlung absorption and the ponderomotive force. This thick-ray model is compared to the standard ray-tracing (RT) approach, both in the chic code. The PCGO model leads to different power deposition patterns and better diffraction modeling compared to standard RT codes. The intensity-reconstruction technique used in RT codes to model nonlinear LPI leads to artificial filamentation and fails to reproduce realistic ponderomotive self-focusing distances, intensity amplifications, and density channel depletions, whereas PCGO succeeds. Bundles of Gaussian thick rays can be used to model realistic non-Gaussian ICF beams. The PCGO approach is expected to improve the accuracy of ICF simulations and serve as a basis to implement diverse LPI effects in large-scale hydrocodes.
A Nonlinear Model for Gene-Based Gene-Environment Interaction
Jian Sa
2016-06-01
Full Text Available A vast amount of literature has confirmed the role of gene-environment (G×E interaction in the etiology of complex human diseases. Traditional methods are predominantly focused on the analysis of interaction between a single nucleotide polymorphism (SNP and an environmental variable. Given that genes are the functional units, it is crucial to understand how gene effects (rather than single SNP effects are influenced by an environmental variable to affect disease risk. Motivated by the increasing awareness of the power of gene-based association analysis over single variant based approach, in this work, we proposed a sparse principle component regression (sPCR model to understand the gene-based G×E interaction effect on complex disease. We first extracted the sparse principal components for SNPs in a gene, then the effect of each principal component was modeled by a varying-coefficient (VC model. The model can jointly model variants in a gene in which their effects are nonlinearly influenced by an environmental variable. In addition, the varying-coefficient sPCR (VC-sPCR model has nice interpretation property since the sparsity on the principal component loadings can tell the relative importance of the corresponding SNPs in each component. We applied our method to a human birth weight dataset in Thai population. We analyzed 12,005 genes across 22 chromosomes and found one significant interaction effect using the Bonferroni correction method and one suggestive interaction. The model performance was further evaluated through simulation studies. Our model provides a system approach to evaluate gene-based G×E interaction.
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
Stochastic forward and inverse groundwater flow and solute transport modeling
Janssen, G.M.C.M.
2008-01-01
Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers
This thesis offers three new approaches that contribute
Lewiński, Paweł M.; Dudziak, Sławomir
2018-01-01
In the paper, two kinds of constitutive models for ground and structure were adopted for the nonlinear interaction analysis of the RC cylindrical tank with subsoil. The paper discusses deformational and incremental approaches to a nonlinear FE analysis of soil-structure interaction including the description of behaviour of the RC structure and the subsoil under short-term loading. Moreover, a non-linear elastic-brittle-plastic analysis of RC axisymmetric structures using finite element iterative techniques is presented. The constitutive laws for concrete and subsoil are developed in compliance with the deformational and plastic flow theories of plasticity. Two examples of an FE analysis of soil-structure interaction were performed and the results were analysed.
Stochastic growth of localized plasma waves
Robinson, P.A.; Cairns, I.H.
2000-01-01
Full text: Localized bursty plasma waves occur in many natural systems, where they are detected by spacecraft. The large spatiotemporal scales involved imply that beam and other instabilities relax to marginal stability and that mean wave energies are low. Stochastic wave growth occurs when ambient fluctuations perturb the wave-driver interaction, causing fluctuations about marginal stability. This yields regions where growth is enhanced and others where damping is increased; observed bursts are associated with enhanced growth and can occur even when the mean growth rate is negative. In stochastic growth, energy loss from the source is suppressed relative to secular growth, preserving it for much longer times and distances than otherwise possible. Linear stochastic growth can operate at wave levels below thresholds of nonlinear wave-clumping mechanisms such as strong-turbulence modulational instability and is not subject to their coherence and wavelength limits. Growth mechanisms can be distinguished by statistics of the fields, whose strengths are lognormally distributed if stochastically growing, power-law distributed in strong turbulence, and uniformly distributed in log under secular growth. After delineating stochastic growth and strong-turbulence regimes, recent applications of stochastic growth theory (SGT) are described, involving bursty plasma waves and unstable particle distributions in type II and III solar radio sources, foreshock regions upstream of the bow shocks of Earth and planets, and Earth's magnetosheath, auroras, and polar-caps. It is shown that when combined with wave-wave processes, SGT accounts for type II and III solar radio emissions. SGT thus removes longstanding problems in understanding persistent unstable distributions, bursty fields, and radio emissions observed in space
Non-linear interactions of multi-level atoms with a near-resonant standing wave
O'Kane, T.J.; Scholten, R.E.; Walkiewicz, M.R.; Farrell, P.M.
1998-01-01
Using a semiclassical density matrix formalism we have calculated the behavior of multi-level atoms interacting with a standing wave field, and show how complex non-linear phenomena, including multi-photon effects, combine to produce saturation spectra as observed in experiments. We consider both 20-level sodium and 24-level rubidium models, contrasting these with a simple 2-level case. The influence of parameters such as atomic trajectory and the time the atom remains in the beam are shown to have a critical effect on the lineshape of these resonances and the emission/absorption processes. Stable oscillations in the excited state populations for both the two-level and multi-level cases are shown to be limit cycles. These limit cycles undergo period doubling as the system evolves into chaos. Finally, using a Monte Carlo treatment, these processes average to produce saturated absorption spectra complete with power and Doppler broadening effects consistent with experiment. (authors)
The nonlinear interaction of convection modes in a box of a saturated porous medium
Florio, Brendan J.; Bassom, Andrew P.; Fowkes, Neville; Judd, Kevin; Stemler, Thomas
2015-05-01
A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number Rc for onset is different for each mode, and in practice the mode with the lowest associated Rc is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common Rc. For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.
On the solution of the equations for nonlinear interaction of three damped waves
1976-01-01
Three-wave interactions are analyzed in a coherent wave description assuming different linear damping (or growth) of the individual waves. It is demonstrated that when two of the coefficients of dissipation are equal, the set of equations can be reduced to a single equivalent equation, which in the nonlinearly unstable case, where one wave is undamped, asymptotically takes the form of an equation defining the third Painleve transcendent. It is then possible to find an asymptotic expansion near the time of explosion. This solution is of principal interest since it indicates that the solution of the general three-wave system, where the waves undergo different individual dissipations, belongs to a higher class of functions, which reduces to Jacobian elliptic functions only in the case where all waves suffer the same damping [fr
Beam interaction of a pulsed, nonlinear in-vacuum injection magnet
Rast, Helge
2013-01-01
Theme of this thesis is the study of the interaction of the injection magnet designed for BESSY II with the electron beam. The main topic of this thesis lies in the numerical and measurement-technical study of the loss factor, the wake potential, and the wake impedance of the nonlinear kicker magnet with the aim of an optimization of the magnet design, so that a stable operation of the kicker in the BESSY II storage ring is made possible. A further main topic of this thesis is a study on the matching of the injection scheme with a single kicker to the conditions of the DELTA storage ring, which is operated by the TU Dortmund.
Zaman, M.; Mamoon, S.M.
1989-01-01
Analysis of seismic response of structures located at a site with potential for soil liquefaction has drawn attention of many researchers. The topic is particularly important in the design of critical facilities like nuclear reactors and defense installations. This paper presents the results of a study involving evaluation of coupled seismic response of structures (model nuclear reactors) and characteristics of soil liquefaction at a site. The analysis procedure employed is based on the nonlinear finite element (FE) technique and accounts for the interaction effects due to a neighboring structure. Emphasis is given to the following features: prediction of spatial and temporal variation of pore water pressure; identification of the on-set of liquefaction based on the effective stress approach, and tracing the propagation of the liquefied zones with time and resulting response of the structures
Etienne Thoret
2016-06-01
Full Text Available In this paper, a flexible control strategy for a synthesis model dedicated to nonlinear friction phenomena is proposed. This model enables to synthesize different types of sound sources, such as creaky doors, singing glasses, squeaking wet plates or bowed strings. Based on the perceptual stance that a sound is perceived as the result of an action on an object we propose a genuine source/filter synthesis approach that enables to elude physical constraints induced by the coupling between the interacting objects. This approach makes it possible to independently control and freely combine the action and the object. Different implementations and applications related to computer animation, gesture learning for rehabilitation and expert gestures are presented at the end of this paper.
