WorldWideScience

Sample records for equations dynamical systems

  1. Introduction to differential equations with dynamical systems

    CERN Document Server

    Campbell, Stephen L

    2011-01-01

    Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.

  2. Systems of quasilinear equations and their applications to gas dynamics

    CERN Document Server

    Roždestvenskiĭ, B L; Schulenberger, J R

    1983-01-01

    This book is essentially a new edition, revised and augmented by results of the last decade, of the work of the same title published in 1968 by "Nauka." It is devoted to mathematical questions of gas dynamics. Topics covered include Foundations of the Theory of Systems of Quasilinear Equations of Hyperbolic Type in Two Independent Variables; Classical and Generalized Solutions of One-Dimensional Gas Dynamics; Difference Methods for Solving the Equations of Gas Dynamics; and Generalized Solutions of Systems of Quasilinear Equations of Hyperbolic Type.

  3. Using Difference Equation to Model Discrete-time Behavior in System Dynamics Modeling

    NARCIS (Netherlands)

    Hesan, R.; Ghorbani, A.; Dignum, M.V.

    2014-01-01

    In system dynamics modeling, differential equations have been used as the basic mathematical operator. Using difference equation to build system dynamics models instead of differential equation, can be insightful for studying small organizations or systems with micro behavior. In this paper we

  4. Differential equations a dynamical systems approach ordinary differential equations

    CERN Document Server

    Hubbard, John H

    1991-01-01

    This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.

  5. The Mathlet Toolkit: Creating Dynamic Applets for Differential Equations and Dynamical Systems

    Science.gov (United States)

    Decker, Robert

    2011-01-01

    Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and…

  6. Differential equations, dynamical systems, and an introduction to chaos

    CERN Document Server

    Smale, Stephen; Devaney, Robert L

    2003-01-01

    Thirty years in the making, this revised text by three of the world''s leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field''s Medal for his work in dynamical systems.* Developed by award-winning researchers and authors* Provides a rigorous yet accessible introduction to differential equations and dynamical systems* Includes bifurcation theory throughout* Contains numerous explorations for students to embark uponNEW IN THIS EDITION* New contemporary material and updated applications* Revisions throughout the text, including simplification...

  7. An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part Two: Multibody Systems

    Directory of Open Access Journals (Sweden)

    Pål Johan From

    2012-04-01

    Full Text Available This paper presents the explicit dynamic equations of multibody mechanical systems. This is the second paper on this topic. In the first paper the dynamics of a single rigid body from the Boltzmann--Hamel equations were derived. In this paper these results are extended to also include multibody systems. We show that when quasi-velocities are used, the part of the dynamic equations that appear from the partial derivatives of the system kinematics are identical to the single rigid body case, but in addition we get terms that come from the partial derivatives of the inertia matrix, which are not present in the single rigid body case. We present for the first time the complete and correct derivation of multibody systems based on the Boltzmann--Hamel formulation of the dynamics in Lagrangian form where local position and velocity variables are used in the derivation to obtain the singularity-free dynamic equations. The final equations are written in global variables for both position and velocity. The main motivation of these papers is to allow practitioners not familiar with differential geometry to implement the dynamic equations of rigid bodies without the presence of singularities. Presenting the explicit dynamic equations also allows for more insight into the dynamic structure of the system. Another motivation is to correct some errors commonly found in the literature. Unfortunately, the formulation of the Boltzmann-Hamel equations used here are presented incorrectly. This has been corrected by the authors, but we present here, for the first time, the detailed mathematical details on how to arrive at the correct equations. We also show through examples that using the equations presented here, the dynamics of a single rigid body is reduced to the standard equations on a Lagrangian form, for example Euler's equations for rotational motion and Euler--Lagrange equations for free motion.

  8. Coupled replicator equations for the dynamics of learning in multiagent systems

    Science.gov (United States)

    Sato, Yuzuru; Crutchfield, James P.

    2003-01-01

    Starting with a group of reinforcement-learning agents we derive coupled replicator equations that describe the dynamics of collective learning in multiagent systems. We show that, although agents model their environment in a self-interested way without sharing knowledge, a game dynamics emerges naturally through environment-mediated interactions. An application to rock-scissors-paper game interactions shows that the collective learning dynamics exhibits a diversity of competitive and cooperative behaviors. These include quasiperiodicity, stable limit cycles, intermittency, and deterministic chaos—behaviors that should be expected in heterogeneous multiagent systems described by the general replicator equations we derive.

  9. Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

    Science.gov (United States)

    Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

    2016-04-12

    Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

  10. Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

    International Nuclear Information System (INIS)

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

    The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

  11. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  12. Dynamics of partial differential equations

    CERN Document Server

    Wayne, C Eugene

    2015-01-01

    This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation.   The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...

  13. Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual

    Science.gov (United States)

    Peng, NaiFu; Guan, Hui; Wu, ChuiJie

    2016-04-01

    In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.

  14. Quasi-gas dynamic equations

    CERN Document Server

    Elizarova, Tatiana G

    2009-01-01

    This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.

  15. Equation-free model reduction for complex dynamical systems

    International Nuclear Information System (INIS)

    Le Maitre, O. P.; Mathelin, L.; Le Maitre, O. P.

    2010-01-01

    This paper presents a reduced model strategy for simulation of complex physical systems. A classical reduced basis is first constructed relying on proper orthogonal decomposition of the system. Then, unlike the alternative approaches, such as Galerkin projection schemes for instance, an equation-free reduced model is constructed. It consists in the determination of an explicit transformation, or mapping, for the evolution over a coarse time-step of the projection coefficients of the system state on the reduced basis. The mapping is expressed as an explicit polynomial transformation of the projection coefficients and is computed once and for all in a pre-processing stage using the detailed model equation of the system. The reduced system can then be advanced in time by successive applications of the mapping. The CPU cost of the method lies essentially in the mapping approximation which is performed offline, in a parallel fashion, and only once. Subsequent application of the mapping to perform a time-integration is carried out at a low cost thanks to its explicit character. Application of the method is considered for the 2-D flow around a circular cylinder. We investigate the effectiveness of the reduced model in rendering the dynamics for both asymptotic state and transient stages. It is shown that the method leads to a stable and accurate time-integration for only a fraction of the cost of a detailed simulation, provided that the mapping is properly approximated and the reduced basis remains relevant for the dynamics investigated. (authors)

  16. Differential equation models for sharp threshold dynamics.

    Science.gov (United States)

    Schramm, Harrison C; Dimitrov, Nedialko B

    2014-01-01

    We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations. Published by Elsevier Inc.

  17. Single particle dynamics of many-body systems described by Vlasov-Fokker-Planck equations

    International Nuclear Information System (INIS)

    Frank, T.D.

    2003-01-01

    Using Langevin equations we describe the random walk of single particles that belong to particle systems satisfying Vlasov-Fokker-Planck equations. In doing so, we show that Haissinski distributions of bunched particles in electron storage rings can be derived from a particle dynamics model

  18. The three-body problem and the equations of dynamics Poincaré’s foundational work on dynamical systems theory

    CERN Document Server

    Poincaré, Henri

    2017-01-01

    Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. .

  19. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

    Institute of Scientific and Technical Information of China (English)

    WANG; Shunjin; ZHANG; Hua

    2006-01-01

    The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.

  20. Pod systems: an equivariant ordinary differential equation approach to dynamical systems on a spatial domain

    International Nuclear Information System (INIS)

    Elmhirst, Toby; Stewart, Ian; Doebeli, Michael

    2008-01-01

    We present a class of systems of ordinary differential equations (ODEs), which we call 'pod systems', that offers a new perspective on dynamical systems defined on a spatial domain. Such systems are typically studied as partial differential equations, but pod systems bring the analytic techniques of ODE theory to bear on the problems, and are thus able to study behaviours and bifurcations that are not easily accessible to the standard methods. In particular, pod systems are specifically designed to study spatial dynamical systems that exhibit multi-modal solutions. A pod system is essentially a linear combination of parametrized functions in which the coefficients and parameters are variables whose dynamics are specified by a system of ODEs. That is, pod systems are concerned with the dynamics of functions of the form Ψ(s, t) = y 1 (t) φ(s; x 1 (t)) + ··· + y N (t) φ(s; x N (t)), where s in R n is the spatial variable and φ: R n × R d → R. The parameters x i in R d and coefficients y i in R are dynamic variables which evolve according to some system of ODEs, x-dot i = G i (x, y) and y-dot i = H i (x, y), for i = 1, ..., N. The dynamics of Ψ in function space can then be studied through the dynamics of the x and y in finite dimensions. A vital feature of pod systems is that the ODEs that specify the dynamics of the x and y variables are not arbitrary; restrictions on G i and H i are required to guarantee that the dynamics of Ψ in function space are well defined (that is, that trajectories are unique). One important restriction is symmetry in the ODEs which arises because Ψ is invariant under permutations of the indices of the (x i , y i ) pairs. However, this is not the whole story, and the primary goal of this paper is to determine the necessary structure of the ODEs explicitly to guarantee that the dynamics of Ψ are well defined

  1. Comprehensive solutions to the Bloch equations and dynamical models for open two-level systems

    Science.gov (United States)

    Skinner, Thomas E.

    2018-01-01

    The Bloch equation and its variants constitute the fundamental dynamical model for arbitrary two-level systems. Many important processes, including those in more complicated systems, can be modeled and understood through the two-level approximation. It is therefore of widespread relevance, especially as it relates to understanding dissipative processes in current cutting-edge applications of quantum mechanics. Although the Bloch equation has been the subject of considerable analysis in the 70 years since its inception, there is still, perhaps surprisingly, significant work that can be done. This paper extends the scope of previous analyses. It provides a framework for more fully understanding the dynamics of dissipative two-level systems. A solution is derived that is compact, tractable, and completely general, in contrast to previous results. Any solution of the Bloch equation depends on three roots of a cubic polynomial that are crucial to the time dependence of the system. The roots are typically only sketched out qualitatively, with no indication of their dependence on the physical parameters of the problem. Degenerate roots, which modify the solutions, have been ignored altogether. Here the roots are obtained explicitly in terms of a single real-valued root that is expressed as a simple function of the system parameters. For the conventional Bloch equation, a simple graphical representation of this root is presented that makes evident the explicit time dependence of the system for each point in the parameter space. Several intuitive, visual models of system dynamics are developed. A Euclidean coordinate system is identified in which any generalized Bloch equation is separable, i.e., the sum of commuting rotation and relaxation operators. The time evolution in this frame is simply a rotation followed by relaxation at modified rates that play a role similar to the standard longitudinal and transverse rates. These rates are functions of the applied field, which

  2. An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part one: Single Rigid Bodies

    Directory of Open Access Journals (Sweden)

    Pål Johan From

    2012-04-01

    Full Text Available This paper presents the explicit dynamic equations of a mechanical system. The equations are presented so that they can easily be implemented in a simulation software or controller environment and are also well suited for system and controller analysis. The dynamics of a general mechanical system consisting of one or more rigid bodies can be derived from the Lagrangian. We can then use several well known properties of Lie groups to guarantee that these equations are well defined. This will, however, often lead to rather abstract formulation of the dynamic equations that cannot be implemented in a simulation software directly. In this paper we close this gap and show what the explicit dynamic equations look like. These equations can then be implemented directly in a simulation software and no background knowledge on Lie theory and differential geometry on the practitioner's side is required. This is the first of two papers on this topic. In this paper we derive the dynamics for single rigid bodies, while in the second part we study multibody systems. In addition to making the equations more accessible to practitioners, a motivation behind the papers is to correct a few errors commonly found in literature. For the first time, we show the detailed derivations and how to arrive at the correct set of equations. We also show through some simple examples that these correspond with the classical formulations found from Lagrange's equations. The dynamics is derived from the Boltzmann--Hamel equations of motion in terms of local position and velocity variables and the mapping to the corresponding quasi-velocities. Finally we present a new theorem which states that the Boltzmann--Hamel formulation of the dynamics is valid for all transformations with a Lie group topology. This has previously only been indicated through examples, but here we also present the formal proof. The main motivation of these papers is to allow practitioners not familiar with

  3. Numerical simulation of stochastic point kinetic equation in the dynamical system of nuclear reactor

    International Nuclear Information System (INIS)

    Saha Ray, S.

    2012-01-01

    Highlights: ► In this paper stochastic neutron point kinetic equations have been analyzed. ► Euler–Maruyama method and Strong Taylor 1.5 order method have been discussed. ► These methods are applied for the solution of stochastic point kinetic equations. ► Comparison between the results of these methods and others are presented in tables. ► Graphs for neutron and precursor sample paths are also presented. -- Abstract: In the present paper, the numerical approximation methods, applied to efficiently calculate the solution for stochastic point kinetic equations () in nuclear reactor dynamics, are investigated. A system of Itô stochastic differential equations has been analyzed to model the neutron density and the delayed neutron precursors in a point nuclear reactor. The resulting system of Itô stochastic differential equations are solved over each time-step size. The methods are verified by considering different initial conditions, experimental data and over constant reactivities. The computational results indicate that the methods are simple and suitable for solving stochastic point kinetic equations. In this article, a numerical investigation is made in order to observe the random oscillations in neutron and precursor population dynamics in subcritical and critical reactors.

  4. Dynamical TAP equations for non-equilibrium Ising spin glasses

    DEFF Research Database (Denmark)

    Roudi, Yasser; Hertz, John

    2011-01-01

    We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix, and the external fields can be time-dependent. In the synchronously updated model, the TAP...... equations take the form of self consistent equations for magnetizations at time t+1, given the magnetizations at time t. In the asynchronously updated model, the TAP equations determine the time derivatives of the magnetizations at each time, again via self consistent equations, given the current values...... of the magnetizations. Numerical simulations suggest that the TAP equations become exact for large systems....

  5. Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

    Science.gov (United States)

    Martirosyan, A; Saakian, David B

    2011-08-01

    We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

  6. Long-Term Dynamics of Autonomous Fractional Differential Equations

    Science.gov (United States)

    Liu, Tao; Xu, Wei; Xu, Yong; Han, Qun

    This paper aims to investigate long-term dynamic behaviors of autonomous fractional differential equations with effective numerical method. The long-term dynamic behaviors predict where systems are heading after long-term evolution. We make some modification and transplant cell mapping methods to autonomous fractional differential equations. The mapping time duration of cell mapping is enlarged to deal with the long memory effect. Three illustrative examples, i.e. fractional Lotka-Volterra equation, fractional van der Pol oscillator and fractional Duffing equation, are studied with our revised generalized cell mapping method. We obtain long-term dynamics, such as attractors, basins of attraction, and saddles. Compared with some existing stability and numerical results, the validity of our method is verified. Furthermore, we find that the fractional order has its effect on the long-term dynamics of autonomous fractional differential equations.

  7. On the dynamics of a non-local parabolic equation arising from the Gierer-Meinhardt system

    Science.gov (United States)

    Kavallaris, Nikos I.; Suzuki, Takashi

    2017-05-01

    The purpose of the current paper is to contribute to the comprehension of the dynamics of the shadow system of an activator-inhibitor system known as a Gierer-Meinhardt model. Shadow systems are intended to work as an intermediate step between single equations and reaction-diffusion systems. In the case where the inhibitor’s response to the activator’s growth is rather weak, then the shadow system of the Gierer-Meinhardt model is reduced to a single though non-local equation whose dynamics will be investigated. We mainly focus on the derivation of blow-up results for this non-local equation which can be seen as instability patterns of the shadow system. In particular, a diffusion driven instability (DDI), or Turing instability, in the neighbourhood of a constant stationary solution, which it is destabilised via diffusion-driven blow-up, is obtained. The latter actually indicates the formation of some unstable patterns, whilst some stability results of global-in-time solutions towards non-constant steady states guarantee the occurrence of some stable patterns.

  8. Dynamic data analysis modeling data with differential equations

    CERN Document Server

    Ramsay, James

    2017-01-01

    This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...

  9. Stability theory for dynamic equations on time scales

    CERN Document Server

    Martynyuk, Anatoly A

    2016-01-01

    This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems. In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Ma...

  10. State-dependent neutral delay equations from population dynamics.

    Science.gov (United States)

    Barbarossa, M V; Hadeler, K P; Kuttler, C

    2014-10-01

    A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.

  11. Symbolic-Numeric Integration of the Dynamical Cosserat Equations

    KAUST Repository

    Lyakhov, Dmitry A.

    2017-08-29

    We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\\\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

  12. Symbolic-Numeric Integration of the Dynamical Cosserat Equations

    KAUST Repository

    Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Weber, Andreas G.; Michels, Dominik L.

    2017-01-01

    We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.

  13. Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space

    International Nuclear Information System (INIS)

    Rodriguez D, R.

    2007-01-01

    In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)

  14. Attractors of equations of non-Newtonian fluid dynamics

    International Nuclear Information System (INIS)

    Zvyagin, V G; Kondrat'ev, S K

    2014-01-01

    This survey describes a version of the trajectory-attractor method, which is applied to study the limit asymptotic behaviour of solutions of equations of non-Newtonian fluid dynamics. The trajectory-attractor method emerged in papers of the Russian mathematicians Vishik and Chepyzhov and the American mathematician Sell under the condition that the corresponding trajectory spaces be invariant under the translation semigroup. The need for such an approach was caused by the fact that for many equations of mathematical physics for which the Cauchy initial-value problem has a global (weak) solution with respect to the time, the uniqueness of such a solution has either not been established or does not hold. In particular, this is the case for equations of fluid dynamics. At the same time, trajectory spaces invariant under the translation semigroup could not be constructed for many equations of non-Newtonian fluid dynamics. In this connection, a different approach to the construction of trajectory attractors for dissipative systems was proposed in papers of Zvyagin and Vorotnikov without using invariance of trajectory spaces under the translation semigroup and is based on the topological lemma of Shura-Bura. This paper presents examples of equations of non-Newtonian fluid dynamics (the Jeffreys system describing movement of the Earth's crust, the model of motion of weak aqueous solutions of polymers, a system with memory) for which the aforementioned construction is used to prove the existence of attractors in both the autonomous and the non-autonomous cases. At the beginning of the paper there is also a brief exposition of the results of Ladyzhenskaya on the existence of attractors of the two-dimensional Navier-Stokes system and the result of Vishik and Chepyzhov for the case of attractors of the three-dimensional Navier-Stokes system. Bibliography: 34 titles

  15. Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

    Science.gov (United States)

    Marston, J. B.; Hastings, M. B.

    2005-03-01

    The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

  16. High-precision numerical integration of equations in dynamics

    Science.gov (United States)

    Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

    2018-05-01

    An important requirement for the process of solving differential equations in Dynamics, such as the equations of the motion of celestial bodies and, in particular, the motion of cosmic robotic systems is high accuracy at large time intervals. One of effective tools for obtaining such solutions is the Taylor series method. In this connection, we note that it is very advantageous to reduce the given equations of Dynamics to systems with polynomial (in unknowns) right-hand sides. This allows us to obtain effective algorithms for finding the Taylor coefficients, a priori error estimates at each step of integration, and an optimal choice of the order of the approximation used. In the paper, these questions are discussed and appropriate algorithms are considered.

  17. Inverse operator method for solutions of nonlinear dynamical system and application to Lorentz equation

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    1993-01-01

    The inverse operator method (IOM) for solutions of nonlinear dynamical systems (NDS) is briefly described and realized by the Mathematics-Mechanization (MM) in computers. For the first time IOM and MM are successfully applied to study the chaotic behaviors of Lorentz equation

  18. Sparse dynamics for partial differential equations.

    Science.gov (United States)

    Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley

    2013-04-23

    We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

  19. Sparse learning of stochastic dynamical equations

    Science.gov (United States)

    Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia

    2018-06-01

    With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.

  20. Chaotic dynamics and diffusion in a piecewise linear equation

    International Nuclear Information System (INIS)

    Shahrear, Pabel; Glass, Leon; Edwards, Rod

    2015-01-01

    Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems

  1. Chaotic dynamics and diffusion in a piecewise linear equation

    Science.gov (United States)

    Shahrear, Pabel; Glass, Leon; Edwards, Rod

    2015-03-01

    Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

  2. On the validity of non-Markovian master equation approaches for the entanglement dynamics of two-qubit systems

    Energy Technology Data Exchange (ETDEWEB)

    Ferraro, E; Scala, M; Napoli, A [CNISM and Dipartimento di Scienze Fisiche ed Astronomiche, Universita di Palermo, via Archirafi 36, 90123 Palermo (Italy); Migliore, R, E-mail: ferraro@fisica.unipa.i, E-mail: matteo.scala@fisica.unipa.i [CNR-INFM, Research Unit CNISM of Palermo, via Archirafi 36, 90123 Palermo (Italy)

    2010-09-01

    In the framework of the dissipative dynamics of coupled qubits interacting with independent reservoirs, a comparison between non-Markovian master equation techniques and an exact solution is presented here. We study various regimes in order to find the limits of validity of the Nakajima-Zwanzig and the time-convolutionless master equations in the description of the entanglement dynamics. A comparison between the performances of the concurrence and the negativity as entanglement measures for the system under study is also presented.

  3. Fractional dynamic calculus and fractional dynamic equations on time scales

    CERN Document Server

    Georgiev, Svetlin G

    2018-01-01

    Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.  Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales. .

  4. Dynamical equations for the optical potential

    International Nuclear Information System (INIS)

    Kowalski, K.L.

    1981-01-01

    Dynamical equations for the optical potential are obtained starting from a wide class of N-particle equations. This is done with arbitrary multiparticle interactions to allow adaptation to few-body models of nuclear reactions and including all effects of nucleon identity. Earlier forms of the optical potential equations are obtained as special cases. Particular emphasis is placed upon obtaining dynamical equations for the optical potential from the equations of Kouri, Levin, and Tobocman including all effects of particle identity

  5. Post-Newtonian celestial dynamics in cosmology: Field equations

    Science.gov (United States)

    Kopeikin, Sergei M.; Petrov, Alexander N.

    2013-02-01

    formulated in terms of the field variables which play a role of generalized coordinates in the Lagrangian formalism. It allows us to implement the powerful methods of variational calculus to derive the gauge-invariant field equations of the post-Newtonian celestial mechanics of an isolated astronomical system in an expanding universe. These equations generalize the field equations of the post-Newtonian theory in asymptotically flat spacetime by taking into account the cosmological effects explicitly and in a self-consistent manner without assuming the principle of liner superposition of the fields or a vacuole model of the isolated system, etc. The field equations for matter dynamic variables and gravitational field perturbations are coupled in the most general case of an arbitrary equation of state of matter of the background universe. We introduce a new cosmological gauge which generalizes the de Donder (harmonic) gauge of the post-Newtonian theory in asymptotically flat spacetime. This gauge significantly simplifies the gravitational field equations and allows one to find out the approximations where the field equations can be fully decoupled and solved analytically. The residual gauge freedom is explored and the residual gauge transformations are formulated in the form of the wave equations for the gauge functions. We demonstrate how the cosmological effects interfere with the local system and affect the local distribution of matter of the isolated system and its orbital dynamics. Finally, we worked out the precise mathematical definition of the Newtonian limit for an isolated system residing on the cosmological manifold. The results of the present paper can be useful in the Solar System for calculating more precise ephemerides of the Solar System bodies on extremely long time intervals, in galactic astronomy to study the dynamics of clusters of galaxies, and in gravitational wave astronomy for discussing the impact of cosmology on generation and propagation of

  6. Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices

    International Nuclear Information System (INIS)

    Sechin, Ivan; Zotov, Andrei

    2016-01-01

    In this paper we propose versions of the associative Yang-Baxter equation and higher order R-matrix identities which can be applied to quantum dynamical R-matrices. As is known quantum non-dynamical R-matrices of Baxter-Belavin type satisfy this equation. Together with unitarity condition and skew-symmetry it provides the quantum Yang-Baxter equation and a set of identities useful for different applications in integrable systems. The dynamical R-matrices satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation between the dynamical and non-dynamical cases is described by the IRF (interaction-round-a-face)-Vertex transformation. An alternative approach to quantum (semi-)dynamical R-matrices and related quantum algebras was suggested by Arutyunov, Chekhov, and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The purpose of this paper is twofold. First, we prove that the ACF elliptic R-matrix satisfies the associative Yang-Baxter equation with shifted spectral parameters. Second, we directly prove a simple relation of the IRF-Vertex type between the Baxter-Belavin and the ACF elliptic R-matrices predicted previously by Avan and Rollet. It provides the higher order R-matrix identities and an explanation of the obtained equations through those for non-dynamical R-matrices. As a by-product we also get an interpretation of the intertwining transformation as matrix extension of scalar theta function likewise R-matrix is interpreted as matrix extension of the Kronecker function. Relations to the Gervais-Neveu-Felder equation and identities for the Felder’s elliptic R-matrix are also discussed.

  7. Symbolic dynamics of the Lorenz equations

    International Nuclear Information System (INIS)

    Fang Hai-ping; Hao Bailin.

    1994-07-01

    The Lorenz equations are investigated in a wide range of parameters by using the method of symbolic dynamics. First, the systematics of stable periodic orbits in the Lorenz equations is compared with that of the one-dimensional cubic map, which shares the same discrete symmetry with the Lorenz model. The systematics is then ''corrected'' in such a way as to encompass all the known periodic windows of the Lorenz equations with only one exception. Second, in order to justify the above approach and to understand the exceptions, another 1D map with a discontinuity is extracted from an extension of the geometric Lorenz attractor and its symbolic dynamics is constructed. All this has to be done in light of symbolic dynamics of two-dimensional maps. Finally, symbolic dynamics for the actual Poincare return map of the Lorenz equations is constructed in a heuristic way. New periodic windows of the Lorenz equations and their parameters can be predicted from this symbolic dynamics in combination with the 1D cubic map. The extended geometric 2D Lorenz map and the 1D antisymmetric map with a discontinuity describe the topological aspects of the Lorenz equations to high accuracy. (author). 44 refs, 17 figs, 8 tabs

  8. Cross Coursing in Mathematics: Physical Modelling in Differential Equations Crossing to Discrete Dynamical Systems

    Science.gov (United States)

    Winkel, Brian

    2012-01-01

    We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)

  9. The fractional dynamics of quantum systems

    Science.gov (United States)

    Lu, Longzhao; Yu, Xiangyang

    2018-05-01

    The fractional dynamic process of a quantum system is a novel and complicated problem. The establishment of a fractional dynamic model is a significant attempt that is expected to reveal the mechanism of fractional quantum system. In this paper, a generalized time fractional Schrödinger equation is proposed. To study the fractional dynamics of quantum systems, we take the two-level system as an example and derive the time fractional equations of motion. The basic properties of the system are investigated by solving this set of equations in the absence of light field analytically. Then, when the system is subject to the light field, the equations are solved numerically. It shows that the two-level system described by the time fractional Schrödinger equation we proposed is a confirmable system.

  10. Electron transfer dynamics: Zusman equation versus exact theory

    International Nuclear Information System (INIS)

    Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing

    2009-01-01

    The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.

  11. Fractional neutron point kinetics equations for nuclear reactor dynamics

    International Nuclear Information System (INIS)

    Espinosa-Paredes, Gilberto; Polo-Labarrios, Marco-A.; Espinosa-Martinez, Erick-G.; Valle-Gallegos, Edmundo del

    2011-01-01

    The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.

  12. Entropy equilibrium equation and dynamic entropy production in environment liquid

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications.

  13. Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

    Science.gov (United States)

    Gumral, Hasan

    Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

  14. A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion

    Directory of Open Access Journals (Sweden)

    Tagade Piyush M.

    2017-06-01

    Full Text Available This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.

  15. Dynamical systems

    CERN Document Server

    Sternberg, Shlomo

    2010-01-01

    Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides for professors and MATLAB exercises.""Even though there are many dynamical systems books on the market, this book is bound to become a classic. The the

  16. Relativistic three-particle dynamical equations: I. Theoretical development

    International Nuclear Information System (INIS)

    Adhikari, S.K.; Tomio, L.; Frederico, T.

    1993-11-01

    Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, three dimensional scattering integral equations satisfying constrains of relativistic unitarity and covariance are rederived. These equations were first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence it is shown to perform and relate dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, several three dimensional three-particle scattering equations satisfying constraints of relativistic unitary and covariance are derived. Two of these three-particle equations are related by a transformation of variables as in the two-particle case. The three-particle equations obtained are very practical and suitable for performing relativistic scattering calculations. (author)

  17. Generalized Langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems

    Science.gov (United States)

    Stella, L.; Lorenz, C. D.; Kantorovich, L.

    2014-04-01

    The generalized Langevin equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general nonequilibrium processes. In this approach, a part of the whole system (an open system), which interacts and exchanges energy with its dissipative environment, is studied. Because the GLE is derived by projecting out exactly the harmonic environment, the coupling to it is realistic, while the equations of motion are non-Markovian. Although the GLE formalism has already found promising applications, e.g., in nanotribology and as a powerful thermostat for equilibration in classical molecular dynamics simulations, efficient algorithms to solve the GLE for realistic memory kernels are highly nontrivial, especially if the memory kernels decay nonexponentially. This is due to the fact that one has to generate a colored noise and take account of the memory effects in a consistent manner. In this paper, we present a simple, yet efficient, algorithm for solving the GLE for practical memory kernels and we demonstrate its capability for the exactly solvable case of a harmonic oscillator coupled to a Debye bath.

  18. Boltzmann-Langevin equation, dynamical instability and multifragmentation

    International Nuclear Information System (INIS)

    Feng-Shou Zhang

    1993-02-01

    By using simulations of the Boltzmann-Langevin equation which incorporates dynamical fluctuations beyond usual transport theories and by coupling it with a coalescence model, we obtain information on multifragmentation in heavy-ion collisions. From a calculation of the 40 Ca + 40 Ca system, we recover some trends of recent multifragmentation data

  19. A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

    Science.gov (United States)

    Moix, Jeremy M.; Cao, Jianshu

    2013-10-01

    The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

  20. Three-dimensional poor man's Navier-Stokes equation: a discrete dynamical system exhibiting k(-5/3) inertial subrange energy scaling.

    Science.gov (United States)

    McDonough, J M

    2009-06-01

    Outline of the derivation and mathematical and physical interpretations are presented for a discrete dynamical system known as the "poor man's Navier-Stokes equation." Numerical studies demonstrate that velocity fields produced by this dynamical system are similar to those seen in laboratory experiments and in detailed simulations, and they lead to scaling for the turbulence kinetic energy spectrum in accord with Kolmogorov K41 theory.

  1. The numerical dynamic for highly nonlinear partial differential equations

    Science.gov (United States)

    Lafon, A.; Yee, H. C.

    1992-01-01

    Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

  2. Out-of-equilibrium dynamical mean-field equations for the perceptron model

    Science.gov (United States)

    Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco

    2018-02-01

    Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.

  3. Dynamical symmetries of the Klein-Gordon equation

    International Nuclear Information System (INIS)

    Zhang Fulin; Chen Jingling

    2009-01-01

    The dynamical symmetries of the two-dimensional Klein-Gordon equations with equal scalar and vector potentials (ESVPs) are studied. The dynamical symmetries are considered in the plane and the sphere, respectively. The generators of the SO(3) group corresponding to the Coulomb potential and the SU(2) group corresponding to the harmonic oscillator potential are derived. Moreover, the generators in the sphere construct the Higgs algebra. With the help of the Casimir operators, the energy levels of the Klein-Gordon systems are yielded naturally

  4. Methods of mathematical modelling continuous systems and differential equations

    CERN Document Server

    Witelski, Thomas

    2015-01-01

    This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

  5. Schrödinger–Langevin equation with quantum trajectories for photodissociation dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

    2017-02-15

    The Schrödinger–Langevin equation is integrated to study the wave packet dynamics of quantum systems subject to frictional effects by propagating an ensemble of quantum trajectories. The equations of motion for the complex action and quantum trajectories are derived from the Schrödinger–Langevin equation. The moving least squares approach is used to evaluate the spatial derivatives of the complex action required for the integration of the equations of motion. Computational results are presented and analyzed for the evolution of a free Gaussian wave packet, a two-dimensional barrier model, and the photodissociation dynamics of NOCl. The absorption spectrum of NOCl obtained from the Schrödinger–Langevin equation displays a redshift when frictional effects increase. This computational result agrees qualitatively with the experimental results in the solution-phase photochemistry of NOCl.

  6. Linear integral equations and soliton systems

    International Nuclear Information System (INIS)

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  7. Stochastic differential equations for quantum dynamics of spin-boson networks

    International Nuclear Information System (INIS)

    Mandt, Stephan; Sadri, Darius; Houck, Andrew A; Türeci, Hakan E

    2015-01-01

    A popular approach in quantum optics is to map a master equation to a stochastic differential equation, where quantum effects manifest themselves through noise terms. We generalize this approach based on the positive-P representation to systems involving spin, in particular networks or lattices of interacting spins and bosons. We test our approach on a driven dimer of spins and photons, compare it to the master equation, and predict a novel dynamic phase transition in this system. Our numerical approach has scaling advantages over existing methods, but typically requires regularization in terms of drive and dissipation. (paper)

  8. Global dynamics for switching systems and their extensions by linear differential equations.

    Science.gov (United States)

    Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

    2018-03-15

    Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

  9. Global dynamics for switching systems and their extensions by linear differential equations

    Science.gov (United States)

    Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

    2018-03-01

    Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

  10. Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

    Science.gov (United States)

    Hu, Wenjie; Duan, Yueliang

    2018-04-01

    We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

  11. Interactive Dynamic-System Simulation

    CERN Document Server

    Korn, Granino A

    2010-01-01

    Showing you how to use personal computers for modeling and simulation, Interactive Dynamic-System Simulation, Second Edition provides a practical tutorial on interactive dynamic-system modeling and simulation. It discusses how to effectively simulate dynamical systems, such as aerospace vehicles, power plants, chemical processes, control systems, and physiological systems. Written by a pioneer in simulation, the book introduces dynamic-system models and explains how software for solving differential equations works. After demonstrating real simulation programs with simple examples, the author

  12. Solving Algebraic Riccati Equation Real Time for Integrated Vehicle Dynamics Control

    NARCIS (Netherlands)

    Kunnappillil Madhusudhanan, A; Corno, M.; Bonsen, B.; Holweg, E.

    2012-01-01

    In this paper we present a comparison study of different computational methods to implement State Dependent Riccati Equation (SDRE) based control in real time for a vehicle dynamics control application. Vehicles are mechatronic systems with nonlinear dynamics. One of the promising nonlinear control

  13. Discovering governing equations from data by sparse identification of nonlinear dynamics

    Science.gov (United States)

    Brunton, Steven

    The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled advanced technology, including aircraft, combustion engines, satellites, and electrical power. There are many more critical data-driven problems, such as understanding cognition from neural recordings, inferring patterns in climate, determining stability of financial markets, predicting and suppressing the spread of disease, and controlling turbulence for greener transportation and energy. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an increasingly important role in these efforts. This work develops a general framework to discover the governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity-promoting techniques and machine learning. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions. This perspective, combining dynamical systems with machine learning and sparse sensing, is explored with the overarching goal of real-time closed-loop feedback control of complex systems. This is joint work with Joshua L. Proctor and J. Nathan Kutz. Video Abstract: https://www.youtube.com/watch?v=gSCa78TIldg

  14. System dynamics and control with bond graph modeling

    CERN Document Server

    Kypuros, Javier

    2013-01-01

    Part I Dynamic System ModelingIntroduction to System DynamicsIntroductionSystem Decomposition and Model ComplexityMathematical Modeling of Dynamic SystemsAnalysis and Design of Dynamic SystemsControl of Dynamic SystemsDiagrams of Dynamic SystemsA Graph-Centered Approach to ModelingSummaryPracticeExercisesBasic Bond Graph ElementsIntroductionPower and Energy VariablesBasic 1-Port ElementsBasic 2-Ports ElementsJunction ElementsSimple Bond Graph ExamplesSummaryPracticeExercisesBond Graph Synthesis and Equation DerivationIntroductionGeneral GuidelinesMechanical TranslationMechanical RotationElectrical CircuitsHydraulic CircuitsMixed SystemsState Equation DerivationState-Space RepresentationsAlgebraic Loops and Derivative CausalitySummaryPracticeExercisesImpedance Bond GraphsIntroductionLaplace Transform of the State-Space EquationBasic 1-Port ImpedancesImpedance Bond Graph SynthesisJunctions, Transformers, and GyratorsEffort and Flow DividersSign ChangesTransfer Function DerivationAlternative Derivation of Transf...

  15. Differential Equations Compatible with KZ Equations

    International Nuclear Information System (INIS)

    Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

    2000-01-01

    We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

  16. A canonical form of the equation of motion of linear dynamical systems

    Science.gov (United States)

    Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias

    2018-03-01

    The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.

  17. Generalized Lorentz-Force equations

    International Nuclear Information System (INIS)

    Yamaleev, R.M.

    2001-01-01

    Guided by Nambu (n+1)-dimensional phase space formalism we build a new system of dynamic equations. These equations describe a dynamic state of the corporeal system composed of n subsystems. The dynamic equations are formulated in terms of dynamic variables of the subsystems as well as in terms of dynamic variables of the corporeal system. These two sets of variables are related respectively as roots and coefficients of the n-degree polynomial equation. In the special n=2 case, this formalism reproduces relativistic dynamics for the charged spinning particles

  18. Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations

    Science.gov (United States)

    Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.

    2017-12-01

    The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.

  19. Conservation properties and potential systems of vorticity-type equations

    International Nuclear Information System (INIS)

    Cheviakov, Alexei F.

    2014-01-01

    Partial differential equations of the form divN=0, N t +curl M=0 involving two vector functions in R 3 depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R 4 (t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations, it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented

  20. Self-Supervised Dynamical Systems

    Science.gov (United States)

    Zak, Michail

    2003-01-01

    Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and

  1. Functional System Dynamics

    NARCIS (Netherlands)

    Ligterink, N.E.

    2007-01-01

    Functional system dynamics is the analysis, modelling, and simulation of continuous systems usually described by partial differential equations. From the infinite degrees of freedom of such systems only a finite number of relevant variables have to be chosen for a practical model description. The

  2. On the Schrodinger equation in fluid-dynamical form

    International Nuclear Information System (INIS)

    Wong, C.Y.

    1976-01-01

    The fluid-dynamical form of the Schrodinger equations is studied to examine the nature of the quantum forces arising from the quantum potential of Madelung and Bohm. It is found that they are in the form of a stress tensor having diagonal and nondiagonal components. Future studies of these quantum stress tensors in a many-body system may shed some light on the mechanism of spontaneous symmetry breaking and the generation of vorticity in many nuclear systems

  3. Kinetic equations within the formalism of non-equilibrium thermo field dynamics

    International Nuclear Information System (INIS)

    Arimitsu, Toshihico

    1988-01-01

    After reviewing the real-time formalism of dissipative quantum field theory, i.e. non-equilibrium thermo field dynamics (NETFD), a kinetic equation, a self-consistent equation for the dissipation coefficient and a ''mass'' or ''chemical potential'' renormalization equation for non-equilibrium transient situations are extracted out of the two-point Green's function of the Heisenberg field, in their most general forms upon the basic requirements of NETFD. The formulation is applied to the electron-phonon system, as an example, where the gradient expansion and the quasi-particle approximation are performed. The formalism of NETFD is reinvestigated in connection with the kinetic equations. (orig.)

  4. Decomposition and Cross-Product-Based Method for Computing the Dynamic Equation of Robots

    Directory of Open Access Journals (Sweden)

    Ching-Long Shih

    2012-08-01

    Full Text Available This paper aims to demonstrate a clear relationship between Lagrange equations and Newton-Euler equations regarding computational methods for robot dynamics, from which we derive a systematic method for using either symbolic or on-line numerical computations. Based on the decomposition approach and cross-product operation, a computing method for robot dynamics can be easily developed. The advantages of this computing framework are that: it can be used for both symbolic and on-line numeric computation purposes, and it can also be applied to biped systems, as well as some simple closed-chain robot systems.

  5. Conservation form of the equations of fluid dynamics in general nonsteady coordinates

    Science.gov (United States)

    Zhang, H.; Camarero, R.; Kahawita, R.

    1985-11-01

    Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.

  6. Conservation form of the equations of fluid dynamics in general nonsteady coordinates

    International Nuclear Information System (INIS)

    Zhang, H.; Camarero, R.; Kahawita, R.

    1985-01-01

    Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations. 6 references

  7. The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.

    Science.gov (United States)

    Lehtonen, Jussi

    2018-01-01

    A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.

  8. Multiscale equation-free algorithms for molecular dynamics

    Science.gov (United States)

    Abi Mansour, Andrew

    Molecular dynamics is a physics-based computational tool that has been widely employed to study the dynamics and structure of macromolecules and their assemblies at the atomic scale. However, the efficiency of molecular dynamics simulation is limited because of the broad spectrum of timescales involved. To overcome this limitation, an equation-free algorithm is presented for simulating these systems using a multiscale model cast in terms of atomistic and coarse-grained variables. Both variables are evolved in time in such a way that the cross-talk between short and long scales is preserved. In this way, the coarse-grained variables guide the evolution of the atom-resolved states, while the latter provide the Newtonian physics for the former. While the atomistic variables are evolved using short molecular dynamics runs, time advancement at the coarse-grained level is achieved with a scheme that uses information from past and future states of the system while accounting for both the stochastic and deterministic features of the coarse-grained dynamics. To complete the multiscale cycle, an atom-resolved state consistent with the updated coarse-grained variables is recovered using algorithms from mathematical optimization. This multiscale paradigm is extended to nanofluidics using concepts from hydrodynamics, and it is demonstrated for macromolecular and nanofluidic systems. A toolkit is developed for prototyping these algorithms, which are then implemented within the GROMACS simulation package and released as an open source multiscale simulator.

  9. Integrating factors and conservation theorems for Hamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems

    Institute of Scientific and Technical Information of China (English)

    李仁杰; 乔永芬; 刘洋

    2002-01-01

    We present a general approach to the construction of conservation laws for variable mass nonholonomic noncon-servative systems. First, we give the definition of integrating factors, and we study in detail the necessary conditionsfor the existence of the conserved quantities. Then, we establish the conservation theorem and its inverse theorem forHamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems. Finally,we give an example to illustrate the application of the results.

  10. Dynamical systems in population biology

    CERN Document Server

    Zhao, Xiao-Qiang

    2017-01-01

    This research monograph provides an introduction to the theory of nonautonomous semiflows with applications to population dynamics. It develops dynamical system approaches to various evolutionary equations such as difference, ordinary, functional, and partial differential equations, and pays more attention to periodic and almost periodic phenomena. The presentation includes persistence theory, monotone dynamics, periodic and almost periodic semiflows, basic reproduction ratios, traveling waves, and global analysis of prototypical population models in ecology and epidemiology. Research mathematicians working with nonlinear dynamics, particularly those interested in applications to biology, will find this book useful. It may also be used as a textbook or as supplementary reading for a graduate special topics course on the theory and applications of dynamical systems. Dr. Xiao-Qiang Zhao is a University Research Professor at Memorial University of Newfoundland, Canada. His main research interests involve applied...

  11. A Symbolic and Graphical Computer Representation of Dynamical Systems

    Science.gov (United States)

    Gould, Laurence I.

    2005-04-01

    AUTONO is a Macsyma/Maxima program, designed at the University of Hartford, for solving autonomous systems of differential equations as well as for relating Lagrangians and Hamiltonians to their associated dynamical equations. AUTONO can be used in a number of fields to decipher a variety of complex dynamical systems with ease, producing their Lagrangian and Hamiltonian equations in seconds. These equations can then be incorporated into VisSim, a modeling and simulation program, which yields graphical representations of motion in a given system through easily chosen input parameters. The program, along with the VisSim differential-equations graphical package, allows for resolution and easy understanding of complex problems in a relatively short time; thus enabling quicker and more advanced computing of dynamical systems on any number of platforms---from a network of sensors on a space probe, to the behavior of neural networks, to the effects of an electromagnetic field on components in a dynamical system. A flowchart of AUTONO, along with some simple applications and VisSim output, will be shown.

  12. The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems

    CERN Document Server

    Etingof, Pavel

    2005-01-01

    The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.

  13. Functional System Dynamics

    OpenAIRE

    Ligterink, N.E.

    2007-01-01

    Functional system dynamics is the analysis, modelling, and simulation of continuous systems usually described by partial differential equations. From the infinite degrees of freedom of such systems only a finite number of relevant variables have to be chosen for a practical model description. The proper input and output of the system are an important part of the relevant variables.

  14. Bubble dynamics equations in Newton fluid

    International Nuclear Information System (INIS)

    Xiao, J

    2008-01-01

    For the high-speed flow of Newton fluid, bubble is produced and expanded when it moves toward the surface of fluid. Bubble dynamics is a very important research field to understand the intrinsic feature of bubble production and motion. This research formulates the bubble expansion by expansion-local rotation transformation, which can be calculated by the measured velocity field. Then, the related dynamic equations are established to describe the interaction between the fluid and the bubble. The research shows that the bubble production condition can be expressed by critical vortex value and fluid pressure; and the bubble expansion rate can be obtained by solving the non-linear dynamic equation of bubble motion. The results may help the related research as it shows a special kind of fluid motion in theoretic sense. As an application example, the nanofiber radium-voltage relation and threshold voltage-surface tension relation in electrospinning process are discussed

  15. Constraint elimination in dynamical systems

    Science.gov (United States)

    Singh, R. P.; Likins, P. W.

    1989-01-01

    Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.

  16. Bifurcation dynamics of the tempered fractional Langevin equation

    Energy Technology Data Exchange (ETDEWEB)

    Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)

    2016-08-15

    Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.

  17. Equation-free modeling unravels the behavior of complex ecological systems

    Science.gov (United States)

    DeAngelis, Donald L.; Yurek, Simeon

    2015-01-01

    Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.

  18. The Dynamical Invariant of Open Quantum System

    OpenAIRE

    Wu, S. L.; Zhang, X. Y.; Yi, X. X.

    2015-01-01

    The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...

  19. Riccati and Ermakov Equations in Time-Dependent and Time-Independent Quantum Systems

    Directory of Open Access Journals (Sweden)

    Dieter Schuch

    2008-05-01

    Full Text Available The time-evolution of the maximum and the width of exact analytic wave packet (WP solutions of the time-dependent Schrödinger equation (SE represents the particle and wave aspects, respectively, of the quantum system. The dynamics of the maximum, located at the mean value of position, is governed by the Newtonian equation of the corresponding classical problem. The width, which is directly proportional to the position uncertainty, obeys a complex nonlinear Riccati equation which can be transformed into a real nonlinear Ermakov equation. The coupled pair of these equations yields a dynamical invariant which plays a key role in our investigation. It can be expressed in terms of a complex variable that linearizes the Riccati equation. This variable also provides the time-dependent parameters that characterize the Green's function, or Feynman kernel, of the corresponding problem. From there, also the relation between the classical and quantum dynamics of the systems can be obtained. Furthermore, the close connection between the Ermakov invariant and the Wigner function will be shown. Factorization of the dynamical invariant allows for comparison with creation/annihilation operators and supersymmetry where the partner potentials fulfil (real Riccati equations. This provides the link to a nonlinear formulation of time-independent quantum mechanics in terms of an Ermakov equation for the amplitude of the stationary state wave functions combined with a conservation law. Comparison with SUSY and the time-dependent problems concludes our analysis.

  20. Complexified dynamical systems

    International Nuclear Information System (INIS)

    Bender, Carl M; Holm, Darryl D; Hook, Daniel W

    2007-01-01

    Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely those having PT symmetry. The condition of PT symmetry selects out complex solutions that are periodic. (fast track communication)

  1. Controlling chaos in dynamical systems described by maps

    International Nuclear Information System (INIS)

    Crispin, Y.; Marduel, C.

    1994-01-01

    The problem of suppressing chaotic behavior in dynamical systems is treated using a feedback control method with limited control effort. The proposed method is validated on archetypal systems described by maps, i.e. discrete-time difference equations. The method is also applicable to dynamical systems described by flows, i.e. by systems of ordinary differential equations. Results are presented for the one-dimensional logistic map and for a two-dimensional Lotka-Volterra map describing predator-prey population dynamics. It is shown that chaos can be suppressed and the system stabilized about a period-1 fixed point of the maps

  2. Bifurcation and chaos in simple jerk dynamical systems

    Indian Academy of Sciences (India)

    - ferential equation, named as jerk equation, represents an interesting sub-class of dynam- ical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we investigate the global dynamics of a special family ...

  3. Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations

    KAUST Repository

    Lorz, Alexander

    2011-01-17

    Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses coexist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a kind of Lyapunov functional. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.

  4. Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft

    Science.gov (United States)

    Taylor, Lawrence W., Jr.; Rajiyah, H.

    1991-01-01

    Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.

  5. Integrating factors and conservation theorems for Hamilton‘s canonical equations of motion of variable mass nonholonmic nonconservative dynamical systems

    Institute of Scientific and Technical Information of China (English)

    李仁杰; 刘洋; 等

    2002-01-01

    We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton's canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results.

  6. Nonlinear transport of dynamic system phase space

    International Nuclear Information System (INIS)

    Xie Xi; Xia Jiawen

    1993-01-01

    The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example

  7. A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

    International Nuclear Information System (INIS)

    Momeni, M; Kourakis, I; Moslehi-Fard, M; Shukla, P K

    2007-01-01

    The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol-Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge-Kutta method. The presence of chaotic limit cycles is pointed out. (fast track communication)

  8. Multiscale functions, scale dynamics, and applications to partial differential equations

    Science.gov (United States)

    Cresson, Jacky; Pierret, Frédéric

    2016-05-01

    Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

  9. Resummed memory kernels in generalized system-bath master equations

    International Nuclear Information System (INIS)

    Mavros, Michael G.; Van Voorhis, Troy

    2014-01-01

    Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the “Landau-Zener resummation” of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics

  10. Chaotic dynamics in the Maxwell-Bloch equations

    International Nuclear Information System (INIS)

    Holm, D.D.; Kovacic, G.

    1992-01-01

    In the slowly varying envelope approximation and the rotating wave approximation for the Maxwell-Bloch equations, we describe how the presence of a small-amplitude probe laser in an excited, two-level, resonant medium leads to homoclinic chaos in the laser-matter dynamics. We also describe a derivation of the Maxwell-Bloch equations from an action principle

  11. Simulation of quantum dynamics based on the quantum stochastic differential equation.

    Science.gov (United States)

    Li, Ming

    2013-01-01

    The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

  12. Relativistic three-particle dynamical equations: II. Application to the trinucleon system

    International Nuclear Information System (INIS)

    Adhikari, S.K.; Tomio, L.

    1993-11-01

    The contribution of relativistic dynamics on the neutron-deuteron scattering length and triton binding energy is calculated employing five sets tri nucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off-and on-shell variations of two and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics. (author)

  13. Singular multiparameter dynamic equations with distributional ...

    African Journals Online (AJOL)

    Singular multiparameter dynamic equations with distributional potentials on time scales. ... In this paper, we consider both singular single and several multiparameter ... multiple function which is of one sign and nonzero on the given time scale.

  14. Parametric Borel summability for some semilinear system of partial differential equations

    Directory of Open Access Journals (Sweden)

    Hiroshi Yamazawa

    2015-01-01

    Full Text Available In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \\(n\\ independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002, 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.

  15. Dynamics of unstable systems

    International Nuclear Information System (INIS)

    Posch, H.A.; Narnhofer, H.; Thirring, W.

    1990-01-01

    We study the dynamics of classical particles interacting with attractive Gaussian potentials. This system is thermodynamically not stable and exhibits negative specific heat. The results of the computer simulation of the dynamics are discussed in comparison with various theories. In particular, we find that the condensed phase is a stationary solution of the Vlasov equation, but the Vlasov dynamics cannot describe the collapse. 14 refs., 1 tab., 11 figs. (Authors)

  16. Nonlinear PDEs a dynamical systems approach

    CERN Document Server

    Schneider, Guido

    2017-01-01

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

  17. Interpreting experimental data on egg production--applications of dynamic differential equations.

    Science.gov (United States)

    France, J; Lopez, S; Kebreab, E; Dijkstra, J

    2013-09-01

    This contribution focuses on applying mathematical models based on systems of ordinary first-order differential equations to synthesize and interpret data from egg production experiments. Models based on linear systems of differential equations are contrasted with those based on nonlinear systems. Regression equations arising from analytical solutions to linear compartmental schemes are considered as candidate functions for describing egg production curves, together with aspects of parameter estimation. Extant candidate functions are reviewed, a role for growth functions such as the Gompertz equation suggested, and a function based on a simple new model outlined. Structurally, the new model comprises a single pool with an inflow and an outflow. Compartmental simulation models based on nonlinear systems of differential equations, and thus requiring numerical solution, are next discussed, and aspects of parameter estimation considered. This type of model is illustrated in relation to development and evaluation of a dynamic model of calcium and phosphorus flows in layers. The model consists of 8 state variables representing calcium and phosphorus pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. Experiments that measure Ca and P uptake in layers fed different calcium concentrations during shell-forming days are used to evaluate the model. In addition to providing a useful management tool, such a simulation model also provides a means to evaluate feeding strategies aimed at reducing excretion of potential pollutants in poultry manure to the environment.

  18. Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

    Energy Technology Data Exchange (ETDEWEB)

    Kelly, Aaron; Markland, Thomas E., E-mail: tmarkland@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States); Brackbill, Nora [Department of Physics, Stanford University, Stanford, California 94305 (United States)

    2015-03-07

    In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

  19. Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations.

    Science.gov (United States)

    Kelly, Aaron; Brackbill, Nora; Markland, Thomas E

    2015-03-07

    In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

  20. Nonlinear dynamics in the Einstein-Friedmann equation

    International Nuclear Information System (INIS)

    Tanaka, Yosuke; Mizuno, Yuji; Ohta, Shigetoshi; Mori, Keisuke; Horiuchi, Tanji

    2009-01-01

    We have studied the gravitational field equations on the basis of general relativity and nonlinear dynamics. The space component of the Einstein-Friedmann equation shows the chaotic behaviours in case the following conditions are satisfied: (i)the expanding ratio: h=x . /x max = +0.14) for the occurrence of the chaotic behaviours in the Einstein-Friedmann equation (0 ≤ λ ≤ +0.14). The numerical calculations are performed with the use of the Microsoft EXCEL(2003), and the results are shown in the following cases; λ = 2b = +0.06 and +0.14.

  1. GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: Dynamics and stochastic simulations

    Science.gov (United States)

    Antoine, Xavier; Duboscq, Romain

    2015-08-01

    GPELab is a free Matlab toolbox for modeling and numerically solving large classes of systems of Gross-Pitaevskii equations that arise in the physics of Bose-Einstein condensates. The aim of this second paper, which follows (Antoine and Duboscq, 2014), is to first present the various pseudospectral schemes available in GPELab for computing the deterministic and stochastic nonlinear dynamics of Gross-Pitaevskii equations (Antoine, et al., 2013). Next, the corresponding GPELab functions are explained in detail. Finally, some numerical examples are provided to show how the code works for the complex dynamics of BEC problems.

  2. Complex dynamics in Duffing-Van der Pol equation

    International Nuclear Information System (INIS)

    Jing Zhujun; Yang, Zhiyan; Jiang Tao

    2006-01-01

    Duffing-Van der Pol equation with fifth nonlinear-restoring force and two external forcing terms is investigated. The threshold values of existence of chaotic motion are obtained under the periodic perturbation. By second-order averaging method and Melnikov method, we prove the criterion of existence of chaos in averaged system under quasi-periodic perturbation for ω 2 nω 1 + εσ, n = 1, 3, 5, and cannot prove the criterion of existence of chaos in second-order averaged system under quasi-periodic perturbation for ω 2 = nω 1 + εσ, n = 2, 4, 6, 7, 8, 9, 10, where σ is not rational to ω 1 , but can show the occurrence of chaos in original system by numerical simulation. Numerical simulations including heteroclinic and homoclinic bifurcation surfaces, bifurcation diagrams, Lyapunov exponent, phase portraits and Poincare map, not only show the consistence with the theoretical analysis but also exhibit the more new complex dynamical behaviors. We show that cascades of interlocking period-doubling and reverse period-doubling bifurcations from period-2 to -4 and -6 orbits, interleaving occurrence of chaotic behaviors and quasi-periodic orbits, transient chaos with a great abundance of period windows, symmetry-breaking of periodic orbits in chaotic regions, onset of chaos which occurs more than one, chaos suddenly disappearing to period orbits, interior crisis, strange non-chaotic attractor, non-attracting chaotic set and nice chaotic attractors. Our results show many dynamical behaviors and some of them are strictly departure from the behaviors of Duffing-Van der Pol equation with a cubic nonlinear-restoring force and one external forcing

  3. Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

    Science.gov (United States)

    Sels, Dries; Brosens, Fons

    2013-10-01

    The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

  4. Zeno dynamics and high-temperature master equations beyond secular approximation

    International Nuclear Information System (INIS)

    Militello, B; Messina, A; Scala, M

    2013-01-01

    Complete positivity of a class of maps generated by master equations derived beyond the secular approximation is discussed. The connection between such a class of evolutions and the physical properties of the system is analyzed in depth. It is also shown that under suitable hypotheses a Zeno dynamics can be induced because of the high temperature of the bath. (paper)

  5. Application of cellular neural network (CNN) method to the nuclear reactor dynamics equations

    International Nuclear Information System (INIS)

    Hadad, K.; Piroozmand, A.

    2007-01-01

    This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the nuclear reactor dynamic equations. An equivalent electrical circuit is analyzed and the governing equations of a bare, homogeneous reactor core are modeled via CNN. The validity of the CNN result is compared with numerical solution of the system of nonlinear governing partial differential equations (PDE) using MATLAB. Steady state as well as transient simulations, show very good comparison between the two methods. We used our CNN model to simulate space-time response of different reactivity excursions in a typical nuclear reactor. On line solution of reactor dynamic equations is used as an aid to reactor operation decision making. The complete algorithm could also be implemented using very large scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for small size nuclear reactors such as the ones used in space missions

  6. Dynamics of second order rational difference equations with open problems and conjectures

    CERN Document Server

    Kulenovic, Mustafa RS

    2001-01-01

    This self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. After classifying the various types of these equations and introducing some preliminary results, the authors systematically investigate each equation for semicycles, invariant intervals, boundedness, periodicity, and global stability. Of paramount importance in their own right, the results presented also offer prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. The techniques and results in this monograph are also extremely useful in analyzing the equations in the mathematical models of various biological systems and other applications. Each chapter contains a section of open problems and conjectures that will stimulate further research interest in working towards a complete understanding of the dynamics of the equation and its functional generalizations-many of them ideal for research project...

  7. Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System

    Science.gov (United States)

    Amjad, Hussain; Syed Tauseef, Mohyud-Din; Ahmet, Yildirim

    2012-03-01

    MacMillan's equations are extended to Poincaré's formalism, and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincaré parameters. The equivalence of the results obtained here with other forms of equations of motion is demonstrated. An illustrative example of the theory is provided as well.

  8. Dynamic modeling of interfacial structures via interfacial area transport equation

    International Nuclear Information System (INIS)

    Seungjin, Kim; Mamoru, Ishii

    2004-01-01

    Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport equation can make a leapfrog improvement in the current capability of the two-fluid model from both scientific and practical point of view. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. The coalescence mechanisms include the random collision driven by turbulence, and the entrainment of trailing bubbles in the wake region of the preceding bubble. The disintegration mechanisms include the break-up by turbulence impact, shearing-off at the rim of large cap bubbles and the break-up of large cap

  9. Bifurcation and chaos in simple jerk dynamical systems

    Indian Academy of Sciences (India)

    In recent years, it is observed that the third-order explicit autonomous differential equation, named as jerk equation, represents an interesting sub-class of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we investigate the global dynamics of a special family of jerk ...

  10. A stochastic differential equation analysis of cerebrospinal fluid dynamics.

    Science.gov (United States)

    Raman, Kalyan

    2011-01-18

    Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

  11. Vortex dynamics equation in type-II superconductors in a temperature gradient

    International Nuclear Information System (INIS)

    Vega Monroy, R.; Sarmiento Castillo, J.; Puerta Torres, D.

    2010-01-01

    In this work we determined a vortex dynamics equation in a temperature gradient in the frame of the time dependent Ginzburg-Landau equation. In this sense, we derived a local solvability condition, which governs the vortex dynamics. Also, we calculated the explicit form for the force coefficients, which are the keys for the understanding of the balance equation due to vortex interactions with the environment. (author)

  12. Vortex dynamics equation in type-II superconductors in a temperature gradient

    Energy Technology Data Exchange (ETDEWEB)

    Vega Monroy, R.; Sarmiento Castillo, J. [Universidad del Atlantico, Barranquilla (Colombia). Facultad de Ciencias Basicas; Puerta Torres, D. [Universidad de Cartagena (Colombia). Facultad de Ciencias Exactas

    2010-12-15

    In this work we determined a vortex dynamics equation in a temperature gradient in the frame of the time dependent Ginzburg-Landau equation. In this sense, we derived a local solvability condition, which governs the vortex dynamics. Also, we calculated the explicit form for the force coefficients, which are the keys for the understanding of the balance equation due to vortex interactions with the environment. (author)

  13. Fractal differential equations and fractal-time dynamical systems

    Indian Academy of Sciences (India)

    like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation ... involving scaling and memory effects. But most of ..... begin by recalling the definition of the Riemann integral in ordinary calculus [33]. Let g: [a ...

  14. The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

    Science.gov (United States)

    Sorokin, Sergey V

    2011-03-01

    Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

  15. Stochastic runaway of dynamical systems

    International Nuclear Information System (INIS)

    Pfirsch, D.; Graeff, P.

    1984-10-01

    One-dimensional, stochastic, dynamical systems are well studied with respect to their stability properties. Less is known for the higher dimensional case. This paper derives sufficient and necessary criteria for the asymptotic divergence of the entropy (runaway) and sufficient ones for the moments of n-dimensional, stochastic, dynamical systems. The crucial implication is the incompressibility of their flow defined by the equations of motion in configuration space. Two possible extensions to compressible flow systems are outlined. (orig.)

  16. Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach

    Science.gov (United States)

    Chen, Yusui; You, J. Q.; Yu, Ting

    2014-11-01

    A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.

  17. Oscillation theory for second order dynamic equations

    CERN Document Server

    Agarwal, Ravi P; O''Regan, Donal

    2003-01-01

    The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journal. Many books deal exclusively with the oscillation of solutions of differential equations, but most of these books appeal only to researchers who already know the subject. In an effort to bring Oscillation Theory to a new and broader audience, the authors present a compact, but thorough, understanding of Oscillation Theory for second order differential equations. They include several examples throughout the text not only to illustrate the theory, but also to provide new direction.

  18. Dynamical System Approaches to Combinatorial Optimization

    DEFF Research Database (Denmark)

    Starke, Jens

    2013-01-01

    of large times as an asymptotically stable point of the dynamics. The obtained solutions are often not globally optimal but good approximations of it. Dynamical system and neural network approaches are appropriate methods for distributed and parallel processing. Because of the parallelization......Several dynamical system approaches to combinatorial optimization problems are described and compared. These include dynamical systems derived from penalty methods; the approach of Hopfield and Tank; self-organizing maps, that is, Kohonen networks; coupled selection equations; and hybrid methods...... thereof can be used as models for many industrial problems like manufacturing planning and optimization of flexible manufacturing systems. This is illustrated for an example in distributed robotic systems....

  19. Reconstruction of dynamical equations for traffic flow

    OpenAIRE

    Kriso, S.; Friedrich, R.; Peinke, J.; Wagner, P.

    2001-01-01

    Traffic flow data collected by an induction loop detector on the highway close to Koeln-Nord are investigated with respect to their dynamics including the stochastic content. In particular we present a new method, with which the flow dynamics can be extracted directly from the measured data. As a result a Langevin equation for the traffic flow is obtained. From the deterministic part of the flow dynamics, stable fixed points are extracted and set into relation with common features of the fund...

  20. Smooth manifolds for certain dynamical systems and periodic solitons for nonlinear Klein-Gordon equations on R2

    International Nuclear Information System (INIS)

    Vuillermot, P.A.

    1988-01-01

    We present and discuss three new theorems concerning the existence of smooth manifolds associated with certain infinite-dimensional dynamical systems defined from nonlinear Klein-Gordon equations of the form u tt (x, t) = u xx (x, t)-g(u(x, t)), where g: R → R is analytic and where (x, t) ε R 2 . In particular, we prove the nonexistence of small amplitude soliton bound state solutions in the classical Φ 4 -theory, a fact recently brought about by the perturbative analysis of Kruskal and Segur [fr

  1. International Conference on Dynamical Systems : Theory and Applications

    CERN Document Server

    2016-01-01

    The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Lódz, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

  2. International Conference on Dynamical Systems : Theory and Applications

    CERN Document Server

    2016-01-01

    The book is the second volume of a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference "Dynamical Systems: Theory and Applications," held in Lódz, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

  3. Dynamical symmetries of semi-linear Schrodinger and diffusion equations

    International Nuclear Information System (INIS)

    Stoimenov, Stoimen; Henkel, Malte

    2005-01-01

    Conditional and Lie symmetries of semi-linear 1D Schrodinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrodinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf 3 ) C . We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf 3 ) C are classified and the complete list of conditionally invariant semi-linear Schrodinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed

  4. Understanding and Modeling Teams As Dynamical Systems

    Science.gov (United States)

    Gorman, Jamie C.; Dunbar, Terri A.; Grimm, David; Gipson, Christina L.

    2017-01-01

    By its very nature, much of teamwork is distributed across, and not stored within, interdependent people working toward a common goal. In this light, we advocate a systems perspective on teamwork that is based on general coordination principles that are not limited to cognitive, motor, and physiological levels of explanation within the individual. In this article, we present a framework for understanding and modeling teams as dynamical systems and review our empirical findings on teams as dynamical systems. We proceed by (a) considering the question of why study teams as dynamical systems, (b) considering the meaning of dynamical systems concepts (attractors; perturbation; synchronization; fractals) in the context of teams, (c) describe empirical studies of team coordination dynamics at the perceptual-motor, cognitive-behavioral, and cognitive-neurophysiological levels of analysis, and (d) consider the theoretical and practical implications of this approach, including new kinds of explanations of human performance and real-time analysis and performance modeling. Throughout our discussion of the topics we consider how to describe teamwork using equations and/or modeling techniques that describe the dynamics. Finally, we consider what dynamical equations and models do and do not tell us about human performance in teams and suggest future research directions in this area. PMID:28744231

  5. A stochastic differential equation analysis of cerebrospinal fluid dynamics

    Directory of Open Access Journals (Sweden)

    Raman Kalyan

    2011-01-01

    Full Text Available Abstract Background Clinical measurements of intracranial pressure (ICP over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. Methods The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE that accommodates the fluctuations in ICP. Results The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Conclusions Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

  6. Dynamics of Variable Mass Systems

    Science.gov (United States)

    Eke, Fidelis O.

    1998-01-01

    This report presents the results of an investigation of the effects of mass loss on the attitude behavior of spinning bodies in flight. The principal goal is to determine whether there are circumstances under which the motion of variable mass systems can become unstable in the sense that their transverse angular velocities become unbounded. Obviously, results from a study of this kind would find immediate application in the aerospace field. The first part of this study features a complete and mathematically rigorous derivation of a set of equations that govern both the translational and rotational motions of general variable mass systems. The remainder of the study is then devoted to the application of the equations obtained to a systematic investigation of the effect of various mass loss scenarios on the dynamics of increasingly complex models of variable mass systems. It is found that mass loss can have a major impact on the dynamics of mechanical systems, including a possible change in the systems stability picture. Factors such as nozzle geometry, combustion chamber geometry, propellant's initial shape, size and relative mass, and propellant location can all have important influences on the system's dynamic behavior. The relative importance of these parameters on-system motion are quantified in a way that is useful for design purposes.