Quantum mechanical analysis of nonlinear optical response of interacting graphene nanoflakes
Hanying Deng
2018-01-01
Full Text Available We propose a distant-neighbor quantum-mechanical (DNQM approach to study the linear and nonlinear optical properties of graphene nanoflakes (GNFs. In contrast to the widely used tight-binding description of the electronic states that considers only the nearest-neighbor coupling between the atoms, our approach is more accurate and general, as it captures the electron-core interactions between all atoms in the structure. Therefore, as we demonstrate, the DNQM approach enables the investigation of the optical coupling between two closely separated but chemically unbound GNFs. We also find that the optical response of GNFs depends crucially on their shape, size, and symmetry properties. Specifically, increasing the size of nanoflakes is found to shift their accommodated quantum plasmon oscillations to lower frequency. Importantly, we show that by embedding a cavity into GNFs, one can change their symmetry properties, tune their optical properties, or enable otherwise forbidden second-harmonic generation processes.
Nonlinear interaction of an intense radio wave with ionospheric D/E layer plasma
Sodha, Mahendra Singh; Agarwal, Sujeet Kumar
2018-05-01
This paper considers the nonlinear interaction of an intense electromagnetic wave with the D/E layer plasma in the ionosphere. A simultaneous solution of the electromagnetic wave equation and the equations describing the kinetics of D/E layer plasma is obtained; the phenomenon of ohmic heating of electrons by the electric field of the wave causes enhanced collision frequency and ionization of neutral species. Electron temperature dependent recombination of electrons with ions, electron attachment to O 2 molecules, and detachment of electrons from O2 - ions has also been taken into account. The dependence of the plasma parameters on the square of the electric vector of the wave E0 2 has been evaluated for three ionospheric heights (viz., 90, 100, and 110 km) corresponding to the mid-latitude mid-day ionosphere and discussed; these results are used to investigate the horizontal propagation of an intense radio wave at these heights.
Pfaff, Wolfgang; Reagor, Matthew; Heeres, Reinier; Ofek, Nissim; Chou, Kevin; Blumoff, Jacob; Leghtas, Zaki; Touzard, Steven; Sliwa, Katrina; Holland, Eric; Krastanov, Stefan; Frunzio, Luigi; Devoret, Michel; Jiang, Liang; Schoelkopf, Robert
2015-03-01
High-Q microwave resonators show great promise for storing and manipulating quantum states in circuit QED. Using resonator modes as such a resource in quantum information processing applications requires the ability to manipulate the state of a resonator efficiently. Further, one must engineer appropriate coupling channels without spoiling the coherence properties of the resonator. We present an architecture that combines millisecond lifetimes for photonic quantum states stored in a linear resonator with fast measurement provided by a low-Q readout resonator. We demonstrate experimentally how a continuous drive on a transmon can be utilized to generate highly non-classical photonic states inside the high-Q resonator via effective nonlinear resonator mode interactions. Our approach opens new avenues for using modes of long-lived linear resonators in the circuit QED platform for quantum information processing tasks.
Angelino, P; Bottino, A; Hatzky, R; Jolliet, S; Sauter, O; Tran, T M; Villard, L
2006-01-01
The mutual interactions of ion temperature gradient (ITG) driven modes, zonal flows and geodesic acoustic modes (GAM) in tokamak plasmas are investigated using a global nonlinear gyrokinetic formulation with totally unconstrained evolution of temperature gradient and profile. A series of numerical simulations with the same initial temperature and density profile specifications is performed using a sequence of ideal MHD equilibria differing only in the value of the total plasma current, in particular with identical magnetic shear profiles and shapes of magnetic surfaces. On top of a bursty or quasi-steady state behaviour the zonal flows oscillate at the GAM frequency. The amplitude of these oscillations increases with the value of the safety factor q, resulting in a less effective suppression of ITG turbulence by zonal flows at a lower plasma current. The turbulence-driven volume-averaged radial heat transport is found to scale inversely with the total plasma current
Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.
2018-07-01
We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.
Romanelli, N.; Mazelle, C.; Meziane, K.
2018-02-01
Seen from the solar wind (SW) reference frame, the presence of newborn planetary protons upstream from the Martian and Venusian bow shocks and SW protons reflected from each of them constitutes two sources of nonthermal proton populations. In both cases, the resulting proton velocity distribution function is highly unstable and capable of giving rise to ultralow frequency quasi-monochromatic electromagnetic plasma waves. When these instabilities take place, the resulting nonlinear waves are convected by the SW and interact with nonthermal protons located downstream from the wave generation region (upstream from the bow shock), playing a predominant role in their dynamics. To improve our understanding of these phenomena, we study the interaction between a charged particle and a large-amplitude monochromatic circularly polarized electromagnetic wave propagating parallel to a background magnetic field, from first principles. We determine the number of fix points in velocity space, their stability, and their dependence on different wave-particle parameters. Particularly, we determine the temporal evolution of a charged particle in the pitch angle-gyrophase velocity plane under nominal conditions expected for backstreaming protons in planetary foreshocks and for newborn planetary protons in the upstream regions of Venus and Mars. In addition, the inclusion of wave ellipticity effects provides an explanation for pitch angle distributions of suprathermal protons observed at the Earth's foreshock, reported in previous studies. These analyses constitute a mean to evaluate if nonthermal proton velocity distribution functions observed at these plasma environments present signatures that can be understood in terms of nonlinear wave-particle processes.
Rosenbaum, G.; Regenauer-Lieb, K.; Weinberg, R. F.
2009-12-01
We use numerical modelling to investigate the development of crustal and mantle detachment faults during lithospheric extension. Our models simulate a wide range of rift systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles, which grow in response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation at different levels of the lithosphere. Crustal detachment faults are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW/m2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30-40 km) and an intermediate (60-70 mW/m2) heat flow. Results show a non-linear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometime unexpected switches in extension modes (e.g. from diffuse rifting to effective lithospheric-scale rupturing) or from mantle- to crust-dominated strain localization. We interpret this non-linearity to result from the interference of doming wavelengths. Disharmony of crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonious crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged rifting history prior to continental breakup.
Rosenbaum, Gideon; Regenauer-Lieb, Klaus; Weinberg, Roberto F.
2010-11-01
We use numerical modeling to investigate the development of crustal and mantle detachments during lithospheric extension. Our models simulate a wide range of extensional systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles as a response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation. Crustal detachments, here referred as low-angle normal decoupling horizons, are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW m-2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30-40 km) and an intermediate heat flow (60-70 mW m-2). Results show a nonlinear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometimes unexpected switches in extension modes (e.g., from diffuse extensional deformation to effective lithospheric-scale rupturing) or from mantle- to crust-dominated strain localization. We interpret this nonlinearity to result from the interference of doming wavelengths in the presence of multiple necking instabilities. Disharmonic crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonic crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged history of extension prior to continental breakup.
The nonlinear Dirac equation and the study of effective many-particle interactions in QED
Ionescu, D.C.