  7. First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields

    International Nuclear Information System (INIS)

    Alvi, Kashif

    2002-01-01

    First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift in the hyperbolic system could be advantageous for numerical work. In this paper, two first-order symmetrizable hyperbolic systems are presented that include the lapse and shift as dynamical fields and have only physical characteristic speeds

  8. Generalized master equations for non-Poisson dynamics on networks.

    Science.gov (United States)

    Hoffmann, Till; Porter, Mason A; Lambiotte, Renaud

    2012-10-01

    The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

  9. Lozenge Tiling Dynamics and Convergence to the Hydrodynamic Equation

    Science.gov (United States)

    Laslier, Benoît; Toninelli, Fabio Lucio

    2018-03-01

    We study a reversible continuous-time Markov dynamics of a discrete (2 + 1)-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the {L× L} torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in Luby et al. (SIAM J Comput 31:167-192, 2001): in terms of interlaced particles, a particle jump of length n that preserves the interlacement constraints has rate 1/(2 n). This dynamics presents special features: the average mutual volume between two interface configurations decreases with time (Luby et al. 2001) and a certain one-dimensional projection of the dynamics is described by the heat equation (Wilson in Ann Appl Probab 14:274-325, 2004). In this work we prove a hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as L\\to∞ to the solution of a non-linear parabolic PDE. The initial profile is assumed to be C 2 differentiable and to contain no "frozen region". The explicit form of the PDE was recently conjectured (Laslier and Toninelli in Ann Henri Poincaré Theor Math Phys 18:2007-2043, 2017) on the basis of local equilibrium considerations. In contrast with the hydrodynamic equation for the Langevin dynamics of the Ginzburg-Landau model (Funaki and Spohn in Commun Math Phys 85:1-36, 1997; Nishikawa in Commun Math Phys 127:205-227, 2003), here the mobility coefficient turns out to be a non-trivial function of the interface slope.

  10. A theory of electron baths: One-electron system dynamics

    International Nuclear Information System (INIS)

    McDowell, H.K.

    1992-01-01

    The second-quantized, many-electron, atomic, and molecular Hamiltonian is partitioned both by the identity or labeling of the spin orbitals and by the dynamics of the spin orbitals into a system coupled to a bath. The electron bath is treated by a molecular time scale generalized Langevin equation approach designed to include one-electron dynamics in the system dynamics. The bath is formulated as an equivalent chain of spin orbitals through the introduction of equivalent-chain annihilation and creation operators. Both the dynamics and the quantum grand canonical statistical properties of the electron bath are examined. Two versions for the statistical properties of the bath are pursued. Using a weak bath assumption, a bath statistical average is defined which allows one to achieve a reduced dynamics description of the electron system which is coupled to the electron bath. In a strong bath assumption effective Hamiltonians are obtained which reproduce the dynamics of the bath and which lead to the same results as found in the weak bath assumption. The effective (but exact) Hamiltonian is found to be a one-electron Hamiltonian. A reduced dynamics equation of motion for the system population matrix is derived and found to agree with a previous version. This equation of motion is useful for studying electron transfer in the system when coupled to an electron bath

  11. Physical dynamics of quasi-particles in nonlinear wave equations

    International Nuclear Information System (INIS)

    Christov, Ivan; Christov, C.I.

    2008-01-01

    By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field

  12. Physical dynamics of quasi-particles in nonlinear wave equations

    Energy Technology Data Exchange (ETDEWEB)

    Christov, Ivan [Department of Mathematics, Texas A and M University, College Station, TX 77843-3368 (United States)], E-mail: christov@alum.mit.edu; Christov, C.I. [Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010 (United States)], E-mail: christov@louisiana.edu

    2008-02-04

    By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.

  13. Unifying treatment of nonequilibrium and unstable dynamics of cold bosonic atom system with time-dependent order parameter in Thermo Field Dynamics

    International Nuclear Information System (INIS)

    Nakamura, Y.; Yamanaka, Y.

    2011-01-01

    Research highlights: → Cold atoms with time-dependent condensate in nonequilibrium Thermo Field Dynamics. → Coupled equations which describe the temporal evolution of the system are derived. → They are not the naive assemblages of presumable equations, but the self-consistently ones. → Valid even for systems with Landau or dynamical instability, and describing decays. → Transport equation has new collision term that is important in Landau instability. - Abstract: The coupled equations which describe the temporal evolution of the Bose-Einstein condensed system are derived in the framework of nonequilibrium Thermo Field Dynamics. The key element is that they are not the naive assemblages of assumed equations, but are the self-consistent ones derived by appropriate renormalization conditions. While the order parameter is time-dependent, an explicit quasiparticle picture is constructed by a time-dependent expansion. Our formulation is valid even for the system with a unstable condensate, and describes the condensate decay caused by the Landau instability as well as by the dynamical one.

  14. Evolutionary game theory for physical and biological scientists. I. Training and validating population dynamics equations.

    Science.gov (United States)

    Liao, David; Tlsty, Thea D

    2014-08-06

    Failure to understand evolutionary dynamics has been hypothesized as limiting our ability to control biological systems. An increasing awareness of similarities between macroscopic ecosystems and cellular tissues has inspired optimism that game theory will provide insights into the progression and control of cancer. To realize this potential, the ability to compare game theoretic models and experimental measurements of population dynamics should be broadly disseminated. In this tutorial, we present an analysis method that can be used to train parameters in game theoretic dynamics equations, used to validate the resulting equations, and used to make predictions to challenge these equations and to design treatment strategies. The data analysis techniques in this tutorial are adapted from the analysis of reaction kinetics using the method of initial rates taught in undergraduate general chemistry courses. Reliance on computer programming is avoided to encourage the adoption of these methods as routine bench activities.

  15. Schwinger Dyson equations: Dynamical chiral symmetry breaking and confinement

    International Nuclear Information System (INIS)

    Roberts, C.D.

    1992-01-01

    A representative but not exhaustive review of the Schwinger-Dyson equation (SDE) approach to the nonperturbative study of QCD is presented. The main focus is the SDE for the quark self energy but studies of the gluon propagator and quark-gluon vertex are also discussed insofar as they are important to the quark SDE. The scope of this article is the application of these equations to the study of dynamical chiral symmetry breaking, quark confinement and the phenomenology of the spectrum and dynamics of QCD

  16. Dynamics of glassy systems

    International Nuclear Information System (INIS)

    Cugliandolo, Leticia F.

    2003-09-01

    These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario for this temporal evolution derived from the solution to some solvable models (p spin and the like) that are intimately connected to the mode coupling approach (and similar ones) to super-cooled liquids. At the end we list a number of open problems of great relevance in this context. These Sections can be read independently of the body of the paper where we present some of the basic analytic techniques used to study the out of equilibrium dynamics of classical and quantum models with and without disorder. We start the technical part by briefly discussing the role played by the environment and by introducing and comparing its representation in the equilibrium and dynamic treatment of classical and quantum systems. We next explain the role played by explicit quenched disorder in both approaches. Later on we focus on analytical techniques; we expand on the dynamic functional methods, and the diagrammatic expansions and resummations used to derive macroscopic equations from the microscopic dynamics. We show why the macroscopic dynamic equations for disordered models and those resulting from self-consistent approximations to non-disordered ones coincide. We review some generic properties of dynamic systems evolving out of equilibrium like the modifications of the fluctuation-dissipation theorem, generic scaling forms of the correlation functions, etc. Finally we solve a family of mean-field models. The connection between the dynamic treatment and the analysis of the free-energy landscape of these models is also presented. We use pedagogical examples all along these lectures to illustrate the properties and results. (author)

  17. Equation-free dynamic renormalization in a glassy compaction model

    International Nuclear Information System (INIS)

    Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.

    2006-01-01

    Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena

  18. Equation-free dynamic renormalization in a glassy compaction model

    Science.gov (United States)

    Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.

    2006-07-01

    Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena.

  19. On theories of gravitation in which the dynamical equations do not follow from the field equations and the Birkhoff theorem

    International Nuclear Information System (INIS)

    Bleyer, U.; Muecket, J.P.

    1980-01-01

    In general the Birkhoff theorem is violated in non-Einsteinian theories of gravitation. We show for theories in which the dynamical equations do not follow from the field equations that time-dependent vacuum solutions are needed in order to join nonstatic spherically symmetric incoherent matter distributions. It is shown for Treder's tetrad theories that such vacuum solutions exist and a continuous and unique junction is possible. In generalization of these results we consider the problem in what theories of gravitation the dynamical equations do not follow from the field equations. This consideration leads to non-Einsteinian theories like bimetric theories or Treder's tetrad theories containing supplementary geometrical quantities which are not dynamical variables of the theory. (author)

  20. Dynamic modeling of interfacial structures via interfacial area transport equation

    International Nuclear Information System (INIS)

    Seungjin, Kim; Mamoru, Ishii

    2005-01-01

    The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. In the present paper, the interfacial area transport equations currently available are reviewed to address the feasibility and reliability of the model along with extensive experimental results. These include the data from adiabatic upward air-water two-phase flow in round tubes of various sizes, from a rectangular duct, and from adiabatic co-current downward air-water two-phase flow in round pipes of two sizes. (authors)

  1. Fault diagnosis for dynamic power system

    International Nuclear Information System (INIS)

    Thabet, A.; Abdelkrim, M.N.; Boutayeb, M.; Didier, G.; Chniba, S.

    2011-01-01

    The fault diagnosis problem for dynamic power systems is treated, the nonlinear dynamic model based on a differential algebraic equations is transformed with reduced index to a simple dynamic model. Two nonlinear observers are used for generating the fault signals for comparison purposes, one of them being an extended Kalman estimator and the other a new extended kalman filter with moving horizon with a study of convergence based on the choice of matrix of covariance of the noises of system and measurements. The paper illustrates a simulation study applied on IEEE 3 buses test system.

  2. Algorithm for Stabilizing a POD-Based Dynamical System

    Science.gov (United States)

    Kalb, Virginia L.

    2010-01-01

    This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

  3. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    Science.gov (United States)

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  4. Ultrafast dynamics of laser-pulse excited semiconductors: non-Markovian quantum kinetic equations with nonequilibrium correlations

    Directory of Open Access Journals (Sweden)

    V.V.Ignatyuk

    2004-01-01

    Full Text Available Non-Markovian kinetic equations in the second Born approximation are derived for a two-zone semiconductor excited by a short laser pulse. Both collision dynamics and running nonequilibrium correlations are taken into consideration. The energy balance and relaxation of the system to equilibrium are discussed. Results of numerical solution of the kinetic equations for carriers and phonons are presented.

  5. A new perspective on the Faddeev equations and the K{sup Macron}NN system from chiral dynamics and unitarity in coupled channels

    Energy Technology Data Exchange (ETDEWEB)

    Oset, E. [Instituto de Fisica Corpuscular (centro mixto CSIC-UV), Institutos de Investigacion de Paterna, Aptdo. 22085, 46071 Valencia (Spain); Jido, D. [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Sekihara, T. [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan); Martinez Torres, A. [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Khemchandani, K.P. [Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka 567-0047 (Japan); Bayar, M., E-mail: melahat@ific.uv.es [Instituto de Fisica Corpuscular (centro mixto CSIC-UV), Institutos de Investigacion de Paterna, Aptdo. 22085, 46071 Valencia (Spain); Department of Physics, Kocaeli University, 41380 Izmit (Turkey); Yamagata-Sekihara, J. [Instituto de Fisica Corpuscular (centro mixto CSIC-UV), Institutos de Investigacion de Paterna, Aptdo. 22085, 46071 Valencia (Spain); Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)

    2012-05-01

    We review recent work concerning the K{sup Macron}N interaction and Faddeev equations with chiral dynamics which allow us to look at the K{sup Macron}NN from a different perspective and pay attention to problems that have been posed in previous studies on the subject. We then show results which provide extra experimental evidence on the existence of two {Lambda}(1405) states. Then show the findings of a recent approach to Faddeev equations using chiral unitary dynamics, where an explicit cancellation of the two-body off-shell amplitude with three-body forces stemming from the same chiral Lagrangians takes place. This removal of the unphysical off-shell part of the amplitudes is most welcome and renders the approach unambiguous, showing that only on-shell two-body amplitudes need to be used. With this information in mind we use an approximation to the Faddeev equations within the fixed center approximation to study the K{sup Macron}NN system, providing answers within this approximation to questions that have been brought before and evaluating binding energies and widths of this three-body system. As a novelty with respect to recent work on the topic we find a bound state of the system with spin S=1, like a bound state of K{sup Macron}-deuteron, less bound that the one of S=0, where all recent efforts have been devoted. The width is relatively large in this case, suggesting problems in a possible experimental observation.

  6. Prolongation Loop Algebras for a Solitonic System of Equations

    Directory of Open Access Journals (Sweden)

    Maria A. Agrotis

    2006-11-01

    Full Text Available We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Bäcklund transformation preserves the reality of the n-soliton potentials and establish their pole structure with respect to the broadening parameter. The natural phase space of the model is embedded in an infinite dimensional loop algebra. The dynamical equations of the model are associated to an infinite family of higher order Hamiltonian systems that are in involution. We present the Hamiltonian functions and the Poisson brackets between the extended potentials.

  7. Finite element formulation for dynamics of planar flexible multi-beam system

    International Nuclear Information System (INIS)

    Liu Zhuyong; Hong Jiazhen; Liu Jinyang

    2009-01-01

    In some previous geometric nonlinear finite element formulations, due to the use of axial displacement, the contribution of all the elements lying between the reference node of zero axial displacement and the element to the foreshortening effect should be taken into account. In this paper, a finite element formulation is proposed based on geometric nonlinear elastic theory and finite element technique. The coupling deformation terms of an arbitrary point only relate to the nodal coordinates of the element at which the point is located. Based on Hamilton principle, dynamic equations of elastic beams undergoing large overall motions are derived. To investigate the effect of coupling deformation terms on system dynamic characters and reduce the dynamic equations, a complete dynamic model and three reduced models of hub-beam are prospected. When the Cartesian deformation coordinates are adopted, the results indicate that the terms related to the coupling deformation in the inertia forces of dynamic equations have small effect on system dynamic behavior and may be neglected, whereas the terms related to coupling deformation in the elastic forces are important for system dynamic behavior and should be considered in dynamic equation. Numerical examples of the rotating beam and flexible beam system are carried out to demonstrate the accuracy and validity of this dynamic model. Furthermore, it is shown that a small number of finite elements are needed to obtain a stable solution using the present coupling finite element formulation

  8. Dynamics of Multibody Systems Near Lagrangian Points

    Science.gov (United States)

    Wong, Brian

    This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the Lagrangian points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid Lagrangian point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. Numerical simulations are used to study the long term

  9. Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems

    Directory of Open Access Journals (Sweden)

    Florian Thüroff

    2014-11-01

    Full Text Available Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system’s dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system’s ordered state nematic, despite purely polar interactions on the level of single particles.

  10. Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

    Science.gov (United States)

    Bianucci, Marco

    2018-05-01

    Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.

  11. New form of the Euler-Bernoulli rod equation applied to robotic systems

    Directory of Open Access Journals (Sweden)

    Filipović Mirjana

    2008-01-01

    Full Text Available This paper presents a theoretical background and an example of extending the Euler-Bernoulli equation from several aspects. Euler-Bernoulli equation (based on the known laws of dynamics should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. The stiffness matrix is a full matrix. Damping is an omnipresent elasticity characteristic of real systems, so that it is naturally included in the Euler-Bernoulli equation. It is shown that Daniel Bernoulli's particular integral is just one component of the total elastic deformation of the tip of any mode to which we have to add a component of the elastic deformation of a stationary regime in accordance with the complexity requirements of motion of an elastic robot system. The elastic line equation mode of link of a complex elastic robot system is defined based on the so-called 'Euler-Bernoulli Approach' (EBA. It is shown that the equation of equilibrium of all forces present at mode tip point ('Lumped-mass approach' (LMA follows directly from the elastic line equation for specified boundary conditions. This, in turn, proves the essential relationship between LMA and EBA approaches. In the defined mathematical model of a robotic system with multiple DOF (degree of freedom in the presence of the second mode, the phenomenon of elasticity of both links and joints are considered simultaneously with the presence of the environment dynamics - all based on the previously presented theoretical premises. Simulation results are presented. .

  12. Geometric methods of global attraction in systems of delay differential equations

    Science.gov (United States)

    El-Morshedy, Hassan A.; Ruiz-Herrera, Alfonso

    2017-11-01

    In this paper we deduce criteria of global attraction in systems of delay differential equations. Our methodology is new and consists in "dominating" the nonlinear terms of the system by a scalar function and then studying some dynamical properties of that function. One of the crucial benefits of our approach is that we obtain delay-dependent results of global attraction that cover the best delay-independent conditions. We apply our results in a gene regulatory model and the classical Nicholson's blowfly equation with patch structure.

  13. Dynamics of wide and snake-like pulses in coupled Schrödinger equations with full-modulated nonlinearities

    Energy Technology Data Exchange (ETDEWEB)

    Yomba, Emmanuel, E-mail: emmanuel.yomba@csun.edu; Zakeri, Gholam-Ali, E-mail: ali.zakeri@csun.edu

    2016-02-05

    We investigate the existence of various solitary wave solutions in coupled Schrödinger equations with specific cubic and quintic nonlinearities. This system arises in wave propagation in fiber optics with focusing and defocusing with modulated nonlinearities. We obtain front–front, bright–bright, dark–dark, and dark–bright like solitons using a direct approach, and then, by reducing the system of equations to a single auxiliary equation of a Duffing-type ordinary differential equation, we provide a large class of Jacobi-elliptic solutions. These solutions are presented in the exact form and analyzed. We find a class of wide localized and snake-like (in both space and time) vector solitons. One of the novel aspects of this study is that we have shown that the qualitative behavior of the solutions is independent of the choice of similarity variables. Numerical results show that the solutions of the above system are stable with up to 10% white noises. - Highlights: • Dynamics of wide and snake-like pulses is analyzed for coupled Schrödinger equations. • Qualitative appearance of solutions is analyzed using various similarity variables. • Effect of change in parameter-values on dynamics of the solutions is investigated. • Vectors front–front, bright–bright, dark–dark and dark–bright solitons are obtained.

  14. Correlations between chaos in a perturbed sine-Gordon equation and a truncated model system

    International Nuclear Information System (INIS)

    Bishop, A.R.; Flesch, R.; Forests, M.G.; Overman, E.A.

    1990-01-01

    The purpose of this paper is to present a first step toward providing coordinates and associated dynamics for low-dimensional attractors in nearly integrable partial differential equations (pdes), in particular, where the truncated system reflects salient geometric properties of the pde. This is achieved by correlating: (1) numerical results on the bifurcations to temporal chaos with spatial coherence of the damped, periodically forced sine-Gordon equation with periodic boundary conditions; (2) an interpretation of the spatial and temporal bifurcation structures of this perturbed integrable system with regard to the exact structure of the sine-Gordon phase space; (3) a model dynamical systems problem, which is itself a perturbed integrable Hamiltonian system, derived from the perturbed sine-Gordon equation by a finite mode Fourier truncation in the nonlinear Schroedinger limit; and (4) the bifurcations to chaos in the truncated phase space. In particular, a potential source of chaos in both the pde and the model ordinary differential equation systems is focused on: the existence of homoclinic orbits in the unperturbed integrable phase space and their continuation in the perturbed problem. The evidence presented here supports the thesis that the chaotic attractors of the weakly perturbed periodic sine-Gordon system consists of low-dimensional metastable attacking states together with intermediate states that are O(1) unstable and correspond to homoclinic states in the integrable phase space. It is surmised that the chaotic dynamics on these attractors is due to the perturbation of these homocline integrable configurations

  15. LSZ asymptotic condition and dynamic equations in quantum field theory

    International Nuclear Information System (INIS)

    Arkhipov, A.A.; Savrin, V.I.

    1983-01-01

    Some techniques that may be appropriate for the derivation of dynamic equations in quantum field theory are considered. A new method of deriving equations based on the use of LSZ asymptotic condition is described. It is proved that with the help of this method it becomes possible to obtain equations for wave functions both of scattering and bound states. Work is described in several papers under the dame title. The first paper is devoted to the Bethe-Salpeter equation

  16. Stability in dynamical systems I

    International Nuclear Information System (INIS)

    Courant, E.D.; Ruth, R.D.; Weng, W.T.

    1984-08-01

    We have reviewed some of the basic techniques which can be used to analyze stability in nonlinear dynamical systems, particularly in circular particle accelerators. We have concentrated on one-dimensional systems in the examples in order to simply illustrate the general techniques. We began with a review of Hamiltonian dynamics and canonical transformations. We then reviewed linear equations with periodic coefficients using the basic techniques from accelerator theory. To handle nonlinear terms we developed a canonical perturbation theory. From this we calculated invariants and the amplitude dependence of the frequency. This led us to resonances. We studied the cubic resonance in detail by using a rotating coordinate system in phase space. We then considered a general isolated nonlinear resonance. In this case we calculated the width of the resonance and estimated the spacing of resonances in order to use the Chirikov criterion to restrict the validity of the analysis. Finally the resonance equation was reduced to the pendulum equation, and we examined the motion on a separatrix. This brought us to the beginnings of stochastic behavior in the neighborhood of the separatrix. It is this complex behavior in the neighborhood of the separatrix which causes the perturbation theory used here to diverge in many cases. In spite of this the methods developed here have been and are used quite successfully to study nonlinear effects in nearly integrable systems. When used with caution and in conjunction with numerical work they give tremendous insight into the nature of the phase space structure and the stability of nonlinear differential equations. 14 references

  17. Self-supervised dynamical systems

    International Nuclear Information System (INIS)

    Zak, Michail

    2004-01-01

    A new type of dynamical systems which capture the interactions via information flows typical for active multi-agent systems is introduced. The mathematical formalism is based upon coupling the classical dynamical system (with random components caused by uncertainties in initial conditions as well as by Langevin forces) with the corresponding Liouville or the Fokker-Planck equations describing evolution of these uncertainties in terms of probability density. The coupling is implemented by information-based supervising forces which fundamentally change the patterns of probability evolution. It is demonstrated that the probability density can approach prescribed attractors while exhibiting such patterns as shock waves, solitons and chaos in probability space. Applications of these phenomena to information-based neural nets, expectation-based cooperation, self-programmed systems, control chaos using terminal attractors as well as to games with incomplete information, are addressed. A formal similarity between the mathematical structure of the introduced dynamical systems and quantum mechanics is discussed

  18. Extraction of dynamical equations from chaotic data

    International Nuclear Information System (INIS)

    Rowlands, G.; Sprott, J.C.

    1991-02-01

    A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs

  19. Quantum algorithm for simulating the dynamics of an open quantum system

    International Nuclear Information System (INIS)

    Wang Hefeng; Ashhab, S.; Nori, Franco

    2011-01-01

    In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment, and their interaction: One basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system + environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.

  20. Trajectory attractors of equations of mathematical physics

    International Nuclear Information System (INIS)

    Vishik, Marko I; Chepyzhov, Vladimir V

    2011-01-01

    In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.

  1. Molecular dynamics studies of transport properties and equation of state of supercritical fluids

    Science.gov (United States)

    Nwobi, Obika C.

    Many chemical propulsion systems operate with one or more of the reactants above the critical point in order to enhance their performance. Most of the computational fluid dynamics (CFD) methods used to predict these flows require accurate information on the transport properties and equation of state at these supercritical conditions. This work involves the determination of transport coefficients and equation of state of supercritical fluids by equilibrium molecular dynamics (MD) simulations on parallel computers using the Green-Kubo formulae and the virial equation of state, respectively. MD involves the solution of equations of motion of a system of molecules that interact with each other through an intermolecular potential. Provided that an accurate potential can be found for the system of interest, MD can be used regardless of the phase and thermodynamic conditions of the substances involved. The MD program uses the effective Lennard-Jones potential, with system sizes of 1000-1200 molecules and, simulations of 2,000,000 time-steps for computing transport coefficients and 200,000 time-steps for pressures. The computer code also uses linked cell lists for efficient sorting of molecules, periodic boundary conditions, and a modified velocity Verlet algorithm for particle displacement. Particle decomposition is used for distributing the molecules to different processors of a parallel computer. Simulations have been carried out on pure argon, nitrogen, oxygen and ethylene at various supercritical conditions, with self-diffusion coefficients, shear viscosity coefficients, thermal conductivity coefficients and pressures computed for most of the conditions. Results compare well with experimental and the National Institute of Standards and Technology (NIST) values. The results show that the number of molecules and the potential cut-off radius have no significant effect on the computed coefficients, while long-time integration is necessary for accurate determination of the

  2. Real-time dynamics of dissipative quantum systems

    International Nuclear Information System (INIS)

    Chow, K.S.

    1988-01-01

    The first part of this thesis motivates a real time approach to the dynamics of dissipative quantum systems. We review previous imaginary time methods for calculating escape rates and discuss their applications to the analysis of data in macroscopic quantum tunneling experiments. In tunneling experiments on heavily damped Superconducting Quantum Interference Devices, the instanton method gave results that compare reasonably well with data. In tunneling experiments on weakly damped Current Biased Josephson Junctions, two problems arise. First, the classical limit of the instanton result disagrees with the classical rate of thermal activation. Second, the instanton method cannot predict the microwave enhancement of escape rates. In the third chapter, we discuss our real time approach to the dynamics of dissipative systems in terms of a kinetic equation for the reduced density matrix. We demonstrate some known equilibrium properties of dissipative systems through the kinetic equation and derived the bath induced widths and energy shifts. In the low damping limit, the kinetic equation reduces to a much simpler master equation. The classical limit of the master equation is completely equivalent to the Fokker-Planck equation that describes thermal activation. In the fourth chapter, we apply the master equation to the problem of tunneling and resonance enhancement of tunneling in weakly damped current biased Josephson junctions. In the classical regime, microwaves of the appropriate frequency induce resonances between many neighboring levels and an asymmetrical resonance peak is measured. We can calibrate the junction parameters by fitting the stationary solution of the master equation to the classical resonance data. In the quantum regime, the stationary solution of the master equation, predicts well-resolved resonance peaks which agree very well with the observed data

  3. Modeling tree crown dynamics with 3D partial differential equations.

    Science.gov (United States)

    Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry

    2014-01-01

    We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

  4. Boundary-value problems with free boundaries for elliptic systems of equations

    CERN Document Server

    Monakhov, V N

    1983-01-01

    This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.

  5. Modified dynamical equation for dye doped nematic liquid crystals

    Energy Technology Data Exchange (ETDEWEB)

    Manohar, Rajiv, E-mail: rajlu1@rediffmail.co [Liquid Crystal Research Lab, Physics Department, University of Lucknow, Lucknow 226007 (India); Misra, Abhishek Kumar; Srivastava, Abhishek Kumar [Liquid Crystal Research Lab, Physics Department, University of Lucknow, Lucknow 226007 (India)

    2010-04-15

    Dye doped liquid crystals show changed dielectric properties in comparison to pure liquid crystals. These changes are strongly dependent on the concentration of dye. In the present work we have measured dielectric properties of standard nematic liquid crystals E-24 and its two guest host mixtures of different concentrations with Anthraquinone dye D5. The experimental results are fitted using linear response and in the light of this we have proposed some modifications in the dynamical equation for the nematic liquid crystals by introducing two new variables as dye concentration coefficients. The limitations of the proposed equation in high temperature range have also been discussed. With the help of the proposed dynamical equation for the guest-host liquid crystals (GHLCs) it is possible to predict the various parameters like rotational viscosity, dielectric anisotropy and relaxation time for GHLCs at other concentrations of dye in liquid crystals theoretically.

  6. Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

    Science.gov (United States)

    Daniele, C. J.; Lorenzo, C. F.

    1979-01-01

    Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

  7. Reduction of Large Dynamical Systems by Minimization of Evolution Rate

    Science.gov (United States)

    Girimaji, Sharath S.

    1999-01-01

    Reduction of a large system of equations to a lower-dimensional system of similar dynamics is investigated. For dynamical systems with disparate timescales, a criterion for determining redundant dimensions and a general reduction method based on the minimization of evolution rate are proposed.

  8. Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations

    KAUST Repository

    Lorz, Alexander; Mirrahimi, Sepideh; Perthame, Benoî t

    2011-01-01

    simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.

  9. Lectures on chaotic dynamical systems

    CERN Document Server

    Afraimovich, Valentin

    2002-01-01

    This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics. The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.

  10. Computational Cellular Dynamics Based on the Chemical Master Equation: A Challenge for Understanding Complexity.

    Science.gov (United States)

    Liang, Jie; Qian, Hong

    2010-01-01

    Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume (i.e., mesoscopic) in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation (CME). Similar to the wavefunction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved: multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand "complex behavior" and complexity theory, and from which important biological insight can be gained.

  11. OSCILLATION CRITERIA FOR A FOURTH ORDER SUBLINEAR DYNAMIC EQUATION ON TIME SCALE

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    Some new criteria for the oscillation of a fourth order sublinear and/or linear dynamic equation on time scale are established. Our results are new for the corresponding fourth order differential equations as well as difference equations.

  12. Relations between nonlinear Riccati equations and other equations in fundamental physics

    International Nuclear Information System (INIS)

    Schuch, Dieter

    2014-01-01

    Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown

  13. Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

    Science.gov (United States)

    Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

    2014-04-02

    The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

  14. Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type

    International Nuclear Information System (INIS)

    Basharov, A. M.

    2012-01-01

    It is shown that the effective Hamiltonian representation, as it is formulated in author’s papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are “locked” inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.

  15. Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

    Science.gov (United States)

    Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

    2018-06-01

    Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

  16. Nonautonomous dynamical systems in the life sciences

    CERN Document Server

    Pötzsche, Christian

    2013-01-01

    Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.

  17. Investigating non-Markovian dynamics of quantum open systems

    Science.gov (United States)

    Chen, Yusui

    Quantum open system coupled to a non-Markovian environment has recently attracted widespread interest for its important applications in quantum information processing and quantum dissipative systems. New phenomena induced by the non-Markovian environment have been discovered in variety of research areas ranging from quantum optics, quantum decoherence to condensed matter physics. However, the study of the non-Markovian quantum open system is known a difficult problem due to its technical complexity in deriving the fundamental equation of motion and elusive conceptual issues involving non-equilibrium dynamics for a strong coupled environment. The main purpose of this thesis is to introduce several new techniques of solving the quantum open systems including a systematic approach to dealing with non-Markovian master equations from a generic quantum-state diffusion (QSD) equation. In the first part of this thesis, we briefly introduce the non-Markovian quantum-state diffusion approach, and illustrate some pronounced non-Markovian quantum effects through numerical investigation on a cavity-QED model. Then we extend the non-Markovian QSD theory to an interesting model where the environment has a hierarchical structure, and find out the exact non-Markovian QSD equation of this model system. We observe the generation of quantum entanglement due to the interplay between the non-Markovian environment and the cavity. In the second part, we show an innovative method to obtain the exact non-Markovian master equations for a set of generic quantum open systems based on the corresponding non-Markovian QSD equations. Multiple-qubit systems and multilevel systems are discussed in details as two typical examples. Particularly, we derive the exact master equation for a model consisting of a three-level atom coupled to an optical cavity and controlled by an external laser field. Additionally, we discuss in more general context the mathematical similarity between the multiple

  18. Numerical solutions of the aerosol general dynamic equation for nuclear reactor safety studies

    International Nuclear Information System (INIS)

    Park, J.W.

    1988-01-01

    Methods and approximations inherent in modeling of aerosol dynamics and evolution for nuclear reactor source term estimation have been investigated. Several aerosol evolution problems are considered to assess numerical methods of solving the aerosol dynamic equation. A new condensational growth model is constructed by generalizing Mason's formula to arbitrary particle sizes, and arbitrary accommodation of the condensing vapor and background gas at particle surface. Analytical solution is developed for the aerosol growth equation employing the new condensation model. The space-dependent aerosol dynamic equation is solved to assess implications of spatial homogenization of aerosol distributions. The results of our findings are as follows. The sectional method solving the aerosol dynamic equation is quite efficient in modeling of coagulation problems, but should be improved for simulation of strong condensation problems. The J-space transform method is accurate in modeling of condensation problems, but is very slow. For the situation considered, the new condensation model predicts slower aerosol growth than the corresponding isothermal model as well as Mason's model, the effect of partial accommodation is considerable on the particle evolution, and the effect of the energy accommodation coefficient is more pronounced than that of the mass accommodation coefficient. For the initial conditions considered, the space-dependent aerosol dynamics leads to results that are substantially different from those based on the spatially homogeneous aerosol dynamic equation

  19. Optimal reduction of flexible dynamic system

    International Nuclear Information System (INIS)

    Jankovic, J.

    1994-01-01

    Dynamic system reduction is basic procedure in various problems of active control synthesis of flexible structures. In this paper is presented direct method for system reduction by explicit extraction of modes included in reduced model form. Criterion for optimal system discrete approximation in synthesis reduced dynamic model is also presented. Subjected method of system decomposition is discussed in relation to the Schur method of solving matrix algebraic Riccati equation as condition for system reduction. By using exposed method procedure of flexible system reduction in addition with corresponding example is presented. Shown procedure is powerful in problems of active control synthesis of flexible system vibrations

  20. Nonoscillation of half-linear dynamic equations

    Czech Academy of Sciences Publication Activity Database

    Matucci, S.; Řehák, Pavel

    2010-01-01

    Roč. 60, č. 5 (2010), s. 1421-1429 ISSN 0898-1221 R&D Projects: GA AV ČR KJB100190701 Grant - others:GA ČR(CZ) GA201/07/0145 Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear dynamic equation * time scale * (non)oscillation * Riccati technique Subject RIV: BA - General Mathematics Impact factor: 1.472, year: 2010 http://www.sciencedirect.com/science/article/pii/S0898122110004384

  1. Master equations in the microscopic theory of nuclear collective dynamics

    International Nuclear Information System (INIS)

    Matsuo, M.; Sakata, F.; Marumori, T.; Zhuo, Y.

    1988-07-01

    In the first half of this paper, the authors describe briefly a recent theoretical approach where the mechanism of the large-amplitude dissipative collective motions can be investigated on the basis of the microscopic theory of nuclear collective dynamics. Namely, we derive the general coupled master equations which can disclose, in the framework of the TDHF theory, not only non-linear dynamics among the collective and the single-particle modes of motion but also microscopic dynamics responsible for the dissipative processes. In the latter half, the authors investigate, without relying on any statistical hypothesis, one possible microscopic origin which leads us to the transport equation of the Fokker-Planck type so that usefullness of the general framework is demonstrated. (author)

  2. Accelerating the convergence of path integral dynamics with a generalized Langevin equation

    Science.gov (United States)

    Ceriotti, Michele; Manolopoulos, David E.; Parrinello, Michele

    2011-02-01

    The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

  3. Accelerating the convergence of path integral dynamics with a generalized Langevin equation.

    Science.gov (United States)

    Ceriotti, Michele; Manolopoulos, David E; Parrinello, Michele

    2011-02-28

    The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

  4. Energy flow theory of nonlinear dynamical systems with applications

    CERN Document Server

    Xing, Jing Tang

    2015-01-01

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

  5. Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

    Science.gov (United States)

    Rosenbaum, J. S.

    1971-01-01

    Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

  6. Is DNA a nonlinear dynamical system where solitary conformational ...

    Indian Academy of Sciences (India)

    Unknown

    DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The ... nonlinear differential equations and their soliton-like solu- .... structure and dynamics can be added till the most accurate.

  7. On the constraints violation in forward dynamics of multibody systems

    Energy Technology Data Exchange (ETDEWEB)

    Marques, Filipe [University of Minho, Department of Mechanical Engineering (Portugal); Souto, António P. [University of Minho, Department of Textile Engineering (Portugal); Flores, Paulo, E-mail: pflores@dem.uminho.pt [University of Minho, Department of Mechanical Engineering (Portugal)

    2017-04-15

    It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method.

  8. Dynamics of the diffusive DM-DE interaction – Dynamical system approach

    Energy Technology Data Exchange (ETDEWEB)

    Haba, Zbigniew [Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50-204 Wrocław (Poland); Stachowski, Aleksander; Szydłowski, Marek, E-mail: zhab@ift.uni.wroc.pl, E-mail: aleksander.stachowski@uj.edu.pl, E-mail: marek.szydlowski@uj.edu.pl [Astronomical Observatory, Jagiellonian University, Orla 171, 30-244 Krakow (Poland)

    2016-07-01

    We discuss dynamics of a model of an energy transfer between dark energy (DE) and dark matter (DM) . The energy transfer is determined by a non-conservation law resulting from a diffusion of dark matter in an environment of dark energy. The relativistic invariance defines the diffusion in a unique way. The system can contain baryonic matter and radiation which do not interact with the dark sector. We treat the Friedman equation and the conservation laws as a closed dynamical system. The dynamics of the model is examined using the dynamical systems methods for demonstration how solutions depend on initial conditions. We also fit the model parameters using astronomical observation: SNIa, H ( z ), BAO and Alcock-Paczynski test. We show that the model with diffuse DM-DE is consistent with the data.

  9. Nonlinear dynamic response of cable-suspended systems under swinging and heaving motion

    International Nuclear Information System (INIS)

    Cao, Guohua; Wang, Naige; Wang, Lei; Zhu, Zhencai

    2017-01-01

    In order to enhance the fidelity, convenient and flexibility of swinging motion, the structure of incompletely restrained cablesuspended system controlled by two drums was proposed, and the dynamic response of the system under swinging and heaving motion were investigated in this paper. The cables are spatially discretized using the assumed modes method and the system equations of motion are derived by Lagrange equations of the first kind. Based on geometric boundary conditions and linear complementary theory, the differential algebraic equations are transformed to a set of classical difference equations. Nonlinear dynamic behavior occurs under certain range of rotational velocity and frequency. The results show that asynchronous motion of suspension platform is easily caused imbalance for cable tension. Dynamic response of different swing frequencies were obtained via power frequency analysis, which could be used in the selection of the working frequency of the swing motion. The work will contribute to a better understanding of the swing frequency, cable tension and posture with dynamic characteristics of unilateral geometric and kinematic constraints in this system, and it is also useful to investigate the accuracy and reliability of instruments in future.

  10. Nonlinear dynamic response of cable-suspended systems under swinging and heaving motion

    Energy Technology Data Exchange (ETDEWEB)

    Cao, Guohua; Wang, Naige; Wang, Lei; Zhu, Zhencai [China University of Mining and Technology, Xuzhou (China)

    2017-07-15

    In order to enhance the fidelity, convenient and flexibility of swinging motion, the structure of incompletely restrained cablesuspended system controlled by two drums was proposed, and the dynamic response of the system under swinging and heaving motion were investigated in this paper. The cables are spatially discretized using the assumed modes method and the system equations of motion are derived by Lagrange equations of the first kind. Based on geometric boundary conditions and linear complementary theory, the differential algebraic equations are transformed to a set of classical difference equations. Nonlinear dynamic behavior occurs under certain range of rotational velocity and frequency. The results show that asynchronous motion of suspension platform is easily caused imbalance for cable tension. Dynamic response of different swing frequencies were obtained via power frequency analysis, which could be used in the selection of the working frequency of the swing motion. The work will contribute to a better understanding of the swing frequency, cable tension and posture with dynamic characteristics of unilateral geometric and kinematic constraints in this system, and it is also useful to investigate the accuracy and reliability of instruments in future.

  11. 18th International Conference on Difference Equations and Applications

    CERN Document Server

    Cushing, Jim; Elaydi, Saber; Pinto, Alberto

    2016-01-01

    These proceedings of the 18th International Conference on Difference Equations and Applications cover a number of different aspects of difference equations and discrete dynamical systems, as well as the interplay between difference equations and dynamical systems. The conference was organized by the Department of Mathematics at the Universitat Autònoma de Barcelona (UAB) under the auspices of the International Society of Difference Equations (ISDE) and held in Barcelona (Catalonia, Spain) in July 2012. Its purpose was to bring together experts and novices in these fields to discuss the latest developments. The book gathers contributions in the field of combinatorial and topological dynamics, complex dynamics, applications of difference equations to biology, chaotic linear dynamics, economic dynamics and control and asymptotic behavior, and periodicity of difference equations. As such it is of interest to researchers and scientists engaged in the theory and applications of difference equations and discrete dy...

  12. Dynamic behavior of district heating systems

    International Nuclear Information System (INIS)

    Kunz, J.

    1994-01-01

    The goal of this study is to develop a simulation model of a hot water system taking into account the time dependent phenomena which are important for the operational management of such a system. A state of the art literature review has shown that there is no such model considering all parts from the generation of the heat at the plant to its consumption in the connected buildings so far. First, an exhaustive list of all dynamic phenomena occurring in district heating systems has been drawn and analyzed. Considering this list, this thesis proposes that a model which satisfies the criteria listed above can be developed by superposing four sub-models which are a dynamic model of the heat generation plant, a steady state model of the hydraulic calculation of the distribution network, a dynamic model of the thermal behavior of the network and a dynamic model of the heat consumers. The development of the four sub-models starts from the fundamental conservation equations for fluid systems, i.e. the conservation of mass, momentum and energy. The transformations of those general equations into simple calculation formulas show and justify the hypotheses made in the modeling process. The heat generation plant model itself is a set of sub-models: the models for steam boilers, hot water boilers and heat accumulators which take account of the dynamic evolution of the water temperature by a simple form of the energy conservation equation, as well as the steady state models for circulation pumps and pressurizers. Since the velocities in the network pipes are small, a consideration of steady states is adopted. A network model allowing to calculate the hydraulic variables in every point is adopted from the graph theory. The pressures and flow rates in the network are calculated at discrete time steps and they are considered to be constant for the duration between the time steps. (author) figs., tabs., refs

  13. Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

    Directory of Open Access Journals (Sweden)

    Mostafa M.A. Khater

    Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

  14. Utility rate equations of group population dynamics in biological and social systems.

    Directory of Open Access Journals (Sweden)

    Vyacheslav I Yukalov

    Full Text Available We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors and of three groups (cooperators, defectors, and regulators and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about [Formula: see text] each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.

  15. Utility Rate Equations of Group Population Dynamics in Biological and Social Systems

    Science.gov (United States)

    Yukalov, Vyacheslav I.; Yukalova, Elizaveta P.; Sornette, Didier

    2013-01-01

    We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita. PMID:24386163

  16. Inverse operator method for solutions of nonlinear dynamical equations and some typical applications

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    1993-01-01

    The inverse operator method (IOM) is described briefly. We have realized the IOM for the solutions of nonlinear dynamical equations by the mathematics-mechanization (MM) with computers. They can then offer a new and powerful method applicable to many areas of physics. We have applied them successfully to study the chaotic behaviors of some nonlinear dynamical equations. As typical examples, the well-known Lorentz equation, generalized Duffing equation and two coupled generalized Duffing equations are investigated by using the IOM and the MM. The results are in good agreement with those given by Runge-Kutta method. So the IOM realized by the MM is of potential application valuable in nonlinear physics and many other fields

  17. Gauge-invariant cosmic structures---A dynamic systems approach

    International Nuclear Information System (INIS)

    Woszczyna, A.

    1992-01-01

    Gravitational instability is expressed in terms of the dynamic systems theory. The gauge-invariant Ellis-Bruni equation and Bardeen's equation are discussed in detail. It is shown that in an open universe filled with matter of constant sound velocity the Jeans criterion does not adequately define the length scale of the gravitational structure

  18. Modelling Hermetic Compressors Using Different Constraint Equations to Accommodate Multibody Dynamics and Hydrodynamic Lubrication

    DEFF Research Database (Denmark)

    Estupinan, Edgar Alberto; Santos, Ilmar

    2009-01-01

    elements are supported by fluid film bearings, where the hydrodynamic interaction forces are described by the Reynolds equation. The system of nonlinear equations is numerically solved for three different restrictive conditions of the motion of the crank, where the third case takes into account lateral...... and tilting oscillations of the extremity of the crankshaft. The numerical results of the behaviour of the journal bearings for each case are presented giving some insights into design parameters such as, maximum oil film pressure, minimum oil film thickness, maximum vibration levels and dynamic reaction...

  19. 22nd International Conference on Difference Equations and Applications

    CERN Document Server

    Hamaya, Yoshihiro; Matsunaga, Hideaki; Pötzsche, Christian

    2017-01-01

    This volume contains the proceedings of the 22nd International Conference on Difference Equations and Applications, held at Osaka Prefecture University, Osaka, Japan, in July 2016. The conference brought together both experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete dynamical systems with applications to mathematical sciences and, in particular, mathematical biology and economics. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete dynamical systems, and their applications.

  20. Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type

    Energy Technology Data Exchange (ETDEWEB)

    Basharov, A. M., E-mail: basharov@gmail.com [National Research Centre ' Kurchatov Institute,' (Russian Federation)

    2012-09-15

    It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are 'locked' inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.

  1. ALTERNATIVE EQUATIONS FOR DYNAMIC BEHAVIOR OF IONIC CHANNEL ACTIVATION AND INACTIVATION GATES

    Directory of Open Access Journals (Sweden)

    Mahmut ÖZER

    2003-03-01

    Full Text Available In this paper, alternative equations for dynamics of ionic channel activation and inactivation gates are proposed based on the path probability method. Dynamic behavior of a voltage-gated ionic channel is modeled by the conventional Hodgkin-Huxley (H-H mathematical formalism. In that model, conductance of the channel is defined in terms of activation and inactivation gates. Dynamics of the activation and inactivation gates is modeled by first-order differential equations dependent on the gate variable and the membrane potential. In the new approach proposed in this study, dynamic behavior of activation and inactivation gates is modeled by a firstorder differential equation dependent on internal energy and membrane potential by using the path probability method which is widely used in statistical physics. The new model doesn't require the time constant and steadystate values which are used explicitly in the H-H model. The numerical results show validity of the proposed method.

  2. Dynamic Analysis of a Pendulum Dynamic Automatic Balancer

    Directory of Open Access Journals (Sweden)

    Jin-Seung Sohn

    2007-01-01

    Full Text Available The automatic dynamic balancer is a device to reduce the vibration from unbalanced mass of rotors. Instead of considering prevailing ball automatic dynamic balancer, pendulum automatic dynamic balancer is analyzed. For the analysis of dynamic stability and behavior, the nonlinear equations of motion for a system are derived with respect to polar coordinates by the Lagrange's equations. The perturbation method is applied to investigate the dynamic behavior of the system around the equilibrium position. Based on the linearized equations, the dynamic stability of the system around the equilibrium positions is investigated by the eigenvalue analysis.

  3. Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

    Science.gov (United States)

    Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

    2016-01-01

    Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

  4. 19th International Conference on Difference Equations and Applications

    CERN Document Server

    Cushing, Jim; Elaydi, Saber

    2014-01-01

    This volume contains the proceedings of the 19th International Conference on Difference Equations and Applications, held at Sultan Qaboos University, Muscat, Oman in May 2013. The conference brought together experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete time dynamical systems with applications to mathematical sciences and, in particular, mathematical biology, ecology, and epidemiology. It includes four invited papers and eight contributed papers. Topics covered include: competitive exclusion through discrete time models, Benford solutions of linear difference equations, chaos and wild chaos in Lorenz-type systems, advances in periodic difference equations, the periodic decomposition problem, dynamic selection systems and replicator equations, and asymptotic equivalence of difference equations in Banach Space. This book will appeal to researchers, scientists, and educators who work in th...

  5. Nonlinear dynamics in the relativistic field equation

    International Nuclear Information System (INIS)

    Tanaka, Yosuke; Mizuno, Yuji; Kado, Tatsuhiko; Zhao, Hua-An

    2007-01-01

    We have investigated relativistic equations and chaotic behaviors of the gravitational field with the use of general relativity and nonlinear dynamics. The space component of the Friedmann equation shows chaotic behaviors in case of the inflation (h=G-bar /G>0) and open (ζ=-1) universe. In other cases (h= 0 andx-bar 0 ) and the parameters (a, b, c and d); (2) the self-similarity of solutions in the x-x-bar plane and the x-ρ plane. We carried out the numerical calculations with the use of the microsoft EXCEL. The self-similarity and the hierarchy structure of the universe have been also discussed on the basis of E-infinity theory

  6. The Financial Accounting Model from a System Dynamics' Perspective

    OpenAIRE

    Melse, Eric

    2006-01-01

    This paper explores the foundation of the financial accounting model. We examine the properties of the accounting equation as the principal algorithm for the design and the development of a System Dynamics model. Key to the perspective is the foundational requirement that resolves the temporal conflict that resides in a stock and flow model. Through formal analysis the accounting equation is redefined as a cybernetic model by expressing the temporal and dynamic properties of its terms. Articu...

  7. Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system

    International Nuclear Information System (INIS)

    Brett, Tobias; Galla, Tobias

    2014-01-01

    We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period

  8. Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system.

    Science.gov (United States)

    Brett, Tobias; Galla, Tobias

    2014-03-28

    We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.

  9. Dynamical Systems Method and Applications Theoretical Developments and Numerical Examples

    CERN Document Server

    Ramm, Alexander G

    2012-01-01

    Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and

  10. Dynamic equations for gauge-invariant wave functions

    International Nuclear Information System (INIS)

    Kapshaj, V.N.; Skachkov, N.B.; Solovtsov, I.L.

    1984-01-01

    The Bethe-Salpeter and quasipotential dynamic equations for wave functions of relative quark motion, have been derived. Wave functions are determined by the gauge invariant method. The V.A. Fock gauge condition is used in the construction. Despite the transl tional noninvariance of the gauge condition the standard separation of variables has been obtained and wave function doesn't contain gauge exponents

  11. The coupled nonlinear dynamics of a lift system

    Energy Technology Data Exchange (ETDEWEB)

    Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)

    2014-12-10

    Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.

  12. Simulation of dynamic systems with Matlab and Simulink

    CERN Document Server

    Klee, Harold

    2011-01-01

    Mathematical ModelingDerivation of a Mathematical ModelDifference EquationsFirst Look at Discrete-Time SystemsCase Study: Population Dynamics (Single Species)Continuous-Time SystemsFirst-Order SystemsSecond-Order SystemsSimulation DiagramsHigher-Order SystemsState VariablesNonlinear SystemsCase Study: Submarine Depth Control SystemElementary Numerical IntegrationDiscrete-Time System Approximation of a Continuous-

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

    Science.gov (United States)

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

    2017-04-01

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

  14. Parametric Resonance in Dynamical Systems

    CERN Document Server

    Nijmeijer, Henk

    2012-01-01

    Parametric Resonance in Dynamical Systems discusses the phenomenon of parametric resonance and its occurrence in mechanical systems,vehicles, motorcycles, aircraft and marine craft, and micro-electro-mechanical systems. The contributors provide an introduction to the root causes of this phenomenon and its mathematical equivalent, the Mathieu-Hill equation. Also included is a discussion of how parametric resonance occurs on ships and offshore systems and its frequency in mechanical and electrical systems. This book also: Presents the theory and principles behind parametric resonance Provides a unique collection of the different fields where parametric resonance appears including ships and offshore structures, automotive vehicles and mechanical systems Discusses ways to combat, cope with and prevent parametric resonance including passive design measures and active control methods Parametric Resonance in Dynamical Systems is ideal for researchers and mechanical engineers working in application fields such as MEM...

  15. N-body bound state relativistic wave equations

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1988-06-01

    The manifestly covariant formalism with constraints is used for the construction of relativistic wave equations to describe the dynamics of N interacting spin 0 and/or spin 1/2 particles. The total and relative time evolutions of the system are completely determined by means of kinematic type wave equations. The internal dynamics of the system is 3 N-1 dimensional, besides the contribution of the spin degrees of freedom. It is governed by a single dynamical wave equation, that determines the eigenvalue of the total mass squared of the system. The interaction is introduced in a closed form by means of two-body potentials. The system satisfies an approximate form of separability

  16. Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system

    Directory of Open Access Journals (Sweden)

    Boris V. Kapitonov

    2010-02-01

    Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.

  17. Dynamic analysis of floating wave energy generation system with mooring system

    International Nuclear Information System (INIS)

    Choi, Gyu Seok; Sohn, Jeong Hyun

    2013-01-01

    In this study, dynamic behaviors of a wave energy generation system (WEGS) that converts wave energy into electric energy are analyzed using multibody dynamics techniques. Many studies have focused on reducing the effects of a mooring system on the motion of a WEGS. Several kinematic constraints and force elements are employed in the modeling stage. Three dimensional wave load equations are used to implement wave loads. The dynamic behaviors of a WEGS are analyzed under several wave conditions by using MSC/ADAMS, and the rotating speed of the generating shaft is investigated for predicting the electricity capacity. The dynamic behaviors of a WEGS with a mooring system are compared with those of a WEGS without a mooring system. Stability evaluation of a WEGS is carried out through simulation under extreme wave load

  18. The coordinate system transformation of a serial kinematic structures and use in the derivation of systems motion equations

    Directory of Open Access Journals (Sweden)

    Zátopek Jiří

    2016-01-01

    Full Text Available This text discusses the use of transformation matrices to determine the motion equations of the complex mechanical structure. Use of the transformation matrix does not apply only to motion equations but has the general use in relative positions determine of objects in the 3D space. Analysed model is divided into seven physical objects, the transformation matrix and the corresponding inertia/pseudo-inertia matrix is included in each of them. This matrices are strictly necessary to the system dynamic description using the matrix form of Lagrange Equations of the Second Type. Another possibility to use the transformation matrix is shown in the camera system measurement. Model was designed in 3D CAD system SolidWorks, MATLAB was used for the mathematical calculations.

  19. Three-parameter relativistic dynamics. 1. Equation of motion, energy conservation

    International Nuclear Information System (INIS)

    Rogachevskii, A.G.

    1995-01-01

    A formally geometric analog of the relativistic dynamics of a point charged particle is constructed. Time as a function of the spatial coordinates is taken as the trajectory equation, i.e., the trajectory is a hypersurface in Minkowski space. The dynamics is presented. The law of open-quotes energyclose quotes conservation is examined

  20. A dynamical-systems approach for computing ice-affected streamflow

    Science.gov (United States)

    Holtschlag, David J.

    1996-01-01

    A dynamical-systems approach was developed and evaluated for computing ice-affected streamflow. The approach provides for dynamic simulation and parameter estimation of site-specific equations relating ice effects to routinely measured environmental variables. Comparison indicates that results from the dynamical-systems approach ranked higher than results from 11 analytical methods previously investigated on the basis of accuracy and feasibility criteria. Additional research will likely lead to further improvements in the approach.

  1. Oscillation criteria for fourth-order nonlinear delay dynamic equations

    Directory of Open Access Journals (Sweden)

    Yunsong Qi

    2013-03-01

    Full Text Available We obtain criteria for the oscillation of all solutions to a fourth-order nonlinear delay dynamic equation on a time scale that is unbounded from above. The results obtained are illustrated with examples

  2. Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

    Science.gov (United States)

    Park, K. C.; Belvin, W. Keith

    1990-01-01

    A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

  3. Nonlinear dynamics of a coherent polariton-biexciton system

    International Nuclear Information System (INIS)

    Nguyen Trung Dan; Vo Tinh

    1994-08-01

    The nonlinear dynamics of a coherent interacting polariton-biexciton system in optically excited semiconductors is investigated. We consider the case when two macroscopically coherent modes - a lower branch polariton and a biexciton existing simultaneously in a direct-gap semiconductor. The conditions for exhibiting optical bistability in stationary regime are obtained. Numerical simulation for the nonlinear dynamics equations of the system is also carried out. (author). 16 refs, 4 figs

  4. Master equations for degenerate systems: electron radiative cascade in a Coulomb potential

    International Nuclear Information System (INIS)

    Uskov, D B; Pratt, R H

    2004-01-01

    We examine the effects of degeneracy and its lifting for the problem of electron radiative cascade, described by master equations of the Lindblad form (quantum optical master equations). A weak external field approximation is used to study the resulting gradual transformation of cascade dynamics between degenerate and non-degenerate forms. Exploiting the spherical symmetry properties of the system we demonstrate significant difference between perturbations commuting with angular momentum and perturbations breaking the spherical symmetry, such as a homogeneous external field. We discuss the possibility and the general approach for reduction of the Lindblad master equations in the case of spectral degeneracy to the Pauli balance equations. This determines the appropriate choice of basis as, for example, spherical or parabolic

  5. Fine tuning classical and quantum molecular dynamics using a generalized Langevin equation

    Science.gov (United States)

    Rossi, Mariana; Kapil, Venkat; Ceriotti, Michele

    2018-03-01

    Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level of control can be achieved for the dynamical properties computed from thermostatted trajectories. We develop quantitative measures of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic oscillator, and show that these analytical results accurately predict the behavior of strongly anharmonic systems. We also show that it is possible to correct, to a significant extent, the effects of the GLE term onto the corresponding microcanonical dynamics, which puts on more solid grounds the use of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and could help improve the prediction of dynamical quantities from techniques that use a Langevin term to stabilize dynamics. Finally we address the use of thermostats in the context of approximate path-integral-based models of quantum nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some of the artifacts associated with these techniques, improving the quality of results for the modeling of vibrational dynamics of molecules, liquids, and solids.

  6. Consistency of direct integral estimator for partially observed systems of ordinary differential equations

    NARCIS (Netherlands)

    Vujačić, Ivan; Dattner, Itai

    In this paper we use the sieve framework to prove consistency of the ‘direct integral estimator’ of parameters for partially observed systems of ordinary differential equations, which are commonly used for modeling dynamic processes.

  7. Memory Effects and Nonequilibrium Correlations in the Dynamics of Open Quantum Systems

    Science.gov (United States)

    Morozov, V. G.

    2018-01-01

    We propose a systematic approach to the dynamics of open quantum systems in the framework of Zubarev's nonequilibrium statistical operator method. The approach is based on the relation between ensemble means of the Hubbard operators and the matrix elements of the reduced statistical operator of an open quantum system. This key relation allows deriving master equations for open systems following a scheme conceptually identical to the scheme used to derive kinetic equations for distribution functions. The advantage of the proposed formalism is that some relevant dynamical correlations between an open system and its environment can be taken into account. To illustrate the method, we derive a non-Markovian master equation containing the contribution of nonequilibrium correlations associated with energy conservation.

  8. OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

    Science.gov (United States)

    Ott, William; Rivas, Mauricio A; West, James

    2015-12-01

    Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

  9. The dynamics of second-order equations with delayed feedback and a large coefficient of delayed control

    Science.gov (United States)

    Kashchenko, Sergey A.

    2016-12-01

    The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.

  10. Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

    Science.gov (United States)

    Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

    2009-03-01

    We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

  11. Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

    Science.gov (United States)

    Franz, Delbert D.; Melching, Charles S.

    1997-01-01

    The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The

  12. Advanced-Retarded Differential Equations in Quantum Photonic Systems

    Science.gov (United States)

    Alvarez-Rodriguez, Unai; Perez-Leija, Armando; Egusquiza, Iñigo L.; Gräfe, Markus; Sanz, Mikel; Lamata, Lucas; Szameit, Alexander; Solano, Enrique

    2017-01-01

    We propose the realization of photonic circuits whose dynamics is governed by advanced-retarded differential equations. Beyond their mathematical interest, these photonic configurations enable the implementation of quantum feedback and feedforward without requiring any intermediate measurement. We show how this protocol can be applied to implement interesting delay effects in the quantum regime, as well as in the classical limit. Our results elucidate the potential of the protocol as a promising route towards integrated quantum control systems on a chip. PMID:28230090

  13. Third post-Newtonian dynamics of compact binaries: equations of motion in the centre-of-mass frame

    CERN Document Server

    Blanchet, L

    2003-01-01

    The equations of motion of compact binary systems and their associated Lagrangian formulation have been derived in previous works at the third post-Newtonian (3PN) approximation of general relativity in harmonic coordinates. In the present work, we investigate the binary's relative dynamics in the centre-of-mass frame (centre of mass located at the origin of the coordinates). We obtain the 3PN-accurate expressions of the centre-of-mass positions and equations of the relative binary motion. We show that the equations derive from a Lagrangian (neglecting the radiation reaction), from which we deduce the conserved centre-of-mass energy and angular momentum at the 3PN order. The harmonic-coordinates centre-of-mass Lagrangian is equivalent, via a contact transformation of the particles' variables, to the centre-of-mass Hamiltonian in ADM coordinates that is known from the post-Newtonian ADM-Hamiltonian formalism. As an application we investigate the dynamical stability of circular binary orbits at the 3PN order.

  14. General solution of the aerosol dynamic equation: growth and diffusion processes

    International Nuclear Information System (INIS)

    Elgarayhi, A.; Elhanbaly, A.

    2004-01-01

    The dispersion of aerosol particles in a fluid media is studied considering the main mechanism for condensation and diffusion. This has been done when the technique of Lie is used for solving the aerosol dynamic equation. This method is very useful in sense that it reduces the partial differential equation to some ordinary differential equations. So, different classes of similarity solutions have been obtained. The quantity of well-defined physical interest is the mean particle volume has been calculated

  15. Nonlinear Dynamics, Fixed Points and Coupled Fixed Points in Generalized Gauge Spaces with Applications to a System of Integral Equations

    Directory of Open Access Journals (Sweden)

    Adrian Petruşel

    2015-01-01

    Full Text Available We will discuss discrete dynamics generated by single-valued and multivalued operators in spaces endowed with a generalized metric structure. More precisely, the behavior of the sequence (fn(xn∈N of successive approximations in complete generalized gauge spaces is discussed. In the same setting, the case of multivalued operators is also considered. The coupled fixed points for mappings t1:X1×X2→X1 and t2:X1×X2→X2 are discussed and an application to a system of nonlinear integral equations is given.

  16. Finite difference evolution equations and quantum dynamical semigroups

    International Nuclear Information System (INIS)

    Ghirardi, G.C.; Weber, T.

    1983-12-01

    We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)→rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)

  17. Application of flexible model in neutron dynamics equations

    International Nuclear Information System (INIS)

    Liu Cheng; Zhao Fuyu; Fu Xiangang

    2009-01-01

    Big errors will occur in the modeling by multimode methodology when the available core physical parameter sets are insufficient. In this paper, the fuzzy logic membership function is introduced to figure out the values of these parameters on any point of lifetime through limited several sets of values, and thus to obtain the neutron dynamics equations on any point of lifetime. In order to overcome the effect of subjectivity in the membership function selection on the parameter calculation, quadratic optimization is carried out to the membership function by genetic algorithm, to result in a more accurate neutron kinetics equation on any point of lifetime. (authors)

  18. Intrinsic information carriers in combinatorial dynamical systems.

    Science.gov (United States)

    Harmer, Russ; Danos, Vincent; Feret, Jérôme; Krivine, Jean; Fontana, Walter

    2010-09-01

    Many proteins are composed of structural and chemical features--"sites" for short--characterized by definite interaction capabilities, such as noncovalent binding or covalent modification of other proteins. This modularity allows for varying degrees of independence, as the behavior of a site might be controlled by the state of some but not all sites of the ambient protein. Independence quickly generates a startling combinatorial complexity that shapes most biological networks, such as mammalian signaling systems, and effectively prevents their study in terms of kinetic equations-unless the complexity is radically trimmed. Yet, if combinatorial complexity is key to the system's behavior, eliminating it will prevent, not facilitate, understanding. A more adequate representation of a combinatorial system is provided by a graph-based framework of rewrite rules where each rule specifies only the information that an interaction mechanism depends on. Unlike reactions, which deal with molecular species, rules deal with patterns, i.e., multisets of molecular species. Although the stochastic dynamics induced by a collection of rules on a mixture of molecules can be simulated, it appears useful to capture the system's average or deterministic behavior by means of differential equations. However, expansion of the rules into kinetic equations at the level of molecular species is not only impractical, but conceptually indefensible. If rules describe bona fide patterns of interaction, molecular species are unlikely to constitute appropriate units of dynamics. Rather, we must seek aggregate variables reflective of the causal structure laid down by the rules. We call these variables "fragments" and the process of identifying them "fragmentation." Ideally, fragments are aspects of the system's microscopic population that the set of rules can actually distinguish on average; in practice, it may only be feasible to identify an approximation to this. Most importantly, fragments are

  19. Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

    Directory of Open Access Journals (Sweden)

    Taher S. Hassan

    2016-01-01

    Full Text Available We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t≔ri(tϕαixi-1Δ(t,  i=1,…,n-1,   with  x0=x,  ϕβ(u≔uβsgn⁡u, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.

  20. A computational method for direct integration of motion equations of structural systems

    International Nuclear Information System (INIS)

    Brusa, L.; Ciacci, R.; Creco, A.; Rossi, F.

    1975-01-01

    The dynamic analysis of structural systems requires the solution of the matrix equations: Md 2 delta/dt(t) + Cddelta/dt(t) + Kdelta(t) = F(t). Many numerical methods are available for direct integration of this equation and their efficiency is due to the fulfillment of the following requirements: A reasonable order of accuracy must be obtained for the approximation of the response relevant to the first modes: the model contributions relevant to the eigenvalues with large real part must be essentially neglected. This paper presents a step-by-step numerical scheme for the integration of this equation which satisfies the requirements previously mentioned. (Auth.)

  1. System Dynamics and Modified Cumulant Neglect Closure Schemes

    DEFF Research Database (Denmark)

    Köylüoglu, H. Ugur; Nielsen, Søren R.K.

    Dealing with multipeaked problems, the goal of the paper is to improve the quality of the approximations for the expectations appearing in the differential equations written for the statistical moments of the state vector, guided by insight in the system dynamics. For systems with polynomial non...

  2. On generalized fractional vibration equation

    International Nuclear Information System (INIS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-01-01

    Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

  3. New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

    Directory of Open Access Journals (Sweden)

    Mohamed S. Al-luhaibi

    2015-01-01

    Full Text Available This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

  4. On non-linear dynamics of a coupled electro-mechanical system

    DEFF Research Database (Denmark)

    Darula, Radoslav; Sorokin, Sergey

    2012-01-01

    Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a......, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical...

  5. Maxwell-Vlasov equations as a continuous Hamiltonian system

    International Nuclear Information System (INIS)

    Morrison, P.J.

    1980-09-01

    The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion

  6. A stochastic differential equation framework for the timewise dynamics of turbulent velocities

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen

    2008-01-01

    We discuss a stochastic differential equation as a modeling framework for the timewise dynamics of turbulent velocities. The equation is capable of capturing basic stylized facts of the statistics of temporal velocity increments. In particular, we focus on the evolution of the probability density...

  7. Exactly integrable two-dimensional dynamical systems related with supersymmetric algebras

    International Nuclear Information System (INIS)

    Leznov, A.N.

    1983-01-01

    A wide class of exactly integrable dynamical systems in two-dimensional space related with superalgebras, which generalize supersymmetric Liouville equation, is constructed. The equations can be interpretated as nonlinearly interacting Bose and Fermi fields belonging within classical limit to even and odd parts of the Grassman space. Explicit expressions for the solutions of the constructed systems are obtained on the basis of standard perturbation theory

  8. Is w≠-1 evidence for a dynamical dark energy equation of state?

    International Nuclear Information System (INIS)

    Avelino, P. P.; Trindade, A. M. M.; Viana, P. T. P.

    2009-01-01

    Current constraints on the dark energy equation of state parameter, w, are expected to be improved by more than 1 order of magnitude in the next decade. If |w-1| > or approx. 0.01 around the present time, but the dark energy dynamics is sufficiently slow, it is possible that future constraints will rule out a cosmological constant while being consistent with a time-independent equation of state parameter. In this paper, we show that although models with such behavior can be constructed, they do require significant fine-tuning. Therefore, if the observed acceleration of the Universe is induced by a dark energy component, then finding w≠-1 would, on its own, constitute very strong evidence for a dynamical dark energy equation of state.

  9. Parametric dynamic analysis of a superconducting bearing system

    Energy Technology Data Exchange (ETDEWEB)

    Cansiz, A; Hasar, U C; Cam, B Ates [Electrical and Electronics Engineering Department, Ataturk University, Erzurum (Turkey); Gundogdu, Oe, E-mail: acansiz@atauni.edu.t [Mechanical Engineering Department, Ataturk University, Erzurum (Turkey)

    2009-03-01

    The dynamics of a disk-shaped permanent-magnet rotor levitated over a high-temperature superconductor is studied. The interaction between the rotor magnet and the superconductor is modelled by assuming the magnet to be a magnetic dipole and the superconductor as a diamagnetic material. In the magneto-mechanical analysis of the superconductor part, the frozen image concept is combined with the diamagnetic image and the damping in the system was neglected. The interaction potential of the system is the combination of magnetic and gravitational potential. From the dynamical analysis, the equations of motion of the permanent magnet are stated as a function of lateral, vertical and tilt directions. The vibration behaviour of the permanent magnet is analyzed with a numerical calculation obtained by the non-dimensionalized differential equations for small initial impulses.