1987-12-01
The starting point of the discussion was extended Lagrangian density for the classical Dirac field. The considered additional terms we had thereby interpreted as effective interactions because the corresponding field theory was not renormalizable. A scalar coupling as well as a vectorial coupling were put into calculation. The equation of motion for the system was thereby a one-particle equation which separated for s 1/2 and p 1/2 states and led to a system of coupled differential equations for the radial part. The derived radial equations were studied on three different levels. First we considered ordinary systems from atomic physics with ordinal numbers Z ≤ 110 in order to obtain from precision experiments of quantum electrodynamics upper bounds for the coupling constants. Second we have studied the influence of these additional interactions on the energy levels of the superheavy systems with ordinal numbers 110 ≤ Z ≤ 190. Third we have searched for bound states of a nonlinear Dirac equation which should exist only because of the effective interaction. In the further study we have then changed to a field-quantized consideration because our hitherto analysis was purely classical. In this connection we have studied the (e + e - ) 2 system with a (anti ΨΓΨ) 2 interaction. From the corresponding many-particle equation we have then by means of the Hartree-Fock method derived the one-particle equation of the system. Finally we had studied the electron-positron interaction by exchange of a massive intermediate vector boson. (orig./HSI) [de
Stability, diffusion and interactions of nonlinear excitations in a many body system
Coste, Christophe; Jean, Michel Saint; Dessup, Tommy
2017-04-01
When repelling particles are confined in a quasi-one-dimensional trap by a transverse potential, a configurational phase transition happens. All particles are aligned along the trap axis at large confinement, but below a critical transverse confinement they adopt a staggered row configuration (zigzag phase). This zigzag transition is a subcritical pitchfork bifurcation in extended systems and in systems with cyclic boundary conditions in the longitudinal direction. Among many evidences, phase coexistence is exhibited by localized nonlinear patterns made of a zigzag phase embedded in otherwise aligned particles. We give the normal form at the bifurcation and we show that these patterns can be described as solitary wave envelopes that we call bubbles. They are stable in a large temperature range and can diffuse as quasi-particles, with a diffusion coefficient that may be deduced from the normal form. The potential energy of a bubble is found to be lower than that of the homogeneous bifurcated phase, which explains their stability. We observe also metastable states, that are pairs of solitary wave envelopes which spontaneously evolve toward a stable single bubble. We evidence a strong effect of the discreteness of the underlying particles system and introduce the concept of topological frustration of a bubble pair. A configuration is frustrated when the particles between the two bubbles are not organized in a modulated staggered row. For a nonfrustrated (NF) bubble pair configuration, the bubbles interaction is attractive so that the bubbles come closer and eventually merge as a single bubble. In contrast, the bubbles interaction is found to be repulsive for a frustrated (F) configuration. We describe a model of interacting solitary wave that provides all qualitative characteristics of the interaction force: it is attractive for NF-systems, repulsive for F-systems, and decreases exponentially with the bubbles distance.
Blumenthal, Nils R; Hermanson, Ola; Heimrich, Bernd; Shastri, V Prasad
2014-11-11
Extracellular soluble signals are known to play a critical role in maintaining neuronal function and homeostasis in the CNS. However, the CNS is also composed of extracellular matrix macromolecules and glia support cells, and the contribution of the physical attributes of these components in maintenance and regulation of neuronal function is not well understood. Because these components possess well-defined topography, we theorize a role for topography in neuronal development and we demonstrate that survival and function of hippocampal neurons and differentiation of telencephalic neural stem cells is modulated by nanoroughness. At roughnesses corresponding to that of healthy astrocytes, hippocampal neurons dissociated and survived independent from astrocytes and showed superior functional traits (increased polarity and calcium flux). Furthermore, telencephalic neural stem cells differentiated into neurons even under exogenous signals that favor astrocytic differentiation. The decoupling of neurons from astrocytes seemed to be triggered by changes to astrocyte apical-surface topography in response to nanoroughness. Blocking signaling through mechanosensing cation channels using GsMTx4 negated the ability of neurons to sense the nanoroughness and promoted decoupling of neurons from astrocytes, thus providing direct evidence for the role of nanotopography in neuron-astrocyte interactions. We extrapolate the role of topography to neurodegenerative conditions and show that regions of amyloid plaque buildup in brain tissue of Alzheimer's patients are accompanied by detrimental changes in tissue roughness. These findings suggest a role for astrocyte and ECM-induced topographical changes in neuronal pathologies and provide new insights for developing therapeutic targets and engineering of neural biomaterials.
Plastino, A. R.; Curado, E. M. F.; Nobre, F. D.; Tsallis, C.
2018-02-01
Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q -Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.
Separable quadratic stochastic operators
Rozikov, U.A.; Nazir, S.
2009-04-01
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)
Hueffel, H.
1990-01-01
After a brief review of the BRST formalism and of the Parisi-Wu stochastic quantization method we introduce the BRST stochastic quantization scheme. It allows the second quantization of constrained Hamiltonian systems in a manifestly gauge symmetry preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed by a discussion on the interacting field theory associated to the relativistic point particle system. 58 refs. (Author)
Neurosurgery simulation using non-linear finite element modeling and haptic interaction
Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet
2012-02-01
Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.
Nonlinear seismic soil-structure interaction analysis of nuclear power plant structures
Khanna, J.K.; Setlur, A.V.; Pathak, D.V.
1977-01-01
The heterogeneous and nonlinear soil medium and the detailed three-dimensional structure are synthesized to determine the seismic response to soil-structure systems. The approach is particularly attractive in a design office environment since it: a) leads to interactive motion at the soil-structure interface; b) uses existing public domain programs such as SAPIV, LUSH and FLUSH with marginal modifications; and c) meets current regulatory requirements for soil-structure interaction analysis. Past methods differ from each other depending on the approach adopted for soil and structure representations and procedures for solving the governing differential equations. Advantages and limitations of these methods are reviewed. In the current approach, the three-dimensional structure is represented by the dynamic characteristics of its fixed base condition. This representation is ideal when structures are designed to be within elastic range. An important criterion is the design of the nuclear power plant structures. Model damping coefficients are varied to reflect the damping properties of different structural component materials. The detailed structural model is systematically reduced to reflect important dynamic behavior with simultaneous storing of intermediate information for retrieval of detailed structural response. Validity of the approach has been established with simple numerical experiments. (Auth.)
Nonlinear interaction of a parallel-flow relativistic electron beam with a plasma
Jungwirth, K.; Koerbel, S.; Simon, P.; Vrba, P.
1975-01-01
Nonlinear evolution of single-mode high-frequency instabilities (ω approximately ksub(parallel)vsub(b)) excited by a parallel-flow high-current relativistic electron beam in a magnetized plasma is investigated. Fairly general dimensionless equations are derived. They describe both the temporal and the spatial evolution of amplitude and phase of the fundamental wave. Numerically, the special case of excitation of the linearly most unstable mode is solved in detail assuming that the wave energy dissipation is negligible. Then the strength of interaction and the relativistic properties of the beam are fully respected by a single parameter lambda. The value of lambda ensuring the optimum efficiency of the wave excitation as well as the efficiency of the self-acceleration of some beam electrons at higher values of lambda>1 are determined in the case of a fully compensated relativistic beam. Finally, the effect of the return current dissipation is also included (phenomenologically) into the theoretical model, its role for the beam-plasma interaction being checked numerically. (J.U.)
Chaos and Structures in Nonlinear Plasmas
Chen, James
In recent decades, the concepts and applications of chaos, complexity, and nonlinear dynamics have profoundly influenced scientific as well as literary thinking. Some aspects of these concepts are used in almost all of the geophysical disciplines. Chaos and Structures in Nonlinear Plasmas, written by two respected plasma physicists, focuses on nonlinear phenomena in laboratory and space plasmas, which are rich in nonlinear and complex collective effects. Chaos is treated only insofar as it relates to some aspects of nonlinear plasma physics.At the outset, the authors note that plasma physics research has made fundamental contributions to modern nonlinear sciences. For example, the Poincare surface of section technique was extensively used in studies of stochastic field lines in magnetically confined plasmas and turbulence. More generally, nonlinearity in plasma waves and wave-wave and wave-particle interactions critically determines the propagation of energy through a plasma medium. The book also makes it clear that the importance of understanding nonlinear waves goes beyond plasma physics, extending to such diverse fields as solid state physics, fluid dynamics, atmospheric physics, and optics. In space physics, non-linear plasma physics is essential for interpreting in situ as well as remote-sensing data.
Steffen, T; Tanimura, Y
The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by
Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.
2018-04-01
Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.
Stochastic Analysis and Related Topics
Ustunel, Ali
1988-01-01
The Silvri Workshop was divided into a short summer school and a working conference, producing lectures and research papers on recent developments in stochastic analysis on Wiener space. The topics treated in the lectures relate to the Malliavin calculus, the Skorohod integral and nonlinear functionals of white noise. Most of the research papers are applications of these subjects. This volume addresses researchers and graduate students in stochastic processes and theoretical physics.
Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit
Balsa, Thomas F.; Gartside, James
1995-01-01
The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.
Stochasticity in the Josephson map
Nomura, Y.; Ichikawa, Y.H.; Filippov, A.T.
1996-04-01
The Josephson map describes nonlinear dynamics of systems characterized by standard map with the uniform external bias superposed. The intricate structures of the phase space portrait of the Josephson map are examined on the basis of the tangent map associated with the Josephson map. Numerical observation of the stochastic diffusion in the Josephson map is examined in comparison with the renormalized diffusion coefficient calculated by the method of characteristic function. The global stochasticity of the Josephson map occurs at the values of far smaller stochastic parameter than the case of the standard map. (author)
Kennedy, R.P.; Short, S.A.; Wesley, D.A.; Lee, T.H.
1975-01-01
The importance of the nonlinear soil-structure interaction effects resulting from substantial base slab uplift occurring during a seismic excitation are evaluated. The structure considered consisted of the containment building and prestressed concrete reactor vessel for a typical HTGR plant. A simplified dynamic mathematical model was utilized consisting of a conventional lumped mass structure with soil-structure interaction accounted for by translational and rotational springs whose properties are determined by elastic half space theory. Three different site soil conditions (a rock site, a moderately stiff soil and a soft soil site) and two levels of horizontal ground motion (0.3g and 0.5g earthquakes) were considered. It may be concluded that linear analysis can be used to conservatively estimate the important behavior of the base slab, even under conditions of substantial base slab uplift. For all cases investigated, linear analysis resulted in higher base overturning moments, greater toe pressures, and greater heel uplift distances than nonlinear analyses. It may also be concluded that the nonlinear effect of uplift does not result in any significant lengthening of the fundamental period of the structure. Also, except in the short period region only negligible differences exist between instructure response spectra based on linear analysis and those based on nonlinear analysis. Finally, for sites in which soil-structure interaction is not significant, as for the rock site, the peak structural response at all locations above the base mat are not significantly influenced by the nonlinear effects of base slab uplift. However, for the two soil sites, the peak shears and moments are, in a few instances, significantly different between linear and nonlinear analyses
Wang Lei; Zhu Yujie; Wang Ziqi; Xu Tao; Qi Fenghua; Xue Yushan
2016-01-01
We study the nonlinear localized waves on constant backgrounds of the Hirota–Maxwell–Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons. (author)
Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan
2016-02-01
We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.
Woldeyesus, Tibebe Argaw
Water supply constraints can significantly restrict electric power generation, and such constraints are expected to worsen with future climate change. The overarching goal of this thesis is to incorporate stochastic water-climate interactions into electricity portfolio models and evaluate various pathways for water savings in co-managed water-electric utilities. Colorado Springs Utilities (CSU) is used as a case study to explore the above issues. The thesis consists of three objectives: Characterize seasonality of water withdrawal intensity factors (WWIF) for electric power generation and develop a risk assessment framework due to water shortages; Incorporate water constraints into electricity portfolio models and evaluate the impact of varying capital investments (both power generation and cooling technologies) on water use and greenhouse gas emissions; Compare the unit cost and overall water savings from both water and electric sectors in co-managed utilities to facilitate overall water management. This thesis provided the first discovery and characterization of seasonality of WWIF with distinct summertime and wintertime variations of +/-17% compared to the power plant average (0.64gal/kwh) which itself is found to be significantly higher than the literature average (0.53gal/kwh). Both the streamflow and WWIF are found to be highly correlated with monthly average temperature (r-sq = 89%) and monthly precipitation (r-sq of 38%) enabling stochastic simulation of future WWIF under moderate climate change scenario. Future risk to electric power generation also showed the risk to be underestimated significantly when using either the literature average or the power plant average WWIF. Seasonal variation in WWIF along with seasonality in streamflow, electricity demand and other municipal water demands along with storage are shown to be important factors for more realistic risk estimation. The unlimited investment in power generation and/or cooling technologies is also
Wellens, Thomas; Shatokhin, Vyacheslav; Buchleitner, Andreas
2004-01-01
We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes. At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems-an issue that has received limited attention in earlier review papers on the topic. The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise
Stochastic inflation in phase space: is slow roll a stochastic attractor?
Grain, Julien [Institut d' Astrophysique Spatiale, UMR8617, CNRS, Univ. Paris Sud, Université Paris-Saclay, Bt. 121, Orsay, F-91405 (France); Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO13FX (United Kingdom)
2017-05-01
An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.
Seismic induced nonlinear rotor-bearing-casing interaction of rotating nuclear components
Choy, F.K.; Padovan, J.; Li, W.H.
1989-01-01
The study of the dynamics of turbomachinery during seismic events has been of continuous interest to both researchers and designers of large rotating equipment. Failure in such equipment, especially those associated with nuclear power generation, can lead to catastrophic consequences. Hence, there is a general trend for corporations to overdesign the equipment without any indepth understanding of the dynamical performance of the machine under extreme operating conditions. The overall objective of this paper are fourfold, namely: (1) To study the nonlinear dynamics of rotor-bearing casing system during rub interactions; (2) To examine the effects of suddenly induced imbalance and base motion in the global dynamical behavior of the system; (3) To develop engineering insights through the modal parameters in both time and frequency domain; (4) To generate signature analysis on rub forces for pattern recognition. These goals are achieved through the development of a modal impact model. Accuracy and efficiency of this transient model are maintained using a self-adaptive integration scheme
Schmitt, Michael
2004-09-01
We study networks of spiking neurons that use the timing of pulses to encode information. Nonlinear interactions model the spatial groupings of synapses on the neural dendrites and describe the computations performed at local branches. Within a theoretical framework of learning we analyze the question of how many training examples these networks must receive to be able to generalize well. Bounds for this sample complexity of learning can be obtained in terms of a combinatorial parameter known as the pseudodimension. This dimension characterizes the computational richness of a neural network and is given in terms of the number of network parameters. Two types of feedforward architectures are considered: constant-depth networks and networks of unconstrained depth. We derive asymptotically tight bounds for each of these network types. Constant depth networks are shown to have an almost linear pseudodimension, whereas the pseudodimension of general networks is quadratic. Networks of spiking neurons that use temporal coding are becoming increasingly more important in practical tasks such as computer vision, speech recognition, and motor control. The question of how well these networks generalize from a given set of training examples is a central issue for their successful application as adaptive systems. The results show that, although coding and computation in these networks is quite different and in many cases more powerful, their generalization capabilities are at least as good as those of traditional neural network models.
Nagatomo, Makoto; Kaya, Nobuyuki; Matsumoto, Hiroshi
The Microwave Ionosphere Nonlinear Interaction Experiment (MINIX) is a sounding rocket experiment to study possible effects of strong microwave fields in case it is used for energy transmission from the Solar Power Satellite (SPS) upon the Earth's atmosphere. Its secondary objective is to develop high power microwave technology for space use. Two rocket-borne magnetrons were used to emit 2.45 GHz microwave in order to make a simulated condition of power transmission from an SPS to a ground station. Sounding of the environment radiated by microwave was conducted by the diagnostic package onboard the daughter unit which was separated slowly from the mother unit. The main design drivers of this experiment were to build such high power equipments in a standard type of sounding rocket, to keep the cost within the budget and to perform a series of experiments without complete loss of the mission. The key technology for this experiment is a rocket-borne magnetron and high voltage converter. Location of position of the daughter unit relative to the mother unit was a difficult requirement for a spin-stabilized rocket. These problems were solved by application of such a low cost commercial products as a magnetron for microwave oven and a video tape recorder and camera.
Nonlinear collisionless electron cyclotron interaction in the pre-ionisation stage
Farina, D.
2018-06-01
Electron cyclotron (EC) wave-particle interaction is theoretically investigated in the pre-ionisation phase, much before collisions and other mechanisms can play a role. In the very first phase of a plasma discharge with EC-assisted breakdown, the motion of an electron at room temperature in a static magnetic field under the action of a localised microwave beam is nonlinear, and transition to states of larger energy can occur via wave trapping. Within a Hamiltonian adiabatic formalism, the conditions at which the particles gain energy in single beam crossing are derived in a rigorous way, and the energy variation is characterized quantitatively as a function of the wave frequency, harmonic number, polarisation and EC power and beam width. Estimates of interest for applications to tokamak start-up are obtained for the first, second and third cyclotron harmonic. The investigation confirms that electrons can easily gain energies well above the ionisation energy in most conditions at the first two harmonics, while not at the third harmonic, as observed in experiments.