  10. Parametric dynamic analysis of a superconducting bearing system

    International Nuclear Information System (INIS)

    Cansiz, A; Hasar, U C; Cam, B Ates; Gundogdu, Oe

    2009-01-01

    The dynamics of a disk-shaped permanent-magnet rotor levitated over a high-temperature superconductor is studied. The interaction between the rotor magnet and the superconductor is modelled by assuming the magnet to be a magnetic dipole and the superconductor as a diamagnetic material. In the magneto-mechanical analysis of the superconductor part, the frozen image concept is combined with the diamagnetic image and the damping in the system was neglected. The interaction potential of the system is the combination of magnetic and gravitational potential. From the dynamical analysis, the equations of motion of the permanent magnet are stated as a function of lateral, vertical and tilt directions. The vibration behaviour of the permanent magnet is analyzed with a numerical calculation obtained by the non-dimensionalized differential equations for small initial impulses.

  11. Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System

    Directory of Open Access Journals (Sweden)

    Qilin Huang

    2013-01-01

    Full Text Available A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM. Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.

  12. An uncoupling strategy for numerically solving the dynamic thermoelasticity equations

    International Nuclear Information System (INIS)

    Moura, C.A. de; Feijoo, R.A.

    1981-01-01

    The dynamic equations of coupled linear thermoelasticity are presented. A numerical algorithm which combines finite-element space approximation with a two-step time discretization in such a way as to reach significant computational savings is presented: It features a strategy for independently calculating the displacement and temperature fields through equations that nevertheless remain coupled. The scheme convergence was shown to be optimal and its machine performance, as ilustrated by some examples, fairly satisfactory. (Author) [pt

  13. Polynomial f (R ) Palatini cosmology: Dynamical system approach

    Science.gov (United States)

    Szydłowski, Marek; Stachowski, Aleksander

    2018-05-01

    We investigate cosmological dynamics based on f (R ) gravity in the Palatini formulation. In this study, we use the dynamical system methods. We show that the evolution of the Friedmann equation reduces to the form of the piecewise smooth dynamical system. This system is reduced to a 2D dynamical system of the Newtonian type. We demonstrate how the trajectories can be sewn to guarantee C0 extendibility of the metric similarly as "Milne-like" Friedmann-Lemaître-Robertson-Walker spacetimes are C0-extendible. We point out that importance of the dynamical system of the Newtonian type with nonsmooth right-hand sides in the context of Palatini cosmology. In this framework, we can investigate singularities which appear in the past and future of the cosmic evolution. We consider cosmological systems in both Einstein and Jordan frames. We show that at each frame the topological structures of phase space are different.

  14. Simulation of noisy dynamical system by Deep Learning

    Science.gov (United States)

    Yeo, Kyongmin

    2017-11-01

    Deep learning has attracted huge attention due to its powerful representation capability. However, most of the studies on deep learning have been focused on visual analytics or language modeling and the capability of the deep learning in modeling dynamical systems is not well understood. In this study, we use a recurrent neural network to model noisy nonlinear dynamical systems. In particular, we use a long short-term memory (LSTM) network, which constructs internal nonlinear dynamics systems. We propose a cross-entropy loss with spatial ridge regularization to learn a non-stationary conditional probability distribution from a noisy nonlinear dynamical system. A Monte Carlo procedure to perform time-marching simulations by using the LSTM is presented. The behavior of the LSTM is studied by using noisy, forced Van der Pol oscillator and Ikeda equation.

  15. Integrated vehicle dynamics control using State Dependent Riccati Equations

    NARCIS (Netherlands)

    Bonsen, B.; Mansvelders, R.; Vermeer, E.

    2010-01-01

    In this paper we discuss a State Dependent Riccati Equations (SDRE) solution for Integrated Vehicle Dynamics Control (IVDC). The SDRE approach is a nonlinear variant of the well known Linear Quadratic Regulator (LQR) and implements a quadratic cost function optimization. A modified version of this

  16. System dynamics an introduction for mechanical engineers

    CERN Document Server

    Seeler, Karl A

    2014-01-01

    This essential textbook takes the student from the initial steps in modeling a dynamic system through development of the mathematical models needed for feedback control.  The generously-illustrated, student-friendly text focuses on fundamental theoretical development rather than the application of commercial software.  Practical details of machine design are included to motivate the non-mathematically inclined student. This book also: Emphasizes the linear graph method for modeling dynamic systems Offers a systematic approach for creating an engineering model, extracting information, and formulating mathematical analyses Adopts a unifying theme of power flow as the dynamic agent that eases analysis of hybrid systems, such as machinery Presents differential equations as dynamic operators and stresses input/output relationships Introduces Mathcad and programming in MATLAB Allows for use of Open Source Computational Software (R or C) Features over 1000 illustrations

  17. Integrable systems of partial differential equations determined by structure equations and Lax pair

    International Nuclear Information System (INIS)

    Bracken, Paul

    2010-01-01

    It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.

  18. Equations of multiparticle dynamics

    International Nuclear Information System (INIS)

    Chao, A.W.

    1987-01-01

    The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions

  19. Simulation of the dynamic response of radioactive material shipping package - railcar systems during coupling operations

    International Nuclear Information System (INIS)

    Fields, S.R.

    1981-12-01

    The basic equations of the computer model CARDS (Cask-Railcar Dynamic Simulator), developed for the U.S. Nuclear Regulatory Commission to simulate the dynamic behavior of radioactive material shipping package - railcar systems, are presented. A companion model, CARRS (Casks Railcar Response Spectrum Generator), that generates system response as frequency response spectra is also presented in terms of its basic equations

  20. Simulation of the dynamic response of radioactive material shipping package-railcar systems during coupling operations

    International Nuclear Information System (INIS)

    Fields, S.R.

    1983-10-01

    The basic equations of the computer model CARDS (Cask-Railcar Dynamic Simulator), developed for the US Nuclear Regulatory Commission to simulate the dynamic behavior of radioactive material shipping package - railcar systems, are presented. A companion model, CARRS (Cask Railcar Response Spectrum Generator), that generates system response as frequency response spectra is also presented in terms of its basic equations. 1 reference, 18 figures

  1. Driven-dissipative Euler close-quote s equations for a rigid body: A chaotic system relevant to fluid dynamics

    International Nuclear Information System (INIS)

    Turner, L.

    1996-01-01

    Adhering to the lore that vorticity is a critical ingredient of fluid turbulence, a triad of coupled helicity (vorticity) states of the incompressible Navier-Stokes fluid are followed. Effects of the remaining states of the fluid on the triad are then modeled as a simple driving term. Numerical solution of the equations yield attractors that seem strange and chaotic. This suggests that the unpredictability of nonlinear fluid dynamics (i.e., turbulence) may be traced back to the most primordial structure of the Navier-Stokes equation; namely, the driven triadic interaction. copyright 1996 The American Physical Society

  2. Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

    Science.gov (United States)

    Hunt, L. R.; Villarreal, Ramiro

    1987-01-01

    System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

  3. Estimating Dynamical Systems: Derivative Estimation Hints from Sir Ronald A. Fisher

    Science.gov (United States)

    Deboeck, Pascal R.

    2010-01-01

    The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common…

  4. Differential Equations Models to Study Quorum Sensing.

    Science.gov (United States)

    Pérez-Velázquez, Judith; Hense, Burkhard A

    2018-01-01

    Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

  5. Adaptive synchronization between two different order and topology dynamical systems

    International Nuclear Information System (INIS)

    Bowong, S.; Moukam Kakmeni, F.M.; Yamapi, R.

    2006-07-01

    This contribution studies adaptive synchronization between two dynamical systems of different order whose topological structure is also different. By order we mean the number of first order differential equations. The problem is closely related to the synchronization of strictly different systems. The master system is given by a sixth order equation with chaotic behavior whereas the slave system is a fourth-order nonautonomous with rational nonlinear terms. Based on the Lyapunov stability theory, sufficient conditions for the synchronization have been analyzed theoretically and numerically. (author)

  6. Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions

    Directory of Open Access Journals (Sweden)

    R. Naz

    2015-01-01

    Full Text Available We study a dynamic fourth-order Euler-Bernoulli partial differential equation having a constant elastic modulus and area moment of inertia, a variable lineal mass density g(x, and the applied load denoted by f(u, a function of transverse displacement u(t,x. The complete Lie group classification is obtained for different forms of the variable lineal mass density g(x and applied load f(u. The equivalence transformations are constructed to simplify the determining equations for the symmetries. The principal algebra is one-dimensional and it extends to two- and three-dimensional algebras for an arbitrary applied load, general power-law, exponential, and log type of applied loads for different forms of g(x. For the linear applied load case, we obtain an infinite-dimensional Lie algebra. We recover the Lie symmetry classification results discussed in the literature when g(x is constant with variable applied load f(u. For the general power-law and exponential case the group invariant solutions are derived. The similarity transformations reduce the fourth-order partial differential equation to a fourth-order ordinary differential equation. For the power-law applied load case a compatible initial-boundary value problem for the clamped and free end beam cases is formulated. We deduce the fourth-order ordinary differential equation with appropriate initial and boundary conditions.

  7. Abstraction of Dynamical Systems by Timed Automata

    DEFF Research Database (Denmark)

    Wisniewski, Rafael; Sloth, Christoffer

    2011-01-01

    To enable formal verification of a dynamical system, given by a set of differential equations, it is abstracted by a finite state model. This allows for application of methods for model checking. Consequently, it opens the possibility of carrying out the verification of reachability and timing re...

  8. Linear dynamic coupling in geared rotor systems

    Science.gov (United States)

    David, J. W.; Mitchell, L. D.

    1986-01-01

    The effects of high frequency oscillations caused by the gear mesh, on components of a geared system that can be modeled as rigid discs are analyzed using linear dynamic coupling terms. The coupled, nonlinear equations of motion for a disc attached to a rotating shaft are presented. The results of a trial problem analysis show that the inclusion of the linear dynamic coupling terms can produce significant changes in the predicted response of geared rotor systems, and that the produced sideband responses are greater than the unbalanced response. The method is useful in designing gear drives for heavy-lift helicopters, industrial speed reducers, naval propulsion systems, and heavy off-road equipment.

  9. Dynamic analysis, controlling chaos and chaotification of a SMIB power system

    International Nuclear Information System (INIS)

    Chen, H.-K.; Lin, T.-N.; Chen, J.-H.

    2005-01-01

    The dynamic behaviors of a SMIB power system are studied in this paper. A single modal equation is used to analyze the qualitative behaviors of the system. The famous equation of motion is called 'swing equation'. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of the system. The bifurcation of the parameter dependent system is studied numerically. Besides, the phase portraits, the Poincare maps, and the Lyapunov exponents are presented to observe periodic and chaotic motions. Further, the addition of periodic force and the feedback control are used to control chaos effectively. Finally, the chaotification problem of the SMIB power system is also issued

  10. Model Selection and Risk Estimation with Applications to Nonlinear Ordinary Differential Equation Systems

    DEFF Research Database (Denmark)

    Mikkelsen, Frederik Vissing

    eective computational tools for estimating unknown structures in dynamical systems, such as gene regulatory networks, which may be used to predict downstream eects of interventions in the system. A recommended algorithm based on the computational tools is presented and thoroughly tested in various......Broadly speaking, this thesis is devoted to model selection applied to ordinary dierential equations and risk estimation under model selection. A model selection framework was developed for modelling time course data by ordinary dierential equations. The framework is accompanied by the R software...... package, episode. This package incorporates a collection of sparsity inducing penalties into two types of loss functions: a squared loss function relying on numerically solving the equations and an approximate loss function based on inverse collocation methods. The goal of this framework is to provide...

  11. The Scherrer equation and the dynamical theory of X-ray diffraction.

    Science.gov (United States)

    Muniz, Francisco Tiago Leitão; Miranda, Marcus Aurélio Ribeiro; Morilla Dos Santos, Cássio; Sasaki, José Marcos

    2016-05-01

    The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6 and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm(-1) the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.

  12. Nambu-Poisson reformulation of the finite dimensional dynamical systems

    International Nuclear Information System (INIS)

    Baleanu, D.; Makhaldiani, N.

    1998-01-01

    A system of nonlinear ordinary differential equations which in a particular case reduces to Volterra's system is introduced. We found in two simplest cases the complete sets of the integrals of motion using Nambu-Poisson reformulation of the Hamiltonian dynamics. In these cases we have solved the systems by quadratures

  13. Nonlinear integrodifferential equations as discrete systems

    Science.gov (United States)

    Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

    1999-06-01

    We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

  14. Optimal Operation of Radial Distribution Systems Using Extended Dynamic Programming

    DEFF Research Database (Denmark)

    Lopez, Juan Camilo; Vergara, Pedro P.; Lyra, Christiano

    2018-01-01

    An extended dynamic programming (EDP) approach is developed to optimize the ac steady-state operation of radial electrical distribution systems (EDS). Based on the optimality principle of the recursive Hamilton-Jacobi-Bellman equations, the proposed EDP approach determines the optimal operation o...... approach is illustrated using real-scale systems and comparisons with commercial programming solvers. Finally, generalizations to consider other EDS operation problems are also discussed.......An extended dynamic programming (EDP) approach is developed to optimize the ac steady-state operation of radial electrical distribution systems (EDS). Based on the optimality principle of the recursive Hamilton-Jacobi-Bellman equations, the proposed EDP approach determines the optimal operation...... of the EDS by setting the values of the controllable variables at each time period. A suitable definition for the stages of the problem makes it possible to represent the optimal ac power flow of radial EDS as a dynamic programming problem, wherein the 'curse of dimensionality' is a minor concern, since...

  15. Solutions of system of P1 equations without use of auxiliary differential equations coupled

    International Nuclear Information System (INIS)

    Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos

    2000-01-01

    The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)

  16. Relativistic point dynamics general equations, constant proper masses, interactions between electric charges, variable proper masses, collisions

    CERN Document Server

    Arzeliès, Henri

    1972-01-01

    Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int

  17. Theoretical foundation for the discrete dynamics of physicochemical systems: Chaos, self-organization, time and space in complex systems

    Directory of Open Access Journals (Sweden)

    V. Gontar

    1997-01-01

    Full Text Available A new theoretical foundation for the discrete dynamics of physicochemical systems is presented. Based on the analogy between the π-theorem of the theory of dimensionality, the second law of thermodynamics and the stoichiometry of complex physicochemical reactions, basic dynamic equations and an extreme principle were formulated. The meaning of discrete time and space in the proposed equations is discussed. Some results of numerical calculations are presented to demonstrate the potential of the proposed approach to the mathematical simulation of spatiotemporal physicochemical reaction dynamics.

  18. Effective equations for the precession dynamics of electron spins and electron–impurity correlations in diluted magnetic semiconductors

    International Nuclear Information System (INIS)

    Cygorek, M; Axt, V M

    2015-01-01

    Starting from a quantum kinetic theory for the spin dynamics in diluted magnetic semiconductors, we derive simplified equations that effectively describe the spin transfer between carriers and magnetic impurities for an arbitrary initial impurity magnetization. Taking the Markov limit of these effective equations, we obtain good quantitative agreement with the full quantum kinetic theory for the spin dynamics in bulk systems at high magnetic doping. In contrast, the standard rate description where the carrier–dopant interaction is treated according to Fermi’s golden rule, which involves the assumption of a short memory as well as a perturbative argument, has been shown previously to fail if the impurity magnetization is non-zero. The Markov limit of the effective equations is derived, assuming only a short memory, while higher order terms are still accounted for. These higher order terms represent the precession of the carrier–dopant correlations in the effective magnetic field due to the impurity spins. Numerical calculations show that the Markov limit of our effective equations reproduces the results of the full quantum kinetic theory very well. Furthermore, this limit allows for analytical solutions and for a physically transparent interpretation. (paper)

  19. Domestic and outbound tourism demand in Australia: a System-of-Equations Approach

    OpenAIRE

    George Athanasopoulos; Minfeng Deng; Gang Li; Haiyan Song

    2013-01-01

    This study uses a system-of-equations approach to model the substitution relationship between Australian domestic and outbound tourism demand. A new price variable based on relative ratios of purchasing power parity index is developed for the substitution analysis. Short-run demand elasticities are calculated based on the estimated dynamic almost ideal demand system. The empirical results reveal significant substitution relationships between Australian domestic tourism and outbound travel to ...

  20. Dynamic Modeling and Simulation of an Underactuated System

    International Nuclear Information System (INIS)

    Duarte Madrid, Juan Libardo; Querubín, E González; Henao, P A Ospina

    2017-01-01

    In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in SOLIDWORKS 3D CAD software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the results obtained, a comparison the CAD model simulated in the environment SimMechanics of MATLAB software with the mathematical model who was consisting of Euler-Lagrange’s equations implemented in Simulink MATLAB, solved with the ODE23tb method, included in the MATLAB libraries for the solution of systems of equations of the type and order obtained. This article also has a topological analysis of pendulum trajectories through a phase space diagram, which allows the identification of stable and unstable regions of the system. (paper)

  1. Potential and flux field landscape theory. II. Non-equilibrium thermodynamics of spatially inhomogeneous stochastic dynamical systems

    International Nuclear Information System (INIS)

    Wu, Wei; Wang, Jin

    2014-01-01

    We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series

  2. Vlasov dynamics of periodically driven systems

    Science.gov (United States)

    Banerjee, Soumyadip; Shah, Kushal

    2018-04-01

    Analytical solutions of the Vlasov equation for periodically driven systems are of importance in several areas of plasma physics and dynamical systems and are usually approximated using ponderomotive theory. In this paper, we derive the plasma distribution function predicted by ponderomotive theory using Hamiltonian averaging theory and compare it with solutions obtained by the method of characteristics. Our results show that though ponderomotive theory is relatively much easier to use, its predictions are very restrictive and are likely to be very different from the actual distribution function of the system. We also analyse all possible initial conditions which lead to periodic solutions of the Vlasov equation for periodically driven systems and conjecture that the irreducible polynomial corresponding to the initial condition must only have squares of the spatial and momentum coordinate. The resulting distribution function for other initial conditions is aperiodic and can lead to complex relaxation processes within the plasma.

  3. Double compactons in the Olver–Rosenau equation

    Indian Academy of Sciences (India)

    2013-03-01

    Mar 1, 2013 ... are treated by the dynamical systems theory and a phase-space analysis ... The distinguishing feature of the systems ... This equation has attracted a lot of attention ... integration over ξ leads to an ordinary differential equation.

  4. Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics

    International Nuclear Information System (INIS)

    Le Bourdiec, S.

    2007-03-01

    Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

  5. Equation of state of dense plasmas: Orbital-free molecular dynamics as the limit of quantum molecular dynamics for high-Z elements

    Energy Technology Data Exchange (ETDEWEB)

    Danel, J.-F.; Blottiau, P.; Kazandjian, L.; Piron, R.; Torrent, M. [CEA, DAM, DIF, 91297 Arpajon (France)

    2014-10-15

    The applicability of quantum molecular dynamics to the calculation of the equation of state of a dense plasma is limited at high temperature by computational cost. Orbital-free molecular dynamics, based on a semiclassical approximation and possibly on a gradient correction, is a simulation method available at high temperature. For a high-Z element such as lutetium, we examine how orbital-free molecular dynamics applied to the equation of state of a dense plasma can be regarded as the limit of quantum molecular dynamics at high temperature. For the normal mass density and twice the normal mass density, we show that the pressures calculated with the quantum approach converge monotonically towards those calculated with the orbital-free approach; we observe a faster convergence when the orbital-free approach includes the gradient correction. We propose a method to obtain an equation of state reproducing quantum molecular dynamics results up to high temperatures where this approach cannot be directly implemented. With the results already obtained for low-Z plasmas, the present study opens the way for reproducing the quantum molecular dynamics pressure for all elements up to high temperatures.

  6. Effects produced by oscillations applied to nonlinear dynamic systems: a general approach and examples

    DEFF Research Database (Denmark)

    Blekhman, I. I.; Sorokin, V. S.

    2016-01-01

    A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics.......g., the requirement for the involved nonlinearities to be weak. The approach is illustrated by several relevant examples from various fields of science, e.g., mechanics, physics, chemistry and biophysics....... equations). The approach is named as the oscillatory strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that capture the averaged effect of oscillations. The method of direct separation of motions appears to be an efficient...

  7. Stabilization of computational procedures for constrained dynamical systems

    Science.gov (United States)

    Park, K. C.; Chiou, J. C.

    1988-01-01

    A new stabilization method of treating constraints in multibody dynamical systems is presented. By tailoring a penalty form of the constraint equations, the method achieves stabilization without artificial damping and yields a companion matrix differential equation for the constraint forces; hence, the constraint forces are obtained by integrating the companion differential equation for the constraint forces in time. A principal feature of the method is that the errors committed in each constraint condition decay with its corresponding characteristic time scale associated with its constraint force. Numerical experiments indicate that the method yields a marked improvement over existing techniques.

  8. The principal equations of state for classical particles, photons, and neutrinos

    DEFF Research Database (Denmark)

    Essex, Christopher; Andresen, Bjarne Bøgeskov

    2013-01-01

    Functions, not dynamical equations, are the definitive mathematical objects in equilibrium thermodynamics. However, more than one function is often described as “the” equation of state for any one physical system. Usually these so named equations only capture incomplete physical content in the re......Functions, not dynamical equations, are the definitive mathematical objects in equilibrium thermodynamics. However, more than one function is often described as “the” equation of state for any one physical system. Usually these so named equations only capture incomplete physical content...

  9. Self-Consistent System of Equations for a Kinetic Description of the Low-Pressure Discharges Accounting for the Nonlocal and Collisionless Electron Dynamics

    International Nuclear Information System (INIS)

    Kaganovich, Igor D.; Polomarov, Oleg

    2003-01-01

    In low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially non-local. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the non-local conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, non-uniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the non-uniform plasma density profile on both the current density profile and the EEDF is demonstrated

  10. Effective Hamiltonians, two level systems, and generalized Maxwell-Bloch equations

    International Nuclear Information System (INIS)

    Sczaniecki, L.

    1981-02-01

    A new method is proposed involving a canonical transformation leading to the non-secular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating wave approximation is written anew within the framework of our formalism. (author)

  11. Perturbation Solutions for Random Linear Structural Systems subject to Random Excitation using Stochastic Differential Equations

    DEFF Research Database (Denmark)

    Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.

    1994-01-01

    perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect......The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...

  12. Extension of the Method of Direct Separation of Motions for Problems of Oscillating Action on Dynamical Systems

    DEFF Research Database (Denmark)

    Blekhman, Iliya I.; Sorokin, Vladislav

    2016-01-01

    A general approach to study oscillating action on nonlinear dynamical systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics equations). The approach...... is named as the Oscillatory Strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that represent the averaged effect of the oscillating action. The method of direct separation of motions (MDSM) appears to be an efficient...

  13. Dynamics of Nonlinear Time-Delay Systems

    CERN Document Server

    Lakshmanan, Muthusamy

    2010-01-01

    Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...

  14. Feedback coupling in dynamical systems

    Science.gov (United States)

    Trimper, Steffen; Zabrocki, Knud

    2003-05-01

    Different evolution models are considered with feedback-couplings. In particular, we study the Lotka-Volterra system under the influence of a cumulative term, the Ginzburg-Landau model with a convolution memory term and chemical rate equations with time delay. The memory leads to a modified dynamical behavior. In case of a positive coupling the generalized Lotka-Volterra system exhibits a maximum gain achieved after a finite time, but the population will die out in the long time limit. In the opposite case, the time evolution is terminated in a crash. Due to the nonlinear feedback coupling the two branches of a bistable model are controlled by the the strength and the sign of the memory. For a negative coupling the system is able to switch over between both branches of the stationary solution. The dynamics of the system is further controlled by the initial condition. The diffusion-limited reaction is likewise studied in case the reacting entities are not available simultaneously. Whereas for an external feedback the dynamics is altered, but the stationary solution remain unchanged, a self-organized internal feedback leads to a time persistent solution.

  15. Dynamic Systems and Software

    DEFF Research Database (Denmark)

    Thomsen, Per Grove

    1996-01-01

    A one-dimensional model with axial discretization of engine components has been formulated using tha balance equations for mass energy and momentum and the ideal gas equation of state. ODE's that govern the dynamic behaviour of the regenerator matrix temperatures are included in the model. Known...

  16. Parameter estimation of a delay dynamical system using synchronization in presence of noise

    International Nuclear Information System (INIS)

    Rakshit, Biswambhar; Chowdhury, A. Roy; Saha, Papri

    2007-01-01

    A method of parameter estimation of a time delay chaotic system through synchronization is discussed. It is assumed that the observed data can always be effected with some white Gaussian noise. A least square approach is used to derive a system of differential equations which governs the temporal evolution of the parameters. These system of equations together with the coupled delay dynamical systems, when integrated, leads to asymptotic convergence to the value of the parameter along with synchronization of the two system variables. This method is quite effective for estimating the delay time which is an important characteristic feature of a delay dynamical system. The procedure is quite robust in the presence of noise

  17. On the dynamics of chain systems. [applications in manipulator and human body models

    Science.gov (United States)

    Huston, R. L.; Passerello, C. E.

    1974-01-01

    A computer-oriented method for obtaining dynamical equations of motion for chain systems is presented. A chain system is defined as an arbitrarily assembled set of rigid bodies such that adjoining bodies have at least one common point and such that closed loops are not formed. The equations of motion are developed through the use of Lagrange's form of d'Alembert's principle. The method and procedure is illustrated with an elementary study of a tripod space manipulator. The method is designed for application with systems such as human body models, chains and cables, and dynamic finite-segment models.

  18. The Schroedinger-Poisson equations as the large-N limit of the Newtonian N-body system. Applications to the large scale dark matter dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Briscese, Fabio [Northumbria University, Department of Mathematics, Physics and Electrical Engineering, Newcastle upon Tyne (United Kingdom); Citta Universitaria, Istituto Nazionale di Alta Matematica Francesco Severi, Gruppo Nazionale di Fisica Matematica, Rome (Italy)

    2017-09-15

    In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schroedinger-Poisson equations in the large N limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as ℎ ∝ M{sup 5/3}G{sup 1/2}(N/ left angle ρ right angle){sup 1/6}, where is G the gravitational constant, N and M are the number and the mass of the bodies, and left angle ρ right angle is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schroedinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales. (orig.)

  19. Torsional vibration of crankshaft in an engine propeller nonlinear dynamical system

    Science.gov (United States)

    Zhang, X.; Yu, S. D.

    2009-01-01

    Theoretical and experimental studies on torsional vibration of an aircraft engine-propeller system are presented in this paper. Two system models—a rigid body model and a flexible body model, are developed for predicting torsional vibrations of the crankshaft under different engine powers and propeller pitch settings. In the flexible body model, the distributed torsional flexibility and mass moment of inertia of the crankshaft are considered using the finite element method. The nonlinear autonomous equations of motion for the engine-propeller dynamical system are established using the augmented Lagrange equations, and solved using the Runge-Kutta method after a degrees of freedom reduction scheme is applied. Experiments are carried out on a three-cylinder four-stroke engine. Both theoretical and experimental studies reveal that the crankshaft flexibility has significant influence on the system dynamical behavior.

  20. On the coupling of systems of hyperbolic conservation laws with ordinary differential equations

    International Nuclear Information System (INIS)

    Borsche, Raul; Colombo, Rinaldo M; Garavello, Mauro

    2010-01-01

    Motivated by applications to the piston problem, to a manhole model, to blood flow and to supply chain dynamics, this paper deals with a system of conservation laws coupled with a system of ordinary differential equations. The former is defined on a domain with boundary and the coupling is provided by the boundary condition. For each of the examples considered, numerical integrations are provided

  1. Optimal Control Strategies in a Two Dimensional Differential Game Using Linear Equation under a Perturbed System

    Directory of Open Access Journals (Sweden)

    Musa Danjuma SHEHU

    2008-06-01

    Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.

  2. On the Dynamic Programming Approach for the 3D Navier-Stokes Equations

    International Nuclear Information System (INIS)

    Manca, Luigi

    2008-01-01

    The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed

  3. Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

    Science.gov (United States)

    Abdulwahhab, Muhammad Alim

    2016-10-01

    Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

  4. Einstein-Friedmann equation, nonlinear dynamics and chaotic behaviours

    International Nuclear Information System (INIS)

    Tanaka, Yosuke; Nakano, Shingo; Ohta, Shigetoshi; Mori, Keisuke; Horiuchi, Tanji

    2009-01-01

    We have studied the Einstein-Friedmann equation [Case 1] on the basis of the bifurcation theory and shown that the chaotic behaviours in the Einstein-Friedmann equation [Case 1] are reduced to the pitchfork bifurcation and the homoclinic bifurcation. We have obtained the following results: (i) 'The chaos region diagram' (the p-λ plane) in the Einstein-Friedmann equation [Case 1]. (ii) 'The chaos inducing chart' of the homoclinic orbital systems in the unforced differential equations. We have discussed the non-integrable conditions in the Einstein-Friedmann equation and proposed the chaotic model: p=p 0 ρ n (n≥0). In case n≠0,1, the Einstein-Friedmann equation is not integrable and there may occur chaotic behaviours. The cosmological constant (λ) turns out to play important roles for the non-integrable condition in the Einstein-Friedmann equation and also for the pitchfork bifurcation and the homoclinic bifurcation in the relativistic field equation. With the use of the E-infinity theory, we have also discussed the physical quantities in the gravitational field equations, and obtained the formula logκ=-10(1/φ) 2 [1+(φ) 8 ]=-26.737, which is in nice agreement with the experiment (-26.730).

  5. Multiparameter Stochastic Dynamics of Ecological Tourism System with Continuous Visitor Education Interventions

    Directory of Open Access Journals (Sweden)

    Dongping Wei

    2015-01-01

    Full Text Available Management of ecological tourism in protected areas faces many challenges, with visitation-related resource degradations and cultural impacts being two of them. To address those issues, several strategies including regulations, site managements, and visitor education programs have been commonly used in China and other countries. This paper presents a multiparameter stochastic differential equation model of an Ecological Tourism System to study how the populations of stakeholders vary in a finite time. The solution of Ordinary Differential Equation of Ecological Tourism System reveals that the system collapses when there is a lack of visitor educational intervention. Hence, the Stochastic Dynamic of Ecological Tourism System is introduced to suppress the explosion of the system. But the simulation results of the Stochastic Dynamic of Ecological Tourism System show that the system is still unstable and chaos in some small time interval. The Multiparameters Stochastic Dynamics of Ecological Tourism System is proposed to improve the performance in this paper. The Multiparameters Stochastic Dynamics of Ecological Tourism System not only suppresses the explosion of the system in a finite time, but also keeps the populations of stakeholders in an acceptable level. In conclusion, the Ecological Tourism System develops steadily and sustainably when land managers employ effective visitor education intervention programs to deal with recreation impacts.

  6. Flux weighted method for solution of stiff neutron dynamic equations and its application

    International Nuclear Information System (INIS)

    Li Huiyun; Jiao Huixian

    1987-12-01

    To analyze reactivity event for nuclear power plants, it is necessary to solve the neutron dynamic equations, which is a group of typical stiff constant differential equations. Very small time steps could only be adopted when the group of equations is solved by common methods. However, a large time steps might be selected if the Flux Weighted Medthod introduced in this paper is used. Generally, weighted factor θ i1 is set as a constant. Naturally, this treatment method can decrease the accuracy of calculation for the increase of the steadiness of solving the equations. An accurate theoretical formula of 4 x 4 matrix of θ i1 is rigorously derived so that the accuracy of calculation is ensured, as well as the steadiness of solved equations is increased. This method have the advantage over classical Runge-kutta Method and other methods. The time steps could be increased by a factor of 1 ∼ 3 orders of magnitude so as to save a lot of computating time. The programe solving neutron dynamic equation, which is prepared by using Flux Weighted Method, could be sued for real time analog of training simulator, as well as for analysis and computation of reactivity event (including rod jumping out event)

  7. Hybrid Approximate Dynamic Programming Approach for Dynamic Optimal Energy Flow in the Integrated Gas and Power Systems

    DEFF Research Database (Denmark)

    Shuai, Hang; Ai, Xiaomeng; Wen, Jinyu

    2017-01-01

    This paper proposes a hybrid approximate dynamic programming (ADP) approach for the multiple time-period optimal power flow in integrated gas and power systems. ADP successively solves Bellman's equation to make decisions according to the current state of the system. So, the updated near future...

  8. On stochastic differential equations with random delay

    International Nuclear Information System (INIS)

    Krapivsky, P L; Luck, J M; Mallick, K

    2011-01-01

    We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an nth-order equation with random delay, the corresponding deterministic equation has order n + 1. We analyze various examples of dynamical systems of this kind, and find a number of unusual behaviors. For instance, for the harmonic oscillator with random delay, the energy grows as exp((3/2) t 2/3 ) in reduced units. We then investigate the effect of introducing a discrete time step ε. At variance with the continuous situation, the discrete random recursion relations thus obtained have intrinsic fluctuations. The crossover between the fluctuating discrete problem and the deterministic continuous one as ε goes to zero is studied in detail on the example of a first-order linear differential equation

  9. Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

    Science.gov (United States)

    Shotorban, Babak

    2010-04-01

    The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

  10. Applications of Parameterized Nonlinear Ordinary Differential Equations and Dynamic Systems: An Example of the Taiwan Stock Index

    Directory of Open Access Journals (Sweden)

    Meng-Rong Li

    2018-01-01

    Full Text Available Considering the phenomenon of the mean reversion and the different speeds of stock prices in the bull market and in the bear market, we propose four dynamic models each of which is represented by a parameterized ordinary differential equation in this study. Based on existing studies, the models are in the form of either the logistic growth or the law of Newton’s cooling. We solve the models by dynamic integration and apply them to the daily closing prices of the Taiwan stock index, Taiwan Stock Exchange Capitalization Weighted Stock Index. The empirical study shows that some of the models fit the prices well and the forecasting ability of the best model is acceptable even though the martingale forecasts the prices slightly better. To increase the forecasting ability and to broaden the scope of applications of the dynamic models, we will model the coefficients of the dynamic models in the future. Applying the models to the market without the price limit is also our future work.