Vučićević, Katarina; Jovanović, Marija; Golubović, Bojana; Kovačević, Sandra Vezmar; Miljković, Branislava; Martinović, Žarko; Prostran, Milica
2015-02-01
The present study aimed to establish population pharmacokinetic model for phenobarbital (PB), examining and quantifying the magnitude of PB interactions with other antiepileptic drugs concomitantly used and to demonstrate its use for individualization of PB dosing regimen in adult epileptic patients. In total 205 PB concentrations were obtained during routine clinical monitoring of 136 adult epilepsy patients. PB steady state concentrations were measured by homogeneous enzyme immunoassay. Nonlinear mixed effects modelling (NONMEM) was applied for data analyses and evaluation of the final model. According to the final population model, significant determinant of apparent PB clearance (CL/F) was daily dose of concomitantly given valproic acid (VPA). Typical value of PB CL/F for final model was estimated at 0.314 l/h. Based on the final model, co-therapy with usual VPA dose of 1000 mg/day, resulted in PB CL/F average decrease of about 25 %, while 2000 mg/day leads to an average 50 % decrease in PB CL/F. Developed population PB model may be used in estimating individual CL/F for adult epileptic patients and could be applied for individualizing dosing regimen taking into account dose-dependent effect of concomitantly given VPA.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
Foroutan, Mohammadreza; Zamanpour, Isa; Manafian, Jalil
2017-10-01
This paper presents a number of new solutions obtained for solving a complex nonlinear equation describing dynamics of nonlinear chains of atoms via the improved Bernoulli sub-ODE method (IBSOM) and the extended trial equation method (ETEM). The proposed solutions are kink solitons, anti-kink solitons, soliton solutions, hyperbolic solutions, trigonometric solutions, and bellshaped soliton solutions. Then our new results are compared with the well-known results. The methods used here are very simple and succinct and can be also applied to other nonlinear models. The balance number of these methods is not constant contrary to other methods. The proposed methods also allow us to establish many new types of exact solutions. By utilizing the Maple software package, we show that all obtained solutions satisfy the conditions of the studied model. More importantly, the solutions found in this work can have significant applications in Hamilton's equations and generalized momentum where solitons are used for long-range interactions.
Sequential neural models with stochastic layers
Fraccaro, Marco; Sønderby, Søren Kaae; Paquet, Ulrich
2016-01-01
How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural...... generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over...
Builes-Jaramillo, Alejandro; Marwan, Norbert; Poveda, Germán; Kurths, Jürgen
2018-04-01
We study the physical processes involved in the potential influence of Amazon (AM) hydroclimatology over the Tropical North Atlantic (TNA) Sea Surface Temperatures (SST) at interannual timescales, by analyzing time series of the precipitation index (P-E) over AM, as well as the surface atmospheric pressure gradient between both regions, and TNA SSTs. We use a recurrence joint probability based analysis that accounts for the lagged nonlinear dependency between time series, which also allows quantifying the statistical significance, based on a twin surrogates technique of the recurrence analysis. By means of such nonlinear dependence analysis we find that at interannual timescales AM hydrology influences future states of the TNA SSTs from 0 to 2 months later with a 90-95% statistical confidence. It also unveils the existence of two-way feedback mechanisms between the variables involved in the processes: (1) precipitation over AM leads the atmospheric pressure gradient between TNA and AM from 0 to 2 month lags, (2) the pressure gradient leads the trade zonal winds over the TNA from 0 to 3 months and from 7 to 12 months, (3) the zonal winds lead the SSTs from 0 to 3 months, and (4) the SSTs lead precipitation over AM by 1 month lag. The analyses were made for time series spanning from 1979 to 2008, and for extreme precipitation events in the AM during the years 1999, 2005, 2009 and 2010. We also evaluated the monthly mean conditions of the relevant variables during the extreme AM droughts of 1963, 1980, 1983, 1997, 1998, 2005, and 2010, and also during the floods of 1989, 1999, and 2009. Our results confirm that the Amazon River basin acts as a land surface-atmosphere bridge that links the Tropical Pacific and TNA SSTs at interannual timescales. The identified mutual interactions between TNA and AM are of paramount importance for a deeper understanding of AM hydroclimatology but also of a suite of oceanic and atmospheric phenomena over the TNA, including recently
Petrila, Iulian; Bodale, Ilie; Rotarescu, Cristian; Stancu, Alexandru
2011-01-01
A comparative analysis between linear and non-linear energy barriers used for modeling statistical thermally-excited ferromagnetic systems is presented. The linear energy barrier is obtained by new symmetry considerations about the anisotropy energy and the link with the non-linear energy barrier is also presented. For a relevant analysis we compare the effects of linear and non-linear energy barriers implemented in two different models: Preisach-Neel and Ising-Metropolis. The differences between energy barriers which are reflected in different coercive field dependence of the temperature are also presented. -- Highlights: → The linear energy barrier is obtained from symmetry considerations. → The linear and non-linear energy barriers are calibrated and implemented in Preisach-Neel and Ising-Metropolis models. → The temperature and time effects of the linear and non-linear energy barriers are analyzed.
Stochasticity and transport in Hamiltonian systems
MacKay, R.S.; Meiss, J.D.; Percival, I.C.
1983-08-01
The theory of transport in nonlinear dynamics is developed in terms of leaky barriers which remain when invariant tori are destroyed. We describe the organization of stochastic motion by these barriers and give an explanation of long-time correlations in the stochastic regime
Noise-sustained fluctuations in stochastic dynamics with a delay.
D'Odorico, Paolo; Laio, Francesco; Ridolfi, Luca
2012-04-01
Delayed responses to external drivers are ubiquitous in environmental, social, and biological processes. Delays may induce oscillations, Hopf bifurcations, and instabilities in deterministic systems even in the absence of nonlinearities. Despite recent advances in the study of delayed stochastic differential equations, the interaction of random drivers with delays remains poorly understood. In particular, it is unclear whether noise-induced behaviors may emerge from these interactions. Here we show that noise may enhance and sustain transient periodic oscillations inherent to deterministic delayed systems. We investigate the conditions conducive to the emergence and disappearance of these dynamics in a linear system in the presence of both additive and multiplicative noise.
Raghavan, S.
1997-06-01
We extend our analysis of the effects of the interplay of quantum phases and nonlinearity to address saturation effects in small quantum systems. We find that initial phases dramatically control the dependence of self-trapping on initial asymmetry of quasiparticle population and can compete or act with nonlinearity as well as saturation effects. We find that there is a minimum finite saturation value in order to obtain self-trapping that crucially depends on the initial quasiparticle phases and present a detailed phase-diagram in terms of the control parameters of the system: nonlinearity and saturation. (author). 14 refs, 3 figs
Momentum Maps and Stochastic Clebsch Action Principles
Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.
2018-01-01
We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.
Neilson, Peter D; Neilson, Megan D
2005-09-01
Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.
Nonlinear wave-particle interaction upstream from the Earth's bow shock
C. Mazelle
2000-01-01
Full Text Available Well-defined ring-like backstreaming ion distributions have been recently reported from observations made by the 3DP/PESA-High analyzer onboard the WIND spacecraft in the Earth's foreshock at large distances from the bow shock, which suggests a local production mechanism. The maximum phase space density for these distributions remains localized at a nearly constant pitch-angle value for a large number of gyroperiods while the shape of the distribution remains very steady. These distributions are also observed in association with quasi-monochromatic low frequency (~ 50 mHz waves with substantial amplitude (δB/B>0.2. The analysis of the magnetic field data has shown that the waves are propagating parallel to the background field in the right-hand mode. Parallel ion beams are also often observed in the same region before the observation of both the ring-like distributions and the waves. The waves appear in cyclotron resonance with the ion parallel beams. We investigate first the possibility that the ion beams could provide the free energy source for driving an ion/ion instability responsible for the ULF wave occurrence. For that, we solve the wave dispersion relation with the observed parameters. Second, we show that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered on a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions are in good quantitative agreement with the observations
How useful is slow light in enhancing nonlinear interactions in lossy periodic nanostructures?
Saravi, Sina; Quintero-Bermudez, Rafael; Setzpfandt, Frank
2016-01-01
We investigate analytically, and with nonlinear simulations, the extent of usefulness of slow light for enhancing the efficiency of second harmonic generation in lossy nanostructures, and find that the slower is not always the better....
Ulku, Huseyin Arda; Sayed, Sadeed Bin; Bagci, Hakan
2014-01-01
solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation
Cantrell, John H., Jr.; Cantrell, Sean A.