  11. Dynamical real numbers and living systems

    International Nuclear Information System (INIS)

    Datta, Dhurjati Prasad

    2004-01-01

    Recently uncovered second derivative discontinuous solutions of the simplest linear ordinary differential equation define not only an nonstandard extension of the framework of the ordinary calculus, but also provide a dynamical representation of the ordinary real number system. Every real number can be visualized as a living cell-like structure, endowed with a definite evolutionary arrow. We discuss the relevance of this extended calculus in the study of living systems. We also present an intelligent version of the Newton's first law of motion

  12. Study on the Dynamics of Laser Gyro Strapdown Inertial Measurement Unit System Based on Transfer Matrix Method for Multibody System

    Directory of Open Access Journals (Sweden)

    Gangli Chen

    2013-01-01

    Full Text Available The dynamic test precision of the strapdown inertial measurement unit (SIMU is the basis of estimating accurate motion of various vehicles such as warships, airplanes, spacecrafts, and missiles. So, it is paid great attention in the above fields to increase the dynamic precision of SIMU by decreasing the vibration of the vehicles acting on the SIMU. In this paper, based on the transfer matrix method for multibody system (MSTMM, the multibody system dynamics model of laser gyro strapdown inertial measurement unit (LGSIMU is developed; the overall transfer equation of the system is deduced automatically. The computational results show that the frequency response function of the LGSIMU got by the proposed method and Newton-Euler method have good agreements. Further, the vibration reduction performance and the attitude error responses under harmonic and random excitations are analyzed. The proposed method provides a powerful technique for studying dynamics of LGSIMU because of using MSTMM and its following features: without the global dynamics equations of the system, high programming, low order of system matrix, and high computational speed.

  13. Dynamical System Analysis of Reynolds Stress Closure Equations

    Science.gov (United States)

    Girimaji, Sharath S.

    1997-01-01

    In this paper, we establish the causality between the model coefficients in the standard pressure-strain correlation model and the predicted equilibrium states for homogeneous turbulence. We accomplish this by performing a comprehensive fixed point analysis of the modeled Reynolds stress and dissipation rate equations. The results from this analysis will be very useful for developing improved pressure-strain correlation models to yield observed equilibrium behavior.

  14. 4th International Conference on Particle Systems and Partial Differential Equations

    CERN Document Server

    Soares, Ana

    2017-01-01

    'This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the dynamic Ö4  theory in three space dimensions, as well as selected contributions presented at the fourth meeting on Particle Systems and PDEs, which was held at the University of Minho’s Centre of Mathematics in December 2015. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, offering them a forum to present their recent results and discuss their topics of expertise. The meeting was also intended to present to a vast and varied public, including young researchers, the area of interacting particle systems, its underlying motivation, and its relation to partial differential equations.  The book w...

  15. Dynamic statistical information theory

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

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

  16. Improved dynamic equations for the generally configured Stewart platform manipulator

    International Nuclear Information System (INIS)

    Pedrammehr, Siamak; Mahboubkhah, Mehran; Khani, Navid

    2012-01-01

    In this paper, a Newton-Euler approach is utilized to generate the improved dynamic equations of the generally configured Stewart platform. Using the kinematic model of the universal joint, the rotational degree of freedom of the pods around the axial direction is taken into account in the formulation. The justifiable direction of the reaction moment on each pod is specified and considered in deriving the dynamic equations. Considering the theorem of parallel axes, the inertia tensors for different elements of the manipulator are obtained in this study. From a theoretical point, the improved formulation is more accurate in comparison with previous ones, and the necessity of the improvement is clear evident from significant differences in the simulation results for the improved model and the model without improvement. In addition to more feasibility of the structure and higher accuracy, the model is highly compatible with computer arithmetic and suitable for online applications for loop control problems in hardware

  17. Intrinsic information carriers in combinatorial dynamical systems

    Science.gov (United States)

    Harmer, Russ; Danos, Vincent; Feret, Jérôme; Krivine, Jean; Fontana, Walter

    2010-09-01

    Many proteins are composed of structural and chemical features—"sites" for short—characterized by definite interaction capabilities, such as noncovalent binding or covalent modification of other proteins. This modularity allows for varying degrees of independence, as the behavior of a site might be controlled by the state of some but not all sites of the ambient protein. Independence quickly generates a startling combinatorial complexity that shapes most biological networks, such as mammalian signaling systems, and effectively prevents their study in terms of kinetic equations—unless the complexity is radically trimmed. Yet, if combinatorial complexity is key to the system's behavior, eliminating it will prevent, not facilitate, understanding. A more adequate representation of a combinatorial system is provided by a graph-based framework of rewrite rules where each rule specifies only the information that an interaction mechanism depends on. Unlike reactions, which deal with molecular species, rules deal with patterns, i.e., multisets of molecular species. Although the stochastic dynamics induced by a collection of rules on a mixture of molecules can be simulated, it appears useful to capture the system's average or deterministic behavior by means of differential equations. However, expansion of the rules into kinetic equations at the level of molecular species is not only impractical, but conceptually indefensible. If rules describe bona fide patterns of interaction, molecular species are unlikely to constitute appropriate units of dynamics. Rather, we must seek aggregate variables reflective of the causal structure laid down by the rules. We call these variables "fragments" and the process of identifying them "fragmentation." Ideally, fragments are aspects of the system's microscopic population that the set of rules can actually distinguish on average; in practice, it may only be feasible to identify an approximation to this. Most importantly, fragments are

  18. Some aspects of the dynamic analysis of piping systems

    International Nuclear Information System (INIS)

    Galeao, A.C.N.R.

    1981-04-01

    Some aspects of vibration and dynamic response of piping systems are presented. The following subjects were analysed: sources of dynamic excitation; steady-state response-periodic excitation; resonance; flow induced vibrations; transient response - seismic excitations; non-linear transient response - pipe - whip. For each of these topics, the mathematical models, the governing equations and the approximate methods of solution, showing some numerical results obtained from the literature. (Author) [pt

  19. Dynamic behavior of a nonlinear rational difference equation and generalization

    Directory of Open Access Journals (Sweden)

    Shi Qihong

    2011-01-01

    Full Text Available Abstract This paper is concerned about the dynamic behavior for the following high order nonlinear difference equation x n = (x n-k + x n-m + x n-l /(x n-k x n-m + x n-m x n-l +1 with the initial data { x - l , x - l + 1 , … , x - 1 } ∈ ℝ + l and 1 ≤ k ≤ m ≤ l. The convergence of solution to this equation is investigated by introducing a new sequence, which extends and includes corresponding results obtained in the references (Li in J Math Anal Appl 312:103-111, 2005; Berenhaut et al. Appl. Math. Lett. 20:54-58, 2007; Papaschinopoulos and Schinas J Math Anal Appl 294:614-620, 2004 to a large extent. In addition, some propositions for generalized equations are reported.

  20. A Few Integrable Dynamical Systems, Recurrence Operators, Expanding Integrable Models and Hamiltonian Structures by the r -Matrix Method

    International Nuclear Information System (INIS)

    Zhang Yu-Feng; Muhammad, Iqbal; Yue Chao

    2017-01-01

    We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov–Lax equation so that a series of novel dynamical systems including generalized Burgers dynamical system, heat equation, and so on, are followed to be generated. Then we expand some differential operators presented in the paper to deduce two types of expanding dynamical models. By taking the generalized Burgers dynamical system as an example, we deform its expanding model to get a half-expanding system, whose recurrence operator is derived from Lax representation, and its Hamiltonian structure is also obtained by adopting a new way. Finally, we expand the generalized Burgers dynamical system to the (2+1)-dimensional case whose Hamiltonian structure is derived by Poisson tensor and gradient of the Casimir function. Besides, a kind of (2+1)-dimensional expanding dynamical model of the (2+1)-dimensional dynamical system is generated as well. (paper)

  1. Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems

    International Nuclear Information System (INIS)

    Deumens, E.; Diz, A.; Longo, R.; Oehrn, Y.

    1994-01-01

    An overview is presented of methods for time-dependent treatments of molecules as systems of electrons and nuclei. The theoretical details of these methods are reviewed and contrasted in the light of a recently developed time-dependent method called electron-nuclear dynamics. Electron-nuclear dynamics (END) is a formulation of the complete dynamics of electrons and nuclei of a molecular system that eliminates the necessity of constructing potential-energy surfaces. Because of its general formulation, it encompasses many aspects found in other formulations and can serve as a didactic device for clarifying many of the principles and approximations relevant in time-dependent treatments of molecular systems. The END equations are derived from the time-dependent variational principle applied to a chosen family of efficiently parametrized approximate state vectors. A detailed analysis of the END equations is given for the case of a single-determinantal state for the electrons and a classical treatment of the nuclei. The approach leads to a simple formulation of the fully nonlinear time-dependent Hartree-Fock theory including nuclear dynamics. The nonlinear END equations with the ab initio Coulomb Hamiltonian have been implemented at this level of theory in a computer program, ENDyne, and have been shown feasible for the study of small molecular systems. Implementation of the Austin Model 1 semiempirical Hamiltonian is discussed as a route to large molecular systems. The linearized END equations at this level of theory are shown to lead to the random-phase approximation for the coupled system of electrons and nuclei. The qualitative features of the general nonlinear solution are analyzed using the results of the linearized equations as a first approximation. Some specific applications of END are presented, and the comparison with experiment and other theoretical approaches is discussed

  2. Studying language change using price equation and Pólya-urn dynamics.

    Science.gov (United States)

    Gong, Tao; Shuai, Lan; Tamariz, Mónica; Jäger, Gerhard

    2012-01-01

    Language change takes place primarily via diffusion of linguistic variants in a population of individuals. Identifying selective pressures on this process is important not only to construe and predict changes, but also to inform theories of evolutionary dynamics of socio-cultural factors. In this paper, we advocate the Price equation from evolutionary biology and the Pólya-urn dynamics from contagion studies as efficient ways to discover selective pressures. Using the Price equation to process the simulation results of a computer model that follows the Pólya-urn dynamics, we analyze theoretically a variety of factors that could affect language change, including variant prestige, transmission error, individual influence and preference, and social structure. Among these factors, variant prestige is identified as the sole selective pressure, whereas others help modulate the degree of diffusion only if variant prestige is involved. This multidisciplinary study discerns the primary and complementary roles of linguistic, individual learning, and socio-cultural factors in language change, and offers insight into empirical studies of language change.

  3. 20th International Conference on Difference Equations and Applications

    CERN Document Server

    Ding, Yiming; Došlý, Ondřej

    2015-01-01

    These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences (Hubei, China), under the auspices of the International Society of Difference Equations (ISDE) in July 2014. Its purpose was to bring together renowned researchers working actively in the respective fields, to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations. This book will appeal to researchers and scientists working in the fields of difference equations, discrete dynamical systems and their applications.

  4. On the Boussinesq-Burgers equations driven by dynamic boundary conditions

    Science.gov (United States)

    Zhu, Neng; Liu, Zhengrong; Zhao, Kun

    2018-02-01

    We study the qualitative behavior of the Boussinesq-Burgers equations on a finite interval subject to the Dirichlet type dynamic boundary conditions. Assuming H1 ×H2 initial data which are compatible with boundary conditions and utilizing energy methods, we show that under appropriate conditions on the dynamic boundary data, there exist unique global-in-time solutions to the initial-boundary value problem, and the solutions converge to the boundary data as time goes to infinity, regardless of the magnitude of the initial data.

  5. Dynamic magnetic properties of the mixed spin-1 and spin-3/2 Ising system on a two-layer square lattice

    International Nuclear Information System (INIS)

    Temizer, Ümüt

    2014-01-01

    In this study, the dynamic critical behavior of the mixed spin-1 and spin-3/2 Ising system on a bilayer square lattice is studied by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic (FM/FM) and antiferromagnetic/ferromagnetic (AFM/FM) interactions in the presence of a time-varying external magnetic field. The dynamic equations describing the time-dependencies of the average magnetizations are derived from the Master equation. The phases in the system are obtained by solving these dynamic equations. The temperature dependence of the dynamic magnetizations is investigated in order to characterize the nature (first- or second-order) of the dynamic phase transitions and to obtain the dynamic phase transition temperatures. The dynamic phase diagrams are constructed in seven different planes for both FM/FM and AFM/FM interactions and the effects of the related interaction parameters on the dynamic phase diagrams are examined. It is found that the dynamic phase diagrams display many dynamic critical points, such as tricritical point, triple point (TP), quadruple point (QP), double critical end point (B), multicritical point (A) and tetracritical point (M). Moreover, the reentrant behavior is observed for AFM/FM interaction in the system. - Highlights: • The mixed spin (1, 3/2) Ising system is studied on a two-layer square lattice. • The Glauber transition rates are employed to construct the dynamic equations. • The dynamic phase diagrams are presented in seven different planes. • The system displays many dynamic critical points. • The reentrant behavior is observed for AFM/FM interaction

  6. The dynamics of a Beddington-type system with impulsive control strategy

    International Nuclear Information System (INIS)

    Li Zhenqing; Wang Weiming; Wang Hailing

    2006-01-01

    In this paper, by using the theories and methods of ecology and ordinary differential equation, a prey-predator system with Beddington-type functional response and impulsive control strategy is established. Conditions for the system to be extinct are given by using the theories of impulsive equation and small amplitude perturbation skills. It is proved that the system is permanent via the method of comparison involving multiple Liapunov functions. Furthermore, by using the method of numerical simulation, the influence of the impulsive control strategy on the inherent oscillation are investigated, which shows rich dynamics, such as period doubling bifurcation, crises, symmetry-breaking pitchfork bifurcations, chaotic bands, quasi-periodic oscillation, narrow periodic window, wide periodic window, period-halving bifurcation, etc. That will be useful for study of the dynamic complexity of ecosystems

  7. Integrable motion of curves in self-consistent potentials: Relation to spin systems and soliton equations

    Energy Technology Data Exchange (ETDEWEB)

    Myrzakulov, R.; Mamyrbekova, G.K.; Nugmanova, G.N.; Yesmakhanova, K.R. [Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Lakshmanan, M., E-mail: lakshman@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India)

    2014-06-13

    Motion of curves and surfaces in R{sup 3} lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota–Maxwell–Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability. - Highlights: • Geometry of continuum spin chain with self-consistent potentials explored. • Mapping on moving space curves in R{sup 3} in the presence of potential fields carried out. • Equivalent generalized nonlinear Schrödinger (NLS) family of equations identified. • Integrability of identified nonlinear systems proved by deducing appropriate Lax pairs.

  8. Numerical simulations of earthquakes and the dynamics of fault systems using the Finite Element method.

    Science.gov (United States)

    Kettle, L. M.; Mora, P.; Weatherley, D.; Gross, L.; Xing, H.

    2006-12-01

    Simulations using the Finite Element method are widely used in many engineering applications and for the solution of partial differential equations (PDEs). Computational models based on the solution of PDEs play a key role in earth systems simulations. We present numerical modelling of crustal fault systems where the dynamic elastic wave equation is solved using the Finite Element method. This is achieved using a high level computational modelling language, escript, available as open source software from ACcESS (Australian Computational Earth Systems Simulator), the University of Queensland. Escript is an advanced geophysical simulation software package developed at ACcESS which includes parallel equation solvers, data visualisation and data analysis software. The escript library was implemented to develop a flexible Finite Element model which reliably simulates the mechanism of faulting and the physics of earthquakes. Both 2D and 3D elastodynamic models are being developed to study the dynamics of crustal fault systems. Our final goal is to build a flexible model which can be applied to any fault system with user-defined geometry and input parameters. To study the physics of earthquake processes, two different time scales must be modelled, firstly the quasi-static loading phase which gradually increases stress in the system (~100years), and secondly the dynamic rupture process which rapidly redistributes stress in the system (~100secs). We will discuss the solution of the time-dependent elastic wave equation for an arbitrary fault system using escript. This involves prescribing the correct initial stress distribution in the system to simulate the quasi-static loading of faults to failure; determining a suitable frictional constitutive law which accurately reproduces the dynamics of the stick/slip instability at the faults; and using a robust time integration scheme. These dynamic models generate data and information that can be used for earthquake forecasting.

  9. Correlated Levy Noise in Linear Dynamical Systems

    International Nuclear Information System (INIS)

    Srokowski, T.

    2011-01-01

    Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed symmetric white noise. Correlation properties of the process are discussed. The Fokker-Planck equation driven by that noise is solved. Distributions have the Levy shape and their width, for a given time, is smaller than for processes in the white noise limit. Applicability of the adiabatic approximation in the case of the linear force is discussed. (author)

  10. NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications

    CERN Document Server

    2008-01-01

    Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continu...

  11. On modulated complex non-linear dynamical systems

    International Nuclear Information System (INIS)

    Mahmoud, G.M.; Mohamed, A.A.; Rauh, A.

    1999-01-01

    This paper is concerned with the development of an approximate analytical method to investigate periodic solutions and their stability in the case of modulated non-linear dynamical systems whose equation of motion is describe. Such differential equations appear, for example, in problems of colliding particle beams in high-energy accelerators or one-mass systems with two or more degrees of freedom, e.g. rotors. The significance of periodic solutions lies on the fact that all non-periodic responses, if convergent, would approach to periodic solutions at the steady-state conditions. The example shows a good agreement between numerical and analytical results for small values of ε. The effect of the periodic modulation on the stability of the 2π-periodic solutions is discussed

  12. Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

    Science.gov (United States)

    Lan, C. Edward; Ge, Fuying

    1989-01-01

    Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

  13. The foam drainage equation for drainage dynamics in unsaturated porous media

    Science.gov (United States)

    Lehmann, P.; Hoogland, F.; Assouline, S.; Or, D.

    2017-07-01

    Similarity in liquid-phase configuration and drainage dynamics of wet foam and gravity drainage from unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation—SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. The study provides new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions. Two novel analytical solutions for saturation profile evolution were derived and tested in good agreement with a numerical solution of the SFDE. The study and the proposed solutions rectify the original formulation of foam drainage dynamics of Or and Assouline (2013). The new framework broadens the scope of methods available for quantifying unsaturated flow in porous media, where the intrinsic conductivity and geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.

  14. A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations

    Energy Technology Data Exchange (ETDEWEB)

    Dubina, Sean Hyun, E-mail: sdubin2@uic.edu; Wedgewood, Lewis Edward, E-mail: wedge@uic.edu [Department of Chemical Engineering, University of Illinois at Chicago, 810 S. Clinton St. (MC 110), Chicago, Illinois 60607-4408 (United States)

    2016-07-15

    Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.

  15. A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations

    International Nuclear Information System (INIS)

    Dubina, Sean Hyun; Wedgewood, Lewis Edward

    2016-01-01

    Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.

  16. Conservative fourth-order time integration of non-linear dynamic systems

    DEFF Research Database (Denmark)

    Krenk, Steen

    2015-01-01

    An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...

  17. Oscillation of second order neutral dynamic equations with distributed delay

    Directory of Open Access Journals (Sweden)

    Qiaoshun Yang

    2016-06-01

    Full Text Available In this paper, we establish new oscillation criteria for second order neutral dynamic equations with distributed delay by employing the generalized Riccati transformation. The obtained theorems essentially improve the oscillation results in the literature. And two examples are provided to illustrate to the versatility of our main results.

  18. Dynamic Systems Driven by Non-Poissonian Impulses

    DEFF Research Database (Denmark)

    Nielsen, Søren R.K.; Iwankiewicz, R.

    interarrival times. The moment equations for the augmented Poisson driven system are derived and closed by an ordinary cumulant neglect closure at the order N=4. The obtained moments are compared with these obtained by Monte Carlo simulations for both the original process with lognormally distributed......Dynamic systems under random trains of impulses driven by renewal point processes are studied. Then the system state variables no longer form a Markov vector as it is in the case of Poisson impulses. A general format is given for the replacing an ordinary renewal process by an equivalent Poisson...... process at the expense of the introduction of auxiliary state variables. A technique is devised for truncating the hierarchy of stochastic equations governing the auxiliary state variables. For the generalized Erlang process, suitable for approximating a wide class of renewal processes, the technique...

  19. Gravitational closure of matter field equations

    Science.gov (United States)

    Düll, Maximilian; Schuller, Frederic P.; Stritzelberger, Nadine; Wolz, Florian

    2018-04-01

    The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can equip the coefficients of a given system of matter field equations with causally compatible canonical dynamics. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows one to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.

  20. Study of the dynamics of an equation with two large different-order delays

    International Nuclear Information System (INIS)

    Kashchenko, I.S.

    2016-01-01

    The case where the larger delay is proportional to the square of the smaller delay is studied in detail. Regions of stability and instability of the equilibrium state and critical cases are found. In all critical cases, special evolutionary equations (quasinormal forms) are constructed. Their non-local dynamics determines the local behavior of solutions of the original equation [ru

  1. Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

    International Nuclear Information System (INIS)

    Fouxon, Itzhak; Oz, Yaron

    2008-01-01

    We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them

  2. Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

    Science.gov (United States)

    Fouxon, Itzhak; Oz, Yaron

    2008-12-31

    We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

  3. The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems

    CERN Document Server

    Snook, Ian

    2007-01-01

    The Langevin and Generalised Langevin Approach To The Dynamics Of Atomic, Polymeric And Colloidal Systems is concerned with the description of aspects of the theory and use of so-called random processes to describe the properties of atomic, polymeric and colloidal systems in terms of the dynamics of the particles in the system. It provides derivations of the basic equations, the development of numerical schemes to solve them on computers and gives illustrations of application to typical systems.Extensive appendices are given to enable the reader to carry out computations to illustrate many of the points made in the main body of the book.* Starts from fundamental equations* Gives up-to-date illustration of the application of these techniques to typical systems of interest* Contains extensive appendices including derivations, equations to be used in practice and elementary computer codes

  4. Bifurcation methods of dynamical systems for handling nonlinear ...

    Indian Academy of Sciences (India)

    physics pp. 863–868. Bifurcation methods of dynamical systems for handling nonlinear wave equations. DAHE FENG and JIBIN LI. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology .... (b) It can be shown from (15) and (18) that the balance between the weak nonlinear.

  5. Study of fission dynamics with the three-dimensional Langevin equations

    Energy Technology Data Exchange (ETDEWEB)

    Eslamizadeh, H. [Persian Gulf University, Department of Physics, Bushehr (Iran, Islamic Republic of)

    2011-11-15

    The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei {sup 210}Po and {sup 224}Th formed in the fusion-fission reactions {sup 4}He+{sup 206}Pb, {sup 16}O+{sup 208}Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data. (orig.)

  6. Systems of Inhomogeneous Linear Equations

    Science.gov (United States)

    Scherer, Philipp O. J.

    Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

  7. Dynamic analysis of Free-Piston Stirling Engine/Linear Alternator-load system-experimentally validated

    Science.gov (United States)

    Kankam, M. David; Rauch, Jeffrey S.; Santiago, Walter

    1992-01-01

    This paper discusses the effects of variations in system parameters on the dynamic behavior of the Free-Piston Stirling Engine/Linear Alternator (FPSE/LA)-load system. The mathematical formulations incorporate both the mechanical and thermodynamic properties of the FPSE, as well as the electrical equations of the connected load. A state-space technique in the frequency domain is applied to the resulting system of equations to facilitate the evaluation of parametric impacts on the system dynamic stability. Also included is a discussion on the system transient stability as affected by sudden changes in some key operating conditions. Some representative results are correlated with experimental data to verify the model and analytic formulation accuracies. Guidelines are given for ranges of the system parameters which will ensure an overall stable operation.

  8. A low dimensional dynamical system for the wall layer

    Science.gov (United States)

    Aubry, N.; Keefe, L. R.

    1987-01-01

    Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

  9. Integrability of dynamical systems algebra and analysis

    CERN Document Server

    Zhang, Xiang

    2017-01-01

    This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the center—focus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology. Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems.

  10. Existence and global exponential stability of periodic solutions for n-dimensional neutral dynamic equations on time scales.

    Science.gov (United States)

    Li, Bing; Li, Yongkun; Zhang, Xuemei

    2016-01-01

    In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale [Formula: see text]) and the case of difference equations (time scale [Formula: see text]).

  11. Computational Fluid Dynamics

    International Nuclear Information System (INIS)

    Myeong, Hyeon Guk

    1999-06-01

    This book deals with computational fluid dynamics with basic and history of numerical fluid dynamics, introduction of finite volume method using one-dimensional heat conduction equation, solution of two-dimensional heat conduction equation, solution of Navier-Stokes equation, fluid with heat transport, turbulent flow and turbulent model, Navier-Stokes solution by generalized coordinate system such as coordinate conversion, conversion of basic equation, program and example of calculation, application of abnormal problem and high speed solution of numerical fluid dynamics.

  12. Optimizing Technology-Oriented Constructional Paramour's of complex dynamic systems

    International Nuclear Information System (INIS)

    Novak, S.M.

    1998-01-01

    Creating optimal vibro systems requires sequential solving of a few problems: selecting the basic pattern of dynamic actions, synthesizing the dynamic active systems, optimizing technological, technical, economic and design parameters. This approach is illustrated by an example of a high-efficiency vibro system synthesized for forming building structure components. When using only one single source to excite oscillations, resonance oscillations are imparted to the product to be formed in the horizontal and vertical planes. In order to obtain versatile and dynamically optimized parameters, a factor is introduced into the differential equations of the motion, accounting for the relationship between the parameters, which determine the frequency characteristics of the system and the parameter variation range. This results in obtaining non-sophisticated mathematical models of the system under investigation, convenient for optimization and for engineering design and calculations as well

  13. Approximating chaotic saddles for delay differential equations.

    Science.gov (United States)

    Taylor, S Richard; Campbell, Sue Ann

    2007-04-01

    Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a "logistic" delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.

  14. Approximating chaotic saddles for delay differential equations

    Science.gov (United States)

    Taylor, S. Richard; Campbell, Sue Ann

    2007-04-01

    Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a “logistic” delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.

  15. A dynamic model of the reactor coolant system flow for KMRR plant simulation

    International Nuclear Information System (INIS)

    Rhee, B.W.; Noh, T.W.; Park, C.; Sim, B.S.; Oh, S.K.

    1990-01-01

    To support computer simulation studies for reactor control system design and performance evaluation, a dynamic model of the reactor coolant system (RCS) and reflector cooling system has been developed. This model is composed of the reactor coolant loop momentum equation, RCS pump dynamic equation, RCS pump characteristic equation, and the energy equation for the coolant inside the various components and piping. The model is versatile enough to simulate the normal steady-state conditions as well as most of the anticipated flow transients without pipe rupture. This model has been successfully implemented as the plant simulation code KMRRSIM for the Korea Multi-purpose Research Reactor and is now under extensive validation testing. The initial stage of validation has been comparison of its result with that of already validated, more detailed reactor system transient codes such as RELAP5. The results, as compared to the predictions by RELAP5 simulation, have been generally found to be very encouraging and the model is judged to be accurate enough to fulfill its intended purpose. However, this model will continue to be validated against other plant's data and eventually will be assessed by test data from KMRR

  16. The financial accounting model from a system dynamics' perspective

    NARCIS (Netherlands)

    Melse, E.

    2006-01-01

    This paper explores the foundation of the financial accounting model. We examine the properties of the accounting equation as the principal algorithm for the design and the development of a System Dynamics model. Key to the perspective is the foundational requirement that resolves the temporal

  17. Dynamical theory of neutron diffraction. [One-body Schroedinger equation, review

    Energy Technology Data Exchange (ETDEWEB)

    Sears, V F [Atomic Energy of Canada Ltd., Chalk River, Ontario. Chalk River Nuclear Labs.

    1978-10-01

    We present a review of the dynamical theory of neutron diffraction by macroscopic bodies which provides the theoretical basis for the study of neutron optics. We consider both the theory of dispersion, in which it is shown that the coherent wave in the medium satisfies a macroscopic one-body Schroedinger equation, and the theory of reflection, refraction, and diffraction in which the above equation is solved for a number of special cases of interest. The theory is illustrated with the help of experimental results obtained over the past 10 years by a number of new techniques such as neutron gravity refractometry. Pendelloesung interference, and neutron interferometry.

  18. On identification of dynamic system parameters from experimental data

    CSIR Research Space (South Africa)

    Shatalov, M

    2007-08-01

    Full Text Available -linear differen- tial equations frequently used to describe the dynamics of biological systems in which two species interact. They were proposed independently by Alfred J. Lotka [1] and Vito Volterra in 1926 [2]. This system can be written in the form x′1(t...) = x1 (a11 − a12x2) x′2(t) = x2 (ηa12x1 − a22) When solved for x1 and x2 the above system of equations yields x1 = 0, x1 = 0 and 1 x1 = a22 ηa12 , x1 = a11 a12 hence there are two equilibria. The solution in the neighborhood of the first...

  19. Effective action and the quantum equation of motion

    International Nuclear Information System (INIS)

    Branchina, V.; Faivre, H.; Zappala, D.

    2004-01-01

    We carefully analyze the use of the effective action in dynamical problems, in particular the conditions under which the equation (δΓ)/(δφ) = 0 can be used as a quantum equation of motion and illustrate in detail the crucial relation between the asymptotic states involved in the definition of Γ and the initial state of the system. Also, by considering the quantum-mechanical example of a double-well potential, where we can get exact results for the time evolution of the system, we show that an approximation to the effective potential in the quantum equation of motion that correctly describes the dynamical evolution of the system is obtained with the help of the wilsonian RG equation (already at the lowest order of the derivative expansion), while the commonly used one-loop effective potential fails to reproduce the exact results. (orig.)

  20. Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

    Science.gov (United States)

    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.

  1. Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

    Science.gov (United States)

    Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

    2017-02-01

    We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

  2. Finite difference method for inner-layer equations in the resistive MagnetoHydroDynamic stability analysis

    International Nuclear Information System (INIS)

    Tokuda, Shinji; Watanabe, Tomoko.

    1996-08-01

    The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)

  3. Dynamics for the complex Ginzburg-Landau equation on non-cylindrical domains II: The monotone case

    Science.gov (United States)

    Zhou, Feng; Sun, Chunyou; Cheng, Jiaqi

    2018-02-01

    In this article, we continue the study of the dynamics of the following complex Ginzburg-Landau equation ∂tu - (λ + iα)Δu + (κ + iβ)|u|p-2u - γu = f(t) on non-cylindrical domains. We assume that the spatial domains are bounded and increase with time, which is different from the diffeomorphism case presented in Zhou and Sun [Discrete Contin. Dyn. Syst., Ser. B 21, 3767-3792 (2016)]. We develop a new penalty function to establish the existence and uniqueness of a variational solution satisfying energy equality as well as some energy inequalities and prove the existence of a D -pullback attractor for the non-autonomous dynamical system generated by this class of solutions.

  4. General conditions for the existence of non-standard Lagrangians for dissipative dynamical systems

    International Nuclear Information System (INIS)

    Musielak, Z.E.

    2009-01-01

    Equations of motion describing dissipative dynamical systems with coefficients varying either in time or in space are considered. To identify the equations that admit a Lagrangian description, two classes of non-standard Lagrangians are introduced and general conditions required for the existence of these Lagrangians are determined. The conditions are used to obtain some non-standard Lagrangians and derive equations of motion resulting from these Lagrangians.

  5. Three-pattern decomposition of global atmospheric circulation: part II—dynamical equations of horizontal, meridional and zonal circulations

    Science.gov (United States)

    Hu, Shujuan; Cheng, Jianbo; Xu, Ming; Chou, Jifan

    2018-04-01

    The three-pattern decomposition of global atmospheric circulation (TPDGAC) partitions three-dimensional (3D) atmospheric circulation into horizontal, meridional and zonal components to study the 3D structures of global atmospheric circulation. This paper incorporates the three-pattern decomposition model (TPDM) into primitive equations of atmospheric dynamics and establishes a new set of dynamical equations of the horizontal, meridional and zonal circulations in which the operator properties are studied and energy conservation laws are preserved, as in the primitive equations. The physical significance of the newly established equations is demonstrated. Our findings reveal that the new equations are essentially the 3D vorticity equations of atmosphere and that the time evolution rules of the horizontal, meridional and zonal circulations can be described from the perspective of 3D vorticity evolution. The new set of dynamical equations includes decomposed expressions that can be used to explore the source terms of large-scale atmospheric circulation variations. A simplified model is presented to demonstrate the potential applications of the new equations for studying the dynamics of the Rossby, Hadley and Walker circulations. The model shows that the horizontal air temperature anomaly gradient (ATAG) induces changes in meridional and zonal circulations and promotes the baroclinic evolution of the horizontal circulation. The simplified model also indicates that the absolute vorticity of the horizontal circulation is not conserved, and its changes can be described by changes in the vertical vorticities of the meridional and zonal circulations. Moreover, the thermodynamic equation shows that the induced meridional and zonal circulations and advection transport by the horizontal circulation in turn cause a redistribution of the air temperature. The simplified model reveals the fundamental rules between the evolution of the air temperature and the horizontal, meridional

  6. Modeling a nucleon system: static and dynamical properties - density fluctuations

    International Nuclear Information System (INIS)

    Idier, D.

    1997-01-01

    This thesis sets forth a quasi-particle model for the static and dynamical properties of nuclear matter. This model is based on a scale ratio of quasi-particle to nucleons and the projection of the semi-classical distribution on a coherent Gaussian state basis. The first chapter is dealing with the transport equations, particularly with the Vlasov equation for Wigner distribution function. The second one is devoted to the statics of nuclear matter. Here, the sampling effect upon the nuclear density is treated and the state equation of the Gaussian fluid is compared with that given by Hartree-Fock approximation. We define state equation as the relationship between the nucleon binding energy and density, for a given temperature. The curvature around the state equation minimum of the quasi-particle system is shown to be related to the speed of propagation of density perturbation. The volume energy and the surface properties of a (semi-)infinite nucleon system are derived. For the resultant saturated auto-coherent semi-infinite system of quasi-particles the surface coefficient appearing in the mass formula is extracted as well as the system density profile. The third chapter treats the dynamics of the two-particle residual interactions. The effect of different parameters on relaxation of a nucleon system without a mean field is studied by means of a Eulerian and Lagrangian modeling. The fourth chapter treats the volume instabilities (spinodal decomposition) in nuclear matter. The quasi-particle systems, initially prepared in the spinodal region of the utilized interaction, are set to evolve. It is shown then that the scale ratio acts upon the amount of fluctuations injected in the system. The inhomogeneity degree and a proper time are defined and the role of collisions in the spinodal decomposition as well as that of the initial temperature and density, are investigated. Assuming different effective macroscopic interactions, the influence of quantities as

  7. Noise-sustained structure, Intermittency, and the Ginzburg--Landau equation

    International Nuclear Information System (INIS)

    Deissler, R.J.