2008-01-01
A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.
A nonsmooth nonlinear conjugate gradient method for interactive contact force problems
Silcowitz, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny
2010-01-01
of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...... and present experimental convergence behavior and properties of the new method. Our results show that the NNCG method has at least the same convergence rate as PGS, and in many cases better....
Parzen, Emanuel
1962-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution
Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi
2018-05-01
In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.
Intrinsic periodic and aperiodic stochastic resonance in an electrochemical cell
Tiwari, Ishant; Phogat, Richa; Parmananda, P.; Ocampo-Espindola, J. L.; Rivera, M.
2016-08-01
In this paper we show the interaction of a composite of a periodic or aperiodic signal and intrinsic electrochemical noise with the nonlinear dynamics of an electrochemical cell configured to study the corrosion of iron in an acidic media. The anodic voltage setpoint (V0) in the cell is chosen such that the anodic current (I ) exhibits excitable fixed point behavior in the absence of noise. The subthreshold periodic (aperiodic) signal consists of a train of rectangular pulses with a fixed amplitude and width, separated by regular (irregular) time intervals. The irregular time intervals chosen are of deterministic and stochastic origins. The amplitude of the intrinsic internal noise, regulated by the concentration of chloride ions, is then monotonically increased, and the provoked dynamics are analyzed. The signal to noise ratio and the cross-correlation coefficient versus the chloride ions' concentration curves have a unimodal shape indicating the emergence of an intrinsic periodic or aperiodic stochastic resonance. The abscissa for the maxima of these unimodal curves correspond to the optimum value of intrinsic noise where maximum regularity of the invoked dynamics is observed. In the particular case of the intrinsic periodic stochastic resonance, the scanning electron microscope images for the electrode metal surfaces are shown for certain values of chloride ions' concentrations. These images, qualitatively, corroborate the emergence of order as a result of the interaction between the nonlinear dynamics and the composite signal.
Liu, Zhaohong; Liu, Simin; Guo, Ru; Song, Tao; Zhu, Nan
2007-01-01
We study experimentally the interaction of a dark spot with a nonlinear photonic lattice with fully incoherent white light emitted from an incandescent bulb in the self-defocussing photovoltaic media when the dark spot is aimed at different positions of lattices with different lattice spacing. In this case a host of novel phenomena is demonstrated, including dark spot induced lattice dislocation-deformation, the annihilation of the dark spot and so on. Results demonstrate that the interaction between incoherent dark spot and photonic lattice is always attraction and the large-spacing photonic lattice is analogous to the continuous medium
Nonlinear interaction of infrared waves on a VO2 surface at a semiconductor-metal phase transition
Berger, N. K.; Zhukov, E. A.; Novokhatskii, V. V.
1984-04-01
Nonlinear interactions (including wavefront reversal) of light from CW or pulsed 10.6-micron CO2 lasers at the semiconductor-metal phase transition in a VO2 film are investigated experimentally. The results are presented in graphs and characterized in detail. The intensity reflection coefficients of the three-wave interactions are found to be 0.5 percent for a CW reference wave of intensity 900 mW/sq cm and 42 percent for a pulsed reference wave of threshold density 600-800 microjoule/sq cm.
Economic policy optimization based on both one stochastic model and the parametric control theory
Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit
2016-06-01
A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)
Solberg, Jerome M., E-mail: solberg2@llnl.gov [Methods Development Group, Lawrence Livermore Nat’l Lab, P.O. Box 808, Mailstop L-125, Livermore, CA 94550 (United States); Hossain, Quazi, E-mail: hossain1@llnl.gov [Structural and Applied Mechanics Group, Lawrence Livermore Nat’l Lab, P.O. Box 808, Mailstop L-129, Livermore, CA 94550 (United States); Mseis, George, E-mail: george.mseis@gmail.com [Structural and Applied Mechanics Group, Lawrence Livermore Nat’l Lab, P.O. Box 808, Mailstop L-129, Livermore, CA 94550 (United States)
2016-08-01
Highlights: • Derived modified version of Bielak’s SSI method for nonlinear time-domain analysis. • Utilized a Ramberg–Osgood material with parameters that can be fit to EPRI data. • Matched vertically propagating shear wave results from CARES. • Applied this technique to a representative SMR, compared well with SASSI. • The technique is extensible to other material models and nonlinear effects. - Abstract: A generalized time-domain method for soil–structure interaction analysis is developed, based upon an extension of the work of the domain reduction method of Bielak et al. The methodology is combined with the use of a simple hysteretic soil model based upon the Ramberg–Osgood formulation and applied to a notional Small Modular Reactor. These benchmark results compare well (with some caveats) with those obtained by using the industry-standard frequency-domain code SASSI. The methodology provides a path forward for investigation of other sources of nonlinearity, including those associated with the use of more physically-realistic material models incorporating pore-pressure effects, gap opening/closing, the effect of nonlinear structural elements, and 3D seismic inputs.
Laboratory Evidence for Stochastic Plasma-Wave Growth
Austin, D. R.; Hole, M. J.; Robinson, P. A.; Cairns, Iver H.; Dallaqua, R.
2007-01-01
The first laboratory confirmation of stochastic growth theory is reported. Floating potential fluctuations are measured in a vacuum arc centrifuge using a Langmuir probe. Statistical analysis of the energy density reveals a lognormal distribution over roughly 2 orders of magnitude, with a high-field nonlinear cutoff whose spatial dependence is consistent with the predicted eigenmode profile. These results are consistent with stochastic growth and nonlinear saturation of a spatially extended eigenmode, the first evidence for stochastic growth of an extended structure
Stochastic modelling of turbulence
Sørensen, Emil Hedevang Lohse
previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...
Nonlinearities in Behavioral Macroeconomics.
Gomes, Orlando
2017-07-01
This article undertakes a journey across the literature on behavioral macroeconomics, with attention concentrated on the nonlinearities that the behavioral approach typically suggests or implies. The emphasis is placed on thinking the macro economy as a living organism, composed of many interacting parts, each one having a will of its own, which is in sharp contrast with the mechanism of the orthodox view (well represented by the neoclassical or new Keynesian dynamic stochastic general equilibrium - DSGE - model). The paper advocates that a thorough understanding of individual behavior in collective contexts is the only possible avenue to further explore macroeconomic phenomena and the often observed 'anomalies' that the benchmark DSGE macro framework is unable to explain or justify. After a reflection on the role of behavioral traits as a fundamental component of a new way of thinking the economy, the article proceeds with a debate on some of the most relevant frameworks in the literature that somehow link macro behavior and nonlinearities; covered subjects include macro models with disequilibrium rules, agent-based models that highlight interaction and complexity, evolutionary switching frameworks, and inattention based decision problems. These subjects have, as a fundamental point in common, the use of behavioral elements to transform existing interpretations of the economic reality, making it more evident how irregular fluctuations emerge and unfold on the aggregate.
Klauder, J.R.
1983-01-01
The author provides an introductory survey to stochastic quantization in which he outlines this new approach for scalar fields, gauge fields, fermion fields, and condensed matter problems such as electrons in solids and the statistical mechanics of quantum spins. (Auth.)
Mann, Nishan Singh
Photonic crystal waveguides (PCWs) are nano-scale devices offering an exciting platform for exploring and exploiting enhanced linear and nonlinear light-matter interactions, aided in-part by slowing down the group velocity (vg) of on-chip photons. However, with potential applications in telecommunications, bio-sensing and quantum computing, the road to commercialization and practical devices is hindered by our limited understanding of the influence of structural disorder on linear and nonlinear light propagation. This thesis refines and develops state-of-the-art mathematical and numerical models for understanding the important role of disorder-related optical phenomena for PCWs in the linear and optical nonlinear regime. The importance of Bloch modes is demonstrated by computing the power loss caused by disorder-induced scattering for various dispersion engineered PCWs. The theoretical results are found to be in very good agreement with related experiments and it is shown how dispersion engineered designs can minimize the Bloch fields around spatial imperfections resulting in a radical departure from the usual assumed scaling vg. -2 of backscatteringlosses. We also conduct a systematic investigation of the influence of intra-hole correlation length, a parameter characterizing disorder on backscattering losses and find the loss behaviour to be qualitatively dependent on waveguide design and frequency. We then model disorder-induced resonance shifts to compute the ensemble averaged disordered density of states, accounting for important local field effects which are crucial in achieving good qualitative agreement with experiments. Lastly, motivated by emerging experiments examining enhanced nonlinear interactions, we develop an intuitive time dependent coupled mode formalism to derive propagation equations describing nonlinear pulse propagation in the presence of disorder-induced multiple scattering. The framework establishes a natural length scale for each physical
Andersson, P. B. U.; Kropp, W.
2008-11-01
Rolling resistance, traction, wear, excitation of vibrations, and noise generation are all attributes to consider in optimisation of the interaction between automotive tyres and wearing courses of roads. The key to understand and describe the interaction is to include a wide range of length scales in the description of the contact geometry. This means including scales on the order of micrometres that have been neglected in previous tyre/road interaction models. A time domain contact model for the tyre/road interaction that includes interfacial details is presented. The contact geometry is discretised into multiple elements forming pairs of matching points. The dynamic response of the tyre is calculated by convolving the contact forces with pre-calculated Green's functions. The smaller-length scales are included by using constitutive interfacial relations, i.e. by using nonlinear contact springs, for each pair of contact elements. The method is presented for normal (out-of-plane) contact and a method for assessing the stiffness of the nonlinear springs based on detailed geometry and elastic data of the tread is suggested. The governing equations of the nonlinear contact problem are solved with the Newton-Raphson iterative scheme. Relations between force, indentation, and contact stiffness are calculated for a single tread block in contact with a road surface. The calculated results have the same character as results from measurements found in literature. Comparison to traditional contact formulations shows that the effect of the small-scale roughness is large; the contact stiffness is only up to half of the stiffness that would result if contact is made over the whole element directly to the bulk of the tread. It is concluded that the suggested contact formulation is a suitable model to include more details of the contact interface. Further, the presented result for the tread block in contact with the road is a suitable input for a global tyre/road interaction model
Han, Jiu-Ning, E-mail: hanjiuning@126.com; Luo, Jun-Hua; Li, Jun-Xiu [Institute of Theoretical Physics and College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China); Li, Sheng-Chang [School of Science, Xi' an Jiaotong University, Xi' an 710049 (China); Liu, Shi-Wei; Yang, Yang; Duan, Wen-Shan; Han, Juan-Fang [Joint Laboratory of Atomic and Molecular Physics of NWNU and IMPCAS and College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070 (China)
2015-06-15
We study the basic physical properties of composite nonlinear structure induced by the head-on collision of magnetosonic solitons. Solitary waves are assumed to propagate in a quantum electron-ion magnetoplasma with spin-1/2 degenerate electrons. The main interest of the present work is to investigate the time evolution of the merged composite structure during a specific time interval of the wave interaction process. We consider three cases of colliding-situation, namely, compressive-rarefactive solitons interaction, compressive-compressive solitons interaction, and rarefactive-rarefactive solitons interaction, respectively. Compared with the last two colliding cases, the changing process of the composite structure is more complex for the first situation. Moreover, it is found that they are obviously different for the last two colliding cases.
Nonlinear dynamic of interaction of the relativistic electron beam with plasma
Dorofeenko, V.G.; Krasovitskii, V.B.; Osmolovsky, S.I.
1994-01-01
Quasi-transverse instability of thin relativistic electron beam in a dense plasma is studied numerically and analytically in a broad range of the frequency of the beam modulation and external longitudinal magnetic field. It is shown that the nonlinear stage of solution depends on the increment of the instability. It is permitted to classify possible nonlinear solutions and also to determine optimal regimes of the modulation for transport of beam along magnetic field in a plasma without substantial radial divergence. Numerical calculations show, that injection of the bunches with parameters, corresponding nonlinear regime of the beam's instability, in neutrally-charged plasma permits to output on the stationary regime without loss of particles
Stochastic pump effect and geometric phases in dissipative and stochastic systems
Sinitsyn, Nikolai [Los Alamos National Laboratory
2008-01-01
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
Nonlinear phenomena in the interaction of microwaves with the low-temperature argon plasma flux
Armand, N.A.; Lisitskaya, A.A.; Rogashkov, S.A.; Rogashkova, A.I.; Chmil', A.I.; Shustin, E.G.
1982-01-01
Theoretical and experimental investigations of nonlinear effects arising during the passing of SHF waves across an argon plasma jet flowing from an arc plasmatron have been carried on. It is shown that under conditions of the radiowave propagation through low temperature plasma moving across the direction of the wave propagation modes of both the wave self-focusing and its nonlinear asymmetrical refaction can be accomplished. The effect of the formation and propagation of the additional ionization region in a microwave flow initiated with plasma independently produced in the region of the maximum amplitude of the SHF field has been experimentally discovered [ru
2016 CIME Course on Nonlocal and Nonlinear Diffusions and Interactions : New Methods and Directions
Grillo, Gabriele
2017-01-01
Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.
Hosseini, Mahdi
Our ability to engineer quantum states of light and matter has significantly advanced over the past two decades, resulting in the production of both Gaussian and non-Gaussian optical states. The resulting tailored quantum states enable quantum technologies such as quantum optical communication, quantum sensing as well as quantum photonic computation. The strong nonlinear light-atom interaction is the key to deterministic quantum state preparation and quantum photonic processing. One route to enhancing the usually weak nonlinear light-atom interactions is to approach the regime of cavity quantum electrodynamics (cQED) interaction by means of high finesse optical resonators. I present results from the MIT experiment of large conditional cross-phase modulation between a signal photon, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. I also present a scheme to probabilistically change the amplitude and phase of a signal photon qubit to, in principle, arbitrary values by postselection on a control photon that has interacted with that state. Notably, small changes of the control photon polarization measurement basis by few degrees can substantially change the amplitude and phase of the signal state. Finally, I present our ongoing effort at Purdue to realize similar peculiar quantum phenomena at the single photon level on chip scale photonic systems.
AUTHOR|(CDS)2160109; Støvneng, Jon Andreas
2017-08-15
The performance of high-energy circular hadron colliders, as the Large Hadron Collider, is limited by beam-beam interactions. The strength of the beam-beam interactions will be higher after the upgrade to the High-Luminosity Large Hadron Collider, and also in the next generation of machines, as the Future Circular Hadron Collider. The strongly nonlinear force between the two opposing beams causes diverging Hamiltonians and drives resonances, which can lead to a reduction of the lifetime of the beams. The nonlinearity makes the effect of the force difficult to study analytically, even at first order. Numerical models are therefore needed to evaluate the overall effect of different configurations of the machines. For this thesis, a new code named CABIN (Cuda-Accelerated Beam-beam Interaction) has been developed to study the limitations caused by the impact of strong beam-beam interactions. In particular, the evolution of the beam emittance and beam intensity has been monitored to study the impact quantitatively...
STOCHASTIC ASSESSMENT OF NIGERIAN STOCHASTIC ...
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STOCHASTIC ASSESSMENT OF NIGERIAN WOOD FOR BRIDGE DECKS ... abandoned bridges with defects only in their decks in both rural and urban locations can be effectively .... which can be seen as the detection of rare physical.
Analysis of stochastic effects in Kaldor-type business cycle discrete model
Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna
2016-07-01
We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.
Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich
2011-01-01
A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hami...... is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.......A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...... the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions...
Stochastic approach to microphysics
Aron, J.C.
1987-01-01
The presently widespread idea of ''vacuum population'', together with the quantum concept of vacuum fluctuations leads to assume a random level below that of matter. This stochastic approach starts by a reminder of the author's previous work, first on the relation of diffusion laws with the foundations of microphysics, and then on hadron spectrum. Following the latter, a random quark model is advanced; it gives to quark pairs properties similar to those of a harmonic oscillator or an elastic string, imagined as an explanation to their asymptotic freedom and their confinement. The stochastic study of such interactions as electron-nucleon, jets in e/sup +/e/sup -/ collisions, or pp -> ..pi../sup 0/ + X, gives form factors closely consistent with experiment. The conclusion is an epistemological comment (complementarity between stochastic and quantum domains, E.P.R. paradox, etc...).