    1985-01-01

    The time-dependent generalized Ginzburg--Landau equation is an equation that is related to many physical systems. Solutions of this equation in the presence of low-level external noise are studied. Numerical solutions of this equation in the stationary frame of refernce and with nonzero group velocity that is greater than a critical velocity exhibit a selective spatial amplification of noise resulting in spatially growing waves. These waves in turn result in the formation of a dynamic structure. It is found that the microscopic noise plays an importuant role in the macroscopic dynamics of the system. For certain parameter values the system exhibits intermittent turbulent behavior in which the random nature of the external noise plays a crucial role. A mechanism which may be responsible for the intermittent turbulence occurring in some fluid systems is suggested

  8. Quantum master equation method based on the broken-symmetry time-dependent density functional theory: application to dynamic polarizability of open-shell molecular systems.

    Science.gov (United States)

    Kishi, Ryohei; Nakano, Masayoshi

    2011-04-21

    A novel method for the calculation of the dynamic polarizability (α) of open-shell molecular systems is developed based on the quantum master equation combined with the broken-symmetry (BS) time-dependent density functional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic α density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to α and its density. To demonstrate the performance of this method, we examine the real part of dynamic α of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of α, in particular in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character. Under sufficiently off-resonant condition, the dynamic α is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange-correlation functional, which enhances the spin polarization, due to the decrease in the delocalization effects of π-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functional also turns out to semiquantitatively reproduce the α spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.

  9. Label-free nanoscale characterization of red blood cell structure and dynamics using single-shot transport of intensity equation

    Science.gov (United States)

    Poola, Praveen Kumar; John, Renu

    2017-10-01

    We report the results of characterization of red blood cell (RBC) structure and its dynamics with nanometric sensitivity using transport of intensity equation microscopy (TIEM). Conventional transport of intensity technique requires three intensity images and hence is not suitable for studying real-time dynamics of live biological samples. However, assuming the sample to be homogeneous, phase retrieval using transport of intensity equation has been demonstrated with single defocused measurement with x-rays. We adopt this technique for quantitative phase light microscopy of homogenous cells like RBCs. The main merits of this technique are its simplicity, cost-effectiveness, and ease of implementation on a conventional microscope. The phase information can be easily merged with regular bright-field and fluorescence images to provide multidimensional (three-dimensional spatial and temporal) information without any extra complexity in the setup. The phase measurement from the TIEM has been characterized using polymeric microbeads and the noise stability of the system has been analyzed. We explore the structure and real-time dynamics of RBCs and the subdomain membrane fluctuations using this technique.

  10. Efficiency Analysis of a Wave Power Generation System by Using Multibody Dynamics

    International Nuclear Information System (INIS)

    Kim, Min Soo; Sohn, Jeong Hyun; Kim, Jung Hee; Sung, Yong Jun

    2016-01-01

    The energy absorption efficiency of a wave power generation system is calculated as the ratio of the wave power to the power of the system. Because absorption efficiency depends on the dynamic behavior of the wave power generation system, a dynamic analysis of the wave power generation system is required to estimate the energy absorption efficiency of the system. In this study, a dynamic analysis of the wave power generation system under wave loads is performed to estimate the energy absorption efficiency. RecurDyn is employed to carry out the dynamic analysis of the system, and the Morison equation is used for the wave load model. According to the results, the lower the wave height and the shorter the period, the higher is the absorption efficiency of the system

  11. Efficiency Analysis of a Wave Power Generation System by Using Multibody Dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Min Soo; Sohn, Jeong Hyun [Pukyong National Univ., Busan (Korea, Republic of); Kim, Jung Hee; Sung, Yong Jun [INGINE Inc., Seoul (Korea, Republic of)

    2016-06-15

    The energy absorption efficiency of a wave power generation system is calculated as the ratio of the wave power to the power of the system. Because absorption efficiency depends on the dynamic behavior of the wave power generation system, a dynamic analysis of the wave power generation system is required to estimate the energy absorption efficiency of the system. In this study, a dynamic analysis of the wave power generation system under wave loads is performed to estimate the energy absorption efficiency. RecurDyn is employed to carry out the dynamic analysis of the system, and the Morison equation is used for the wave load model. According to the results, the lower the wave height and the shorter the period, the higher is the absorption efficiency of the system.

  12. Stochastic population dynamics in spatially extended predator-prey systems

    Science.gov (United States)

    Dobramysl, Ulrich; Mobilia, Mauro; Pleimling, Michel; Täuber, Uwe C.

    2018-02-01

    Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator-prey competition invalidates the neutral Lotka-Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator-prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi-Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May-Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex

  13. Critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics

    International Nuclear Information System (INIS)

    Diestler, D.J.; Riley, M.E.

    1985-01-01

    We consider the classical motion of a harmonic lattice in which only those atoms in a certain subset of the lattice (primary zone) may interact with an external force. The formally exact generalized Langevin equation (GLE) for the primary zone is an appropriate description of the dynamics. We examine a previously proposed Brownian, or frictional damping, approximation that reduces the GLE to a set of coupled ordinary Langevin equations for the primary atoms. It is shown that the solution of these equations can contain undamped motion if there is more than one atom in the primary zone. Such motion is explicitly demonstrated for a model that has been used to describe energy transfer in atom--surface collisions. The inability of the standard Brownian approximation to yield an acceptable, physically meaningful result for primary zones comprising more than one atom suggests that the Brownian approximation may introduce other spurious dynamical effects. Further work on damping of correlated motion in lattices is needed

  14. Two-dimensional nonlinear equations of supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1985-01-01

    Supersymmetric generalization of two-dimensional nonlinear dynamical equations of gauge theories is presented. The nontrivial dynamics of a physical system in the supersymmetry and supergravity theories for (2+2)-dimensions is described by the integrable embeddings of Vsub(2/2) superspace into the flat enveloping superspace Rsub(N/M), supplied with the structure of a Lie superalgebra. An equation is derived which describes a supersymmetric generalization of the two-dimensional Toda lattice. It contains both super-Liouville and Sinh-Gordon equations

  15. Quantum Dynamics in Biological Systems

    Science.gov (United States)

    Shim, Sangwoo

    In the first part of this dissertation, recent efforts to understand quantum mechanical effects in biological systems are discussed. Especially, long-lived quantum coherences observed during the electronic energy transfer process in the Fenna-Matthews-Olson complex at physiological condition are studied extensively using theories of open quantum systems. In addition to the usual master equation based approaches, the effect of the protein structure is investigated in atomistic detail through the combined application of quantum chemistry and molecular dynamics simulations. To evaluate the thermalized reduced density matrix, a path-integral Monte Carlo method with a novel importance sampling approach is developed for excitons coupled to an arbitrary phonon bath at a finite temperature. In the second part of the thesis, simulations of molecular systems and applications to vibrational spectra are discussed. First, the quantum dynamics of a molecule is simulated by combining semiclassical initial value representation and density funcitonal theory with analytic derivatives. A computationally-tractable approximation to the sum-of-states formalism of Raman spectra is subsequently discussed.

  16. A mixed Fourier–Galerkin–finite-volume method to solve the fluid dynamics equations in cylindrical geometries

    International Nuclear Information System (INIS)

    Núñez, Jóse; Ramos, Eduardo; Lopez, Juan M

    2012-01-01

    We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to solve the coupled mass and momentum conservation equations similar to a pressure-correction SIMPLE method that is adapted for the present formulation. Using the Fourier–Galerkin method for the azimuthal direction has two advantages. Firstly, it has a high-order approximation of the partial derivatives in the angular direction, and secondly, it naturally satisfies the azimuthal periodic boundary conditions. Also, using the finite-volume method in the r and z directions allows one to handle boundary conditions with discontinuities in those directions. It is important to remark that with this method, the resulting linear system of equations are band-diagonal, leading to fast and efficient solvers. The benefits of the mixed method are illustrated with example problems. (paper)

  17. Differential equations and applications recent advances

    CERN Document Server

    2014-01-01

    Differential Equations and Applications : Recent Advances focus on the latest developments in Nonlinear Dynamical Systems, Neural Networks, Fluid Dynamics, Fractional Differential Systems, Mathematical Modelling and Qualitative Theory. Different aspects such as Existence, Stability, Controllability, Viscosity and Numerical Analysis for different systems have been discussed in this book. This book will be of great interest and use to researchers in Applied Mathematics, Engineering and Mathematical Physics.

  18. Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

    International Nuclear Information System (INIS)

    Jia Liqun; Cui Jinchao; Zhang Yaoyu; Luo Shaokai

    2009-01-01

    Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results. (general)

  19. Relativistic two-and three-particle scattering equations using instant and light-front dynamics

    International Nuclear Information System (INIS)

    Adhikari, S.K.; Tomio, L.; Frederico, T.

    1992-01-01

    Starting from the Bethe-Salpeter equation for two particles in the ladder approximation and integrating over the time component of momentum we derive three dimensional scattering integral equations satisfying constraints of unitarity and relativity, both employing the light-front and instant-form variables. The equations we arrive at are those first derived by Weinberg and by Blankenbecler and Sugar, and are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. We extends this procedure to the case of three particles interacting via two-particle separable potentials. Using light-front and instant form variables we suggest a couple of three dimensional three-particle scattering equations satisfying constraints of two and three-particle unitarity and relativity. The three-particle light-front equation is shown to be approximately related by a transformation of variables to one of the instant-form three-particle equations. (author)

  20. Soliton equations and Hamiltonian systems

    CERN Document Server

    Dickey, L A

    2002-01-01

    The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau

  1. Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

    Science.gov (United States)

    Cotter, C J; Gottwald, G A; Holm, D D

    2017-09-01

    In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

  2. Partial differential equations for scientists and engineers

    CERN Document Server

    Farlow, Stanley J

    1993-01-01

    Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th

  3. Behavior of Poisson Bracket Mapping Equation in Studying Excitation Energy Transfer Dynamics of Cryptophyte Phycocyanin 645 Complex

    International Nuclear Information System (INIS)

    Lee, Weon Gyu; Kelly, Aaron; Rhee, Young Min

    2012-01-01

    Recently, it has been shown that quantum coherence appears in energy transfers of various photosynthetic light harvesting complexes at from cryogenic to even room temperatures. Because the photosynthetic systems are inherently complex, these findings have subsequently interested many researchers in the field of both experiment and theory. From the theoretical part, simplified dynamics or semiclassical approaches have been widely used. In these approaches, the quantum-classical Liouville equation (QCLE) is the fundamental starting point. Toward the semiclassical scheme, approximations are needed to simplify the equations of motion of various degrees of freedom. Here, we have adopted the Poisson bracket mapping equation (PBME) as an approximate form of QCLE and applied it to find the time evolution of the excitation in a photosynthetic complex from marine algae. The benefit of using PBME is its similarity to conventional Hamiltonian dynamics. Through this, we confirmed the coherent population transfer behaviors in short time domain as previously reported with a more accurate but more time-consuming iterative linearized density matrix approach. However, we find that the site populations do not behave according to the Boltzmann law in the long time limit. We also test the effect of adding spurious high frequency vibrations to the spectral density of the bath, and find that their existence does not alter the dynamics to any significant extent as long as the associated reorganization energy is changed not too drastically. This suggests that adopting classical trajectory based ensembles in semiclassical simulations should not influence the coherence dynamics in any practical manner, even though the classical trajectories often yield spurious high frequency vibrational features in the spectral density

  4. Dynamical Signatures of Living Systems

    Science.gov (United States)

    Zak, M.

    1999-01-01

    One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion

  5. Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations.

    Science.gov (United States)

    Kilic, Mustafa Sabri; Bazant, Martin Z; Ajdari, Armand

    2007-02-01

    In situations involving large potentials or surface charges, the Poisson-Boltzman (PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community, leading to the development of various alternative models resulting in different sets "modified PB equations," which have had at least qualitative success in predicting equilibrium ion distributions. On the other hand, the literature is scarce in terms of descriptions of concentration dynamics in these regimes. Here, adapting strategies developed to modify the PB equation, we propose a simple modification of the widely used Poisson-Nernst-Planck (PNP) equations for ionic transport, which at least qualitatively accounts for steric effects. We analyze numerical solutions of these modified PNP equations on the model problem of the charging of a simple electrolyte cell, and compare the outcome to that of the standard PNP equations. Finally, we repeat the asymptotic analysis of Bazant, Thornton, and Ajdari [Phys. Rev. E 70, 021506 (2004)] for this new system of equations to further document the interest and limits of validity of the simpler equivalent electrical circuit models introduced in Part I [Kilic, Bazant, and Ajdari, Phys. Rev. E 75, 021502 (2007)] for such problems.

  6. The flow equation approach to many-particle systems

    CERN Document Server

    Kehrein, Stefan; Fujimori, A; Varma, C; Steiner, F

    2006-01-01

    This self-contained monograph addresses the flow equation approach to many-particle systems. The flow equation approach consists of a sequence of infinitesimal unitary transformations and is conceptually similar to renormalization and scaling methods. Flow equations provide a framework for analyzing Hamiltonian systems where these conventional many-body techniques fail. The text first discusses the general ideas and concepts of the flow equation method. In a second part these concepts are illustrated with various applications in condensed matter theory including strong-coupling problems and non-equilibrium systems. The monograph is accessible to readers familiar with graduate- level solid-state theory.

  7. Simulation, optimal control and parametric sensitivity analysis of a molten carbonate fuel cell using a partial differential algebraic dynamic equation system; Simulation, Optimale Steuerung und Sensitivitaetsanalyse einer Schmelzkarbonat-Brennstoffzelle mithilfe eines partiellen differential-algebraischen dynamischen Gleichungssystems

    Energy Technology Data Exchange (ETDEWEB)

    Sternberg, K

    2007-02-08

    Molten carbonate fuel cells (MCFCs) allow an efficient and environmentally friendly energy production by converting the chemical energy contained in the fuel gas in virtue of electro-chemical reactions. In order to predict the effect of the electro-chemical reactions and to control the dynamical behavior of the fuel cell a mathematical model has to be found. The molten carbonate fuel cell (MCFC) can indeed be described by a highly complex,large scale, semi-linear system of partial differential algebraic equations. This system includes a reaction-diffusion-equation of parabolic type, several reaction-transport-equations of hyperbolic type, several ordinary differential equations and finally a system of integro-differential algebraic equations which describes the nonlinear non-standard boundary conditions for the entire partial differential algebraic equation system (PDAE-system). The existence of an analytical or the computability of a numerical solution for this high-dimensional PDAE-system depends on the kind of the differential equations and their special characteristics. Apart from theoretical investigations, the real process has to be controlled, more precisely optimally controlled. Hence, on the basis of the PDAE-system an optimal control problem is set up, whose analytical and numerical solvability is closely linked to the solvability of the PDAE-system. Moreover the solution of that optimal control problem is made more difficult by inaccuracies in the underlying database, which does not supply sufficiently accurate values for the model parameters. Therefore the optimal control problem must also be investigated with respect to small disturbances of model parameters. The aim of this work is to analyze the relevant dynamic behavior of MCFCs and to develop concepts for their optimal process control. Therefore this work is concerned with the simulation, the optimal control and the sensitivity analysis of a mathematical model for MCDCs, which can be characterized

  8. Dirac equations for generalised Yang-Mills systems

    International Nuclear Information System (INIS)

    Lechtenfeld, O.; Nahm, W.; Tchrakian, D.H.

    1985-06-01

    We present Dirac equations in 4p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a 'BPST' background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results. (orig.)

  9. Algebraic limit cycles in polynomial systems of differential equations

    International Nuclear Information System (INIS)

    Llibre, Jaume; Zhao Yulin

    2007-01-01

    Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4

  10. Gauge theory for finite-dimensional dynamical systems

    International Nuclear Information System (INIS)

    Gurfil, Pini

    2007-01-01

    Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This concept has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems. We focus on the concept of rescriptive gauge symmetry, which is, in essence, rescaling of an independent variable. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently ''disordered'' flow into a regular dynamical process, and that there exists a strong connection between gauge transformations and reduction theory of ordinary differential equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse fields, including quantum mechanics, chemistry, rigid-body dynamics, and information theory

  11. Relativistic quantum vorticity of the quadratic form of the Dirac equation

    International Nuclear Information System (INIS)

    Asenjo, Felipe A; Mahajan, Swadesh M

    2015-01-01

    We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the Feynman–Gell-Mann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and non-relativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system. (paper)

  12. Equivalent formulations of “the equation of life”

    International Nuclear Information System (INIS)

    Ao Ping

    2014-01-01

    Motivated by progress in theoretical biology a recent proposal on a general and quantitative dynamical framework for nonequilibrium processes and dynamics of complex systems is briefly reviewed. It is nothing but the evolutionary process discovered by Charles Darwin and Alfred Wallace. Such general and structured dynamics may be tentatively named “the equation of life”. Three equivalent formulations are discussed, and it is also pointed out that such a quantitative dynamical framework leads naturally to the powerful Boltzmann-Gibbs distribution and the second law in physics. In this way, the equation of life provides a logically consistent foundation for thermodynamics. This view clarifies a particular outstanding problem and further suggests a unifying principle for physics and biology. (topical review - statistical physics and complex systems)

  13. Parametric Identification of Nonlinear Dynamical Systems

    Science.gov (United States)

    Feeny, Brian

    2002-01-01

    In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

  14. State-space representation of the reactor dynamics equations

    International Nuclear Information System (INIS)

    Bernard, J.A.

    1995-01-01

    This paper describes a novel formulation of the reactor space-independent kinetics equations. The intent is to present these equations in a form that is both compatible with modern control theory and mathematically rigorous. It is desired to write the kinetics equations in the standard state variable representation, x = Ax, where x is the state vector and A is the system matrix and, at the same time, avoid mathematical compromises such as the linearization of an equation about a particular operating point. The advantage to this proposed formulation is that it may allow the lateral transfer of existing control concepts, some that have been developed for other fields, to the operation of nuclear reactors. For example, sliding mode control has been developed to allow robots to function in a robust manner in the presence of changes in the system model. This is necessary because a robot is expected to be capable of picking up an object of unknown mass and moving that object along a specified trajectory. The variability of the object's mass introduces an uncertainty into the system model that is used to deduce the appropriate control action. Thus, the robot controller must be made robust against such variations. Sliding mode control is one means of accomplishing this. A reactor controller might benefit from the same concept if its objective were to cause the reactor power to move along a demanded trajectory despite the presence of some uncertainty in the net amount of reactivity that is present

  15. Dynamical systems V bifurcation theory and catastrophe theory

    CERN Document Server

    1994-01-01

    Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of w...

  16. Program packages for dynamics systems analysis and design

    International Nuclear Information System (INIS)

    Athani, V.V.

    1976-01-01

    The development of computer program packages for dynamic system analysis and design are reported. The purpose of developing these program packages is to take the burden of writing computer programs off the mind of the system engineer and to enable him to concentrate on his main system analysis and design work. Towards this end, four standard computer program packages have been prepared : (1) TFANA - starting from system transfer function this program computes transient response, frequency response, root locus and stability by Routh Hurwitz criterion, (2) TFSYN - classical synthesis using algebraic method of Shipley, (3) MODANA - starting from state equations of the system this program computes solution of state equations, controllability, observability and stability, (4) OPTCON - This program obtains solutions of (i) linear regulator problem, (ii) servomechanism problems and (iii) problem of pole placement. The paper describes these program packages with the help of flowcharts and illustrates their use with the help of examples. (author)

  17. Peculiarities in power type comparison results for half-linear dynamic equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    2012-01-01

    Roč. 42, č. 6 (2012), s. 1995-2013 ISSN 0035-7596 R&D Projects: GA AV ČR KJB100190701 Institutional support: RVO:67985840 Keywords : half-linear dynamic equation * time scale * comparison theorem Subject RIV: BA - General Mathematics Impact factor: 0.389, year: 2012 http://projecteuclid.org/euclid.rmjm/1361800616

  18. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    1978-01-01

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)

  19. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)

  20. Molecular dynamics equation designed for realizing arbitrary density: Application to sampling method utilizing the Tsallis generalized distribution

    International Nuclear Information System (INIS)

    Fukuda, Ikuo; Nakamura, Haruki

    2010-01-01

    Several molecular dynamics techniques applying the Tsallis generalized distribution are presented. We have developed a deterministic dynamics to generate an arbitrary smooth density function ρ. It creates a measure-preserving flow with respect to the measure ρdω and realizes the density ρ under the assumption of the ergodicity. It can thus be used to investigate physical systems that obey such distribution density. Using this technique, the Tsallis distribution density based on a full energy function form along with the Tsallis index q ≥ 1 can be created. From the fact that an effective support of the Tsallis distribution in the phase space is broad, compared with that of the conventional Boltzmann-Gibbs (BG) distribution, and the fact that the corresponding energy-surface deformation does not change energy minimum points, the dynamics enhances the physical state sampling, in particular for a rugged energy surface spanned by a complicated system. Other feature of the Tsallis distribution is that it provides more degree of the nonlinearity, compared with the case of the BG distribution, in the deterministic dynamics equation, which is very useful to effectively gain the ergodicity of the dynamical system constructed according to the scheme. Combining such methods with the reconstruction technique of the BG distribution, we can obtain the information consistent with the BG ensemble and create the corresponding free energy surface. We demonstrate several sampling results obtained from the systems typical for benchmark tests in MD and from biomolecular systems.

  1. P-Adic Analog of Navier–Stokes Equations: Dynamics of Fluid’s Flow in Percolation Networks (from Discrete Dynamics with Hierarchic Interactions to Continuous Universal Scaling Model

    Directory of Open Access Journals (Sweden)

    Klaudia Oleschko

    2017-04-01

    Full Text Available Recently p-adic (and, more generally, ultrametric spaces representing tree-like networks of percolation, and as a special case of capillary patterns in porous media, started to be used to model the propagation of fluids (e.g., oil, water, oil-in-water, and water-in-oil emulsion. The aim of this note is to derive p-adic dynamics described by fractional differential operators (Vladimirov operators starting with discrete dynamics based on hierarchically-structured interactions between the fluids’ volumes concentrated at different levels of the percolation tree and coming to the multiscale universal topology of the percolating nets. Similar systems of discrete hierarchic equations were widely applied to modeling of turbulence. However, in the present work this similarity is only formal since, in our model, the trees are real physical patterns with a tree-like topology of capillaries (or fractures in random porous media (not cascade trees, as in the case of turbulence, which we will be discussed elsewhere for the spinner flowmeter commonly used in the petroleum industry. By going to the “continuous limit” (with respect to the p-adic topology we represent the dynamics on the tree-like configuration space as an evolutionary nonlinear p-adic fractional (pseudo- differential equation, the tree-like analog of the Navier–Stokes equation. We hope that our work helps to come closer to a nonlinear equation solution, taking into account the scaling, hierarchies, and formal derivations, imprinted from the similar properties of the real physical world. Once this coupling is resolved, the more problematic question of information scaling in industrial applications will be achieved.

  2. Numerical computation of soliton dynamics for NLS equations in a driving potential

    Directory of Open Access Journals (Sweden)

    Marco Caliari

    2010-06-01

    Full Text Available We provide numerical computations for the soliton dynamics of the nonlinear Schrodinger equation with an external potential. After computing the ground state solution r of a related elliptic equation we show that, in the semi-classical regime, the center of mass of the solution with initial datum built upon r is driven by the solution to $ddot x=- abla V(x$. Finally, we provide examples and analyze the numerical errors in the two dimensional case when V is a harmonic potential.

  3. Least squares shadowing sensitivity analysis of a modified Kuramoto–Sivashinsky equation

    International Nuclear Information System (INIS)

    Blonigan, Patrick J.; Wang, Qiqi

    2014-01-01

    Highlights: •Modifying the Kuramoto–Sivashinsky equation and changing its boundary conditions make it an ergodic dynamical system. •The modified Kuramoto–Sivashinsky equation exhibits distinct dynamics for three different ranges of system parameters. •Least squares shadowing sensitivity analysis computes accurate gradients for a wide range of system parameters. - Abstract: Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto–Sivashinsky (K–S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K–S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters

  4. Automated design of complex dynamic systems.

    Directory of Open Access Journals (Sweden)

    Michiel Hermans

    Full Text Available Several fields of study are concerned with uniting the concept of computation with that of the design of physical systems. For example, a recent trend in robotics is to design robots in such a way that they require a minimal control effort. Another example is found in the domain of photonics, where recent efforts try to benefit directly from the complex nonlinear dynamics to achieve more efficient signal processing. The underlying goal of these and similar research efforts is to internalize a large part of the necessary computations within the physical system itself by exploiting its inherent non-linear dynamics. This, however, often requires the optimization of large numbers of system parameters, related to both the system's structure as well as its material properties. In addition, many of these parameters are subject to fabrication variability or to variations through time. In this paper we apply a machine learning algorithm to optimize physical dynamic systems. We show that such algorithms, which are normally applied on abstract computational entities, can be extended to the field of differential equations and used to optimize an associated set of parameters which determine their behavior. We show that machine learning training methodologies are highly useful in designing robust systems, and we provide a set of both simple and complex examples using models of physical dynamical systems. Interestingly, the derived optimization method is intimately related to direct collocation a method known in the field of optimal control. Our work suggests that the application domains of both machine learning and optimal control have a largely unexplored overlapping area which envelopes a novel design methodology of smart and highly complex physical systems.

  5. Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems.

    Science.gov (United States)

    Sivak, David A; Chodera, John D; Crooks, Gavin E

    2014-06-19

    When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

  6. FEQinput—An editor for the full equations (FEQ) hydraulic modeling system

    Science.gov (United States)

    Ancalle, David S.; Ancalle, Pablo J.; Domanski, Marian M.

    2017-10-30

    IntroductionThe Full Equations Model (FEQ) is a computer program that solves the full, dynamic equations of motion for one-dimensional unsteady hydraulic flow in open channels and through control structures. As a result, hydrologists have used FEQ to design and operate flood-control structures, delineate inundation maps, and analyze peak-flow impacts. To aid in fighting floods, hydrologists are using the software to develop a system that uses flood-plain models to simulate real-time streamflow.Input files for FEQ are composed of text files that contain large amounts of parameters, data, and instructions that are written in a format exclusive to FEQ. Although documentation exists that can aid in the creation and editing of these input files, new users face a steep learning curve in order to understand the specific format and language of the files.FEQinput provides a set of tools to help a new user overcome the steep learning curve associated with creating and modifying input files for the FEQ hydraulic model and the related utility tool, Full Equations Utilities (FEQUTL).

  7. On the properties of a variant of the Riccati system of equations

    International Nuclear Information System (INIS)

    Sarkar, Amartya; Guha, Partha; Bhattacharjee, J K; Mallik, A K; Ghose-Choudhury, Anindya; Leach, P G L

    2012-01-01

    A variant of the generalized Riccati system of equations is considered. It is shown that for α = 2n + 3 the system admits a bilagrangian description and the dynamics has a node at the origin, whereas for α much smaller than a critical value the dynamics is periodic, the origin being a centre. It is found that the solution changes from being periodic to aperiodic at a critical point, α c = 2√(2(n+1)), which is independent of the initial conditions. This behaviour is explained by finding a scaling argument via which the phase trajectories corresponding to different initial conditions collapse onto a single universal orbit. Numerical evidence for the transition is shown. Further, using a perturbative renormalization group argument, it is conjectured that the oscillator exhibits isochronous oscillations. The correctness of the conjecture is established numerically. (paper)

  8. Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

    International Nuclear Information System (INIS)

    Hedrih, K

    2008-01-01

    This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

  9. Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

    Science.gov (United States)

    Stevanović Hedrih, K.

    2008-02-01

    This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

  10. Theorems on Existence and Global Dynamics for the Einstein Equations

    Directory of Open Access Journals (Sweden)

    Rendall Alan

    2002-01-01

    Full Text Available This article is a guide to theorems on existence and global dynamics of solutions ofthe Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.

  11. Theorems on Existence and Global Dynamics for the Einstein Equations

    Directory of Open Access Journals (Sweden)

    Rendall Alan D.

    2005-10-01

    Full Text Available This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.

  12. ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY

    OpenAIRE

    Enrique Gonzalo Reyes Garcia

    2004-01-01

    ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY Equations in partial derivatives appeared in the 18th century as essential tools for the analytic study of physical models and, later, they proved to be fundamental for the progress of mathematics. For example, fundamental results of modern differential geometry are based on deep theorems on differential equations. Reciprocally, it is possible to study differential equations through geometrical means just like it was done by o...

  13. Dynamical systems with applications using MATLAB

    CERN Document Server

    Lynch, Stephen

    2014-01-01

    This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB®, Simulink®, the Image Processing Toolbox™, and the Symbolic Math Toolbox™, including MuPAD. Features new to the second edition include, sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization; chapters on image processing and binary oscillator computing; hundreds of new illustrations, examples, and exercises with solutions; and over eighty up-to-date MATLAB® program files and Simulink model files available online. These files were voted MATLAB® Central Pick of the Week in July 2013.  The hands-on approach of Dynamical Systems with Applications using MATLAB®, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equ...

  14. System dynamics

    International Nuclear Information System (INIS)

    Kim, Do Hun; Mun, Tae Hun; Kim, Dong Hwan

    1999-02-01

    This book introduces systems thinking and conceptual tool and modeling tool of dynamics system such as tragedy of single thinking, accessible way of system dynamics, feedback structure and causal loop diagram analysis, basic of system dynamics modeling, causal loop diagram and system dynamics modeling, information delay modeling, discovery and application for policy, modeling of crisis of agricultural and stock breeding products, dynamic model and lesson in ecosystem, development and decadence of cites and innovation of education forward system thinking.

  15. Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

    International Nuclear Information System (INIS)

    Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.

    2010-01-01

    We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delay time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.

  16. Navier-Stokes equations an introduction with applications

    CERN Document Server

    Łukaszewicz, Grzegorz

    2016-01-01

    This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior o...

  17. Dynamics of a deep-sea cable system

    International Nuclear Information System (INIS)

    Gulyaev, V.I.; Koshkin, V.L.; Serpak, I.O.

    1995-01-01

    We consider the problem of the dynamics of a deep-sea cable system consisting of branches of constant and variable length, interacting with an undercurrent which is variable in depth and direction. We construct a mathematical model for the motion of the element of the cable system. The cables are modeled as inextensible, flexible filaments of variable length. For numerical realization of the problem, we suggest special regularizing transformations of the variables, making it possible (without additional simplifications) to take into account all the characteristic features of the motion of the filaments and to avoid difficulties in the integration of the equations of motion connected with the variability of the length of the branches of the cable system. The proposed mathematical model and the technique for its numerical analysis is applicable for the investigation of the dynamics of a complex for mining minerals from the ocean floor

  18. An information-theoretic approach to assess practical identifiability of parametric dynamical systems.

    Science.gov (United States)

    Pant, Sanjay; Lombardi, Damiano

    2015-10-01

    A new approach for assessing parameter identifiability of dynamical systems in a Bayesian setting is presented. The concept of Shannon entropy is employed to measure the inherent uncertainty in the parameters. The expected reduction in this uncertainty is seen as the amount of information one expects to gain about the parameters due to the availability of noisy measurements of the dynamical system. Such expected information gain is interpreted in terms of the variance of a hypothetical measurement device that can measure the parameters directly, and is related to practical identifiability of the parameters. If the individual parameters are unidentifiable, correlation between parameter combinations is assessed through conditional mutual information to determine which sets of parameters can be identified together. The information theoretic quantities of entropy and information are evaluated numerically through a combination of Monte Carlo and k-nearest neighbour methods in a non-parametric fashion. Unlike many methods to evaluate identifiability proposed in the literature, the proposed approach takes the measurement-noise into account and is not restricted to any particular noise-structure. Whilst computationally intensive for large dynamical systems, it is easily parallelisable and is non-intrusive as it does not necessitate re-writing of the numerical solvers of the dynamical system. The application of such an approach is presented for a variety of dynamical systems--ranging from systems governed by ordinary differential equations to partial differential equations--and, where possible, validated against results previously published in the literature. Copyright © 2015 Elsevier Inc. All rights reserved.

  19. Lie symmetries for systems of evolution equations

    Science.gov (United States)

    Paliathanasis, Andronikos; Tsamparlis, Michael

    2018-01-01

    The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.

  20. Introduction to Hamiltonian dynamical systems and the N-body problem

    CERN Document Server

    Meyer, Kenneth R

    2017-01-01

    This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary exa...

  1. Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics

    Directory of Open Access Journals (Sweden)

    Weam Alharbi

    2018-04-01

    Full Text Available A telegraph equation is believed to be an appropriate model of population dynamics as it accounts for the directional persistence of individual animal movement. Being motivated by the problem of habitat fragmentation, which is known to be a major threat to biodiversity that causes species extinction worldwide, we consider the reaction–telegraph equation (i.e., telegraph equation combined with the population growth on a bounded domain with the goal to establish the conditions of species survival. We first show analytically that, in the case of linear growth, the expression for the domain’s critical size coincides with the critical size of the corresponding reaction–diffusion model. We then consider two biologically relevant cases of nonlinear growth, i.e., the logistic growth and the growth with a strong Allee effect. Using extensive numerical simulations, we show that in both cases the critical domain size of the reaction–telegraph equation is larger than the critical domain size of the reaction–diffusion equation. Finally, we discuss possible modifications of the model in order to enhance the positivity of its solutions.

  2. Principal and nonprincipal solutions of symplectic dynamic systems on time scales

    Directory of Open Access Journals (Sweden)

    Ondrej Dosly

    2000-01-01

    Full Text Available We establish the concept of the principal and nonprincipal solution for the so-called symplectic dynamic systems on time scales. We also present a brief survey of the history of these concept for differential and difference equations.

  3. Dynamics of movie competition and popularity spreading in recommender systems.

    Science.gov (United States)

    Yeung, C H; Cimini, G; Jin, C-H

    2011-01-01

    We introduce a simple model to study movie competition in recommender systems. Movies of heterogeneous quality compete against each other through viewers' reviews and generate interesting dynamics at the box office. By assuming mean-field interactions between the competing movies, we show that the runaway effect of popularity spreading is triggered by defeating the average review score, leading to box-office hits: Popularity rises and peaks before fade-out. The average review score thus characterizes the critical movie quality necessary for transition from box-office bombs to blockbusters. The major factors affecting the critical review score are examined. By iterating the mean-field dynamical equations, we obtain qualitative agreements with simulations and real systems in the dynamical box-office forms, revealing the significant role of competition in understanding box-office dynamics.

  4. Dynamics of movie competition and popularity spreading in recommender systems

    Science.gov (United States)

    Yeung, C. H.; Cimini, G.; Jin, C.-H.