Giant nonlinear interaction between two optical beams via a quantum dot embedded in a photonic wire
Nguyen, H. A.; Grange, T.; Reznychenko, B.; Yeo, I.; de Assis, P.-L.; Tumanov, D.; Fratini, F.; Malik, N. S.; Dupuy, E.; Gregersen, N.; Auffèves, A.; Gérard, J.-M.; Claudon, J.; Poizat, J.-Ph.
2018-05-01
Optical nonlinearities usually appear for large intensities, but discrete transitions allow for giant nonlinearities operating at the single-photon level. This has been demonstrated in the last decade for a single optical mode with cold atomic gases, or single two-level systems coupled to light via a tailored photonic environment. Here, we demonstrate a two-mode giant nonlinearity with a single semiconductor quantum dot (QD) embedded in a photonic wire antenna. We exploit two detuned optical transitions associated with the exciton-biexciton QD level scheme. Owing to the broadband waveguide antenna, the two transitions are efficiently interfaced with two free-space laser beams. The reflection of one laser beam is then controlled by the other beam, with a threshold power as low as 10 photons per exciton lifetime (1.6 nW ). Such a two-color nonlinearity opens appealing perspectives for the realization of ultralow-power logical gates and optical quantum gates, and could also be implemented in an integrated photonic circuit based on planar waveguides.
Detection of interactions between myogenic and TGF mechanisms using nonlinear analysis
Chon, K H; Chen, Y M; Marmarelis, V Z
1994-01-01
for computation of the kernels have made this technique more attractive for the study of the dynamics of nonlinear physiological systems, such as the system mediating renal autoregulation. In this study, the general theory and requirements for using this technique are discussed. The feasibility of using...
Non-linear contributions to interactions in climate networks: sources, relevance, nonstationarity
Hlinka, Jaroslav; Hartman, David; Vejmelka, Martin; Paluš, Milan
2012-01-01
Roč. 14, - (2012), s. 14274 ISSN 1607-7962. [European Geosciences Union General Assembly 2012. 22.04.2012-27.04.2012, Vienna] R&D Projects: GA ČR GCP103/11/J068 Institutional support: RVO:67985807 Keywords : correlation * mutual information * test of nonlinearity * surrogate data * complex networks * climate network Subject RIV: BB - Applied Statistics, Operational Research
Giant nonlinear interaction between two optical beams via a quantum dot embedded in a photonic wire
Nguyen, H.A.; Grange, T.; Reznychenko, B.
2018-01-01
a tailored photonic environment. Here, we demonstrate a two-mode giant nonlinearity with a single semiconductor quantum dot (QD) embedded in a photonic wire antenna. We exploit two detuned optical transitions associated with the exciton-biexciton QD level scheme. Owing to the broadband waveguide antenna...
A direct approach to nonlinear shells with application to surface-substrate interactions
Šilhavý, Miroslav
2013-01-01
Roč. 1, č. 2 (2013), s. 211-232 ISSN 2326-7186 Institutional support: RVO:67985840 Keywords : thin films * nonlinear shells * surface geometry Subject RIV: BA - General Mathematics http://msp.org/memocs/2013/1-2/p04.xhtml
Guo, Yujin; Zeng, Xiaoyu; Zhou, Huan-Song
2018-01-01
We consider a nonlinear Schrödinger system arising in a two-component Bose-Einstein condensate (BEC) with attractive intraspecies interactions and repulsive interspecies interactions in R2. We get ground states of this system by solving a constrained minimization problem. For some kinds of trapping potentials, we prove that the minimization problem has a minimizer if and only if the attractive interaction strength ai (i = 1 , 2) of each component of the BEC system is strictly less than a threshold a*. Furthermore, as (a1 ,a2) ↗ (a* ,a*), the asymptotical behavior for the minimizers of the minimization problem is discussed. Our results show that each component of the BEC system concentrates at a global minimum of the associated trapping potential.
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...
Eslami, Sohrab; Jalili, Nader
2012-01-01
Precise and accurate representation of an Atomic Force Microscopy (AFM) system is essential in studying the effects of boundary interaction forces present between the probe's tip and the sample. In this paper, a comprehensive analytical model for the AFM system utilizing a distributed-parameters based approach is proposed. More specifically, we consider two important attributes of these systems; namely the rotary inertia and shear deformation when compared with the Euler–Bernoulli beam theory. Moreover, a comprehensive nonlinear interaction force is assumed between probe's and sample in order to reveal the response of the system more realistically. This nanoscale interaction force is based on a general form consisting of both attractive and repulsive components as well as a function of the tip-sample distance and the microcantilever's base and sample oscillations. Mechanical properties of the sample could interact with the nanomechanical coupling field between the probe' tip and sample and be implemented in studying the composition information of the sample and the ultra-small features inside it. Therefore, by modulating the dynamics of the AFM system such as the driving amplitude of the microcantilever the procedure for the subsurface imaging is described. The presented approach here could be implemented for designing the AFM probes by examining the tip-sample interaction forces dominant by the van der Waals forces. Several numerical case studies are presented and the force–distance diagram reveals that the proposed nonlinear nanomechanical force along with the distributed-parameters model for the microcantilever is able to fulfill the mechanics of the Lennard–Jones potential. -- Highlights: ► We present a comprehensive distributed-parameters model for AFM microcantilever. ► Assuming a nonlinear and implicit interaction force between tip and sample. ► Timoshenko beam is compared with the Euler–Bernoulli having the same force model. ► Frequency
Aihara, S.; Atsumi, K.; Ujiie, K.; Emori, K.; Odajima, M.; Masuda, K.
1983-01-01
The objective of this paper is to evaluate the nonlinear soil-structure interaction effects resulting from base mat uplift for static lateral loads. Nonlinear soil-structure interaction effects are modeled through the use of equivalent soil-structure interaction frictional and axial springs, which properties are determined by results of experimental data. It is assumed that normal stresses in compression and corresponding shear stresses, and friction, can occur in the area of contact between the embedded structure and soil. The remaining parts of the structure and soil are based on elastic analysis. A two-dimensional finite element method with incremental loadings is applied. The substructuring technique is used to reduce computation time. The results of this method with respect to the contact ratio of the base mat are compared with the values obtained by static elastic calculation which is simply derived from an overturning moment and a vertical load of the structure. This analytical concept will be developed into dynamic problems, and then it will be possible to state whether or not this concept can represent a true alternative for the contact ratio of the base mat of a structure. (orig./HP)
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Variance decomposition in stochastic simulators.
Le Maître, O P; Knio, O M; Moraes, A
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maître, O. P., E-mail: olm@limsi.fr [LIMSI-CNRS, UPR 3251, Orsay (France); Knio, O. M., E-mail: knio@duke.edu [Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708 (United States); Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa [King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maî tre, O. P.; Knio, O. M.; Moraes, Alvaro
2015-01-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
On an aggregation in birth-and-death stochastic dynamics
Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena
2014-06-01
We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation.
On an aggregation in birth-and-death stochastic dynamics
Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena
2014-01-01
We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation. (paper)
Kaya, N. (Kobe University, Kobe, Japan); Tsutsui, M. (Kyoto University, Uji, Japan); Matsumoto, H. (Kyoto University, Kyoto, Japan)
1980-09-01
A pre-flight test experiment of a microwave-ionosphere nonlinear interaction rocket experiment (MINIX) has been carried out in a space plasma simulation chamber. Though the first rocket experiment ended up in failure because of a high voltage trouble, interesting results are observed in the pre-flight experiment. A significant microwave heating of plasma up to 300% temperature increase is observed. Strong excitations of plasma waves by the transmitted microwaves in the VLF and HF range are observed as well. These microwave effects may have to be taken into account in solar power satellite projects in the future.
Khadzhi, P. I.; Lyakhomskaya, K. D.; Nadkin, L. Y.; Markov, D. A.
2002-05-01
The characteristic peculiarities of the self-reflection of a strong electromagnetic wave in a system of coherent excitons and biexcitons due to the exciton-photon interaction and optical exciton-biexciton conversion in semiconductors were investigated as one of the manifestations of nonlinear optical Stark-effect. It was found that a monotonously decreasing standing wave with an exponential decreasing spatial tail is formed in the semiconductor. Under the action of the field of a strong pulse, an optically homogeneous medium is converted, into the medium with distributed feedback. The appearance of the spatially separated narrow pears of the reflective index, extinction and reflection coefficients is predicted.