    2011-01-01

    We introduce a simple model to study movie competition in recommender systems. Movies of heterogeneous quality compete against each other through viewers’ reviews and generate interesting dynamics at the box office. By assuming mean-field interactions between the competing movies, we show that the runaway effect of popularity spreading is triggered by defeating the average review score, leading to box-office hits: Popularity rises and peaks before fade-out. The average review score thus characterizes the critical movie quality necessary for transition from box-office bombs to blockbusters. The major factors affecting the critical review score are examined. By iterating the mean-field dynamical equations, we obtain qualitative agreements with simulations and real systems in the dynamical box-office forms, revealing the significant role of competition in understanding box-office dynamics.

  5. Influence of Shaft Torsional Stiffness on Dynamic Response of Four-Stage Main Transmission System

    Directory of Open Access Journals (Sweden)

    Yuan Chen

    2018-01-01

    Full Text Available Dynamic response analysis has potential for increasing fatigue life of the components in the transmission of a multistage main transmission system. The calculated data can demonstrate the influence of shaft torsional stiffness on dynamic characteristics of the system. Detecting key shafts of the system and analyzing their sensitivity are important for the design of four-stage helicopter gear box. Lumped mass method is applied for dynamic modeling and Fourier method is used to solve differential equation of the system. Results of the analysis indicate that key shafts can be designed carefully to improve the performance of the transmission system.

  6. THE GROSSER ALETSCHGLETSCHER DYNAMICS: FROM A “MINIMAL MODEL” TO A STOCHASTIC EQUATION

    Directory of Open Access Journals (Sweden)

    Alexander V. Kislov

    2016-01-01

    Full Text Available Mountain glaciers manifest oscillations at different time-scales. Apart from synchronous reaction to lasting changes, there is asynchronism between climatic forcing and observed anomalies of the glaciers. Based on general theories on the laws of temporal dynamics relating to massive inertial objects, the observed interannual changes of glacier length could result from the accumulation of small anomalies in the heat/water fluxes. Despite the fact that the original model of the dynamics of mountain glaciers is deterministically based on the physical law of conservation of water mass, the model of length change is interpreted as stochastic; from this perspective, it is the Langevin equation that incorporates the action of temperature anomalies and precipitation like random white noise. The process is analogous to Brownian motion. Under these conditions, the Grosser Aletschgletscher (selected as an example is represented by a system undergoing a random walk. It was shown that the possible range of variability covers the observed interval of length fluctuations.

  7. Analysis of the gravitational coupled collisionless Boltzmann-poisson equations and numerical simulations of the formation of self-gravitating systems

    International Nuclear Information System (INIS)

    Roy, Fabrice

    2004-01-01

    We study the formation of self-gravitating systems and their properties by means of N-body simulations of gravitational collapse. First, we summarize the major analytical results concerning the collisionless Boltzmann equation and the Poisson's equation which describe the dynamics of collisionless gravitational systems. We present a study of some analytical solutions of this coupled system of equations. We then present the software used to perform the simulations. Some of this has been parallelized and implemented with the aid of MPI. For this reason we give a brief overview of it. Finally, we present the results of the numerical simulations. Analysis of these results allows us to explain some features of self-gravitating systems and the initial conditions needed to trigger the Antonov instability and the radial orbit instability. (author) [fr

  8. Dynamics of quantum tomography in an open system

    Science.gov (United States)

    Uchiyama, Chikako

    2015-06-01

    In this study, we provide a way to describe the dynamics of quantum tomography in an open system with a generalized master equation, considering a case where the relevant system under tomographic measurement is influenced by the environment. We apply this to spin tomography because such situations typically occur in μSR (muon spin rotation/relaxation/resonance) experiments where microscopic features of the material are investigated by injecting muons as probes. As a typical example to describe the interaction between muons and a sample material, we use a spin-boson model where the relevant spin interacts with a bosonic environment. We describe the dynamics of a spin tomogram using a time-convolutionless type of generalized master equation that enables us to describe short time scales and/or low-temperature regions. Through numerical evaluation for the case of Ohmic spectral density with an exponential cutoff, a clear interdependency is found between the time evolution of elements of the density operator and a spin tomogram. The formulation in this paper may provide important fundamental information for the analysis of results from, for example, μSR experiments on short time scales and/or in low-temperature regions using spin tomography.

  9. Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

    Directory of Open Access Journals (Sweden)

    Y. N. Pavlov

    2015-01-01

    Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

  10. The numerical solution of linear multi-term fractional differential equations: systems of equations

    Science.gov (United States)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  11. Data-driven discovery of partial differential equations.

    Science.gov (United States)

    Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

    2017-04-01

    We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

  12. Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System

    DEFF Research Database (Denmark)

    Zhusubaliyev, Z.T.; Soukhoterin, E.A.; Mosekilde, Erik

    2002-01-01

    Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject...... of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border......-collision bifurcations. The paper contains a detailed analysis of this type of bifurcational transition in the dynamics of the voltage converter, in particular, the merging and subsequent disappearance of cycles of different types, change of solution type, and period-doubling, -tripling, -quadrupling and -quintupling...

  13. Periodic solutions of first-order functional differential equations in population dynamics

    CERN Document Server

    Padhi, Seshadev; Srinivasu, P D N

    2014-01-01

    This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, a...

  14. Effects of system-bath coupling on a photosynthetic heat engine: A polaron master-equation approach

    Science.gov (United States)

    Qin, M.; Shen, H. Z.; Zhao, X. L.; Yi, X. X.

    2017-07-01

    Stimulated by suggestions of quantum effects in energy transport in photosynthesis, the fundamental principles responsible for the near-unit efficiency of the conversion of solar to chemical energy became active again in recent years. Under natural conditions, the formation of stable charge-separation states in bacteria and plant reaction centers is strongly affected by the coupling of electronic degrees of freedom to a wide range of vibrational motions. These inspire and motivate us to explore the effects of the environment on the operation of such complexes. In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect the exciton-transfer processes in the Photosystem II reaction center described by a quantum heat engine (QHE) model over a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in detail. We interpret these results in terms of noise-assisted transport effect and dynamical localization, which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is the dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization dominates the dynamics and temperature modulates the balance of the two mechanisms. Furthermore, these two mechanisms can be attributed to one physical origin: bath-induced fluctuations. The two mechanisms are manifestations of the dual role played by bath-induced fluctuations depending on the range of parameters. The origin and role of coherence are also discussed. It is the constructive interplay between noise and coherent dynamics, rather

  15. A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

    Science.gov (United States)

    Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

    2018-06-01

    This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

  16. A variational master equation approach to quantum dynamics with off-diagonal coupling in a sub-Ohmic environment

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Ke-Wei [School of Science, Hangzhou Dianzi University, Hangzhou 310018 (China); Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Fujihashi, Yuta; Ishizaki, Akihito [Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585 (Japan); Zhao, Yang, E-mail: YZhao@ntu.edu.sg [Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore)

    2016-05-28

    A master equation approach based on an optimized polaron transformation is adopted for dynamics simulation with simultaneous diagonal and off-diagonal spin-boson coupling. Two types of bath spectral density functions are considered, the Ohmic and the sub-Ohmic. The off-diagonal coupling leads asymptotically to a thermal equilibrium with a nonzero population difference P{sub z}(t → ∞) ≠ 0, which implies localization of the system, and it also plays a role in restraining coherent dynamics for the sub-Ohmic case. Since the new method can extend to the stronger coupling regime, we can investigate the coherent-incoherent transition in the sub-Ohmic environment. Relevant phase diagrams are obtained for different temperatures. It is found that the sub-Ohmic environment allows coherent dynamics at a higher temperature than the Ohmic environment.

  17. Dynamic reliability and risk assessment of the accident localization system of the Ignalina NPP RBMK-1500 reactor

    International Nuclear Information System (INIS)

    Kopustinskas, V.; Augutis, J.; Rimkevicius, S.

    2005-01-01

    The paper presents reliability and risk analysis of the RBMK-1500 reactor accident localization system (ALS) (confinement), which prevents radioactive releases to the environment. Reliability of the system was estimated and compared by two methods: the conventional fault tree method and an innovative dynamic reliability model, based on stochastic differential equations. Frequency of radioactive release through ALS was also estimated. The results of the study indicate that conventional fault tree modeling techniques in this case apply high degree of conservatism in the system reliability estimates. One of the purposes of the ALS reliability study was to demonstrate advantages of the dynamic reliability analysis against the conventional fault/event tree methods. The Markovian framework to deal with dynamic aspects of system behavior is presented. Although not analyzed in detail, the framework is also capable of accounting for non-constant component failure rates. Computational methods are proposed to solve stochastic differential equations, including analytical solution, which is possible only for relatively small and simple systems. Other numerical methods, like Monte Carlo and numerical schemes of differential equations are analyzed and compared. The study is finalized with concluding remarks regarding both the studied system reliability and computational methods used

  18. Dynamics of dissipative systems and computational physics

    International Nuclear Information System (INIS)

    Adam, Gh.; Scutaru, H.; Ixaru, L.; Adam, S.; Rizea, M.; Stefanescu, E.; Mihalache, D.; Mazilu, D.; Crasovan, L.

    2002-01-01

    During the first year of research activity in the frame of this project there have been investigated two main topics: I. Dynamics of systems of fermions in complex dissipative media; II. Solitons with topologic charge in dissipative systems. An essential problem of the quantum information systems is the controllability and observability of the quantum states, generally described by Lindblad's master equation with phenomenological coefficients. In its usual form, this equation describes a decay of the mean-values, but not necessarily the expected decaying transitions. The basic and very difficult problem of a dissipative quantum theory is to project the evolution of the total system (the system of interest + the environment) on the space of the system of interest. In this case, one obtains a quantum master equation where the system evolution is described by two terms: 1) a Hamiltonian term for the processes with energy conservation, and 2) a non-Hamiltonian term with coefficients depending on the dissipative coupling. That means that a master equation is based on some approximations enabling the replacement of the operators of the dissipative environment with average value coefficients. It is often assumed that the evolution operators of the dissipative system define a semigroup, not a group as in the case of an isolated system. In this framework, Lindblad obtained a quantum master equation in agreement with all the quantum-mechanical principles. However, the Lindblad master equation was unable to secure a correct description of the decaying states. To do that, one has to take into account the transition operators between the system eigenstates with appropriate coefficients. Within this investigation, we have obtained an equation obeying to this requirement, giving the ρ(t) time derivative in terms of creation-annihilation operators of the single-particle states |i>, and λ ij , representing the dissipative coefficients, the microscopic expressions of which are

  19. Lagrangian structures, integrability and chaos for 3D dynamical equations

    International Nuclear Information System (INIS)

    Bustamante, Miguel D; Hojman, Sergio A

    2003-01-01

    In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, we show that the so-called ABC system is completely integrable if it possesses one constant of the motion

  20. Analysis of an Nth-order nonlinear differential-delay equation

    Science.gov (United States)

    Vallée, Réal; Marriott, Christopher

    1989-01-01

    The problem of a nonlinear dynamical system with delay and an overall response time which is distributed among N individual components is analyzed. Such a system can generally be modeled by an Nth-order nonlinear differential delay equation. A linear-stability analysis as well as a numerical simulation of that equation are performed and a comparison is made with the experimental results. Finally, a parallel is established between the first-order differential equation with delay and the Nth-order differential equation without delay.

  1. Modeling and Optimal Control of a Class of Warfare Hybrid Dynamic Systems Based on Lanchester (n,1) Attrition Model

    OpenAIRE

    Chen, Xiangyong; Zhang, Ancai

    2014-01-01

    For the particularity of warfare hybrid dynamic process, a class of warfare hybrid dynamic systems is established based on Lanchester equation in a (n,1) battle, where a heterogeneous force of n different troop types faces a homogeneous force. This model can be characterized by the interaction of continuous-time models (governed by Lanchester equation), and discrete event systems (described by variable tactics). Furthermore, an expository discussion is presented on an optimal variable tact...

  2. uncertain dynamic systems on time scales

    Directory of Open Access Journals (Sweden)

    V. Lakshmikantham

    1995-01-01

    Full Text Available A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.

  3. Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

    Science.gov (United States)

    Hu, Wei; Tian, Qiang; Hu, HaiYan

    2018-04-01

    As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.

  4. Spatiotemporal dynamics of a digital phase-locked loop based coupled map lattice system

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, Tanmoy, E-mail: tbanerjee@phys.buruniv.ac.in; Paul, Bishwajit; Sarkar, B. C. [Department of Physics, University of Burdwan, Burdwan, West Bengal 713 104 (India)

    2014-03-15

    We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strength the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.

  5. Dynamic Phase Transitions In The Spin-2 Ising System Under An Oscillating Magnetic Field Within The Effective-Field Theory

    International Nuclear Information System (INIS)

    Ertas, Mehmet; Keskin, Mustafa; Deviren, Bayram

    2010-01-01

    The dynamic phase transitions are studied in the spin-2 Ising model under a time-dependent oscillating magnetic field by using the effective-field theory with correlations. The effective-field dynamic equation is derived by employing the Glauber transition rates and the phases in the system are obtained by solving this dynamic equation. The nature (first- or second-order) of the dynamic phase transition is characterized by investigating the thermal behavior of the dynamic order parameter and the dynamic phase transition temperatures are obtained. The dynamic phase diagrams are presented in (T/zJ, h/zJ) plane.

  6. A modelling of robot manipulator dynamics based on Newton-Euler's equations

    International Nuclear Information System (INIS)

    Sasaki, Shinobu

    1990-09-01

    In this paper is presented an algorithm for solving the inverse dynamics of robot manipulators. In comparison with the dynamical equations derived from the Lagrange's mechanics, the relations to be treated are of simple forms due to recursive expressions of relative link motions. A computer simulation for applying the algorithm to a six-link manipulator indicated that the present method might be most appropriate among the existing approaches from the viewpoint of computational efficiency. In particular, it is noted that the increase of the number of links has hardly great effect on the intricacy of calculation. (author)

  7. Converting differential-equation models of biological systems to membrane computing.

    Science.gov (United States)

    Muniyandi, Ravie Chandren; Zin, Abdullah Mohd; Sanders, J W

    2013-12-01

    This paper presents a method to convert the deterministic, continuous representation of a biological system by ordinary differential equations into a non-deterministic, discrete membrane computation. The dynamics of the membrane computation is governed by rewrite rules operating at certain rates. That has the advantage of applying accurately to small systems, and to expressing rates of change that are determined locally, by region, but not necessary globally. Such spatial information augments the standard differentiable approach to provide a more realistic model. A biological case study of the ligand-receptor network of protein TGF-β is used to validate the effectiveness of the conversion method. It demonstrates the sense in which the behaviours and properties of the system are better preserved in the membrane computing model, suggesting that the proposed conversion method may prove useful for biological systems in particular. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

  8. Optical solver for a system of ordinary differential equations based on an external feedback assisted microring resonator.

    Science.gov (United States)

    Hou, Jie; Dong, Jianji; Zhang, Xinliang

    2017-06-15

    Systems of ordinary differential equations (SODEs) are crucial for describing the dynamic behaviors in various systems such as modern control systems which require observability and controllability. In this Letter, we propose and experimentally demonstrate an all-optical SODE solver based on the silicon-on-insulator platform. We use an add/drop microring resonator to construct two different ordinary differential equations (ODEs) and then introduce two external feedback waveguides to realize the coupling between these ODEs, thus forming the SODE solver. A temporal coupled mode theory is used to deduce the expression of the SODE. A system experiment is carried out for further demonstration. For the input 10 GHz NRZ-like pulses, the measured output waveforms of the SODE solver agree well with the calculated results.

  9. Electron-nuclear dynamics of molecular systems

    International Nuclear Information System (INIS)

    Diz, A.; Oehrn, Y.

    1994-01-01

    The content of an ab initio time-dependent theory of quantum molecular dynamics of electrons and atomic nuclei is presented. Employing the time-dependent variational principle and a family of approximate state vectors yields a set of dynamical equations approximating the time-dependent Schroedinger equation. These equations govern the time evolution of the relevant state vector parameters as molecular orbital coefficients, nuclear positions, and momenta. This approach does not impose the Born-Oppenheimer approximation, does not use potential energy surfaces, and takes into account electron-nuclear coupling. Basic conservation laws are fully obeyed. The simplest model of the theory employs a single determinantal state for the electrons and classical nuclei and is implemented in the computer code ENDyne. Results from this ab-initio theory are reported for ion-atom and ion-molecule collisions

  10. From dynamical systems with time-varying delay to circle maps and Koopman operators

    Science.gov (United States)

    Müller, David; Otto, Andreas; Radons, Günter

    2017-06-01

    In this paper, we investigate the influence of the retarded access by a time-varying delay on the dynamics of delay systems. We show that there are two universality classes of delays, which lead to fundamental differences in dynamical quantities such as the Lyapunov spectrum. Therefore, we introduce an operator theoretic framework, where the solution operator of the delay system is decomposed into the Koopman operator describing the delay access and an operator similar to the solution operator known from systems with constant delay. The Koopman operator corresponds to an iterated map, called access map, which is defined by the iteration of the delayed argument of the delay equation. The dynamics of this one-dimensional iterated map determines the universality classes of the infinite-dimensional state dynamics governed by the delay differential equation. In this way, we connect the theory of time-delay systems with the theory of circle maps and the framework of the Koopman operator. In this paper, we extend our previous work [A. Otto, D. Müller, and G. Radons, Phys. Rev. Lett. 118, 044104 (2017), 10.1103/PhysRevLett.118.044104] by elaborating the mathematical details and presenting further results also on the Lyapunov vectors.

  11. Dynamics of interface in three-dimensional anisotropic bistable reaction-diffusion system

    International Nuclear Information System (INIS)

    He Zhizhu; Liu, Jing

    2010-01-01

    This paper presents a theoretical investigation of dynamics of interface (wave front) in three-dimensional (3D) reaction-diffusion (RD) system for bistable media with anisotropy constructed by means of anisotropic surface tension. An equation of motion for the wave front is derived to carry out stability analysis of transverse perturbations, which discloses mechanism of pattern formation such as labyrinthine in 3D bistable media. Particularly, the effects of anisotropy on wave propagation are studied. It was found that, sufficiently strong anisotropy can induce dynamical instabilities and lead to breakup of the wave front. With the fast-inhibitor limit, the bistable system can further be described by a variational dynamics so that the boundary integral method is adopted to study the dynamics of wave fronts.

  12. Mathematical modeling of earth's dynamical systems a primer

    CERN Document Server

    Slingerland, Rudy

    2011-01-01

    Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be f...

  13. Dynamical equations and transport coefficients for the metals at high pulse electromagnetic fields

    International Nuclear Information System (INIS)

    Volkov, N B; Chingina, E A; Yalovets, A P

    2016-01-01

    We offer a metal model suitable for the description of fast electrophysical processes in conductors under influence of powerful electronic and laser radiation of femto- and picosecond duration, and also high-voltage electromagnetic pulses with picosecond front and duration less than 1 ns. The obtained dynamic equations for metal in approximation of one quasineutral liquid are in agreement with the equations received by other authors formerly. New wide-range expressions for the electronic conduction in strong electromagnetic fields are obtained and analyzed. (paper)

  14. Optimal control theory for quantum-classical systems: Ehrenfest molecular dynamics based on time-dependent density-functional theory

    International Nuclear Information System (INIS)

    Castro, A; Gross, E K U

    2014-01-01

    We derive the fundamental equations of an optimal control theory for systems containing both quantum electrons and classical ions. The system is modeled with Ehrenfest dynamics, a non-adiabatic variant of molecular dynamics. The general formulation, that needs the fully correlated many-electron wavefunction, can be simplified by making use of time-dependent density-functional theory. In this case, the optimal control equations require some modifications that we will provide. The abstract general formulation is complemented with the simple example of the H 2 + molecule in the presence of a laser field. (paper)

  15. Analogy between soap film and gas dynamics. I. Equations and shock jump conditions

    Energy Technology Data Exchange (ETDEWEB)

    Wen, C.Y.; Lai, J.Y. [Department of Mechanical Engineering, Da-Yeh University, Chang-Hwa (Taiwan)

    2003-01-01

    The governing equations of compressible flows in soap films are formulated based on the very specific property equations of soap films. The basic normal shock relations and the Rankine-Hugoniot equation are derived for steady one-dimensional flows in soap films. The results are similar to those of compressible gases. The analogy between compressible flows in soap films and that in gases is discussed. On short time scales, the dynamic response of the film is characterized by the Marangoni elasticity, and soap films are shown to be analogous to compressible gases with a specific heat ratio of {gamma}=1.0. Results for Gibbs elasticity are also presented for reference, and no clear analogy to compressible gases is obtained. (orig.)

  16. On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

    International Nuclear Information System (INIS)

    Prykarpatsky, Yarema A.; Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.; Samoylenko, Valeriy H.

    2010-12-01

    A gradient-holonomic approach for the Lax type integrability analysis of differential-discrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied and the related gradient identity is stated. The integrability of a discrete nonlinear Schroedinger type dynamical system is treated in detail. The integrability of a generalized Riemann type discrete hydrodynamical system is discussed. (author)

  17. Statistical dynamics of ultradiffusion in hierarchical systems

    International Nuclear Information System (INIS)

    Gardner, S.

    1987-01-01

    In many types of disordered systems which exhibit frustration and competition, an ultrametric topology is found to exist in the space of allowable states. This ultrametric topology of states is associated with a hierarchical relaxation process called ultradiffusion. Ultradiffusion occurs in hierarchical non-linear (HNL) dynamical systems when constraints cause large scale, slow modes of motion to be subordinated to small scale, fast modes. Examples of ultradiffusion are found throughout condensed matter physics and critical phenomena (e.g. the states of spin glasses), in biophysics (e.g. the states of Hopfield networks) and in many other fields including layered computing based upon nonlinear dynamics. The statistical dynamics of ultradiffusion can be treated as a random walk on an ultrametric space. For reversible bifurcating ultrametric spaces the evolution equation governing the probability of a particle being found at site i at time t has a highly degenerate transition matrix. This transition matrix has a fractal geometry similar to the replica form proposed for spin glasses. The authors invert this fractal matrix using a recursive quad-tree (QT) method. Possible applications of hierarchical systems to communications and symbolic computing are discussed briefly

  18. Stochastic optimal control in infinite dimension dynamic programming and HJB equations

    CERN Document Server

    Fabbri, Giorgio; Święch, Andrzej

    2017-01-01

    Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...

  19. RG-Whitham dynamics and complex Hamiltonian systems

    Directory of Open Access Journals (Sweden)

    A. Gorsky

    2015-06-01

    Full Text Available Inspired by the Seiberg–Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG-like Whitham behavior. We show that at the Argyres–Douglas (AD point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne–Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory.

  20. The lie-algebraic structures and integrability of differential and differential-difference nonlinear dynamical systems

    International Nuclear Information System (INIS)

    Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.

    2007-05-01

    The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)

  1. System Dynamics and Feedforward Control for Tether-Net Space Robot System

    Directory of Open Access Journals (Sweden)

    Guang Zhai

    2009-06-01

    Full Text Available A new concept using flexible tether-net system to capture space debris is presented in this paper. With a mass point assumption the tether-net system dynamic model is established in orbital frame by applying Lagrange Equations. In order to investigate the net in-plane trajectories during after cast, the non-control R-bar and V-bar captures are simulated with ignoring the out-of-plane libration, the effect of in-plane libration on the trajectories of the capture net is demonstrated by simulation results. With an effort to damp the in-plane libration, the control scheme based on tether tension is investigated firstly, after that an integrated control scheme is proposed by introduced the thrusters into the system, the nonlinear close-loop dynamics is linearised by feedforward strategy, the simulation results show that feedforward controllor is effective for in-plane libration damping and enable the capture net to track an expected trajectory.

  2. Development of kinetics equations from the Boltzmann equation; Etablissement des equations de la cinetique a partir de l'equation de Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    Plas, R.

    1962-07-01

    The author reports a study on kinetics equations for a reactor. He uses the conventional form of these equations but by using a dynamic multiplication factor. Thus, constants related to delayed neutrons are not modified by efficiency factors. The author first describes the theoretic kinetic operation of a reactor and develops the associated equations. He reports the development of equations for multiplication factors.

  3. On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or

  4. Solving differential–algebraic equation systems by means of index reduction methodology

    DEFF Research Database (Denmark)

    Sørensen, Kim; Houbak, Niels; Condra, Thomas

    2006-01-01

    of a number of differential equations and algebraic equations — a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODEs and index 1 DAEs by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of ordinary differential equations — ODEs....

  5. Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows

    International Nuclear Information System (INIS)

    Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.

    2013-01-01

    The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier–Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.

  6. Dynamical analysis of an n‑H‑T cosmological quintessence real gas model with a general equation of state

    Science.gov (United States)

    Ivanov, Rossen I.; Prodanov, Emil M.

    2018-01-01

    The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. The cyclic solutions exhibit regions characterized by inflation and deflation, while the open trajectories are characterized by inflation in a “fly-by” near an unstable critical point.

  7. Delay dynamical systems and applications to nonlinear machine-tool chatter

    International Nuclear Information System (INIS)

    Fofana, M.S.

    2003-01-01

    The stability behaviour of machine chatter that exhibits Hopf and degenerate bifurcations has been examined without the assumption of small delays between successive cuts. Delay dynamical system theory leading to the reduction of the infinite-dimensional character of the governing delay differential equations (DDEs) to a finite-dimensional set of ordinary differential equations have been employed. The essential mathematical arguments for these systems in the context of retarded DDEs are summarized. Then the application of these arguments in the stability study of machine-tool chatter with multiple time delays is presented. Explicit analytical expressions ensuring stable and unstable machining when perturbations are periodic, stochastic and nonlinear have been derived using the integral averaging method and Lyapunov exponents

  8. The 'strength' of a system of differential equations

    International Nuclear Information System (INIS)

    Hoenselaers, C.

    1977-01-01

    A review of Einstein's concept of ''strength'' of a system of differential equations is given. As an example the strength of the Einstein-Maxwell equations for non-null Maxwell field is calculated and shown to be the same as for the pure vacuum Einstein equations. (auth.)

  9. Network Reconstruction From High-Dimensional Ordinary Differential Equations.

    Science.gov (United States)

    Chen, Shizhe; Shojaie, Ali; Witten, Daniela M

    2017-01-01

    We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.

  10. Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.

    1996-01-01

    Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...

  11. Modelling system dynamics and phytoplankton diversity at Ranchi lake using the carbon and nutrient mass balance equations.

    Science.gov (United States)

    Mukherjee, B; Nivedita, M; Mukherjee, D

    2014-05-01

    Modelling system dynamics in a hyper-eutrophic lake is quite complex especially with a constant influx of detergents and sewage material which continually changes the state variables and interferes with the assessment of the chemical rhythm occurring in polluted conditions as compared to unpolluted systems. In this paper, a carbon and nutrient mass balance model for predicting system dynamics in a complex environment was studied. Studies were conducted at Ranchi lake to understand the altered environmental dynamics in hyper-eutrophic conditions, and its impact on the plankton community. The lake was monitored regularly for five years (2007 - 2011) and the data collected on the carbon flux, nitrates, phosphates and silicates was used to design a mass balance model for evaluating and predicting the system. The model was then used to correlate the chemical rhythm with that of the phytoplankton dynamics and diversity. Nitrates and phosphates were not limiting (mean nitrate and phosphate concentrations were 1.74 and 0.83 mgl⁻¹ respectively). Free carbon dioxide was found to control the system and, interacting with other parameters determined the diversity and dynamics of the plankton community. N/P ratio determined which group of phytoplankton dominated the community, above 5 it favoured the growth of chlorophyceae while below 5 cyanobacteria dominates. TOC/TIC ratio determined the abundance. The overall system was controlled by the availability of free carbon dioxide which served as a limiting factor.

  12. Finite-dimensional attractor for a composite system of wave/plate equations with localized damping

    International Nuclear Information System (INIS)

    Bucci, Francesca; Toundykov, Daniel

    2010-01-01

    The long-term behaviour of solutions to a model for acoustic–structure interactions is addressed; the system consists of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of interest are the existence of a global attractor for the dynamics generated by this composite system as well as dimensionality and regularity of the attractor. A distinct and challenging feature of the problem is the geometrically restricted dissipation on the wave component of the system. It is shown that the existence of a global attractor of finite fractal dimension—established in a previous work by Bucci et al (2007 Commun. Pure Appl. Anal. 6 113–40) only in the presence of full-interior acoustic damping—holds even in the case of localized dissipation. This nontrivial generalization is inspired by, and consistent with, the recent advances in the study of wave equations with nonlinear localized damping

  13. Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities

    International Nuclear Information System (INIS)

    Kuramoto, Y.; Nishikawa, I.

    1987-01-01

    A model dynamical system with a great many degrees of freedom is proposed for which the critical condition for the onset of collective oscillations, the evolution of a suitably defined order parameter, and its fluctuations around steady states can be studied analytically. This is a rotator model appropriate for a large population of limit cycle oscillators. It is assumed that the natural frequencies of the oscillators are distributed and that each oscillator interacts with all the others uniformly. An exact self-consistent equation for the stationary amplitude of the collective oscillation is derived and is extended to a dynamical form. This dynamical extension is carried out near the transition point where the characteristic time scales of the order parameter and of the individual oscillators become well separated from each other. The macroscopic evolution equation thus obtained generally involves a fluctuating term whose irregular temporal variation comes from a deterministic torus motion of a subpopulation. The analysis of this equation reveals order parameter behavior qualitatively different from that in thermodynamic phase transitions, especially in that the critical fluctuations in the present system are extremely small

  14. Two-fluid equations for a nuclear system with arbitrary motions

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Byoung Jae [Chungnam National University, Daejeon (Korea, Republic of); Kim, Kyung Doo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2016-10-15

    Ocean nuclear systems include a seabed-type plant, a floating-type plant, and a nuclear-propulsion ship. We asked ourselves, 'What governing equations should be used for ocean nuclear systems?' Since ocean nuclear systems are apt to move arbitrarily, the two-fluid model must be formulated in the non-inertial frame of reference that is undergoing acceleration with respect to an inertial frame. Two-phase flow systems with arbitrary motions are barely reported. Kim et al. (1996) added the centripetal and Euler acceleration forces to the homogeneous equilibrium momentum equation embedded in the RETRAN code. However, they did not look into the mass and energy equations. The purpose of this study is to derive general two-fluid equations in the non-inertial frame of reference, which can be used for safety analysis of ocean nuclear systems. The two-fluid equation forms for scalar properties such as mass, internal energy, and enthalpy equation in the moving frame are the same as those in the absolute frame. On the other hand, the fictitious effect must be included in the momentum equation.

  15. Nonlinear dynamics of quadratically cubic systems

    International Nuclear Information System (INIS)

    Rudenko, O V

    2013-01-01

    We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

  16. Solving differential-algebraic equation systems by means of index reduction methodology

    DEFF Research Database (Denmark)

    Sørensen, Kim; Houbak, Niels; Condra, Thomas Joseph

    2006-01-01

    of a number of differential equations and algebraic equations - a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODE’s and index 1 DAE’s by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of Ordinary- Differential-Equations - ODE’s....

  17. ESTIMATION OF CONSTANT AND TIME-VARYING DYNAMIC PARAMETERS OF HIV INFECTION IN A NONLINEAR DIFFERENTIAL EQUATION MODEL.

    Science.gov (United States)

    Liang, Hua; Miao, Hongyu; Wu, Hulin

    2010-03-01

    Modeling viral dynamics in HIV/AIDS studies has resulted in deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper, we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies. We applied the proposed techniques to estimate the key HIV viral dynamic parameters for two individual AIDS patients treated with antiretroviral therapies. We demonstrate that HIV viral dynamics can be well characterized and

  18. High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

    KAUST Repository

    Abdulle, Assyr

    2012-01-01

    © 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.

  19. Complex dynamical behaviors of compact solitary waves in the perturbed mKdV equation

    International Nuclear Information System (INIS)

    Yin Jiu-Li; Xing Qian-Qian; Tian Li-Xin

    2014-01-01

    In this paper, we give a detailed discussion about the dynamical behaviors of compact solitary waves subjected to the periodic perturbation. By using the phase portrait theory, we find one of the nonsmooth solitary waves of the mKdV equation, namely, a compact solitary wave, to be a weak solution, which can be proved. It is shown that the compact solitary wave easily turns chaotic from the Melnikov theory. We focus on the sufficient conditions by keeping the system stable through selecting a suitable controller. Furthermore, we discuss the chaotic threshold for a perturbed system. Numerical simulations including chaotic thresholds, bifurcation diagrams, the maximum Lyapunov exponents, and phase portraits demonstrate that there exists a special frequency which has a great influence on our system; with the increase of the controller strength, chaos disappears in the perturbed system. But if the controller strength is sufficiently large, the solitary wave vibrates violently. (general)

  20. Simulating Dynamics of the System of Articulated Rigid Bodies with Joint Friction

    Directory of Open Access Journals (Sweden)

    M. V. Michaylyuk

    2016-01-01

    Full Text Available The subject of the work is to simulate dynamics of the system of articulated rigid bodies in the virtual environment complexes. The work aim is to develop algorithms and methods to simulate the multi-body system dynamics with joint friction to ensure all calculations in real time in line with visual realistic behavior of objects in a scene.The paper describes the multibody system based on a maximal set of coordinates, and to simulate the joint friction is used a Coulomb's law of dry friction. Joints are described using the holonomic constraints and their derivatives that specify the constraints on velocities of joined bodies. Based on The Coulomb’s law a correlation for the friction impulse values has been derived as an inequality. If the friction impulse performs a constraint that is a lack of relative motion of two joint-joined bodies, there is a static friction in the joint. Otherwise, there is a dynamic friction in the joint. Using a semi-implicit Euler method allows us to describe dynamics of articulated rigid bodies with joint friction as a system of linear algebraic equations and inequalities for the unknown velocities and impulse values.To solve the obtained system of equations and inequalities is used an iterative method of sequential impulses, which sequentially processes constraints for each joint with impulse calculation and its application to the joined bodies rather than considers the entire system. To improve the method convergence, at each iteration the calculated impulses are accumulated for their further using as an initial approximation at the next step of simulation.The proposed algorithms and methods have been implemented in the training complex dynamics subsystem, developed in SRISA RAS. Evaluation of these methods and algorithms has demonstrated their full adequacy to requirements for virtual environment systems and training complexes.